0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : eprover --auto -s --tableau=1 [--tableau-equality=1] --tableau-depth=10 %s 0.12/0.33 % Computer : n025.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 960 0.12/0.34 % WCLimit : 120 0.12/0.34 % DateTime : Thu Jul 2 09:06:03 EDT 2020 0.12/0.34 % CPUTime : 0.85/1.04 % Running in FOF/CNF-non-UEQ mode 4.25/4.46 # No SInE strategy applied 4.25/4.46 # Auto-Mode selected heuristic C07_19_nc_SAT001_MinMin_rr 4.25/4.46 # and selection function SelectMaxLComplexAvoidPosPred. 4.25/4.46 # 4.25/4.46 # Presaturation interreduction done 4.25/4.46 # Number of axioms: 7299 Number of unprocessed: 5925 4.25/4.46 # Tableaux proof search. 4.25/4.46 # 5925 beginning clauses after preprocessing and clausification 4.25/4.46 # Creating start rules for all conjectures. 4.25/4.46 # 1523 unit axioms, 1 start rules, and 4402 other extension candidates. 4.25/4.46 ## Beginning tableaux proof search with 1 start rule applications. 4.46/4.67 # Beginning deep saturation check 4.46/4.67 # Saturate returned empty clause 0x403dc60. 4.46/4.67 # Success 4.46/4.67 # SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p 4.46/4.67 # SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 4.46/4.67 # Begin clausification derivation 4.46/4.67 fof(fact_diff__bin__simps_I2_J, axiom, ![X15]:c_Int_Osucc(X15)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X15),c_Int_OMin), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I2_J)). 4.46/4.67 fof(fact_succ__Min, axiom, c_Int_OPls=c_Int_Osucc(c_Int_OMin), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_succ__Min)). 4.46/4.67 fof(fact_succ__def, axiom, ![X15]:c_Int_Osucc(X15)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),c_Groups_Oone__class_Oone(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_succ__def)). 4.46/4.67 fof(fact_succ__pred, axiom, ![X48]:X48=c_Int_Osucc(c_Int_Opred(X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_succ__pred)). 4.46/4.67 fof(fact_add__Min__right, axiom, ![X15]:c_Int_Opred(X15)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),c_Int_OMin), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Min__right)). 4.46/4.67 fof(fact_Pls__def, axiom, c_Int_OPls=c_Groups_Ozero__class_Ozero(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pls__def)). 4.46/4.67 fof(fact_add__Min, axiom, ![X15]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X15)=c_Int_Opred(X15), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Min)). 4.46/4.67 fof(fact_rel__simps_I42_J, axiom, ![X31]:c_Int_OMin!=c_Int_OBit0(X31), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I42_J)). 4.46/4.67 fof(fact_pred__Bit1, axiom, ![X15]:c_Int_OBit0(X15)=c_Int_Opred(c_Int_OBit1(X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__Bit1)). 4.46/4.67 fof(fact_Bit1__def, axiom, ![X15]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X15)),X15)=c_Int_OBit1(X15), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Bit1__def)). 4.46/4.67 fof(fact_diff__bin__simps_I4_J, axiom, ![X31]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X31))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I4_J)). 4.46/4.67 fof(fact_Bit0__def, axiom, ![X15]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),X15)=c_Int_OBit0(X15), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Bit0__def)). 4.46/4.67 fof(fact_add__Pls__right, axiom, ![X15]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),c_Int_OPls)=X15, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Pls__right)). 4.46/4.67 fof(fact_upt__0, axiom, ![X21]:c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X21,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__0)). 4.46/4.67 fof(fact_sorted__list__of__set__range, axiom, ![X14, X22]:c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22),X14))=c_List_Oupt(X22,X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__list__of__set__range)). 4.46/4.67 fof(fact_vimage__Collect__eq, axiom, ![X28, X27, X3, X4]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(X3,tc_HOL_Obool,X4),X28),X27))=hAPP(c_Set_Ovimage(X4,X3,X27),hAPP(c_Set_OCollect(X3),X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Collect__eq)). 4.46/4.67 fof(fact_Collect__def, axiom, ![X28, X4]:X28=hAPP(c_Set_OCollect(X4),X28), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__def)). 4.46/4.67 fof(fact_Collect__mem__eq, axiom, ![X2, X4]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2))=X2, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__mem__eq)). 4.46/4.67 fof(fact_Collect__split, axiom, ![X80, X28, X3, X4]:hAPP(hAPP(c_Product__Type_OSigma(X4,X3),hAPP(c_Set_OCollect(X4),X28)),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Set_OCollect(X3),X80)))=hAPP(c_Set_OCollect(tc_prod(X4,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),X28))),X80))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__split)). 4.46/4.67 fof(fact_power2__eq__1__iff, axiom, ![X18, X4]:((c_Groups_Oone__class_Oone(X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X18),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))<=>(X18=c_Groups_Oone__class_Oone(X4)|X18=hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))))<=class_Rings_Oring__1__no__zero__divisors(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power2__eq__1__iff)). 4.46/4.67 fof(fact_zero__less__power2, axiom, ![X18, X4]:(class_Rings_Olinordered__idom(X4)=>(c_Groups_Ozero__class_Ozero(X4)!=X18<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X18),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__power2)). 4.46/4.67 fof(fact_less__2__cases, axiom, ![X17]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=>(X17=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X17=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__2__cases)). 4.46/4.67 fof(fact_power2__less__0, axiom, ![X12, X4]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power2__less__0)). 4.46/4.67 fof(fact_nat__number__of__def, axiom, ![X63]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)=hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of__def)). 4.46/4.67 fof(fact_number__of__is__id, axiom, ![X15]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15)=X15, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__is__id)). 4.46/4.67 fof(fact_pred__def, axiom, ![X15]:c_Int_Opred(X15)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X15),c_Groups_Oone__class_Oone(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__def)). 4.46/4.67 fof(fact_Collect__conj__eq, axiom, ![X80, X28, X4]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),X28)),X80))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_OCollect(X4),X28)),hAPP(c_Set_OCollect(X4),X80)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__conj__eq)). 4.46/4.67 fof(fact_rel__simps_I38_J, axiom, ![X67]:(c_Int_OPls=c_Int_OBit0(X67)<=>X67=c_Int_OPls), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I38_J)). 4.46/4.67 fof(conj_7, conjecture, c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,v_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_7)). 4.46/4.67 fof(fact_singleton__conv2, axiom, ![X18, X4]:hAPP(c_Set_OCollect(X4),hAPP(c_fequal,X18))=hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_singleton__conv2)). 4.46/4.67 fof(fact_eq__int__code_I7_J, axiom, ![X130]:~(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X130)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I7_J)). 4.46/4.67 fof(fact_eq__int__code_I11_J, axiom, ![X131]:~(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X131)),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I11_J)). 4.46/4.67 fof(fact_rel__simps_I46_J, axiom, ![X15]:c_Int_OPls!=c_Int_OBit1(X15), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I46_J)). 4.46/4.67 fof(fact_length__transpose, axiom, ![X7, X4]:c_List_Ofoldr(tc_List_Olist(X4),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X4)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X4))),X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),c_List_Otranspose(X4,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__transpose)). 4.46/4.67 fof(fact_foldr__foldl, axiom, ![X18, X7, X27, X4, X3]:c_List_Ofoldr(X3,X4,X27,X7,X18)=hAPP(c_List_Ofoldl(X4,X3,hAPP(c_COMBC(X3,X4,X4),X27),X18),hAPP(c_List_Orev(X3),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldr__foldl)). 4.46/4.67 fof(fact_add__Suc, axiom, ![X17, X19]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19)),X17)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Suc)). 4.46/4.67 fof(fact_add__Suc__shift, axiom, ![X17, X19]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),hAPP(c_Nat_OSuc,X17))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19)),X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Suc__shift)). 4.46/4.67 fof(fact_transpose__aux__filter__head, axiom, ![X113, X4]:c_List_Oconcat(X4,hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_Olist__case(tc_List_Olist(X4),X4,c_List_Olist_ONil(X4),hAPP(hAPP(c_COMBB(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),X4),c_COMBK(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_COMBC(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_OCons(X4)),c_List_Olist_ONil(X4))))),X113))=hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),X4),c_List_Ohd(X4)),hAPP(c_List_Ofilter(tc_List_Olist(X4),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X4)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(X4),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X4)))),X113)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__aux__filter__head)). 4.46/4.67 fof(fact_concat__conv__foldl, axiom, ![X113, X4]:c_List_Oconcat(X4,X113)=hAPP(c_List_Ofoldl(tc_List_Olist(X4),tc_List_Olist(X4),c_List_Oappend(X4),c_List_Olist_ONil(X4)),X113), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__conv__foldl)). 4.46/4.67 fof(fact_maps__def, axiom, ![X7, X27, X4, X3]:c_List_Omaps(X3,X4,X27,X7)=c_List_Oconcat(X4,hAPP(hAPP(c_List_Omap(X3,tc_List_Olist(X4)),X27),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_maps__def)). 4.46/4.67 fof(fact_singleton__conv, axiom, ![X18, X4]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X18))=hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_singleton__conv)). 4.46/4.67 fof(fact_Collect__neg__eq, axiom, ![X28, X4]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_OCollect(X4),X28))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__neg__eq)). 4.46/4.67 fof(fact_transpose__aux__filter__tail, axiom, ![X113, X4]:hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Otl(X4)),hAPP(c_List_Ofilter(tc_List_Olist(X4),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X4)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(X4),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X4)))),X113))=c_List_Oconcat(tc_List_Olist(X4),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_List_Olist(tc_List_Olist(X4))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X4)),X4,c_List_Olist_ONil(tc_List_Olist(X4)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X4),tc_List_Olist(tc_List_Olist(X4))),X4),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(tc_List_Olist(X4)),tc_List_Olist(tc_List_Olist(X4))),c_List_Olist_OCons(tc_List_Olist(X4))),c_List_Olist_ONil(tc_List_Olist(X4)))))),X113)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__aux__filter__tail)). 4.46/4.67 fof(fact_diff__bin__simps_I9_J, axiom, ![X31, X15]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X15),X31))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X15)),c_Int_OBit0(X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I9_J)). 4.46/4.67 fof(fact_zadd__commute, axiom, ![X30, X49]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X30),X49)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X49),X30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__commute)). 4.46/4.67 fof(fact_diff__bin__simps_I5_J, axiom, ![X31]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X31))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I5_J)). 4.46/4.67 fof(fact_zadd__assoc, axiom, ![X89, X74, X75]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X75),X74)),X89)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X75),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X74),X89)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__assoc)). 4.46/4.67 fof(fact_Diff__Int2, axiom, ![X1, X52, X2, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X52)),X1)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X52)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X1),X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__Int2)). 4.46/4.67 fof(fact_Int__Diff, axiom, ![X52, X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X1),X52))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)),X52), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Diff)). 4.46/4.67 fof(fact_divmod__int__pdivmod, axiom, ![X67, X45]:((hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Divides_Odivmod__int(X45,X67)<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X45)&(((hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45)=c_Divides_Odivmod__int(X45,X67)<=X67=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X67=>hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X67))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X67)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X67),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X45,X67)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X67))))),c_Divides_Opdivmod(X45,X67))))=c_Divides_Odivmod__int(X45,X67)))<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__pdivmod)). 4.46/4.67 fof(fact_apsnd__def, axiom, ![X27, X4, X29, X3]:c_Product__Type_Oapsnd(X3,X29,X4,X27)=c_Product__Type_Omap__pair(X4,X4,X3,X29,c_Fun_Oid(X4),X27), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apsnd__def)). 4.46/4.67 fof(fact_divmod__int__code, axiom, ![X67, X45]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X45=>hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Divides_Odivmod__int(X45,X67))&(X45!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>((X67!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X67))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,X45)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X67))),c_Divides_Opdivmod(X45,X67)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X67))))),c_Divides_Opdivmod(X45,X67))))=c_Divides_Odivmod__int(X45,X67))&(c_Divides_Odivmod__int(X45,X67)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45)<=X67=c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__code)). 4.46/4.67 fof(fact_of__int__num, axiom, ![X45, X4]:(((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X45=>c_Groups_Ozero__class_Ozero(X4)=hAPP(c_Int_Oring__1__class_Oof__int(X4),X45))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X45=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X45)))=hAPP(c_Int_Oring__1__class_Oof__int(X4),X45))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))=>hAPP(c_Int_Oring__1__class_Oof__int(X4),X45)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X4,X4)),tc_fun(tc_Int_Oint,X4)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,X4),X4),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X4,X4)),tc_fun(tc_Int_Oint,X4)),tc_Int_Oint),c_COMBB(tc_fun(X4,X4),X4,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X4,tc_fun(tc_fun(X4,X4),X4),tc_Int_Oint),c_HOL_OLet(X4,X4)),c_Int_Oring__1__class_Oof__int(X4)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X4,X4),tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,X4)),tc_fun(tc_fun(X4,X4),tc_fun(X4,X4)),tc_Int_Oint),c_COMBS(X4,X4,X4)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X4,X4),tc_fun(X4,tc_fun(X4,X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,X4)),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_fun(X4,X4))),tc_Int_Oint),c_COMBB(X4,tc_fun(X4,X4),X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),tc_Int_Oint),c_If(X4)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(X4,X4,X4),c_Groups_Oplus__class_Oplus(X4)),c_COMBI(X4))))),hAPP(hAPP(c_COMBC(X4,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X4),c_Groups_Oplus__class_Oplus(X4)),hAPP(hAPP(c_COMBS(X4,X4,X4),c_Groups_Oplus__class_Oplus(X4)),c_COMBI(X4)))),c_Groups_Oone__class_Oone(X4))))),c_Divides_Odivmod__int(X45,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__num)). 4.46/4.67 fof(fact_power2__diff, axiom, ![X47, X48, X4]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X47),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X48)),X47))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X48),X47)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power2__diff)). 4.46/4.67 fof(fact_numeral__2__eq__2, axiom, hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_numeral__2__eq__2)). 4.46/4.67 fof(fact_power2__sum, axiom, ![X47, X48, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X48),X47)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X47),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X48)),X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power2__sum)). 4.46/4.67 fof(fact_neg__zmod__mult__2, axiom, ![X11, X12]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11),c_Groups_Oone__class_Oone(tc_Int_Oint)),X12))),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__zmod__mult__2)). 4.46/4.67 fof(fact_int__of__code, axiom, ![X15]:((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X15=>((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X15),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))=hAPP(c_Code__Numeral_Oint__of,X15)<=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X15,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))&(hAPP(c_Code__Numeral_Oint__of,X15)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X15),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))<=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X15,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))&(hAPP(c_Code__Numeral_Oint__of,X15)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__of__code)). 4.46/4.67 fof(fact_pos__zmod__mult__2, axiom, ![X11, X12]:(c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X12))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__zmod__mult__2)). 4.46/4.67 fof(fact_neg__zdiv__mult__2, axiom, ![X11, X12]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X11))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X12))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11),c_Groups_Oone__class_Oone(tc_Int_Oint))),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__zdiv__mult__2)). 4.46/4.67 fof(fact_sum__power2__le__zero__iff, axiom, ![X5, X6, X4]:(((X6=c_Groups_Ozero__class_Ozero(X4)&X5=c_Groups_Ozero__class_Ozero(X4))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X6),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__power2__le__zero__iff)). 4.46/4.67 fof(fact_zmod__number__of__Bit1, axiom, ![X63, X30]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30))))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30)))),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X63)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X30))))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30)))),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X63)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X30)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__number__of__Bit1)). 4.46/4.67 fof(fact_pos__zdiv__mult__2, axiom, ![X11, X12]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X11))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X12))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__zdiv__mult__2)). 4.46/4.67 fof(fact_sum__power2__gt__zero__iff, axiom, ![X5, X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X6),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))<=>(c_Groups_Ozero__class_Ozero(X4)!=X5|X6!=c_Groups_Ozero__class_Ozero(X4)))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__power2__gt__zero__iff)). 4.46/4.67 fof(fact_sum__power2__eq__zero__iff, axiom, ![X5, X6, X4]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X6),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_Groups_Ozero__class_Ozero(X4)<=>(c_Groups_Ozero__class_Ozero(X4)=X5&c_Groups_Ozero__class_Ozero(X4)=X6))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__power2__eq__zero__iff)). 4.46/4.67 fof(fact_sum__power2__ge__zero, axiom, ![X47, X48, X4]:(class_Rings_Olinordered__idom(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X47),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__power2__ge__zero)). 4.46/4.67 fof(fact_power__odd__eq, axiom, ![X17, X12, X4]:(class_Groups_Omonoid__mult(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X17)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__odd__eq)). 4.46/4.67 fof(fact_negDivAlg_Opinduct, axiom, ![X28, X123, X124]:((hBOOL(hAPP(hAPP(X28,X124),X123))<=![X125, X119]:(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X125),X119)))=>(hBOOL(hAPP(hAPP(X28,X125),X119))<=(hBOOL(hAPP(hAPP(X28,X125),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X119)))<=~((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X125),X119)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X119),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))))))<=hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X124),X123)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negDivAlg_Opinduct)). 4.46/4.67 fof(fact_power__minus__even, axiom, ![X17, X12, X4]:(class_Rings_Oring__1(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X17))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__minus__even)). 4.46/4.67 fof(fact_transpose__rectangle, axiom, ![X14, X4, X7]:((c_List_Olist_ONil(tc_List_Olist(X4))=X7=>X14=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=>(hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X4)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X4)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X4),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X4)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X4)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X4),hAPP(hAPP(c_COMBB(tc_List_Olist(X4),tc_fun(tc_Nat_Onat,X4),tc_Nat_Onat),c_List_Onth(X4)),hAPP(c_List_Onth(tc_List_Olist(X4)),X7))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),X7)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14))=c_List_Otranspose(X4,X7)<=![X41]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X4)),X7),X41))=X14<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),X7)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__rectangle)). 4.46/4.67 fof(fact_atLeastLessThan0, axiom, ![X22]:c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan0)). 4.46/4.67 fof(fact_posDivAlg_Opinduct, axiom, ![X28, X123, X124]:(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X124),X123)))=>(![X125, X119]:(((hBOOL(hAPP(hAPP(X28,X125),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X119)))<=~((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X125),X119))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X119),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))=>hBOOL(hAPP(hAPP(X28,X125),X119)))<=hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X125),X119))))=>hBOOL(hAPP(hAPP(X28,X124),X123)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_posDivAlg_Opinduct)). 4.46/4.67 fof(fact_power__even__eq, axiom, ![X17, X12, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X17))<=class_Groups_Omonoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__even__eq)). 4.46/4.67 fof(fact_abs__power2, axiom, ![X12, X4]:(hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__power2)). 4.46/4.67 fof(fact_power2__abs, axiom, ![X12, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power2__abs)). 4.46/4.67 fof(fact_power2__minus, axiom, ![X12, X4]:(class_Rings_Oring__1(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power2__minus)). 4.46/4.67 fof(fact_mod2__gr__0, axiom, ![X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))<=>c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod2__gr__0)). 4.46/4.67 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J, axiom, ![X17, X48, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),X17)))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X17)))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J)). 4.46/4.67 fof(fact_of__nat__double, axiom, ![X48, X4]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onat,X48))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onat,X48)))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X48)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X48)))<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__double)). 4.46/4.67 fof(fact_negDivAlg__eqn, axiom, ![X12, X11]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12),X11)))=>c_Divides_OnegDivAlg(X12,X11)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12),X11)))&(c_Divides_OnegDivAlg(X12,X11)=hAPP(c_Divides_Oadjust(X11),c_Divides_OnegDivAlg(X12,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X11)))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12),X11))))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negDivAlg__eqn)). 4.46/4.67 fof(fact_negDivAlg_Osimps, axiom, ![X11, X12]:((hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12),X11))=c_Divides_OnegDivAlg(X12,X11)<=(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12),X11)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))&(~((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12),X11)))))=>hAPP(c_Divides_Oadjust(X11),c_Divides_OnegDivAlg(X12,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X11)))=c_Divides_OnegDivAlg(X12,X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negDivAlg_Osimps)). 4.46/4.67 fof(fact_vimage__def, axiom, ![X1, X27, X3, X4]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X3,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),X4),c_member(X3)),X27)),X1))=hAPP(c_Set_Ovimage(X4,X3,X27),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__def)). 4.46/4.67 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, axiom, ![X17, X48, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X17))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),X17))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J)). 4.46/4.67 fof(fact_lists__eq__set, axiom, ![X2, X4]:hAPP(c_Set_OCollect(tc_List_Olist(X4)),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X4)),c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool))),c_List_Oset(X4))),X2))=c_List_Olists(X4,X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__eq__set)). 4.46/4.67 fof(fact_odd__power__less__zero, axiom, ![X17, X12, X4]:(class_Rings_Olinordered__idom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X17)))),c_Groups_Ozero__class_Ozero(X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_odd__power__less__zero)). 4.46/4.67 fof(fact_posDivAlg_Osimps, axiom, ![X11, X12]:((~((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),X11))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))=>hAPP(c_Divides_Oadjust(X11),c_Divides_OposDivAlg(X12,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X11)))=c_Divides_OposDivAlg(X12,X11))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),X11)))=>c_Divides_OposDivAlg(X12,X11)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_posDivAlg_Osimps)). 4.46/4.67 fof(fact_posDivAlg__eqn, axiom, ![X12, X11]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),X11))=>hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12)=c_Divides_OposDivAlg(X12,X11))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),X11)))=>hAPP(c_Divides_Oadjust(X11),c_Divides_OposDivAlg(X12,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X11)))=c_Divides_OposDivAlg(X12,X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_posDivAlg__eqn)). 4.46/4.67 fof(fact_Suc__n__div__2__gt__zero, axiom, ![X17]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__n__div__2__gt__zero)). 4.46/4.67 fof(fact_zminus__zadd__distrib, axiom, ![X30, X49]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X49)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X49),X30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zminus__zadd__distrib)). 4.46/4.67 fof(fact_diff__int__def, axiom, ![X30, X49]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X49),X30)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X49),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__int__def)). 4.46/4.67 fof(fact_not__sum__power2__lt__zero, axiom, ![X47, X48, X4]:(class_Rings_Olinordered__idom(X4)=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X47),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__sum__power2__lt__zero)). 4.46/4.67 fof(fact_dropWhile__neq__rev, axiom, ![X6, X7, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X7))=>(hAPP(hAPP(c_List_Olist_OCons(X4),X6),hAPP(c_List_Orev(X4),c_List_OtakeWhile(X4,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X6)),X7)))=c_List_OdropWhile(X4,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X6)),hAPP(c_List_Orev(X4),X7))<=hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__neq__rev)). 4.46/4.67 fof(fact_dropWhile__eq__drop, axiom, ![X7, X28, X4]:hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X28,X7))),X7)=c_List_OdropWhile(X4,X28,X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__eq__drop)). 4.46/4.67 fof(fact_power__minus1__odd, axiom, ![X17, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X17)))=hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__minus1__odd)). 4.46/4.67 fof(fact_half__gt__zero__iff, axiom, ![X16, X4]:((class_Int_Onumber__ring(X4)&class_Fields_Olinordered__field__inverse__zero(X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X16))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X16),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_half__gt__zero__iff)). 4.46/4.67 fof(fact_zero__le__even__power_H, axiom, ![X17, X12, X4]:(class_Rings_Olinordered__idom(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__even__power_H)). 4.46/4.67 fof(fact_power__m1__odd, axiom, ![X17, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X17)))=hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin)<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__m1__odd)). 4.46/4.67 fof(fact_zdiv__number__of__Bit1, axiom, ![X63, X30]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30)))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X63))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X30))))&(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X63))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X30)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__number__of__Bit1)). 4.46/4.67 fof(fact_power__minus1__even, axiom, ![X17, X4]:(c_Groups_Oone__class_Oone(X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X17))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__minus1__even)). 4.46/4.67 fof(fact_div__2__gt__zero, axiom, ![X17]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X17),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__2__gt__zero)). 4.46/4.67 fof(fact_eq__number__of__Suc, axiom, ![X14, X13]:(hAPP(c_Nat_OSuc,X14)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13)<=>hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X13))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X14)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__number__of__Suc)). 4.46/4.67 fof(fact_Collect__imp__eq, axiom, ![X80, X28, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_OCollect(X4),X28))),hAPP(c_Set_OCollect(X4),X80))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fimplies),X28)),X80)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__imp__eq)). 4.46/4.67 fof(fact_Compl__Diff__eq, axiom, ![X1, X2, X4]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X2)),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__Diff__eq)). 4.46/4.67 fof(fact_power__m1__even, axiom, ![X17, X4]:(c_Groups_Oone__class_Oone(X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X17))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__m1__even)). 4.46/4.67 fof(fact_zero__le__power2, axiom, ![X12, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__power2)). 4.46/4.67 fof(fact_Inf__Sup, axiom, ![X2, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>c_Complete__Lattice_OSup__class_OSup(X4,hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OAll(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fimplies),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2)))),c_Orderings_Oord__class_Oless__eq(X4)))))=c_Complete__Lattice_OInf__class_OInf(X4,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__Sup)). 4.46/4.67 fof(fact_Collect__ball__eq, axiom, ![X28, X2, X3, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X3),c_Set_OCollect(X4)),hAPP(c_COMBC(X4,X3,tc_HOL_Obool),X28)))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OAll(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fimplies),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X2)))),X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__ball__eq)). 4.46/4.67 fof(fact_Sup__Inf, axiom, ![X2, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>c_Complete__Lattice_OInf__class_OInf(X4,hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OAll(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fimplies),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2)))),hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X4))))))=c_Complete__Lattice_OSup__class_OSup(X4,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__Inf)). 4.46/4.67 fof(fact_less__Suc__number__of, axiom, ![X13, X14]:(hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X13))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14)),c_Int_Onat)))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__Suc__number__of)). 4.46/4.67 fof(fact_le__Suc__number__of, axiom, ![X13, X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13)))<=>hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X13))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14)),c_Int_Onat)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__Suc__number__of)). 4.46/4.67 fof(fact_mult__2, axiom, ![X49, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X49),X49)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__2)). 4.46/4.67 fof(fact_mult__2__right, axiom, ![X49, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X49),X49)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X49),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__2__right)). 4.46/4.67 fof(fact_power2__eq__square, axiom, ![X12, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X12)<=class_Groups_Omonoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power2__eq__square)). 4.46/4.67 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, axiom, ![X48, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X48),X48)<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J)). 4.46/4.67 fof(fact_power3__eq__cube, axiom, ![X12, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X12)),X12)<=class_Groups_Omonoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power3__eq__cube)). 4.46/4.67 fof(fact_numeral__3__eq__3, axiom, hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_numeral__3__eq__3)). 4.46/4.67 fof(fact_power__number__of__odd, axiom, ![X35, X36, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X36)))=>hAPP(hAPP(c_HOL_OLet(X4,X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X35),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X36))),hAPP(hAPP(c_COMBS(X4,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X4),c_Groups_Otimes__class_Otimes(X4)),hAPP(c_Groups_Otimes__class_Otimes(X4),X35))),c_COMBI(X4)))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X35),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X36))))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X36))))=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),X35),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X36)))=c_Groups_Oone__class_Oone(X4)))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__number__of__odd)). 4.46/4.67 fof(fact_Nitpick_Oprod__def, axiom, ![X1, X2, X3, X4]:c_Nitpick_Oprod(X4,X3,X2,X1)=hAPP(c_Set_OCollect(tc_prod(X4,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2)))),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oprod__def)). 4.46/4.67 fof(fact_zpower__number__of__odd, axiom, ![X35, X36]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X36))))=>hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X35),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X36)))=c_Groups_Oone__class_Oone(tc_Int_Oint))&(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X35),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X36)))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X35),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X36))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X35))),c_COMBI(tc_Int_Oint)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X36))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zpower__number__of__odd)). 4.46/4.67 fof(fact_one__add__one__is__two, axiom, ![X4]:(hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Oone__class_Oone(X4))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__add__one__is__two)). 4.46/4.67 fof(fact_zero__eq__power2, axiom, ![X18, X4]:(class_Rings_Oring__1__no__zero__divisors(X4)=>(c_Groups_Ozero__class_Ozero(X4)=X18<=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X18),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__eq__power2)). 4.46/4.67 fof(fact_takeWhile__neq__rev, axiom, ![X6, X7, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X7))=>(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))=>c_List_OtakeWhile(X4,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X6)),hAPP(c_List_Orev(X4),X7))=hAPP(c_List_Orev(X4),hAPP(c_List_Otl(X4),c_List_OdropWhile(X4,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X6)),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__neq__rev)). 4.46/4.67 fof(fact_drop__tl, axiom, ![X57, X17, X4]:hAPP(hAPP(c_List_Odrop(X4),X17),hAPP(c_List_Otl(X4),X57))=hAPP(c_List_Otl(X4),hAPP(hAPP(c_List_Odrop(X4),X17),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__tl)). 4.46/4.67 fof(fact_drop__Suc, axiom, ![X57, X17, X4]:hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_OSuc,X17)),X57)=hAPP(hAPP(c_List_Odrop(X4),X17),hAPP(c_List_Otl(X4),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__Suc)). 4.46/4.67 fof(fact_power__number__of__even, axiom, ![X36, X35, X4]:(hAPP(hAPP(c_HOL_OLet(X4,X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X35),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X36))),hAPP(hAPP(c_COMBS(X4,X4,X4),c_Groups_Otimes__class_Otimes(X4)),c_COMBI(X4)))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X35),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X36)))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__number__of__even)). 4.46/4.67 fof(fact_one__power2, axiom, ![X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),c_Groups_Oone__class_Oone(X4)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Oone__class_Oone(X4)<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__power2)). 4.46/4.67 fof(fact_zero__power2, axiom, ![X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Ozero__class_Ozero(X4)<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__power2)). 4.46/4.67 fof(fact_length__take, axiom, ![X57, X17, X4]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),X17)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Otake(X4),X17),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__take)). 4.46/4.67 fof(fact_less__number__of__Suc, axiom, ![X14, X13]:(hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X13))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X14))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13)),hAPP(c_Nat_OSuc,X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__number__of__Suc)). 4.46/4.67 fof(fact_Nitpick_Oof__frac__def, axiom, ![X112, X4, X3]:((class_Rings_Oring__1(X3)&class_Rings_Oinverse(X3))=>c_Nitpick_Oof__frac(X4,X3,X112)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),hAPP(c_Int_Oring__1__class_Oof__int(X3),hAPP(c_Nitpick_Onum(X4),X112))),hAPP(c_Int_Oring__1__class_Oof__int(X3),hAPP(c_Nitpick_Odenom(X4),X112)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oof__frac__def)). 4.46/4.67 fof(fact_Nitpick_Onum__def, axiom, ![X4]:c_Nitpick_Onum(X4)=hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X4,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Onum__def)). 4.46/4.67 fof(fact_Nitpick_Odenom__def, axiom, ![X4]:hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X4,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X4))=c_Nitpick_Odenom(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Odenom__def)). 4.46/4.67 fof(fact_le__number__of__Suc, axiom, ![X14, X13]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13)),hAPP(c_Nat_OSuc,X14)))<=>hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X13))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__number__of__Suc)). 4.46/4.67 fof(fact_odd__0__le__power__imp__0__le, axiom, ![X17, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X17))))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_odd__0__le__power__imp__0__le)). 4.46/4.67 fof(fact_map__removeAll__inj__on, axiom, ![X7, X6, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,hAPP(hAPP(c_Set_Oinsert(X4),X6),hAPP(c_List_Oset(X4),X7)))=>hAPP(c_List_OremoveAll(X3,hAPP(X27,X6)),hAPP(hAPP(c_List_Omap(X4,X3),X27),X7))=hAPP(hAPP(c_List_Omap(X4,X3),X27),hAPP(c_List_OremoveAll(X4,X6),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__removeAll__inj__on)). 4.46/4.67 fof(fact_removeAll__filter__not__eq, axiom, ![X6, X4]:c_List_Ofilter(X4,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),hAPP(c_fequal,X6)))=c_List_OremoveAll(X4,X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_removeAll__filter__not__eq)). 4.46/4.67 fof(fact_eq__int__code_I13_J, axiom, ![X126, X127]:(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X127)),c_Int_OBit0(X126)))<=>hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X127),X126))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I13_J)). 4.46/4.67 fof(fact_rel__simps_I14_J, axiom, ![X67, X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),X67))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X45)),c_Int_OBit0(X67)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I14_J)). 4.46/4.67 fof(fact_rel__simps_I31_J, axiom, ![X67, X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X45),X67))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X45)),c_Int_OBit0(X67)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I31_J)). 4.46/4.67 fof(fact_dropWhile__nth, axiom, ![X7, X28, X4, X25]:(hAPP(hAPP(c_List_Onth(X4),c_List_OdropWhile(X4,X28,X7)),X25)=hAPP(hAPP(c_List_Onth(X4),X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X28,X7))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OdropWhile(X4,X28,X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__nth)). 4.46/4.67 fof(fact_nat__number__of__Bit1, axiom, ![X36]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X36)))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X36)))&(~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X36))))=>hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X36)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X36)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of__Bit1)). 4.46/4.67 fof(fact_map__removeAll__inj, axiom, ![X7, X6, X27, X3, X4]:(hAPP(c_List_OremoveAll(X3,hAPP(X27,X6)),hAPP(hAPP(c_List_Omap(X4,X3),X27),X7))=hAPP(hAPP(c_List_Omap(X4,X3),X27),hAPP(c_List_OremoveAll(X4,X6),X7))<=c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__removeAll__inj)). 4.46/4.67 fof(fact_number__of__Bit0, axiom, ![X30, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X30))),hAPP(c_Int_Onumber__class_Onumber__of(X4),X30))=hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit0(X30))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__Bit0)). 4.46/4.67 fof(fact_less__int__code_I14_J, axiom, ![X126, X127]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X127),X126))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X127)),c_Int_OBit1(X126)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__int__code_I14_J)). 4.46/4.67 fof(fact_less__eq__int__code_I14_J, axiom, ![X126, X127]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X127),X126))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X127)),c_Int_OBit1(X126)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__int__code_I14_J)). 4.46/4.67 fof(fact_rel__simps_I16_J, axiom, ![X67, X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),X67))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X45)),c_Int_OBit0(X67)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I16_J)). 4.46/4.67 fof(fact_less__eq__int__code_I15_J, axiom, ![X126, X127]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X127)),c_Int_OBit0(X126)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X127),X126))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__int__code_I15_J)). 4.46/4.67 fof(fact_double__number__of__Bit0, axiom, ![X30, X4]:(hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit0(X30))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Oone__class_Oone(X4))),hAPP(c_Int_Onumber__class_Onumber__of(X4),X30))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__number__of__Bit0)). 4.46/4.67 fof(fact_nat__minus__add__max, axiom, ![X19, X17]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),X19)),X19)=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X17),X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__minus__add__max)). 4.46/4.67 fof(fact_nat__add__commute, axiom, ![X17, X19]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__commute)). 4.46/4.67 fof(fact_Suc__diff__eq__diff__pred, axiom, ![X19, X17]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19)),X17)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__diff__eq__diff__pred)). 4.46/4.67 fof(fact_diff__special_I2_J, axiom, ![X63, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X63)),c_Groups_Oone__class_Oone(X4))=hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X63),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__special_I2_J)). 4.46/4.67 fof(fact_diff__special_I1_J, axiom, ![X30, X4]:(hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),c_Groups_Oone__class_Oone(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X30))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__special_I1_J)). 4.46/4.67 fof(fact_removeAll_Osimps_I2_J, axiom, ![X57, X4, X47, X48]:((X48!=X47=>hAPP(c_List_OremoveAll(X4,X48),hAPP(hAPP(c_List_Olist_OCons(X4),X47),X57))=hAPP(hAPP(c_List_Olist_OCons(X4),X47),hAPP(c_List_OremoveAll(X4,X48),X57)))&(X48=X47=>hAPP(c_List_OremoveAll(X4,X48),hAPP(hAPP(c_List_Olist_OCons(X4),X47),X57))=hAPP(c_List_OremoveAll(X4,X48),X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_removeAll_Osimps_I2_J)). 4.46/4.67 fof(fact_negDivAlg__minus1, axiom, ![X11]:hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X11),c_Groups_Oone__class_Oone(tc_Int_Oint)))=c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negDivAlg__minus1)). 4.46/4.67 fof(fact_fst__eqD, axiom, ![X12, X47, X48, X3, X4]:(X12=hAPP(c_Product__Type_Ofst(X4,X3),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X48),X47))=>X48=X12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fst__eqD)). 4.46/4.67 fof(fact_snd__eqD, axiom, ![X12, X47, X48, X4, X3]:(X12=hAPP(c_Product__Type_Osnd(X3,X4),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X48),X47))=>X12=X47), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snd__eqD)). 4.46/4.67 fof(fact_eq__int__code_I16_J, axiom, ![X126, X127]:(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X127),X126))<=>hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X127)),c_Int_OBit1(X126)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I16_J)). 4.46/4.67 fof(fact_less__int__code_I16_J, axiom, ![X126, X127]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X127)),c_Int_OBit1(X126)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X127),X126))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__int__code_I16_J)). 4.46/4.67 fof(fact_less__eq__int__code_I16_J, axiom, ![X126, X127]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X127)),c_Int_OBit1(X126)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X127),X126))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__int__code_I16_J)). 4.46/4.67 fof(fact_Nitpick_Oless__frac__def, axiom, ![X16, X51, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X4),c_Nitpick_Oplus__frac(X4,X51,c_Nitpick_Ouminus__frac(X4,X16)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>c_Nitpick_Oless__frac(X4,X51,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oless__frac__def)). 4.46/4.67 fof(fact_Nitpick_Oless__eq__frac__def, axiom, ![X16, X51, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X4),c_Nitpick_Oplus__frac(X4,X51,c_Nitpick_Ouminus__frac(X4,X16)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>c_Nitpick_Oless__eq__frac(X4,X51,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oless__eq__frac__def)). 4.46/4.67 fof(fact_add__special_I2_J, axiom, ![X30, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X30))=hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X30))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__special_I2_J)). 4.46/4.67 fof(fact_add__special_I3_J, axiom, ![X63, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X63)),c_Groups_Oone__class_Oone(X4))=hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X63),c_Int_OBit1(c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__special_I3_J)). 4.46/4.67 fof(fact_number__of__Bit1, axiom, ![X30, X4]:(hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit1(X30))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X30))),hAPP(c_Int_Onumber__class_Onumber__of(X4),X30))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__Bit1)). 4.46/4.67 fof(fact_eq__special_I2_J, axiom, ![X5, X4]:(class_Int_Onumber__ring(X4)=>(c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X5))))<=>hAPP(c_Int_Onumber__class_Onumber__of(X4),X5)=c_Groups_Oone__class_Oone(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__special_I2_J)). 4.46/4.67 fof(fact_eq__special_I4_J, axiom, ![X6, X4]:((hAPP(c_Int_Onumber__class_Onumber__of(X4),X6)=c_Groups_Oone__class_Oone(X4)<=>c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__special_I4_J)). 4.46/4.67 fof(fact_less__special_I2_J, axiom, ![X5, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X5)))<=(class_Rings_Olinordered__idom(X4)&class_Int_Onumber__ring(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__special_I2_J)). 4.46/4.67 fof(fact_le__special_I2_J, axiom, ![X5, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X5))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Oone__class_Oone(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X5))))<=(class_Rings_Olinordered__idom(X4)&class_Int_Onumber__ring(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__special_I2_J)). 4.46/4.67 fof(fact_upt__Suc, axiom, ![X20, X21]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20)))=>c_List_Oupt(X21,hAPP(c_Nat_OSuc,X20))=c_List_Olist_ONil(tc_Nat_Onat))&(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X21,X20)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X20),c_List_Olist_ONil(tc_Nat_Onat)))=c_List_Oupt(X21,hAPP(c_Nat_OSuc,X20))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__Suc)). 4.46/4.67 fof(fact_less__special_I4_J, axiom, ![X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),c_Int_OBit1(c_Int_OPls)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X6)),c_Groups_Oone__class_Oone(X4))))<=(class_Rings_Olinordered__idom(X4)&class_Int_Onumber__ring(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__special_I4_J)). 4.46/4.67 fof(fact_le__special_I4_J, axiom, ![X6, X4]:((class_Rings_Olinordered__idom(X4)&class_Int_Onumber__ring(X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6),c_Int_OBit1(c_Int_OPls)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X6)),c_Groups_Oone__class_Oone(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__special_I4_J)). 4.46/4.67 fof(fact_interv__listsum__conv__setsum__set__nat, axiom, ![X14, X22, X27, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X4),X27),c_List_Oupt(X22,X14)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X22,X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_interv__listsum__conv__setsum__set__nat)). 4.46/4.67 fof(fact_atLeastLessThan__upt, axiom, ![X25, X24]:hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X24,X25))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24),X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__upt)). 4.46/4.67 fof(fact_iszero__number__of__Bit0, axiom, ![X36, X4]:((c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),X36))<=>c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit0(X36))))<=(class_Int_Onumber__ring(X4)&class_Int_Oring__char__0(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_iszero__number__of__Bit0)). 4.46/4.67 fof(fact_Suc__nat__number__of__add, axiom, ![X17, X63]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X17)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),X17))<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63))))&(~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63))))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X63))),X17)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__nat__number__of__add)). 4.46/4.67 fof(fact_Collect__disj__eq, axiom, ![X80, X28, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_OCollect(X4),X28)),hAPP(c_Set_OCollect(X4),X80))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fdisj),X28)),X80)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__disj__eq)). 4.46/4.67 fof(fact_eq__int__code_I9_J, axiom, ![X127]:(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X127),c_Int_OPls))<=>hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X127)),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I9_J)). 4.46/4.67 fof(fact_rel__simps_I11_J, axiom, ![X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X45)),c_Int_OMin))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X45),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I11_J)). 4.46/4.67 fof(fact_rel__simps_I10_J, axiom, ![X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X45)),c_Int_OPls))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I10_J)). 4.46/4.67 fof(fact_rel__simps_I28_J, axiom, ![X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X45)),c_Int_OMin))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X45),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I28_J)). 4.46/4.67 fof(fact_rel__simps_I27_J, axiom, ![X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X45),c_Int_OPls))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X45)),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I27_J)). 4.46/4.67 fof(fact_neg__number__of__Bit0, axiom, ![X36]:(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X36))))<=>hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X36)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__number__of__Bit0)). 4.46/4.67 fof(fact_eq__int__code_I3_J, axiom, ![X126]:(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X126)))<=>hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X126))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I3_J)). 4.46/4.67 fof(fact_rel__simps_I8_J, axiom, ![X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X45))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I8_J)). 4.46/4.67 fof(fact_rel__simps_I4_J, axiom, ![X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X45))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I4_J)). 4.46/4.67 fof(fact_rel__simps_I25_J, axiom, ![X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X45)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I25_J)). 4.46/4.67 fof(fact_rel__simps_I21_J, axiom, ![X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X45))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I21_J)). 4.46/4.67 fof(fact_upt__eq__Cons__conv, axiom, ![X7, X6, X25, X24]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))&X7=c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X25))&X24=X6)<=>c_List_Oupt(X24,X25)=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X6),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__eq__Cons__conv)). 4.46/4.67 fof(fact_psubset__insert__iff, axiom, ![X1, X6, X2, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X2),X1))<=hBOOL(hAPP(hAPP(c_member(X4),X6),X1)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X1))<=hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))))<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),X1)))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubset__insert__iff)). 4.46/4.67 fof(fact_subset__iff__psubset__eq, axiom, ![X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X2),X1))|X2=X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__iff__psubset__eq)). 4.46/4.67 fof(fact_irrefl__tranclI, axiom, ![X6, X16, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X4,X4),X16)),c_Transitive__Closure_Ortrancl(X4,X16))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))=>~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X6)),c_Transitive__Closure_Otrancl(X4,X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_irrefl__tranclI)). 4.46/4.67 fof(fact_trancl__unfold__left, axiom, ![X16, X4]:hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X16),c_Transitive__Closure_Ortrancl(X4,X16))=c_Transitive__Closure_Otrancl(X4,X16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__unfold__left)). 4.46/4.67 fof(fact_dom__map__of__conv__image__fst, axiom, ![X70, X3, X4]:hAPP(c_Set_Oimage(tc_prod(X4,X3),X4,c_Product__Type_Ofst(X4,X3)),hAPP(c_List_Oset(tc_prod(X4,X3)),X70))=c_Map_Odom(X4,X3,hAPP(c_Map_Omap__of(X4,X3),X70)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__map__of__conv__image__fst)). 4.46/4.67 fof(fact_fst__eq__Domain, axiom, ![X26, X3, X4]:hAPP(c_Set_Oimage(tc_prod(X4,X3),X4,c_Product__Type_Ofst(X4,X3)),X26)=hAPP(c_Relation_ODomain(X4,X3),X26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fst__eq__Domain)). 4.46/4.67 fof(fact_rel__simps_I48_J, axiom, ![X67, X45]:(c_Int_OBit0(X45)=c_Int_OBit0(X67)<=>X67=X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I48_J)). 4.46/4.67 fof(fact_Suc__diff__number__of, axiom, ![X19, X63]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X63)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X63))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__diff__number__of)). 4.46/4.67 fof(fact_divide__Numeral1, axiom, ![X48, X4]:(X48=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit1(c_Int_OPls)))<=(class_Int_Onumber__ring(X4)&class_Fields_Ofield(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__Numeral1)). 4.46/4.67 fof(fact_nat__of__aux__code, axiom, ![X17, X21]:((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X21=>c_Code__Numeral_Onat__of__aux(X21,X17)=X17)&(c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X21),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X17))=c_Code__Numeral_Onat__of__aux(X21,X17)<=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__of__aux__code)). 4.46/4.67 fof(fact_nat__of__aux__def, axiom, ![X17, X21]:c_Code__Numeral_Onat__of__aux(X21,X17)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X21)),X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__of__aux__def)). 4.46/4.67 fof(fact_removeAll__filter__not, axiom, ![X7, X4, X6, X28]:(~(hBOOL(hAPP(X28,X6)))=>hAPP(c_List_Ofilter(X4,X28),X7)=hAPP(c_List_OremoveAll(X4,X6),hAPP(c_List_Ofilter(X4,X28),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_removeAll__filter__not)). 4.46/4.67 fof(fact_filter__filter, axiom, ![X7, X80, X28, X4]:hAPP(c_List_Ofilter(X4,hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),X80)),X28)),X7)=hAPP(c_List_Ofilter(X4,X28),hAPP(c_List_Ofilter(X4,X80),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__filter)). 4.46/4.67 fof(fact_mult__numeral__1, axiom, ![X12, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit1(c_Int_OPls))),X12)=X12<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__numeral__1)). 4.46/4.67 fof(fact_mult__numeral__1__right, axiom, ![X12, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit1(c_Int_OPls)))=X12<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__numeral__1__right)). 4.46/4.67 fof(fact_eq__int__code_I12_J, axiom, ![X127]:(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X127),c_Int_OMin))<=>hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X127)),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I12_J)). 4.46/4.67 fof(fact_rel__simps_I13_J, axiom, ![X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),c_Int_OMin))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X45)),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I13_J)). 4.46/4.67 fof(fact_rel__simps_I12_J, axiom, ![X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),c_Int_OPls))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X45)),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I12_J)). 4.46/4.67 fof(fact_rel__simps_I30_J, axiom, ![X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X45)),c_Int_OMin))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X45),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I30_J)). 4.46/4.67 fof(fact_rel__simps_I29_J, axiom, ![X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),c_Int_OPls))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X45)),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I29_J)). 4.46/4.67 fof(fact_neg__number__of__Bit1, axiom, ![X36]:(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X36))))<=>hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X36)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__number__of__Bit1)). 4.46/4.67 fof(fact_eq__int__code_I8_J, axiom, ![X126]:(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X126)))<=>hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X126))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I8_J)). 4.46/4.67 fof(fact_rel__simps_I9_J, axiom, ![X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X45))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I9_J)). 4.46/4.67 fof(fact_rel__simps_I5_J, axiom, ![X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X45))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I5_J)). 4.46/4.67 fof(fact_rel__simps_I26_J, axiom, ![X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X45)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I26_J)). 4.46/4.67 fof(fact_rel__simps_I22_J, axiom, ![X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X45)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I22_J)). 4.46/4.67 fof(fact_Collect__conv__if2, axiom, ![X4, X18, X28]:((~(hBOOL(hAPP(X28,X18)))=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(c_fequal,X18))),X28)))&(hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(c_fequal,X18))),X28))<=hBOOL(hAPP(X28,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__conv__if2)). 4.46/4.67 fof(fact_nat__number__of__diff__1, axiom, ![X63]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),c_Groups_Oone__class_Oone(tc_Nat_Onat))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X63),c_Int_OPls)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X63),c_Int_OPls)))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X63)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of__diff__1)). 4.46/4.67 fof(fact_nat__1__add__number__of, axiom, ![X63]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X63),c_Int_OPls)))=>hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X63))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X63),c_Int_OPls))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63))=c_Groups_Oone__class_Oone(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__1__add__number__of)). 4.46/4.67 fof(fact_add__Pls, axiom, ![X15]:X15=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X15), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Pls)). 4.46/4.67 fof(fact_removeAll__id, axiom, ![X7, X6, X4]:(X7=hAPP(c_List_OremoveAll(X4,X6),X7)<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_removeAll__id)). 4.46/4.67 fof(fact_semiring__norm_I110_J, axiom, ![X4]:(class_Int_Onumber__ring(X4)=>c_Groups_Oone__class_Oone(X4)=hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit1(c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_semiring__norm_I110_J)). 4.46/4.67 fof(fact_distinct__remove1__removeAll, axiom, ![X48, X57, X4]:(hAPP(c_List_OremoveAll(X4,X48),X57)=c_List_Oremove1(X4,X48,X57)<=hBOOL(hAPP(c_List_Odistinct(X4),X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__remove1__removeAll)). 4.46/4.67 fof(fact_rel__simps_I51_J, axiom, ![X67, X45]:(c_Int_OBit1(X45)=c_Int_OBit1(X67)<=>X45=X67), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I51_J)). 4.46/4.67 fof(fact_number__of__succ, axiom, ![X15, X4]:(hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_Osucc(X15))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X15))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__succ)). 4.46/4.67 fof(fact_Suc__nat__number__of, axiom, ![X63]:((c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63))<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63))))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X63))=hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63))<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__nat__number__of)). 4.46/4.67 fof(fact_neg__number__of__pred__iff__0, axiom, ![X13]:(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X13))))<=>hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__number__of__pred__iff__0)). 4.46/4.67 fof(fact_iszero__number__of__Bit1, axiom, ![X30, X4]:((class_Int_Oring__char__0(X4)&class_Int_Onumber__ring(X4))=>~(c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit1(X30))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_iszero__number__of__Bit1)). 4.46/4.67 fof(fact_not__iszero__Numeral1, axiom, ![X4]:(class_Int_Onumber__ring(X4)=>~(c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit1(c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__iszero__Numeral1)). 4.46/4.67 fof(fact_rel__simps_I47_J, axiom, ![X45]:(X45=c_Int_OMin<=>c_Int_OBit1(X45)=c_Int_OMin), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I47_J)). 4.46/4.67 fof(fact_MGF, axiom, ![X39]:(((hBOOL(hAPP(c_Com_OWT,X39))=>c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X39)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))))<=c_Com_OWT__bodies)<=c_Hoare__Mirabelle_Ostate__not__singleton), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_MGF)). 4.46/4.67 fof(fact_code__numeral_Oinject, axiom, ![X305, X252]:(c_Code__Numeral_OSuc__code__numeral(X305)=c_Code__Numeral_OSuc__code__numeral(X252)<=>X305=X252), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Oinject)). 4.46/4.67 fof(fact_Suc__code__numeral__def, axiom, ![X15]:hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X15)))=c_Code__Numeral_OSuc__code__numeral(X15), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__code__numeral__def)). 4.46/4.67 fof(fact_eq__int__code_I14_J, axiom, ![X130, X131]:~(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X131)),c_Int_OBit1(X130)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I14_J)). 4.46/4.67 fof(fact_eq__int__code_I15_J, axiom, ![X130, X131]:~(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X131)),c_Int_OBit0(X130)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I15_J)). 4.46/4.67 fof(fact_rel__simps_I50_J, axiom, ![X31, X15]:c_Int_OBit1(X15)!=c_Int_OBit0(X31), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I50_J)). 4.46/4.67 fof(fact_eq__int__code_I10_J, axiom, ![X131]:~(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X131)),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I10_J)). 4.46/4.67 fof(fact_eq__int__code_I4_J, axiom, ![X130]:~(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X130)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I4_J)). 4.46/4.67 fof(fact_code__numeral_Osimps_I3_J, axiom, ![X277]:c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=c_Code__Numeral_OSuc__code__numeral(X277), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Osimps_I3_J)). 4.46/4.67 fof(fact_trancl__insert, axiom, ![X16, X6, X5, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X4,X16)),hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X4,X4))),hAPP(hAPP(c_COMBC(X4,X4,tc_prod(X4,X4)),c_Product__Type_OPair(X4,X4)),X5))),c_Transitive__Closure_Ortrancl(X4,X16))))),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X4,X4))),hAPP(c_Product__Type_OPair(X4,X4),X6))),c_Transitive__Closure_Ortrancl(X4,X16))))))=c_Transitive__Closure_Otrancl(X4,hAPP(hAPP(c_Set_Oinsert(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X5),X6)),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__insert)). 4.46/4.67 fof(fact_sublist__shift__lemma, axiom, ![X24, X7, X2, X4]:hAPP(hAPP(c_List_Omap(tc_prod(X4,tc_Nat_Onat),X4),c_Product__Type_Ofst(X4,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X4,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X4,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X4,tc_Nat_Onat))),X2)),hAPP(hAPP(c_List_Ozip(X4,tc_Nat_Onat),X7),c_List_Oupt(X24,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))))))=hAPP(hAPP(c_List_Omap(tc_prod(X4,tc_Nat_Onat),X4),c_Product__Type_Ofst(X4,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X4,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X4,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X4,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(X4,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X4,tc_Nat_Onat))),X24))),X2)),hAPP(hAPP(c_List_Ozip(X4,tc_Nat_Onat),X7),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__shift__lemma)). 4.46/4.67 fof(fact_arith__series__int, axiom, ![X14, X87, X18]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X87))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X14)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X87)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_arith__series__int)). 4.46/4.67 fof(fact_zmod__number__of__Bit0, axiom, ![X30, X63]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X63)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__number__of__Bit0)). 4.46/4.67 fof(fact_transpose__max__length, axiom, ![X7, X4]:c_List_Ofoldr(tc_List_Olist(X4),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X4)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X4))),c_List_Otranspose(X4,X7),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),hAPP(c_List_Ofilter(tc_List_Olist(X4),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X4)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(X4),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X4)))),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__max__length)). 4.46/4.67 fof(fact_add__Bit1__Bit1, axiom, ![X31, X15]:c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),c_Int_Osucc(X31)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X15)),c_Int_OBit1(X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Bit1__Bit1)). 4.46/4.67 fof(fact_nat__mult__2, axiom, ![X49]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X49)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X49),X49), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__2)). 4.46/4.67 fof(fact_nat__mult__2__right, axiom, ![X49]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X49),X49)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X49),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__2__right)). 4.46/4.67 fof(fact_zpower__number__of__even, axiom, ![X36, X35]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X35),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X36)))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X35),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X36))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zpower__number__of__even)). 4.46/4.67 fof(fact_add__Bit0__Bit1, axiom, ![X31, X15]:c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),X31))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X15)),c_Int_OBit1(X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Bit0__Bit1)). 4.46/4.67 fof(fact_add__Bit1__Bit0, axiom, ![X31, X15]:c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),X31))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X15)),c_Int_OBit0(X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Bit1__Bit0)). 4.46/4.67 fof(fact_map__concat, axiom, ![X7, X27, X4, X3]:c_List_Oconcat(X4,hAPP(hAPP(c_List_Omap(tc_List_Olist(X3),tc_List_Olist(X4)),hAPP(c_List_Omap(X3,X4),X27)),X7))=hAPP(hAPP(c_List_Omap(X3,X4),X27),c_List_Oconcat(X3,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__concat)). 4.46/4.67 fof(fact_mult__Bit1, axiom, ![X31, X15]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X15)),X31)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15),X31))),X31), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__Bit1)). 4.46/4.67 fof(fact_mult__Bit0, axiom, ![X31, X15]:c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15),X31))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X15)),X31), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__Bit0)). 4.46/4.67 fof(fact_nat__number__of__Bit0, axiom, ![X36]:hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X36)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of__Bit0)). 4.46/4.67 fof(fact_succ__Bit1, axiom, ![X15]:c_Int_OBit0(c_Int_Osucc(X15))=c_Int_Osucc(c_Int_OBit1(X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_succ__Bit1)). 4.46/4.67 fof(fact_com_Osize_I12_J, axiom, ![X167, X168]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X168)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X167))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X168,X167)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I12_J)). 4.46/4.67 fof(fact_nat__add__assoc, axiom, ![X15, X17, X19]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X15))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17)),X15), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__assoc)). 4.46/4.67 fof(fact_Suc__eq__plus1, axiom, ![X17]:hAPP(c_Nat_OSuc,X17)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),c_Groups_Oone__class_Oone(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__eq__plus1)). 4.46/4.67 fof(fact_com_Osize_I4_J, axiom, ![X167, X168]:c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X168,X167))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X168)),c_Com_Ocom_Ocom__size(X167))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I4_J)). 4.46/4.67 fof(fact_adjust__def, axiom, ![X37]:hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X37))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X37))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))=c_Divides_Oadjust(X37), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_adjust__def)). 4.46/4.67 fof(fact_adjust__eq, axiom, ![X16, X51, X37]:hAPP(c_Divides_Oadjust(X37),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X51),X16))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X16),X37)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X51)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X51)),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_adjust__eq)). 4.46/4.67 fof(fact_Nitpick_Oplus__frac__def, axiom, ![X16, X51, X4]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X4),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X4),X51),hAPP(c_Nitpick_Odenom(X4),X16))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X4),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X4),tc_Int_Oint),c_Nitpick_Ofrac(X4)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X4),X51))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X4),X51))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X4),X16))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X4),X16)))))),c_COMBI(tc_Int_Oint)))=c_Nitpick_Oplus__frac(X4,X51,X16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oplus__frac__def)). 4.46/4.67 fof(fact_transpose_Osimps_I3_J, axiom, ![X113, X7, X6, X4]:hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X6),c_List_Oconcat(X4,hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_Olist__case(tc_List_Olist(X4),X4,c_List_Olist_ONil(X4),hAPP(hAPP(c_COMBB(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),X4),c_COMBK(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_COMBC(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_OCons(X4)),c_List_Olist_ONil(X4))))),X113)))),c_List_Otranspose(X4,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X4)),X7),c_List_Oconcat(tc_List_Olist(X4),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_List_Olist(tc_List_Olist(X4))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X4)),X4,c_List_Olist_ONil(tc_List_Olist(X4)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X4),tc_List_Olist(tc_List_Olist(X4))),X4),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(tc_List_Olist(X4)),tc_List_Olist(tc_List_Olist(X4))),c_List_Olist_OCons(tc_List_Olist(X4))),c_List_Olist_ONil(tc_List_Olist(X4)))))),X113)))))=c_List_Otranspose(X4,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)),X113)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose_Osimps_I3_J)). 4.46/4.67 fof(fact_transpose__aux__max, axiom, ![X113, X3, X7, X4]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))),c_List_Ofoldr(tc_List_Olist(X3),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3))),X113,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)),c_List_Ofoldr(tc_List_Olist(X3),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X3),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X3)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_List_Olist(X3),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X3)))),X113),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__aux__max)). 4.46/4.67 fof(fact_nat__rec__add__eq__if, axiom, ![X14, X13, X27, X18, X4]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X13))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X4,X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),tc_Int_Oint),c_If(X4)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X4,X18,X27),X14))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X4,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X4,X4),tc_Int_Oint),X27),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X14))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Int_Oint),c_Nat_Onat_Onat__rec(X4,X18,X27)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X14)))))=hAPP(c_Nat_Onat_Onat__rec(X4,X18,X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13)),X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__rec__add__eq__if)). 4.46/4.67 fof(fact_div2__Suc__Suc, axiom, ![X19]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X19))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div2__Suc__Suc)). 4.46/4.67 fof(fact_nat__case__add__eq__if, axiom, ![X14, X13, X27, X18, X4]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X13))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X4,X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),tc_Int_Oint),c_If(X4)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X4,X18,X27,X14))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Int_Oint),X27),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X14))))=c_Nat_Onat_Onat__case(X4,X18,X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13)),X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__case__add__eq__if)). 4.46/4.67 fof(fact_mod2__Suc__Suc, axiom, ![X19]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X19)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod2__Suc__Suc)). 4.46/4.67 fof(fact_Nitpick_Otimes__frac__def, axiom, ![X111, X112, X4]:hAPP(hAPP(c_Nitpick_Ofrac(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X4),X112)),hAPP(c_Nitpick_Onum(X4),X111))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X4),X112)),hAPP(c_Nitpick_Odenom(X4),X111)))=c_Nitpick_Otimes__frac(X4,X112,X111), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Otimes__frac__def)). 4.46/4.67 fof(fact_max__Suc__number__of, axiom, ![X14, X13]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13)),hAPP(c_Nat_OSuc,X14))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X13))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X14))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__Suc__number__of)). 4.46/4.67 fof(fact_Id__def, axiom, ![X4]:c_Relation_OId(X4)=hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X4,X4)),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBC(tc_prod(X4,X4),tc_fun(X4,tc_prod(X4,X4)),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_prod(X4,X4)),tc_fun(X4,tc_HOL_Obool)),tc_prod(X4,X4)),c_COMBB(tc_prod(X4,X4),tc_HOL_Obool,X4)),c_fequal)),hAPP(hAPP(c_COMBS(X4,X4,tc_prod(X4,X4)),c_Product__Type_OPair(X4,X4)),c_COMBI(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__def)). 4.46/4.67 fof(fact_rtrancl__empty, axiom, ![X4]:c_Transitive__Closure_Ortrancl(X4,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)))=c_Relation_OId(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__empty)). 4.46/4.67 fof(fact_nat__rec__number__of, axiom, ![X13, X27, X18, X4]:hAPP(c_Nat_Onat_Onat__rec(X4,X18,X27),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X13))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X4,X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),tc_Int_Oint),c_If(X4)),c_Nat__Numeral_Oneg)),X18)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X4,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X4,X4),tc_Int_Oint),X27),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Int_Oint),c_Nat_Onat_Onat__rec(X4,X18,X27)),c_Int_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__rec__number__of)). 4.46/4.67 fof(fact_min__Suc__number__of, axiom, ![X14, X13]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X13))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),X14))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13)),hAPP(c_Nat_OSuc,X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__Suc__number__of)). 4.46/4.67 fof(fact_n__lists_Osimps_I2_J, axiom, ![X7, X14, X4]:c_List_Oconcat(tc_List_Olist(X4),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_List_Olist(tc_List_Olist(X4))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(X4),tc_List_Olist(tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_List_Olist(X4)),tc_fun(tc_List_Olist(X4),tc_List_Olist(tc_List_Olist(X4))),tc_List_Olist(X4)),c_List_Omap(X4,tc_List_Olist(X4))),hAPP(c_COMBC(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_OCons(X4)))),X7)),c_Enum_On__lists(X4,X14,X7)))=c_Enum_On__lists(X4,hAPP(c_Nat_OSuc,X14),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_n__lists_Osimps_I2_J)). 4.46/4.67 fof(fact_max__number__of__Suc, axiom, ![X13, X14]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X13))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X14))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X14)),c_Int_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__number__of__Suc)). 4.46/4.67 fof(fact_min__number__of__Suc, axiom, ![X13, X14]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X13))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X14)),c_Int_Onat))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__number__of__Suc)). 4.46/4.67 fof(fact_sublist__def, axiom, ![X2, X7, X4]:hAPP(hAPP(c_List_Omap(tc_prod(X4,tc_Nat_Onat),X4),c_Product__Type_Ofst(X4,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X4,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X4,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X4,tc_Nat_Onat))),X2)),hAPP(hAPP(c_List_Ozip(X4,tc_Nat_Onat),X7),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))))=c_List_Osublist(X4,X7,X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__def)). 4.46/4.67 fof(fact_add__Bit0__Bit0, axiom, ![X31, X15]:c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),X31))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X15)),c_Int_OBit0(X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Bit0__Bit0)). 4.46/4.67 fof(fact_diff__bin__simps_I7_J, axiom, ![X31, X15]:c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X15),X31))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X15)),c_Int_OBit0(X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I7_J)). 4.46/4.67 fof(fact_Inter__eq, axiom, ![X2, X4]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OAll(tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),X4),hAPP(c_COMBS(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X4,tc_HOL_Obool))),X2)))),c_member(X4))))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__eq)). 4.46/4.67 fof(fact_nat__case__number__of, axiom, ![X13, X27, X18, X4]:c_Nat_Onat_Onat__case(X4,X18,X27,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X13))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X4,X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),tc_Int_Oint),c_If(X4)),c_Nat__Numeral_Oneg)),X18)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Int_Oint),X27),c_Int_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__case__number__of)). 4.46/4.67 fof(fact_diff__bin__simps_I8_J, axiom, ![X31, X15]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X15)),X31))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X15)),c_Int_OBit1(X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I8_J)). 4.46/4.67 fof(fact_add__self__div__2, axiom, ![X19]:X19=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X19)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__self__div__2)). 4.46/4.67 fof(fact_zdiv__number__of__Bit0, axiom, ![X30, X63]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X63))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__number__of__Bit0)). 4.46/4.67 fof(fact_add__2__eq__Suc_H, axiom, ![X17]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__2__eq__Suc_H)). 4.46/4.67 fof(fact_dom__def, axiom, ![X22, X3, X4]:c_Map_Odom(X4,X3,X22)=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),hAPP(hAPP(c_COMBC(X4,tc_Option_Ooption(X3),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X3),tc_fun(tc_Option_Ooption(X3),tc_HOL_Obool),X4),c_fequal),X22)),c_Option_Ooption_ONone(X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__def)). 4.46/4.67 fof(fact_concat__map__singleton, axiom, ![X7, X27, X3, X4]:hAPP(hAPP(c_List_Omap(X3,X4),X27),X7)=c_List_Oconcat(X4,hAPP(hAPP(c_List_Omap(X3,tc_List_Olist(X4)),hAPP(hAPP(c_COMBC(X3,tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_COMBB(X4,tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),X3),c_List_Olist_OCons(X4)),X27)),c_List_Olist_ONil(X4))),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__map__singleton)). 4.46/4.67 fof(fact_New__DSequence_Opos__not__seq__def, axiom, ![X24, X107]:hAPP(c_New__DSequence_Opos__not__seq(X107),X24)=c_Lazy__Sequence_Ohb__not__seq(hAPP(X107,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X24))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Opos__not__seq__def)). 4.46/4.67 fof(fact_int__ge__less__than__def, axiom, ![X87]:hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87)))),c_Orderings_Oord__class_Oless(tc_Int_Oint))))=c_Int_Oint__ge__less__than(X87), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__ge__less__than__def)). 4.46/4.67 fof(fact_SetCompr__Sigma__eq, axiom, ![X80, X28, X3, X4]:hAPP(c_Set_OCollect(tc_prod(X4,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X4,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),X28))),X80)))=hAPP(hAPP(c_Product__Type_OSigma(X4,X3),hAPP(c_Set_OCollect(X4),X28)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),c_Set_OCollect(X3)),X80)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SetCompr__Sigma__eq)). 4.46/4.67 fof(fact_card__UNIV__bool, axiom, hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__UNIV__bool)). 4.46/4.67 fof(fact_diff__bin__simps_I10_J, axiom, ![X31, X15]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X15)),c_Int_OBit1(X31))=c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X15),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I10_J)). 4.46/4.67 fof(fact_Nitpick_Ouminus__frac__def, axiom, ![X112, X4]:c_Nitpick_OAbs__Frac(X4,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(X4),X112))),hAPP(c_Nitpick_Odenom(X4),X112)))=c_Nitpick_Ouminus__frac(X4,X112), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Ouminus__frac__def)). 4.46/4.67 fof(fact_trancl__reflcl, axiom, ![X16, X4]:c_Transitive__Closure_Ortrancl(X4,X16)=c_Transitive__Closure_Otrancl(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),c_Relation_OId(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__reflcl)). 4.46/4.67 fof(fact_rtrancl__reflcl, axiom, ![X26, X4]:c_Transitive__Closure_Ortrancl(X4,X26)=c_Transitive__Closure_Ortrancl(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X26),c_Relation_OId(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__reflcl)). 4.46/4.67 fof(fact_diff__bin__simps_I3_J, axiom, ![X31]:c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X31))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I3_J)). 4.46/4.67 fof(fact_Nitpick_Oint__lcm__def, axiom, ![X47, X48]:c_Nitpick_Oint__lcm(X48,X47)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X48)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oint__lcm__def)). 4.46/4.67 fof(fact_Nitpick_Onat__lcm__def, axiom, ![X47, X48]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X47)),c_Nitpick_Onat__gcd(X48,X47))=c_Nitpick_Onat__lcm(X48,X47), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Onat__lcm__def)). 4.46/4.67 fof(fact_nat__abs__mult__distrib, axiom, ![X49, X30]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X30))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X49)))=hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X49))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__abs__mult__distrib)). 4.46/4.67 fof(fact_diff__bin__simps_I6_J, axiom, ![X31]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X31))=c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I6_J)). 4.46/4.67 fof(fact_minus__Bit1, axiom, ![X15]:c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X15)))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__Bit1)). 4.46/4.67 fof(fact_rev__concat, axiom, ![X7, X4]:c_List_Oconcat(X4,hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Orev(X4)),hAPP(c_List_Orev(tc_List_Olist(X4)),X7)))=hAPP(c_List_Orev(X4),c_List_Oconcat(X4,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__concat)). 4.46/4.67 fof(fact_minus__Bit0, axiom, ![X15]:c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X15))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__Bit0)). 4.46/4.67 fof(fact_filter__concat, axiom, ![X7, X109, X4]:c_List_Oconcat(X4,hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Ofilter(X4,X109)),X7))=hAPP(c_List_Ofilter(X4,X109),c_List_Oconcat(X4,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__concat)). 4.46/4.67 fof(fact_trancl__unfold, axiom, ![X16, X4]:c_Transitive__Closure_Otrancl(X4,X16)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),c_Transitive__Closure_Otrancl(X4,X16)),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__unfold)). 4.46/4.67 fof(fact_trancl__unfold__right, axiom, ![X16, X4]:hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),c_Transitive__Closure_Ortrancl(X4,X16)),X16)=c_Transitive__Closure_Otrancl(X4,X16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__unfold__right)). 4.46/4.67 fof(fact_transfer__nat__int__list__functions_I1_J, axiom, ![X19, X31]:c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(X31)),c_List_Oembed__list(X19)))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X31),X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__list__functions_I1_J)). 4.46/4.67 fof(fact_return__list__def, axiom, ![X67]:c_List_Oreturn__list(X67)=hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X67), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_return__list__def)). 4.46/4.67 fof(fact_embed__list__def, axiom, ![X67]:c_List_Oembed__list(X67)=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X67), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_embed__list__def)). 4.46/4.67 fof(fact_insert__Collect, axiom, ![X28, X18, X4]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X18)))),X28))=hAPP(hAPP(c_Set_Oinsert(X4),X18),hAPP(c_Set_OCollect(X4),X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__Collect)). 4.46/4.67 fof(fact_foldl__foldr, axiom, ![X7, X18, X27, X3, X4]:c_List_Ofoldr(X3,X4,hAPP(c_COMBC(X4,X3,X4),X27),hAPP(c_List_Orev(X3),X7),X18)=hAPP(c_List_Ofoldl(X4,X3,X27,X18),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__foldr)). 4.46/4.67 fof(fact_rtrancl__unfold, axiom, ![X16, X4]:c_Transitive__Closure_Ortrancl(X4,X16)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Relation_OId(X4)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),c_Transitive__Closure_Ortrancl(X4,X16)),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__unfold)). 4.46/4.67 fof(fact_Diff__Int__distrib2, axiom, ![X52, X1, X2, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X52)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X1),X52))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)),X52), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__Int__distrib2)). 4.46/4.67 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J, axiom, ![X28]:c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J)). 4.46/4.67 fof(fact_map__Suc__upt, axiom, ![X14, X22]:hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X22,X14))=c_List_Oupt(hAPP(c_Nat_OSuc,X22),hAPP(c_Nat_OSuc,X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__Suc__upt)). 4.46/4.67 fof(fact_vimage__singleton__eq, axiom, ![X37, X27, X3, X18, X4]:(X37=hAPP(X27,X18)<=>hBOOL(hAPP(hAPP(c_member(X4),X18),hAPP(c_Set_Ovimage(X4,X3,X27),hAPP(hAPP(c_Set_Oinsert(X3),X37),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__singleton__eq)). 4.46/4.67 fof(fact_image__Suc__atLeastLessThan, axiom, ![X25, X24]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24)),hAPP(c_Nat_OSuc,X25))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Suc__atLeastLessThan)). 4.46/4.67 fof(fact_atLeastLessThanSuc__atLeastAtMost, axiom, ![X23, X67]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X67,X23)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X67),hAPP(c_Nat_OSuc,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThanSuc__atLeastAtMost)). 4.46/4.67 fof(fact_code__numeral_Osize_I4_J, axiom, ![X176]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X176)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X176)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Osize_I4_J)). 4.46/4.67 fof(fact_card__greaterThanAtMost__int, axiom, ![X23, X67]:hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23),X67))=hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X67,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__greaterThanAtMost__int)). 4.46/4.67 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int, axiom, ![X23, X67]:c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X67,X23)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X67),c_Groups_Oone__class_Oone(tc_Int_Oint)),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastPlusOneAtMost__greaterThanAtMost__int)). 4.46/4.67 fof(fact_card__atLeastAtMost__int, axiom, ![X23, X67]:hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23),X67)),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X67,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__atLeastAtMost__int)). 4.46/4.67 fof(fact_rel__simps_I2_J, axiom, ~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I2_J)). 4.46/4.67 fof(fact_rotate__is__Nil__conv, axiom, ![X7, X14, X4]:(c_List_Olist_ONil(X4)=X7<=>hAPP(c_List_Orotate(X4,X14),X7)=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__is__Nil__conv)). 4.46/4.67 fof(fact_rotate__def, axiom, ![X14, X4]:hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X4),tc_List_Olist(X4)),X14),c_List_Orotate1(X4))=c_List_Orotate(X4,X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__def)). 4.46/4.67 fof(fact_atLeastAtMost__upt, axiom, ![X22, X14]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X14,X22)=hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X14,hAPP(c_Nat_OSuc,X22))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastAtMost__upt)). 4.46/4.67 fof(fact_code__numeral_Osize_I2_J, axiom, ![X176]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X176)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X176)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Osize_I2_J)). 4.46/4.67 fof(fact_code__numeral_Osimps_I5_J, axiom, ![X252, X169, X38, X4]:hAPP(X169,X252)=c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X4,X38,X169,c_Code__Numeral_OSuc__code__numeral(X252)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Osimps_I5_J)). 4.46/4.67 fof(fact_Suc__code__numeral__minus__one, axiom, ![X17]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X17)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))=X17, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__code__numeral__minus__one)). 4.46/4.67 fof(fact_card__greaterThanAtMost, axiom, ![X23, X67]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23),X67)=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X67,X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__greaterThanAtMost)). 4.46/4.67 fof(fact_atLeastSucAtMost__greaterThanAtMost, axiom, ![X23, X67]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X67),X23)=c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X67,X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastSucAtMost__greaterThanAtMost)). 4.46/4.67 fof(fact_zadd__zminus__inverse2, axiom, ![X49]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X49)),X49)=c_Groups_Ozero__class_Ozero(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__zminus__inverse2)). 4.46/4.67 fof(fact_empty__def, axiom, ![X4]:c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_OCollect(X4),hAPP(c_COMBK(tc_HOL_Obool,X4),c_fFalse)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__def)). 4.46/4.67 fof(fact_UNIV__def, axiom, ![X4]:hAPP(c_Set_OCollect(X4),hAPP(c_COMBK(tc_HOL_Obool,X4),c_fTrue))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__def)). 4.46/4.67 fof(fact_atLeastLessThan__singleton, axiom, ![X22]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22),hAPP(c_Nat_OSuc,X22))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X22),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__singleton)). 4.46/4.67 fof(fact_setsum__mult__setsum__if__inj, axiom, ![X1, X2, X50, X27, X3, X4, X29]:(class_Rings_Osemiring__0(X29)=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29,X29),c_Fun_Oid(X29)),hAPP(c_Set_OCollect(X29),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X29),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X3,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool),X29),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X3))),hAPP(hAPP(c_COMBC(X29,tc_fun(X4,tc_fun(X3,tc_HOL_Obool)),tc_fun(X4,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),tc_fun(tc_fun(X4,tc_fun(X3,tc_HOL_Obool)),tc_fun(X4,tc_fun(X3,tc_HOL_Obool))),X29),c_COMBS(X4,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X4,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),X29),hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X3,tc_HOL_Obool)),tc_fun(X4,tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X29),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj))),hAPP(hAPP(c_COMBC(X29,tc_fun(X4,tc_fun(X3,X29)),tc_fun(X4,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,X29),tc_fun(X3,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_fun(X3,X29)),tc_fun(X4,tc_fun(X3,tc_HOL_Obool))),X29),c_COMBB(tc_fun(X3,X29),tc_fun(X3,tc_HOL_Obool),X4)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_HOL_Obool),tc_fun(tc_fun(X3,X29),tc_fun(X3,tc_HOL_Obool)),X29),c_COMBB(X29,tc_HOL_Obool,X3)),c_fequal))),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,X29),tc_fun(X3,X29)),hAPP(hAPP(c_COMBB(tc_fun(X29,X29),tc_fun(tc_fun(X3,X29),tc_fun(X3,X29)),X4),c_COMBB(X29,X29,X3)),hAPP(hAPP(c_COMBB(X29,tc_fun(X29,X29),X4),c_Groups_Otimes__class_Otimes(X29)),X27))),X50)))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2)))),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X1)))))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X29),X27),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X29),X50),X1))<=c_Fun_Oinj__on(tc_prod(X4,X3),X29,hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,X29),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,X29),tc_fun(X3,X29)),hAPP(hAPP(c_COMBB(tc_fun(X29,X29),tc_fun(tc_fun(X3,X29),tc_fun(X3,X29)),X4),c_COMBB(X29,X29,X3)),hAPP(hAPP(c_COMBB(X29,tc_fun(X29,X29),X4),c_Groups_Otimes__class_Otimes(X29)),X27))),X50)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__mult__setsum__if__inj)). 4.46/4.67 fof(fact_min__max_Osup__Inf2__distrib, axiom, ![X1, X2, X4]:(class_Orderings_Olinorder(X4)=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>(c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),tc_fun(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X4),c_COMBS(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),X4),hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X4),hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_fun(X4,X4)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_fun(X4,X4)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X4),c_COMBB(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool),X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal))),c_Orderings_Oord__class_Omax(X4)))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X1)))))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X2)),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X1))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__Inf2__distrib)). 4.46/4.67 fof(fact_min__max_Oinf__Sup2__distrib, axiom, ![X1, X2, X4]:(class_Orderings_Olinorder(X4)=>((((c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),tc_fun(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X4),c_COMBS(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),X4),hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X4),hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_fun(X4,X4)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_fun(X4,X4)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X4),c_COMBB(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool),X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal))),c_Orderings_Oord__class_Omin(X4)))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X1)))))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X2)),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X1))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X1)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1)))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__Sup2__distrib)). 4.46/4.67 fof(fact_inf__Sup2__distrib, axiom, ![X1, X2, X4]:(class_Lattices_Odistrib__lattice(X4)=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>(X1!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),c_Big__Operators_Olattice__class_OSup__fin(X4,X2)),c_Big__Operators_Olattice__class_OSup__fin(X4,X1))=c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),tc_fun(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X4),c_COMBS(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),X4),hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X4),hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_fun(X4,X4)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_fun(X4,X4)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X4),c_COMBB(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool),X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X4)))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X1))))))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__Sup2__distrib)). 4.46/4.67 fof(fact_sup__Inf2__distrib, axiom, ![X1, X2, X4]:(class_Lattices_Odistrib__lattice(X4)=>(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),c_Big__Operators_Olattice__class_OInf__fin(X4,X2)),c_Big__Operators_Olattice__class_OInf__fin(X4,X1))=c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),tc_fun(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X4),c_COMBS(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),X4),hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X4),hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_fun(X4,X4)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_fun(X4,X4)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X4),c_COMBB(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool),X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X4)))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X1)))))))<=X1!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__Inf2__distrib)). 4.46/4.67 fof(fact_One__nat__def, axiom, c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_One__nat__def)). 4.46/4.67 fof(fact_setsum__setsum__restrict, axiom, ![X26, X27, X110, X3, X46, X4, X29]:(class_Groups_Ocomm__monoid__add(X29)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X46))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X29),hAPP(hAPP(c_COMBS(X3,tc_fun(X4,tc_HOL_Obool),X29),hAPP(hAPP(c_COMBB(tc_fun(X4,X29),tc_fun(tc_fun(X4,tc_HOL_Obool),X29),X3),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X29)),hAPP(c_COMBC(X4,X3,X29),X27))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X3),c_Set_OCollect(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X3),hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X46)))),hAPP(c_COMBC(X4,X3,tc_HOL_Obool),X26))))),X110)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X29),hAPP(hAPP(c_COMBS(X4,tc_fun(X3,tc_HOL_Obool),X29),hAPP(hAPP(c_COMBB(tc_fun(X3,X29),tc_fun(tc_fun(X3,tc_HOL_Obool),X29),X4),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X29)),X27)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),c_Set_OCollect(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X110)))),X26)))),X46)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X110))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__setsum__restrict)). 4.46/4.67 fof(fact_finite__pointwise, axiom, ![X80, X28, X81, X209, X210, X82, X3, X211, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X211))=>((c_Hoare__Mirabelle_Ohoare__derivs(X3,X82,hAPP(c_Set_Oimage(X4,tc_Hoare__Mirabelle_Otriple(X3),hAPP(hAPP(c_COMBS(X4,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X3)),hAPP(hAPP(c_COMBS(X4,tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X3))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X3))),X4),c_Hoare__Mirabelle_Otriple_Otriple(X3)),X28)),X209)),X80)),X211))<=c_Hoare__Mirabelle_Ohoare__derivs(X3,X82,hAPP(c_Set_Oimage(X4,tc_Hoare__Mirabelle_Otriple(X3),hAPP(hAPP(c_COMBS(X4,tc_fun(X3,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X3)),hAPP(hAPP(c_COMBS(X4,tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X3))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X3,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X3))),X4),c_Hoare__Mirabelle_Otriple_Otriple(X3)),X210)),X209)),X81)),X211)))<=![X212]:(c_Hoare__Mirabelle_Ohoare__derivs(X3,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),hAPP(X210,X212)),hAPP(X209,X212)),hAPP(X81,X212))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_HOL_Obool))))=>c_Hoare__Mirabelle_Ohoare__derivs(X3,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),hAPP(X28,X212)),hAPP(X209,X212)),hAPP(X80,X212))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__pointwise)). 4.46/4.67 fof(fact_reflcl__set__eq, axiom, ![X5, X6, X16, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),c_Relation_OId(X4))))<=>hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X4,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X4,X4)))),c_Product__Type_OPair(X4,X4)))),X16)),c_fequal),X6),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_reflcl__set__eq)). 4.46/4.67 fof(fact_setsum__multicount__gen, axiom, ![X45, X26, X64, X3, X68, X4]:(((![X42]:(hAPP(c_Finite__Set_Ocard(X4),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X68))),hAPP(hAPP(c_COMBC(X4,X3,tc_HOL_Obool),X26),X42))))=hAPP(X45,X42)<=hBOOL(hAPP(hAPP(c_member(X3),X42),X64)))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_Nat_Onat,X4),c_Finite__Set_Ocard(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),c_Set_OCollect(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X64)))),X26)))),X68)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X45),X64))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X64)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X68))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__multicount__gen)). 4.46/4.67 fof(fact_min__max_Oinf__Sup1__distrib, axiom, ![X6, X2, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X4),X6))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2)))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X6),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X2))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__Sup1__distrib)). 4.46/4.67 fof(fact_min__max_Osup__Inf1__distrib, axiom, ![X6, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X6),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X2))=c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X4),X6))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2)))))<=X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__Inf1__distrib)). 4.46/4.67 fof(fact_small__lazy__list_Osimps, axiom, ![X87, X4]:(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X4),X87)=c_Lazy__Sequence_Oappend(tc_List_Olist(X4),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X4))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X87)),hAPP(c_Lazy__Sequence_Obind(tc_prod(X4,tc_List_Olist(X4)),tc_List_Olist(X4),c_Lazy__Sequence_Oproduct(X4,tc_List_Olist(X4),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X87),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X87),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(X4,tc_List_Olist(X4),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),tc_fun(tc_List_Olist(X4),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X4))),X4),hAPP(c_COMBB(tc_List_Olist(X4),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X4)),tc_List_Olist(X4)),c_Lazy__Sequence_Osingle(tc_List_Olist(X4)))),c_List_Olist_OCons(X4))))),c_Lazy__Sequence_Oempty(tc_List_Olist(X4))))<=class_Lazy__Sequence_Osmall__lazy(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__lazy__list_Osimps)). 4.46/4.67 fof(fact_setsum__multicount, axiom, ![X45, X26, X110, X3, X46, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X46))=>((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_Nat_Onat,X4),c_Finite__Set_Ocard(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),c_Set_OCollect(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X110)))),X26)))),X46)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),hAPP(c_Finite__Set_Ocard(X3),X110))<=![X42]:(hBOOL(hAPP(hAPP(c_member(X3),X42),X110))=>X45=hAPP(c_Finite__Set_Ocard(X4),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X46))),hAPP(hAPP(c_COMBC(X4,X3,tc_HOL_Obool),X26),X42))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X110)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__multicount)). 4.46/4.67 fof(fact_sup__Inf1__distrib, axiom, ![X6, X2, X4]:(class_Lattices_Odistrib__lattice(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X6))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X6),c_Big__Operators_Olattice__class_OInf__fin(X4,X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__Inf1__distrib)). 4.46/4.67 fof(fact_add__Min__commute, axiom, ![X45, X122, X4]:(class_Groups_Olinordered__ab__semigroup__add(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X122))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X122=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X45),c_Big__Operators_Olinorder__class_OMin(X4,X122))=c_Big__Operators_Olinorder__class_OMin(X4,hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X4),X45))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X122)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Min__commute)). 4.46/4.67 fof(fact_inf__Sup1__distrib, axiom, ![X6, X2, X4]:(class_Lattices_Odistrib__lattice(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X6),c_Big__Operators_Olattice__class_OSup__fin(X4,X2))=c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X6))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__Sup1__distrib)). 4.46/4.67 fof(fact_add__Max__commute, axiom, ![X45, X122, X4]:(class_Groups_Olinordered__ab__semigroup__add(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X122))=>(X122!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>c_Big__Operators_Olinorder__class_OMax(X4,hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X4),X45))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X122)))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X45),c_Big__Operators_Olinorder__class_OMax(X4,X122))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Max__commute)). 4.46/4.67 fof(fact_map_Osimps_I1_J, axiom, ![X27, X4, X3]:c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Omap(X3,X4),X27),c_List_Olist_ONil(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map_Osimps_I1_J)). 4.46/4.67 fof(fact_arith__series__general, axiom, ![X14, X87, X18, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X14)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X18),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X87))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Oone__class_Oone(X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(hAPP(c_COMBB(X4,X4,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X4),X18)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X4)),c_Nat_Osemiring__1__class_Oof__nat(X4))),X87))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X14)))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_arith__series__general)). 4.46/4.67 fof(fact_atLeast0LessThan, axiom, ![X14]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14)=hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast0LessThan)). 4.46/4.67 fof(fact_setsum__cases, axiom, ![X50, X27, X28, X2, X4, X3]:(class_Groups_Ocomm__monoid__add(X3)=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),hAPP(hAPP(c_COMBS(X4,X3,X3),hAPP(hAPP(c_COMBS(X4,X3,tc_fun(X3,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3,tc_fun(X3,X3)),X4),c_If(X3)),X28)),X27)),X50)),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_Set_OCollect(X4),X28)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_OCollect(X4),X28)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__cases)). 4.46/4.67 fof(fact_Diff__eq, axiom, ![X1, X2, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__eq)). 4.46/4.67 fof(fact_setsum__image__gen, axiom, ![X27, X29, X50, X46, X4, X3]:((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29,X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),X3,X29),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X29),c_Set_OCollect(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X29),hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X46)))),hAPP(c_COMBC(X4,X29,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X29,tc_fun(X29,tc_HOL_Obool),X4),c_fequal),X27)))))),hAPP(c_Set_Oimage(X4,X29,X27),X46))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),X46)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X46)))<=class_Groups_Ocomm__monoid__add(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__image__gen)). 4.46/4.67 fof(fact_less, axiom, ![X13, X23, X5, X6]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23),X13)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less)). 4.46/4.67 fof(fact_le, axiom, ![X13, X23, X5, X6]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23),X13)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le)). 4.46/4.67 fof(fact_finite__image__set, axiom, ![X27, X3, X28, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X3),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBC(X3,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X3),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj)),hAPP(hAPP(c_COMBC(X3,tc_fun(X4,X3),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X4,X3),tc_fun(X4,tc_HOL_Obool)),X3),c_COMBB(X3,tc_HOL_Obool,X4)),c_fequal)),X27)))),X28)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Set_OCollect(X4),X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__image__set)). 4.46/4.67 fof(fact_card__less__Suc2, axiom, ![X24, X153]:(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X153))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X24)))))=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X153))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X24))))<=~(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X153)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__less__Suc2)). 4.46/4.67 fof(fact_set__map__of__compr, axiom, ![X7, X3, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(tc_prod(X4,X3),X4),c_Product__Type_Ofst(X4,X3)),X7)))=>hAPP(c_Set_OCollect(tc_prod(X4,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,tc_Option_Ooption(X3)),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X3),tc_HOL_Obool),tc_fun(tc_fun(X3,tc_Option_Ooption(X3)),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBB(tc_Option_Ooption(X3),tc_HOL_Obool,X3)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X3),tc_fun(tc_Option_Ooption(X3),tc_HOL_Obool),X4),c_fequal),hAPP(c_Map_Omap__of(X4,X3),X7)))),c_Option_Ooption_OSome(X3))))=hAPP(c_List_Oset(tc_prod(X4,X3)),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__map__of__compr)). 4.46/4.67 fof(fact_card__less__Suc, axiom, ![X24, X153]:(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X153))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X24)))))=hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X153))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X24)))))<=hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X153))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__less__Suc)). 4.46/4.67 fof(fact_wf__if__measure, axiom, ![X4, X50, X27, X28]:(![X42]:(hBOOL(hAPP(X28,X42))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X27,hAPP(X50,X42))),hAPP(X27,X42))))=>c_Wellfounded_Owf(X4,hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),X28))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal)),X50)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__if__measure)). 4.46/4.67 fof(fact_Body1, axiom, ![X263, X287, X80, X28, X82, X4]:((hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X263),X287))=>c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),hAPP(X28,X263)),hAPP(c_Com_Ocom_OBODY,X263)),hAPP(X80,X263))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool)))))<=c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool)),X82),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X4),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X4)),X28)),c_Com_Ocom_OBODY)),X80)),X287)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X4),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X4)),X28)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X80)),X287))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Body1)). 4.46/4.67 fof(fact_finite__lists__length__le, axiom, ![X14, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X4)),hAPP(c_Set_OCollect(tc_List_Olist(X4)),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X4)),c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool))),c_List_Oset(X4))),X2))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X4)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),X14)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__lists__length__le)). 4.46/4.67 fof(fact_finite__lists__length__eq, axiom, ![X14, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X4)),hAPP(c_Set_OCollect(tc_List_Olist(X4)),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X4)),c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool))),c_List_Oset(X4))),X2))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),X14)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__lists__length__eq)). 4.46/4.67 fof(fact_min__ext__compat, axiom, ![X46, X26, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X4,X26)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X4,X46)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X4,X26)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X26),X46)),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__ext__compat)). 4.46/4.67 fof(fact_max__ext__compat, axiom, ![X46, X26, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X26),X46)),X26))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X4,X26)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X4,X46)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X4,X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__ext__compat)). 4.46/4.67 fof(fact_zminus1__lemma, axiom, ![X16, X51, X37, X18]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18),X37),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X16),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X51)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X51)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X16),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X37),X16)))))<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X18,X37),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X51),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zminus1__lemma)). 4.46/4.67 fof(fact_small_H_Opinduct, axiom, ![X28, X135, X123, X124]:((hBOOL(hAPP(hAPP(hAPP(X28,X124),X123),X135))<=![X40, X190, X41]:((hBOOL(hAPP(hAPP(hAPP(X28,X40),X190),X41))<=((hAPP(X40,X41)=c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))=>hBOOL(hAPP(hAPP(hAPP(X28,X40),X190),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X41),c_Groups_Oone__class_Oone(tc_Int_Oint)))))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X190),X41)))))<=hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X40),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X190),X41))))))<=hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X124),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X123),X135))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small_H_Opinduct)). 4.46/4.67 fof(fact_divmod__nat__rel__add1__eq, axiom, ![X245, X246, X11, X247, X248, X10, X12]:(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X12,X10),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X248),X247)))=>(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X11,X10),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X246),X245)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10))=>hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X11),X10),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X248),X246)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X247),X245)),X10))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X247),X245),X10))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel__add1__eq)). 4.46/4.67 fof(fact_zadd1__lemma, axiom, ![X245, X246, X11, X247, X248, X10, X12]:(((hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12),X11),X10),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X248),X246)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X247),X245)),X10))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X247),X245),X10))))<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X10)<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,X10),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X246),X245))))<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,X10),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X248),X247)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd1__lemma)). 4.46/4.67 fof(fact_setprod__gen__delta, axiom, ![X39, X37, X18, X46, X4, X3]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X46))=>((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),hAPP(hAPP(c_COMBC(X4,X3,X3),hAPP(hAPP(c_COMBS(X4,X3,tc_fun(X3,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3,tc_fun(X3,X3)),X4),c_If(X3)),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X18))),X37)),X39)),X46)=hAPP(hAPP(c_Power_Opower__class_Opower(X3),X39),hAPP(c_Finite__Set_Ocard(X4),X46))<=~(hBOOL(hAPP(hAPP(c_member(X4),X18),X46))))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(X37,X18)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X39),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X46)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),hAPP(hAPP(c_COMBC(X4,X3,X3),hAPP(hAPP(c_COMBS(X4,X3,tc_fun(X3,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3,tc_fun(X3,X3)),X4),c_If(X3)),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X18))),X37)),X39)),X46)<=hBOOL(hAPP(hAPP(c_member(X4),X18),X46)))))<=class_Groups_Ocomm__monoid__mult(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__gen__delta)). 4.46/4.67 fof(fact_diff__nat__number__of, axiom, ![X13, X224]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X224),c_Int_OPls)))=>hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X224)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X224)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X224))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X224),c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__nat__number__of)). 4.46/4.67 fof(fact_setsum__natinterval__difff, axiom, ![X27, X14, X22, X4]:(class_Groups_Oab__group__add(X4)=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14)))=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X4)),X27)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Nat_Onat),X27),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X22,X14)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X4)),X27)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Nat_Onat),X27),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X22,X14))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(X27,X22)),hAPP(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),c_Groups_Oone__class_Oone(tc_Nat_Onat))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__natinterval__difff)). 4.46/4.67 fof(fact_equiv__intrel__iff, axiom, ![X5, X6]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),X5)),c_Int_Ointrel))<=>hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))=hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__intrel__iff)). 4.46/4.67 fof(fact_refl__on__def_H, axiom, ![X16, X2, X4]:(c_Relation_Orefl__on(X4,X2,X16)<=>(![X42]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X42)),X16))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X2)))&![X42]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X42),X16))=>hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2))),X42))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__def_H)). 4.46/4.67 fof(fact_setsum__restrict__set, axiom, ![X1, X27, X2, X4, X3]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),hAPP(hAPP(c_COMBC(X4,X3,X3),hAPP(hAPP(c_COMBS(X4,X3,tc_fun(X3,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3,tc_fun(X3,X3)),X4),c_If(X3)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X1))),X27)),c_Groups_Ozero__class_Ozero(X3))),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=class_Groups_Ocomm__monoid__add(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__restrict__set)). 4.46/4.67 fof(fact_Nitpick_Osetsum_H__def, axiom, ![X27, X2, X4, X3]:(class_Groups_Ocomm__monoid__add(X3)=>((~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))=>c_Groups_Ozero__class_Ozero(X3)=c_Nitpick_Osetsum_H(X4,X3,X27,X2))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(c_List_Omonoid__add__class_Olistsum(X3),hAPP(hAPP(c_List_Omap(X4,X3),X27),c_Hilbert__Choice_OEps(tc_List_Olist(X4),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_List_Oset(X4))),X2))),c_List_Odistinct(X4)))))=c_Nitpick_Osetsum_H(X4,X3,X27,X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Osetsum_H__def)). 4.46/4.67 fof(fact_Int__commute, axiom, ![X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X1),X2)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__commute)). 4.46/4.67 fof(fact_sum__diff__distrib, axiom, ![X14, X28, X80]:(![X42]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X80,X42)),hAPP(X28,X42)))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X28)),X80)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X14))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X28),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X14))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X80),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__diff__distrib)). 4.46/4.67 fof(fact_less__eq__Suc__le__raw, axiom, ![X14]:hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14))=hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__Suc__le__raw)). 4.46/4.67 fof(fact_vimage__if, axiom, ![X1, X3, X87, X2, X39, X4]:((((hBOOL(hAPP(hAPP(c_member(X4),X87),X2))=>hAPP(c_Set_Ovimage(X3,X4,hAPP(hAPP(c_COMBC(X3,X4,X4),hAPP(hAPP(c_COMBC(X3,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X3),c_If(X4)),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X1))),X39)),X87)),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),X1))&(~(hBOOL(hAPP(hAPP(c_member(X4),X87),X2)))=>c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X3,X4,hAPP(hAPP(c_COMBC(X3,X4,X4),hAPP(hAPP(c_COMBC(X3,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X3),c_If(X4)),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X1))),X39)),X87)),X2)))<=~(hBOOL(hAPP(hAPP(c_member(X4),X39),X2))))&(((hAPP(c_Set_Ovimage(X3,X4,hAPP(hAPP(c_COMBC(X3,X4,X4),hAPP(hAPP(c_COMBC(X3,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X3),c_If(X4)),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X1))),X39)),X87)),X2)=X1<=~(hBOOL(hAPP(hAPP(c_member(X4),X87),X2))))&(hBOOL(hAPP(hAPP(c_member(X4),X87),X2))=>hAPP(c_Set_Ovimage(X3,X4,hAPP(hAPP(c_COMBC(X3,X4,X4),hAPP(hAPP(c_COMBC(X3,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X3),c_If(X4)),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X1))),X39)),X87)),X2)=c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))<=hBOOL(hAPP(hAPP(c_member(X4),X39),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__if)). 4.46/4.67 fof(fact_listrel__subset, axiom, ![X2, X16, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool)),c_List_Olistrel(X4,X16)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olists(X4,X2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_List_Olist(X4)),c_List_Olists(X4,X2)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__subset)). 4.46/4.67 fof(fact_concat__eq__concat__iff, axiom, ![X32, X7, X4]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),X7)=>(X7=X32<=>c_List_Oconcat(X4,X7)=c_List_Oconcat(X4,X32)))<=![X42]:(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X4),tc_List_Olist(X4),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_Nat_Onat),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X4),tc_Nat_Onat),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_List_Olist(X4)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X4))))),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),X42))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),X42),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__eq__concat__iff)). 4.46/4.67 fof(fact_concat__injective, axiom, ![X32, X7, X4]:(((![X42]:(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X4),tc_List_Olist(X4),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_Nat_Onat),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X4),tc_Nat_Onat),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_List_Olist(X4)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X4))))),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),X42))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),X42),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)))))=>X7=X32)<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),X7))<=c_List_Oconcat(X4,X32)=c_List_Oconcat(X4,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__injective)). 4.46/4.67 fof(fact_setprod__delta, axiom, ![X37, X18, X46, X4, X3]:(class_Groups_Ocomm__monoid__mult(X3)=>(((~(hBOOL(hAPP(hAPP(c_member(X4),X18),X46)))=>c_Groups_Oone__class_Oone(X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),hAPP(hAPP(c_COMBC(X4,X3,X3),hAPP(hAPP(c_COMBS(X4,X3,tc_fun(X3,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3,tc_fun(X3,X3)),X4),c_If(X3)),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X18))),X37)),c_Groups_Oone__class_Oone(X3))),X46))&(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),hAPP(hAPP(c_COMBC(X4,X3,X3),hAPP(hAPP(c_COMBS(X4,X3,tc_fun(X3,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3,tc_fun(X3,X3)),X4),c_If(X3)),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X18))),X37)),c_Groups_Oone__class_Oone(X3))),X46)=hAPP(X37,X18)<=hBOOL(hAPP(hAPP(c_member(X4),X18),X46))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X46)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__delta)). 4.46/4.67 fof(fact_setprod_OF__eq, axiom, ![X50, X2, X4, X3]:(((~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))=>c_Groups_Oone__class_Oone(X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),X2))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),X2)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),X50),c_Groups_Oone__class_Oone(X3)),X2)))<=class_Groups_Ocomm__monoid__mult(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod_OF__eq)). 4.46/4.67 fof(fact_setsum__delta, axiom, ![X37, X18, X46, X4, X3]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X46))=>((hBOOL(hAPP(hAPP(c_member(X4),X18),X46))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),hAPP(hAPP(c_COMBC(X4,X3,X3),hAPP(hAPP(c_COMBS(X4,X3,tc_fun(X3,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3,tc_fun(X3,X3)),X4),c_If(X3)),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X18))),X37)),c_Groups_Ozero__class_Ozero(X3))),X46)=hAPP(X37,X18))&(~(hBOOL(hAPP(hAPP(c_member(X4),X18),X46)))=>c_Groups_Ozero__class_Ozero(X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),hAPP(hAPP(c_COMBC(X4,X3,X3),hAPP(hAPP(c_COMBS(X4,X3,tc_fun(X3,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3,tc_fun(X3,X3)),X4),c_If(X3)),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X18))),X37)),c_Groups_Ozero__class_Ozero(X3))),X46))))<=class_Groups_Ocomm__monoid__add(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__delta)). 4.46/4.67 fof(fact_setsum__infinite, axiom, ![X27, X2, X4, X3]:(class_Groups_Ocomm__monoid__add(X3)=>(c_Groups_Ozero__class_Ozero(X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X2)<=~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__infinite)). 4.46/4.67 fof(fact_trancl__trans, axiom, ![X39, X16, X37, X18, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X39)),c_Transitive__Closure_Otrancl(X4,X16)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X37),X39)),c_Transitive__Closure_Otrancl(X4,X16))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),c_Transitive__Closure_Otrancl(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__trans)). 4.46/4.67 fof(fact_lexord__take__index__conv, axiom, ![X16, X5, X6, X4]:((?[X41]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X6)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5))))&hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(hAPP(c_List_Onth(X4),X6),X41)),hAPP(hAPP(c_List_Onth(X4),X5),X41))),X16)))&hAPP(hAPP(c_List_Otake(X4),X41),X6)=hAPP(hAPP(c_List_Otake(X4),X41),X5))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X6)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5)))&X6=hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X6)),X5)))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X6),X5)),c_List_Olexord(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__take__index__conv)). 4.46/4.67 fof(fact_map__upd__upds__conv__if, axiom, ![X5, X27, X7, X32, X3, X6, X4]:((c_Map_Omap__upds(X4,X3,X27,X7,X32)=c_Map_Omap__upds(X4,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),X27),X6),hAPP(c_Option_Ooption_OSome(X3),X5)),X7,X32)<=hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32)),X7)))))&(c_Map_Omap__upds(X4,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),X27),X6),hAPP(c_Option_Ooption_OSome(X3),X5)),X7,X32)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),c_Map_Omap__upds(X4,X3,X27,X7,X32)),X6),hAPP(c_Option_Ooption_OSome(X3),X5))<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32)),X7))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upd__upds__conv__if)). 4.46/4.67 fof(fact_map__upds__Cons, axiom, ![X260, X37, X172, X18, X22, X3, X4]:c_Map_Omap__upds(X4,X3,X22,hAPP(hAPP(c_List_Olist_OCons(X4),X18),X172),hAPP(hAPP(c_List_Olist_OCons(X3),X37),X260))=c_Map_Omap__upds(X4,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),X22),X18),hAPP(c_Option_Ooption_OSome(X3),X37)),X172,X260), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upds__Cons)). 4.46/4.67 fof(fact_transfer__nat__int__set__cong, axiom, ![X210, X28]:(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X28))=hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X210))<=![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X42))=>(hBOOL(hAPP(X210,X42))<=>hBOOL(hAPP(X28,X42))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__cong)). 4.46/4.67 fof(fact_zip__obtain__same__length, axiom, ![X28, X32, X3, X7, X4]:(hBOOL(hAPP(X28,hAPP(hAPP(c_List_Ozip(X4,X3),X7),X32)))<=(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),hAPP(hAPP(c_List_Otake(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32))),X32))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32))),X7))=>hBOOL(hAPP(X28,hAPP(hAPP(c_List_Ozip(X4,X3),hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32))),X7)),hAPP(hAPP(c_List_Otake(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32))),X32)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__obtain__same__length)). 4.46/4.67 fof(fact_inf__nat__def, axiom, c_Orderings_Oord__class_Omin(tc_Nat_Onat)=c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__nat__def)). 4.46/4.67 fof(fact_diff__nat__eq__if, axiom, ![X35, X121]:((~(hBOOL(hAPP(c_Nat__Numeral_Oneg,X121)))=>hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X35),X121)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X35)),hAPP(c_Int_Onat,X121)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X35)),hAPP(c_Int_Onat,X121))=hAPP(c_Int_Onat,X35)<=hBOOL(hAPP(c_Nat__Numeral_Oneg,X121)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__nat__eq__if)). 4.46/4.67 fof(fact_in__lex__prod, axiom, ![X68, X16, X278, X223, X37, X18, X3, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X223)),X16))|(hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X37),X278)),X68))&X18=X223))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X4,X3),tc_prod(X4,X3))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X4,X3),tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X18),X37)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X223),X278))),c_Wellfounded_Olex__prod(X4,X3,X16,X68)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__lex__prod)). 4.46/4.67 fof(fact_rtrancl__trancl__trancl, axiom, ![X35, X16, X5, X6, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X5),X35)),c_Transitive__Closure_Otrancl(X4,X16)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X35)),c_Transitive__Closure_Otrancl(X4,X16))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_Transitive__Closure_Ortrancl(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__trancl__trancl)). 4.46/4.67 fof(fact_trancl__rtrancl__trancl, axiom, ![X39, X16, X37, X18, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),c_Transitive__Closure_Otrancl(X4,X16)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X39)),c_Transitive__Closure_Otrancl(X4,X16)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X37),X39)),c_Transitive__Closure_Ortrancl(X4,X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__rtrancl__trancl)). 4.46/4.67 fof(fact_UN__finite2__subset, axiom, ![X1, X45, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X1)))<=![X199]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X199)),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X199),X45))),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__finite2__subset)). 4.46/4.67 fof(fact_conseq1, axiom, ![X28, X80, X39, X210, X82, X4]:(c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X210),X39),X80)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))=>(c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X28),X39),X80)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))<=![X83, X84]:(hBOOL(hAPP(hAPP(X28,X83),X84))=>hBOOL(hAPP(hAPP(X210,X83),X84))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conseq1)). 4.46/4.67 fof(fact_conseq2, axiom, ![X80, X81, X39, X28, X82, X4]:(c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X28),X39),X81)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))=>(c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X28),X39),X80)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))<=![X83, X84]:(hBOOL(hAPP(hAPP(X81,X83),X84))=>hBOOL(hAPP(hAPP(X80,X83),X84))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conseq2)). 4.46/4.67 fof(fact_trancl__into__trancl2, axiom, ![X39, X16, X37, X18, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),X16))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X39)),c_Transitive__Closure_Otrancl(X4,X16)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X37),X39)),c_Transitive__Closure_Otrancl(X4,X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__into__trancl2)). 4.46/4.67 fof(fact_Transitive__Closure_Otrancl__into__trancl, axiom, ![X39, X16, X37, X18, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X37),X39)),X16))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X39)),c_Transitive__Closure_Otrancl(X4,X16))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),c_Transitive__Closure_Otrancl(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Transitive__Closure_Otrancl__into__trancl)). 4.46/4.67 fof(fact_finite__Collect__bounded__ex, axiom, ![X80, X3, X28, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Set_OCollect(X4),X28)))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X3),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X3),hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),X28))),X80)))))<=>![X44]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBC(X3,X4,tc_HOL_Obool),X80),X44))))<=hBOOL(hAPP(X28,X44))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Collect__bounded__ex)). 4.46/4.67 fof(fact_setsum__delta_H, axiom, ![X37, X18, X46, X4, X3]:(class_Groups_Ocomm__monoid__add(X3)=>(((~(hBOOL(hAPP(hAPP(c_member(X4),X18),X46)))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),hAPP(hAPP(c_COMBC(X4,X3,X3),hAPP(hAPP(c_COMBS(X4,X3,tc_fun(X3,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3,tc_fun(X3,X3)),X4),c_If(X3)),hAPP(c_fequal,X18))),X37)),c_Groups_Ozero__class_Ozero(X3))),X46)=c_Groups_Ozero__class_Ozero(X3))&(hAPP(X37,X18)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),hAPP(hAPP(c_COMBC(X4,X3,X3),hAPP(hAPP(c_COMBS(X4,X3,tc_fun(X3,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3,tc_fun(X3,X3)),X4),c_If(X3)),hAPP(c_fequal,X18))),X37)),c_Groups_Ozero__class_Ozero(X3))),X46)<=hBOOL(hAPP(hAPP(c_member(X4),X18),X46))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X46)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__delta_H)). 4.46/4.67 fof(fact_dropWhile__append1, axiom, ![X32, X28, X7, X6, X4]:((~(hBOOL(hAPP(X28,X6)))=>hAPP(hAPP(c_List_Oappend(X4),c_List_OdropWhile(X4,X28,X7)),X32)=c_List_OdropWhile(X4,X28,hAPP(hAPP(c_List_Oappend(X4),X7),X32)))<=hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__append1)). 4.46/4.67 fof(fact_listrel1I, axiom, ![X32, X196, X197, X7, X16, X5, X6, X4]:((X7=hAPP(hAPP(c_List_Oappend(X4),X197),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X196))=>(X32=hAPP(hAPP(c_List_Oappend(X4),X197),hAPP(hAPP(c_List_Olist_OCons(X4),X5),X196))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)),c_List_Olistrel1(X4,X16)))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1I)). 4.46/4.67 fof(fact_setprod__delta_H, axiom, ![X37, X18, X46, X4, X3]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X46))=>((~(hBOOL(hAPP(hAPP(c_member(X4),X18),X46)))=>c_Groups_Oone__class_Oone(X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),hAPP(hAPP(c_COMBC(X4,X3,X3),hAPP(hAPP(c_COMBS(X4,X3,tc_fun(X3,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3,tc_fun(X3,X3)),X4),c_If(X3)),hAPP(c_fequal,X18))),X37)),c_Groups_Oone__class_Oone(X3))),X46))&(hBOOL(hAPP(hAPP(c_member(X4),X18),X46))=>hAPP(X37,X18)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),hAPP(hAPP(c_COMBC(X4,X3,X3),hAPP(hAPP(c_COMBS(X4,X3,tc_fun(X3,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3,tc_fun(X3,X3)),X4),c_If(X3)),hAPP(c_fequal,X18))),X37)),c_Groups_Oone__class_Oone(X3))),X46))))<=class_Groups_Ocomm__monoid__mult(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__delta_H)). 4.46/4.67 fof(fact_o__apply, axiom, ![X6, X50, X27, X29, X4, X3]:hAPP(X27,hAPP(X50,X6))=hAPP(hAPP(c_Fun_Ocomp(X3,X4,X29,X27),X50),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_o__apply)). 4.46/4.67 fof(fact_distinct__concat, axiom, ![X7, X4]:(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X4)),X7))=>(![X8]:(hBOOL(hAPP(c_List_Odistinct(X4),X8))<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X8),hAPP(c_List_Oset(tc_List_Olist(X4)),X7))))=>(hBOOL(hAPP(c_List_Odistinct(X4),c_List_Oconcat(X4,X7)))<=![X8]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X8),hAPP(c_List_Oset(tc_List_Olist(X4)),X7)))=>![X9]:((X9!=X8=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X8)),hAPP(c_List_Oset(X4),X9))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X9),hAPP(c_List_Oset(tc_List_Olist(X4)),X7)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__concat)). 4.46/4.67 fof(fact_hoare__derivs_OIf, axiom, ![X87, X80, X39, X37, X28, X82, X4]:(c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),c_Hoare__Mirabelle_Opeek__and(X4,X28,X37)),X39),X80)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))=>(c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),c_Hoare__Mirabelle_Opeek__and(X4,X28,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X37))),X87),X80)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))=>c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X28),c_Com_Ocom_OCond(X37,X39,X87)),X80)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hoare__derivs_OIf)). 4.46/4.67 fof(fact_divmod__nat__if, axiom, ![X22, X14]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X14))|X14=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=>hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22)=c_Divides_Odivmod__nat(X22,X14))&(~((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X14))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X14))=>c_Divides_Odivmod__nat(X22,X14)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22),X14),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__if)). 4.46/4.67 fof(fact_divmod__nat__def, axiom, ![X14, X22]:c_Divides_Odivmod__nat(X22,X14)=c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X22,X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__def)). 4.46/4.67 fof(fact_Nitpick_Ocard_H__def, axiom, ![X2, X4]:((~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Nitpick_Ocard_H(X4,X2))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_Hilbert__Choice_OEps(tc_List_Olist(X4),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_List_Oset(X4))),X2))),c_List_Odistinct(X4))))=c_Nitpick_Ocard_H(X4,X2)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Ocard_H__def)). 4.46/4.67 fof(fact_of__int, axiom, ![X25, X24, X4]:(class_Rings_Oring__1(X4)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X24)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X25))=hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X24),X25)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int)). 4.46/4.67 fof(fact_lexord__cons__cons, axiom, ![X16, X5, X37, X6, X18, X4]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X6),X5)),c_List_Olexord(X4,X16)))&X18=X37)|hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),X16)))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X18),X6)),hAPP(hAPP(c_List_Olist_OCons(X4),X37),X5))),c_List_Olexord(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__cons__cons)). 4.46/4.67 fof(fact_append__listrel1I, axiom, ![X196, X197, X16, X32, X7, X4]:(((X196=X197&hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)),c_List_Olistrel1(X4,X16))))|(X32=X7&hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X197),X196)),c_List_Olistrel1(X4,X16)))))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Oappend(X4),X7),X197)),hAPP(hAPP(c_List_Oappend(X4),X32),X196))),c_List_Olistrel1(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__listrel1I)). 4.46/4.67 fof(fact_Cons__in__lex, axiom, ![X16, X32, X5, X7, X6, X4]:(((X5=X6&hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)),c_List_Olex(X4,X16))))|(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),X16))&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)),hAPP(hAPP(c_List_Olist_OCons(X4),X5),X32))),c_List_Olex(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cons__in__lex)). 4.46/4.67 fof(fact_setsum__ub__add__nat, axiom, ![X109, X27, X14, X22, X4]:(class_Groups_Ocomm__monoid__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X22,X14))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X109))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X22,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X109))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__ub__add__nat)). 4.46/4.67 fof(fact_listrel1__iff__update, axiom, ![X16, X32, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)),c_List_Olistrel1(X4,X16)))<=>?[X44, X199]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(hAPP(c_List_Onth(X4),X7),X199)),X44)),X16))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X199),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))))&hAPP(hAPP(c_List_Olist__update(X4,X7),X199),X44)=X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1__iff__update)). 4.46/4.67 fof(fact_rtrancl__into__trancl1, axiom, ![X39, X16, X37, X18, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),c_Transitive__Closure_Ortrancl(X4,X16)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X37),X39)),X16))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X39)),c_Transitive__Closure_Otrancl(X4,X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__into__trancl1)). 4.46/4.67 fof(fact_eq__equiv__class__iff2, axiom, ![X5, X6, X16, X2, X4]:(c_Equiv__Relations_Oequiv(X4,X2,X16)=>((hBOOL(hAPP(hAPP(c_member(X4),X5),X2))=>(hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X16)=hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X16)<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),X16))))<=hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__equiv__class__iff2)). 4.46/4.67 fof(fact_equiv__class__eq__iff, axiom, ![X5, X6, X16, X2, X4]:(c_Equiv__Relations_Oequiv(X4,X2,X16)=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),X16))<=>((hBOOL(hAPP(hAPP(c_member(X4),X5),X2))&hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))&hAPP(c_Relation_OImage(X4,X4,X16),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X4,X4,X16),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__class__eq__iff)). 4.46/4.67 fof(fact_quotient__eq__iff, axiom, ![X5, X6, X76, X173, X16, X2, X4]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X173),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X2),X16)))=>(((hBOOL(hAPP(hAPP(c_member(X4),X5),X76))=>(X173=X76<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),X16))))<=hBOOL(hAPP(hAPP(c_member(X4),X6),X173)))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X76),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X2),X16)))))<=c_Equiv__Relations_Oequiv(X4,X2,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotient__eq__iff)). 4.46/4.67 fof(fact_divmod__nat__step, axiom, ![X19, X17]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),X19))=>c_Divides_Odivmod__nat(X19,X17)=hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17)),X17))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__step)). 4.46/4.67 fof(fact_r__r__into__trancl, axiom, ![X39, X26, X37, X18, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),X26))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X37),X39)),X26))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X39)),c_Transitive__Closure_Otrancl(X4,X26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_r__r__into__trancl)). 4.46/4.67 fof(fact_lexord__lex, axiom, ![X16, X5, X6, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X6),X5)),c_List_Olex(X4,X16)))<=>(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X6)&hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X6),X5)),c_List_Olexord(X4,X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__lex)). 4.46/4.67 fof(fact_divmod__nat__rel__def, axiom, ![X292, X14, X22]:(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22,X14),X292))<=>(((X14=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X292)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X292)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X292))))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X292)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X292)),X14)))))<=X14!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&X22=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X292)),X14)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X292)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel__def)). 4.46/4.67 fof(fact_less__eq__nat_Osimps_I1_J, axiom, ![X17]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__nat_Osimps_I1_J)). 4.46/4.67 fof(fact_Int__Collect__mono, axiom, ![X80, X28, X1, X2, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_Set_OCollect(X4),X28))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X1),hAPP(c_Set_OCollect(X4),X80))))<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>(hBOOL(hAPP(X28,X42))=>hBOOL(hAPP(X80,X42)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Collect__mono)). 4.46/4.67 fof(fact_minus__fold__remove, axiom, ![X1, X2, X4]:(hAPP(hAPP(c_Finite__Set_Ofold(X4,tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Set_Oinsert(X4)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X1),X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X1),X2)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__fold__remove)). 4.46/4.67 fof(fact_fold__image__def, axiom, ![X50, X27, X3, X4]:hAPP(c_Finite__Set_Ofold__image(X4,X3,X27),X50)=c_Finite__Set_Ofold(X3,X4,hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X3),X27),X50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__def)). 4.46/4.67 fof(fact_append__eq__append__conv__if, axiom, ![X185, X186, X187, X188, X4]:((((hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X186)),X188)),X187)=X185&hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X186)),X188)=X186)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X188)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X186)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X188)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X186)))=>(X188=hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X188)),X186)&X187=hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X188)),X186)),X185))))<=>hAPP(hAPP(c_List_Oappend(X4),X186),X185)=hAPP(hAPP(c_List_Oappend(X4),X188),X187)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__eq__append__conv__if)). 4.46/4.67 fof(fact_UN__finite2__eq, axiom, ![X1, X45, X2, X4]:(![X199]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X199)),X2)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X199),X45))),X1)=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__finite2__eq)). 4.46/4.67 fof(fact_trancl__subset__Sigma, axiom, ![X2, X16, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X2))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X4,X16)),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__subset__Sigma)). 4.46/4.67 fof(fact_the__inv__into__comp, axiom, ![X6, X2, X50, X29, X27, X3, X4]:((c_Fun_Oinj__on(X29,X4,X50,X2)=>(hAPP(hAPP(c_Fun_Ocomp(X4,X29,X3,c_Fun_Othe__inv__into(X29,X4,X2,X50)),c_Fun_Othe__inv__into(X4,X3,hAPP(c_Set_Oimage(X29,X4,X50),X2),X27)),X6)=hAPP(c_Fun_Othe__inv__into(X29,X3,X2,hAPP(c_Fun_Ocomp(X4,X3,X29,X27),X50)),X6)<=hBOOL(hAPP(hAPP(c_member(X3),X6),hAPP(c_Set_Oimage(X4,X3,X27),hAPP(c_Set_Oimage(X29,X4,X50),X2))))))<=c_Fun_Oinj__on(X4,X3,X27,hAPP(c_Set_Oimage(X29,X4,X50),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__inv__into__comp)). 4.46/4.67 fof(fact_small__lazy_H_Opinduct, axiom, ![X28, X123, X124]:((hBOOL(hAPP(hAPP(X28,X124),X123))<=![X190, X41]:(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X190),X41)))=>((hBOOL(hAPP(hAPP(X28,X190),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X41),c_Groups_Oone__class_Oone(tc_Int_Oint))))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X190),X41))))=>hBOOL(hAPP(hAPP(X28,X190),X41)))))<=hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X124),X123)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__lazy_H_Opinduct)). 4.46/4.67 fof(fact_inj__vimage__singleton, axiom, ![X18, X27, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4,X3,X27),hAPP(hAPP(c_Set_Oinsert(X3),X18),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X4),c_HOL_OThe(X4,hAPP(hAPP(c_COMBC(X4,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,tc_HOL_Obool),X4),c_fequal),X27)),X18))),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))<=c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__vimage__singleton)). 4.46/4.67 fof(fact_wf__union__merge, axiom, ![X46, X26, X4]:(c_Wellfounded_Owf(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X26),X26)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X46),X26))),X46))<=>c_Wellfounded_Owf(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X26),X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__union__merge)). 4.46/4.67 fof(fact_Un__assoc, axiom, ![X52, X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X1),X52))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)),X52), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__assoc)). 4.46/4.67 fof(fact_Un__commute, axiom, ![X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X1),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__commute)). 4.46/4.67 fof(fact_card__Diff2__less, axiom, ![X5, X6, X2, X4]:(((hBOOL(hAPP(hAPP(c_member(X4),X5),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X4),X2))))<=hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff2__less)). 4.46/4.67 fof(fact_Diff__insert2, axiom, ![X1, X18, X2, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__insert2)). 4.46/4.67 fof(fact_length__drop, axiom, ![X57, X17, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Odrop(X4),X17),X57))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__drop)). 4.46/4.67 fof(fact_trancl__Int__subset, axiom, ![X68, X16, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X4,X16)),X68))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X4,X16)),X68)),X16)),X68)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),X68))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__Int__subset)). 4.46/4.67 fof(fact_dropWhile__append2, axiom, ![X32, X28, X7, X4]:(![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7)))=>hBOOL(hAPP(X28,X42)))=>c_List_OdropWhile(X4,X28,hAPP(hAPP(c_List_Oappend(X4),X7),X32))=c_List_OdropWhile(X4,X28,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__append2)). 4.46/4.67 fof(fact_bset_I8_J, axiom, ![X1, X64, X65]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X64),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))=>![X42]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X64),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X42),X65)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X64),X42)))<=![X66]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X65)))=>![X200]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X200),X1))=>X42!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X200),X66)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bset_I8_J)). 4.46/4.67 fof(fact_periodic__finite__ex, axiom, ![X28, X87]:(((?[X138]:hBOOL(hAPP(X28,X138))<=>?[X42]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X42),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X87)))&hBOOL(hAPP(X28,X42))))<=![X42, X266]:(hBOOL(hAPP(X28,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X266),X87))))<=>hBOOL(hAPP(X28,X42))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X87))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_periodic__finite__ex)). 4.46/4.67 fof(fact_zmult__commute, axiom, ![X30, X49]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X49),X30)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X49), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__commute)). 4.46/4.67 fof(fact_setsum__ivl__cong, axiom, ![X50, X27, X87, X37, X39, X18, X4, X3]:((class_Orderings_Oord(X4)&class_Groups_Ocomm__monoid__add(X3))=>(X39=X18=>((![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X39),X42))=>(hAPP(X27,X42)=hAPP(X50,X42)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X42),X87))))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X18),X37))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X39),X87)))<=X37=X87))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__ivl__cong)). 4.46/4.67 fof(fact_pigeonhole__infinite, axiom, ![X27, X3, X2, X4]:((?[X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))&~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2))),hAPP(hAPP(c_COMBC(X4,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,tc_HOL_Obool),X4),c_fequal),X27)),hAPP(X27,X42))))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X4,X3,X27),X2))))<=~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pigeonhole__infinite)). 4.46/4.67 fof(fact_nat__intermed__int__val, axiom, ![X45, X27, X14, X22]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X27,X22)),X45))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X45),hAPP(X27,X14)))=>?[X41]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X41),X14))&hAPP(X27,X41)=X45)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X41)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X14)))<=![X41]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X41),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X27,X41)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))<=(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X41))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),X14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__intermed__int__val)). 4.46/4.67 fof(fact_restrict__fun__upd, axiom, ![X5, X22, X3, X65, X6, X4]:((c_Map_Orestrict__map(X4,X3,X22,X65)=c_Map_Orestrict__map(X4,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),X22),X6),X5),X65)<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),X65))))&(hBOOL(hAPP(hAPP(c_member(X4),X6),X65))=>c_Map_Orestrict__map(X4,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),X22),X6),X5),X65)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),c_Map_Orestrict__map(X4,X3,X22,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X65),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),X6),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__fun__upd)). 4.46/4.67 fof(fact_fun__upd__restrict, axiom, ![X5, X6, X65, X22, X3, X4]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),c_Map_Orestrict__map(X4,X3,X22,X65)),X6),X5)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),c_Map_Orestrict__map(X4,X3,X22,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X65),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),X6),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__restrict)). 4.46/4.67 fof(fact_lists__IntI, axiom, ![X1, X2, X67, X4]:((hBOOL(hAPP(c_List_Olistsp(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X1))),X67))<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X67),c_List_Olists(X4,X1))))<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X67),c_List_Olists(X4,X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__IntI)). 4.46/4.67 fof(fact_card__partition, axiom, ![X45, X52, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,tc_HOL_Obool)),X52))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X52)))=>((hAPP(c_Finite__Set_Ocard(X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X52))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),hAPP(c_Finite__Set_Ocard(tc_fun(X4,tc_HOL_Obool)),X52))<=![X154]:(![X155]:((X155!=X154=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X154),X155)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X155),X52)))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X154),X52))))<=![X156]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X156),X52))=>hAPP(c_Finite__Set_Ocard(X4),X156)=X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__partition)). 4.46/4.67 fof(fact_finite__UnionD, axiom, ![X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,tc_HOL_Obool)),X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UnionD)). 4.46/4.67 fof(fact_Cons__eq__filter__iff, axiom, ![X32, X28, X7, X6, X4]:(hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)=hAPP(c_List_Ofilter(X4,X28),X32)<=>?[X219, X220]:(((X32=hAPP(hAPP(c_List_Oappend(X4),X219),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X220))&hBOOL(hAPP(X28,X6)))&X7=hAPP(c_List_Ofilter(X4,X28),X220))&![X42]:(~(hBOOL(hAPP(X28,X42)))<=hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X219)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cons__eq__filter__iff)). 4.46/4.67 fof(fact_rev__update, axiom, ![X47, X57, X4, X15]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))=>hAPP(c_List_Orev(X4),hAPP(hAPP(c_List_Olist__update(X4,X57),X15),X47))=hAPP(hAPP(c_List_Olist__update(X4,hAPP(c_List_Orev(X4),X57)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),X15)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__update)). 4.46/4.67 fof(fact_diff__diff__left, axiom, ![X15, X20, X21]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X15))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21),X20)),X15), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__diff__left)). 4.46/4.67 fof(fact_escape, axiom, ![X80, X39, X82, X4, X28]:(![X83, X84]:(hBOOL(hAPP(hAPP(X28,X83),X84))=>c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X4),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),X84))),X39),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X4),hAPP(X80,X83)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool)))))=>c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X28),X39),X80)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_escape)). 4.46/4.67 fof(fact_Comp, axiom, ![X26, X87, X80, X39, X28, X82, X4]:((c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X80),X87),X26)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))=>c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X28),c_Com_Ocom_OSemi(X39,X87)),X26)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool)))))<=c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X28),X39),X80)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Comp)). 4.46/4.67 fof(fact_map__upds__twist, axiom, ![X260, X37, X22, X3, X172, X18, X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X18),hAPP(c_List_Oset(X4),X172))))=>hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),c_Map_Omap__upds(X4,X3,X22,X172,X260)),X18),hAPP(c_Option_Ooption_OSome(X3),X37))=c_Map_Omap__upds(X4,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),X22),X18),hAPP(c_Option_Ooption_OSome(X3),X37)),X172,X260)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upds__twist)). 4.46/4.67 fof(fact_tranclD, axiom, ![X26, X5, X6, X4]:(?[X132]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X132),X5)),c_Transitive__Closure_Ortrancl(X4,X26)))&hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X132)),X26)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_Transitive__Closure_Otrancl(X4,X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tranclD)). 4.46/4.67 fof(fact_tranclD2, axiom, ![X26, X5, X6, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_Transitive__Closure_Otrancl(X4,X26)))=>?[X132]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X132),X5)),X26))&hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X132)),c_Transitive__Closure_Ortrancl(X4,X26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tranclD2)). 4.46/4.67 fof(fact_trancl__mono, axiom, ![X68, X16, X109, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X109),c_Transitive__Closure_Otrancl(X4,X16)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X109),c_Transitive__Closure_Otrancl(X4,X68)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),X68)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__mono)). 4.46/4.67 fof(fact_upto_Opinduct, axiom, ![X28, X123, X124]:((![X41, X98]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X41),X98))=>hBOOL(hAPP(hAPP(X28,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X41),c_Groups_Oone__class_Oone(tc_Int_Oint))),X98)))=>hBOOL(hAPP(hAPP(X28,X41),X98)))<=hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X41),X98))))=>hBOOL(hAPP(hAPP(X28,X124),X123)))<=hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X124),X123)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upto_Opinduct)). 4.46/4.67 fof(fact_neq0__conv, axiom, ![X14]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X14<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neq0__conv)). 4.46/4.67 fof(fact_filter__eq__Cons__iff, axiom, ![X7, X6, X32, X28, X4]:(hAPP(c_List_Ofilter(X4,X28),X32)=hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)<=>?[X219, X220]:(((hBOOL(hAPP(X28,X6))&X7=hAPP(c_List_Ofilter(X4,X28),X220))&![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X219)))=>~(hBOOL(hAPP(X28,X42)))))&X32=hAPP(hAPP(c_List_Oappend(X4),X219),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X220)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__eq__Cons__iff)). 4.46/4.67 fof(fact_nat0__intermed__int__val, axiom, ![X45, X27, X14]:(![X41]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),X14))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X41),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X27,X41)))),c_Groups_Oone__class_Oone(tc_Int_Oint))))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X27,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X45))=>(?[X41]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X41),X14))&X45=hAPP(X27,X41))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X45),hAPP(X27,X14)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat0__intermed__int__val)). 4.46/4.67 fof(fact_upt__add__eq__append, axiom, ![X15, X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))=>c_List_Oupt(X21,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X15))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X21,X20)),c_List_Oupt(X20,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X15)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__add__eq__append)). 4.46/4.67 fof(fact_int__val__lemma, axiom, ![X45, X27, X14]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X27,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X45))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X45),hAPP(X27,X14)))=>?[X41]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X41),X14))&X45=hAPP(X27,X41))))<=![X41]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X41),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X27,X41)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__val__lemma)). 4.46/4.67 fof(fact_take__zip, axiom, ![X72, X57, X17, X3, X4]:hAPP(hAPP(c_List_Ozip(X4,X3),hAPP(hAPP(c_List_Otake(X4),X17),X57)),hAPP(hAPP(c_List_Otake(X3),X17),X72))=hAPP(hAPP(c_List_Otake(tc_prod(X4,X3)),X17),hAPP(hAPP(c_List_Ozip(X4,X3),X57),X72)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__zip)). 4.46/4.67 fof(fact_nat__eq__add__iff2, axiom, ![X14, X22, X23, X25, X24]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X23)),X14)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X23)),X22)<=>X22=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X24)),X23)),X14))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__eq__add__iff2)). 4.46/4.67 fof(fact_left__add__mult__distrib, axiom, ![X15, X20, X195, X21]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20)),X195)),X15)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X195)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X195)),X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_left__add__mult__distrib)). 4.46/4.67 fof(fact_sup__nat__def, axiom, c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)=c_Orderings_Oord__class_Omax(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__nat__def)). 4.46/4.67 fof(fact_rtrancl__eq__or__trancl, axiom, ![X26, X5, X6, X4]:(((X6!=X5&hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_Transitive__Closure_Otrancl(X4,X26))))|X6=X5)<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_Transitive__Closure_Ortrancl(X4,X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__eq__or__trancl)). 4.46/4.67 fof(fact_Loop__sound__lemma, axiom, ![X39, X37, X28, X82, X4]:(c_Hoare__Mirabelle_Ohoare__valids(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X28),c_Com_Ocom_OWhile(X37,X39)),c_Hoare__Mirabelle_Opeek__and(X4,X28,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X37)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))<=c_Hoare__Mirabelle_Ohoare__valids(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),c_Hoare__Mirabelle_Opeek__and(X4,X28,X37)),X39),X28)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Loop__sound__lemma)). 4.46/4.67 fof(fact_transpose__transpose, axiom, ![X7, X4]:(c_List_Otranspose(X4,c_List_Otranspose(X4,X7))=c_List_OtakeWhile(tc_List_Olist(X4),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X4)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(X4),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X4))),X7)<=c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X4))),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__transpose)). 4.46/4.67 fof(fact_ran__distinct, axiom, ![X206, X3, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(tc_prod(X4,X3),X4),c_Product__Type_Ofst(X4,X3)),X206)))=>c_Map_Oran(X4,X3,hAPP(c_Map_Omap__of(X4,X3),X206))=hAPP(c_Set_Oimage(tc_prod(X4,X3),X3,c_Product__Type_Osnd(X4,X3)),hAPP(c_List_Oset(tc_prod(X4,X3)),X206))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ran__distinct)). 4.46/4.67 fof(fact_snd__eq__Range, axiom, ![X26, X4, X3]:hAPP(c_Set_Oimage(tc_prod(X3,X4),X4,c_Product__Type_Osnd(X3,X4)),X26)=hAPP(c_Relation_ORange(X3,X4),X26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snd__eq__Range)). 4.46/4.67 fof(fact_decr__lemma, axiom, ![X49, X48, X133]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X133))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X48),X49))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X133))),X49))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_decr__lemma)). 4.46/4.67 fof(fact_incr__lemma, axiom, ![X48, X49, X133]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X133))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X49),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X48),X49))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X133))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_incr__lemma)). 4.46/4.67 fof(fact_New__DSequence_Oneg__decr__bind__def, axiom, ![X27, X6, X4, X3, X24]:((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X24=>hAPP(c_New__DSequence_Oneg__decr__bind(X3,X4,X6,X27),X24)=c_Lazy__Sequence_Ohit__bound(X4))&(c_Lazy__Sequence_Ohb__bind(X3,X4,hAPP(X6,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X24),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X3,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4))),X27),X24))=hAPP(c_New__DSequence_Oneg__decr__bind(X3,X4,X6,X27),X24)<=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Oneg__decr__bind__def)). 4.46/4.67 fof(fact_hb__bind__def, axiom, ![X27, X107, X4, X3]:c_Lazy__Sequence_Ohb__flat(X4,c_Lazy__Sequence_Ohb__map(X3,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4)),X27,X107))=c_Lazy__Sequence_Ohb__bind(X3,X4,X107,X27), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hb__bind__def)). 4.46/4.67 fof(fact_zip__same, axiom, ![X7, X37, X18, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),hAPP(c_List_Oset(tc_prod(X4,X4)),hAPP(hAPP(c_List_Ozip(X4,X4),X7),X7))))<=>(X37=X18&hBOOL(hAPP(hAPP(c_member(X4),X18),hAPP(c_List_Oset(X4),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__same)). 4.46/4.67 fof(fact_dropWhile_Osimps_I2_J, axiom, ![X7, X4, X6, X28]:((hBOOL(hAPP(X28,X6))=>c_List_OdropWhile(X4,X28,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7))=c_List_OdropWhile(X4,X28,X7))&(~(hBOOL(hAPP(X28,X6)))=>hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)=c_List_OdropWhile(X4,X28,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile_Osimps_I2_J)). 4.46/4.67 fof(fact_rtrancl__Int__subset, axiom, ![X16, X68, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Relation_OId(X4)),X68))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4,X16)),X68)),X16)),X68))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4,X16)),X68)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__Int__subset)). 4.46/4.67 fof(fact_eq__add__iff2, axiom, ![X87, X37, X39, X106, X18, X4]:(class_Rings_Oring(X4)=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X106)),X39)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X37),X106)),X87)<=>X39=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X37),X18)),X106)),X87))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__add__iff2)). 4.46/4.67 fof(fact_map__sorted__distinct__set__unique, axiom, ![X32, X7, X27, X4, X3]:(class_Orderings_Olinorder(X3)=>(c_Fun_Oinj__on(X4,X3,X27,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X7)),hAPP(c_List_Oset(X4),X32)))=>((hBOOL(hAPP(c_List_Odistinct(X3),hAPP(hAPP(c_List_Omap(X4,X3),X27),X7)))=>(c_List_Olinorder__class_Osorted(X3,hAPP(hAPP(c_List_Omap(X4,X3),X27),X32))=>(hBOOL(hAPP(c_List_Odistinct(X3),hAPP(hAPP(c_List_Omap(X4,X3),X27),X32)))=>(X7=X32<=hAPP(c_List_Oset(X4),X7)=hAPP(c_List_Oset(X4),X32)))))<=c_List_Olinorder__class_Osorted(X3,hAPP(hAPP(c_List_Omap(X4,X3),X27),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__sorted__distinct__set__unique)). 4.46/4.67 fof(fact_set__append, axiom, ![X32, X7, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X7)),hAPP(c_List_Oset(X4),X32))=hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Oappend(X4),X7),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__append)). 4.46/4.67 fof(fact_zmod__zmult2__eq, axiom, ![X11, X12, X10]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11),X10))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zmult2__eq)). 4.46/4.67 fof(fact_transfer__nat__int__numerals_I2_J, axiom, c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__numerals_I2_J)). 4.46/4.67 fof(fact_nat__number__of__Pls, axiom, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of__Pls)). 4.46/4.67 fof(fact_Loop, axiom, ![X39, X37, X28, X82, X4]:(c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),c_Hoare__Mirabelle_Opeek__and(X4,X28,X37)),X39),X28)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))=>c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X28),c_Com_Ocom_OWhile(X37,X39)),c_Hoare__Mirabelle_Opeek__and(X4,X28,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X37)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Loop)). 4.46/4.67 fof(fact_split__pos__lemma, axiom, ![X14, X28, X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))=>(![X41, X98]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),X45)))&X14=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X45),X41)),X98))=>hBOOL(hAPP(hAPP(X28,X41),X98)))<=>hBOOL(hAPP(hAPP(X28,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14),X45)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X14,X45))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__pos__lemma)). 4.46/4.67 fof(fact_dropWhile__eq__Cons__conv, axiom, ![X32, X5, X7, X28, X4]:((X7=hAPP(hAPP(c_List_Oappend(X4),c_List_OtakeWhile(X4,X28,X7)),hAPP(hAPP(c_List_Olist_OCons(X4),X5),X32))&~(hBOOL(hAPP(X28,X5))))<=>hAPP(hAPP(c_List_Olist_OCons(X4),X5),X32)=c_List_OdropWhile(X4,X28,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__eq__Cons__conv)). 4.46/4.67 fof(fact_split__neg__lemma, axiom, ![X14, X28, X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>(![X41, X98]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),X98))&X14=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X45),X41)),X98))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))=>hBOOL(hAPP(hAPP(X28,X41),X98)))<=>hBOOL(hAPP(hAPP(X28,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14),X45)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X14,X45))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__neg__lemma)). 4.46/4.67 fof(fact_trancl__power, axiom, ![X26, X109, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X109),c_Transitive__Closure_Otrancl(X4,X26)))<=>?[X199]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X199))&hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X109),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X199),X26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__power)). 4.46/4.67 fof(fact_add__number__of__diff2, axiom, ![X30, X10, X63, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X63)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X10),hAPP(c_Int_Onumber__class_Onumber__of(X4),X30)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X63),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30)))),X10)<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__number__of__diff2)). 4.46/4.67 fof(fact_div__pos__neg__1__number__of, axiom, ![X30]:(hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30)))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__pos__neg__1__number__of)). 4.46/4.67 fof(fact_negateSnd__eq, axiom, ![X111, X112]:hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X112),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X111))=hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X112),X111)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negateSnd__eq)). 4.46/4.67 fof(fact_setsum__op__ivl__Suc, axiom, ![X27, X22, X14, X4]:(class_Groups_Ocomm__monoid__add(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X22))=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22),hAPP(c_Nat_OSuc,X14))))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22),X14))),hAPP(X27,X14))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22),hAPP(c_Nat_OSuc,X14)))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X22)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__op__ivl__Suc)). 4.46/4.67 fof(fact_mod__pos__neg__1__number__of, axiom, ![X30]:(c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30))=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__pos__neg__1__number__of)). 4.46/4.67 fof(fact_nat__number__of__add__left, axiom, ![X15, X71, X63]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63)))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71)),X15))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71)),X15))&(~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63))))=>((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71)),X15))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X63),X71))),X15)<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X71)))))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),X15)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71)),X15))<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X71))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of__add__left)). 4.46/4.67 fof(fact_acyclic__def, axiom, ![X16, X4]:(![X42]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X42)),c_Transitive__Closure_Otrancl(X4,X16))))<=>c_Wellfounded_Oacyclic(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclic__def)). 4.46/4.67 fof(fact_acyclicI, axiom, ![X16, X4]:(![X42]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X42)),c_Transitive__Closure_Otrancl(X4,X16))))=>c_Wellfounded_Oacyclic(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclicI)). 4.46/4.67 fof(fact_flat__lub__def, axiom, ![X37, X2, X4]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X37),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=>c_Partial__Function_Oflat__lub(X4,X37,X2)=c_HOL_OThe(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X37),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))&(c_Partial__Function_Oflat__lub(X4,X37,X2)=X37<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X37),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_flat__lub__def)). 4.46/4.67 fof(fact_incr__mult__lemma, axiom, ![X45, X28, X87]:((![X42]:(hBOOL(hAPP(X28,X42))=>hBOOL(hAPP(X28,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X42),X87))))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))=>![X42]:(hBOOL(hAPP(X28,X42))=>hBOOL(hAPP(X28,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X45),X87)))))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X87))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_incr__mult__lemma)). 4.46/4.67 fof(fact_divmod__int__relI, axiom, ![X111, X112, X11, X12]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X112)),X111)=X12=>(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,X11),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X112),X111)))<=(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X111))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X111),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X111),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),X111)))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__relI)). 4.46/4.67 fof(fact_image__minus__const__atLeastLessThan__nat, axiom, ![X6, X5, X39]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X39),X5))=>hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6),X39)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),X39))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X39)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6),X5)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X39),X5)))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X5))=>hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X39)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6),X5))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))&(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X39)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6),X5))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__minus__const__atLeastLessThan__nat)). 4.46/4.67 fof(fact_take__upt, axiom, ![X17, X19, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X19)),X17))=>c_List_Oupt(X21,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X19))=hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X19),c_List_Oupt(X21,X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__upt)). 4.46/4.67 fof(fact_divmod__int__rel__div__eq, axiom, ![X313, X47, X302, X303]:(X303=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X302),X47)),X313)=>((hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X303),X302)=X47<=X302!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))<=((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X302)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X302),X313))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X313),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X302))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X313),X302))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X313))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__div__eq)). 4.46/4.67 fof(fact_takeWhile__eq__filter, axiom, ![X7, X28, X4]:(hAPP(c_List_Ofilter(X4,X28),X7)=c_List_OtakeWhile(X4,X28,X7)<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),c_List_OdropWhile(X4,X28,X7))))=>~(hBOOL(hAPP(X28,X42))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__eq__filter)). 4.46/4.67 fof(fact_pick__same, axiom, ![X7, X4, X67]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X67),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))=>hAPP(hAPP(c_List_Onth(X4),X7),X67)=hAPP(c_Random_Opick(X4,hAPP(hAPP(c_List_Omap(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,X4)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X4),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X7)),hAPP(c_Code__Numeral_Oof__nat,X67))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pick__same)). 4.46/4.67 fof(fact_bset_I3_J, axiom, ![X1, X64, X65]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))=>(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X64),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))=>(X64=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X64),X65)<=![X42]:(![X66]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X66),X42)!=X64<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),X1)))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X42),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X65))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bset_I3_J)). 4.46/4.67 fof(fact_strong__setprod__reindex__cong, axiom, ![X58, X50, X1, X2, X27, X3, X4, X29]:(class_Groups_Ocomm__monoid__mult(X29)=>(((![X42]:(hAPP(X50,X42)=hAPP(hAPP(c_Fun_Ocomp(X3,X29,X4,X58),X27),X42)<=hBOOL(hAPP(hAPP(c_member(X4),X42),X2)))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X29),X50),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X29),X58),X1))<=X1=hAPP(c_Set_Oimage(X4,X3,X27),X2))<=c_Fun_Oinj__on(X4,X3,X27,X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_strong__setprod__reindex__cong)). 4.46/4.67 fof(fact_setsum__reindex__cong, axiom, ![X58, X50, X1, X2, X27, X3, X4, X29]:((((![X125]:(hBOOL(hAPP(hAPP(c_member(X4),X125),X2))=>hAPP(X58,hAPP(X27,X125))=hAPP(X50,X125))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X29),X50),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X29),X58),X1))<=X1=hAPP(c_Set_Oimage(X4,X3,X27),X2))<=c_Fun_Oinj__on(X4,X3,X27,X2))<=class_Groups_Ocomm__monoid__add(X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__reindex__cong)). 4.46/4.67 fof(fact_hd__rotate__conv__nth, axiom, ![X17, X4, X57]:(hAPP(hAPP(c_List_Onth(X4),X57),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))=hAPP(c_List_Ohd(X4),hAPP(c_List_Orotate(X4,X17),X57))<=c_List_Olist_ONil(X4)!=X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__rotate__conv__nth)). 4.46/4.67 fof(fact_foldr__max__sorted, axiom, ![X5, X7, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Osorted(X4,hAPP(c_List_Orev(X4),X7))=>((X7=c_List_Olist_ONil(X4)=>X5=c_List_Ofoldr(X4,X4,c_Orderings_Oord__class_Omax(X4),X7,X5))&(X7!=c_List_Olist_ONil(X4)=>c_List_Ofoldr(X4,X4,c_Orderings_Oord__class_Omax(X4),X7,X5)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_List_Onth(X4),X7),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldr__max__sorted)). 4.46/4.67 fof(fact_map__of__eq__dom, axiom, ![X32, X7, X3, X4]:(hAPP(c_Map_Omap__of(X4,X3),X32)=hAPP(c_Map_Omap__of(X4,X3),X7)=>hAPP(c_Set_Oimage(tc_prod(X4,X3),X4,c_Product__Type_Ofst(X4,X3)),hAPP(c_List_Oset(tc_prod(X4,X3)),X32))=hAPP(c_Set_Oimage(tc_prod(X4,X3),X4,c_Product__Type_Ofst(X4,X3)),hAPP(c_List_Oset(tc_prod(X4,X3)),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__eq__dom)). 4.46/4.67 fof(fact_nat__number__of__mult__left, axiom, ![X15, X71, X63]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71)),X15))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X63),c_Int_OPls)))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71)),X15))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X63),X71))),X15)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X63),c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of__mult__left)). 4.46/4.67 fof(fact_foldl__foldr1__lemma, axiom, ![X7, X18, X4]:(class_Groups_Omonoid__add(X4)=>hAPP(c_List_Ofoldl(X4,X4,c_Groups_Oplus__class_Oplus(X4),X18),X7)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X18),c_List_Ofoldr(X4,X4,c_Groups_Oplus__class_Oplus(X4),X7,c_Groups_Ozero__class_Ozero(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__foldr1__lemma)). 4.46/4.67 fof(fact_int__power__div__base, axiom, ![X15, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19))=>(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X15),X19)),X15)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__power__div__base)). 4.46/4.67 fof(fact_nth__map__upt, axiom, ![X27, X4, X22, X14, X24]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14),X22)))=>hAPP(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X24))=hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X4),X27),c_List_Oupt(X22,X14))),X24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__map__upt)). 4.46/4.67 fof(fact_sup__SUPR__fold__sup, axiom, ![X27, X1, X2, X4, X3]:(class_Complete__Lattice_Ocomplete__lattice(X3)=>(hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,hAPP(hAPP(c_COMBB(X3,tc_fun(X3,X3),X4),c_Lattices_Osemilattice__sup__class_Osup(X3)),X27)),X1),X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3),X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X3),X2),X27))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__SUPR__fold__sup)). 4.46/4.67 fof(fact_inf__INFI__fold__inf, axiom, ![X27, X1, X2, X4, X3]:(class_Complete__Lattice_Ocomplete__lattice(X3)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3),X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X3),X2),X27))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,hAPP(hAPP(c_COMBB(X3,tc_fun(X3,X3),X4),c_Lattices_Osemilattice__inf__class_Oinf(X3)),X27)),X1),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__INFI__fold__inf)). 4.46/4.67 fof(fact_setsum__head, axiom, ![X28, X14, X22, X4]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(X28,X22)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X28),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X22,X14)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X28),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X22,X14))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14)))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__head)). 4.46/4.67 fof(fact_divmod__int__rel__mod__eq, axiom, ![X47, X301, X302, X303]:(X303=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X302),X301)),X47)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X302))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X47))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X47),X302))))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X302)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X302),X47))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X47),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))=>(X47=c_Divides_Odiv__class_Omod(tc_Int_Oint,X303,X302)<=X302!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__mod__eq)). 4.46/4.67 fof(fact_in__measure, axiom, ![X27, X5, X6, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),hAPP(c_Wellfounded_Omeasure(X4),X27)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X27,X6)),hAPP(X27,X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__measure)). 4.46/4.67 fof(fact_measure__def, axiom, ![X4]:hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X4),c_Wellfounded_Oless__than)=c_Wellfounded_Omeasure(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_measure__def)). 4.46/4.67 fof(fact_transfer__nat__int__sum__prod__cong_I2_J, axiom, ![X50, X27, X1, X2, X4]:((class_Groups_Ocomm__monoid__add(X4)&class_Groups_Ocomm__monoid__mult(X4))=>((c_Nat__Transfer_Onat__set(X1)=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X4),X27),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X4),X50),X1)<=![X42]:(hAPP(X27,X42)=hAPP(X50,X42)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X42)))))<=X2=X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__sum__prod__cong_I2_J)). 4.46/4.67 fof(fact_transfer__nat__int__sum__prod__cong_I1_J, axiom, ![X50, X27, X1, X2, X4]:(((c_Nat__Transfer_Onat__set(X1)=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X4),X27),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X4),X50),X1)<=![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X42))=>hAPP(X27,X42)=hAPP(X50,X42))))<=X1=X2)<=(class_Groups_Ocomm__monoid__mult(X4)&class_Groups_Ocomm__monoid__add(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__sum__prod__cong_I1_J)). 4.46/4.67 fof(fact_setsum__nonneg__leq__bound, axiom, ![X24, X1, X27, X68, X4, X3]:(((((hBOOL(hAPP(hAPP(c_member(X4),X24),X68))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(X27,X24)),X1)))<=X1=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X68))<=![X41]:(hBOOL(hAPP(hAPP(c_member(X4),X41),X68))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(X27,X41)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X68)))<=class_Groups_Oordered__ab__group__add(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__nonneg__leq__bound)). 4.46/4.67 fof(fact_apsnd__eq__conv, axiom, ![X50, X6, X27, X4, X3, X29]:(hAPP(c_Product__Type_Oapsnd(X29,X3,X4,X27),X6)=hAPP(c_Product__Type_Oapsnd(X29,X3,X4,X50),X6)<=>hAPP(X50,hAPP(c_Product__Type_Osnd(X4,X29),X6))=hAPP(X27,hAPP(c_Product__Type_Osnd(X4,X29),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apsnd__eq__conv)). 4.46/4.67 fof(fact_apfst__eq__conv, axiom, ![X50, X6, X27, X3, X4, X29]:(hAPP(c_Product__Type_Oapfst(X29,X4,X3,X27),X6)=hAPP(c_Product__Type_Oapfst(X29,X4,X3,X50),X6)<=>hAPP(X50,hAPP(c_Product__Type_Ofst(X29,X3),X6))=hAPP(X27,hAPP(c_Product__Type_Ofst(X29,X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apfst__eq__conv)). 4.46/4.67 fof(fact_apfst__def, axiom, ![X27, X3, X29, X4]:c_Product__Type_Oapfst(X4,X29,X3,X27)=c_Product__Type_Omap__pair(X4,X29,X3,X3,X27,c_Fun_Oid(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apfst__def)). 4.46/4.67 fof(fact_order__fun_I2_J, axiom, ![X50, X27, X4, X3]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X3)),X27),X50))&hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X4),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),hAPP(hAPP(c_COMBS(X4,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,tc_HOL_Obool),X4),c_fequal),X27)),X50)))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,X3)),X27),X50)))<=(class_Enum_Oenum(X4)&class_Orderings_Oorder(X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__fun_I2_J)). 4.46/4.67 fof(fact_setsum__shift__bounds__Suc__ivl, axiom, ![X14, X22, X27, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X22)),hAPP(c_Nat_OSuc,X14)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Nat_Onat),X27),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__shift__bounds__Suc__ivl)). 4.46/4.67 fof(fact_sum__squares__le__zero__iff, axiom, ![X5, X6, X4]:(class_Rings_Olinordered__ring__strict(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X5),X5))),c_Groups_Ozero__class_Ozero(X4)))<=>(X6=c_Groups_Ozero__class_Ozero(X4)&c_Groups_Ozero__class_Ozero(X4)=X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__squares__le__zero__iff)). 4.46/4.67 fof(fact_bset_I4_J, axiom, ![X1, X64, X65]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X64),X1))=>![X42]:(![X66]:(![X200]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X200),X1))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X200),X66)!=X42)<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X65))))=>(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X42),X65)!=X64<=X64!=X42)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bset_I4_J)). 4.46/4.67 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J, axiom, ![X1, X2]:(c_Nat__Transfer_Onat__set(X2)=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X2),X1)=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)))<=c_Nat__Transfer_Onat__set(X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J)). 4.46/4.67 fof(fact_image__Un, axiom, ![X1, X2, X27, X4, X3]:hAPP(c_Set_Oimage(X3,X4,X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X4,X27),X2)),hAPP(c_Set_Oimage(X3,X4,X27),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Un)). 4.46/4.67 fof(fact_image__image, axiom, ![X2, X50, X29, X27, X4, X3]:hAPP(c_Set_Oimage(X29,X4,hAPP(hAPP(c_COMBB(X3,X4,X29),X27),X50)),X2)=hAPP(c_Set_Oimage(X3,X4,X27),hAPP(c_Set_Oimage(X29,X3,X50),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__image)). 4.46/4.67 fof(fact_Nil__eq__concat__conv, axiom, ![X113, X4]:(c_List_Oconcat(X4,X113)=c_List_Olist_ONil(X4)<=>![X42]:(X42=c_List_Olist_ONil(X4)<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X42),hAPP(c_List_Oset(tc_List_Olist(X4)),X113))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nil__eq__concat__conv)). 4.46/4.67 fof(fact_aset_I4_J, axiom, ![X2, X64, X65]:((![X42]:((X42!=X64=>X64!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X42),X65))<=![X66]:(![X200]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X200),X2))=>X42!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X200),X66))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X65)))))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X64),X2)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_aset_I4_J)). 4.46/4.67 fof(fact_concat__eq__Nil__conv, axiom, ![X113, X4]:(![X42]:(X42=c_List_Olist_ONil(X4)<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X42),hAPP(c_List_Oset(tc_List_Olist(X4)),X113))))<=>c_List_Oconcat(X4,X113)=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__eq__Nil__conv)). 4.46/4.67 fof(fact_crossproduct__noteq, axiom, ![X87, X39, X37, X18, X4]:(((X37!=X18&X39!=X87)<=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X87)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X37),X39))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X37),X87)))<=class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_crossproduct__noteq)). 4.46/4.67 fof(fact_atLeastatMost__psubset__iff, axiom, ![X87, X39, X37, X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X18,X37)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X39,X87)))<=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),X37)))|((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X39),X18))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),X87)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X37),X87))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),X18)))))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X39),X87))))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastatMost__psubset__iff)). 4.46/4.67 fof(fact_order__less__le, axiom, ![X5, X6, X4]:(class_Orderings_Oorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),X5))<=>(X6!=X5&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__less__le)). 4.46/4.67 fof(fact_split__div, axiom, ![X45, X14, X28]:(hBOOL(hAPP(X28,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X14),X45)))<=>((X45!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>![X41, X98]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X45))=>(hBOOL(hAPP(X28,X41))<=X14=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X41)),X98))))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X45=>hBOOL(hAPP(X28,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__div)). 4.46/4.67 fof(fact_INFI__fold__inf, axiom, ![X27, X2, X4, X3]:(class_Complete__Lattice_Ocomplete__lattice(X3)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X3),X2),X27)=hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,hAPP(hAPP(c_COMBB(X3,tc_fun(X3,X3),X4),c_Lattices_Osemilattice__inf__class_Oinf(X3)),X27)),c_Orderings_Otop__class_Otop(X3)),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INFI__fold__inf)). 4.46/4.67 fof(fact_BodyN, axiom, ![X82, X80, X263, X28, X4]:(c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X28),hAPP(c_Com_Ocom_OBODY,X263)),X80)),X82),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X28),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X263))),X80)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))=>c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X28),hAPP(c_Com_Ocom_OBODY,X263)),X80)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_BodyN)). 4.46/4.67 fof(fact_setsum__lessThan__Suc, axiom, ![X14, X27, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X14))),hAPP(X27,X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__lessThan__Suc)). 4.46/4.67 fof(fact_map__of__eq__None__iff, axiom, ![X6, X70, X4, X3]:(hAPP(hAPP(c_Map_Omap__of(X3,X4),X70),X6)=c_Option_Ooption_ONone(X4)<=>~(hBOOL(hAPP(hAPP(c_member(X3),X6),hAPP(c_Set_Oimage(tc_prod(X3,X4),X3,c_Product__Type_Ofst(X3,X4)),hAPP(c_List_Oset(tc_prod(X3,X4)),X70)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__eq__None__iff)). 4.46/4.67 fof(fact_setsum__atMost__Suc, axiom, ![X14, X27, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X14))),hAPP(X27,hAPP(c_Nat_OSuc,X14)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__atMost__Suc)). 4.46/4.67 fof(fact_atLeast0AtMost, axiom, ![X14]:hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X14)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast0AtMost)). 4.46/4.67 fof(fact_setprod__reindex__cong, axiom, ![X58, X50, X1, X2, X27, X3, X4, X29]:((c_Fun_Oinj__on(X4,X3,X27,X2)=>(hAPP(c_Set_Oimage(X4,X3,X27),X2)=X1=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X29),X50),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X29),X58),X1)<=hAPP(c_Fun_Ocomp(X3,X29,X4,X58),X27)=X50)))<=class_Groups_Ocomm__monoid__mult(X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__reindex__cong)). 4.46/4.67 fof(fact_card__less, axiom, ![X24, X153]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X153))=>hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X153))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X24)))))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__less)). 4.46/4.67 fof(fact_uminus__listsum__map, axiom, ![X7, X27, X3, X4]:(hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X3,X4),X27),X7)))=hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X3,X4),hAPP(c_Fun_Ocomp(X4,X4,X3,c_Groups_Ouminus__class_Ouminus(X4)),X27)),X7))<=class_Groups_Oab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_uminus__listsum__map)). 4.46/4.67 fof(fact_map__map, axiom, ![X7, X50, X29, X27, X4, X3]:hAPP(hAPP(c_List_Omap(X3,X4),X27),hAPP(hAPP(c_List_Omap(X29,X3),X50),X7))=hAPP(hAPP(c_List_Omap(X29,X4),hAPP(c_Fun_Ocomp(X3,X4,X29,X27),X50)),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__map)). 4.46/4.67 fof(fact_setsum__eq__Suc0__iff, axiom, ![X27, X2, X4]:((hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X27),X2)<=>?[X42]:((hBOOL(hAPP(hAPP(c_member(X4),X42),X2))&![X66]:(hBOOL(hAPP(hAPP(c_member(X4),X66),X2))=>(X66!=X42=>hAPP(X27,X66)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&hAPP(X27,X42)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__eq__Suc0__iff)). 4.46/4.67 fof(fact_SUPR__fold__sup, axiom, ![X27, X2, X4, X3]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,hAPP(hAPP(c_COMBB(X3,tc_fun(X3,X3),X4),c_Lattices_Osemilattice__sup__class_Osup(X3)),X27)),c_Orderings_Obot__class_Obot(X3)),X2)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X3),X2),X27))<=class_Complete__Lattice_Ocomplete__lattice(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUPR__fold__sup)). 4.46/4.67 fof(fact_filter__in__sublist, axiom, ![X68, X7, X4]:(hAPP(c_List_Ofilter(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),hAPP(c_List_Oset(X4),c_List_Osublist(X4,X7,X68)))),X7)=c_List_Osublist(X4,X7,X68)<=hBOOL(hAPP(c_List_Odistinct(X4),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__in__sublist)). 4.46/4.67 fof(fact_takeWhile__not__last, axiom, ![X4, X7]:(X7!=c_List_Olist_ONil(X4)=>(c_List_Obutlast(X4,X7)=c_List_OtakeWhile(X4,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),c_List_Olast(X4,X7))),X7)<=hBOOL(hAPP(c_List_Odistinct(X4),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__not__last)). 4.46/4.67 fof(fact_list__ex1__simps_I2_J, axiom, ![X7, X6, X28, X4]:(c_List_Olist__ex1(X4,X28,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7))<=>((c_List_Olist__ex1(X4,X28,X7)<=~(hBOOL(hAPP(X28,X6))))&(hBOOL(hAPP(X28,X6))=>c_List_Olist__all(X4,hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),X28))),hAPP(c_fequal,X6)),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex1__simps_I2_J)). 4.46/4.67 fof(fact_n__less__n__mult__m, axiom, ![X19, X17]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X19)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_n__less__n__mult__m)). 4.46/4.67 fof(fact_n__less__m__mult__n, axiom, ![X19, X17]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X17))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X17)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_n__less__m__mult__n)). 4.46/4.67 fof(fact_split__mod, axiom, ![X45, X14, X28]:(((X45=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>hBOOL(hAPP(X28,X14)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X45=>![X41, X98]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X45))=>(hBOOL(hAPP(X28,X98))<=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X41)),X98)=X14))))<=>hBOOL(hAPP(X28,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X14,X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__mod)). 4.46/4.67 fof(fact_trancl__into__rtrancl, axiom, ![X16, X37, X18, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),c_Transitive__Closure_Ortrancl(X4,X16)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),c_Transitive__Closure_Otrancl(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__into__rtrancl)). 4.46/4.67 fof(fact_zdiv__zminus2__eq__if, axiom, ![X12, X11]:(X11!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>((c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11)))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11)=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11))),c_Groups_Oone__class_Oone(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__zminus2__eq__if)). 4.46/4.67 fof(fact_vimage__subsetI, axiom, ![X2, X1, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4,X3,X27),X1)),X2))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_Set_Oimage(X4,X3,X27),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__subsetI)). 4.46/4.67 fof(fact_vimage__subsetD, axiom, ![X2, X1, X27, X4, X3]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),hAPP(c_Set_Oimage(X3,X4,X27),X2)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X3,X4,X27),X1)),X2)))<=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_Oimage(X3,X4,X27),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__subsetD)). 4.46/4.67 fof(fact_partition__set, axiom, ![X309, X310, X7, X28, X4]:(hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X310),X309)=c_List_Opartition(X4,X28,X7)=>hAPP(c_List_Oset(X4),X7)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X310)),hAPP(c_List_Oset(X4),X309))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition__set)). 4.46/4.67 fof(fact_Nat_Odiff__diff__eq, axiom, ![X17, X19, X15]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15),X19))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15),X17))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X15)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),X15))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat_Odiff__diff__eq)). 4.46/4.67 fof(fact_map__comp__Some__iff, axiom, ![X13, X45, X100, X99, X29, X4, X3]:(c_Map_Omap__comp(X3,X4,X29,X99,X100,X45)=hAPP(c_Option_Ooption_OSome(X4),X13)<=>?[X181]:(hAPP(X100,X45)=hAPP(c_Option_Ooption_OSome(X3),X181)&hAPP(X99,X181)=hAPP(c_Option_Ooption_OSome(X4),X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__comp__Some__iff)). 4.46/4.67 fof(fact_map__comp__def, axiom, ![X45, X50, X27, X29, X4, X3]:hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X4),X3,c_Option_Ooption_ONone(X4),X27),hAPP(X50,X45))=c_Map_Omap__comp(X3,X4,X29,X27,X50,X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__comp__def)). 4.46/4.67 fof(fact_foldl__foldr1, axiom, ![X7, X4]:(class_Groups_Omonoid__add(X4)=>hAPP(c_List_Ofoldl(X4,X4,c_Groups_Oplus__class_Oplus(X4),c_Groups_Ozero__class_Ozero(X4)),X7)=c_List_Ofoldr(X4,X4,c_Groups_Oplus__class_Oplus(X4),X7,c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__foldr1)). 4.46/4.67 fof(fact_inj__on__iff__surj, axiom, ![X92, X3, X4, X2]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>(?[X225]:X2=hAPP(c_Set_Oimage(X3,X4,X225),X92)<=>?[X40]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X3,X40),X2)),X92))&c_Fun_Oinj__on(X4,X3,X40,X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__iff__surj)). 4.46/4.67 fof(fact_finite__less__ub, axiom, ![X23, X27]:(![X199]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X199),hAPP(X27,X199)))=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X27)),X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__less__ub)). 4.46/4.67 fof(fact_finite__conv__nat__seg__image, axiom, ![X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))<=>?[X199, X40]:X2=hAPP(c_Set_Oimage(tc_Nat_Onat,X4,X40),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X199)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__conv__nat__seg__image)). 4.46/4.67 fof(fact_mod__nat__number__of, axiom, ![X71, X63]:((~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63))))=>((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X71)))=>c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63))&(~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X71))))=>hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X71)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71)))))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63)))=>c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__nat__number__of)). 4.46/4.67 fof(fact_Collect__conv__if, axiom, ![X4, X18, X28]:((hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X18))),X28))<=hBOOL(hAPP(X28,X18)))&(~(hBOOL(hAPP(X28,X18)))=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X18))),X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__conv__if)). 4.46/4.67 fof(fact_set__mp, axiom, ![X6, X1, X2, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hBOOL(hAPP(hAPP(c_member(X4),X6),X1)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__mp)). 4.46/4.67 fof(fact_snd__image__times, axiom, ![X1, X3, X4, X2]:((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>hAPP(c_Set_Oimage(tc_prod(X4,X3),X3,c_Product__Type_Osnd(X4,X3)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),X1)))=X1)&(hAPP(c_Set_Oimage(tc_prod(X4,X3),X3,c_Product__Type_Osnd(X4,X3)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),X1)))=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snd__image__times)). 4.46/4.67 fof(fact_fst__image__times, axiom, ![X2, X3, X4, X1]:((hAPP(c_Set_Oimage(tc_prod(X3,X4),X3,c_Product__Type_Ofst(X3,X4)),hAPP(hAPP(c_Product__Type_OSigma(X3,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X3),X1)))=X2<=X1!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&(hAPP(c_Set_Oimage(tc_prod(X3,X4),X3,c_Product__Type_Ofst(X3,X4)),hAPP(hAPP(c_Product__Type_OSigma(X3,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X3),X1)))=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fst__image__times)). 4.46/4.67 fof(fact_one__less__mult, axiom, ![X19, X17]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X17))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__less__mult)). 4.46/4.67 fof(fact_one__le__mult__iff, axiom, ![X14, X22]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X14))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X22)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__le__mult__iff)). 4.46/4.67 fof(fact_dom__map__of__zip, axiom, ![X32, X3, X7, X4]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32)=>(hBOOL(hAPP(c_List_Odistinct(X4),X7))=>c_Map_Odom(X4,X3,hAPP(c_Map_Omap__of(X4,X3),hAPP(hAPP(c_List_Ozip(X4,X3),X7),X32)))=hAPP(c_List_Oset(X4),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__map__of__zip)). 4.46/4.67 fof(fact_nat__mult__distrib__neg, axiom, ![X139, X49]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X49),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X49))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X139)))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X49),X139))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__distrib__neg)). 4.46/4.67 fof(fact_mult__0__right, axiom, ![X19]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__0__right)). 4.46/4.67 fof(fact_Nat_Oadd__0__right, axiom, ![X19]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X19, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat_Oadd__0__right)). 4.46/4.67 fof(fact_div__nat__number__of, axiom, ![X71, X63]:((~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63))))=>hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X71)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71))<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__nat__number__of)). 4.46/4.67 fof(fact_dropWhile__eq__Nil__conv, axiom, ![X7, X28, X4]:(c_List_Olist_ONil(X4)=c_List_OdropWhile(X4,X28,X7)<=>![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7)))=>hBOOL(hAPP(X28,X42)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__eq__Nil__conv)). 4.46/4.67 fof(fact_r__into__trancl_H, axiom, ![X16, X109, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X109),X16))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X109),c_Transitive__Closure_Otrancl(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_r__into__trancl_H)). 4.46/4.67 fof(fact_map__comp__None__iff, axiom, ![X45, X100, X99, X29, X4, X3]:(c_Option_Ooption_ONone(X4)=c_Map_Omap__comp(X3,X4,X29,X99,X100,X45)<=>(c_Option_Ooption_ONone(X3)=hAPP(X100,X45)|?[X181]:(hAPP(c_Option_Ooption_OSome(X3),X181)=hAPP(X100,X45)&c_Option_Ooption_ONone(X4)=hAPP(X99,X181)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__comp__None__iff)). 4.46/4.67 fof(fact_foldr__conv__foldl, axiom, ![X18, X7, X4]:(c_List_Ofoldr(X4,X4,c_Groups_Oplus__class_Oplus(X4),X7,X18)=hAPP(c_List_Ofoldl(X4,X4,c_Groups_Oplus__class_Oplus(X4),X18),X7)<=class_Groups_Oab__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldr__conv__foldl)). 4.46/4.67 fof(fact_upt__rec, axiom, ![X20, X21]:((c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X21,X20)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))=>c_List_Oupt(X21,X20)=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X21),c_List_Oupt(hAPP(c_Nat_OSuc,X21),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__rec)). 4.46/4.67 fof(fact_mod__pos__pos__1__number__of, axiom, ![X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30)))=>c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30))=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__pos__pos__1__number__of)). 4.46/4.67 fof(fact_setsum__shift__lb__Suc0__0__upt, axiom, ![X45, X27, X4]:((c_Groups_Ozero__class_Ozero(X4)=hAPP(X27,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X45))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X45)))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__shift__lb__Suc0__0__upt)). 4.46/4.67 fof(fact_div__pos__pos__1__number__of, axiom, ![X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30)))=>hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__pos__pos__1__number__of)). 4.46/4.67 fof(fact_acyclicP__converse, axiom, ![X16, X4]:(c_Wellfounded_Oacyclic(X4,hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),X16)))<=>c_Wellfounded_Oacyclic(X4,hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),c_Predicate_Oconversep(X4,X4,X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclicP__converse)). 4.46/4.67 fof(fact_Id__on__eqI, axiom, ![X2, X4, X37, X18]:((hBOOL(hAPP(hAPP(c_member(X4),X18),X2))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),c_Relation_OId__on(X4,X2))))<=X37=X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__on__eqI)). 4.46/4.67 fof(fact_setsum__shift__lb__Suc0__0, axiom, ![X45, X27]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(X27,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X27),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X45))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X27),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__shift__lb__Suc0__0)). 4.46/4.67 fof(fact_IdE, axiom, ![X109, X4]:(~(![X42]:hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X42)!=X109)<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X109),c_Relation_OId(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_IdE)). 4.46/4.67 fof(fact_add__nat__number__of, axiom, ![X71, X63]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X63),c_Int_OPls)))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),c_Int_OPls))=>hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71)))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X63),X71))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),c_Int_OPls))))))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X63),c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__nat__number__of)). 4.46/4.67 fof(fact_vimage__mono, axiom, ![X27, X3, X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X3,X4,X27),X2)),hAPP(c_Set_Ovimage(X3,X4,X27),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__mono)). 4.46/4.67 fof(fact_ivl__disj__un_I6_J, axiom, ![X23, X67, X4]:(class_Orderings_Olinorder(X4)=>(c_SetInterval_Oord__class_OatLeastAtMost(X4,X67,X23)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X67),X23)),hAPP(hAPP(c_Set_Oinsert(X4),X23),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X67),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I6_J)). 4.46/4.67 fof(fact_Un__insert__right, axiom, ![X1, X18, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),X1))=hAPP(hAPP(c_Set_Oinsert(X4),X18),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__insert__right)). 4.46/4.67 fof(fact_Un__empty__right, axiom, ![X2, X4]:X2=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__empty__right)). 4.46/4.67 fof(fact_eq__nat__number__of, axiom, ![X224, X13]:(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X224)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13)<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X224)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X13))))&(~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X13))))=>((~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X224))))=>X224=X13)&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X224)))=>hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X13)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__nat__number__of)). 4.46/4.67 fof(fact_zip__eq__conv, axiom, ![X88, X32, X3, X7, X4]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)=>((X32=hAPP(hAPP(c_List_Omap(tc_prod(X4,X3),X3),c_Product__Type_Osnd(X4,X3)),X88)&X7=hAPP(hAPP(c_List_Omap(tc_prod(X4,X3),X4),c_Product__Type_Ofst(X4,X3)),X88))<=>X88=hAPP(hAPP(c_List_Ozip(X4,X3),X7),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__eq__conv)). 4.46/4.67 fof(fact_ivl__disj__un_I3_J, axiom, ![X23, X67, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X67),X23))=>hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X67),X23)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X67),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X67,X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I3_J)). 4.46/4.67 fof(fact_Un__insert__left, axiom, ![X52, X1, X18, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X18),X1)),X52)=hAPP(hAPP(c_Set_Oinsert(X4),X18),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X1),X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__insert__left)). 4.46/4.67 fof(fact_Un__empty__left, axiom, ![X1, X4]:X1=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__empty__left)). 4.46/4.67 fof(fact_ivl__disj__un_I5_J, axiom, ![X23, X67, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X67),X23))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X67),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X67,X23))=c_SetInterval_Oord__class_OatLeastAtMost(X4,X67,X23))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I5_J)). 4.46/4.67 fof(fact_inj__on__mapI, axiom, ![X2, X27, X3, X4]:(c_Fun_Oinj__on(tc_List_Olist(X4),tc_List_Olist(X3),hAPP(c_List_Omap(X4,X3),X27),X2)<=c_Fun_Oinj__on(X4,X3,X27,c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool),c_List_Oset(X4)),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__mapI)). 4.46/4.67 fof(fact_Union__image__eq, axiom, ![X2, X1, X3, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)=c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(c_Set_Oimage(X3,tc_fun(X4,tc_HOL_Obool),X1),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__image__eq)). 4.46/4.67 fof(fact_ivl__disj__un_I4_J, axiom, ![X23, X67, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X67),X23))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X67,X23)),hAPP(hAPP(c_Set_Oinsert(X4),X23),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X67,X23))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I4_J)). 4.46/4.67 fof(fact_transfer__nat__int__set__return__embed, axiom, ![X2]:(X2=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2))<=c_Nat__Transfer_Onat__set(X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__return__embed)). 4.46/4.67 fof(fact_MGT__Body, axiom, ![X287, X82]:(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),X82),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),X287)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X287))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),X287))=>c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X82,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),X287)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_MGT__Body)). 4.46/4.67 fof(fact_sorted_Osimps, axiom, ![X18, X4]:(class_Orderings_Olinorder(X4)=>((?[X157, X42]:((c_List_Olinorder__class_Osorted(X4,X157)&![X66]:(hBOOL(hAPP(hAPP(c_member(X4),X66),hAPP(c_List_Oset(X4),X157)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X42),X66))))&hAPP(hAPP(c_List_Olist_OCons(X4),X42),X157)=X18)|X18=c_List_Olist_ONil(X4))<=>c_List_Olinorder__class_Osorted(X4,X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted_Osimps)). 4.46/4.67 fof(fact_nth__upt, axiom, ![X20, X15, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X15)),X20))=>hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X21,X20)),X15)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__upt)). 4.46/4.67 fof(fact_range__ex1__eq, axiom, ![X37, X27, X3, X4]:((hBOOL(hAPP(hAPP(c_member(X3),X37),hAPP(c_Set_Oimage(X4,X3,X27),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))<=>?[X42]:(![X44]:(X37=hAPP(X27,X44)=>X42=X44)&X37=hAPP(X27,X42)))<=c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_range__ex1__eq)). 4.46/4.67 fof(fact_rangeI, axiom, ![X3, X6, X27, X4]:hBOOL(hAPP(hAPP(c_member(X4),hAPP(X27,X6)),hAPP(c_Set_Oimage(X3,X4,X27),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rangeI)). 4.46/4.67 fof(fact_hd__dropWhile, axiom, ![X7, X28, X4]:(~(hBOOL(hAPP(X28,hAPP(c_List_Ohd(X4),c_List_OdropWhile(X4,X28,X7)))))<=c_List_Olist_ONil(X4)!=c_List_OdropWhile(X4,X28,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__dropWhile)). 4.46/4.67 fof(fact_total__on__diff__Id, axiom, ![X16, X2, X4]:(c_Relation_Ototal__on(X4,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),c_Relation_OId(X4)))<=>c_Relation_Ototal__on(X4,X2,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_total__on__diff__Id)). 4.46/4.67 fof(fact_setsum__set__upto__conv__listsum__int, axiom, ![X25, X24, X27, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X4),X27),c_List_Oupto(X24,X25)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X4),X27),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X24,X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__set__upto__conv__listsum__int)). 4.46/4.67 fof(fact_atLeastAtMost__upto, axiom, ![X25, X24]:hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X24,X25))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24,X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastAtMost__upto)). 4.46/4.67 fof(fact_nat__add__distrib, axiom, ![X139, X49]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X49))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X139))=>hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X49),X139))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X49)),hAPP(c_Int_Onat,X139)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__distrib)). 4.46/4.67 fof(fact_one__mod__nat__number__of, axiom, ![X71]:((c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71))=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X71))))&(c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71))=hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X71)))<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X71)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__mod__nat__number__of)). 4.46/4.67 fof(fact_sum__squares__eq__zero__iff, axiom, ![X5, X6, X4]:(((c_Groups_Ozero__class_Ozero(X4)=X5&X6=c_Groups_Ozero__class_Ozero(X4))<=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X5),X5)))<=class_Rings_Olinordered__ring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__squares__eq__zero__iff)). 4.46/4.67 fof(fact_add__nonneg__eq__0__iff, axiom, ![X5, X6, X4]:(class_Groups_Oordered__comm__monoid__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X6))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X5))=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X6),X5)=c_Groups_Ozero__class_Ozero(X4)<=>(c_Groups_Ozero__class_Ozero(X4)=X5&X6=c_Groups_Ozero__class_Ozero(X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__nonneg__eq__0__iff)). 4.46/4.67 fof(fact_code__numeral__decr, axiom, ![X15]:(hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X15=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X15)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X15)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral__decr)). 4.46/4.67 fof(fact_zero__code__numeral__def, axiom, hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__code__numeral__def)). 4.46/4.67 fof(fact_Code__Numeral_Oof__nat__code, axiom, c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral)=c_Code__Numeral_Oof__nat, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Code__Numeral_Oof__nat__code)). 4.46/4.67 fof(fact_nat__diff__distrib, axiom, ![X49, X139]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X139))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X139),X49))=>hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X49),X139))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X49)),hAPP(c_Int_Onat,X139)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__diff__distrib)). 4.46/4.67 fof(fact_sum__eq__0__conv, axiom, ![X136, X22]:((![X42]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X42<=hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X42),hAPP(c_List_Oset(tc_Nat_Onat),X136))))&c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X22)<=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X136)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__eq__0__conv)). 4.46/4.67 fof(fact_rev__eq__Cons__iff, axiom, ![X32, X5, X7, X4]:(hAPP(hAPP(c_List_Oappend(X4),hAPP(c_List_Orev(X4),X32)),hAPP(hAPP(c_List_Olist_OCons(X4),X5),c_List_Olist_ONil(X4)))=X7<=>hAPP(hAPP(c_List_Olist_OCons(X4),X5),X32)=hAPP(c_List_Orev(X4),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__eq__Cons__iff)). 4.46/4.67 fof(fact_rev_Osimps_I2_J, axiom, ![X57, X48, X4]:hAPP(c_List_Orev(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57))=hAPP(hAPP(c_List_Oappend(X4),hAPP(c_List_Orev(X4),X57)),hAPP(hAPP(c_List_Olist_OCons(X4),X48),c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev_Osimps_I2_J)). 4.46/4.67 fof(fact_mult__nat__number__of, axiom, ![X71, X63]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X63),c_Int_OPls)))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X63),X71))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X63),c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__nat__number__of)). 4.46/4.67 fof(fact_finite__fun__UNIVD1, axiom, ![X3, X4]:((hAPP(c_Finite__Set_Ocard(X3),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,X3)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X4,X3),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__fun__UNIVD1)). 4.46/4.67 fof(fact_listsp__conj__eq, axiom, ![X6, X1, X2, X4]:(hBOOL(hAPP(c_List_Olistsp(X4,hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),X2)),X1)),X6))<=>(hBOOL(hAPP(c_List_Olistsp(X4,X1),X6))&hBOOL(hAPP(c_List_Olistsp(X4,X2),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp__conj__eq)). 4.46/4.67 fof(fact_divide__eq__eq__number__of, axiom, ![X36, X39, X37, X4]:((class_Fields_Ofield__inverse__zero(X4)&class_Int_Onumber(X4))=>(((X39=c_Groups_Ozero__class_Ozero(X4)=>hAPP(c_Int_Onumber__class_Onumber__of(X4),X36)=c_Groups_Ozero__class_Ozero(X4))&(c_Groups_Ozero__class_Ozero(X4)!=X39=>X37=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X36)),X39)))<=>hAPP(c_Int_Onumber__class_Onumber__of(X4),X36)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X37),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__eq__eq__number__of)). 4.46/4.67 fof(fact_Divides_Otransfer__nat__int__functions_I2_J, axiom, ![X47, X48]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X48))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X47))=>c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X48),hAPP(c_Int_Onat,X47))=hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X48,X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Otransfer__nat__int__functions_I2_J)). 4.46/4.67 fof(fact_power__nat__number__of, axiom, ![X17, X63]:((hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63)),X17))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),X17)<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63)))))&(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),X17)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__nat__number__of)). 4.46/4.67 fof(fact_weak__Body, axiom, ![X80, X263, X28, X82, X4]:(c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X28),hAPP(c_Com_Ocom_OBODY,X263)),X80)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))<=c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X28),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X263))),X80)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_weak__Body)). 4.46/4.67 fof(fact_split__div__lemma, axiom, ![X22, X51, X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14))=>(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X22),X14)=X51<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X51)),X22))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),hAPP(c_Nat_OSuc,X51))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__div__lemma)). 4.46/4.67 fof(fact_div__mult__mult1__if, axiom, ![X11, X12, X10, X4]:(class_Divides_Osemiring__div(X4)=>((X10!=c_Groups_Ozero__class_Ozero(X4)=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X12),X11))&(hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11))=c_Groups_Ozero__class_Ozero(X4)<=X10=c_Groups_Ozero__class_Ozero(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__mult1__if)). 4.46/4.67 fof(fact_image__atLeastZeroLessThan__int, axiom, ![X23]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))=>hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,X23)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__atLeastZeroLessThan__int)). 4.46/4.67 fof(fact_finite__trancl, axiom, ![X16, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X4)),X16))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X4)),c_Transitive__Closure_Otrancl(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__trancl)). 4.46/4.67 fof(fact_le__diff__conv2, axiom, ![X24, X25, X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X25))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X45)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X45)),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__diff__conv2)). 4.46/4.67 fof(fact_add__leD2, axiom, ![X17, X15, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15),X17))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X15)),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__leD2)). 4.46/4.67 fof(fact_Int__Collect, axiom, ![X28, X2, X6, X4]:((hBOOL(hAPP(X28,X6))&hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))<=>hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_Set_OCollect(X4),X28))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Collect)). 4.46/4.67 fof(fact_finite__Collect__subsets, axiom, ![X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool))),X2))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Collect__subsets)). 4.46/4.67 fof(fact_Suc__eq__plus1__left, axiom, ![X17]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X17)=hAPP(c_Nat_OSuc,X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__eq__plus1__left)). 4.46/4.67 fof(fact_listsp__lists__eq, axiom, ![X6, X2, X4]:(hBOOL(hAPP(c_List_Olistsp(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2)),X6))<=>hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X6),c_List_Olists(X4,X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp__lists__eq)). 4.46/4.67 fof(fact_equal__fun__def, axiom, ![X50, X27, X4, X3]:((![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),c_Enum_Oenum__class_Oenum(X4))))=>hAPP(X27,X42)=hAPP(X50,X42))<=>hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X4,X3)),X27),X50)))<=(class_Enum_Oenum(X4)&class_HOL_Oequal(X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equal__fun__def)). 4.46/4.67 fof(fact_in__enum, axiom, ![X6, X4]:(class_Enum_Oenum(X4)=>hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),c_Enum_Oenum__class_Oenum(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__enum)). 4.46/4.67 fof(fact_min__max_OInf__fin__set__fold, axiom, ![X7, X6, X4]:(class_Orderings_Olinorder(X4)=>c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)))=hAPP(c_List_Ofoldl(X4,X4,c_Orderings_Oord__class_Omin(X4),X6),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin__set__fold)). 4.46/4.67 fof(fact_List_Oset_Osimps_I2_J, axiom, ![X7, X6, X4]:hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7))=hAPP(hAPP(c_Set_Oinsert(X4),X6),hAPP(c_List_Oset(X4),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Oset_Osimps_I2_J)). 4.46/4.67 fof(fact_min__max_OSup__fin__set__fold, axiom, ![X7, X6, X4]:(class_Orderings_Olinorder(X4)=>hAPP(c_List_Ofoldl(X4,X4,c_Orderings_Oord__class_Omax(X4),X6),X7)=c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin__set__fold)). 4.46/4.67 fof(fact_SetInterval_Otransfer__int__nat__set__functions, axiom, ![X14, X22]:((c_Nat__Transfer_Ois__nat(X14)=>hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,X22),hAPP(c_Int_Onat,X14)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X22,X14))<=c_Nat__Transfer_Ois__nat(X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SetInterval_Otransfer__int__nat__set__functions)). 4.46/4.67 fof(fact_of__int__of__nat, axiom, ![X15, X4]:(class_Rings_Oring__1(X4)=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onat,X15))=hAPP(c_Int_Oring__1__class_Oof__int(X4),X15))&(hAPP(c_Int_Oring__1__class_Oof__int(X4),X15)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X15))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__of__nat)). 4.46/4.67 fof(fact_eq__number__of__eq, axiom, ![X5, X6, X4]:(class_Int_Onumber__ring(X4)=>(c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X5))))<=>hAPP(c_Int_Onumber__class_Onumber__of(X4),X6)=hAPP(c_Int_Onumber__class_Onumber__of(X4),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__number__of__eq)). 4.46/4.67 fof(fact_distinct__rotate, axiom, ![X7, X14, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X7))<=>hBOOL(hAPP(c_List_Odistinct(X4),hAPP(c_List_Orotate(X4,X14),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__rotate)). 4.46/4.67 fof(fact_in__set__conv__nth, axiom, ![X7, X6, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))<=>?[X41]:(X6=hAPP(hAPP(c_List_Onth(X4),X7),X41)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__conv__nth)). 4.46/4.67 fof(fact_number__of__pred, axiom, ![X30, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))),hAPP(c_Int_Onumber__class_Onumber__of(X4),X30))=hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_Opred(X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__pred)). 4.46/4.67 fof(fact_rotate__length01, axiom, ![X17, X57, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=>hAPP(c_List_Orotate(X4,X17),X57)=X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__length01)). 4.46/4.67 fof(fact_map__comp__simps_I2_J, axiom, ![X99, X3, X29, X221, X4, X45, X100]:(hAPP(X99,X221)=c_Map_Omap__comp(X4,X29,X3,X99,X100,X45)<=hAPP(c_Option_Ooption_OSome(X4),X221)=hAPP(X100,X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__comp__simps_I2_J)). 4.46/4.67 fof(fact_wf__converse__trancl, axiom, ![X16, X4]:(c_Wellfounded_Owf(X4,hAPP(c_Relation_Oconverse(X4,X4),c_Transitive__Closure_Otrancl(X4,X16)))<=c_Wellfounded_Owf(X4,hAPP(c_Relation_Oconverse(X4,X4),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__converse__trancl)). 4.46/4.67 fof(fact_Powp__Pow__eq, axiom, ![X6, X2, X4]:(hBOOL(hAPP(c_Predicate_OPowp(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2)),X6))<=>hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X6),hAPP(c_Set_OPow(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Powp__Pow__eq)). 4.46/4.67 fof(fact_reflp__def, axiom, ![X16, X4]:(c_Predicate_Oreflp(X4,X16)<=>c_Relation_Orefl__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_reflp__def)). 4.46/4.67 fof(fact_nat__one__le__power, axiom, ![X17, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X17)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X21))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__one__le__power)). 4.46/4.67 fof(fact_transfer__int__nat__set__relations_I2_J, axiom, ![X2, X6]:(c_Nat__Transfer_Ois__nat(X6)=>(c_Nat__Transfer_Onat__set(X2)=>(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X6)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))<=>hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X6),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__set__relations_I2_J)). 4.46/4.67 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J, axiom, ![X6, X2]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X6),X2))=>c_Nat__Transfer_Ois__nat(X6))<=c_Nat__Transfer_Onat__set(X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J)). 4.46/4.67 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J, axiom, ![X47, X48]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X47))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X48)),hAPP(c_Int_Onat,X47))=hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X48,X47)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X48))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J)). 4.46/4.67 fof(fact_list__eq__iff__zip__eq, axiom, ![X4, X32, X7]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)&![X42]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X42),hAPP(c_List_Oset(tc_prod(X4,X4)),hAPP(hAPP(c_List_Ozip(X4,X4),X7),X32))))=>hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),c_fequal),X42))))<=>X7=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__eq__iff__zip__eq)). 4.46/4.67 fof(fact_card__Pow, axiom, ![X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(X4),X2))=hAPP(c_Finite__Set_Ocard(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_OPow(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Pow)). 4.46/4.67 fof(fact_ex__least__nat__less, axiom, ![X14, X28]:((hBOOL(hAPP(X28,X14))=>?[X266]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X266),X14))&![X41]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X41),X266))=>~(hBOOL(hAPP(X28,X41)))))&hBOOL(hAPP(X28,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X266),c_Groups_Oone__class_Oone(tc_Nat_Onat))))))<=~(hBOOL(hAPP(X28,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__least__nat__less)). 4.46/4.67 fof(fact_append__eq__conv__conj, axiom, ![X88, X32, X7, X4]:(hAPP(hAPP(c_List_Oappend(X4),X7),X32)=X88<=>(hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)),X88)=X7&X32=hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)),X88))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__eq__conv__conj)). 4.46/4.67 fof(fact_surj__image__vimage__eq, axiom, ![X2, X27, X4, X3]:(hAPP(c_Set_Oimage(X3,X4,X27),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=>hAPP(c_Set_Oimage(X3,X4,X27),hAPP(c_Set_Ovimage(X3,X4,X27),X2))=X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_surj__image__vimage__eq)). 4.46/4.67 fof(fact_inj__vimage__image__eq, axiom, ![X2, X27, X3, X4]:(hAPP(c_Set_Ovimage(X4,X3,X27),hAPP(c_Set_Oimage(X4,X3,X27),X2))=X2<=c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__vimage__image__eq)). 4.46/4.67 fof(fact_finite__vimageD, axiom, ![X62, X58, X3, X4]:((c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))=hAPP(c_Set_Oimage(X4,X3,X58),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X62)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Set_Ovimage(X4,X3,X58),X62)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__vimageD)). 4.46/4.67 fof(fact_finite__vimageI, axiom, ![X58, X3, X62, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X62))=>(c_Fun_Oinj__on(X3,X4,X58,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Ovimage(X3,X4,X58),X62))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__vimageI)). 4.46/4.67 fof(fact_vimageI2, axiom, ![X3, X2, X18, X27, X4]:(hBOOL(hAPP(hAPP(c_member(X4),hAPP(X27,X18)),X2))=>hBOOL(hAPP(hAPP(c_member(X3),X18),hAPP(c_Set_Ovimage(X3,X4,X27),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimageI2)). 4.46/4.67 fof(fact_vimageD, axiom, ![X2, X27, X3, X18, X4]:(hBOOL(hAPP(hAPP(c_member(X3),hAPP(X27,X18)),X2))<=hBOOL(hAPP(hAPP(c_member(X4),X18),hAPP(c_Set_Ovimage(X4,X3,X27),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimageD)). 4.46/4.67 fof(fact_last__upt, axiom, ![X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))=>c_List_Olast(tc_Nat_Onat,c_List_Oupt(X21,X20))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),c_Groups_Oone__class_Oone(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__upt)). 4.46/4.67 fof(fact_vimage__const, axiom, ![X3, X2, X39, X4]:((~(hBOOL(hAPP(hAPP(c_member(X4),X39),X2)))=>c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X3,X4,hAPP(c_COMBK(X4,X3),X39)),X2))&(hBOOL(hAPP(hAPP(c_member(X4),X39),X2))=>c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X3,X4,hAPP(c_COMBK(X4,X3),X39)),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__const)). 4.46/4.67 fof(fact_add__scale__eq__noteq, axiom, ![X133, X10, X11, X12, X111, X4]:((((X10!=X133&X11=X12)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X111),X10))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X111),X133)))<=c_Groups_Ozero__class_Ozero(X4)!=X111)<=class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__scale__eq__noteq)). 4.46/4.67 fof(fact_ivl__disj__un_I2_J, axiom, ![X23, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X23)),hAPP(hAPP(c_Set_Oinsert(X4),X23),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=hAPP(c_SetInterval_Oord__class_OatMost(X4),X23)<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I2_J)). 4.46/4.67 fof(fact_eq__special_I1_J, axiom, ![X5, X4]:(class_Int_Onumber__ring(X4)=>(c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X5))))<=>c_Groups_Ozero__class_Ozero(X4)=hAPP(c_Int_Onumber__class_Onumber__of(X4),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__special_I1_J)). 4.46/4.67 fof(fact_eq__special_I3_J, axiom, ![X6, X4]:(class_Int_Onumber__ring(X4)=>(hAPP(c_Int_Onumber__class_Onumber__of(X4),X6)=c_Groups_Ozero__class_Ozero(X4)<=>c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__special_I3_J)). 4.46/4.67 fof(fact_minus__Pls, axiom, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)=c_Int_OPls, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__Pls)). 4.46/4.67 fof(fact_rotate__id, axiom, ![X57, X4, X17]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57))=>X57=hAPP(c_List_Orotate(X4,X17),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__id)). 4.46/4.67 fof(fact_le__nat__number__of, axiom, ![X224, X13]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13),X224)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13),c_Int_OPls)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X224)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__nat__number__of)). 4.46/4.67 fof(fact_last__list__update, axiom, ![X48, X15, X4, X57]:(((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X15=>c_List_Olast(X4,X57)=c_List_Olast(X4,hAPP(hAPP(c_List_Olist__update(X4,X57),X15),X48)))&(X48=c_List_Olast(X4,hAPP(hAPP(c_List_Olist__update(X4,X57),X15),X48))<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X15))<=X57!=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__list__update)). 4.46/4.67 fof(fact_div__pos__neg__trivial, axiom, ![X11, X12]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12),X11)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__pos__neg__trivial)). 4.46/4.67 fof(fact_Sup__fin__set__fold, axiom, ![X7, X6, X4]:(c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)))=hAPP(c_List_Ofoldl(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4),X6),X7)<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin__set__fold)). 4.46/4.67 fof(fact_Min__fin__set__fold, axiom, ![X7, X6, X4]:(class_Orderings_Olinorder(X4)=>c_Big__Operators_Olinorder__class_OMin(X4,hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)))=hAPP(c_List_Ofoldl(X4,X4,c_Orderings_Oord__class_Omin(X4),X6),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__fin__set__fold)). 4.46/4.67 fof(fact_Max__fin__set__fold, axiom, ![X7, X6, X4]:(class_Orderings_Olinorder(X4)=>hAPP(c_List_Ofoldl(X4,X4,c_Orderings_Oord__class_Omax(X4),X6),X7)=c_Big__Operators_Olinorder__class_OMax(X4,hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__fin__set__fold)). 4.46/4.67 fof(fact_Inf__fin__set__fold, axiom, ![X7, X6, X4]:(hAPP(c_List_Ofoldl(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4),X6),X7)=c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin__set__fold)). 4.46/4.67 fof(fact_inj__on__map__eq__map, axiom, ![X32, X7, X27, X3, X4]:((hAPP(hAPP(c_List_Omap(X4,X3),X27),X32)=hAPP(hAPP(c_List_Omap(X4,X3),X27),X7)<=>X32=X7)<=c_Fun_Oinj__on(X4,X3,X27,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X7)),hAPP(c_List_Oset(X4),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__map__eq__map)). 4.46/4.67 fof(fact_card__Suc__eq, axiom, ![X45, X2, X4]:(?[X119, X120]:((((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X120<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X45)&hAPP(c_Finite__Set_Ocard(X4),X120)=X45)&~(hBOOL(hAPP(hAPP(c_member(X4),X119),X120))))&hAPP(hAPP(c_Set_Oinsert(X4),X119),X120)=X2)<=>hAPP(c_Nat_OSuc,X45)=hAPP(c_Finite__Set_Ocard(X4),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Suc__eq)). 4.46/4.67 fof(fact_less__special_I3_J, axiom, ![X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),c_Int_OPls))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X6)),c_Groups_Ozero__class_Ozero(X4))))<=(class_Rings_Olinordered__idom(X4)&class_Int_Onumber__ring(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__special_I3_J)). 4.46/4.67 fof(fact_le__special_I3_J, axiom, ![X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X6)),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6),c_Int_OPls)))<=(class_Int_Onumber__ring(X4)&class_Rings_Olinordered__idom(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__special_I3_J)). 4.46/4.67 fof(fact_less__special_I1_J, axiom, ![X5, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X5))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X5))))<=(class_Rings_Olinordered__idom(X4)&class_Int_Onumber__ring(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__special_I1_J)). 4.46/4.67 fof(fact_nat__div__distrib, axiom, ![X47, X48]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X48)),hAPP(c_Int_Onat,X47))=hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X48),X47))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X48))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__div__distrib)). 4.46/4.67 fof(fact_nat__mult__distrib, axiom, ![X139, X49]:(hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X49),X139))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X49)),hAPP(c_Int_Onat,X139))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X49))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__distrib)). 4.46/4.67 fof(fact_le__special_I1_J, axiom, ![X5, X4]:((class_Int_Onumber__ring(X4)&class_Rings_Olinordered__idom(X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X5))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__special_I1_J)). 4.46/4.67 fof(fact_zless__nat__conj, axiom, ![X35, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X36)),hAPP(c_Int_Onat,X35)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),X35))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__nat__conj)). 4.46/4.67 fof(fact_nat__less__eq__zless, axiom, ![X35, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X36)),hAPP(c_Int_Onat,X35)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__less__eq__zless)). 4.46/4.67 fof(fact_sorted__same, axiom, ![X7, X50, X4]:(class_Orderings_Olinorder(X4)=>c_List_Olinorder__class_Osorted(X4,hAPP(c_List_Ofilter(X4,hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),hAPP(X50,X7))),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__same)). 4.46/4.67 fof(fact_nat__less__iff, axiom, ![X22, X36]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X36)),X22))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__less__iff)). 4.46/4.67 fof(fact_in__set__replicate, axiom, ![X5, X14, X6, X4]:((X6=X5&X14!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=>hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),c_List_Oreplicate(X4,X14,X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__replicate)). 4.46/4.67 fof(fact_zmod__minus1, axiom, ![X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X11)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X11),c_Groups_Oone__class_Oone(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__minus1)). 4.46/4.67 fof(fact_of__nat__number__of__lemma, axiom, ![X63, X4]:(class_Int_Onumber__ring(X4)=>((hAPP(c_Int_Onumber__class_Onumber__of(X4),X63)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63))))&(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63))=c_Groups_Ozero__class_Ozero(X4)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__number__of__lemma)). 4.46/4.67 fof(fact_atLeastLessThanSuc, axiom, ![X14, X22]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14)))=>c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22),hAPP(c_Nat_OSuc,X14)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))=>hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X14),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22),X14))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22),hAPP(c_Nat_OSuc,X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThanSuc)). 4.46/4.67 fof(fact_sum__squares__gt__zero__iff, axiom, ![X5, X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X5),X5))))<=>(X5!=c_Groups_Ozero__class_Ozero(X4)|c_Groups_Ozero__class_Ozero(X4)!=X6))<=class_Rings_Olinordered__ring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__squares__gt__zero__iff)). 4.46/4.67 fof(fact_ivl__disj__un_I1_J, axiom, ![X67, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X67),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X67))=hAPP(c_SetInterval_Oord__class_OatLeast(X4),X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I1_J)). 4.46/4.67 fof(fact_snoc__eq__iff__butlast, axiom, ![X32, X6, X7, X4]:(((X32!=c_List_Olist_ONil(X4)&X7=c_List_Obutlast(X4,X32))&c_List_Olast(X4,X32)=X6)<=>hAPP(hAPP(c_List_Oappend(X4),X7),hAPP(hAPP(c_List_Olist_OCons(X4),X6),c_List_Olist_ONil(X4)))=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snoc__eq__iff__butlast)). 4.46/4.67 fof(fact_card_Oneutral, axiom, ![X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>((c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=?[X42]:hBOOL(hAPP(hAPP(c_member(X4),X42),X2)))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card_Oneutral)). 4.46/4.67 fof(fact_card__def, axiom, ![X2, X4]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X4),X2)<=~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))))&(hAPP(c_Finite__Set_Ocard(X4),X2)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X4),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__def)). 4.46/4.67 fof(fact_split__nat, axiom, ![X24, X28]:((![X199]:(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X199)=X24=>hBOOL(hAPP(X28,X199)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hBOOL(hAPP(X28,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))<=>hBOOL(hAPP(X28,hAPP(c_Int_Onat,X24)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__nat)). 4.46/4.67 fof(fact_zle__diff1__eq, axiom, ![X35, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X36),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X35),c_Groups_Oone__class_Oone(tc_Int_Oint))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__diff1__eq)). 4.46/4.67 fof(fact_wf, axiom, ![X4]:(class_Orderings_Owellorder(X4)=>c_Wellfounded_Owf(X4,hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf)). 4.46/4.67 fof(fact_transfer__nat__int__list__return__embed, axiom, ![X31]:(c_List_Onat__list(X31)=>X31=c_List_Oembed__list(c_List_Oreturn__list(X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__list__return__embed)). 4.46/4.67 fof(fact_norm__frac_Osimps, axiom, ![X18, X37]:((c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X37))=c_Nitpick_Onorm__frac(X18,X37)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&(((~((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X37|X18=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>c_Nitpick_Onorm__frac(X18,X37)=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X18),X37)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X18))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37))))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X37|X18=c_Groups_Ozero__class_Ozero(tc_Int_Oint))=>c_Nitpick_Onorm__frac(X18,X37)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_norm__frac_Osimps)). 4.46/4.67 fof(fact_Nats__number__of, axiom, ![X36, X4]:((hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X36)),c_Nat_Osemiring__1__class_ONats(X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X36)))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nats__number__of)). 4.46/4.67 fof(fact_nat__power__eq, axiom, ![X17, X49]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X49))=>hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X49)),X17)=hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X49),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__power__eq)). 4.46/4.67 fof(fact_of__nat__number__of__eq, axiom, ![X63, X4]:(((~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63))))=>hAPP(c_Int_Onumber__class_Onumber__of(X4),X63)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)))&(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63))=c_Groups_Ozero__class_Ozero(X4)<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63)))))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__number__of__eq)). 4.46/4.67 fof(fact_wfP__acyclicP, axiom, ![X16, X4]:(c_Wellfounded_Oacyclic(X4,hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),X16)))<=c_Wellfounded_OwfP(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__acyclicP)). 4.46/4.67 fof(fact_wfP__def, axiom, ![X16, X4]:(c_Wellfounded_OwfP(X4,X16)<=>c_Wellfounded_Owf(X4,hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__def)). 4.46/4.67 fof(fact_nat__le__eq__zle, axiom, ![X35, X36]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X36)),hAPP(c_Int_Onat,X35)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X36),X35)))<=(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X35))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__le__eq__zle)). 4.46/4.67 fof(fact_one__less__nat__eq, axiom, ![X35]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X35))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__less__nat__eq)). 4.46/4.67 fof(fact_Suc__nat__eq__nat__zadd1, axiom, ![X49]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X49))=>hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X49))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X49))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__nat__eq__nat__zadd1)). 4.46/4.67 fof(fact_hd__upt, axiom, ![X20, X21]:(hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X21,X20))=X21<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__upt)). 4.46/4.67 fof(fact_disjoint__iff__not__equal, axiom, ![X1, X2, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=>![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>![X66]:(X42!=X66<=hBOOL(hAPP(hAPP(c_member(X4),X66),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_disjoint__iff__not__equal)). 4.46/4.67 fof(fact_div__eq__minus1, axiom, ![X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__eq__minus1)). 4.46/4.67 fof(fact_abs__le__zero__iff, axiom, ![X18, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X18)),c_Groups_Ozero__class_Ozero(X4)))<=>c_Groups_Ozero__class_Ozero(X4)=X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__le__zero__iff)). 4.46/4.67 fof(fact_Ints__double__eq__0__iff, axiom, ![X18, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X18),c_Int_Oring__1__class_OInts(X4)))=>(X18=c_Groups_Ozero__class_Ozero(X4)<=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X18),X18)=c_Groups_Ozero__class_Ozero(X4)))<=class_Int_Oring__char__0(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__double__eq__0__iff)). 4.46/4.67 fof(fact_hoare__derivs_Oinsert, axiom, ![X202, X64, X82, X4]:(c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),X64),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))=>(c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),X64),X202))<=c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,X202))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hoare__derivs_Oinsert)). 4.46/4.67 fof(fact_eq__divide__eq, axiom, ![X39, X37, X18, X4]:((((X39=c_Groups_Ozero__class_Ozero(X4)=>X18=c_Groups_Ozero__class_Ozero(X4))&(X37=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)<=c_Groups_Ozero__class_Ozero(X4)!=X39))<=>X18=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X37),X39))<=class_Fields_Ofield__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__divide__eq)). 4.46/4.67 fof(fact_le__iff__pred__less, axiom, ![X67, X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X45),X67))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X45)),X67))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__iff__pred__less)). 4.46/4.67 fof(fact_divide__eq__eq, axiom, ![X18, X39, X37, X4]:((((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)=X37<=X39!=c_Groups_Ozero__class_Ozero(X4))&(c_Groups_Ozero__class_Ozero(X4)=X18<=X39=c_Groups_Ozero__class_Ozero(X4)))<=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X37),X39)=X18)<=class_Fields_Ofield__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__eq__eq)). 4.46/4.67 fof(fact_comp__equivI, axiom, ![X2, X16, X4]:((c_Equiv__Relations_Oequiv(X4,X2,X16)<=X2=hAPP(c_Relation_ODomain(X4,X4),X16))<=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(c_Relation_Oconverse(X4,X4),X16)),X16)=X16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comp__equivI)). 4.46/4.67 fof(fact_zero__less__zpower__abs__iff, axiom, ![X14, X6]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X6|X14=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X6)),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__zpower__abs__iff)). 4.46/4.67 fof(fact_remove1__filter__not, axiom, ![X7, X4, X6, X28]:(~(hBOOL(hAPP(X28,X6)))=>hAPP(c_List_Ofilter(X4,X28),X7)=c_List_Oremove1(X4,X6,hAPP(c_List_Ofilter(X4,X28),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1__filter__not)). 4.46/4.67 fof(fact_filter__remove1, axiom, ![X7, X6, X80, X4]:hAPP(c_List_Ofilter(X4,X80),c_List_Oremove1(X4,X6,X7))=c_List_Oremove1(X4,X6,hAPP(c_List_Ofilter(X4,X80),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__remove1)). 4.46/4.67 fof(fact_pair__in__Id__conv, axiom, ![X37, X18, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),c_Relation_OId(X4)))<=>X18=X37), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__in__Id__conv)). 4.46/4.67 fof(fact_Union__disjoint, axiom, ![X2, X52, X4]:(![X42]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X42),X52))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X42),X2)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X52)),X2)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__disjoint)). 4.46/4.67 fof(fact_nonzero__eq__divide__eq, axiom, ![X37, X18, X39, X4]:(((X37=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)<=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X37),X39)=X18)<=X39!=c_Groups_Ozero__class_Ozero(X4))<=class_Rings_Odivision__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonzero__eq__divide__eq)). 4.46/4.67 fof(fact_wf__trancl, axiom, ![X16, X4]:(c_Wellfounded_Owf(X4,X16)=>c_Wellfounded_Owf(X4,c_Transitive__Closure_Otrancl(X4,X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__trancl)). 4.46/4.67 fof(fact_finite__sorted__distinct__unique, axiom, ![X2, X4]:(class_Orderings_Olinorder(X4)=>(?[X42]:(((hAPP(c_List_Oset(X4),X42)=X2&![X44]:(X42=X44<=((hAPP(c_List_Oset(X4),X44)=X2&hBOOL(hAPP(c_List_Odistinct(X4),X44)))&c_List_Olinorder__class_Osorted(X4,X44))))&hBOOL(hAPP(c_List_Odistinct(X4),X42)))&c_List_Olinorder__class_Osorted(X4,X42))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__sorted__distinct__unique)). 4.46/4.67 fof(fact_finite__set, axiom, ![X7, X4]:hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_List_Oset(X4),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__set)). 4.46/4.67 fof(fact_zero__less__nat__eq, axiom, ![X35]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X35)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__nat__eq)). 4.46/4.67 fof(fact_MGF__complete, axiom, ![X80, X28, X39]:(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X39)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))=>(c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X28),X39),X80)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))=>c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X28),X39),X80)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_MGF__complete)). 4.46/4.67 fof(fact_upt__eq__Nil__conv, axiom, ![X25, X24]:(c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X24,X25)<=>(X25=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__eq__Nil__conv)). 4.46/4.67 fof(fact_less__eq__nat_Osimps_I2_J, axiom, ![X14, X22]:(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22)),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__nat_Osimps_I2_J)). 4.46/4.67 fof(fact_WT__bodies__def, axiom, (c_Com_OWT__bodies<=>![X42]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),X42),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))=>hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),X42)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WT__bodies__def)). 4.46/4.67 fof(fact_MGF__lemma1, axiom, ![X39, X82]:(((hBOOL(hAPP(c_Com_OWT,X39))=>c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X39)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))))<=![X42]:(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X42))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))<=hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X42),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))))<=c_Hoare__Mirabelle_Ostate__not__singleton), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_MGF__lemma1)). 4.46/4.67 fof(fact_square__eq__iff, axiom, ![X37, X18, X4]:(class_Rings_Oidom(X4)=>((X37=X18|hAPP(c_Groups_Ouminus__class_Ouminus(X4),X37)=X18)<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X18)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X37),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_square__eq__iff)). 4.46/4.67 fof(fact_zsgn__def, axiom, ![X21]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X21=>((hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Osgn__class_Osgn(tc_Int_Oint,X21)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21))))&(c_Groups_Oone__class_Oone(tc_Int_Oint)=c_Groups_Osgn__class_Osgn(tc_Int_Oint,X21)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21)))))&(c_Groups_Osgn__class_Osgn(tc_Int_Oint,X21)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zsgn__def)). 4.46/4.67 fof(fact_all__nat, axiom, ![X28]:(![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X42))=>hBOOL(hAPP(X28,hAPP(c_Int_Onat,X42))))<=>![X138]:hBOOL(hAPP(X28,X138))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__nat)). 4.46/4.67 fof(fact_not__less__eq__eq, axiom, ![X14, X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14)),X22))<=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__less__eq__eq)). 4.46/4.67 fof(fact_less__code__numeral__code, axiom, ![X22, X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X14)),hAPP(c_Code__Numeral_Oof__nat,X22)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X22))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__code__numeral__code)). 4.46/4.67 fof(fact_divmod__nat__eq, axiom, ![X97, X17, X19]:(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X19,X17),X97))=>X97=c_Divides_Odivmod__nat(X19,X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__eq)). 4.46/4.67 fof(fact_less__eq__code__numeral__code, axiom, ![X22, X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X14)),hAPP(c_Code__Numeral_Oof__nat,X22)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14),X22))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__code__numeral__code)). 4.46/4.67 fof(fact_add__is__1, axiom, ![X14, X22]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X14)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=>((hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X14&X22=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|(X14=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&X22=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__is__1)). 4.46/4.67 fof(fact_upt__conv__Nil, axiom, ![X21, X20]:(c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X21,X20)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20),X21))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__conv__Nil)). 4.46/4.67 fof(fact_of__nat__nat, axiom, ![X49, X4]:(class_Rings_Oring__1(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X49))=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onat,X49))=hAPP(c_Int_Oring__1__class_Oof__int(X4),X49))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__nat)). 4.46/4.67 fof(fact_derivs__insertD, axiom, ![X202, X64, X82, X4]:((c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),X64),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))))&c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,X202))<=c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),X64),X202))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_derivs__insertD)). 4.46/4.67 fof(fact_zless__nat__eq__int__zless, axiom, ![X35, X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22)),X35))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),hAPP(c_Int_Onat,X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__nat__eq__int__zless)). 4.46/4.67 fof(fact_code__numeral__not__eq__zero, axiom, ![X24]:(X24!=hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X24))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral__not__eq__zero)). 4.46/4.67 fof(fact_ex__nat, axiom, ![X28]:(?[X138]:hBOOL(hAPP(X28,X138))<=>?[X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X42))&hBOOL(hAPP(X28,hAPP(c_Int_Onat,X42))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__nat)). 4.46/4.67 fof(fact_square__eq__1__iff, axiom, ![X6, X4]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X6)=c_Groups_Oone__class_Oone(X4)<=>(hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))=X6|c_Groups_Oone__class_Oone(X4)=X6))<=class_Rings_Oring__1__no__zero__divisors(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_square__eq__1__iff)). 4.46/4.67 fof(fact_int__nat__eq, axiom, ![X49]:((hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X49))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X49))))&(X49=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X49))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X49)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__nat__eq)). 4.46/4.67 fof(fact_divide__Numeral0, axiom, ![X48, X4]:((class_Int_Onumber__ring(X4)&class_Fields_Ofield__inverse__zero(X4))=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__Numeral0)). 4.46/4.67 fof(fact_eq__nat__nat__iff, axiom, ![X121, X35]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X35))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))=>(X121=X35<=>hAPP(c_Int_Onat,X121)=hAPP(c_Int_Onat,X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__nat__nat__iff)). 4.46/4.67 fof(fact_divide__eq__eq__number__of1, axiom, ![X18, X36, X37, X4]:((class_Int_Onumber(X4)&class_Fields_Ofield__inverse__zero(X4))=>(((hAPP(c_Int_Onumber__class_Onumber__of(X4),X36)=c_Groups_Ozero__class_Ozero(X4)=>X18=c_Groups_Ozero__class_Ozero(X4))&(X37=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),hAPP(c_Int_Onumber__class_Onumber__of(X4),X36))<=c_Groups_Ozero__class_Ozero(X4)!=hAPP(c_Int_Onumber__class_Onumber__of(X4),X36)))<=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X37),hAPP(c_Int_Onumber__class_Onumber__of(X4),X36))=X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__eq__eq__number__of1)). 4.46/4.67 fof(fact_power__eq__0__iff, axiom, ![X14, X18, X4]:((((class_Rings_Ono__zero__divisors(X4)&class_Rings_Ozero__neq__one(X4))&class_Rings_Omult__zero(X4))&class_Power_Opower(X4))=>(c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X18),X14)<=>(c_Groups_Ozero__class_Ozero(X4)=X18&X14!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__eq__0__iff)). 4.46/4.67 fof(fact_nat__power__eq__Suc__0__iff, axiom, ![X22, X6]:(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X6),X22)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=>(X6=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__power__eq__Suc__0__iff)). 4.46/4.67 fof(fact_zmult__eq__1__iff, axiom, ![X14, X22]:(((X14=c_Groups_Oone__class_Oone(tc_Int_Oint)&c_Groups_Oone__class_Oone(tc_Int_Oint)=X22)|(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X22&X14=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)))<=>c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22),X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__eq__1__iff)). 4.46/4.67 fof(fact_split__zdiv, axiom, ![X45, X14, X28]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))=>![X41]:(?[X98]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))&X14=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X45),X41)),X98))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),X45)))=>hBOOL(hAPP(X28,X41))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>![X41]:(?[X98]:((X14=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X45),X41)),X98)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),X98)))=>hBOOL(hAPP(X28,X41)))))&(hBOOL(hAPP(X28,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=X45=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>hBOOL(hAPP(X28,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__zdiv)). 4.46/4.67 fof(fact_eq__neg__iff__add__eq__0, axiom, ![X37, X18, X4]:(class_Groups_Ogroup__add(X4)=>(X18=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X37)<=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X18),X37)=c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__neg__iff__add__eq__0)). 4.46/4.67 fof(fact_length__remdups__eq, axiom, ![X7, X4]:(c_List_Oremdups(X4,X7)=X7<=>hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Oremdups(X4,X7))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__remdups__eq)). 4.46/4.67 fof(fact_length__remdups__card__conv, axiom, ![X7, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Oremdups(X4,X7))=hAPP(c_Finite__Set_Ocard(X4),hAPP(c_List_Oset(X4),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__remdups__card__conv)). 4.46/4.67 fof(fact_add__numeral__0, axiom, ![X12, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OPls)),X12)=X12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__numeral__0)). 4.46/4.67 fof(fact_add__numeral__0__right, axiom, ![X12, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OPls))=X12<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__numeral__0__right)). 4.46/4.67 fof(fact_nat__eq__iff2, axiom, ![X36, X22]:(((hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22)=X36<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36)))=>X22=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<=>X22=hAPP(c_Int_Onat,X36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__eq__iff2)). 4.46/4.67 fof(fact_empty__Collect__eq, axiom, ![X28, X4]:(![X42]:~(hBOOL(hAPP(X28,X42)))<=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_OCollect(X4),X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__Collect__eq)). 4.46/4.67 fof(fact_Collect__empty__eq, axiom, ![X28, X4]:(![X42]:~(hBOOL(hAPP(X28,X42)))<=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_OCollect(X4),X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__empty__eq)). 4.46/4.67 fof(fact_diff__eq__diff__eq, axiom, ![X87, X39, X37, X18, X4]:(((X87=X39<=>X37=X18)<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X18),X37)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X39),X87))<=class_Groups_Oab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__eq__diff__eq)). 4.46/4.67 fof(fact_mult__eq__0__iff, axiom, ![X37, X18, X4]:(class_Rings_Oring__no__zero__divisors(X4)=>((X18=c_Groups_Ozero__class_Ozero(X4)|c_Groups_Ozero__class_Ozero(X4)=X37)<=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__eq__0__iff)). 4.46/4.67 fof(fact_int__nat__number__of, axiom, ![X63]:((hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63))))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63))<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X63)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__nat__number__of)). 4.46/4.67 fof(fact_MGT__BodyN, axiom, ![X82, X263]:(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X263))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))<=c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X263))),X82),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X263)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_MGT__BodyN)). 4.46/4.67 fof(conj_1, hypothesis, c_Com_OWT__bodies, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_1)). 4.46/4.67 fof(conj_0, hypothesis, c_Hoare__Mirabelle_Ostate__not__singleton, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_0)). 4.46/4.67 fof(fact_double__zero__sym, axiom, ![X18, X4]:(class_Groups_Olinordered__ab__group__add(X4)=>(c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X18),X18)<=>c_Groups_Ozero__class_Ozero(X4)=X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__zero__sym)). 4.46/4.67 fof(fact_order__le__less, axiom, ![X5, X6, X4]:(class_Orderings_Oorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X5))<=>(X5=X6|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__le__less)). 4.46/4.67 fof(fact_add__0__iff, axiom, ![X18, X37, X4]:((X18=c_Groups_Ozero__class_Ozero(X4)<=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X37),X18)=X37)<=class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__0__iff)). 4.46/4.67 fof(fact_eq__iff__diff__eq__0, axiom, ![X37, X18, X4]:(class_Groups_Oab__group__add(X4)=>(c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X18),X37)<=>X18=X37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__iff__diff__eq__0)). 4.46/4.67 fof(fact_equation__minus__iff, axiom, ![X37, X18, X4]:(class_Groups_Ogroup__add(X4)=>(hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)=X37<=>X18=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equation__minus__iff)). 4.46/4.67 fof(fact_not__neg__nat, axiom, ![X49]:(~(hBOOL(hAPP(c_Nat__Numeral_Oneg,X49)))=>X49=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X49))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__neg__nat)). 4.46/4.67 fof(fact_zero__less__abs__iff, axiom, ![X18, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Groups_Oabs__class_Oabs(X4),X18)))<=>c_Groups_Ozero__class_Ozero(X4)!=X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__abs__iff)). 4.46/4.67 fof(fact_less__Suc0, axiom, ![X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))<=>X14=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__Suc0)). 4.46/4.67 fof(fact_eq__0__number__of, axiom, ![X13]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__0__number__of)). 4.46/4.67 fof(fact_nat__0__iff, axiom, ![X24]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,X24)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__0__iff)). 4.46/4.67 fof(fact_neg__nat, axiom, ![X49]:(hBOOL(hAPP(c_Nat__Numeral_Oneg,X49))=>hAPP(c_Int_Onat,X49)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__nat)). 4.46/4.67 fof(fact_split__zmod, axiom, ![X45, X14, X28]:(hBOOL(hAPP(X28,c_Divides_Odiv__class_Omod(tc_Int_Oint,X14,X45)))<=>(((X45=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>hBOOL(hAPP(X28,X14)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>![X41, X98]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),X98))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X45),X41)),X98)=X14)=>hBOOL(hAPP(X28,X98)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))=>![X41, X98]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),X45))&hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X45),X41)),X98)=X14)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98)))=>hBOOL(hAPP(X28,X98)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__zmod)). 4.46/4.67 fof(fact_iszero__Numeral0, axiom, ![X4]:(class_Int_Onumber__ring(X4)=>c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_iszero__Numeral0)). 4.46/4.67 fof(fact_of__int__eq__0__iff, axiom, ![X35, X4]:(class_Int_Oring__char__0(X4)=>(X35=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<=>hAPP(c_Int_Oring__1__class_Oof__int(X4),X35)=c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__eq__0__iff)). 4.46/4.67 fof(fact_equal__neg__zero, axiom, ![X18, X4]:(class_Groups_Olinordered__ab__group__add(X4)=>(X18=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)<=>X18=c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equal__neg__zero)). 4.46/4.67 fof(fact_sgn__0__0, axiom, ![X18, X4]:(class_Rings_Olinordered__idom(X4)=>(X18=c_Groups_Ozero__class_Ozero(X4)<=>c_Groups_Osgn__class_Osgn(X4,X18)=c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__0__0)). 4.46/4.67 fof(fact_order__less__imp__not__eq, axiom, ![X47, X48, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),X47))=>X48!=X47)<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__less__imp__not__eq)). 4.46/4.67 fof(fact_linorder__neq__iff, axiom, ![X5, X6, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X5),X6))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),X5)))<=>X6!=X5)<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__neq__iff)). 4.46/4.67 fof(fact_WT__bodiesD, axiom, ![X11, X249]:((hBOOL(hAPP(c_Com_OWT,X11))<=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X11)=hAPP(c_Com_Obody,X249))<=c_Com_OWT__bodies), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WT__bodiesD)). 4.46/4.67 fof(fact_number__of__Pls, axiom, ![X4]:(class_Int_Onumber__ring(X4)=>hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OPls)=c_Groups_Ozero__class_Ozero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__Pls)). 4.46/4.67 fof(fact_Code__Numeral_Oof__nat__inject, axiom, ![X22, X14]:(X22=X14<=>hAPP(c_Code__Numeral_Oof__nat,X14)=hAPP(c_Code__Numeral_Oof__nat,X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Code__Numeral_Oof__nat__inject)). 4.46/4.67 fof(fact_max__ext_Osimps, axiom, ![X26, X135, X123, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X123),X135)),c_Wellfounded_Omax__ext(X4,X26)))<=>(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X135))&![X42]:(?[X66]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X66)),X26))&hBOOL(hAPP(hAPP(c_member(X4),X66),X135)))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X123))))&X135!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X123)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__ext_Osimps)). 4.46/4.67 fof(fact_conversep__noteq, axiom, ![X5, X6, X4]:(X5!=X6<=>hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4,X4,hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot)),c_fequal)),X6),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conversep__noteq)). 4.46/4.67 fof(fact_psubset__eq, axiom, ![X1, X2, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))&X2!=X1)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubset__eq)). 4.46/4.67 fof(fact_zless__le, axiom, ![X36, X35]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X35),X36))&X35!=X36)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X35),X36))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__le)). 4.46/4.67 fof(fact_max__extp_Oequations, axiom, ![X135, X123, X26, X4]:(c_Wellfounded_Omax__extp(X4,X26,X123,X135)<=>(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X135))&X135!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&![X42]:(?[X66]:(hBOOL(hAPP(hAPP(c_member(X4),X66),X135))&hBOOL(hAPP(hAPP(X26,X42),X66)))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X123))))&hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X123)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__extp_Oequations)). 4.46/4.67 fof(fact_eq__int__code_I5_J, axiom, ~(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I5_J)). 4.46/4.67 fof(fact_eq__int__code_I2_J, axiom, ~(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I2_J)). 4.46/4.67 fof(fact_rel__simps_I3_J, axiom, ~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I3_J)). 4.46/4.67 fof(fact_rel__simps_I20_J, axiom, ~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I20_J)). 4.46/4.67 fof(fact_mult, axiom, ![X13, X23, X5, X6]:hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X13))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X23)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23),X13)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult)). 4.46/4.67 fof(fact_dom__if, axiom, ![X50, X27, X28, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X3,X27)),hAPP(c_Set_OCollect(X4),X28))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X3,X50)),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),X28))))=c_Map_Odom(X4,X3,hAPP(hAPP(c_COMBS(X4,tc_Option_Ooption(X3),tc_Option_Ooption(X3)),hAPP(hAPP(c_COMBS(X4,tc_Option_Ooption(X3),tc_fun(tc_Option_Ooption(X3),tc_Option_Ooption(X3))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X3),tc_fun(tc_Option_Ooption(X3),tc_Option_Ooption(X3))),X4),c_If(tc_Option_Ooption(X3))),X28)),X27)),X50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__if)). 4.46/4.67 fof(fact_if__image__distrib, axiom, ![X46, X50, X27, X28, X4, X3]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X4,X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X46),hAPP(c_Set_OCollect(X3),X28)))),hAPP(c_Set_Oimage(X3,X4,X50),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X46),hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),X28)))))=hAPP(c_Set_Oimage(X3,X4,hAPP(hAPP(c_COMBS(X3,X4,X4),hAPP(hAPP(c_COMBS(X3,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X3),c_If(X4)),X28)),X27)),X50)),X46), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_if__image__distrib)). 4.46/4.67 fof(fact_arith__series__nat, axiom, ![X14, X87, X18]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X87))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X87))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_arith__series__nat)). 4.46/4.67 fof(fact_map__pair__surj__on, axiom, ![X267, X1, X50, X29, X59, X92, X2, X27, X4, X3]:((hAPP(c_Set_Oimage(X59,X29,X50),X1)=X267=>hAPP(hAPP(c_Product__Type_OSigma(X4,X29),X92),hAPP(c_COMBK(tc_fun(X29,tc_HOL_Obool),X4),X267))=hAPP(c_Set_Oimage(tc_prod(X3,X59),tc_prod(X4,X29),c_Product__Type_Omap__pair(X3,X4,X59,X29,X27,X50)),hAPP(hAPP(c_Product__Type_OSigma(X3,X59),X2),hAPP(c_COMBK(tc_fun(X59,tc_HOL_Obool),X3),X1))))<=X92=hAPP(c_Set_Oimage(X3,X4,X27),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair__surj__on)). 4.46/4.67 fof(fact_dropWhile__map, axiom, ![X7, X27, X3, X28, X4]:hAPP(hAPP(c_List_Omap(X3,X4),X27),c_List_OdropWhile(X3,hAPP(c_Fun_Ocomp(X4,tc_HOL_Obool,X3,X28),X27),X7))=c_List_OdropWhile(X4,X28,hAPP(hAPP(c_List_Omap(X3,X4),X27),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__map)). 4.46/4.67 fof(fact_length__sublist, axiom, ![X73, X7, X4]:hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X73))))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Osublist(X4,X7,X73)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__sublist)). 4.46/4.67 fof(fact_foldr__map, axiom, ![X18, X7, X27, X29, X50, X4, X3]:c_List_Ofoldr(X29,X4,hAPP(c_Fun_Ocomp(X3,tc_fun(X4,X4),X29,X50),X27),X7,X18)=c_List_Ofoldr(X3,X4,X50,hAPP(hAPP(c_List_Omap(X29,X3),X27),X7),X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldr__map)). 4.46/4.67 fof(fact_Image__singleton, axiom, ![X18, X16, X4, X3]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X3,X4),tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X3,X4))),hAPP(c_Product__Type_OPair(X3,X4),X18))),X16))=hAPP(c_Relation_OImage(X3,X4,X16),hAPP(hAPP(c_Set_Oinsert(X3),X18),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__singleton)). 4.46/4.67 fof(fact_UN__le__add__shift, axiom, ![X45, X153, X14, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X45,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X45))),X153)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X14)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool),tc_Nat_Onat),X153),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__le__add__shift)). 4.46/4.67 fof(fact_apsnd__apfst__commute, axiom, ![X109, X50, X59, X27, X4, X3, X29]:hAPP(c_Product__Type_Oapfst(X59,X4,X3,X50),hAPP(c_Product__Type_Oapsnd(X29,X3,X59,X27),X109))=hAPP(c_Product__Type_Oapsnd(X29,X3,X4,X27),hAPP(c_Product__Type_Oapfst(X59,X4,X29,X50),X109)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apsnd__apfst__commute)). 4.46/4.67 fof(fact_zadd__zmult__distrib2, axiom, ![X74, X75, X30]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X75)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X74))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X75),X74)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__zmult__distrib2)). 4.46/4.67 fof(fact_apsnd__apfst, axiom, ![X6, X50, X59, X27, X4, X3, X29]:hAPP(c_Product__Type_Oapsnd(X29,X3,X4,X27),hAPP(c_Product__Type_Oapfst(X59,X4,X29,X50),X6))=hAPP(hAPP(c_Product__Type_OPair(X4,X3),hAPP(X50,hAPP(c_Product__Type_Ofst(X59,X29),X6))),hAPP(X27,hAPP(c_Product__Type_Osnd(X59,X29),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apsnd__apfst)). 4.46/4.67 fof(fact_apfst__apsnd, axiom, ![X6, X50, X59, X27, X3, X4, X29]:hAPP(c_Product__Type_Oapfst(X29,X4,X3,X27),hAPP(c_Product__Type_Oapsnd(X59,X3,X29,X50),X6))=hAPP(hAPP(c_Product__Type_OPair(X4,X3),hAPP(X27,hAPP(c_Product__Type_Ofst(X29,X59),X6))),hAPP(X50,hAPP(c_Product__Type_Osnd(X29,X59),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apfst__apsnd)). 4.46/4.67 fof(fact_foldr_Osimps_I2_J, axiom, ![X18, X7, X6, X27, X4, X3]:hAPP(hAPP(X27,X6),c_List_Ofoldr(X3,X4,X27,X7,X18))=c_List_Ofoldr(X3,X4,X27,hAPP(hAPP(c_List_Olist_OCons(X3),X6),X7),X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldr_Osimps_I2_J)). 4.46/4.67 fof(fact_apsnd__compose, axiom, ![X6, X50, X59, X27, X4, X3, X29]:hAPP(c_Product__Type_Oapsnd(X29,X3,X4,X27),hAPP(c_Product__Type_Oapsnd(X59,X29,X4,X50),X6))=hAPP(c_Product__Type_Oapsnd(X59,X3,X4,hAPP(c_Fun_Ocomp(X29,X3,X59,X27),X50)),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apsnd__compose)). 4.46/4.67 fof(fact_apfst__compose, axiom, ![X6, X50, X59, X27, X3, X4, X29]:hAPP(c_Product__Type_Oapfst(X59,X4,X3,hAPP(c_Fun_Ocomp(X29,X4,X59,X27),X50)),X6)=hAPP(c_Product__Type_Oapfst(X29,X4,X3,X27),hAPP(c_Product__Type_Oapfst(X59,X29,X3,X50),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apfst__compose)). 4.46/4.67 fof(fact_rotate__map, axiom, ![X7, X27, X3, X14, X4]:hAPP(c_List_Orotate(X4,X14),hAPP(hAPP(c_List_Omap(X3,X4),X27),X7))=hAPP(hAPP(c_List_Omap(X3,X4),X27),hAPP(c_List_Orotate(X3,X14),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__map)). 4.46/4.67 fof(fact_set__Cons__sing__Nil, axiom, ![X2, X4]:hAPP(c_Set_Oimage(X4,tc_List_Olist(X4),hAPP(hAPP(c_COMBC(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_OCons(X4)),c_List_Olist_ONil(X4))),X2)=c_List_Oset__Cons(X4,X2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__Cons__sing__Nil)). 4.46/4.67 fof(fact_length__concat, axiom, ![X113, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Oconcat(X4,X113))=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X4))),X113)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__concat)). 4.46/4.67 fof(fact_dom__fun__upd, axiom, ![X6, X27, X3, X4, X5]:((c_Option_Ooption_ONone(X4)!=X5=>hAPP(hAPP(c_Set_Oinsert(X3),X6),c_Map_Odom(X3,X4,X27))=c_Map_Odom(X3,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X4)),X27),X6),X5)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),c_Map_Odom(X3,X4,X27)),hAPP(hAPP(c_Set_Oinsert(X3),X6),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))=c_Map_Odom(X3,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X4)),X27),X6),X5))<=c_Option_Ooption_ONone(X4)=X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__fun__upd)). 4.46/4.67 fof(fact_list_Osize_I2_J, axiom, ![X85, X18, X86, X4]:c_List_Olist_Olist__size(X4,X86,hAPP(hAPP(c_List_Olist_OCons(X4),X18),X85))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X86,X18)),c_List_Olist_Olist__size(X4,X86,X85))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osize_I2_J)). 4.46/4.67 fof(fact_lazy__sequence_Osize_I2_J, axiom, ![X242, X18, X86, X4]:hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X4,X86),c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X18,X242))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X86,X18)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X4,X86),X242))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Osize_I2_J)). 4.46/4.67 fof(fact_Range__Collect__split, axiom, ![X28, X4, X3]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X3)),hAPP(c_COMBC(X3,X4,tc_HOL_Obool),X28)))=hAPP(c_Relation_ORange(X3,X4),hAPP(c_Set_OCollect(tc_prod(X3,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X4,tc_HOL_Obool),X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__Collect__split)). 4.46/4.67 fof(fact_com_Osize_I13_J, axiom, ![X77, X78, X34]:hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X34,X78,X77))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X78)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X77))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I13_J)). 4.46/4.67 fof(fact_vimage__compose, axiom, ![X6, X27, X50, X29, X3, X4]:hAPP(c_Set_Ovimage(X4,X3,hAPP(c_Fun_Ocomp(X29,X3,X4,X50),X27)),X6)=hAPP(c_Set_Ovimage(X4,X29,X27),hAPP(c_Set_Ovimage(X29,X3,X50),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__compose)). 4.46/4.67 fof(fact_divmod__nat__div__mod, axiom, ![X17, X19]:c_Divides_Odivmod__nat(X19,X17)=hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19),X17)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__div__mod)). 4.46/4.67 fof(fact_com_Osize_I5_J, axiom, ![X77, X78, X34]:c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X34,X78,X77))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X78)),c_Com_Ocom_Ocom__size(X77))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I5_J)). 4.46/4.67 fof(fact_Field__Union, axiom, ![X26, X4]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),c_Relation_OField(X4)),X26))=hAPP(c_Relation_OField(X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Field__Union)). 4.46/4.67 fof(fact_vimage__Compl, axiom, ![X2, X27, X3, X4]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4,X3,X27),X2))=hAPP(c_Set_Ovimage(X4,X3,X27),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Compl)). 4.46/4.67 fof(fact_image__vimage__eq, axiom, ![X2, X27, X4, X3]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X3,X4,X27),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))=hAPP(c_Set_Oimage(X3,X4,X27),hAPP(c_Set_Ovimage(X3,X4,X27),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__vimage__eq)). 4.46/4.67 fof(fact_anamorph_Osimps, axiom, ![X6, X27, X4, X3, X45]:((hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),X3),c_List_Olist_ONil(X4)),X6)=hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X3,X4,X27),X45),X6)<=X45=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))&(hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X4),X3),tc_prod(X4,X3),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),X3),c_List_Olist_ONil(X4)),X6),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_prod(tc_List_Olist(X4),X3)),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,tc_prod(tc_List_Olist(X4),X3)),tc_fun(X3,tc_prod(tc_List_Olist(X4),X3))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X4),X3),tc_prod(tc_List_Olist(X4),X3)),tc_fun(tc_fun(X3,tc_prod(tc_List_Olist(X4),X3)),tc_fun(X3,tc_prod(tc_List_Olist(X4),X3))),X4),c_COMBB(tc_prod(tc_List_Olist(X4),X3),tc_prod(tc_List_Olist(X4),X3),X3)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_fun(X3,tc_prod(tc_List_Olist(X4),X3))),tc_fun(tc_prod(tc_List_Olist(X4),X3),tc_prod(tc_List_Olist(X4),X3)),X4),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X4),X3,tc_prod(tc_List_Olist(X4),X3))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),tc_fun(tc_List_Olist(X4),tc_fun(X3,tc_prod(tc_List_Olist(X4),X3))),X4),hAPP(c_COMBB(tc_List_Olist(X4),tc_fun(X3,tc_prod(tc_List_Olist(X4),X3)),tc_List_Olist(X4)),c_Product__Type_OPair(tc_List_Olist(X4),X3))),c_List_Olist_OCons(X4))))),hAPP(c_Lazy__Sequence_Oanamorph(X3,X4,X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X45),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(X27,X6))=hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X3,X4,X27),X45),X6)<=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_anamorph_Osimps)). 4.46/4.67 fof(fact_relpow_Osimps_I1_J, axiom, ![X26, X4]:c_Relation_OId(X4)=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_relpow_Osimps_I1_J)). 4.46/4.67 fof(fact_Pow__def, axiom, ![X2, X4]:hAPP(c_Set_OCollect(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool))),X2))=hAPP(c_Set_OPow(X4),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__def)). 4.46/4.67 fof(fact_lenlex__conv, axiom, ![X16, X4]:hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X4),tc_List_Olist(X4),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_List_Olist(X4)),c_COMBS(tc_List_Olist(X4),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X4)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_Nat_Onat),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X4),tc_Nat_Onat),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_List_Olist(X4)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X4)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X4))))),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_List_Olist(X4)),c_COMBS(tc_List_Olist(X4),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X4)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_Nat_Onat),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X4),tc_Nat_Onat),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_List_Olist(X4)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X4))))),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_fun(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_List_Olist(X4)),c_COMBC(tc_List_Olist(X4),tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),tc_fun(tc_List_Olist(X4),tc_fun(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X4)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X4)),c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))))),c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4))))),c_List_Olex(X4,X16))))))=c_List_Olenlex(X4,X16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lenlex__conv)). 4.46/4.67 fof(fact_set__Cons__def, axiom, ![X229, X2, X4]:hAPP(c_Set_OCollect(tc_List_Olist(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X4)),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool),tc_List_Olist(X4)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(tc_List_Olist(X4)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool))),tc_fun(tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool))),tc_List_Olist(X4)),c_COMBS(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X4,tc_fun(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool))),tc_List_Olist(X4)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),X4),c_COMBS(tc_List_Olist(X4),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X4)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_List_Olist(X4))),tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_List_Olist(X4))),tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool))),tc_List_Olist(X4)),c_COMBB(tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),tc_fun(tc_List_Olist(X4),tc_HOL_Obool),X4)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_List_Olist(X4)),c_COMBB(tc_List_Olist(X4),tc_HOL_Obool,tc_List_Olist(X4))),c_fequal))),c_List_Olist_OCons(X4)))))),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X4))),X229))))))=c_List_Oset__Cons(X4,X2,X229), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__Cons__def)). 4.46/4.67 fof(fact_rel__comp__def, axiom, ![X68, X16, X3, X29, X4]:hAPP(c_Set_OCollect(tc_prod(X4,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(X29,tc_HOL_Obool)),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_COMBB(tc_fun(X29,tc_HOL_Obool),tc_HOL_Obool,X3),c_HOL_OEx(X29))),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,tc_fun(X29,tc_HOL_Obool)),tc_fun(X3,tc_fun(X29,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29,tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),tc_fun(tc_fun(X3,tc_fun(X29,tc_HOL_Obool)),tc_fun(X3,tc_fun(X29,tc_HOL_Obool))),X4),c_COMBB(tc_fun(X29,tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool),X3)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X29,tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),X4),c_COMBS(X29,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_HOL_Obool),tc_fun(X29,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29),c_fconj)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_fun(tc_fun(tc_prod(X4,X29),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),X4),c_COMBC(X29,tc_fun(tc_prod(X4,X29),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_prod(X4,X29)),tc_fun(X29,tc_fun(tc_fun(tc_prod(X4,X29),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X29),tc_fun(tc_fun(tc_prod(X4,X29),tc_HOL_Obool),tc_HOL_Obool),X29),c_member(tc_prod(X4,X29)))),c_Product__Type_OPair(X4,X29)))),X16))))),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X29,X3),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_fun(tc_fun(tc_prod(X29,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29,X3),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),X3),c_COMBC(X29,tc_fun(tc_prod(X29,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_prod(X29,X3)),tc_fun(X29,tc_fun(tc_fun(tc_prod(X29,X3),tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_prod(X29,X3),tc_fun(tc_fun(tc_prod(X29,X3),tc_HOL_Obool),tc_HOL_Obool),X29),c_member(tc_prod(X29,X3)))),hAPP(c_COMBC(X29,X3,tc_prod(X29,X3)),c_Product__Type_OPair(X29,X3))))),X68)))))=hAPP(hAPP(c_Relation_Orel__comp(X4,X29,X3),X16),X68), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__def)). 4.46/4.67 fof(fact_lexn_Osimps_I2_J, axiom, ![X14, X16, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X4,tc_List_Olist(X4)),tc_prod(X4,tc_List_Olist(X4))),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),c_Product__Type_Omap__pair(tc_prod(X4,tc_List_Olist(X4)),tc_List_Olist(X4),tc_prod(X4,tc_List_Olist(X4)),tc_List_Olist(X4),hAPP(c_Product__Type_Oprod_Oprod__case(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_OCons(X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_OCons(X4)))),c_Wellfounded_Olex__prod(X4,tc_List_Olist(X4),X16,hAPP(c_List_Olexn(X4,X16),X14)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X4),tc_List_Olist(X4),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_List_Olist(X4)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),hAPP(c_Nat_OSuc,X14))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),hAPP(c_Nat_OSuc,X14))))))=hAPP(c_List_Olexn(X4,X16),hAPP(c_Nat_OSuc,X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexn_Osimps_I2_J)). 4.46/4.67 fof(fact_set__zip, axiom, ![X32, X7, X3, X4]:hAPP(c_List_Oset(tc_prod(X4,X3)),hAPP(hAPP(c_List_Ozip(X4,X3),X7),X32))=hAPP(c_Set_OCollect(tc_prod(X4,X3)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X4,X3)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X4,X3),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X4,X3)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(X4,X3)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(X4,X3),tc_fun(tc_Nat_Onat,tc_prod(X4,X3)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X4,X3)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X4,X3)),c_COMBB(tc_prod(X4,X3),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X3,tc_prod(X4,X3)),hAPP(hAPP(c_COMBB(X4,tc_fun(X3,tc_prod(X4,X3)),tc_Nat_Onat),c_Product__Type_OPair(X4,X3)),hAPP(c_List_Onth(X4),X7))),hAPP(c_List_Onth(X3),X32)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__zip)). 4.46/4.67 fof(fact_map__add__map__of__foldr, axiom, ![X108, X22, X3, X4]:c_Map_Omap__add(X4,X3,X22,hAPP(c_Map_Omap__of(X4,X3),X108))=c_List_Ofoldr(tc_prod(X4,X3),tc_fun(X4,tc_Option_Ooption(X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_fun(tc_fun(X4,tc_Option_Ooption(X3)),tc_fun(X4,tc_Option_Ooption(X3)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,tc_Option_Ooption(X3)),tc_fun(X3,tc_fun(tc_fun(X4,tc_Option_Ooption(X3)),tc_fun(X4,tc_Option_Ooption(X3))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X3),tc_fun(tc_fun(X4,tc_Option_Ooption(X3)),tc_fun(X4,tc_Option_Ooption(X3)))),tc_fun(tc_fun(X3,tc_Option_Ooption(X3)),tc_fun(X3,tc_fun(tc_fun(X4,tc_Option_Ooption(X3)),tc_fun(X4,tc_Option_Ooption(X3))))),X4),c_COMBB(tc_Option_Ooption(X3),tc_fun(tc_fun(X4,tc_Option_Ooption(X3)),tc_fun(X4,tc_Option_Ooption(X3))),X3)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_Option_Ooption(X3)),tc_fun(tc_Option_Ooption(X3),tc_fun(X4,tc_Option_Ooption(X3)))),tc_fun(tc_Option_Ooption(X3),tc_fun(tc_fun(X4,tc_Option_Ooption(X3)),tc_fun(X4,tc_Option_Ooption(X3)))),X4),c_COMBC(tc_fun(X4,tc_Option_Ooption(X3)),tc_Option_Ooption(X3),tc_fun(X4,tc_Option_Ooption(X3)))),hAPP(c_COMBC(tc_fun(X4,tc_Option_Ooption(X3)),X4,tc_fun(tc_Option_Ooption(X3),tc_fun(X4,tc_Option_Ooption(X3)))),c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)))))),c_Option_Ooption_OSome(X3))),X108,X22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__map__of__foldr)). 4.46/4.67 fof(fact_divmod__int__rel__def, axiom, ![X37, X18]:hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,X18))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X37)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),X37))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))))=c_Divides_Odivmod__int__rel(X18,X37), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__def)). 4.46/4.67 fof(fact_inv__image__def, axiom, ![X27, X16, X4, X3]:hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBC(X4,tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X3,X3)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X3,X3),tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X3,X3)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,X3),tc_fun(X4,tc_prod(X3,X3))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X3,X3)),tc_fun(tc_fun(X4,X3),tc_fun(X4,tc_prod(X3,X3))),X4),c_COMBB(X3,tc_prod(X3,X3),X4)),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,tc_prod(X3,X3)),X4),c_Product__Type_OPair(X3,X3)),X27))),X27)))),X16)))=hAPP(hAPP(c_Relation_Oinv__image(X3,X4),X16),X27), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inv__image__def)). 4.46/4.67 fof(fact_lazy__sequence__size__code, axiom, ![X107, X68, X4]:hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X4,tc_Lazy__Sequence_Olazy__sequence(X4)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X4,tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat),hAPP(hAPP(c_COMBC(X4,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat)),X4),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X4),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X4)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat)),X4),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X4))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X68))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X4,X68))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(X4),X107))=hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X4,X68),X107), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence__size__code)). 4.46/4.67 fof(fact_seq__case, axiom, ![X107, X50, X27, X3, X4]:c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X4,X3,X27,X50,X107)=hAPP(c_Option_Ooption_Ooption__case(X4,tc_prod(X3,tc_Lazy__Sequence_Olazy__sequence(X3)),X27,hAPP(c_Product__Type_Oprod_Oprod__case(X3,tc_Lazy__Sequence_Olazy__sequence(X3),X4),X50)),hAPP(c_Lazy__Sequence_Oyield(X3),X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_seq__case)). 4.46/4.67 fof(fact_set__sublist, axiom, ![X73, X7, X4]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X4),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_Nat_Onat,X4),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X4),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X4),X7))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X73)))))=hAPP(c_List_Oset(X4),c_List_Osublist(X4,X7,X73)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__sublist)). 4.46/4.67 fof(fact_converse__def, axiom, ![X16, X4, X3]:hAPP(c_Set_OCollect(tc_prod(X4,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBC(X3,tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X3,X4)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X3,X4),tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X3,X4)))),hAPP(c_COMBC(X3,X4,tc_prod(X3,X4)),c_Product__Type_OPair(X3,X4))))),X16)))=hAPP(c_Relation_Oconverse(X3,X4),X16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__def)). 4.46/4.67 fof(fact_Pow__Compl, axiom, ![X2, X4]:hAPP(c_Set_OCollect(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X4,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),c_COMBS(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X4,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X4,tc_HOL_Obool)),hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X2)),c_Set_OPow(X4)))))=hAPP(c_Set_OPow(X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__Compl)). 4.46/4.67 fof(fact_set__conv__nth, axiom, ![X7, X4]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X4),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_Nat_Onat,X4),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X4),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X4),X7))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))))=hAPP(c_List_Oset(X4),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__conv__nth)). 4.46/4.67 fof(fact_zip__map__map, axiom, ![X32, X50, X59, X7, X27, X29, X3, X4]:hAPP(hAPP(c_List_Ozip(X4,X3),hAPP(hAPP(c_List_Omap(X29,X4),X27),X7)),hAPP(hAPP(c_List_Omap(X59,X3),X50),X32))=hAPP(hAPP(c_List_Omap(tc_prod(X29,X59),tc_prod(X4,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X29,X59,tc_prod(X4,X3)),hAPP(hAPP(c_COMBC(X29,tc_fun(X59,X3),tc_fun(X59,tc_prod(X4,X3))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(tc_fun(X59,X3),tc_fun(X59,tc_prod(X4,X3))),X29),c_COMBB(X3,tc_prod(X4,X3),X59)),hAPP(hAPP(c_COMBB(X4,tc_fun(X3,tc_prod(X4,X3)),X29),c_Product__Type_OPair(X4,X3)),X27))),X50))),hAPP(hAPP(c_List_Ozip(X29,X59),X7),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__map__map)). 4.46/4.67 fof(fact_map__pair__def, axiom, ![X50, X27, X59, X3, X29, X4]:hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_prod(X29,X59)),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,X59),tc_fun(X3,tc_prod(X29,X59))),hAPP(hAPP(c_COMBB(tc_fun(X59,tc_prod(X29,X59)),tc_fun(tc_fun(X3,X59),tc_fun(X3,tc_prod(X29,X59))),X4),c_COMBB(X59,tc_prod(X29,X59),X3)),hAPP(hAPP(c_COMBB(X29,tc_fun(X59,tc_prod(X29,X59)),X4),c_Product__Type_OPair(X29,X59)),X27))),X50))=c_Product__Type_Omap__pair(X4,X29,X3,X59,X27,X50), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair__def)). 4.46/4.67 fof(fact_nat__def, axiom, ![X35]:c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X35)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))))=hAPP(c_Int_Onat,X35), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__def)). 4.46/4.67 fof(fact_transfer__int__nat__numerals_I3_J, axiom, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__numerals_I3_J)). 4.46/4.67 fof(fact_add, axiom, ![X13, X23, X5, X6]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23),X13)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))=hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X13))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add)). 4.46/4.67 fof(fact_set__n__lists, axiom, ![X7, X14, X4]:hAPP(c_List_Oset(tc_List_Olist(X4)),c_Enum_On__lists(X4,X14,X7))=hAPP(c_Set_OCollect(tc_List_Olist(X4)),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),X14))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X4)),c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool))),c_List_Oset(X4))),hAPP(c_List_Oset(X4),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__n__lists)). 4.46/4.67 fof(fact_Id__on__def, axiom, ![X2, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X4),c_Set_Oinsert(tc_prod(X4,X4))),hAPP(hAPP(c_COMBS(X4,X4,tc_prod(X4,X4)),c_Product__Type_OPair(X4,X4)),c_COMBI(X4)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))))=c_Relation_OId__on(X4,X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__on__def)). 4.46/4.67 fof(fact_image__eq__UN, axiom, ![X2, X27, X4, X3]:hAPP(c_Set_Oimage(X3,X4,X27),X2)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X3,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X3),c_Set_Oinsert(X4)),X27)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__eq__UN)). 4.46/4.67 fof(fact_transfer__int__nat__numerals_I4_J, axiom, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__numerals_I4_J)). 4.46/4.67 fof(fact_INTER__def, axiom, ![X1, X2, X4, X3]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OAll(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fimplies),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X2)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X3)),c_member(X4))),X1))))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INTER__def)). 4.46/4.67 fof(fact_dom__override__on, axiom, ![X2, X50, X27, X3, X4]:c_Map_Odom(X4,X3,c_Fun_Ooverride__on(X4,tc_Option_Ooption(X3),X27,X50,X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X3,X27)),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),c_Map_Odom(X4,X3,X50)))))),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),c_Map_Odom(X4,X3,X50))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__override__on)). 4.46/4.67 fof(fact_sublist__Cons, axiom, ![X2, X67, X6, X4]:hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X4)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),hAPP(hAPP(c_List_Olist_OCons(X4),X6),c_List_Olist_ONil(X4))),c_List_Olist_ONil(X4))),c_List_Osublist(X4,X67,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X2))))=c_List_Osublist(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X67),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__Cons)). 4.46/4.67 fof(fact_lenlex__def, axiom, ![X16, X4]:c_List_Olenlex(X4,X16)=hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X4)),tc_List_Olist(X4)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X4),c_Wellfounded_Oless__than,c_List_Olex(X4,X16))),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_List_Olist(X4),tc_prod(tc_Nat_Onat,tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X4),tc_prod(tc_Nat_Onat,tc_List_Olist(X4))),tc_List_Olist(X4)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X4))),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),c_COMBI(tc_List_Olist(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lenlex__def)). 4.46/4.67 fof(fact_mlex__prod__def, axiom, ![X26, X27, X4]:c_Wellfounded_Omlex__prod(X4,X27,X26)=hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X4),X4),c_Wellfounded_Olex__prod(tc_Nat_Onat,X4,c_Wellfounded_Oless__than,X26)),hAPP(hAPP(c_COMBS(X4,X4,tc_prod(tc_Nat_Onat,X4)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X4,tc_prod(tc_Nat_Onat,X4)),X4),c_Product__Type_OPair(tc_Nat_Onat,X4)),X27)),c_COMBI(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mlex__prod__def)). 4.46/4.67 fof(fact_size__code, axiom, ![X107, X4]:hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X4)),X107)=hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X4,tc_Lazy__Sequence_Olazy__sequence(X4)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X4,tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat),X4),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X4)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X4)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(c_Lazy__Sequence_Oyield(X4),X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_size__code)). 4.46/4.67 fof(fact_lists__Int__eq, axiom, ![X1, X2, X4]:c_List_Olistsp(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X1)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X4))),c_List_Olists(X4,X2))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X4))),c_List_Olists(X4,X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__Int__eq)). 4.46/4.67 fof(fact_select__def, axiom, ![X7, X4]:hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))),hAPP(hAPP(c_COMBB(X4,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X4),X7)),c_Code__Numeral_Onat__of)))=c_Random_Oselect(X4,X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select__def)). 4.46/4.67 fof(fact_minus, axiom, ![X5, X6]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))=hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X5),X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus)). 4.46/4.67 fof(fact_sublist__append, axiom, ![X2, X295, X67, X4]:c_List_Osublist(X4,hAPP(hAPP(c_List_Oappend(X4),X67),X295),X2)=hAPP(hAPP(c_List_Oappend(X4),c_List_Osublist(X4,X67,X2)),c_List_Osublist(X4,X295,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X67)))),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__append)). 4.46/4.67 fof(fact_quotient__def, axiom, ![X16, X2, X4]:hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X2),X16)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X4),c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X4),c_Relation_OImage(X4,X4,X16)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Set_Oinsert(X4)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotient__def)). 4.46/4.67 fof(fact_vimage__Times, axiom, ![X1, X2, X27, X29, X3, X4]:hAPP(c_Set_Ovimage(X4,tc_prod(X3,X29),X27),hAPP(hAPP(c_Product__Type_OSigma(X3,X29),X2),hAPP(c_COMBK(tc_fun(X29,tc_HOL_Obool),X3),X1)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4,X3,hAPP(c_Fun_Ocomp(tc_prod(X3,X29),X3,X4,c_Product__Type_Ofst(X3,X29)),X27)),X2)),hAPP(c_Set_Ovimage(X4,X29,hAPP(c_Fun_Ocomp(tc_prod(X3,X29),X29,X4,c_Product__Type_Osnd(X3,X29)),X27)),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Times)). 4.46/4.67 fof(fact_finite__psubset__def, axiom, ![X4]:hAPP(c_Set_OCollect(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),c_COMBS(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X4))))=c_Wellfounded_Ofinite__psubset(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__psubset__def)). 4.46/4.67 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, axiom, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J)). 4.46/4.67 fof(fact_map__filter__def, axiom, ![X7, X27, X4, X3]:c_List_Omap__filter(X3,X4,X27,X7)=hAPP(hAPP(c_List_Omap(X3,X4),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X4),X4,X3,c_Option_Othe(X4)),X27)),hAPP(c_List_Ofilter(X3,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),hAPP(hAPP(c_COMBC(X3,tc_Option_Ooption(X4),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X4),tc_fun(tc_Option_Ooption(X4),tc_HOL_Obool),X3),c_fequal),X27)),c_Option_Ooption_ONone(X4)))),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__filter__def)). 4.46/4.67 fof(fact_listrel__Cons, axiom, ![X7, X6, X16, X4]:hAPP(c_Relation_OImage(tc_List_Olist(X4),tc_List_Olist(X4),c_List_Olistrel(X4,X16)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X4),tc_HOL_Obool))))=c_List_Oset__Cons(X4,hAPP(c_Relation_OImage(X4,X4,X16),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X4),tc_List_Olist(X4),c_List_Olistrel(X4,X16)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X4)),X7),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X4),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__Cons)). 4.46/4.67 fof(fact_The__split__eq, axiom, ![X5, X6, X3, X4]:c_HOL_OThe(tc_prod(X4,X3),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(c_fequal,X6)))),hAPP(c_fequal,X5))))=hAPP(hAPP(c_Product__Type_OPair(X4,X3),X6),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_The__split__eq)). 4.46/4.67 fof(fact_Eps__split__eq, axiom, ![X5, X6, X3, X4]:c_Hilbert__Choice_OEps(tc_prod(X4,X3),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(c_fequal,X6)))),hAPP(c_fequal,X5))))=hAPP(hAPP(c_Product__Type_OPair(X4,X3),X6),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Eps__split__eq)). 4.46/4.67 fof(fact_length__filter__conv__card, axiom, ![X7, X109, X4]:hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))),hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,tc_Nat_Onat),X109),hAPP(c_List_Onth(X4),X7)))))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Ofilter(X4,X109),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__filter__conv__card)). 4.46/4.67 fof(fact_UN__UN__finite__eq, axiom, ![X2, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X2))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__UN__finite__eq)). 4.46/4.67 fof(fact_UN__simps_I9_J, axiom, ![X52, X1, X2, X29, X4, X3]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29,tc_fun(X3,tc_HOL_Obool)),X2),X1)),X52)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29,tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X29,tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),X29),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool))),X1)),X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I9_J)). 4.46/4.67 fof(fact_Un__Int__crazy, axiom, ![X52, X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X1),X52))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X52),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X1),X52))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X52),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Int__crazy)). 4.46/4.67 fof(fact_Int__assoc, axiom, ![X52, X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X1),X52))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)),X52), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__assoc)). 4.46/4.67 fof(fact_div__add1__eq, axiom, ![X10, X11, X12]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X11)),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X12),X10)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X11),X10))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X10)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X11,X10))),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__add1__eq)). 4.46/4.67 fof(fact_zdiv__zadd1__eq, axiom, ![X10, X11, X12]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12),X11)),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X10)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X10))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X10)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X10))),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__zadd1__eq)). 4.46/4.67 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, axiom, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J)). 4.46/4.67 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J, axiom, c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J)). 4.46/4.67 fof(fact_rotate__rev, axiom, ![X57, X17, X4]:hAPP(c_List_Orev(X4),hAPP(c_List_Orotate(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))),X57))=hAPP(c_List_Orotate(X4,X17),hAPP(c_List_Orev(X4),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__rev)). 4.46/4.67 fof(fact_the__inv__into__def, axiom, ![X6, X27, X2, X3, X4]:hAPP(c_Fun_Othe__inv__into(X4,X3,X2,X27),X6)=c_HOL_OThe(X4,hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X2))),hAPP(hAPP(c_COMBC(X4,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,tc_HOL_Obool),X4),c_fequal),X27)),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__inv__into__def)). 4.46/4.67 fof(fact_ran__def, axiom, ![X22, X4, X3]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X3)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X4),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_COMBC(X3,tc_Option_Ooption(X4),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X4),tc_fun(tc_Option_Ooption(X4),tc_HOL_Obool),X3),c_fequal),X22))),c_Option_Ooption_OSome(X4))))=c_Map_Oran(X3,X4,X22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ran__def)). 4.46/4.67 fof(fact_zadd__left__commute, axiom, ![X49, X47, X48]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X48),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X47),X49))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X47),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X48),X49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__left__commute)). 4.46/4.67 fof(fact_rotate__drop__take, axiom, ![X57, X17, X4]:hAPP(c_List_Orotate(X4,X17),X57)=hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Odrop(X4),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57))),X57)),hAPP(hAPP(c_List_Otake(X4),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57))),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__drop__take)). 4.46/4.67 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J, axiom, c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J)). 4.46/4.67 fof(fact_trancl__subset__Field2, axiom, ![X16, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X4,X16)),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),hAPP(c_Relation_OField(X4),X16)),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_Relation_OField(X4),X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__subset__Field2)). 4.46/4.67 fof(fact_LoopF, axiom, ![X39, X37, X28, X82, X4]:c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X4),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),X28))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),X37))),c_Com_Ocom_OWhile(X37,X39)),X28)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_LoopF)). 4.46/4.67 fof(fact_rev__map, axiom, ![X7, X27, X3, X4]:hAPP(hAPP(c_List_Omap(X3,X4),X27),hAPP(c_List_Orev(X3),X7))=hAPP(c_List_Orev(X4),hAPP(hAPP(c_List_Omap(X3,X4),X27),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__map)). 4.46/4.67 fof(fact_nat, axiom, ![X5, X6]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6),X5)=hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat)). 4.46/4.67 fof(fact_rotate__rotate, axiom, ![X57, X17, X19, X4]:hAPP(c_List_Orotate(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17)),X57)=hAPP(c_List_Orotate(X4,X19),hAPP(c_List_Orotate(X4,X17),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__rotate)). 4.46/4.67 fof(fact_lexord__append__rightI, axiom, ![X16, X6, X4, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X6),hAPP(hAPP(c_List_Oappend(X4),X6),X5))),c_List_Olexord(X4,X16)))<=?[X119, X132]:hAPP(hAPP(c_List_Olist_OCons(X4),X119),X132)=X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__append__rightI)). 4.46/4.67 fof(fact_int__def, axiom, ![X22]:hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__def)). 4.46/4.67 fof(fact_O__assoc, axiom, ![X110, X46, X26, X59, X3, X29, X4]:hAPP(hAPP(c_Relation_Orel__comp(X4,X59,X3),X26),hAPP(hAPP(c_Relation_Orel__comp(X59,X29,X3),X46),X110))=hAPP(hAPP(c_Relation_Orel__comp(X4,X29,X3),hAPP(hAPP(c_Relation_Orel__comp(X4,X59,X29),X26),X46)),X110), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_O__assoc)). 4.46/4.67 fof(fact_eq__Abs__Integ, axiom, ![X35]:~(![X42, X44]:hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X42),X44)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))!=X35), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__Abs__Integ)). 4.46/4.67 fof(fact_int__ge__less__than2__def, axiom, ![X87]:hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87)))),c_Orderings_Oord__class_Oless(tc_Int_Oint))))=c_Int_Oint__ge__less__than2(X87), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__ge__less__than2__def)). 4.46/4.67 fof(fact_sum__length__filter__compl, axiom, ![X7, X28, X4]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Ofilter(X4,X28),X7))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Ofilter(X4,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),X28)),X7)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__length__filter__compl)). 4.46/4.67 fof(fact_length__append, axiom, ![X72, X57, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Oappend(X4),X57),X72))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X72)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__append)). 4.46/4.67 fof(fact_prod__size__simp, axiom, ![X109, X50, X27, X3, X4]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X27,hAPP(c_Product__Type_Ofst(X4,X3),X109))),hAPP(X50,hAPP(c_Product__Type_Osnd(X4,X3),X109)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Product__Type_Oprod_Oprod__size(X4,X3,X27,X50,X109), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_prod__size__simp)). 4.46/4.67 fof(fact_lexord__Nil__left, axiom, ![X16, X5, X4]:(?[X125, X42]:hAPP(hAPP(c_List_Olist_OCons(X4),X125),X42)=X5<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_ONil(X4)),X5)),c_List_Olexord(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__Nil__left)). 4.46/4.67 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J, axiom, ![X28]:hAPP(c_Set_OCollect(tc_Nat_Onat),X28)=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),X28),c_Int_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J)). 4.46/4.67 fof(fact_set__filter, axiom, ![X7, X28, X4]:hAPP(c_List_Oset(X4),hAPP(c_List_Ofilter(X4,X28),X7))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),hAPP(c_List_Oset(X4),X7)))),X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__filter)). 4.46/4.67 fof(fact_map__append, axiom, ![X32, X7, X27, X4, X3]:hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Omap(X3,X4),X27),X7)),hAPP(hAPP(c_List_Omap(X3,X4),X27),X32))=hAPP(hAPP(c_List_Omap(X3,X4),X27),hAPP(hAPP(c_List_Oappend(X3),X7),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__append)). 4.46/4.67 fof(fact_pdivmod__def, axiom, ![X31, X15]:hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X15)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X31))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X15),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X31)))=c_Divides_Opdivmod(X15,X31), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pdivmod__def)). 4.46/4.67 fof(fact_divmod__int__mod__div, axiom, ![X112, X236]:c_Divides_Odivmod__int(X236,X112)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X236),X112)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X236,X112)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__mod__div)). 4.46/4.67 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J, axiom, ![X28]:hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X28))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),X28),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J)). 4.46/4.67 fof(fact_UN__simps_I2_J, axiom, ![X1, X2, X3, X4, X52]:((X52!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool))),X2)),X1))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),X2)),X1))&(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool))),X2)),X1))=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I2_J)). 4.46/4.67 fof(fact_rev__rev__ident, axiom, ![X57, X4]:X57=hAPP(c_List_Orev(X4),hAPP(c_List_Orev(X4),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__rev__ident)). 4.46/4.67 fof(fact_mod__mult2__eq, axiom, ![X10, X11, X12]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X10))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X12),X11),X10))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult2__eq)). 4.46/4.67 fof(fact_vimage__INT, axiom, ![X1, X2, X29, X27, X3, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29,tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X29),c_Set_Ovimage(X4,X3,X27)),X1))=hAPP(c_Set_Ovimage(X4,X3,X27),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29,tc_fun(X3,tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__INT)). 4.46/4.67 fof(fact_vimage__UN, axiom, ![X1, X2, X29, X27, X3, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29,tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X29),c_Set_Ovimage(X4,X3,X27)),X1))=hAPP(c_Set_Ovimage(X4,X3,X27),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29,tc_fun(X3,tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__UN)). 4.46/4.67 fof(fact_rotate__conv__mod, axiom, ![X57, X17, X4]:hAPP(c_List_Orotate(X4,X17),X57)=hAPP(c_List_Orotate(X4,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57))),X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__conv__mod)). 4.46/4.67 fof(fact_Field__insert, axiom, ![X16, X37, X18, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X18),hAPP(hAPP(c_Set_Oinsert(X4),X37),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),hAPP(c_Relation_OField(X4),X16))=hAPP(c_Relation_OField(X4),hAPP(hAPP(c_Set_Oinsert(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Field__insert)). 4.46/4.67 fof(fact_listrel__Nil, axiom, ![X16, X4]:hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)))=hAPP(c_Relation_OImage(tc_List_Olist(X4),tc_List_Olist(X4),c_List_Olistrel(X4,X16)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__Nil)). 4.46/4.67 fof(fact_max__Suc2, axiom, ![X14, X22]:c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X14),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),X14)),X22)=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22),hAPP(c_Nat_OSuc,X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__Suc2)). 4.46/4.67 fof(fact_length__map, axiom, ![X7, X27, X3, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Omap(X3,X4),X27),X7))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__map)). 4.46/4.67 fof(fact_New__DSequence_Oneg__bind__def, axiom, ![X24, X27, X6, X4, X3]:c_Lazy__Sequence_Ohb__bind(X3,X4,hAPP(X6,X24),hAPP(hAPP(c_COMBC(X3,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4))),X27),X24))=hAPP(c_New__DSequence_Oneg__bind(X3,X4,X6,X27),X24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Oneg__bind__def)). 4.46/4.67 fof(fact_min__Suc2, axiom, ![X14, X22]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X22),hAPP(c_Nat_OSuc,X14))=c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),X14)),X22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__Suc2)). 4.46/4.67 fof(fact_rel__pow__commute, axiom, ![X14, X26, X4]:hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X14),X26)),X26)=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X26),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X14),X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__commute)). 4.46/4.67 fof(fact_relpow_Osimps_I2_J, axiom, ![X26, X14, X4]:hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X14),X26)),X26)=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),hAPP(c_Nat_OSuc,X14)),X26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_relpow_Osimps_I2_J)). 4.46/4.67 fof(fact_vimage__Un, axiom, ![X1, X2, X27, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4,X3,X27),X2)),hAPP(c_Set_Ovimage(X4,X3,X27),X1))=hAPP(c_Set_Ovimage(X4,X3,X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Un)). 4.46/4.67 fof(fact_vimage__Int, axiom, ![X1, X2, X27, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4,X3,X27),X2)),hAPP(c_Set_Ovimage(X4,X3,X27),X1))=hAPP(c_Set_Ovimage(X4,X3,X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Int)). 4.46/4.67 fof(fact_vimage__Diff, axiom, ![X1, X2, X27, X3, X4]:hAPP(c_Set_Ovimage(X4,X3,X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4,X3,X27),X2)),hAPP(c_Set_Ovimage(X4,X3,X27),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Diff)). 4.46/4.67 fof(fact_length__zip, axiom, ![X72, X57, X3, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X4,X3))),hAPP(hAPP(c_List_Ozip(X4,X3),X57),X72))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X72)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__zip)). 4.46/4.67 fof(fact_finite__M__bounded__by__nat, axiom, ![X24, X28]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),X28)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X24))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__M__bounded__by__nat)). 4.46/4.67 fof(fact_zip__replicate, axiom, ![X47, X20, X48, X21, X3, X4]:hAPP(hAPP(c_List_Ozip(X4,X3),c_List_Oreplicate(X4,X21,X48)),c_List_Oreplicate(X3,X20,X47))=c_List_Oreplicate(tc_prod(X4,X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X21),X20),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X48),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__replicate)). 4.46/4.67 fof(fact_dom__eq__singleton__conv, axiom, ![X6, X27, X3, X4]:(?[X160]:X27=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),hAPP(c_COMBK(tc_Option_Ooption(X3),X4),c_Option_Ooption_ONone(X3))),X6),hAPP(c_Option_Ooption_OSome(X3),X160))<=>c_Map_Odom(X4,X3,X27)=hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__eq__singleton__conv)). 4.46/4.67 fof(fact_set__concat, axiom, ![X7, X4]:hAPP(c_List_Oset(X4),c_List_Oconcat(X4,X7))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X4)),X7)),c_List_Oset(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__concat)). 4.46/4.67 fof(fact_rotate__Suc, axiom, ![X57, X17, X4]:hAPP(c_List_Orotate(X4,hAPP(c_Nat_OSuc,X17)),X57)=hAPP(c_List_Orotate1(X4),hAPP(c_List_Orotate(X4,X17),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__Suc)). 4.46/4.67 fof(fact_foldl__conv__concat, axiom, ![X113, X7, X4]:hAPP(c_List_Ofoldl(tc_List_Olist(X4),tc_List_Olist(X4),c_List_Oappend(X4),X7),X113)=hAPP(hAPP(c_List_Oappend(X4),X7),c_List_Oconcat(X4,X113)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__conv__concat)). 4.46/4.67 fof(fact_map__of__Cons__code_I2_J, axiom, ![X237, X63, X29, X3, X15, X31]:((hAPP(hAPP(c_Map_Omap__of(X3,X29),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X3,X29)),hAPP(hAPP(c_Product__Type_OPair(X3,X29),X31),X63)),X237)),X15)=hAPP(hAPP(c_Map_Omap__of(X3,X29),X237),X15)<=X31!=X15)&(hAPP(hAPP(c_Map_Omap__of(X3,X29),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X3,X29)),hAPP(hAPP(c_Product__Type_OPair(X3,X29),X31),X63)),X237)),X15)=hAPP(c_Option_Ooption_OSome(X29),X63)<=X15=X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__Cons__code_I2_J)). 4.46/4.67 fof(fact_finite__dom__map__of, axiom, ![X67, X3, X4]:hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Map_Odom(X4,X3,hAPP(c_Map_Omap__of(X4,X3),X67)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__dom__map__of)). 4.46/4.67 fof(fact_Diff__Un, axiom, ![X52, X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X52))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X1),X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__Un)). 4.46/4.67 fof(fact_Diff__Int__distrib, axiom, ![X1, X2, X52, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X52),X2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X52),X1))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X52),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__Int__distrib)). 4.46/4.67 fof(fact_Domain__Collect__split, axiom, ![X28, X3, X4]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X3)),X28))=hAPP(c_Relation_ODomain(X4,X3),hAPP(c_Set_OCollect(tc_prod(X4,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_HOL_Obool),X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__Collect__split)). 4.46/4.67 fof(fact_transfer__int__nat__set__return__embed, axiom, ![X2]:X2=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__set__return__embed)). 4.46/4.67 fof(fact_vimage__Union, axiom, ![X2, X27, X3, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X3,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X2),c_Set_Ovimage(X4,X3,X27))=hAPP(c_Set_Ovimage(X4,X3,X27),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Union)). 4.46/4.67 fof(fact_takeWhile__dropWhile__id, axiom, ![X7, X28, X4]:X7=hAPP(hAPP(c_List_Oappend(X4),c_List_OtakeWhile(X4,X28,X7)),c_List_OdropWhile(X4,X28,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__dropWhile__id)). 4.46/4.67 fof(fact_map__nth, axiom, ![X7, X4]:hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X4),hAPP(c_List_Onth(X4),X7)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))=X7, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__nth)). 4.46/4.67 fof(fact_min__diff, axiom, ![X17, X21, X19]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X21)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),X21))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X19),X17)),X21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__diff)). 4.46/4.67 fof(fact_pair__box_Osize_I1_J, axiom, ![X37, X18, X320, X86, X3, X4]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X86,X18)),hAPP(X320,X37))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Nitpick_Opair__box_Opair__box__size(X4,X3,X86,X320,c_Nitpick_Opair__box_OPairBox(X4,X3,X18,X37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__box_Osize_I1_J)). 4.46/4.67 fof(fact_image__Pow__surj, axiom, ![X1, X2, X27, X4, X3]:(hAPP(c_Set_Oimage(X3,X4,X27),X2)=X1=>hAPP(c_Set_Oimage(tc_fun(X3,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),c_Set_Oimage(X3,X4,X27)),hAPP(c_Set_OPow(X3),X2))=hAPP(c_Set_OPow(X4),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Pow__surj)). 4.46/4.67 fof(fact_singleton__quotient, axiom, ![X16, X6, X4]:hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X16)=hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X16),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_singleton__quotient)). 4.46/4.67 fof(fact_max__Suc1, axiom, ![X22, X14]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14)),X22)=c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X14),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X14)),X22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__Suc1)). 4.46/4.67 fof(fact_list__size__conv__listsum, axiom, ![X7, X27, X4]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X4,tc_Nat_Onat),X27),X7))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))=c_List_Olist_Olist__size(X4,X27,X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__size__conv__listsum)). 4.46/4.67 fof(fact_map__replicate__trivial, axiom, ![X24, X6, X4]:hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X4),hAPP(c_COMBK(X4,tc_Nat_Onat),X6)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24))=c_List_Oreplicate(X4,X24,X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__replicate__trivial)). 4.46/4.67 fof(fact_refl__reflcl, axiom, ![X16, X4]:c_Relation_Orefl__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),c_Relation_OId(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__reflcl)). 4.46/4.67 fof(fact_list_Osize_I4_J, axiom, ![X307, X12, X4]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X307)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X12),X307)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osize_I4_J)). 4.46/4.67 fof(fact_min__Suc1, axiom, ![X22, X14]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14)),X22)=c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X14)),X22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__Suc1)). 4.46/4.67 fof(fact_Suc__diff__diff, axiom, ![X15, X17, X19]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19)),X17)),hAPP(c_Nat_OSuc,X15))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17)),X15), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__diff__diff)). 4.46/4.67 fof(fact_UN__simps_I3_J, axiom, ![X1, X2, X3, X4, X52]:((c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2)),X1))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X52)&(X52!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),X1))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2)),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I3_J)). 4.46/4.67 fof(fact_length__splice, axiom, ![X72, X57, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Osplice(X4,X57,X72))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X72)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__splice)). 4.46/4.67 fof(fact_rtrancl__r__diff__Id, axiom, ![X16, X4]:c_Transitive__Closure_Ortrancl(X4,X16)=c_Transitive__Closure_Ortrancl(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),c_Relation_OId(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__r__diff__Id)). 4.46/4.67 fof(fact_rtrancl__reflcl__absorb, axiom, ![X26, X4]:c_Transitive__Closure_Ortrancl(X4,X26)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4,X26)),c_Relation_OId(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__reflcl__absorb)). 4.46/4.67 fof(fact_drop__upt, axiom, ![X20, X21, X19]:hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X19),c_List_Oupt(X21,X20))=c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X19),X20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__upt)). 4.46/4.67 fof(fact_card_Oempty, axiom, ![X4]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X4),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card_Oempty)). 4.46/4.67 fof(fact_empty__iff, axiom, ![X39, X4]:~(hBOOL(hAPP(hAPP(c_member(X4),X39),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__iff)). 4.46/4.67 fof(fact_length__rotate, axiom, ![X57, X17, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Orotate(X4,X17),X57))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__rotate)). 4.46/4.67 fof(fact_map__comp__empty_I2_J, axiom, ![X6, X22, X29, X4, X3]:c_Option_Ooption_ONone(X4)=c_Map_Omap__comp(X3,X4,X29,hAPP(c_COMBK(tc_Option_Ooption(X4),X3),c_Option_Ooption_ONone(X4)),X22,X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__comp__empty_I2_J)). 4.46/4.67 fof(fact_concat__replicate__trivial, axiom, ![X21, X4]:c_List_Olist_ONil(X4)=c_List_Oconcat(X4,c_List_Oreplicate(tc_List_Olist(X4),X21,c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__replicate__trivial)). 4.46/4.67 fof(fact_zmod__zdiv__equality, axiom, ![X11, X12]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11))=X12, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zdiv__equality)). 4.46/4.67 fof(fact_one__div__nat__number__of, axiom, ![X71]:hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X71)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X71)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__div__nat__number__of)). 4.46/4.67 fof(fact_Compl__Un, axiom, ![X1, X2, X4]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__Un)). 4.46/4.67 fof(fact_image__vimage__subset, axiom, ![X2, X27, X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X4,X27),hAPP(c_Set_Ovimage(X3,X4,X27),X2))),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__vimage__subset)). 4.46/4.67 fof(fact_vimage__UNIV, axiom, ![X27, X3, X4]:hAPP(c_Set_Ovimage(X4,X3,X27),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__UNIV)). 4.46/4.67 fof(fact_vimage__id, axiom, ![X2, X4]:X2=hAPP(c_Set_Ovimage(X4,X4,c_Fun_Oid(X4)),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__id)). 4.46/4.67 fof(fact_vimage__ident, axiom, ![X76, X4]:X76=hAPP(c_Set_Ovimage(X4,X4,c_COMBI(X4)),X76), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__ident)). 4.46/4.67 fof(fact_vimage__empty, axiom, ![X27, X3, X4]:c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X4,X3,X27),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__empty)). 4.46/4.67 fof(fact_Inter__Un__distrib, axiom, ![X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X1))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__Un__distrib)). 4.46/4.67 fof(fact_Inter__insert, axiom, ![X1, X18, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X18),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X1))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),X18),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__insert)). 4.46/4.67 fof(fact_Union__Un__distrib, axiom, ![X1, X2, X4]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__Un__distrib)). 4.46/4.67 fof(fact_Union__insert, axiom, ![X1, X18, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X18),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X1))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),X18),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__insert)). 4.46/4.67 fof(fact_nat__mult__div__cancel__disj, axiom, ![X17, X19, X15]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X17))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X15)&(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X17))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19),X17)<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__div__cancel__disj)). 4.46/4.67 fof(fact_mult__0, axiom, ![X17]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__0)). 4.46/4.67 fof(fact_Nitpick_Oint__gcd__def, axiom, ![X47, X48]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X48)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X47))))=hAPP(hAPP(c_Nitpick_Oint__gcd,X48),X47), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oint__gcd__def)). 4.46/4.67 fof(fact_UN__simps_I1_J, axiom, ![X1, X18, X3, X4, X52]:((hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Set_Oinsert(X3),X18)),X1))=hAPP(hAPP(c_Set_Oinsert(X3),X18),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),X1))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X52)&(X52=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Set_Oinsert(X3),X18)),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I1_J)). 4.46/4.67 fof(fact_in__set__conv__decomp, axiom, ![X7, X6, X4]:(?[X8, X9]:hAPP(hAPP(c_List_Oappend(X4),X8),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X9))=X7<=>hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__conv__decomp)). 4.46/4.67 fof(fact_greaterThan__Suc, axiom, ![X45]:hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X45))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X45)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X45)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThan__Suc)). 4.46/4.67 fof(fact_length__sublists, axiom, ![X57, X4]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),c_Enum_Osublists(X4,X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__sublists)). 4.46/4.67 fof(fact_Divides_Omod__div__equality_H, axiom, ![X17, X19]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19),X17)),X17))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Omod__div__equality_H)). 4.46/4.67 fof(fact_nat__mult__commute, axiom, ![X17, X19]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X17)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__commute)). 4.46/4.67 fof(fact_zmod__zdiv__equality_H, axiom, ![X17, X19]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19),X17)),X17))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zdiv__equality_H)). 4.46/4.67 fof(fact_irrefl__diff__Id, axiom, ![X16, X4]:c_Relation_Oirrefl(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),c_Relation_OId(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_irrefl__diff__Id)). 4.46/4.67 fof(fact_trancl__range, axiom, ![X16, X4]:hAPP(c_Relation_ORange(X4,X4),X16)=hAPP(c_Relation_ORange(X4,X4),c_Transitive__Closure_Otrancl(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__range)). 4.46/4.67 fof(fact_trancl__domain, axiom, ![X16, X4]:hAPP(c_Relation_ODomain(X4,X4),X16)=hAPP(c_Relation_ODomain(X4,X4),c_Transitive__Closure_Otrancl(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__domain)). 4.46/4.67 fof(fact_set__rotate, axiom, ![X7, X14, X4]:hAPP(c_List_Oset(X4),X7)=hAPP(c_List_Oset(X4),hAPP(c_List_Orotate(X4,X14),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__rotate)). 4.46/4.67 fof(fact_lessThan__Suc__eq__insert__0, axiom, ![X14]:hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X14)))=hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessThan__Suc__eq__insert__0)). 4.46/4.67 fof(fact_butlast__list__update, axiom, ![X48, X57, X4, X15]:((hAPP(hAPP(c_List_Olist__update(X4,c_List_Obutlast(X4,X57)),X15),X48)=c_List_Obutlast(X4,hAPP(hAPP(c_List_Olist__update(X4,X57),X15),X48))<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X15)&(X15=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=>c_List_Obutlast(X4,hAPP(hAPP(c_List_Olist__update(X4,X57),X15),X48))=c_List_Obutlast(X4,X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast__list__update)). 4.46/4.67 fof(fact_take__take, axiom, ![X57, X19, X17, X4]:hAPP(hAPP(c_List_Otake(X4),X17),hAPP(hAPP(c_List_Otake(X4),X19),X57))=hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X17),X19)),X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__take)). 4.46/4.67 fof(fact_lazy__sequence_Osize_I4_J, axiom, ![X137, X12, X4]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X4)),X137)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X4)),c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X12,X137)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Osize_I4_J)). 4.46/4.67 fof(fact_atLeast__Suc, axiom, ![X45]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X45)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))=hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast__Suc)). 4.46/4.67 fof(fact_atLeast__Suc__greaterThan, axiom, ![X45]:hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X45))=hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast__Suc__greaterThan)). 4.46/4.67 fof(fact_converse__Id, axiom, ![X4]:c_Relation_OId(X4)=hAPP(c_Relation_Oconverse(X4,X4),c_Relation_OId(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__Id)). 4.46/4.67 fof(fact_Un__eq__Union, axiom, ![X1, X2, X4]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__eq__Union)). 4.46/4.67 fof(fact_Int__eq__Inter, axiom, ![X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)=c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__eq__Inter)). 4.46/4.67 fof(fact_finite__Collect__less__nat, axiom, ![X45]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Collect__less__nat)). 4.46/4.67 fof(fact_finite__Collect__le__nat, axiom, ![X45]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Collect__le__nat)). 4.46/4.67 fof(fact_one__code__numeral__code, axiom, c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__code__numeral__code)). 4.46/4.67 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J, axiom, ![X14]:hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14)))=hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SetInterval_Otransfer__nat__int__set__functions_I1_J)). 4.46/4.67 fof(fact_singleton__rev__conv, axiom, ![X7, X6, X4]:(hAPP(c_List_Orev(X4),X7)=hAPP(hAPP(c_List_Olist_OCons(X4),X6),c_List_Olist_ONil(X4))<=>hAPP(hAPP(c_List_Olist_OCons(X4),X6),c_List_Olist_ONil(X4))=X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_singleton__rev__conv)). 4.46/4.67 fof(fact_div__nat__def, axiom, ![X17, X19]:hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X19,X17))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19),X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__nat__def)). 4.46/4.67 fof(fact_UN__extend__simps_I1_J, axiom, ![X1, X18, X3, X4, X52]:((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X52=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Set_Oinsert(X3),X18)),X1))=hAPP(hAPP(c_Set_Oinsert(X3),X18),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),X1)))&(hAPP(hAPP(c_Set_Oinsert(X3),X18),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(X3),X18),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),X1))<=X52=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__extend__simps_I1_J)). 4.46/4.67 fof(fact_atLeastLessThan__upto, axiom, ![X25, X24]:hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X24,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25),c_Groups_Oone__class_Oone(tc_Int_Oint))))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X24),X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__upto)). 4.46/4.67 fof(fact_take__replicate, axiom, ![X48, X15, X21, X4]:c_List_Oreplicate(X4,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X21),X15),X48)=hAPP(hAPP(c_List_Otake(X4),X21),c_List_Oreplicate(X4,X15,X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__replicate)). 4.46/4.67 fof(fact_length__upt, axiom, ![X20, X21]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X21,X20))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__upt)). 4.46/4.67 fof(fact_zless__iff__Suc__zadd, axiom, ![X35, X36]:(?[X199]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X36),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X199)))=X35<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__iff__Suc__zadd)). 4.46/4.67 fof(fact_Id__O__R, axiom, ![X26, X3, X4]:hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X3),c_Relation_OId(X4)),X26)=X26, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__O__R)). 4.46/4.67 fof(fact_listset_Osimps_I1_J, axiom, ![X4]:hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)))=c_List_Olistset(X4,c_List_Olist_ONil(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listset_Osimps_I1_J)). 4.46/4.67 fof(fact_R__O__Id, axiom, ![X26, X3, X4]:hAPP(hAPP(c_Relation_Orel__comp(X4,X3,X3),X26),c_Relation_OId(X3))=X26, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_R__O__Id)). 4.46/4.67 fof(fact_mod__nat__def, axiom, ![X17, X19]:hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X19,X17))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__nat__def)). 4.46/4.67 fof(fact_trancl__rtrancl__absorb, axiom, ![X26, X4]:c_Transitive__Closure_Ortrancl(X4,c_Transitive__Closure_Otrancl(X4,X26))=c_Transitive__Closure_Ortrancl(X4,X26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__rtrancl__absorb)). 4.46/4.67 fof(fact_UN__constant, axiom, ![X39, X3, X4, X2]:((hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),X39))=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X2)&(X39=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),X39))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__constant)). 4.46/4.67 fof(fact_UN__extend__simps_I2_J, axiom, ![X1, X2, X3, X4, X52]:((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X52=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool))),X2)),X1))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),X2)),X1))&(X1=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),X2)),X1)<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__extend__simps_I2_J)). 4.46/4.67 fof(fact_INT__extend__simps_I4_J, axiom, ![X1, X2, X3, X4, X52]:((hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X2)),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),X1))<=X52!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X52=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),X1))=X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__extend__simps_I4_J)). 4.46/4.67 fof(fact_UN__extend__simps_I3_J, axiom, ![X1, X2, X3, X4, X52]:((X2=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),X1))<=X52=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&(X52!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),X1))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2)),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__extend__simps_I3_J)). 4.46/4.67 fof(fact_zless__add1__eq, axiom, ![X35, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X35),c_Groups_Oone__class_Oone(tc_Int_Oint))))<=>(X36=X35|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__add1__eq)). 4.46/4.67 fof(fact_Plus__eq__empty__conv, axiom, ![X1, X2, X3, X4]:((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X2&X1=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))<=>c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X4,X3),tc_HOL_Obool))=c_Sum__Type_OPlus(X4,X3,X2,X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Plus__eq__empty__conv)). 4.46/4.67 fof(fact_div__code__numeral__def, axiom, ![X19, X17]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X17),X19)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X17)),hAPP(c_Code__Numeral_Onat__of,X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__code__numeral__def)). 4.46/4.67 fof(fact_divmod__nat__zero, axiom, ![X19]:hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19)=c_Divides_Odivmod__nat(X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__zero)). 4.46/4.67 fof(fact_times__code__numeral__def, axiom, ![X19, X17]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X17),X19)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X17)),hAPP(c_Code__Numeral_Onat__of,X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_times__code__numeral__def)). 4.46/4.67 fof(fact_plus__code__numeral__def, axiom, ![X19, X17]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X17),X19)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X17)),hAPP(c_Code__Numeral_Onat__of,X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_plus__code__numeral__def)). 4.46/4.67 fof(fact_minus__code__numeral__def, axiom, ![X19, X17]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X17),X19)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X17)),hAPP(c_Code__Numeral_Onat__of,X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__code__numeral__def)). 4.46/4.67 fof(fact_hoare__derivs_Oequations_I7_J, axiom, ![X135, X123, X4]:c_Hoare__Mirabelle_Ohoare__derivs(X4,X123,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X135),c_Com_Ocom_OSKIP),X135)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hoare__derivs_Oequations_I7_J)). 4.46/4.67 fof(fact_option_Osize_I2_J, axiom, ![X18, X86, X4]:c_Option_Ooption_Ooption__size(X4,X86,hAPP(c_Option_Ooption_OSome(X4),X18))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X86,X18)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Osize_I2_J)). 4.46/4.67 fof(fact_zle__iff__zadd, axiom, ![X35, X36]:(?[X199]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X36),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X199))=X35<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X36),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__iff__zadd)). 4.46/4.67 fof(fact_com_Osize_I11_J, axiom, ![X33, X34, X56]:hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X56,X34,X33))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X33)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I11_J)). 4.46/4.67 fof(fact_max__Suc__Suc, axiom, ![X17, X19]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19)),hAPP(c_Nat_OSuc,X17))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X19),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__Suc__Suc)). 4.46/4.67 fof(fact_min__Suc__Suc, axiom, ![X17, X19]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19)),hAPP(c_Nat_OSuc,X17))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X19),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__Suc__Suc)). 4.46/4.67 fof(fact_times__code__numeral__code, axiom, ![X19, X17]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X17)),hAPP(c_Code__Numeral_Oof__nat,X19))=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_times__code__numeral__code)). 4.46/4.67 fof(fact_plus__code__numeral__code, axiom, ![X19, X17]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X17)),hAPP(c_Code__Numeral_Oof__nat,X19))=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_plus__code__numeral__code)). 4.46/4.67 fof(fact_lists__empty, axiom, ![X4]:hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)))=c_List_Olists(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__empty)). 4.46/4.67 fof(fact_the__eq__trivial, axiom, ![X18, X4]:c_HOL_OThe(X4,hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X18))=X18, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__eq__trivial)). 4.46/4.67 fof(fact_some__eq__trivial, axiom, ![X6, X4]:c_Hilbert__Choice_OEps(X4,hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X6))=X6, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_some__eq__trivial)). 4.46/4.67 fof(fact_fold1Set__sing, axiom, ![X37, X18, X27, X4]:(X18=X37<=>hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,X27,hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1Set__sing)). 4.46/4.67 fof(fact_divmod__nat__rel__divmod__nat, axiom, ![X17, X19]:hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X19,X17),c_Divides_Odivmod__nat(X19,X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel__divmod__nat)). 4.46/4.67 fof(fact_zabs__less__one__iff, axiom, ![X35]:(X35=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X35)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zabs__less__one__iff)). 4.46/4.67 fof(fact_Image__Id, axiom, ![X2, X4]:X2=hAPP(c_Relation_OImage(X4,X4,c_Relation_OId(X4)),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__Id)). 4.46/4.67 fof(fact_less__iff__Suc__add, axiom, ![X14, X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X14))<=>?[X266]:hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X266))=X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__iff__Suc__add)). 4.46/4.67 fof(fact_atMost__Suc, axiom, ![X45]:hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X45)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X45))=hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atMost__Suc)). 4.46/4.67 fof(fact_card__atLeastLessThan__int, axiom, ![X23, X67]:hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X67),X23))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23),X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__atLeastLessThan__int)). 4.46/4.67 fof(fact_com_Osize_I14_J, axiom, ![X33, X34]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X33)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X34,X33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I14_J)). 4.46/4.67 fof(fact_mod__code__numeral__def, axiom, ![X19, X17]:hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X17),hAPP(c_Code__Numeral_Onat__of,X19)))=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X17,X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__code__numeral__def)). 4.46/4.67 fof(fact_mult__Min, axiom, ![X15]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X15)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X15), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__Min)). 4.46/4.67 fof(fact_pdivmod__posDivAlg, axiom, ![X15, X31]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X31=>hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X15))=c_Divides_Opdivmod(X15,X31))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X31=>c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X15),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X31))=c_Divides_Opdivmod(X15,X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pdivmod__posDivAlg)). 4.46/4.67 fof(fact_subtract__code__numeral__code, axiom, ![X19, X17]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),X19))=hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X17)),hAPP(c_Code__Numeral_Oof__nat,X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subtract__code__numeral__code)). 4.46/4.67 fof(fact_card__atLeastAtMost, axiom, ![X23, X67]:hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X67,X23))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X23)),X67), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__atLeastAtMost)). 4.46/4.67 fof(fact_nat_Osize_I2_J, axiom, ![X258]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X258)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X258)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat_Osize_I2_J)). 4.46/4.67 fof(fact_iterate_Osimps, axiom, ![X6, X27, X4, X3, X45]:((hAPP(c_Random_Oiterate(X3,X4,X45,X27),X6)=hAPP(hAPP(c_Product__Type_Oscomp(X4,X3,X4,tc_prod(X3,X4)),hAPP(X27,X6)),c_Random_Oiterate(X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X45),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X27))<=X45!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))&(hAPP(c_Product__Type_OPair(X3,X4),X6)=hAPP(c_Random_Oiterate(X3,X4,X45,X27),X6)<=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_iterate_Osimps)). 4.46/4.67 fof(fact_com_Osize_I3_J, axiom, ![X33, X34, X56]:c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X56,X34,X33))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X33)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I3_J)). 4.46/4.67 fof(fact_wfP__empty, axiom, ![X4]:c_Wellfounded_OwfP(X4,hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBK(tc_HOL_Obool,X4),c_fFalse))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__empty)). 4.46/4.67 fof(fact_distinct__upt, axiom, ![X20, X21]:hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X21,X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__upt)). 4.46/4.67 fof(fact_butlast_Osimps_I2_J, axiom, ![X48, X4, X57]:((hAPP(hAPP(c_List_Olist_OCons(X4),X48),c_List_Obutlast(X4,X57))=c_List_Obutlast(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57))<=c_List_Olist_ONil(X4)!=X57)&(X57=c_List_Olist_ONil(X4)=>c_List_Olist_ONil(X4)=c_List_Obutlast(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast_Osimps_I2_J)). 4.46/4.67 fof(fact_remove1_Osimps_I2_J, axiom, ![X57, X4, X47, X48]:((X48!=X47=>c_List_Oremove1(X4,X48,hAPP(hAPP(c_List_Olist_OCons(X4),X47),X57))=hAPP(hAPP(c_List_Olist_OCons(X4),X47),c_List_Oremove1(X4,X48,X57)))&(X48=X47=>X57=c_List_Oremove1(X4,X48,hAPP(hAPP(c_List_Olist_OCons(X4),X47),X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1_Osimps_I2_J)). 4.46/4.67 fof(fact_single__valued__Id, axiom, ![X4]:c_Relation_Osingle__valued(X4,X4,c_Relation_OId(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__Id)). 4.46/4.67 fof(fact_lessThan__Suc, axiom, ![X45]:hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X45))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X45),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessThan__Suc)). 4.46/4.67 fof(fact_mod__eq__0__iff, axiom, ![X87, X22]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22,X87)<=>?[X144]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),X144)=X22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__eq__0__iff)). 4.46/4.67 fof(fact_sublist__upt__eq__take, axiom, ![X14, X67, X4]:hAPP(hAPP(c_List_Otake(X4),X14),X67)=c_List_Osublist(X4,X67,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__upt__eq__take)). 4.46/4.67 fof(fact_zmod__eq__0__iff, axiom, ![X87, X22]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X22,X87)<=>?[X144]:X22=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X87),X144)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__eq__0__iff)). 4.46/4.67 fof(fact_zdiv__minus1__right, axiom, ![X12]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__minus1__right)). 4.46/4.67 fof(fact_last_Osimps, axiom, ![X48, X4, X57]:((c_List_Olist_ONil(X4)!=X57=>c_List_Olast(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57))=c_List_Olast(X4,X57))&(X57=c_List_Olist_ONil(X4)=>c_List_Olast(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57))=X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last_Osimps)). 4.46/4.67 fof(fact_com_Osize_I6_J, axiom, ![X33, X34]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X33)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X34,X33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I6_J)). 4.46/4.67 fof(fact_New__DSequence_Opos__decr__bind__def, axiom, ![X27, X6, X4, X3, X24]:((X24=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=>c_Lazy__Sequence_Oempty(X4)=hAPP(c_New__DSequence_Opos__decr__bind(X3,X4,X6,X27),X24))&(hAPP(c_Lazy__Sequence_Obind(X3,X4,hAPP(X6,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X24),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X3,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4)),X27),X24))=hAPP(c_New__DSequence_Opos__decr__bind(X3,X4,X6,X27),X24)<=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Opos__decr__bind__def)). 4.46/4.67 fof(fact_Pow__empty, axiom, ![X4]:hAPP(c_Set_OPow(X4),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__empty)). 4.46/4.67 fof(fact_sorted__upt, axiom, ![X20, X21]:c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X21,X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__upt)). 4.46/4.67 fof(fact_nat__zminus__int, axiom, ![X17]:hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__zminus__int)). 4.46/4.67 fof(fact_eq__mem, axiom, ![X5, X6, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_fequal,X5)))<=>X6=X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__mem)). 4.46/4.67 fof(fact_wf__measure, axiom, ![X27, X4]:c_Wellfounded_Owf(X4,hAPP(c_Wellfounded_Omeasure(X4),X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__measure)). 4.46/4.67 fof(fact_Range__empty__iff, axiom, ![X16, X4, X3]:(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X4),tc_HOL_Obool))=X16<=>hAPP(c_Relation_ORange(X3,X4),X16)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__empty__iff)). 4.46/4.67 fof(fact_Domain__empty__iff, axiom, ![X16, X3, X4]:(hAPP(c_Relation_ODomain(X4,X3),X16)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=>X16=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X3),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__empty__iff)). 4.46/4.67 fof(fact_div__1, axiom, ![X19]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=X19, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__1)). 4.46/4.67 fof(fact_list__all2__Nil2, axiom, ![X7, X28, X3, X4]:(c_List_Olist__all2(X4,X3,X28,X7,c_List_Olist_ONil(X3))<=>X7=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__Nil2)). 4.46/4.67 fof(fact_mod__1, axiom, ![X19]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__1)). 4.46/4.67 fof(fact_zmod__minus1__right, axiom, ![X12]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__minus1__right)). 4.46/4.67 fof(fact_power__eq__if, axiom, ![X236, X19]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X236),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X236),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X236),X19)<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X19)&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X19=>c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X236),X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__eq__if)). 4.46/4.67 fof(fact_insert__code, axiom, ![X6, X2, X5, X4]:((hBOOL(hAPP(X2,X6))|X6=X5)<=>hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X4),X5),X2),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__code)). 4.46/4.67 fof(fact_min__0L, axiom, ![X17]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__0L)). 4.46/4.67 fof(fact_nat__int, axiom, ![X17]:X17=hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__int)). 4.46/4.67 fof(fact_min__0R, axiom, ![X17]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__0R)). 4.46/4.67 fof(fact_list__all2__eq, axiom, ![X4, X32, X7]:(c_List_Olist__all2(X4,X4,c_fequal,X7,X32)<=>X7=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__eq)). 4.46/4.67 fof(fact_max__0L, axiom, ![X17]:X17=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__0L)). 4.46/4.67 fof(fact_max__0R, axiom, ![X17]:X17=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__0R)). 4.46/4.67 fof(help_c__fequal__2, axiom, ![X5, X6]:(X6!=X5|hBOOL(hAPP(hAPP(c_fequal,X6),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fequal__2)). 4.46/4.67 fof(fact_diff__bin__simps_I1_J, axiom, ![X15]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X15),c_Int_OPls)=X15, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I1_J)). 4.46/4.67 fof(fact_mult__Pls, axiom, ![X30]:c_Int_OPls=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__Pls)). 4.46/4.67 fof(fact_nat__gcd_Osimps, axiom, ![X48, X47]:((c_Nitpick_Onat__gcd(X47,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X48,X47))=c_Nitpick_Onat__gcd(X48,X47)<=X47!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(X47=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>c_Nitpick_Onat__gcd(X48,X47)=X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__gcd_Osimps)). 4.46/4.67 fof(fact_inc__shift__def, axiom, ![X15, X63]:((c_Random_Oinc__shift(X63,X15)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X15),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))<=X15!=X63)&(X15=X63=>c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=c_Random_Oinc__shift(X63,X15))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inc__shift__def)). 4.46/4.67 fof(fact_nat__of__of__nat, axiom, ![X17]:X17=hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__of__of__nat)). 4.46/4.67 fof(fact_of__nat__nat__of, axiom, ![X15]:X15=hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__nat__of)). 4.46/4.67 fof(fact_pred__comp__rel__comp__eq, axiom, ![X5, X6, X68, X16, X29, X3, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X29)),hAPP(hAPP(c_Product__Type_OPair(X4,X29),X6),X5)),hAPP(hAPP(c_Relation_Orel__comp(X4,X3,X29),X16),X68)))<=>hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X4,X3,X29,hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBC(X3,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X3),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X4,X3)))),c_Product__Type_OPair(X4,X3)))),X16),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_fun(tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),X3),c_COMBC(X29,tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_prod(X3,X29)),tc_fun(X29,tc_fun(tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_prod(X3,X29),tc_fun(tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_HOL_Obool),X29),c_member(tc_prod(X3,X29)))),c_Product__Type_OPair(X3,X29)))),X68)),X6),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__comp__rel__comp__eq)). 4.46/4.67 fof(fact_sup__Un__eq2, axiom, ![X5, X6, X46, X26, X3, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X6),X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X26),X46)))<=>hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBC(X3,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X3),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X4,X3)))),c_Product__Type_OPair(X4,X3)))),X26)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBC(X3,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X3),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X4,X3)))),c_Product__Type_OPair(X4,X3)))),X46)),X6),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__Un__eq2)). 4.46/4.67 fof(fact_inf__Int__eq2, axiom, ![X5, X6, X46, X26, X3, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X6),X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X26),X46)))<=>hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBC(X3,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X3),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X4,X3)))),c_Product__Type_OPair(X4,X3)))),X26)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBC(X3,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X3),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X4,X3)))),c_Product__Type_OPair(X4,X3)))),X46)),X6),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__Int__eq2)). 4.46/4.67 fof(fact_pred__subset__eq2, axiom, ![X46, X26, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBC(X3,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X3),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X4,X3)))),c_Product__Type_OPair(X4,X3)))),X26)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBC(X3,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X3),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X4,X3)))),c_Product__Type_OPair(X4,X3)))),X46)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X26),X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__subset__eq2)). 4.46/4.67 fof(fact_INF__INT__eq2, axiom, ![X5, X6, X16, X29, X3, X4]:(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_fun(X29,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_fun(X3,tc_fun(X29,tc_HOL_Obool)),X4),hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_fun(tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),X3),c_COMBC(X29,tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_prod(X3,X29)),tc_fun(X29,tc_fun(tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_prod(X3,X29),tc_fun(tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_HOL_Obool),X29),c_member(tc_prod(X3,X29)))),c_Product__Type_OPair(X3,X29))))),X16)),X6),X5))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X29)),hAPP(hAPP(c_Product__Type_OPair(X3,X29),X6),X5)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(tc_prod(X3,X29),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__INT__eq2)). 4.46/4.67 fof(fact_SUP__UN__eq2, axiom, ![X5, X6, X16, X29, X3, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X29)),hAPP(hAPP(c_Product__Type_OPair(X3,X29),X6),X5)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(tc_prod(X3,X29),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),X16)))<=>hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_fun(X29,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_fun(X3,tc_fun(X29,tc_HOL_Obool)),X4),hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_fun(tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),X3),c_COMBC(X29,tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_prod(X3,X29)),tc_fun(X29,tc_fun(tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_prod(X3,X29),tc_fun(tc_fun(tc_prod(X3,X29),tc_HOL_Obool),tc_HOL_Obool),X29),c_member(tc_prod(X3,X29)))),c_Product__Type_OPair(X3,X29))))),X16)),X6),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__UN__eq2)). 4.46/4.67 fof(fact_listrel__iff__zip, axiom, ![X16, X32, X7, X4]:((![X42]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X42),hAPP(c_List_Oset(tc_prod(X4,X4)),hAPP(hAPP(c_List_Ozip(X4,X4),X7),X32))))=>hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X4,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X4,X4)))),c_Product__Type_OPair(X4,X4)))),X16)),X42)))&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)),c_List_Olistrel(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__iff__zip)). 4.46/4.67 fof(fact_conversep__converse__eq, axiom, ![X5, X6, X16, X3, X4]:(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4,X3,hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBC(X3,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X3),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X4,X3)))),c_Product__Type_OPair(X4,X3)))),X16)),X6),X5))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X5)),hAPP(c_Relation_Oconverse(X4,X3),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conversep__converse__eq)). 4.46/4.67 fof(fact_max__extp__max__ext__eq, axiom, ![X235, X6, X26, X4]:(c_Wellfounded_Omax__extp(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X4,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X4,X4)))),c_Product__Type_OPair(X4,X4)))),X26),X6,X235)<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X6),X235)),c_Wellfounded_Omax__ext(X4,X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__extp__max__ext__eq)). 4.46/4.67 fof(fact_listrelp__listrel__eq, axiom, ![X235, X6, X16, X4]:(c_List_Olistrelp(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X4,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X4,X4)))),c_Product__Type_OPair(X4,X4)))),X16),X6,X235)<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X6),X235)),c_List_Olistrel(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrelp__listrel__eq)). 4.46/4.67 fof(fact_RangeP__Range__eq, axiom, ![X6, X16, X3, X4]:(hBOOL(hAPP(hAPP(c_member(X3),X6),hAPP(c_Relation_ORange(X4,X3),X16)))<=>hBOOL(hAPP(c_Predicate_ORangeP(X4,X3,hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBC(X3,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X3),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X4,X3)))),c_Product__Type_OPair(X4,X3)))),X16)),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_RangeP__Range__eq)). 4.46/4.67 fof(fact_DomainP__Domain__eq, axiom, ![X6, X16, X3, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_Relation_ODomain(X4,X3),X16)))<=>hBOOL(hAPP(c_Predicate_ODomainP(X4,X3,hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBC(X3,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X3),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X4,X3)))),c_Product__Type_OPair(X4,X3)))),X16)),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DomainP__Domain__eq)). 4.46/4.67 fof(fact_accp__acc__eq, axiom, ![X6, X16, X4]:(hBOOL(hAPP(c_Wellfounded_Oaccp(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X4,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X4,X4)))),c_Product__Type_OPair(X4,X4)))),X16)),X6))<=>hBOOL(hAPP(hAPP(c_member(X4),X6),c_Wellfounded_Oacc(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_accp__acc__eq)). 4.46/4.67 fof(fact_pred__equals__eq2, axiom, ![X46, X26, X3, X4]:(hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBC(X3,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X3),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X4,X3)))),c_Product__Type_OPair(X4,X3)))),X46)=hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_COMBC(X3,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X3),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X4,X3)))),c_Product__Type_OPair(X4,X3)))),X26)<=>X26=X46), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__equals__eq2)). 4.46/4.67 fof(fact_equivp__equiv, axiom, ![X2, X4]:(c_Equiv__Relations_Oequivp(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X4,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X4,X4)))),c_Product__Type_OPair(X4,X4)))),X2))<=>c_Equiv__Relations_Oequiv(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equivp__equiv)). 4.46/4.67 fof(fact_wfP__wf__eq, axiom, ![X16, X4]:(c_Wellfounded_OwfP(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X4,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X4,X4)))),c_Product__Type_OPair(X4,X4)))),X16))<=>c_Wellfounded_Owf(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__wf__eq)). 4.46/4.67 fof(fact_fold__image__Sigma, axiom, ![X50, X1, X3, X2, X4, X29]:(class_Groups_Ocomm__monoid__mult(X29)=>((hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X29,X4,c_Groups_Otimes__class_Otimes(X29)),hAPP(hAPP(c_COMBS(X4,tc_fun(X3,tc_HOL_Obool),X29),hAPP(hAPP(c_COMBC(X4,X29,tc_fun(tc_fun(X3,tc_HOL_Obool),X29)),hAPP(hAPP(c_COMBB(tc_fun(X3,X29),tc_fun(X29,tc_fun(tc_fun(X3,tc_HOL_Obool),X29)),X4),c_Finite__Set_Ofold__image(X29,X3,c_Groups_Otimes__class_Otimes(X29))),X50)),c_Groups_Oone__class_Oone(X29))),X1)),c_Groups_Oone__class_Oone(X29)),X2)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X29,tc_prod(X4,X3),c_Groups_Otimes__class_Otimes(X29)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,X29),X50)),c_Groups_Oone__class_Oone(X29)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),X1))<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X1,X42)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__Sigma)). 4.46/4.67 fof(fact_setsum__product, axiom, ![X1, X50, X29, X2, X27, X3, X4]:(class_Rings_Osemiring__0(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),hAPP(hAPP(c_COMBC(X3,tc_fun(X29,tc_HOL_Obool),X4),hAPP(hAPP(c_COMBB(tc_fun(X29,X4),tc_fun(tc_fun(X29,tc_HOL_Obool),X4),X3),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29,X4)),hAPP(hAPP(c_COMBC(X3,tc_fun(X29,X4),tc_fun(X29,X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,X4),tc_fun(tc_fun(X29,X4),tc_fun(X29,X4)),X3),c_COMBB(X4,X4,X29)),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X3),c_Groups_Otimes__class_Otimes(X4)),X27))),X50))),X1)),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X27),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29,X4),X50),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__product)). 4.46/4.67 fof(fact_wmax__insertI, axiom, ![X229, X6, X228, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X5),X228))=>((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),X229)),X228)),c_FunDef_Omax__weak))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X229),X228)),c_FunDef_Omax__weak)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),X5)),c_FunDef_Opair__leq)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wmax__insertI)). 4.46/4.67 fof(fact_smax__insertI, axiom, ![X173, X6, X76, X5]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X5),X76))=>((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X173),X76)),c_FunDef_Omax__strict))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),X173)),X76)),c_FunDef_Omax__strict)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),X5)),c_FunDef_Opair__less)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_smax__insertI)). 4.46/4.67 fof(fact_smin__insertI, axiom, ![X228, X5, X229, X6]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X229),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X5),X228))),c_FunDef_Omin__strict))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X229),X228)),c_FunDef_Omin__strict)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),X5)),c_FunDef_Opair__less)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),X229))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_smin__insertI)). 4.46/4.67 fof(fact_UN__equiv__class__type2, axiom, ![X1, X145, X146, X27, X29, X147, X148, X3, X149, X150, X4]:(c_Equiv__Relations_Oequiv(X4,X150,X149)=>(c_Equiv__Relations_Oequiv(X3,X148,X147)=>(c_Equiv__Relations_Ocongruent2(X4,X3,tc_fun(X29,tc_HOL_Obool),X149,X147,X27)=>(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X146),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X150),X149)))=>(hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X145),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X148),X147)))=>(hBOOL(hAPP(hAPP(c_member(tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X29,tc_HOL_Obool)),X146),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(X29,tc_HOL_Obool)),tc_fun(X29,tc_HOL_Obool),X4),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X29,tc_HOL_Obool)),X145)),X27))),X1))<=![X138]:(![X151]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(X27,X138),X151)),X1))<=hBOOL(hAPP(hAPP(c_member(X3),X151),X148)))<=hBOOL(hAPP(hAPP(c_member(X4),X138),X150))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__equiv__class__type2)). 4.46/4.67 fof(fact_wmin__insertI, axiom, ![X228, X5, X229, X6]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X229),X228)),c_FunDef_Omin__weak))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X229),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X5),X228))),c_FunDef_Omin__weak)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),X5)),c_FunDef_Opair__leq)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6),X229))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wmin__insertI)). 4.46/4.67 fof(fact_small__prod__def, axiom, ![X87, X27, X4, X3]:((class_Smallcheck_Osmall(X4)&class_Smallcheck_Osmall(X3))=>hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(X4,X3)),X27),X87)=hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(X4),hAPP(hAPP(c_COMBC(X4,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X4),c_Smallcheck_Osmall__class_Osmall(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(X3,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X4),hAPP(c_COMBB(tc_prod(X4,X3),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),X3),X27)),c_Product__Type_OPair(X4,X3)))),X87)),X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__prod__def)). 4.46/4.67 fof(fact_UN__equiv__class2, axiom, ![X135, X123, X27, X29, X147, X148, X3, X149, X150, X4]:(((c_Equiv__Relations_Ocongruent2(X4,X3,tc_fun(X29,tc_HOL_Obool),X149,X147,X27)=>(hBOOL(hAPP(hAPP(c_member(X4),X123),X150))=>(hBOOL(hAPP(hAPP(c_member(X3),X135),X148))=>hAPP(hAPP(X27,X123),X135)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X29,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X149),hAPP(hAPP(c_Set_Oinsert(X4),X123),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(X29,tc_HOL_Obool)),tc_fun(X29,tc_HOL_Obool),X4),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X29,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3,X3,X147),hAPP(hAPP(c_Set_Oinsert(X3),X135),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))),X27)))))<=c_Equiv__Relations_Oequiv(X3,X148,X147))<=c_Equiv__Relations_Oequiv(X4,X150,X149)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__equiv__class2)). 4.46/4.67 fof(fact_Body__sound__lemma, axiom, ![X287, X80, X28, X82, X4]:(c_Hoare__Mirabelle_Ohoare__valids(X4,X82,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X4),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X4)),X28)),c_Com_Ocom_OBODY)),X80)),X287))<=c_Hoare__Mirabelle_Ohoare__valids(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool)),X82),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X4),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X4)),X28)),c_Com_Ocom_OBODY)),X80)),X287)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X4),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X4)),X28)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X80)),X287))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Body__sound__lemma)). 4.46/4.67 fof(fact_setsum__Sigma, axiom, ![X27, X1, X3, X2, X4, X29]:(class_Groups_Ocomm__monoid__add(X29)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X4,X3),X29),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,X29),X27)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),X1))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X29),hAPP(hAPP(c_COMBS(X4,tc_fun(X3,tc_HOL_Obool),X29),hAPP(hAPP(c_COMBB(tc_fun(X3,X29),tc_fun(tc_fun(X3,tc_HOL_Obool),X29),X4),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X29)),X27)),X1)),X2)<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X1,X42))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__Sigma)). 4.46/4.67 fof(fact_hoare__derivs_OBody, axiom, ![X287, X80, X28, X82, X4]:(c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X4),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X4)),X28)),c_Com_Ocom_OBODY)),X80)),X287))<=c_Hoare__Mirabelle_Ohoare__derivs(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool)),X82),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X4),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X4)),X28)),c_Com_Ocom_OBODY)),X80)),X287)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X4),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X4,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X4)),X28)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X80)),X287))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hoare__derivs_OBody)). 4.46/4.67 fof(fact_enum__fun__def, axiom, ![X3, X4]:(hAPP(hAPP(c_List_Omap(tc_List_Olist(X3),tc_fun(X4,X3)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_Option_Ooption(X3)),tc_fun(X4,X3),tc_List_Olist(X3)),c_Fun_Ocomp(tc_Option_Ooption(X3),X3,X4,c_Option_Othe(X3))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X4,X3)),tc_fun(X4,tc_Option_Ooption(X3)),tc_List_Olist(X3)),c_Map_Omap__of(X4,X3)),hAPP(c_List_Ozip(X4,X3),c_Enum_Oenum__class_Oenum(X4))))),c_Enum_On__lists(X3,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_Enum_Oenum__class_Oenum(X4)),c_Enum_Oenum__class_Oenum(X3)))=c_Enum_Oenum__class_Oenum(tc_fun(X4,X3))<=(class_Enum_Oenum(X4)&class_Enum_Oenum(X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__fun__def)). 4.46/4.67 fof(fact_enum__all__fun__def, axiom, ![X28, X4, X3]:((class_Enum_Oenum(X4)&class_Enum_Oenum(X3))=>(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X4,X3)),X28))<=>c_Enum_Oall__n__lists(X3,hAPP(hAPP(c_COMBB(tc_fun(X4,X3),tc_HOL_Obool,tc_List_Olist(X3)),X28),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_Option_Ooption(X3)),tc_fun(X4,X3),tc_List_Olist(X3)),c_Fun_Ocomp(tc_Option_Ooption(X3),X3,X4,c_Option_Othe(X3))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X4,X3)),tc_fun(X4,tc_Option_Ooption(X3)),tc_List_Olist(X3)),c_Map_Omap__of(X4,X3)),hAPP(c_List_Ozip(X4,X3),c_Enum_Oenum__class_Oenum(X4))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_Enum_Oenum__class_Oenum(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__all__fun__def)). 4.46/4.67 fof(fact_enum__ex__fun__def, axiom, ![X28, X4, X3]:((hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X4,X3)),X28))<=>c_Enum_Oex__n__lists(X3,hAPP(hAPP(c_COMBB(tc_fun(X4,X3),tc_HOL_Obool,tc_List_Olist(X3)),X28),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_Option_Ooption(X3)),tc_fun(X4,X3),tc_List_Olist(X3)),c_Fun_Ocomp(tc_Option_Ooption(X3),X3,X4,c_Option_Othe(X3))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X4,X3)),tc_fun(X4,tc_Option_Ooption(X3)),tc_List_Olist(X3)),c_Map_Omap__of(X4,X3)),hAPP(c_List_Ozip(X4,X3),c_Enum_Oenum__class_Oenum(X4))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_Enum_Oenum__class_Oenum(X4))))<=(class_Enum_Oenum(X3)&class_Enum_Oenum(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__ex__fun__def)). 4.46/4.67 fof(fact_fold__image__Un__Int, axiom, ![X50, X1, X2, X4, X3]:(class_Groups_Ocomm__monoid__mult(X3)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),X50),c_Groups_Oone__class_Oone(X3)),X2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),X50),c_Groups_Oone__class_Oone(X3)),X1))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),X50),c_Groups_Oone__class_Oone(X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),X50),c_Groups_Oone__class_Oone(X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__Un__Int)). 4.46/4.67 fof(fact_fold__image__Un__one, axiom, ![X27, X110, X46, X4, X3]:(class_Groups_Ocomm__monoid__mult(X3)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X46))=>((![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X46),X110)))=>c_Groups_Oone__class_Oone(X3)=hAPP(X27,X42))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),X27),c_Groups_Oone__class_Oone(X3)),X46)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),X27),c_Groups_Oone__class_Oone(X3)),X110))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),X27),c_Groups_Oone__class_Oone(X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X46),X110)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X110))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__Un__one)). 4.46/4.67 fof(fact_quotient__diff1, axiom, ![X18, X2, X16, X4]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X2),X16)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X16))=hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X16)<=hBOOL(hAPP(hAPP(c_member(X4),X18),X2)))<=c_Fun_Oinj__on(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X4),c_Equiv__Relations_Oquotient(X4)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Set_Oinsert(X4)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X16),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotient__diff1)). 4.46/4.67 fof(fact_setprod__Un, axiom, ![X27, X1, X2, X4, X3]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>(![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))=>c_Groups_Ozero__class_Ozero(X3)!=hAPP(X27,X42))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),X1))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Fields_Ofield(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__Un)). 4.46/4.67 fof(fact_fold__image__distrib, axiom, ![X58, X50, X2, X4, X3]:(class_Groups_Ocomm__monoid__mult(X3)=>(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),X50),c_Groups_Oone__class_Oone(X3)),X2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),X58),c_Groups_Oone__class_Oone(X3)),X2))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),hAPP(hAPP(c_COMBS(X4,X3,X3),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,X3),X4),c_Groups_Otimes__class_Otimes(X3)),X50)),X58)),c_Groups_Oone__class_Oone(X3)),X2)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__distrib)). 4.46/4.67 fof(fact_setprod__cartesian__product, axiom, ![X2, X1, X27, X29, X3, X4]:(class_Groups_Ocomm__monoid__mult(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X3,X29),X4),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X29,X4),X27)),hAPP(hAPP(c_Product__Type_OSigma(X3,X29),X2),hAPP(c_COMBK(tc_fun(X29,tc_HOL_Obool),X3),X1)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X4),hAPP(hAPP(c_COMBC(X3,tc_fun(X29,tc_HOL_Obool),X4),hAPP(hAPP(c_COMBB(tc_fun(X29,X4),tc_fun(tc_fun(X29,tc_HOL_Obool),X4),X3),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X29,X4)),X27)),X1)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__cartesian__product)). 4.46/4.67 fof(fact_setsum__cartesian__product, axiom, ![X2, X1, X27, X29, X3, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X3,X29),X4),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X29,X4),X27)),hAPP(hAPP(c_Product__Type_OSigma(X3,X29),X2),hAPP(c_COMBK(tc_fun(X29,tc_HOL_Obool),X3),X1)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),hAPP(hAPP(c_COMBC(X3,tc_fun(X29,tc_HOL_Obool),X4),hAPP(hAPP(c_COMBB(tc_fun(X29,X4),tc_fun(tc_fun(X29,tc_HOL_Obool),X4),X3),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29,X4)),X27)),X1)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__cartesian__product)). 4.46/4.67 fof(fact_setprod__Sigma, axiom, ![X27, X1, X3, X2, X4, X29]:(class_Groups_Ocomm__monoid__mult(X29)=>((![X42]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X1,X42)))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X2)))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X4,X3),X29),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,X29),X27)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),X1))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X29),hAPP(hAPP(c_COMBS(X4,tc_fun(X3,tc_HOL_Obool),X29),hAPP(hAPP(c_COMBB(tc_fun(X3,X29),tc_fun(tc_fun(X3,tc_HOL_Obool),X29),X4),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X29)),X27)),X1)),X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__Sigma)). 4.46/4.67 fof(fact_lexord__append__leftD, axiom, ![X16, X13, X23, X6, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Oappend(X4),X6),X23)),hAPP(hAPP(c_List_Oappend(X4),X6),X13))),c_List_Olexord(X4,X16)))=>(![X125]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X125),X125)),X16)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X23),X13)),c_List_Olexord(X4,X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__append__leftD)). 4.46/4.67 fof(fact_rel__comp__subset__Sigma, axiom, ![X52, X68, X29, X1, X2, X16, X3, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X29),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X3,X29),X16),X68)),hAPP(hAPP(c_Product__Type_OSigma(X4,X29),X2),hAPP(c_COMBK(tc_fun(X29,tc_HOL_Obool),X4),X52))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X29),tc_HOL_Obool)),X68),hAPP(hAPP(c_Product__Type_OSigma(X3,X29),X1),hAPP(c_COMBK(tc_fun(X29,tc_HOL_Obool),X3),X52)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X16),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__subset__Sigma)). 4.46/4.67 fof(fact_divmod__nat__rel__mult1__eq, axiom, ![X12, X111, X112, X10, X11]:((hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X11),X10),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X112)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X111)),X10))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X111),X10))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10)))<=hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X11,X10),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X112),X111)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel__mult1__eq)). 4.46/4.67 fof(fact_transpose__column, axiom, ![X24, X7, X4]:(c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X4))),X7)))=>(hAPP(hAPP(c_List_Onth(tc_List_Olist(X4)),X7),X24)=hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),X4),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_Nat_Onat,X4),c_List_Onth(X4)),X24)),hAPP(c_List_Ofilter(tc_List_Olist(X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X4)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24)),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),c_List_Otranspose(X4,X7)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__column)). 4.46/4.67 fof(fact_single__valued__confluent, axiom, ![X35, X5, X6, X16, X4]:(c_Relation_Osingle__valued(X4,X4,X16)=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_Transitive__Closure_Ortrancl(X4,X16)))=>((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X35),X5)),c_Transitive__Closure_Ortrancl(X4,X16)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X5),X35)),c_Transitive__Closure_Ortrancl(X4,X16))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X35)),c_Transitive__Closure_Ortrancl(X4,X16)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__confluent)). 4.46/4.67 fof(fact_zmult1__lemma, axiom, ![X12, X111, X112, X10, X11]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,X10),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X112),X111)))=>(X10!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X11),X10),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X112)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X111)),X10))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X111),X10)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult1__lemma)). 4.46/4.67 fof(fact_map__of__zip__upd, axiom, ![X35, X5, X6, X88, X7, X3, X32, X4]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X88)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X7)=>(~(hBOOL(hAPP(hAPP(c_member(X3),X6),hAPP(c_List_Oset(X3),X7))))=>(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X4)),hAPP(c_Map_Omap__of(X3,X4),hAPP(hAPP(c_List_Ozip(X3,X4),X7),X88))),X6),hAPP(c_Option_Ooption_OSome(X4),X35))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X4)),hAPP(c_Map_Omap__of(X3,X4),hAPP(hAPP(c_List_Ozip(X3,X4),X7),X32))),X6),hAPP(c_Option_Ooption_OSome(X4),X5))=>hAPP(c_Map_Omap__of(X3,X4),hAPP(hAPP(c_List_Ozip(X3,X4),X7),X88))=hAPP(c_Map_Omap__of(X3,X4),hAPP(hAPP(c_List_Ozip(X3,X4),X7),X32)))))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X7)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__zip__upd)). 4.46/4.67 fof(fact_map__of__mapk__SomeI, axiom, ![X6, X45, X64, X29, X27, X3, X4]:((hAPP(c_Option_Ooption_OSome(X29),X6)=hAPP(hAPP(c_Map_Omap__of(X3,X29),hAPP(hAPP(c_List_Omap(tc_prod(X4,X29),tc_prod(X3,X29)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X29,tc_prod(X3,X29)),hAPP(hAPP(c_COMBB(X3,tc_fun(X29,tc_prod(X3,X29)),X4),c_Product__Type_OPair(X3,X29)),X27))),X64)),hAPP(X27,X45))<=hAPP(hAPP(c_Map_Omap__of(X4,X29),X64),X45)=hAPP(c_Option_Ooption_OSome(X29),X6))<=c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__mapk__SomeI)). 4.46/4.67 fof(fact_nth__nth__transpose__sorted, axiom, ![X25, X24, X7, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),hAPP(c_List_Ofilter(tc_List_Olist(X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X4)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24)),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),X7))))=>hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Onth(tc_List_Olist(X4)),c_List_Otranspose(X4,X7)),X24)),X25)=hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Onth(tc_List_Olist(X4)),X7),X25)),X24))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),c_List_Otranspose(X4,X7)))))<=c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X4))),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__nth__transpose__sorted)). 4.46/4.67 fof(fact_setsum__commute, axiom, ![X2, X1, X27, X29, X3, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29,X4),hAPP(hAPP(c_COMBC(X29,tc_fun(X3,tc_HOL_Obool),X4),hAPP(hAPP(c_COMBB(tc_fun(X3,X4),tc_fun(tc_fun(X3,tc_HOL_Obool),X4),X29),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4)),hAPP(c_COMBC(X3,X29,X4),X27))),X2)),X1)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),hAPP(hAPP(c_COMBC(X3,tc_fun(X29,tc_HOL_Obool),X4),hAPP(hAPP(c_COMBB(tc_fun(X29,X4),tc_fun(tc_fun(X29,tc_HOL_Obool),X4),X3),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29,X4)),X27)),X1)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__commute)). 4.46/4.67 fof(fact_map__upds__append1, axiom, ![X6, X22, X32, X3, X7, X4]:(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),c_Map_Omap__upds(X4,X3,X22,X7,X32)),X6),hAPP(c_Option_Ooption_OSome(X3),hAPP(hAPP(c_List_Onth(X3),X32),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))))=c_Map_Omap__upds(X4,X3,X22,hAPP(hAPP(c_List_Oappend(X4),X7),hAPP(hAPP(c_List_Olist_OCons(X4),X6),c_List_Olist_ONil(X4))),X32)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upds__append1)). 4.46/4.67 fof(fact_rtrancl__listrel1__ConsI2, axiom, ![X32, X7, X16, X5, X6, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X4),c_List_Olistrel1(X4,X16))))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)),hAPP(hAPP(c_List_Olist_OCons(X4),X5),X32))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X4),c_List_Olistrel1(X4,X16)))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_Transitive__Closure_Ortrancl(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__listrel1__ConsI2)). 4.46/4.67 fof(fact_listsum__addf, axiom, ![X7, X50, X27, X3, X4]:(hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X3,X4),hAPP(hAPP(c_COMBS(X3,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X3),c_Groups_Oplus__class_Oplus(X4)),X27)),X50)),X7))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X3,X4),X27),X7))),hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X3,X4),X50),X7)))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__addf)). 4.46/4.67 fof(fact_setprod__Un__one, axiom, ![X27, X110, X46, X4, X3]:(class_Groups_Ocomm__monoid__mult(X3)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X46))=>((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),X46)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),X110))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X46),X110))<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X46),X110)))=>c_Groups_Oone__class_Oone(X3)=hAPP(X27,X42)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X110))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__Un__one)). 4.46/4.67 fof(fact_setsum__Un__zero, axiom, ![X27, X110, X46, X4, X3]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X110))=>(![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X46),X110)))=>c_Groups_Ozero__class_Ozero(X3)=hAPP(X27,X42))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X46)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X110))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X46),X110))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X46)))<=class_Groups_Ocomm__monoid__add(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__Un__zero)). 4.46/4.67 fof(fact_setprod_Ounion__inter__neutral, axiom, ![X50, X1, X2, X4, X3]:(class_Groups_Ocomm__monoid__mult(X3)=>(((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),X1))<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))=>hAPP(X50,X42)=c_Groups_Oone__class_Oone(X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod_Ounion__inter__neutral)). 4.46/4.67 fof(fact_setsum_Ounion__inter__neutral, axiom, ![X50, X1, X2, X4, X3]:(class_Groups_Ocomm__monoid__add(X3)=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),X1))<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))=>hAPP(X50,X42)=c_Groups_Ozero__class_Ozero(X3))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum_Ounion__inter__neutral)). 4.46/4.67 fof(fact_listsum__subtractf, axiom, ![X7, X50, X27, X3, X4]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X3,X4),X27),X7))),hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X3,X4),X50),X7)))=hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X3,X4),hAPP(hAPP(c_COMBS(X3,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X3),c_Groups_Ominus__class_Ominus(X4)),X27)),X50)),X7))<=class_Groups_Oab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__subtractf)). 4.46/4.67 fof(fact_reduction__pair__def, axiom, ![X28, X4]:(c_FunDef_Oreduction__pair(X4,X28)<=>(c_Wellfounded_Owf(X4,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X28))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X28)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X28))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X28))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_reduction__pair__def)). 4.46/4.67 fof(fact_rtrancl__Un__separatorE, axiom, ![X80, X28, X37, X18, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),c_Transitive__Closure_Ortrancl(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X28),X80))))=>(![X42]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X42)),c_Transitive__Closure_Ortrancl(X4,X28)))=>![X44]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X44)),X80))=>X44=X42))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),c_Transitive__Closure_Ortrancl(X4,X28))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__Un__separatorE)). 4.46/4.67 fof(fact_rtrancl__Un__separator__converseE, axiom, ![X80, X28, X37, X18, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),c_Transitive__Closure_Ortrancl(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X28),X80))))=>(![X42]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X37)),c_Transitive__Closure_Ortrancl(X4,X28)))=>![X44]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X44),X42)),X80))=>X42=X44))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),c_Transitive__Closure_Ortrancl(X4,X28))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__Un__separator__converseE)). 4.46/4.67 fof(fact_image__INT, axiom, ![X25, X1, X2, X29, X52, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,X52)=>((hBOOL(hAPP(hAPP(c_member(X29),X25),X2))=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29,tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X29),c_Set_Oimage(X4,X3,X27)),X1))=hAPP(c_Set_Oimage(X4,X3,X27),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29,tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(X1,X42)),X52))<=hBOOL(hAPP(hAPP(c_member(X29),X42),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__INT)). 4.46/4.67 fof(fact_lexord__append__left__rightI, axiom, ![X5, X6, X23, X16, X37, X18, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),X16))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Oappend(X4),X23),hAPP(hAPP(c_List_Olist_OCons(X4),X18),X6))),hAPP(hAPP(c_List_Oappend(X4),X23),hAPP(hAPP(c_List_Olist_OCons(X4),X37),X5)))),c_List_Olexord(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__append__left__rightI)). 4.46/4.67 fof(fact_snoc__listrel1__snoc__iff, axiom, ![X16, X5, X32, X6, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Oappend(X4),X7),hAPP(hAPP(c_List_Olist_OCons(X4),X6),c_List_Olist_ONil(X4)))),hAPP(hAPP(c_List_Oappend(X4),X32),hAPP(hAPP(c_List_Olist_OCons(X4),X5),c_List_Olist_ONil(X4))))),c_List_Olistrel1(X4,X16)))<=>((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),X16))&X32=X7)|(X6=X5&hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)),c_List_Olistrel1(X4,X16)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snoc__listrel1__snoc__iff)). 4.46/4.67 fof(fact_nth__transpose, axiom, ![X7, X4, X24]:(hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),X4),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_Nat_Onat,X4),c_List_Onth(X4)),X24)),hAPP(c_List_Ofilter(tc_List_Olist(X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X4)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24)),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),X7))=hAPP(hAPP(c_List_Onth(tc_List_Olist(X4)),c_List_Otranspose(X4,X7)),X24)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),c_List_Otranspose(X4,X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__transpose)). 4.46/4.67 fof(fact_folding__image__simple_Ounion__inter__neutral, axiom, ![X1, X2, X62, X50, X35, X27, X3, X4]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1))=>(![X42]:(hBOOL(hAPP(hAPP(c_member(X3),X42),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X2),X1)))=>X35=hAPP(X50,X42))=>hAPP(hAPP(X27,hAPP(X62,X2)),hAPP(X62,X1))=hAPP(X62,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))<=c_Finite__Set_Ofolding__image__simple(X4,X3,X27,X35,X50,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Ounion__inter__neutral)). 4.46/4.67 fof(fact_same__fstI, axiom, ![X4, X26, X5, X259, X3, X6, X28]:((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X4,X3),tc_prod(X4,X3))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X4,X3),tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X6),X259)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X6),X5))),c_Recdef_Osame__fst(X4,X3,X28,X26)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X259),X5)),hAPP(X26,X6))))<=hBOOL(hAPP(X28,X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_same__fstI)). 4.46/4.67 fof(fact_rel__pow__Suc__I2, axiom, ![X14, X35, X26, X5, X6, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),X26))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X35)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),hAPP(c_Nat_OSuc,X14)),X26)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X5),X35)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X14),X26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__Suc__I2)). 4.46/4.67 fof(fact_fold__Un__disjoint, axiom, ![X50, X1, X2, X4, X3]:((((hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),X50),c_Groups_Oone__class_Oone(X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),X50),c_Groups_Oone__class_Oone(X3)),X2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),X50),c_Groups_Oone__class_Oone(X3)),X1))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Groups_Ocomm__monoid__mult(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__Un__disjoint)). 4.46/4.67 fof(fact_divmod__nat__rel__mult2__eq, axiom, ![X10, X111, X112, X11, X12]:(((hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X12,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X10)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X112),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X112,X10))),X111))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X11)))<=hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X12,X11),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X112),X111)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel__mult2__eq)). 4.46/4.67 fof(fact_setsum__UNION__zero, axiom, ![X27, X46, X4, X3]:(class_Groups_Ocomm__monoid__add(X3)=>((![X42]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X42))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X42),X46)))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X46))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X4,tc_HOL_Obool),X3),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27)),X46)<=![X179]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X179),X46))=>![X180]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X180),X46))=>(X179!=X180=>![X42]:((hBOOL(hAPP(hAPP(c_member(X4),X42),X180))=>hAPP(X27,X42)=c_Groups_Ozero__class_Ozero(X3))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X179))))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,tc_HOL_Obool)),X46)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__UNION__zero)). 4.46/4.67 fof(fact_rel__pow__Suc__I, axiom, ![X35, X26, X14, X5, X6, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X35)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),hAPP(c_Nat_OSuc,X14)),X26)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X5),X35)),X26)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X14),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__Suc__I)). 4.46/4.67 fof(fact_listrel_OCons, axiom, ![X32, X7, X16, X5, X6, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),X16))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)),hAPP(hAPP(c_List_Olist_OCons(X4),X5),X32))),c_List_Olistrel(X4,X16)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)),c_List_Olistrel(X4,X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel_OCons)). 4.46/4.67 fof(fact_transpose__column__length, axiom, ![X24, X7, X4]:(c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X4))),X7)))=>(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X4)),X7),X24))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),hAPP(c_List_Ofilter(tc_List_Olist(X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X4)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24)),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),c_List_Otranspose(X4,X7)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__column__length)). 4.46/4.67 fof(fact_zmult2__lemma, axiom, ![X10, X111, X112, X11, X12]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,X11),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X112),X111)))=>(X11!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))=>hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X10)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X112),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),c_Divides_Odiv__class_Omod(tc_Int_Oint,X112,X10))),X111))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult2__lemma)). 4.46/4.67 fof(fact_lexord__linear, axiom, ![X5, X6, X16, X4]:(![X125, X119]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X119),X125)),X16))|X119=X125|hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X125),X119)),X16)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X6),X5)),c_List_Olexord(X4,X16)))|X6=X5|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X5),X6)),c_List_Olexord(X4,X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__linear)). 4.46/4.67 fof(fact_max__ext__additive, axiom, ![X65, X52, X26, X1, X2, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X52),X65)),c_Wellfounded_Omax__ext(X4,X26)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X52)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X1),X65))),c_Wellfounded_Omax__ext(X4,X26))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X2),X1)),c_Wellfounded_Omax__ext(X4,X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__ext__additive)). 4.46/4.67 fof(fact_congruent__def, axiom, ![X27, X16, X3, X4]:(![X42]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X42),X16))=>hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,X3),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X4,X3),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X3,tc_HOL_Obool,X4)),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,tc_HOL_Obool),X4),c_fequal),X27))),X27)),X42)))<=>c_Equiv__Relations_Ocongruent(X4,X3,X16,X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_congruent__def)). 4.46/4.67 fof(fact_foldl__apply, axiom, ![X68, X50, X58, X27, X3, X29, X7, X4]:(hAPP(c_List_Ofoldl(X29,X4,hAPP(c_COMBC(X4,X29,X29),X27),hAPP(X58,X68)),X7)=hAPP(X58,hAPP(c_List_Ofoldl(X3,X4,hAPP(c_COMBC(X4,X3,X3),X50),X68),X7))<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7)))=>hAPP(c_Fun_Ocomp(X3,X29,X3,X58),hAPP(X50,X42))=hAPP(c_Fun_Ocomp(X29,X29,X3,hAPP(X27,X42)),X58))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__apply)). 4.46/4.67 fof(fact_rtrancl__listrel1__ConsI1, axiom, ![X6, X16, X32, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X32))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X4),c_List_Olistrel1(X4,X16))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X4),c_List_Olistrel1(X4,X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__listrel1__ConsI1)). 4.46/4.67 fof(fact_setsum__shift__bounds__nat__ivl, axiom, ![X14, X45, X22, X27, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X45)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X45)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Nat_Onat),X27),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X45))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__shift__bounds__nat__ivl)). 4.46/4.67 fof(fact_setsum__mono3, axiom, ![X27, X2, X1, X4, X3]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X1)))<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X1),X2)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(X27,X42)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))))<=(class_Groups_Oordered__ab__semigroup__add(X3)&class_Groups_Ocomm__monoid__add(X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__mono3)). 4.46/4.67 fof(fact_setsum__Un, axiom, ![X27, X1, X2, X4, X3]:(class_Groups_Oab__group__add(X3)=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X1))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__Un)). 4.46/4.67 fof(fact_congruent2__implies__congruent__UN, axiom, ![X18, X27, X29, X147, X148, X3, X149, X150, X4]:(c_Equiv__Relations_Oequiv(X4,X150,X149)=>(((c_Equiv__Relations_Ocongruent(X4,tc_fun(X29,tc_HOL_Obool),X149,hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(X29,tc_HOL_Obool)),tc_fun(X29,tc_HOL_Obool),X4),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X29,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3,X3,X147),hAPP(hAPP(c_Set_Oinsert(X3),X18),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))),X27))<=hBOOL(hAPP(hAPP(c_member(X3),X18),X148)))<=c_Equiv__Relations_Ocongruent2(X4,X3,tc_fun(X29,tc_HOL_Obool),X149,X147,X27))<=c_Equiv__Relations_Oequiv(X3,X148,X147))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_congruent2__implies__congruent__UN)). 4.46/4.67 fof(fact_rel__pow__E2, axiom, ![X26, X14, X35, X6, X4]:((~(![X44, X90]:((~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X44),X35)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X90),X26))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X44)),X26)))<=hAPP(c_Nat_OSuc,X90)=X14))<=(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X14=>X35!=X6))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X35)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X14),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__E2)). 4.46/4.67 fof(fact_rel__pow__E, axiom, ![X26, X14, X35, X6, X4]:((~(![X44, X90]:((~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X44),X35)),X26)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X44)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X90),X26))))<=X14=hAPP(c_Nat_OSuc,X90)))<=(X14=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>X6!=X35))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X35)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X14),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__E)). 4.46/4.67 fof(fact_setsum__shift__bounds__cl__nat__ivl, axiom, ![X14, X45, X22, X27, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X45),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X45)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Nat_Onat),X27),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X45))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X22,X14))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__shift__bounds__cl__nat__ivl)). 4.46/4.67 fof(fact_setsum__Un__nat, axiom, ![X27, X1, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X27),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X27),X1))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__Un__nat)). 4.46/4.67 fof(fact_zdiv__mono2__neg__lemma, axiom, ![X177, X178, X91, X111, X112, X11]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X91),X178)),X177)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X112)),X111)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X91),X178)),X177)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X111),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X177))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X91),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X178),X112)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__mono2__neg__lemma)). 4.46/4.67 fof(fact_fold__graph_H_Oequations_I2_J, axiom, ![X297, X123, X135, X253, X250, X3, X4]:((?[X42, X44]:((c_Nitpick_Ofold__graph_H(X4,X3,X250,X253,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X135),hAPP(hAPP(c_Set_Oinsert(X4),X42),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X44)&hBOOL(hAPP(hAPP(c_member(X4),X42),X135)))&hAPP(hAPP(X250,X123),X297)=hAPP(hAPP(X250,X42),X44))|(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X135&X253=hAPP(hAPP(X250,X123),X297)))<=>c_Nitpick_Ofold__graph_H(X4,X3,X250,X253,X135,hAPP(hAPP(X250,X123),X297))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph_H_Oequations_I2_J)). 4.46/4.67 fof(fact_pair__leqI2, axiom, ![X64, X68, X37, X18]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18),X37))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X68),X64))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X18),X68)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X37),X64))),c_FunDef_Opair__leq)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__leqI2)). 4.46/4.67 fof(fact_pair__lessI2, axiom, ![X64, X68, X37, X18]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18),X37))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X68),X64))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X18),X68)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X37),X64))),c_FunDef_Opair__less)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__lessI2)). 4.46/4.67 fof(fact_setsum__mono2, axiom, ![X27, X2, X1, X4, X3]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X1)))<=![X119]:(hBOOL(hAPP(hAPP(c_member(X4),X119),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X1),X2)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(X27,X119)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1)))<=class_Groups_Oordered__comm__monoid__add(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__mono2)). 4.46/4.67 fof(fact_setprod__Un__Int, axiom, ![X50, X1, X2, X4, X3]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),X1))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))))<=class_Groups_Ocomm__monoid__mult(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__Un__Int)). 4.46/4.67 fof(fact_setsum__Un__Int, axiom, ![X50, X1, X2, X4, X3]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),X1))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Groups_Ocomm__monoid__add(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__Un__Int)). 4.46/4.67 fof(fact_Cons__listrel1__Cons, axiom, ![X16, X32, X5, X7, X6, X4]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)),c_List_Olistrel1(X4,X16)))&X5=X6)|(X32=X7&hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),X16))))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)),hAPP(hAPP(c_List_Olist_OCons(X4),X5),X32))),c_List_Olistrel1(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cons__listrel1__Cons)). 4.46/4.67 fof(fact_listrel__iff__nth, axiom, ![X16, X32, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)),c_List_Olistrel(X4,X16)))<=>(![X199]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X199),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(hAPP(c_List_Onth(X4),X7),X199)),hAPP(hAPP(c_List_Onth(X4),X32),X199))),X16)))&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__iff__nth)). 4.46/4.67 fof(fact_zdiv__mono2__lemma, axiom, ![X177, X178, X91, X111, X112, X11]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X112)),X111)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X91),X178)),X177)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X91),X178)),X177)))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X111))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X91),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X112),X178)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X177),X91))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__mono2__lemma)). 4.46/4.67 fof(fact_min__max_OInf__fin_Ounion__inter, axiom, ![X1, X2, X4]:((((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X2)),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Ounion__inter)). 4.46/4.67 fof(fact_setprod__dividef, axiom, ![X50, X27, X2, X4, X3]:((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),hAPP(hAPP(c_COMBS(X4,X3,X3),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,X3),X4),c_Rings_Oinverse__class_Odivide(X3)),X27)),X50)),X2)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Fields_Ofield__inverse__zero(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__dividef)). 4.46/4.67 fof(fact_max__ext_Ointros, axiom, ![X26, X76, X173, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X173))=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X76=>(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X173),X76)),c_Wellfounded_Omax__ext(X4,X26)))<=![X42]:(?[X66]:(hBOOL(hAPP(hAPP(c_member(X4),X66),X76))&hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X66)),X26)))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X173)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X76)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__ext_Ointros)). 4.46/4.67 fof(fact_min__max_OSup__fin_Ounion__inter, axiom, ![X1, X2, X4]:(class_Orderings_Olinorder(X4)=>(((hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X2)),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X1))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Ounion__inter)). 4.46/4.67 fof(fact_prod__fun__imageE, axiom, ![X26, X50, X27, X59, X29, X39, X3, X4]:(~(![X42, X44]:(~(hBOOL(hAPP(hAPP(c_member(tc_prod(X29,X59)),hAPP(hAPP(c_Product__Type_OPair(X29,X59),X42),X44)),X26)))<=hAPP(hAPP(c_Product__Type_OPair(X4,X3),hAPP(X27,X42)),hAPP(X50,X44))=X39))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),X39),hAPP(c_Set_Oimage(tc_prod(X29,X59),tc_prod(X4,X3),c_Product__Type_Omap__pair(X29,X4,X59,X3,X27,X50)),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_prod__fun__imageE)). 4.46/4.67 fof(fact_map__of__eqI, axiom, ![X32, X7, X3, X4]:(hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Omap(tc_prod(X4,X3),X4),c_Product__Type_Ofst(X4,X3)),X32))=hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Omap(tc_prod(X4,X3),X4),c_Product__Type_Ofst(X4,X3)),X7))=>(hAPP(c_Map_Omap__of(X4,X3),X32)=hAPP(c_Map_Omap__of(X4,X3),X7)<=![X42]:(hAPP(hAPP(c_Map_Omap__of(X4,X3),X7),X42)=hAPP(hAPP(c_Map_Omap__of(X4,X3),X32),X42)<=hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Omap(tc_prod(X4,X3),X4),c_Product__Type_Ofst(X4,X3)),X7))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__eqI)). 4.46/4.67 fof(fact_listsum__mono, axiom, ![X50, X27, X7, X4, X3]:((class_Groups_Oordered__ab__semigroup__add(X3)&class_Groups_Omonoid__add(X3))=>(![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(X27,X42)),hAPP(X50,X42)))<=hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_List_Omonoid__add__class_Olistsum(X3),hAPP(hAPP(c_List_Omap(X4,X3),X27),X7))),hAPP(c_List_Omonoid__add__class_Olistsum(X3),hAPP(hAPP(c_List_Omap(X4,X3),X50),X7)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__mono)). 4.46/4.67 fof(fact_abs__diff__triangle__ineq, axiom, ![X133, X10, X11, X12, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X133)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X10))),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X133)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__diff__triangle__ineq)). 4.46/4.67 fof(fact_select__weight__member, axiom, ![X68, X7, X4]:(hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Product__Type_Ofst(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X4,X7),X68))),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X4),X4),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X4)),X7))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X4),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X4)),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select__weight__member)). 4.46/4.67 fof(fact_folding_Ocommute__left__comp_H_H, axiom, ![X50, X29, X1, X2, X62, X27, X3, X4]:(((hAPP(c_Fun_Ocomp(X3,X3,X29,hAPP(X62,X1)),hAPP(c_Fun_Ocomp(X3,X3,X29,hAPP(X62,X2)),X50))=hAPP(c_Fun_Ocomp(X3,X3,X29,hAPP(X62,X2)),hAPP(c_Fun_Ocomp(X3,X3,X29,hAPP(X62,X1)),X50))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=c_Finite__Set_Ofolding(X4,X3,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ocommute__left__comp_H_H)). 4.46/4.67 fof(fact_UN__equiv__class__inject, axiom, ![X76, X173, X27, X3, X16, X2, X4]:(c_Equiv__Relations_Oequiv(X4,X2,X16)=>(c_Equiv__Relations_Ocongruent(X4,tc_fun(X3,tc_HOL_Obool),X16,X27)=>(((hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X76),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X2),X16)))=>(X173=X76<=![X42]:(![X44]:(hBOOL(hAPP(hAPP(c_member(X4),X44),X2))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X44)),X16))<=hAPP(X27,X42)=hAPP(X27,X44)))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X2)))))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X173),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X2),X16))))<=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X76),X27)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X173),X27)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__equiv__class__inject)). 4.46/4.67 fof(fact_intrel__iff, axiom, ![X13, X23, X5, X6]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23),X5)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X13)<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23),X13))),c_Int_Ointrel))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_intrel__iff)). 4.46/4.67 fof(fact_lexord__append__leftI, axiom, ![X6, X16, X13, X23, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X23),X13)),c_List_Olexord(X4,X16)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Oappend(X4),X6),X23)),hAPP(hAPP(c_List_Oappend(X4),X6),X13))),c_List_Olexord(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__append__leftI)). 4.46/4.67 fof(fact_listrel1I2, axiom, ![X6, X16, X32, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X32))),c_List_Olistrel1(X4,X16)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)),c_List_Olistrel1(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1I2)). 4.46/4.67 fof(fact_setsum__reindex__nonzero, axiom, ![X3, X58, X27, X46, X4, X29]:(((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X29),X58),hAPP(c_Set_Oimage(X4,X3,X27),X46))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X29),hAPP(c_Fun_Ocomp(X3,X29,X4,X58),X27)),X46)<=![X42]:(![X44]:(((hAPP(X58,hAPP(X27,X42))=c_Groups_Ozero__class_Ozero(X29)<=hAPP(X27,X44)=hAPP(X27,X42))<=X42!=X44)<=hBOOL(hAPP(hAPP(c_member(X4),X44),X46)))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X46))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X46)))<=class_Groups_Ocomm__monoid__add(X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__reindex__nonzero)). 4.46/4.67 fof(fact_Sigma__mono, axiom, ![X65, X1, X3, X52, X2, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),X1)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X52),X65)))<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(X1,X42)),hAPP(X65,X42)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X52))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__mono)). 4.46/4.67 fof(fact_total__on__def, axiom, ![X16, X2, X4]:(![X42]:(![X66]:(hBOOL(hAPP(hAPP(c_member(X4),X66),X2))=>((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X66)),X16))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X66),X42)),X16)))<=X42!=X66))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X2)))<=>c_Relation_Ototal__on(X4,X2,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_total__on__def)). 4.46/4.67 fof(fact_UN__equiv__class__type, axiom, ![X1, X173, X27, X3, X16, X2, X4]:(c_Equiv__Relations_Oequiv(X4,X2,X16)=>(c_Equiv__Relations_Ocongruent(X4,tc_fun(X3,tc_HOL_Obool),X16,X27)=>(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X173),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X2),X16)))=>(![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),hAPP(X27,X42)),X1)))=>hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X173),X27)),X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__equiv__class__type)). 4.46/4.67 fof(fact_reduction__pair__lemma, axiom, ![X46, X26, X28, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X26),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X28)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X46),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X28)))=>(c_Wellfounded_Owf(X4,X46)=>c_Wellfounded_Owf(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X26),X46)))))<=c_FunDef_Oreduction__pair(X4,X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_reduction__pair__lemma)). 4.46/4.67 fof(fact_map__pair__imageI, axiom, ![X50, X27, X59, X29, X26, X37, X18, X3, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X18),X37)),X26))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X29,X59)),hAPP(hAPP(c_Product__Type_OPair(X29,X59),hAPP(X27,X18)),hAPP(X50,X37))),hAPP(c_Set_Oimage(tc_prod(X4,X3),tc_prod(X29,X59),c_Product__Type_Omap__pair(X4,X29,X3,X59,X27,X50)),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair__imageI)). 4.46/4.67 fof(fact_folding_Ocommute__left__comp_H, axiom, ![X50, X6, X29, X2, X62, X27, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(c_Fun_Ocomp(X3,X3,X29,hAPP(X62,X2)),hAPP(c_Fun_Ocomp(X3,X3,X29,hAPP(X27,X6)),X50))=hAPP(c_Fun_Ocomp(X3,X3,X29,hAPP(X27,X6)),hAPP(c_Fun_Ocomp(X3,X3,X29,hAPP(X62,X2)),X50)))<=c_Finite__Set_Ofolding(X4,X3,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ocommute__left__comp_H)). 4.46/4.67 fof(fact_fun__left__comm_Ofold__graph__insertE__aux, axiom, ![X18, X5, X2, X35, X27, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X3,X27,X35,X2),X5))=>(?[X213]:(hAPP(hAPP(X27,X18),X213)=X5&hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X3,X27,X35,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X213)))<=hBOOL(hAPP(hAPP(c_member(X4),X18),X2))))<=c_Finite__Set_Ofun__left__comm(X4,X3,X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__graph__insertE__aux)). 4.46/4.67 fof(fact_setprod__timesf, axiom, ![X2, X50, X27, X3, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X4),hAPP(hAPP(c_COMBS(X3,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X3),c_Groups_Otimes__class_Otimes(X4)),X27)),X50)),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X4),X27),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X4),X50),X2))<=class_Groups_Ocomm__monoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__timesf)). 4.46/4.67 fof(fact_rel__compI, axiom, ![X68, X39, X29, X16, X37, X18, X3, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X29)),hAPP(hAPP(c_Product__Type_OPair(X4,X29),X18),X39)),hAPP(hAPP(c_Relation_Orel__comp(X4,X3,X29),X16),X68)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X29)),hAPP(hAPP(c_Product__Type_OPair(X3,X29),X37),X39)),X68)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X18),X37)),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__compI)). 4.46/4.67 fof(fact_setsum__addf, axiom, ![X2, X50, X27, X3, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),hAPP(hAPP(c_COMBS(X3,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X3),c_Groups_Oplus__class_Oplus(X4)),X27)),X50)),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X27),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X50),X2))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__addf)). 4.46/4.67 fof(fact_setsum__subtractf, axiom, ![X2, X50, X27, X3, X4]:(class_Groups_Oab__group__add(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),hAPP(hAPP(c_COMBS(X3,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X3),c_Groups_Ominus__class_Ominus(X4)),X27)),X50)),X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X27),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X50),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__subtractf)). 4.46/4.67 fof(fact_convex__bound__lt, axiom, ![X63, X195, X47, X12, X48, X4]:(class_Rings_Olinordered__semiring__1__strict(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X47),X12))=>(((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X195),X63)=c_Groups_Oone__class_Oone(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X195),X48)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X63),X47))),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X63)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X195)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_convex__bound__lt)). 4.46/4.67 fof(fact_convex__bound__le, axiom, ![X63, X195, X47, X12, X48, X4]:((((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X195),X48)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X63),X47))),X12))<=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X195),X63)=c_Groups_Oone__class_Oone(X4))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X63)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X195)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X47),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X12)))<=class_Rings_Olinordered__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_convex__bound__le)). 4.46/4.67 fof(fact_Sup__fin_Ounion__inter, axiom, ![X1, X2, X4]:((((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))),c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),c_Big__Operators_Olattice__class_OSup__fin(X4,X2)),c_Big__Operators_Olattice__class_OSup__fin(X4,X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Ounion__inter)). 4.46/4.67 fof(fact_Min_Ounion__inter, axiom, ![X1, X2, X4]:(class_Orderings_Olinorder(X4)=>(((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))),c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),c_Big__Operators_Olinorder__class_OMin(X4,X2)),c_Big__Operators_Olinorder__class_OMin(X4,X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Ounion__inter)). 4.46/4.67 fof(fact_nat__diff__add__eq1, axiom, ![X17, X19, X195, X21, X20]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X195)),X19)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X195)),X17))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21),X20)),X195)),X19)),X17)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20),X21))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__diff__add__eq1)). 4.46/4.67 fof(fact_nat__diff__add__eq2, axiom, ![X17, X19, X195, X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X21)),X195)),X17))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X195)),X19)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X195)),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__diff__add__eq2)). 4.46/4.67 fof(fact_Times__subset__cancel2, axiom, ![X1, X2, X3, X52, X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X3,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X3),X52))),hAPP(hAPP(c_Product__Type_OSigma(X3,X4),X1),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X3),X52))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X2),X1)))<=hBOOL(hAPP(hAPP(c_member(X4),X6),X52))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Times__subset__cancel2)). 4.46/4.67 fof(fact_setsum__strict__mono, axiom, ![X50, X27, X2, X4, X3]:((class_Groups_Oordered__cancel__ab__semigroup__add(X3)&class_Groups_Ocomm__monoid__add(X3))=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>(![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(X27,X42)),hAPP(X50,X42)))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X2)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),X2)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__strict__mono)). 4.46/4.67 fof(fact_rel__pow__Suc__E2, axiom, ![X26, X14, X35, X6, X4]:(~(![X44]:(~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X44),X35)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X14),X26))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X44)),X26))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X35)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),hAPP(c_Nat_OSuc,X14)),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__Suc__E2)). 4.46/4.67 fof(fact_rel__pow__Suc__D2, axiom, ![X26, X14, X35, X6, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X35)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),hAPP(c_Nat_OSuc,X14)),X26)))=>?[X44]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X44)),X26))&hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X44),X35)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X14),X26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__Suc__D2)). 4.46/4.67 fof(fact_rel__pow__Suc__E, axiom, ![X26, X14, X35, X6, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X35)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),hAPP(c_Nat_OSuc,X14)),X26)))=>~(![X44]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X44)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X14),X26)))=>~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X44),X35)),X26)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__Suc__E)). 4.46/4.67 fof(fact_listrel1I1, axiom, ![X7, X16, X5, X6, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),X16))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)),hAPP(hAPP(c_List_Olist_OCons(X4),X5),X7))),c_List_Olistrel1(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1I1)). 4.46/4.67 fof(fact_Inf__fin_Ounion__inter, axiom, ![X1, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))),c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),c_Big__Operators_Olattice__class_OInf__fin(X4,X2)),c_Big__Operators_Olattice__class_OInf__fin(X4,X1))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Ounion__inter)). 4.46/4.67 fof(fact_fold__graph__permute__diff, axiom, ![X18, X6, X2, X37, X4]:(class_Groups_Oab__semigroup__mult(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X4,c_Groups_Otimes__class_Otimes(X4),X37,X2),X6))=>(hBOOL(hAPP(hAPP(c_member(X4),X18),X2))=>(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X4,c_Groups_Otimes__class_Otimes(X4),X18,hAPP(hAPP(c_Set_Oinsert(X4),X37),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),X6))<=~(hBOOL(hAPP(hAPP(c_member(X4),X37),X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph__permute__diff)). 4.46/4.67 fof(fact_smax__emptyI, axiom, ![X76]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X76))=>(X76!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X76)),c_FunDef_Omax__strict)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_smax__emptyI)). 4.46/4.67 fof(fact_fold__image__reindex, axiom, ![X35, X50, X58, X3, X2, X4, X29]:(((hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X29,X3,c_Groups_Otimes__class_Otimes(X29)),X50),X35),hAPP(c_Set_Oimage(X4,X3,X58),X2))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X29,X4,c_Groups_Otimes__class_Otimes(X29)),hAPP(c_Fun_Ocomp(X3,X29,X4,X50),X58)),X35),X2)<=c_Fun_Oinj__on(X4,X3,X58,X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Groups_Oab__semigroup__mult(X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__reindex)). 4.46/4.67 fof(fact_pick__member, axiom, ![X7, X4, X24]:(hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Random_Opick(X4,X7),X24)),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X4),X4),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X4)),X7))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X24),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X4),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X4)),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pick__member)). 4.46/4.67 fof(fact_fold__image__cong, axiom, ![X35, X58, X50, X2, X4, X3]:(((hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),X50),X35),X2)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),X58),X35),X2)<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hAPP(X58,X42)=hAPP(X50,X42)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Groups_Oab__semigroup__mult(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__cong)). 4.46/4.67 fof(fact_Max_Ounion__inter, axiom, ![X1, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),c_Big__Operators_Olinorder__class_OMax(X4,X2)),c_Big__Operators_Olinorder__class_OMax(X4,X1))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))),c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1))))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Ounion__inter)). 4.46/4.67 fof(fact_measures__lesseq, axiom, ![X115, X4, X5, X6, X27]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X27),X115))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_List_Omeasures(X4,X115))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X27,X6)),hAPP(X27,X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_measures__lesseq)). 4.46/4.67 fof(fact_listrel__Cons2, axiom, ![X16, X32, X5, X7, X4]:(~(![X42, X157]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X5)),X16))=>~(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X157),X32)),c_List_Olistrel(X4,X16)))))<=hAPP(hAPP(c_List_Olist_OCons(X4),X42),X157)=X7))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),hAPP(hAPP(c_List_Olist_OCons(X4),X5),X32))),c_List_Olistrel(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__Cons2)). 4.46/4.67 fof(fact_listrel__Cons1, axiom, ![X16, X7, X32, X5, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X5),X32)),X7)),c_List_Olistrel(X4,X16)))=>~(![X44, X8]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X5),X44)),X16))=>~(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X8)),c_List_Olistrel(X4,X16)))))<=hAPP(hAPP(c_List_Olist_OCons(X4),X44),X8)=X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__Cons1)). 4.46/4.67 fof(fact_in__measures_I2_J, axiom, ![X115, X27, X5, X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X27,X6)),hAPP(X27,X5)))|(hAPP(X27,X6)=hAPP(X27,X5)&hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_List_Omeasures(X4,X115)))))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X27),X115))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__measures_I2_J)). 4.46/4.67 fof(fact_fold__image__insert, axiom, ![X35, X50, X18, X2, X4, X3]:(class_Groups_Oab__semigroup__mult(X3)=>((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(X50,X18)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),X50),X35),X2))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),X50),X35),hAPP(hAPP(c_Set_Oinsert(X4),X18),X2))<=~(hBOOL(hAPP(hAPP(c_member(X4),X18),X2))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__insert)). 4.46/4.67 fof(fact_min__max_OSup__fin_Oremove, axiom, ![X6, X2, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>((c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X2)=X6<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))&(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X6),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Oremove)). 4.46/4.67 fof(fact_aset_I6_J, axiom, ![X2, X64, X65]:((![X42]:(![X66]:(![X200]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X200),X2))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X200),X66)!=X42)<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X65))))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X42),X64))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X42),X65)),X64))))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X64),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_aset_I6_J)). 4.46/4.67 fof(fact_eq__equiv__class, axiom, ![X2, X37, X18, X16, X4]:(hAPP(c_Relation_OImage(X4,X4,X16),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X4,X4,X16),hAPP(hAPP(c_Set_Oinsert(X4),X37),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>(c_Equiv__Relations_Oequiv(X4,X2,X16)=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),X16))<=hBOOL(hAPP(hAPP(c_member(X4),X37),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__equiv__class)). 4.46/4.67 fof(fact_pair__leqI1, axiom, ![X64, X68, X37, X18]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X18),X68)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X37),X64))),c_FunDef_Opair__leq))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__leqI1)). 4.46/4.67 fof(fact_min__max_OInf__fin_Oremove, axiom, ![X6, X2, X4]:(((((X6=c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X2)<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X6),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X2)))<=hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Oremove)). 4.46/4.67 fof(fact_folding_Ounion__inter, axiom, ![X1, X2, X62, X27, X3, X4]:(c_Finite__Set_Ofolding(X4,X3,X27,X62)=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X62,X2)),hAPP(X62,X1))=hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X62,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))),hAPP(X62,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ounion__inter)). 4.46/4.67 fof(fact_pair__lessI1, axiom, ![X64, X68, X37, X18]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),X37))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X18),X68)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X37),X64))),c_FunDef_Opair__less))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__lessI1)). 4.46/4.67 fof(fact_folding__image_Odistrib, axiom, ![X58, X50, X2, X62, X35, X27, X3, X4]:(c_Finite__Set_Ofolding__image(X4,X3,X27,X35,X62)=>(hAPP(hAPP(X27,hAPP(hAPP(X62,X50),X2)),hAPP(hAPP(X62,X58),X2))=hAPP(hAPP(X62,hAPP(hAPP(c_COMBS(X3,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X3),X27),X50)),X58)),X2)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image_Odistrib)). 4.46/4.67 fof(fact_enum__all__prod__def, axiom, ![X28, X4, X3]:((class_Enum_Oenum(X4)&class_Enum_Oenum(X3))=>(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X4,X3)),X28))<=>hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X4),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X4),c_Enum_Oenum__class_Oenum__all(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_COMBB(tc_prod(X4,X3),tc_HOL_Obool,X3),X28)),c_Product__Type_OPair(X4,X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__all__prod__def)). 4.46/4.67 fof(fact_enum__ex__prod__def, axiom, ![X28, X4, X3]:((class_Enum_Oenum(X4)&class_Enum_Oenum(X3))=>(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X4,X3)),X28))<=>hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X4),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X4),c_Enum_Oenum__class_Oenum__ex(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_COMBB(tc_prod(X4,X3),tc_HOL_Obool,X3),X28)),c_Product__Type_OPair(X4,X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__ex__prod__def)). 4.46/4.67 fof(fact_folding_Ocommute__left__comp, axiom, ![X50, X6, X5, X29, X62, X27, X3, X4]:(hAPP(c_Fun_Ocomp(X3,X3,X29,hAPP(X27,X5)),hAPP(c_Fun_Ocomp(X3,X3,X29,hAPP(X27,X6)),X50))=hAPP(c_Fun_Ocomp(X3,X3,X29,hAPP(X27,X6)),hAPP(c_Fun_Ocomp(X3,X3,X29,hAPP(X27,X5)),X50))<=c_Finite__Set_Ofolding(X4,X3,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ocommute__left__comp)). 4.46/4.67 fof(fact_diff__frac__eq, axiom, ![X30, X48, X49, X47, X4]:(class_Fields_Ofield(X4)=>(X47!=c_Groups_Ozero__class_Ozero(X4)=>(c_Groups_Ozero__class_Ozero(X4)!=X49=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X48),X49)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X30),X47))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X47),X49))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X47)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X30),X49))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__frac__eq)). 4.46/4.67 fof(fact_card__Diff__insert, axiom, ![X1, X18, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hBOOL(hAPP(hAPP(c_member(X4),X18),X2))=>(~(hBOOL(hAPP(hAPP(c_member(X4),X18),X1)))=>hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),X1)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff__insert)). 4.46/4.67 fof(fact_min__max_OSup__fin_Oinsert__remove, axiom, ![X6, X2, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>((hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X6),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))&(c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=X6<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Oinsert__remove)). 4.46/4.67 fof(fact_rtrancl__trans, axiom, ![X39, X16, X37, X18, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X37),X39)),c_Transitive__Closure_Ortrancl(X4,X16)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X39)),c_Transitive__Closure_Ortrancl(X4,X16))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),c_Transitive__Closure_Ortrancl(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__trans)). 4.46/4.67 fof(fact_map__of__map__keys, axiom, ![X22, X3, X7, X4]:(hAPP(c_Map_Omap__of(X4,X3),hAPP(hAPP(c_List_Omap(X4,tc_prod(X4,X3)),hAPP(hAPP(c_COMBS(X4,X3,tc_prod(X4,X3)),c_Product__Type_OPair(X4,X3)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X3),X3,X4),c_Option_Othe(X3)),X22))),X7))=X22<=hAPP(c_List_Oset(X4),X7)=c_Map_Odom(X4,X3,X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__map__keys)). 4.46/4.67 fof(fact_add__frac__eq, axiom, ![X30, X48, X49, X47, X4]:(class_Fields_Ofield(X4)=>(X47!=c_Groups_Ozero__class_Ozero(X4)=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X47)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X30),X49))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X48),X49)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X30),X47))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X47),X49))<=c_Groups_Ozero__class_Ozero(X4)!=X49))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__frac__eq)). 4.46/4.67 fof(fact_min__max_OInf__fin_Oinsert__remove, axiom, ![X6, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>((hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X6),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))&(X6=c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Oinsert__remove)). 4.46/4.67 fof(fact_nat__less__add__iff1, axiom, ![X14, X22, X23, X24, X25]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X23)),X22)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X23)),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)),X23)),X22)),X14)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__less__add__iff1)). 4.46/4.67 fof(fact_nat__le__add__iff1, axiom, ![X14, X22, X23, X24, X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)),X23)),X22)),X14))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X23)),X22)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X23)),X14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__le__add__iff1)). 4.46/4.67 fof(fact_nat__less__add__iff2, axiom, ![X14, X22, X23, X25, X24]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X23)),X22)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X23)),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X24)),X23)),X14))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__less__add__iff2)). 4.46/4.67 fof(fact_nat__le__add__iff2, axiom, ![X14, X22, X23, X25, X24]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X23)),X22)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X23)),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X24)),X23)),X14))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__le__add__iff2)). 4.46/4.67 fof(fact_equiv__class__subset, axiom, ![X37, X18, X16, X2, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),X16))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X16),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X4,X4,X16),hAPP(hAPP(c_Set_Oinsert(X4),X37),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))<=c_Equiv__Relations_Oequiv(X4,X2,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__class__subset)). 4.46/4.67 fof(fact_card__quotient__disjoint, axiom, ![X16, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Fun_Oinj__on(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X4),c_Equiv__Relations_Oquotient(X4)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Set_Oinsert(X4)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X16),X2)=>hAPP(c_Finite__Set_Ocard(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X2),X16))=hAPP(c_Finite__Set_Ocard(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__quotient__disjoint)). 4.46/4.67 fof(fact_sequence__trans, axiom, ![X45, X24, X16, X27, X4]:(![X41]:hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(X27,hAPP(c_Nat_OSuc,X41))),hAPP(X27,X41))),c_Transitive__Closure_Ortrancl(X4,X16)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X45))),hAPP(X27,X24))),c_Transitive__Closure_Ortrancl(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sequence__trans)). 4.46/4.67 fof(fact_inj__on__image__set__diff, axiom, ![X1, X2, X52, X27, X3, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X52))=>hAPP(c_Set_Oimage(X4,X3,X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X3,X27),X2)),hAPP(c_Set_Oimage(X4,X3,X27),X1)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X52)))<=c_Fun_Oinj__on(X4,X3,X27,X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__image__set__diff)). 4.46/4.68 fof(fact_inj__on__image__Int, axiom, ![X1, X2, X52, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,X52)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X52))=>(hAPP(c_Set_Oimage(X4,X3,X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X3,X27),X2)),hAPP(c_Set_Oimage(X4,X3,X27),X1))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X52))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__image__Int)). 4.46/4.68 fof(fact_subset__equiv__class, axiom, ![X18, X37, X16, X2, X4]:(c_Equiv__Relations_Oequiv(X4,X2,X16)=>((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),X16))<=hBOOL(hAPP(hAPP(c_member(X4),X37),X2)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X16),hAPP(hAPP(c_Set_Oinsert(X4),X37),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X4,X4,X16),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__equiv__class)). 4.46/4.68 fof(fact_INF__commute, axiom, ![X27, X1, X29, X2, X3, X4]:(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X4),X2),hAPP(hAPP(c_COMBB(tc_fun(X29,X4),X4,X3),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29,X4),X1)),X27))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29,X4),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,X4),X4,X29),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X4),X2)),hAPP(c_COMBC(X3,X29,X4),X27)))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__commute)). 4.46/4.68 fof(fact_SUP__commute, axiom, ![X27, X1, X29, X2, X3, X4]:(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4),X2),hAPP(hAPP(c_COMBB(tc_fun(X29,X4),X4,X3),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29,X4),X1)),X27))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29,X4),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,X4),X4,X29),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4),X2)),hAPP(c_COMBC(X3,X29,X4),X27)))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__commute)). 4.46/4.68 fof(fact_less__add__iff1, axiom, ![X87, X37, X39, X106, X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X106)),X39)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X37),X106)),X87)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X18),X37)),X106)),X39)),X87)))<=class_Rings_Oordered__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__add__iff1)). 4.46/4.68 fof(fact_converse__rtrancl__into__rtrancl, axiom, ![X39, X16, X37, X18, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X37),X39)),c_Transitive__Closure_Ortrancl(X4,X16)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X39)),c_Transitive__Closure_Ortrancl(X4,X16))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__rtrancl__into__rtrancl)). 4.46/4.68 fof(fact_rtrancl_Ortrancl__into__rtrancl, axiom, ![X39, X16, X37, X18, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X37),X39)),X16))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X39)),c_Transitive__Closure_Ortrancl(X4,X16))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),c_Transitive__Closure_Ortrancl(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl_Ortrancl__into__rtrancl)). 4.46/4.68 fof(fact_le__add__iff1, axiom, ![X87, X37, X39, X106, X18, X4]:(class_Rings_Oordered__ring(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X18),X37)),X106)),X39)),X87))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X106)),X39)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X37),X106)),X87))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__add__iff1)). 4.46/4.68 fof(fact_less__add__iff2, axiom, ![X87, X37, X39, X106, X18, X4]:(class_Rings_Oordered__ring(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X106)),X39)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X37),X106)),X87)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X37),X18)),X106)),X87))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__add__iff2)). 4.46/4.68 fof(fact_le__add__iff2, axiom, ![X87, X37, X39, X106, X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X106)),X39)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X37),X106)),X87)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X39),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X37),X18)),X106)),X87))))<=class_Rings_Oordered__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__add__iff2)). 4.46/4.68 fof(fact_listsum__map__filter, axiom, ![X27, X28, X7, X4, X3]:(class_Groups_Omonoid__add(X3)=>(hAPP(c_List_Omonoid__add__class_Olistsum(X3),hAPP(hAPP(c_List_Omap(X4,X3),X27),hAPP(c_List_Ofilter(X4,X28),X7)))=hAPP(c_List_Omonoid__add__class_Olistsum(X3),hAPP(hAPP(c_List_Omap(X4,X3),X27),X7))<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7)))=>(~(hBOOL(hAPP(X28,X42)))=>hAPP(X27,X42)=c_Groups_Ozero__class_Ozero(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__map__filter)). 4.46/4.68 fof(fact_card__SigmaI, axiom, ![X1, X3, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_Nat_Onat,X4),c_Finite__Set_Ocard(X3)),X1)),X2)=hAPP(c_Finite__Set_Ocard(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),X1))<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X1,X42)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__SigmaI)). 4.46/4.68 fof(fact_setprod__mono__one__left, axiom, ![X27, X46, X110, X4, X3]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X110))=>((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),X46)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),X110)<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X110),X46)))=>hAPP(X27,X42)=c_Groups_Oone__class_Oone(X3)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X46),X110))))<=class_Groups_Ocomm__monoid__mult(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__mono__one__left)). 4.46/4.68 fof(fact_setprod__mono__one__right, axiom, ![X27, X46, X110, X4, X3]:(class_Groups_Ocomm__monoid__mult(X3)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X110))=>((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),X110)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),X46)<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X110),X46)))=>hAPP(X27,X42)=c_Groups_Oone__class_Oone(X3)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X46),X110))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__mono__one__right)). 4.46/4.68 fof(fact_setsum__mono__zero__right, axiom, ![X27, X46, X110, X4, X3]:(class_Groups_Ocomm__monoid__add(X3)=>(((![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X110),X46)))=>hAPP(X27,X42)=c_Groups_Ozero__class_Ozero(X3))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X46)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X110))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X46),X110)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X110)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__mono__zero__right)). 4.46/4.68 fof(fact_hom__fold1__commute, axiom, ![X122, X58, X4]:(class_Lattices_Oab__semigroup__idem__mult(X4)=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X122))=>(hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),hAPP(c_Set_Oimage(X4,X4,X58),X122))=hAPP(X58,hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),X122))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X122))<=![X42, X44]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(X58,X42)),hAPP(X58,X44))=hAPP(X58,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X42),X44)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hom__fold1__commute)). 4.46/4.68 fof(fact_ball__Un, axiom, ![X28, X1, X2, X4]:(![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)))=>hBOOL(hAPP(X28,X42)))<=>(![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X1))=>hBOOL(hAPP(X28,X42)))&![X42]:(hBOOL(hAPP(X28,X42))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ball__Un)). 4.46/4.68 fof(fact_nth__zip, axiom, ![X72, X3, X57, X4, X21]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X72)))=>hAPP(hAPP(c_Product__Type_OPair(X4,X3),hAPP(hAPP(c_List_Onth(X4),X57),X21)),hAPP(hAPP(c_List_Onth(X3),X72),X21))=hAPP(hAPP(c_List_Onth(tc_prod(X4,X3)),hAPP(hAPP(c_List_Ozip(X4,X3),X57),X72)),X21))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__zip)). 4.46/4.68 fof(fact_setsum__mono__zero__left, axiom, ![X27, X46, X110, X4, X3]:(class_Groups_Ocomm__monoid__add(X3)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X110))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X46),X110))=>(![X42]:(c_Groups_Ozero__class_Ozero(X3)=hAPP(X27,X42)<=hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X110),X46))))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X46)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X110))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__mono__zero__left)). 4.46/4.68 fof(fact_zmult2__lemma__aux4, axiom, ![X112, X11, X111, X10]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X111),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),c_Divides_Odiv__class_Omod(tc_Int_Oint,X112,X10))),X111)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X10))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X111)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult2__lemma__aux4)). 4.46/4.68 fof(fact_zmult2__lemma__aux1, axiom, ![X112, X111, X11, X10]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),X111))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X111),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),c_Divides_Odiv__class_Omod(tc_Int_Oint,X112,X10))),X111)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult2__lemma__aux1)). 4.46/4.68 fof(fact_setsum__bounded, axiom, ![X264, X27, X2, X4, X3]:((class_Rings_Osemiring__1(X3)&class_Groups_Oordered__ab__semigroup__add(X3))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),hAPP(c_Finite__Set_Ocard(X4),X2))),X264)))<=![X41]:(hBOOL(hAPP(hAPP(c_member(X4),X41),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(X27,X41)),X264))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__bounded)). 4.46/4.68 fof(fact_equiv__class__eq, axiom, ![X37, X18, X16, X2, X4]:(c_Equiv__Relations_Oequiv(X4,X2,X16)=>(hAPP(c_Relation_OImage(X4,X4,X16),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X4,X4,X16),hAPP(hAPP(c_Set_Oinsert(X4),X37),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__class__eq)). 4.46/4.68 fof(fact_Image__INT__eq, axiom, ![X1, X29, X2, X16, X3, X4]:(c_Relation_Osingle__valued(X4,X3,hAPP(c_Relation_Oconverse(X3,X4),X16))=>(hAPP(c_Relation_OImage(X3,X4,X16),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29,tc_fun(X3,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29,tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X29),c_Relation_OImage(X3,X4,X16)),X1))<=X2!=c_Orderings_Obot__class_Obot(tc_fun(X29,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__INT__eq)). 4.46/4.68 fof(fact_folding__one_Ounion__inter, axiom, ![X1, X2, X62, X27, X4]:((((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)=>hAPP(hAPP(X27,hAPP(X62,X2)),hAPP(X62,X1))=hAPP(hAPP(X27,hAPP(X62,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))),hAPP(X62,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=c_Finite__Set_Ofolding__one(X4,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Ounion__inter)). 4.46/4.68 fof(fact_fun__upd__None__restrict, axiom, ![X22, X3, X65, X6, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X6),X65))=>hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),c_Map_Orestrict__map(X4,X3,X22,X65)),X6),c_Option_Ooption_ONone(X3))=c_Map_Orestrict__map(X4,X3,X22,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X65),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))&(c_Map_Orestrict__map(X4,X3,X22,X65)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),c_Map_Orestrict__map(X4,X3,X22,X65)),X6),c_Option_Ooption_ONone(X3))<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),X65))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__None__restrict)). 4.46/4.68 fof(fact_aset_I5_J, axiom, ![X2, X64, X65]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))=>(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X64),X2))=>![X42]:(![X66]:(![X200]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X200),X2))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X200),X66)!=X42)<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X65))))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X42),X64))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X42),X65)),X64)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_aset_I5_J)). 4.46/4.68 fof(fact_bset_I7_J, axiom, ![X1, X64, X65]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X64),X1))=>![X42]:(![X66]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X65)))=>![X200]:(X42!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X200),X66)<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X200),X1))))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X64),X42))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X64),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X42),X65))))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bset_I7_J)). 4.46/4.68 fof(fact_fold__sup__le__sup, axiom, ![X39, X37, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X42),X37)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4)),X39),X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X37),X39)))))<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__sup__le__sup)). 4.46/4.68 fof(fact_min__max_Ofold__sup__le__sup, axiom, ![X39, X37, X2, X4]:(((![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X42),X37)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omax(X4)),X39),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X37),X39))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofold__sup__le__sup)). 4.46/4.68 fof(fact_setprod__diff1, axiom, ![X18, X27, X2, X4, X3]:(((((hBOOL(hAPP(hAPP(c_member(X4),X18),X2))=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),X2)),hAPP(X27,X18))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))&(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),X2)<=~(hBOOL(hAPP(hAPP(c_member(X4),X18),X2)))))<=hAPP(X27,X18)!=c_Groups_Ozero__class_Ozero(X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Fields_Ofield(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__diff1)). 4.46/4.68 fof(fact_inf__le__fold__inf, axiom, ![X39, X37, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),X42)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X37),X39)),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),X39),X2)))))<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__le__fold__inf)). 4.46/4.68 fof(fact_folding__one_Oclosed, axiom, ![X2, X62, X27, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>((![X42, X44]:hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(X27,X42),X44)),hAPP(hAPP(c_Set_Oinsert(X4),X42),hAPP(hAPP(c_Set_Oinsert(X4),X44),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=>hBOOL(hAPP(hAPP(c_member(X4),hAPP(X62,X2)),X2)))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2))<=c_Finite__Set_Ofolding__one(X4,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Oclosed)). 4.46/4.68 fof(fact_min__max_Oinf__le__fold__inf, axiom, ![X39, X37, X2, X4]:(((![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),X42)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X37),X39)),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omin(X4)),X39),X2))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__le__fold__inf)). 4.46/4.68 fof(fact_setsum__diff1, axiom, ![X27, X18, X2, X4, X3]:((((~(hBOOL(hAPP(hAPP(c_member(X4),X18),X2)))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))&(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X2)),hAPP(X27,X18))<=hBOOL(hAPP(hAPP(c_member(X4),X18),X2))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Groups_Oab__group__add(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff1)). 4.46/4.68 fof(fact_listsum__mult__const, axiom, ![X7, X39, X27, X3, X4]:(hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X3,X4),hAPP(hAPP(c_COMBC(X3,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X3),c_Groups_Otimes__class_Otimes(X4)),X27)),X39)),X7))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X3,X4),X27),X7))),X39)<=class_Rings_Osemiring__0(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__mult__const)). 4.46/4.68 fof(fact_restrict__map__upds, axiom, ![X22, X65, X32, X3, X7, X4]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X7)),X65))=>c_Map_Omap__upds(X4,X3,c_Map_Orestrict__map(X4,X3,X22,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X65),hAPP(c_List_Oset(X4),X7))),X7,X32)=c_Map_Orestrict__map(X4,X3,c_Map_Omap__upds(X4,X3,X22,X7,X32),X65))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__map__upds)). 4.46/4.68 fof(fact_setsum__diff1__ring, axiom, ![X27, X18, X2, X4, X3]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X2)),hAPP(X27,X18))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))<=hBOOL(hAPP(hAPP(c_member(X4),X18),X2))))<=class_Rings_Oring(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff1__ring)). 4.46/4.68 fof(fact_INT__extend__simps_I1_J, axiom, ![X1, X2, X3, X4, X52]:((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X52=>X1=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X52),X2)),X1))&(X52!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool))),X2)),X1))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X52),X2)),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__extend__simps_I1_J)). 4.46/4.68 fof(fact_rtrancl__listrel1__if__listrel, axiom, ![X16, X32, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)),c_List_Olistrel(X4,X16)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X4),c_List_Olistrel1(X4,X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__listrel1__if__listrel)). 4.46/4.68 fof(fact_geometric__sum, axiom, ![X14, X6, X4]:(class_Fields_Ofield(X4)=>(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X6),X14)),c_Groups_Oone__class_Oone(X4))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X6),c_Groups_Oone__class_Oone(X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(c_Power_Opower__class_Opower(X4),X6)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14))<=c_Groups_Oone__class_Oone(X4)!=X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_geometric__sum)). 4.46/4.68 fof(fact_INT__simps_I3_J, axiom, ![X1, X2, X3, X4, X52]:((X52!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X52),X2)),X1)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool))),X2)),X1)))&(X52=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool))),X2)),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__simps_I3_J)). 4.46/4.68 fof(fact_map__pair__surj, axiom, ![X50, X29, X59, X27, X4, X3]:((c_Orderings_Otop__class_Otop(tc_fun(X29,tc_HOL_Obool))=hAPP(c_Set_Oimage(X59,X29,X50),c_Orderings_Otop__class_Otop(tc_fun(X59,tc_HOL_Obool)))=>hAPP(c_Set_Oimage(tc_prod(X3,X59),tc_prod(X4,X29),c_Product__Type_Omap__pair(X3,X4,X59,X29,X27,X50)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X3,X59),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X4,X29),tc_HOL_Obool)))<=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_Oimage(X3,X4,X27),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair__surj)). 4.46/4.68 fof(fact_ball__UN, axiom, ![X28, X1, X2, X3, X4]:(![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)))=>hBOOL(hAPP(X28,X42)))<=>![X42]:(hBOOL(hAPP(hAPP(c_member(X3),X42),X2))=>![X66]:(hBOOL(hAPP(X28,X66))<=hBOOL(hAPP(hAPP(c_member(X4),X66),hAPP(X1,X42)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ball__UN)). 4.46/4.68 fof(fact_norm__frac_Opinduct, axiom, ![X28, X123, X124]:(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X124),X123)))=>(![X125, X119]:((hBOOL(hAPP(hAPP(X28,X125),X119))<=(hBOOL(hAPP(hAPP(X28,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X125)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X119)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X119),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))<=hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X125),X119))))=>hBOOL(hAPP(hAPP(X28,X124),X123)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_norm__frac_Opinduct)). 4.46/4.68 fof(fact_setsum__add__nat__ivl, axiom, ![X27, X109, X14, X22, X4]:(class_Groups_Ocomm__monoid__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14),X109))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22),X109))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22),X14))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X14),X109)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__add__nat__ivl)). 4.46/4.68 fof(fact_list__all2I, axiom, ![X28, X37, X18, X3, X4]:(![X42]:(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_HOL_Obool),X28),X42))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),X42),hAPP(c_List_Oset(tc_prod(X4,X3)),hAPP(hAPP(c_List_Ozip(X4,X3),X18),X37)))))=>(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X37)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X18)=>c_List_Olist__all2(X4,X3,X28,X18,X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2I)). 4.46/4.68 fof(fact_list__all2__def, axiom, ![X32, X7, X28, X3, X4]:(c_List_Olist__all2(X4,X3,X28,X7,X32)<=>(![X42]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),X42),hAPP(c_List_Oset(tc_prod(X4,X3)),hAPP(hAPP(c_List_Ozip(X4,X3),X7),X32))))=>hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_HOL_Obool),X28),X42)))&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__def)). 4.46/4.68 fof(fact_image__eq__fold__image, axiom, ![X27, X3, X2, X4]:(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X3,tc_HOL_Obool),X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X4,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X3,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_Set_Oinsert(X3)),X27)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X2)=hAPP(c_Set_Oimage(X4,X3,X27),X2)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__eq__fold__image)). 4.46/4.68 fof(fact_insort__left__comm, axiom, ![X7, X5, X6, X4]:(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)),X6),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)),X5),X7))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)),X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)),X6),X7))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__left__comm)). 4.46/4.68 fof(fact_setsum__diff__nat__ivl, axiom, ![X27, X109, X14, X22, X4]:(class_Groups_Oab__group__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14),X109))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X14),X109))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22),X109))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22),X14)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff__nat__ivl)). 4.46/4.68 fof(fact_smin__emptyI, axiom, ![X173]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X173),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))<=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))!=X173), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_smin__emptyI)). 4.46/4.68 fof(fact_wmax__emptyI, axiom, ![X173]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X173)),c_FunDef_Omax__weak))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X173))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wmax__emptyI)). 4.46/4.68 fof(fact_map__of__inject__set, axiom, ![X32, X7, X3, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(tc_prod(X4,X3),X4),c_Product__Type_Ofst(X4,X3)),X7)))=>(hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(tc_prod(X4,X3),X4),c_Product__Type_Ofst(X4,X3)),X32)))=>(hAPP(c_List_Oset(tc_prod(X4,X3)),X32)=hAPP(c_List_Oset(tc_prod(X4,X3)),X7)<=>hAPP(c_Map_Omap__of(X4,X3),X32)=hAPP(c_Map_Omap__of(X4,X3),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__inject__set)). 4.46/4.68 fof(fact_setsum__Un__disjoint, axiom, ![X50, X1, X2, X4, X3]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),X1))<=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Groups_Ocomm__monoid__add(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__Un__disjoint)). 4.46/4.68 fof(fact_list__all2__map2, axiom, ![X260, X27, X29, X172, X28, X3, X4]:(c_List_Olist__all2(X4,X29,hAPP(hAPP(c_COMBC(X4,tc_fun(X29,X3),tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X29,X3),tc_fun(X29,tc_HOL_Obool)),X4),c_COMBB(X3,tc_HOL_Obool,X29)),X28)),X27),X172,X260)<=>c_List_Olist__all2(X4,X3,X28,X172,hAPP(hAPP(c_List_Omap(X29,X3),X27),X260))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__map2)). 4.46/4.68 fof(fact_equiv__class__nondisjoint, axiom, ![X37, X18, X6, X16, X2, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X16),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X4,X4,X16),hAPP(hAPP(c_Set_Oinsert(X4),X37),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),X16)))<=c_Equiv__Relations_Oequiv(X4,X2,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__class__nondisjoint)). 4.46/4.68 fof(fact_setprod__Un__disjoint, axiom, ![X50, X1, X2, X4, X3]:((((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),X1))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Groups_Ocomm__monoid__mult(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__Un__disjoint)). 4.46/4.68 fof(fact_min__max_OInf__fin_Ohom__commute, axiom, ![X122, X58, X4]:(class_Orderings_Olinorder(X4)=>(((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X122=>hAPP(X58,c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X122))=c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(c_Set_Oimage(X4,X4,X58),X122)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X122)))<=![X42, X44]:hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(X58,X42)),hAPP(X58,X44))=hAPP(X58,hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X42),X44)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Ohom__commute)). 4.46/4.68 fof(fact_min__max_OSup__fin_Ohom__commute, axiom, ![X122, X58, X4]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X122))=>(hAPP(X58,c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X122))=c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(c_Set_Oimage(X4,X4,X58),X122))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X122))<=![X42, X44]:hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(X58,X42)),hAPP(X58,X44))=hAPP(X58,hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X42),X44)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Ohom__commute)). 4.46/4.68 fof(fact_zip__append, axiom, ![X204, X72, X205, X3, X57, X4]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X204)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X72)=>hAPP(hAPP(c_List_Ozip(X4,X3),hAPP(hAPP(c_List_Oappend(X4),X57),X72)),hAPP(hAPP(c_List_Oappend(X3),X205),X204))=hAPP(hAPP(c_List_Oappend(tc_prod(X4,X3)),hAPP(hAPP(c_List_Ozip(X4,X3),X57),X205)),hAPP(hAPP(c_List_Ozip(X4,X3),X72),X204)))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X205)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__append)). 4.46/4.68 fof(fact_map__of__filter__in, axiom, ![X28, X35, X45, X7, X4, X3]:((hBOOL(hAPP(hAPP(X28,X45),X35))=>hAPP(hAPP(c_Map_Omap__of(X3,X4),hAPP(c_List_Ofilter(tc_prod(X3,X4),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X4,tc_HOL_Obool),X28)),X7)),X45)=hAPP(c_Option_Ooption_OSome(X4),X35))<=hAPP(hAPP(c_Map_Omap__of(X3,X4),X7),X45)=hAPP(c_Option_Ooption_OSome(X4),X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__filter__in)). 4.46/4.68 fof(fact_map__add__upd__left, axiom, ![X94, X95, X96, X3, X22, X4]:(c_Map_Omap__add(X4,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),X95),X22),hAPP(c_Option_Ooption_OSome(X3),X94)),X96)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),c_Map_Omap__add(X4,X3,X95,X96)),X22),hAPP(c_Option_Ooption_OSome(X3),X94))<=~(hBOOL(hAPP(hAPP(c_member(X4),X22),c_Map_Odom(X4,X3,X96))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__upd__left)). 4.46/4.68 fof(fact_map__of__zip__enum__inject, axiom, ![X32, X7, X4, X3]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),c_Enum_Oenum__class_Oenum(X3))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)=>(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),c_Enum_Oenum__class_Oenum(X3))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=>(X7=X32<=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X4),X4,X3,c_Option_Othe(X4)),hAPP(c_Map_Omap__of(X3,X4),hAPP(hAPP(c_List_Ozip(X3,X4),c_Enum_Oenum__class_Oenum(X3)),X7)))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X4),X4,X3,c_Option_Othe(X4)),hAPP(c_Map_Omap__of(X3,X4),hAPP(hAPP(c_List_Ozip(X3,X4),c_Enum_Oenum__class_Oenum(X3)),X32))))))<=(class_Enum_Oenum(X4)&class_Enum_Oenum(X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__zip__enum__inject)). 4.46/4.68 fof(fact_insort__key__left__comm, axiom, ![X7, X3, X5, X6, X27, X4]:((hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3,X4,X27),X6),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3,X4,X27),X5),X7))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3,X4,X27),X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3,X4,X27),X6),X7))<=hAPP(X27,X5)!=hAPP(X27,X6))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__key__left__comm)). 4.46/4.68 fof(fact_fold1__in, axiom, ![X2, X4]:(class_Groups_Oab__semigroup__mult(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>(hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),X2)),X2))<=![X42, X44]:hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X42),X44)),hAPP(hAPP(c_Set_Oinsert(X4),X42),hAPP(hAPP(c_Set_Oinsert(X4),X44),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__in)). 4.46/4.68 fof(fact_Sup__fin_Oremove, axiom, ![X6, X2, X4]:(((hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>((hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X6),c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OSup__fin(X4,X2)<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>X6=c_Big__Operators_Olattice__class_OSup__fin(X4,X2))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oremove)). 4.46/4.68 fof(fact_Inf__fin_Oremove, axiom, ![X6, X2, X4]:(class_Lattices_Olattice(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X6),c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OInf__fin(X4,X2))&(c_Big__Operators_Olattice__class_OInf__fin(X4,X2)=X6<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oremove)). 4.46/4.68 fof(fact_Max_Oremove, axiom, ![X6, X2, X4]:(class_Orderings_Olinorder(X4)=>((hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>((X6=c_Big__Operators_Olinorder__class_OMax(X4,X2)<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>c_Big__Operators_Olinorder__class_OMax(X4,X2)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X6),c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Oremove)). 4.46/4.68 fof(fact_Min_Oremove, axiom, ![X6, X2, X4]:(class_Orderings_Olinorder(X4)=>((hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>X6=c_Big__Operators_Olinorder__class_OMin(X4,X2))&(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X6),c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=c_Big__Operators_Olinorder__class_OMin(X4,X2))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Oremove)). 4.46/4.68 fof(fact_fun__left__comm_Ofold__rec, axiom, ![X35, X6, X2, X27, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hAPP(hAPP(X27,X6),hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),X35),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),X35),X2)))<=c_Finite__Set_Ofun__left__comm(X4,X3,X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__rec)). 4.46/4.68 fof(fact_rel__comp__mono, axiom, ![X68, X300, X29, X16, X93, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X93),X16))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X29),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X3,X29),X93),X300)),hAPP(hAPP(c_Relation_Orel__comp(X4,X3,X29),X16),X68)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X29),tc_HOL_Obool)),X300),X68)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__mono)). 4.46/4.68 fof(fact_card_Ounion__inter, axiom, ![X1, X2, X4]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X2)),hAPP(c_Finite__Set_Ocard(X4),X1))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))),hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card_Ounion__inter)). 4.46/4.68 fof(fact_list__update__append, axiom, ![X48, X72, X57, X4, X17]:((hAPP(hAPP(c_List_Oappend(X4),X57),hAPP(hAPP(c_List_Olist__update(X4,X72),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57))),X48))=hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Oappend(X4),X57),X72)),X17),X48)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))=>hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Oappend(X4),X57),X72)),X17),X48)=hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Olist__update(X4,X57),X17),X48)),X72))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__append)). 4.46/4.68 fof(fact_insort__key_Osimps_I2_J, axiom, ![X32, X3, X5, X6, X27, X4]:(((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(X27,X6)),hAPP(X27,X5))))=>hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3,X4,X27),X6),hAPP(hAPP(c_List_Olist_OCons(X3),X5),X32))=hAPP(hAPP(c_List_Olist_OCons(X3),X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3,X4,X27),X6),X32)))&(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3,X4,X27),X6),hAPP(hAPP(c_List_Olist_OCons(X3),X5),X32))=hAPP(hAPP(c_List_Olist_OCons(X3),X6),hAPP(hAPP(c_List_Olist_OCons(X3),X5),X32))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(X27,X6)),hAPP(X27,X5)))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__key_Osimps_I2_J)). 4.46/4.68 fof(fact_bex__Un, axiom, ![X28, X1, X2, X4]:((?[X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X1))&hBOOL(hAPP(X28,X42)))|?[X42]:(hBOOL(hAPP(X28,X42))&hBOOL(hAPP(hAPP(c_member(X4),X42),X2))))<=>?[X42]:(hBOOL(hAPP(X28,X42))&hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bex__Un)). 4.46/4.68 fof(fact_rel__compE, axiom, ![X68, X16, X29, X293, X3, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),X293),hAPP(hAPP(c_Relation_Orel__comp(X4,X29,X3),X16),X68)))=>~(![X42, X44, X132]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X29)),hAPP(hAPP(c_Product__Type_OPair(X4,X29),X42),X44)),X16))=>~(hBOOL(hAPP(hAPP(c_member(tc_prod(X29,X3)),hAPP(hAPP(c_Product__Type_OPair(X29,X3),X44),X132)),X68))))<=hAPP(hAPP(c_Product__Type_OPair(X4,X3),X42),X132)=X293))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__compE)). 4.46/4.68 fof(fact_folding__image__simple_Ounion__inter, axiom, ![X1, X2, X62, X50, X35, X27, X3, X4]:(c_Finite__Set_Ofolding__image__simple(X4,X3,X27,X35,X50,X62)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1))=>hAPP(hAPP(X27,hAPP(X62,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))),hAPP(X62,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X2),X1)))=hAPP(hAPP(X27,hAPP(X62,X2)),hAPP(X62,X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Ounion__inter)). 4.46/4.68 fof(fact_min__max_OInf__fin_Oclosed, axiom, ![X2, X4]:((((hBOOL(hAPP(hAPP(c_member(X4),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X2)),X2))<=![X42, X44]:hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X42),X44)),hAPP(hAPP(c_Set_Oinsert(X4),X42),hAPP(hAPP(c_Set_Oinsert(X4),X44),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Oclosed)). 4.46/4.68 fof(fact_min__max_OSup__fin_Oclosed, axiom, ![X2, X4]:(class_Orderings_Olinorder(X4)=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>(![X42, X44]:hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X42),X44)),hAPP(hAPP(c_Set_Oinsert(X4),X42),hAPP(hAPP(c_Set_Oinsert(X4),X44),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=>hBOOL(hAPP(hAPP(c_member(X4),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X2)),X2))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Oclosed)). 4.46/4.68 fof(fact_nat__gcd_Opinduct, axiom, ![X28, X123, X124]:((![X42, X44]:(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X42),X44)))=>((hBOOL(hAPP(hAPP(X28,X44),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X42,X44)))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X44)=>hBOOL(hAPP(hAPP(X28,X42),X44))))=>hBOOL(hAPP(hAPP(X28,X124),X123)))<=hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X124),X123)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__gcd_Opinduct)). 4.46/4.68 fof(fact_fold1__Un, axiom, ![X1, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>((X1!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)=>hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),X2)),hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),X1))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1)))))<=class_Groups_Oab__semigroup__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__Un)). 4.46/4.68 fof(fact_take__hd__drop, axiom, ![X57, X4, X17]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))=>hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Otake(X4),X17),X57)),hAPP(hAPP(c_List_Olist_OCons(X4),hAPP(c_List_Ohd(X4),hAPP(hAPP(c_List_Odrop(X4),X17),X57))),c_List_Olist_ONil(X4)))=hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_OSuc,X17)),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__hd__drop)). 4.46/4.68 fof(fact_setprod_Oremove, axiom, ![X50, X6, X2, X4, X3]:(class_Groups_Ocomm__monoid__mult(X3)=>((hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(X50,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod_Oremove)). 4.46/4.68 fof(fact_fun__left__comm_Ofold__insert, axiom, ![X35, X6, X2, X27, X3, X4]:(c_Finite__Set_Ofun__left__comm(X4,X3,X27)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))=>hAPP(hAPP(X27,X6),hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),X35),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),X35),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__insert)). 4.46/4.68 fof(fact_setsum_Oremove, axiom, ![X50, X6, X2, X4, X3]:(((hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(X50,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Groups_Ocomm__monoid__add(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum_Oremove)). 4.46/4.68 fof(fact_in__inv__image, axiom, ![X27, X16, X3, X5, X6, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),hAPP(hAPP(c_Relation_Oinv__image(X3,X4),X16),X27)))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),hAPP(X27,X6)),hAPP(X27,X5))),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__inv__image)). 4.46/4.68 fof(fact_refl__on__INTER, axiom, ![X16, X2, X3, X46, X4]:(c_Relation_Orefl__on(X3,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X46),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(tc_prod(X3,X3),tc_HOL_Obool)),X46),X16))<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X46))=>c_Relation_Orefl__on(X3,hAPP(X2,X42),hAPP(X16,X42)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__INTER)). 4.46/4.68 fof(fact_distinct__list__update, axiom, ![X24, X18, X7, X4]:((hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Olist__update(X4,X7),X24),X18)))<=~(hBOOL(hAPP(hAPP(c_member(X4),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X7)),hAPP(hAPP(c_Set_Oinsert(X4),hAPP(hAPP(c_List_Onth(X4),X7),X24)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))))<=hBOOL(hAPP(c_List_Odistinct(X4),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__list__update)). 4.46/4.68 fof(fact_setsum__diff, axiom, ![X27, X1, X2, X4, X3]:(((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X1))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X2)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Groups_Oab__group__add(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff)). 4.46/4.68 fof(fact_setsum__cl__ivl__Suc, axiom, ![X27, X22, X14, X4]:(((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X22,X14))),hAPP(X27,hAPP(c_Nat_OSuc,X14)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X22,hAPP(c_Nat_OSuc,X14)))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14)),X22))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14)),X22))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X22,hAPP(c_Nat_OSuc,X14)))=c_Groups_Ozero__class_Ozero(X4)))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__cl__ivl__Suc)). 4.46/4.68 fof(fact_gauss__sum, axiom, ![X14, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X14)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X14)),c_Groups_Oone__class_Oone(X4)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Oone__class_Oone(X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),c_Nat_Osemiring__1__class_Oof__nat(X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X14)))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_gauss__sum)). 4.46/4.68 fof(fact_take__add, axiom, ![X57, X4, X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))=>hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Otake(X4),X21),X57)),hAPP(hAPP(c_List_Otake(X4),X20),hAPP(hAPP(c_List_Odrop(X4),X21),X57)))=hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20)),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__add)). 4.46/4.68 fof(fact_card_Ounion__inter__neutral, axiom, ![X1, X2, X4]:(((hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X2)),hAPP(c_Finite__Set_Ocard(X4),X1))<=(c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=?[X42]:hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card_Ounion__inter__neutral)). 4.46/4.68 fof(fact_bset_I5_J, axiom, ![X64, X1, X65]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))=>![X42]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X42),X64))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X42),X65)),X64)))<=![X66]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X65)))=>![X200]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X200),X1))=>X42!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X200),X66))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bset_I5_J)). 4.46/4.68 fof(fact_bset_I6_J, axiom, ![X64, X1, X65]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))=>![X42]:(![X66]:(![X200]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X200),X66)!=X42<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X200),X1)))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X65))))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X42),X65)),X64))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X42),X64))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bset_I6_J)). 4.46/4.68 fof(fact_aset_I7_J, axiom, ![X64, X2, X65]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))=>![X42]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X64),X42))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X64),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X42),X65))))<=![X66]:(![X200]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X200),X2))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X200),X66)!=X42)<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X65)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_aset_I7_J)). 4.46/4.68 fof(fact_folding__one_Oremove, axiom, ![X6, X2, X62, X27, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>hAPP(hAPP(X27,X6),hAPP(X62,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(X62,X2))&(X6=hAPP(X62,X2)<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))<=c_Finite__Set_Ofolding__one(X4,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Oremove)). 4.46/4.68 fof(fact_Max_Oinsert__remove, axiom, ![X6, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>((c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X6),c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&(c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=X6<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Oinsert__remove)). 4.46/4.68 fof(fact_fun__upd__twist, axiom, ![X87, X37, X22, X3, X4, X39, X18]:(X39!=X18=>hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X3),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X3),X22),X18),X37)),X39),X87)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X3),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X3),X22),X39),X87)),X18),X37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__twist)). 4.46/4.68 fof(fact_aset_I8_J, axiom, ![X64, X2, X65]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))=>![X42]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X64),X42))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X64),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X42),X65))))<=![X66]:(![X200]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X200),X2))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X200),X66)!=X42)<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X65)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_aset_I8_J)). 4.46/4.68 fof(fact_listrel1E, axiom, ![X16, X32, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)),c_List_Olistrel1(X4,X16)))=>~(![X42, X44]:(![X219, X220]:(X7=hAPP(hAPP(c_List_Oappend(X4),X219),hAPP(hAPP(c_List_Olist_OCons(X4),X42),X220))=>X32!=hAPP(hAPP(c_List_Oappend(X4),X219),hAPP(hAPP(c_List_Olist_OCons(X4),X44),X220)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X44)),X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1E)). 4.46/4.68 fof(fact_Sup__fin_Oinsert__remove, axiom, ![X6, X2, X4]:(class_Lattices_Olattice(X4)=>(((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>X6=c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2)))&(c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X6),c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oinsert__remove)). 4.46/4.68 fof(fact_Inf__fin_Oinsert__remove, axiom, ![X6, X2, X4]:((((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>X6=c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2)))&(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X6),c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oinsert__remove)). 4.46/4.68 fof(fact_Min_Oinsert__remove, axiom, ![X6, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X6),c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))&(c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=X6<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Oinsert__remove)). 4.46/4.68 fof(fact_fun__left__comm_Ofold__insert__remove, axiom, ![X6, X35, X2, X27, X3, X4]:(c_Finite__Set_Ofun__left__comm(X4,X3,X27)=>(hAPP(hAPP(X27,X6),hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),X35),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),X35),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__insert__remove)). 4.46/4.68 fof(fact_insort__key__remove1, axiom, ![X27, X7, X18, X4, X3]:(((c_List_Olinorder__class_Osorted(X3,hAPP(hAPP(c_List_Omap(X4,X3),X27),X7))=>(X7=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X3,X27),X18),c_List_Oremove1(X4,X18,X7))<=hAPP(c_List_Ohd(X4),hAPP(c_List_Ofilter(X4,hAPP(hAPP(c_COMBB(X3,tc_HOL_Obool,X4),hAPP(c_fequal,hAPP(X27,X18))),X27)),X7))=X18))<=hBOOL(hAPP(hAPP(c_member(X4),X18),hAPP(c_List_Oset(X4),X7))))<=class_Orderings_Olinorder(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__key__remove1)). 4.46/4.68 fof(fact_finite__range__updI, axiom, ![X37, X18, X27, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X4)),hAPP(c_Set_Oimage(X3,tc_Option_Ooption(X4),X27),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))))=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X4)),hAPP(c_Set_Oimage(X3,tc_Option_Ooption(X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X4)),X27),X18),hAPP(c_Option_Ooption_OSome(X4),X37))),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__range__updI)). 4.46/4.68 fof(fact_zmult2__lemma__aux2, axiom, ![X112, X111, X11, X10]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),X111))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X111),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),c_Divides_Odiv__class_Omod(tc_Int_Oint,X112,X10))),X111)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult2__lemma__aux2)). 4.46/4.68 fof(fact_zmult2__lemma__aux3, axiom, ![X112, X11, X111, X10]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X111),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),c_Divides_Odiv__class_Omod(tc_Int_Oint,X112,X10))),X111))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X111)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult2__lemma__aux3)). 4.46/4.68 fof(fact_Int_OMin__def, axiom, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Int_OMin, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int_OMin__def)). 4.46/4.68 fof(fact_filter__insort, axiom, ![X6, X28, X7, X27, X3, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X27),X7))=>(hBOOL(hAPP(X28,X6))=>hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3,X4,X27),X6),hAPP(c_List_Ofilter(X3,X28),X7))=hAPP(c_List_Ofilter(X3,X28),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3,X4,X27),X6),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__insort)). 4.46/4.68 fof(fact_setsum__left__distrib, axiom, ![X16, X2, X27, X3, X4]:(class_Rings_Osemiring__0(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),hAPP(hAPP(c_COMBC(X3,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X3),c_Groups_Otimes__class_Otimes(X4)),X27)),X16)),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X27),X2)),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__left__distrib)). 4.46/4.68 fof(fact_length__takeWhile__less__P__nth, axiom, ![X7, X4, X28, X25]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X28,X7))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))))<=![X41]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),X25))=>hBOOL(hAPP(X28,hAPP(hAPP(c_List_Onth(X4),X7),X41))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__takeWhile__less__P__nth)). 4.46/4.68 fof(fact_right__distrib__number__of, axiom, ![X10, X11, X63, X3]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63)),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63)),X10))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X11),X10))<=(class_Int_Onumber(X3)&class_Rings_Osemiring(X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_right__distrib__number__of)). 4.46/4.68 fof(fact_abs__mult__less, axiom, ![X133, X11, X10, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),X10))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),X133))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),hAPP(c_Groups_Oabs__class_Oabs(X4),X11))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X133)))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__mult__less)). 4.46/4.68 fof(fact_right__diff__distrib__number__of, axiom, ![X10, X11, X63, X3]:((class_Rings_Oring(X3)&class_Int_Onumber(X3))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63)),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63)),X10))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X11),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_right__diff__distrib__number__of)). 4.46/4.68 fof(fact_setprod_Oinsert__remove, axiom, ![X6, X50, X2, X4, X3]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(X50,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Groups_Ocomm__monoid__mult(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod_Oinsert__remove)). 4.46/4.68 fof(fact_setsum_Oinsert__remove, axiom, ![X6, X50, X2, X4, X3]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(X50,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Groups_Ocomm__monoid__add(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum_Oinsert__remove)). 4.46/4.68 fof(fact_folding_Ounion, axiom, ![X1, X2, X62, X27, X3, X4]:(c_Finite__Set_Ofolding(X4,X3,X27,X62)=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>(hAPP(X62,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X62,X2)),hAPP(X62,X1))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ounion)). 4.46/4.68 fof(fact_listsum__map__remove1, axiom, ![X27, X7, X6, X4, X3]:(class_Groups_Ocomm__monoid__add(X3)=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(X27,X6)),hAPP(c_List_Omonoid__add__class_Olistsum(X3),hAPP(hAPP(c_List_Omap(X4,X3),X27),c_List_Oremove1(X4,X6,X7))))=hAPP(c_List_Omonoid__add__class_Olistsum(X3),hAPP(hAPP(c_List_Omap(X4,X3),X27),X7))<=hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__map__remove1)). 4.46/4.68 fof(fact_Sup__fin_Oclosed, axiom, ![X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>((![X42, X44]:hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X42),X44)),hAPP(hAPP(c_Set_Oinsert(X4),X42),hAPP(hAPP(c_Set_Oinsert(X4),X44),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=>hBOOL(hAPP(hAPP(c_member(X4),c_Big__Operators_Olattice__class_OSup__fin(X4,X2)),X2)))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oclosed)). 4.46/4.68 fof(fact_Inf__fin_Oclosed, axiom, ![X2, X4]:(class_Lattices_Olattice(X4)=>((X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>(hBOOL(hAPP(hAPP(c_member(X4),c_Big__Operators_Olattice__class_OInf__fin(X4,X2)),X2))<=![X42, X44]:hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X42),X44)),hAPP(hAPP(c_Set_Oinsert(X4),X42),hAPP(hAPP(c_Set_Oinsert(X4),X44),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oclosed)). 4.46/4.68 fof(fact_setsum__divide__distrib, axiom, ![X16, X2, X27, X3, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),hAPP(hAPP(c_COMBC(X3,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X3),c_Rings_Oinverse__class_Odivide(X4)),X27)),X16)),X2)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X27),X2)),X16)<=class_Fields_Ofield(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__divide__distrib)). 4.46/4.68 fof(fact_fun__left__comm_Ofold__insert2, axiom, ![X35, X6, X2, X27, X3, X4]:(c_Finite__Set_Ofun__left__comm(X4,X3,X27)=>((~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))=>hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),X35),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),hAPP(hAPP(X27,X6),X35)),X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__insert2)). 4.46/4.68 fof(fact_folding__one_Oinsert__remove, axiom, ![X6, X2, X62, X27, X4]:((((hAPP(hAPP(X27,X6),hAPP(X62,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(X62,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>X6=hAPP(X62,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=c_Finite__Set_Ofolding__one(X4,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Oinsert__remove)). 4.46/4.68 fof(fact_setsum__diff1__nat, axiom, ![X27, X2, X18, X4]:((~(hBOOL(hAPP(hAPP(c_member(X4),X18),X2)))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X27),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))&(hBOOL(hAPP(hAPP(c_member(X4),X18),X2))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X27),X2)),hAPP(X27,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff1__nat)). 4.46/4.68 fof(fact_mod__lemma, axiom, ![X112, X11, X111, X10]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X111),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X112,X10))),X111)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X10))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__lemma)). 4.46/4.68 fof(fact_trancl__subset__Sigma__aux, axiom, ![X2, X16, X37, X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X2))))=>(X18=X37|hBOOL(hAPP(hAPP(c_member(X4),X18),X2))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X37)),c_Transitive__Closure_Ortrancl(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__subset__Sigma__aux)). 4.46/4.68 fof(fact_measures__less, axiom, ![X115, X4, X5, X6, X27]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X27),X115))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X27,X6)),hAPP(X27,X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_measures__less)). 4.46/4.68 fof(fact_inj__on__insert, axiom, ![X2, X18, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,hAPP(hAPP(c_Set_Oinsert(X4),X18),X2))<=>(~(hBOOL(hAPP(hAPP(c_member(X3),hAPP(X27,X18)),hAPP(c_Set_Oimage(X4,X3,X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))))&c_Fun_Oinj__on(X4,X3,X27,X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__insert)). 4.46/4.68 fof(fact_small_H_Osimps, axiom, ![X27, X24, X87]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),X24))=>c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))=c_Smallcheck_Osmall_H(X27,X87,X24))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),X24)))=>hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X27,X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X27,X24))=c_Smallcheck_Osmall_H(X27,X87,X24))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small_H_Osimps)). 4.46/4.68 fof(fact_folding__one_Ounion__disjoint, axiom, ![X1, X2, X62, X27, X4]:(c_Finite__Set_Ofolding__one(X4,X27,X62)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>(((hAPP(X62,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(X27,hAPP(X62,X2)),hAPP(X62,X1))<=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X1)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Ounion__disjoint)). 4.46/4.68 fof(fact_decr__mult__lemma, axiom, ![X45, X28, X87]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X87))=>(![X42]:(hBOOL(hAPP(X28,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X42),X87)))<=hBOOL(hAPP(X28,X42)))=>(![X42]:(hBOOL(hAPP(X28,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X45),X87))))<=hBOOL(hAPP(X28,X42)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_decr__mult__lemma)). 4.46/4.68 fof(fact_INF__INT__eq, axiom, ![X6, X16, X3, X4]:(hBOOL(hAPP(hAPP(c_member(X3),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),X16)))<=>hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3))),X16)),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__INT__eq)). 4.46/4.68 fof(fact_SUP__UN__eq, axiom, ![X6, X16, X3, X4]:(hBOOL(hAPP(hAPP(c_member(X3),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),X16)))<=>hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3))),X16)),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__UN__eq)). 4.46/4.68 fof(fact_Image__Int__eq, axiom, ![X1, X2, X26, X3, X4]:(c_Relation_Osingle__valued(X4,X3,hAPP(c_Relation_Oconverse(X3,X4),X26))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3,X4,X26),X2)),hAPP(c_Relation_OImage(X3,X4,X26),X1))=hAPP(c_Relation_OImage(X3,X4,X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__Int__eq)). 4.46/4.68 fof(fact_mult__strict__mono, axiom, ![X133, X10, X11, X12, X4]:(class_Rings_Olinordered__semiring__strict(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11))=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X133))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X10),X133))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__strict__mono)). 4.46/4.68 fof(fact_mult__strict__mono_H, axiom, ![X133, X10, X11, X12, X4]:(class_Rings_Olinordered__semiring__strict(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X10),X133))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X133)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__strict__mono_H)). 4.46/4.68 fof(fact_mult__le__less__imp__less, axiom, ![X133, X10, X11, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X133)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X10),X133))))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__less__imp__less)). 4.46/4.68 fof(fact_min__max_OInf__fin_Ounion__idem, axiom, ![X1, X2, X4]:(class_Orderings_Olinorder(X4)=>((X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>((hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X2)),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X1))=c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X1)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Ounion__idem)). 4.46/4.68 fof(fact_mem__splitI2, axiom, ![X39, X35, X29, X3, X4, X109]:(![X125, X119]:(hBOOL(hAPP(hAPP(c_member(X29),X35),hAPP(hAPP(X39,X125),X119)))<=hAPP(hAPP(c_Product__Type_OPair(X4,X3),X125),X119)=X109)=>hBOOL(hAPP(hAPP(c_member(X29),X35),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_fun(X29,tc_HOL_Obool)),X39),X109)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mem__splitI2)). 4.46/4.68 fof(fact_mult__less__le__imp__less, axiom, ![X133, X10, X11, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X10),X133))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X133)))))))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__le__imp__less)). 4.46/4.68 fof(fact_frac__less2, axiom, ![X49, X30, X47, X48, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X48))=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X30),X49))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X49)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X47),X30))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X30)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X47))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_frac__less2)). 4.46/4.68 fof(fact_frac__less, axiom, ![X49, X30, X47, X48, X4]:(class_Fields_Olinordered__field(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X48))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),X47))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X49)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X47),X30)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X30),X49))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_frac__less)). 4.46/4.68 fof(fact_mult__mono_H, axiom, ![X133, X10, X11, X12, X4]:(class_Rings_Oordered__semiring(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X10),X133))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X133)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__mono_H)). 4.46/4.68 fof(fact_min__max_OSup__fin_Ounion__idem, axiom, ![X1, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(((c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X2)),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X1))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X1)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1)))<=X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Ounion__idem)). 4.46/4.68 fof(fact_length__filter__less, axiom, ![X28, X7, X6, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Ofilter(X4,X28),X7))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))<=~(hBOOL(hAPP(X28,X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__filter__less)). 4.46/4.68 fof(fact_setsum__diff__nat, axiom, ![X27, X2, X1, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X27),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X27),X1))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff__nat)). 4.46/4.68 fof(fact_mult__mono, axiom, ![X133, X10, X11, X12, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X10),X133))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X133))))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11)))<=class_Rings_Oordered__semiring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__mono)). 4.46/4.68 fof(fact_frac__le, axiom, ![X49, X30, X47, X48, X4]:(class_Fields_Olinordered__field(X4)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X49)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X47),X30)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X30),X49))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X47)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_frac__le)). 4.46/4.68 fof(fact_map__pair__inj__on, axiom, ![X1, X50, X59, X29, X2, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,X2)=>(c_Fun_Oinj__on(tc_prod(X4,X29),tc_prod(X3,X59),c_Product__Type_Omap__pair(X4,X3,X29,X59,X27,X50),hAPP(hAPP(c_Product__Type_OSigma(X4,X29),X2),hAPP(c_COMBK(tc_fun(X29,tc_HOL_Obool),X4),X1)))<=c_Fun_Oinj__on(X29,X59,X50,X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair__inj__on)). 4.46/4.68 fof(fact_map__of__zip__is__Some, axiom, ![X6, X32, X3, X7, X4]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)=>(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))<=>?[X44]:hAPP(c_Option_Ooption_OSome(X3),X44)=hAPP(hAPP(c_Map_Omap__of(X4,X3),hAPP(hAPP(c_List_Ozip(X4,X3),X7),X32)),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__zip__is__Some)). 4.46/4.68 fof(fact_mlex__leq, axiom, ![X26, X4, X5, X6, X27]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X27,X6)),hAPP(X27,X5)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_Wellfounded_Omlex__prod(X4,X27,X26)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mlex__leq)). 4.46/4.68 fof(fact_filter__equals__takeWhile__sorted__rev, axiom, ![X64, X7, X27, X3, X4]:((hAPP(c_List_Ofilter(X3,hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,X3),hAPP(c_Orderings_Oord__class_Oless(X4),X64)),X27)),X7)=c_List_OtakeWhile(X3,hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,X3),hAPP(c_Orderings_Oord__class_Oless(X4),X64)),X27),X7)<=c_List_Olinorder__class_Osorted(X4,hAPP(c_List_Orev(X4),hAPP(hAPP(c_List_Omap(X3,X4),X27),X7))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__equals__takeWhile__sorted__rev)). 4.46/4.68 fof(fact_setsum__head__upt__Suc, axiom, ![X27, X14, X22, X4]:(class_Groups_Ocomm__monoid__add(X4)=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(X27,X22)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X22)),X14)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X22),X14))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__head__upt__Suc)). 4.46/4.68 fof(fact_id__take__nth__drop, axiom, ![X57, X4, X21]:(X57=hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Otake(X4),X21),X57)),hAPP(hAPP(c_List_Olist_OCons(X4),hAPP(hAPP(c_List_Onth(X4),X57),X21)),hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_OSuc,X21)),X57)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_id__take__nth__drop)). 4.46/4.68 fof(fact_inj__on__Un, axiom, ![X1, X2, X27, X3, X4]:(((c_Fun_Oinj__on(X4,X3,X27,X1)&hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X3,X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1))),hAPP(c_Set_Oimage(X4,X3,X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X1),X2)))=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))&c_Fun_Oinj__on(X4,X3,X27,X2))<=>c_Fun_Oinj__on(X4,X3,X27,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__Un)). 4.46/4.68 fof(fact_folding_Ocommute__comp_H_H, axiom, ![X1, X2, X62, X27, X3, X4]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X62,X1)),hAPP(X62,X2))=hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X62,X2)),hAPP(X62,X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=c_Finite__Set_Ofolding(X4,X3,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ocommute__comp_H_H)). 4.46/4.68 fof(fact_transfer__int__nat__sum__prod2_I2_J, axiom, ![X27, X2, X4]:(![X42]:(c_Nat__Transfer_Ois__nat(hAPP(X27,X42))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X2)))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,tc_Int_Oint),X27),X2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X4),c_Int_Onat),X27)),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__sum__prod2_I2_J)). 4.46/4.68 fof(fact_fold__graph__insert__swap, axiom, ![X35, X5, X2, X37, X4]:(((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X4,c_Groups_Otimes__class_Otimes(X4),X35,hAPP(hAPP(c_Set_Oinsert(X4),X37),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X35),X5)))<=~(hBOOL(hAPP(hAPP(c_member(X4),X37),X2))))<=hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X4,c_Groups_Otimes__class_Otimes(X4),X37,X2),X5)))<=class_Groups_Oab__semigroup__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph__insert__swap)). 4.46/4.68 fof(fact_left__distrib__number__of, axiom, ![X63, X11, X12, X3]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X12),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X11),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X12),X11)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63))<=(class_Int_Onumber(X3)&class_Rings_Osemiring(X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_left__distrib__number__of)). 4.46/4.68 fof(fact_finite__range__map__of__map__add, axiom, ![X67, X27, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X4)),hAPP(c_Set_Oimage(X3,tc_Option_Ooption(X4),c_Map_Omap__add(X3,X4,X27,hAPP(c_Map_Omap__of(X3,X4),X67))),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X4)),hAPP(c_Set_Oimage(X3,tc_Option_Ooption(X4),X27),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__range__map__of__map__add)). 4.46/4.68 fof(fact_combine__common__factor, axiom, ![X10, X11, X318, X12, X4]:(class_Rings_Osemiring(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X318)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X318)),X10))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)),X318)),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_combine__common__factor)). 4.46/4.68 fof(fact_congruent2D, axiom, ![X238, X239, X240, X241, X27, X147, X149, X29, X3, X4]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X239),X238)),X147))=>hAPP(hAPP(X27,X240),X238)=hAPP(hAPP(X27,X241),X239))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X241),X240)),X149)))<=c_Equiv__Relations_Ocongruent2(X4,X3,X29,X149,X147,X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_congruent2D)). 4.46/4.68 fof(fact_divide__strict__left__mono, axiom, ![X10, X12, X11, X4]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X10),X12)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X10),X11))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12)))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__strict__left__mono)). 4.46/4.68 fof(fact_divide__left__mono, axiom, ![X10, X12, X11, X4]:(class_Fields_Olinordered__field(X4)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X10),X12)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X10),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__left__mono)). 4.46/4.68 fof(fact_min__max_Odistrib__inf__le, axiom, ![X49, X47, X48, X4]:(class_Orderings_Olinorder(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),X47)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),X49))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X47),X49))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Odistrib__inf__le)). 4.46/4.68 fof(fact_distrib__inf__le, axiom, ![X49, X47, X48, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X47)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X49))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X47),X49))))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distrib__inf__le)). 4.46/4.68 fof(fact_INFI__set__fold, axiom, ![X27, X7, X3, X4]:(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X4),hAPP(c_List_Oset(X3),X7)),X27)=hAPP(c_List_Ofoldl(X4,X3,hAPP(c_COMBC(X3,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X3),c_Lattices_Osemilattice__inf__class_Oinf(X4)),X27)),c_Orderings_Otop__class_Otop(X4)),X7)<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INFI__set__fold)). 4.46/4.68 fof(fact_divide__strict__left__mono__neg, axiom, ![X10, X11, X12, X4]:(class_Fields_Olinordered__field(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X10),c_Groups_Ozero__class_Ozero(X4)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X10),X12)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X10),X11))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__strict__left__mono__neg)). 4.46/4.68 fof(fact_left__diff__distrib__number__of, axiom, ![X63, X11, X12, X3]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X12),X11)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X12),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X11),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63)))<=(class_Int_Onumber(X3)&class_Rings_Oring(X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_left__diff__distrib__number__of)). 4.46/4.68 fof(fact_min__max_Odistrib__sup__le, axiom, ![X49, X47, X48, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X48),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X47),X49))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X48),X47)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X48),X49))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Odistrib__sup__le)). 4.46/4.68 fof(fact_distrib__sup__le, axiom, ![X49, X47, X48, X4]:(class_Lattices_Olattice(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X47),X49))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X47)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X49))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distrib__sup__le)). 4.46/4.68 fof(fact_folding_Oremove, axiom, ![X6, X2, X62, X27, X3, X4]:(c_Finite__Set_Ofolding(X4,X3,X27,X62)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hAPP(X62,X2)=hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X62,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),hAPP(X27,X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Oremove)). 4.46/4.68 fof(fact_unique__quotient__lemma, axiom, ![X111, X112, X177, X178, X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X178)),X177)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X112)),X111)))=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X111),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X178),X112)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X177),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X177)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_unique__quotient__lemma)). 4.46/4.68 fof(fact_unique__quotient__lemma__neg, axiom, ![X111, X112, X177, X178, X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X178)),X177)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X112)),X111)))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),X111))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X112),X178))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),X177))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X111),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_unique__quotient__lemma__neg)). 4.46/4.68 fof(fact_upd__conv__take__nth__drop, axiom, ![X12, X57, X4, X21]:(hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Otake(X4),X21),X57)),hAPP(hAPP(c_List_Olist_OCons(X4),X12),hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_OSuc,X21)),X57)))=hAPP(hAPP(c_List_Olist__update(X4,X57),X21),X12)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upd__conv__take__nth__drop)). 4.46/4.68 fof(fact_UN__equiv__class, axiom, ![X18, X27, X3, X16, X2, X4]:(((hAPP(X27,X18)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X16),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X27)<=hBOOL(hAPP(hAPP(c_member(X4),X18),X2)))<=c_Equiv__Relations_Ocongruent(X4,tc_fun(X3,tc_HOL_Obool),X16,X27))<=c_Equiv__Relations_Oequiv(X4,X2,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__equiv__class)). 4.46/4.68 fof(fact_lexord__irreflexive, axiom, ![X5, X16, X4]:(![X42]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X42)),X16)))=>~(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X5),X5)),c_List_Olexord(X4,X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__irreflexive)). 4.46/4.68 fof(fact_take__Suc__conv__app__nth, axiom, ![X57, X4, X21]:(hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_OSuc,X21)),X57)=hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Otake(X4),X21),X57)),hAPP(hAPP(c_List_Olist_OCons(X4),hAPP(hAPP(c_List_Onth(X4),X57),X21)),c_List_Olist_ONil(X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Suc__conv__app__nth)). 4.46/4.68 fof(fact_aset_I3_J, axiom, ![X2, X64, X65]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))=>((X64=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X64),X65)<=![X42]:(![X66]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),X2))=>X64!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X66),X42))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X42),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X65)))))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X64),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_aset_I3_J)). 4.46/4.68 fof(fact_SUPR__set__fold, axiom, ![X27, X7, X3, X4]:(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4),hAPP(c_List_Oset(X3),X7)),X27)=hAPP(c_List_Ofoldl(X4,X3,hAPP(c_COMBC(X3,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X3),c_Lattices_Osemilattice__sup__class_Osup(X4)),X27)),c_Orderings_Obot__class_Obot(X4)),X7)<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUPR__set__fold)). 4.46/4.68 fof(fact_setsum__abs, axiom, ![X2, X27, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X27),X2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),hAPP(hAPP(c_COMBB(X4,X4,X3),c_Groups_Oabs__class_Oabs(X4)),X27)),X2)))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__abs)). 4.46/4.68 fof(fact_min__max_Obelow__fold1__iff, axiom, ![X6, X2, X4]:(class_Orderings_Olinorder(X4)=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omin(X4)),X2)))<=>![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X42)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Obelow__fold1__iff)). 4.46/4.68 fof(fact_below__fold1__iff, axiom, ![X6, X2, X4]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),hAPP(c_Finite__Set_Ofold1(X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),X2)))<=>![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X42))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X2))))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_below__fold1__iff)). 4.46/4.68 fof(fact_strict__below__fold1__iff, axiom, ![X6, X2, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omin(X4)),X2)))<=>![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),X42))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_strict__below__fold1__iff)). 4.46/4.68 fof(fact_divide__left__mono__neg, axiom, ![X10, X11, X12, X4]:(class_Fields_Olinordered__field__inverse__zero(X4)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X10),X12)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X10),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X10),c_Groups_Ozero__class_Ozero(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__left__mono__neg)). 4.46/4.68 fof(fact_takeWhile__eq__take__P__nth, axiom, ![X28, X7, X4, X14]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))=>~(hBOOL(hAPP(X28,hAPP(hAPP(c_List_Onth(X4),X7),X14)))))=>c_List_OtakeWhile(X4,X28,X7)=hAPP(hAPP(c_List_Otake(X4),X14),X7))<=![X41]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))=>hBOOL(hAPP(X28,hAPP(hAPP(c_List_Onth(X4),X7),X41))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__eq__take__P__nth)). 4.46/4.68 fof(fact_pair__imageI, axiom, ![X27, X29, X2, X37, X18, X3, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X18),X37)),X2))=>hBOOL(hAPP(hAPP(c_member(X29),hAPP(hAPP(X27,X18),X37)),hAPP(c_Set_Oimage(tc_prod(X4,X3),X29,hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,X29),X27)),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__imageI)). 4.46/4.68 fof(fact_acyclic__insert, axiom, ![X16, X6, X5, X4]:((~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_Transitive__Closure_Ortrancl(X4,X16))))&c_Wellfounded_Oacyclic(X4,X16))<=>c_Wellfounded_Oacyclic(X4,hAPP(hAPP(c_Set_Oinsert(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X5),X6)),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclic__insert)). 4.46/4.68 fof(fact_folding__image__simple_Oremove, axiom, ![X6, X2, X62, X50, X35, X27, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))=>(hBOOL(hAPP(hAPP(c_member(X3),X6),X2))=>hAPP(X62,X2)=hAPP(hAPP(X27,hAPP(X50,X6)),hAPP(X62,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X3),X6),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))))))<=c_Finite__Set_Ofolding__image__simple(X4,X3,X27,X35,X50,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Oremove)). 4.46/4.68 fof(fact_folding__image__simple_Ounion__disjoint, axiom, ![X1, X2, X62, X50, X35, X27, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1))=>(hAPP(X62,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(X27,hAPP(X62,X2)),hAPP(X62,X1))<=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X2),X1))))<=c_Finite__Set_Ofolding__image__simple(X4,X3,X27,X35,X50,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Ounion__disjoint)). 4.46/4.68 fof(fact_listsum__const__mult, axiom, ![X7, X27, X39, X3, X4]:(class_Rings_Osemiring__0(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X39),hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X3,X4),X27),X7)))=hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X3,X4),hAPP(hAPP(c_COMBB(X4,X4,X3),hAPP(c_Groups_Otimes__class_Otimes(X4),X39)),X27)),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__const__mult)). 4.46/4.68 fof(fact_Image__subset__eq, axiom, ![X1, X2, X16, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3,X4,X16),X2)),X1))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X3,hAPP(c_Relation_Oconverse(X3,X4),X16)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__subset__eq)). 4.46/4.68 fof(fact_wf__insert, axiom, ![X16, X6, X5, X4]:((~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_Transitive__Closure_Ortrancl(X4,X16))))&c_Wellfounded_Owf(X4,X16))<=>c_Wellfounded_Owf(X4,hAPP(hAPP(c_Set_Oinsert(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X5),X6)),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__insert)). 4.46/4.68 fof(fact_sorted__rev__nth__mono, axiom, ![X20, X21, X57, X4]:((c_List_Olinorder__class_Osorted(X4,hAPP(c_List_Orev(X4),X57))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_List_Onth(X4),X57),X20)),hAPP(hAPP(c_List_Onth(X4),X57),X21)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57))))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__rev__nth__mono)). 4.46/4.68 fof(fact_inj__on__INTER, axiom, ![X2, X27, X29, X3, X4, X73]:((c_Fun_Oinj__on(X3,X29,X27,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X73),X2))<=![X41]:(hBOOL(hAPP(hAPP(c_member(X4),X41),X73))=>c_Fun_Oinj__on(X3,X29,X27,hAPP(X2,X41))))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X73), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__INTER)). 4.46/4.68 fof(fact_fold1__Un2, axiom, ![X1, X2, X4]:(class_Lattices_Oab__semigroup__idem__mult(X4)=>((X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X1=>hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),X2)),hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),X1)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__Un2)). 4.46/4.68 fof(fact_sorted__list__of__set__insert, axiom, ![X6, X2, X4]:((c_List_Olinorder__class_Osorted__list__of__set(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)),X6),c_List_Olinorder__class_Osorted__list__of__set(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__list__of__set__insert)). 4.46/4.68 fof(fact_reduction__pairI, axiom, ![X46, X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X26),X46)),X26))=>c_FunDef_Oreduction__pair(X4,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X26),X46)))<=c_Wellfounded_Owf(X4,X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_reduction__pairI)). 4.46/4.68 fof(fact_Ints__odd__less__0, axiom, ![X18, X4]:(class_Rings_Olinordered__idom(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),X18)),X18)),c_Groups_Ozero__class_Ozero(X4))))<=hBOOL(hAPP(hAPP(c_member(X4),X18),c_Int_Oring__1__class_OInts(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__odd__less__0)). 4.46/4.68 fof(fact_nth__take__lemma, axiom, ![X72, X57, X4, X15]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X72)))=>(hAPP(hAPP(c_List_Otake(X4),X15),X57)=hAPP(hAPP(c_List_Otake(X4),X15),X72)<=![X41]:(hAPP(hAPP(c_List_Onth(X4),X72),X41)=hAPP(hAPP(c_List_Onth(X4),X57),X41)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),X15)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__take__lemma)). 4.46/4.68 fof(fact_fun__left__comm__idem_Ofold__insert__idem, axiom, ![X6, X35, X2, X27, X3, X4]:(c_Finite__Set_Ofun__left__comm__idem(X4,X3,X27)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),X35),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(hAPP(X27,X6),hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),X35),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem_Ofold__insert__idem)). 4.46/4.68 fof(fact_fun__left__comm__idem_Ofold__insert__idem2, axiom, ![X6, X35, X2, X27, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),X35),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),hAPP(hAPP(X27,X6),X35)),X2))<=c_Finite__Set_Ofun__left__comm__idem(X4,X3,X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem_Ofold__insert__idem2)). 4.46/4.68 fof(fact_folding_Oinsert, axiom, ![X6, X2, X62, X27, X3, X4]:(c_Finite__Set_Ofolding(X4,X3,X27,X62)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))=>hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X62,X2)),hAPP(X27,X6))=hAPP(X62,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Oinsert)). 4.46/4.68 fof(fact_power__Suc__less, axiom, ![X17, X12, X4]:(class_Rings_Olinordered__semidom(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),c_Groups_Oone__class_Oone(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17))),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__Suc__less)). 4.46/4.68 fof(fact_folding_Oinsert__remove, axiom, ![X6, X2, X62, X27, X3, X4]:(c_Finite__Set_Ofolding(X4,X3,X27,X62)=>(hAPP(X62,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X62,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),hAPP(X27,X6))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Oinsert__remove)). 4.46/4.68 fof(fact_listsum__update__nat, axiom, ![X17, X274, X15]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X274)))=>hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X274),X15),X17))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X274)),X17)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X274),X15))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__update__nat)). 4.46/4.68 fof(fact_insort__insert__insort__key, axiom, ![X7, X3, X6, X27, X4]:((hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3,X4,X27),X6),X7)=c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X27,X6,X7)<=~(hBOOL(hAPP(hAPP(c_member(X4),hAPP(X27,X6)),hAPP(c_Set_Oimage(X3,X4,X27),hAPP(c_List_Oset(X3),X7))))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__insert__insort__key)). 4.46/4.68 fof(fact_fold1Set_Oequations, axiom, ![X250, X135, X123, X27, X4]:(hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,X27,hAPP(hAPP(c_Set_Oinsert(X4),X123),X135)),X250))<=>?[X125, X161]:((hAPP(hAPP(c_Set_Oinsert(X4),X123),X135)=hAPP(hAPP(c_Set_Oinsert(X4),X125),X161)&~(hBOOL(hAPP(hAPP(c_member(X4),X125),X161))))&hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X4,X27,X125,X161),X250)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1Set_Oequations)). 4.46/4.68 fof(fact_union__comp__emptyL, axiom, ![X1, X52, X2, X4]:((hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X2),X1)),X52)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))<=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X1),X52)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)))<=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X2),X52)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_union__comp__emptyL)). 4.46/4.68 fof(fact_union__comp__emptyR, axiom, ![X52, X1, X2, X4]:((c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X2),X52)=>hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X1),X52))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)))<=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_union__comp__emptyR)). 4.46/4.68 fof(fact_Diff1__fold__graph, axiom, ![X5, X6, X2, X35, X27, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X3,X27,X35,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X5))=>(hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X3,X27,X35,X2),hAPP(hAPP(X27,X6),X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff1__fold__graph)). 4.46/4.68 fof(fact_mem__splitE, axiom, ![X109, X39, X29, X3, X35, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X35),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3,X29,tc_fun(X4,tc_HOL_Obool)),X39),X109)))=>~(![X42, X44]:(hAPP(hAPP(c_Product__Type_OPair(X3,X29),X42),X44)=X109=>~(hBOOL(hAPP(hAPP(c_member(X4),X35),hAPP(hAPP(X39,X42),X44))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mem__splitE)). 4.46/4.68 fof(fact_sorted__map__same, axiom, ![X7, X50, X27, X3, X4]:(c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X27),hAPP(c_List_Ofilter(X3,hAPP(hAPP(c_COMBC(X3,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,tc_HOL_Obool),X3),c_fequal),X27)),hAPP(X50,X7))),X7)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__map__same)). 4.46/4.68 fof(fact_fun__upd__image, axiom, ![X5, X27, X3, X2, X6, X4]:((hAPP(hAPP(c_Set_Oinsert(X3),X5),hAPP(c_Set_Oimage(X4,X3,X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(c_Set_Oimage(X4,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X3),X27),X6),X5)),X2)<=hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))&(~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))=>hAPP(c_Set_Oimage(X4,X3,X27),X2)=hAPP(c_Set_Oimage(X4,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X3),X27),X6),X5)),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__image)). 4.46/4.68 fof(fact_append__eq__append__conv2, axiom, ![X202, X88, X32, X7, X4]:(hAPP(hAPP(c_List_Oappend(X4),X88),X202)=hAPP(hAPP(c_List_Oappend(X4),X7),X32)<=>?[X219]:((hAPP(hAPP(c_List_Oappend(X4),X219),X202)=X32&hAPP(hAPP(c_List_Oappend(X4),X7),X219)=X88)|(X7=hAPP(hAPP(c_List_Oappend(X4),X88),X219)&hAPP(hAPP(c_List_Oappend(X4),X219),X32)=X202))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__eq__append__conv2)). 4.46/4.68 fof(fact_pick_Osimps, axiom, ![X57, X48, X4, X21]:((hAPP(c_Random_Opick(X4,X57),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X21),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X4),X48)))=hAPP(c_Random_Opick(X4,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X4)),X48),X57)),X21)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X21),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X4),X48)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X21),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X4),X48)))=>hAPP(c_Random_Opick(X4,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X4)),X48),X57)),X21)=hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X4),X48))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pick_Osimps)). 4.46/4.68 fof(fact_zmult__zless__mono2__lemma, axiom, ![X15, X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21),X20))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X15)),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X15)),X20))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__zless__mono2__lemma)). 4.46/4.68 fof(fact_abs__triangle__ineq3, axiom, ![X11, X12, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)))),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__triangle__ineq3)). 4.46/4.68 fof(fact_divide__less__eq, axiom, ![X18, X39, X37, X4]:(class_Fields_Olinordered__field__inverse__zero(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X37),X39)),X18))<=>((((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),c_Groups_Ozero__class_Ozero(X4))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X18)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),c_Groups_Ozero__class_Ozero(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)),X37))))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X39))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X39)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__less__eq)). 4.46/4.68 fof(fact_wfP__SUP, axiom, ![X4, X16, X3]:(![X41]:c_Wellfounded_OwfP(X3,hAPP(X16,X41))=>(c_Wellfounded_OwfP(X3,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_fun(X3,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),X16))<=![X41, X98]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),c_Predicate_ODomainP(X3,X3,hAPP(X16,X41))),c_Predicate_ORangeP(X3,X3,hAPP(X16,X98)))=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))<=hAPP(X16,X41)!=hAPP(X16,X98)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__SUP)). 4.46/4.68 fof(fact_folding__one__idem_Ohom__commute, axiom, ![X122, X58, X62, X27, X4]:(c_Finite__Set_Ofolding__one__idem(X4,X27,X62)=>(![X42, X44]:hAPP(X58,hAPP(hAPP(X27,X42),X44))=hAPP(hAPP(X27,hAPP(X58,X42)),hAPP(X58,X44))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X122))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X122=>hAPP(X58,hAPP(X62,X122))=hAPP(X62,hAPP(c_Set_Oimage(X4,X4,X58),X122)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Ohom__commute)). 4.46/4.68 fof(fact_atLeastLessThan__add__Un, axiom, ![X45, X25, X24]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24),X25)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X45)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X45))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__add__Un)). 4.46/4.68 fof(fact_divide__le__eq, axiom, ![X18, X39, X37, X4]:((((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X39)))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),c_Groups_Ozero__class_Ozero(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)),X37)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X18))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),c_Groups_Ozero__class_Ozero(X4)))))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X39))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X37),X39)),X18)))<=class_Fields_Olinordered__field__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__le__eq)). 4.46/4.68 fof(fact_converseE, axiom, ![X16, X43, X3, X4]:(~(![X42, X44]:(~(hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X42),X44)),X16)))<=hAPP(hAPP(c_Product__Type_OPair(X4,X3),X44),X42)=X43))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),X43),hAPP(c_Relation_Oconverse(X3,X4),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converseE)). 4.46/4.68 fof(fact_fold__image__1, axiom, ![X27, X46, X4, X3]:(((hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Otimes__class_Otimes(X3)),X27),c_Groups_Oone__class_Oone(X3)),X46)=c_Groups_Oone__class_Oone(X3)<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X46))=>c_Groups_Oone__class_Oone(X3)=hAPP(X27,X42)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X46)))<=class_Groups_Ocomm__monoid__mult(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__1)). 4.46/4.68 fof(fact_folding__image__simple_Oinsert__remove, axiom, ![X6, X2, X62, X50, X35, X27, X3, X4]:(c_Finite__Set_Ofolding__image__simple(X4,X3,X27,X35,X50,X62)=>(hAPP(X62,hAPP(hAPP(c_Set_Oinsert(X3),X6),X2))=hAPP(hAPP(X27,hAPP(X50,X6)),hAPP(X62,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X3),X6),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Oinsert__remove)). 4.46/4.68 fof(fact_folding__idem_Ounion__idem, axiom, ![X1, X2, X62, X27, X3, X4]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X62,X2)),hAPP(X62,X1))=hAPP(X62,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=c_Finite__Set_Ofolding__idem(X4,X3,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__idem_Ounion__idem)). 4.46/4.68 fof(fact_setsum__reindex, axiom, ![X58, X1, X27, X3, X4, X29]:((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X29),hAPP(c_Fun_Ocomp(X3,X29,X4,X58),X27)),X1)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X29),X58),hAPP(c_Set_Oimage(X4,X3,X27),X1))<=c_Fun_Oinj__on(X4,X3,X27,X1))<=class_Groups_Ocomm__monoid__add(X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__reindex)). 4.46/4.68 fof(fact_mem__Sigma__iff, axiom, ![X1, X2, X37, X18, X3, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X18),X2))&hBOOL(hAPP(hAPP(c_member(X3),X37),hAPP(X1,X18))))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X18),X37)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mem__Sigma__iff)). 4.46/4.68 fof(fact_card__bij__eq, axiom, ![X50, X1, X2, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,X2)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X3,X27),X2)),X1))=>(c_Fun_Oinj__on(X3,X4,X50,X1)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X4,X50),X1)),X2))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hAPP(c_Finite__Set_Ocard(X4),X2)=hAPP(c_Finite__Set_Ocard(X3),X1)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__bij__eq)). 4.46/4.68 fof(fact_min__max_OInf__fin_Osubset__idem, axiom, ![X1, X2, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>((c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X2)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X1)),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X2))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X2)))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Osubset__idem)). 4.46/4.68 fof(fact_min__max_OSup__fin_Osubset__idem, axiom, ![X1, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(X1!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X2))=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X1)),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X2))=c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X2))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Osubset__idem)). 4.46/4.68 fof(fact_Cons__acc__listrel1I, axiom, ![X7, X16, X6, X4]:((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)),c_Wellfounded_Oacc(tc_List_Olist(X4),c_List_Olistrel1(X4,X16))))<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X7),c_Wellfounded_Oacc(tc_List_Olist(X4),c_List_Olistrel1(X4,X16)))))<=hBOOL(hAPP(hAPP(c_member(X4),X6),c_Wellfounded_Oacc(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cons__acc__listrel1I)). 4.46/4.68 fof(fact_list__size__pointwise, axiom, ![X50, X27, X7, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X4,X27,X7)),c_List_Olist_Olist__size(X4,X50,X7)))<=![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X27,X42)),hAPP(X50,X42)))<=hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__size__pointwise)). 4.46/4.68 fof(fact_le__divide__eq, axiom, ![X39, X37, X18, X4]:((((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),c_Groups_Ozero__class_Ozero(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39))))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),c_Groups_Ozero__class_Ozero(X4))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),c_Groups_Ozero__class_Ozero(X4)))))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X39))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)),X37))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X39))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X37),X39))))<=class_Fields_Olinordered__field__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__divide__eq)). 4.46/4.68 fof(fact_gt__half__sum, axiom, ![X11, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Oone__class_Oone(X4)))),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11)))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_gt__half__sum)). 4.46/4.68 fof(fact_less__divide__eq, axiom, ![X39, X37, X18, X4]:(class_Fields_Olinordered__field__inverse__zero(X4)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X39))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)),X37)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X39)))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),c_Groups_Ozero__class_Ozero(X4))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),c_Groups_Ozero__class_Ozero(X4)))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),c_Groups_Ozero__class_Ozero(X4))))))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X37),X39))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__divide__eq)). 4.46/4.68 fof(fact_less__half__sum, axiom, ![X11, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Oone__class_Oone(X4)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11)))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__half__sum)). 4.46/4.68 fof(fact_folding_Ocommute__comp_H, axiom, ![X6, X2, X62, X27, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X62,X2)),hAPP(X27,X6))=hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X27,X6)),hAPP(X62,X2)))<=c_Finite__Set_Ofolding(X4,X3,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ocommute__comp_H)). 4.46/4.68 fof(fact_nth__append, axiom, ![X72, X57, X4, X17]:((hAPP(hAPP(c_List_Onth(X4),X72),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))=hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Oappend(X4),X57),X72)),X17)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))))&(hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Oappend(X4),X57),X72)),X17)=hAPP(hAPP(c_List_Onth(X4),X57),X17)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__append)). 4.46/4.68 fof(fact_inj__on__iff__card__le, axiom, ![X1, X3, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>((?[X40]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X3,X40),X2)),X1))&c_Fun_Oinj__on(X4,X3,X40,X2))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X2)),hAPP(c_Finite__Set_Ocard(X3),X1))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__iff__card__le)). 4.46/4.68 fof(fact_list__update__append1, axiom, ![X48, X72, X57, X4, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))=>hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Oappend(X4),X57),X72)),X21),X48)=hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Olist__update(X4,X57),X21),X48)),X72)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__append1)). 4.46/4.68 fof(fact_power__strict__mono, axiom, ![X17, X11, X12, X4]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X17))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11)))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__strict__mono)). 4.46/4.68 fof(fact_power__strict__decreasing, axiom, ![X12, X152, X17, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X152))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X152)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),c_Groups_Oone__class_Oone(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12))))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__strict__decreasing)). 4.46/4.68 fof(fact_power__decreasing, axiom, ![X12, X152, X17, X4]:(class_Rings_Olinordered__semidom(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X152)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),c_Groups_Oone__class_Oone(X4)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),X152)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__decreasing)). 4.46/4.68 fof(fact_all__set__conv__all__nth, axiom, ![X28, X7, X4]:(![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7)))=>hBOOL(hAPP(X28,X42)))<=>![X41]:(hBOOL(hAPP(X28,hAPP(hAPP(c_List_Onth(X4),X7),X41)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__set__conv__all__nth)). 4.46/4.68 fof(fact_div__mod__equality, axiom, ![X10, X11, X12, X4]:(class_Divides_Osemiring__div(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X12),X11)),X11)),c_Divides_Odiv__class_Omod(X4,X12,X11))),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mod__equality)). 4.46/4.68 fof(fact_abs__setsum__abs, axiom, ![X2, X27, X3, X4]:(hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),hAPP(hAPP(c_COMBB(X4,X4,X3),c_Groups_Oabs__class_Oabs(X4)),X27)),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),hAPP(hAPP(c_COMBB(X4,X4,X3),c_Groups_Oabs__class_Oabs(X4)),X27)),X2)<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__setsum__abs)). 4.46/4.68 fof(fact_fold1__antimono, axiom, ![X1, X2, X4]:(class_Orderings_Olinorder(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omin(X4)),X1)),hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omin(X4)),X2)))))<=X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__antimono)). 4.46/4.68 fof(fact_div__mod__equality2, axiom, ![X10, X12, X11, X4]:(class_Divides_Osemiring__div(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X12),X11))),c_Divides_Odiv__class_Omod(X4,X12,X11))),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mod__equality2)). 4.46/4.68 fof(fact_diff__card__le__card__Diff, axiom, ![X2, X1, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X2)),hAPP(c_Finite__Set_Ocard(X4),X1))),hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__card__le__card__Diff)). 4.46/4.68 fof(fact_quotient__disj, axiom, ![X76, X173, X16, X2, X4]:(((hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X76),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X2),X16)))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X173),X76)|X173=X76))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X173),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X2),X16))))<=c_Equiv__Relations_Oequiv(X4,X2,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotient__disj)). 4.46/4.68 fof(fact_UN__insert__distrib, axiom, ![X1, X18, X3, X2, X23, X4]:(hAPP(hAPP(c_Set_Oinsert(X3),X18),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Set_Oinsert(X3),X18)),X1))<=hBOOL(hAPP(hAPP(c_member(X4),X23),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__insert__distrib)). 4.46/4.68 fof(fact_transfer__int__nat__sum__prod_I2_J, axiom, ![X27, X2, X4]:((c_Nat__Transfer_Onat__set(X2)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X4),hAPP(hAPP(c_COMBB(tc_Int_Oint,X4,tc_Nat_Onat),X27),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X4),X27),X2))<=(class_Groups_Ocomm__monoid__add(X4)&class_Groups_Ocomm__monoid__mult(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__sum__prod_I2_J)). 4.46/4.68 fof(fact_transfer__int__nat__sum__prod_I1_J, axiom, ![X27, X2, X4]:((c_Nat__Transfer_Onat__set(X2)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X4),X27),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(hAPP(c_COMBB(tc_Int_Oint,X4,tc_Nat_Onat),X27),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))<=(class_Groups_Ocomm__monoid__add(X4)&class_Groups_Ocomm__monoid__mult(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__sum__prod_I1_J)). 4.46/4.68 fof(fact_folding__image__simple_Oinsert, axiom, ![X6, X2, X62, X50, X35, X27, X3, X4]:(((~(hBOOL(hAPP(hAPP(c_member(X3),X6),X2)))=>hAPP(hAPP(X27,hAPP(X50,X6)),hAPP(X62,X2))=hAPP(X62,hAPP(hAPP(c_Set_Oinsert(X3),X6),X2)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))<=c_Finite__Set_Ofolding__image__simple(X4,X3,X27,X35,X50,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Oinsert)). 4.46/4.68 fof(fact_UN__subset__iff, axiom, ![X1, X2, X73, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X73),X2)),X1))<=>![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(X2,X42)),X1))<=hBOOL(hAPP(hAPP(c_member(X3),X42),X73)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__subset__iff)). 4.46/4.68 fof(fact_fold1__below__iff, axiom, ![X6, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omin(X4)),X2)),X6))<=>?[X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X42),X6))))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__below__iff)). 4.46/4.68 fof(fact_INT__subset__iff, axiom, ![X2, X73, X3, X1, X4]:(![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),hAPP(X2,X42)))<=hBOOL(hAPP(hAPP(c_member(X3),X42),X73)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X73),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__subset__iff)). 4.46/4.68 fof(fact_INT__simps_I4_J, axiom, ![X1, X2, X3, X4, X52]:((X52=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X2)),X1)))&(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X2)),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X52),X1))<=X52!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__simps_I4_J)). 4.46/4.68 fof(fact_fold1__strict__below__iff, axiom, ![X6, X2, X4]:(class_Orderings_Olinorder(X4)=>((X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omin(X4)),X2)),X6))<=>?[X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X42),X6)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__strict__below__iff)). 4.46/4.68 fof(fact_INT__simps_I2_J, axiom, ![X1, X2, X3, X4, X52]:((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X52),X1))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X2)),X1))<=X52!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X2)),X1))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__simps_I2_J)). 4.46/4.68 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J, axiom, ![X1, X2]:((c_Nat__Transfer_Onat__set(X1)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X2),X1)=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1))))<=c_Nat__Transfer_Onat__set(X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J)). 4.46/4.68 fof(fact_finite__SigmaI, axiom, ![X1, X3, X2, X4]:((![X125]:(hBOOL(hAPP(hAPP(c_member(X4),X125),X2))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X1,X125))))=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),X1))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__SigmaI)). 4.46/4.68 fof(fact_div__pos__neg, axiom, ![X11, X12]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11)=hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__pos__neg)). 4.46/4.68 fof(fact_sorted__equals__nth__mono, axiom, ![X7, X4]:((![X98]:(![X41]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_List_Onth(X4),X7),X41)),hAPP(hAPP(c_List_Onth(X4),X7),X98)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X41),X98)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))))<=>c_List_Olinorder__class_Osorted(X4,X7))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__equals__nth__mono)). 4.46/4.68 fof(fact_finite__UN__I, axiom, ![X1, X3, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(![X125]:(hBOOL(hAPP(hAPP(c_member(X4),X125),X2))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X1,X125))))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X2),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UN__I)). 4.46/4.68 fof(fact_map__of__zip__map, axiom, ![X27, X3, X7, X6, X4]:((c_Option_Ooption_ONone(X3)=hAPP(hAPP(c_Map_Omap__of(X4,X3),hAPP(hAPP(c_List_Ozip(X4,X3),X7),hAPP(hAPP(c_List_Omap(X4,X3),X27),X7))),X6)<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))))&(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))=>hAPP(hAPP(c_Map_Omap__of(X4,X3),hAPP(hAPP(c_List_Ozip(X4,X3),X7),hAPP(hAPP(c_List_Omap(X4,X3),X27),X7))),X6)=hAPP(c_Option_Ooption_OSome(X3),hAPP(X27,X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__zip__map)). 4.46/4.68 fof(fact_finite__UN, axiom, ![X1, X3, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X2),X1)))<=>![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X1,X42)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UN)). 4.46/4.68 fof(fact_card__Diff1__less, axiom, ![X6, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X4),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff1__less)). 4.46/4.68 fof(fact_mod__pos__neg, axiom, ![X11, X12]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11)=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__pos__neg)). 4.46/4.68 fof(fact_mod__neg__neg, axiom, ![X11, X12]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11)=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__neg__neg)). 4.46/4.68 fof(fact_SUP__le__iff, axiom, ![X23, X153, X2, X3, X4]:((![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(X153,X42)),X23))<=hBOOL(hAPP(hAPP(c_member(X3),X42),X2)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4),X2),X153)),X23)))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__le__iff)). 4.46/4.68 fof(fact_setprod__pos, axiom, ![X27, X2, X4, X3]:(class_Rings_Olinordered__semidom(X3)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),X2)))<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(X27,X42)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__pos)). 4.46/4.68 fof(fact_comp__surj, axiom, ![X50, X29, X27, X4, X3]:(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_Oimage(X3,X4,X27),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))=>(hAPP(c_Set_Oimage(X3,X29,hAPP(c_Fun_Ocomp(X4,X29,X3,X50),X27)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X29,tc_HOL_Obool))<=c_Orderings_Otop__class_Otop(tc_fun(X29,tc_HOL_Obool))=hAPP(c_Set_Oimage(X4,X29,X50),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comp__surj)). 4.46/4.68 fof(fact_insert__partition, axiom, ![X62, X6, X4]:((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X6),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X62))<=![X42]:(![X66]:((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X42),X66)<=X66!=X42)<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X66),hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),X6),X62))))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X42),hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),X6),X62)))))<=~(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X6),X62)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__partition)). 4.46/4.68 fof(fact_setprod__nonneg, axiom, ![X27, X2, X4, X3]:(class_Rings_Olinordered__semidom(X3)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),X2)))<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(X27,X42)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__nonneg)). 4.46/4.68 fof(fact_le__INF__iff, axiom, ![X153, X2, X3, X23, X4]:((![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X23),hAPP(X153,X42)))<=hBOOL(hAPP(hAPP(c_member(X3),X42),X2)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X23),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X4),X2),X153))))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__INF__iff)). 4.46/4.68 fof(fact_zdiv__mono2, axiom, ![X11, X91, X12]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X91),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X91)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__mono2)). 4.46/4.68 fof(fact_zdiv__mono2__neg, axiom, ![X11, X91, X12]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X91),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X91)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__mono2__neg)). 4.46/4.68 fof(fact_Image__subset, axiom, ![X52, X1, X2, X16, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X3,X16),X52)),X1))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X16),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__subset)). 4.46/4.68 fof(fact_Some__eq__map__of__iff, axiom, ![X6, X5, X70, X3, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(tc_prod(X4,X3),X4),c_Product__Type_Ofst(X4,X3)),X70)))=>(hAPP(c_Option_Ooption_OSome(X3),X5)=hAPP(hAPP(c_Map_Omap__of(X4,X3),X70),X6)<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X6),X5)),hAPP(c_List_Oset(tc_prod(X4,X3)),X70))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Some__eq__map__of__iff)). 4.46/4.68 fof(fact_div__neg__neg, axiom, ![X11, X12]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__neg__neg)). 4.46/4.68 fof(fact_surj__Compl__image__subset, axiom, ![X2, X27, X4, X3]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X4,X27),X2))),hAPP(c_Set_Oimage(X3,X4,X27),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),X2))))<=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_Oimage(X3,X4,X27),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_surj__Compl__image__subset)). 4.46/4.68 fof(fact_rev__nth, axiom, ![X57, X4, X17]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))=>hAPP(hAPP(c_List_Onth(X4),X57),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),hAPP(c_Nat_OSuc,X17)))=hAPP(hAPP(c_List_Onth(X4),hAPP(c_List_Orev(X4),X57)),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__nth)). 4.46/4.68 fof(fact_card__Diff__subset__Int, axiom, ![X1, X2, X4]:(hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X2)),hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff__subset__Int)). 4.46/4.68 fof(fact_fold__graph_OinsertI, axiom, ![X5, X35, X27, X3, X2, X6, X4]:((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X3,X27,X35,X2),X5))=>hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X3,X27,X35,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2)),hAPP(hAPP(X27,X6),X5))))<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph_OinsertI)). 4.46/4.68 fof(fact_min__max_Ofold__inf__le__inf, axiom, ![X37, X18, X2, X4]:(((hBOOL(hAPP(hAPP(c_member(X4),X18),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omin(X4)),X37),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X18),X37))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofold__inf__le__inf)). 4.46/4.68 fof(fact_wf__iff__no__infinite__down__chain, axiom, ![X16, X4]:(~(?[X40]:![X41]:hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(X40,hAPP(c_Nat_OSuc,X41))),hAPP(X40,X41))),X16)))<=>c_Wellfounded_Owf(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__iff__no__infinite__down__chain)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, axiom, ![X140, X141, X142, X143, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X143),X141)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X142),X140))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X143),X142)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X141),X140))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J)). 4.46/4.68 fof(fact_setsum__shift__bounds__cl__Suc__ivl, axiom, ![X14, X22, X27, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X22),hAPP(c_Nat_OSuc,X14)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Nat_Onat),X27),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X22,X14))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__shift__bounds__cl__Suc__ivl)). 4.46/4.68 fof(fact_fold__inf__le__inf, axiom, ![X37, X18, X2, X4]:(class_Lattices_Osemilattice__inf(X4)=>((hBOOL(hAPP(hAPP(c_member(X4),X18),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),X37),X2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X18),X37))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__inf__le__inf)). 4.46/4.68 fof(fact_min__max_Osup__le__fold__sup, axiom, ![X37, X18, X2, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X18),X37)),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omax(X4)),X37),X2)))<=hBOOL(hAPP(hAPP(c_member(X4),X18),X2)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__le__fold__sup)). 4.46/4.68 fof(fact_sup__le__fold__sup, axiom, ![X37, X18, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X18),X37)),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4)),X37),X2)))<=hBOOL(hAPP(hAPP(c_member(X4),X18),X2))))<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__le__fold__sup)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, axiom, ![X133, X10, X11, X12, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X133))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X133))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J)). 4.46/4.68 fof(fact_Image__mono, axiom, ![X2, X92, X16, X93, X3, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X92),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X3,X93),X92)),hAPP(c_Relation_OImage(X4,X3,X16),X2))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X93),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__mono)). 4.46/4.68 fof(fact_fun__left__comm_Ofold__graph__insertE, axiom, ![X13, X2, X6, X35, X27, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X3,X27,X35,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2)),X13))=>(~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))=>~(![X44]:(~(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X3,X27,X35,X2),X44)))<=X13=hAPP(hAPP(X27,X6),X44)))))<=c_Finite__Set_Ofun__left__comm(X4,X3,X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__graph__insertE)). 4.46/4.68 fof(fact_folding__image__simple__idem_Ounion__idem, axiom, ![X1, X2, X62, X50, X35, X27, X3, X4]:(c_Finite__Set_Ofolding__image__simple__idem(X4,X3,X27,X35,X50,X62)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1))=>hAPP(X62,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(X27,hAPP(X62,X2)),hAPP(X62,X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple__idem_Ounion__idem)). 4.46/4.68 fof(fact_mult__number__of__left, axiom, ![X49, X30, X63, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X63),X30))),X49)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X63)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X30)),X49))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__number__of__left)). 4.46/4.68 fof(fact_add__number__of__left, axiom, ![X49, X30, X63, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X63),X30))),X49)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X63)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X30)),X49))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__number__of__left)). 4.46/4.68 fof(fact_add__number__of__diff1, axiom, ![X10, X30, X63, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X63),X30))),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X63)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X30)),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__number__of__diff1)). 4.46/4.68 fof(fact_list__all2__update__cong2, axiom, ![X24, X5, X6, X32, X7, X28, X3, X4]:(c_List_Olist__all2(X4,X3,X28,X7,X32)=>(hBOOL(hAPP(hAPP(X28,X6),X5))=>(c_List_Olist__all2(X4,X3,X28,hAPP(hAPP(c_List_Olist__update(X4,X7),X24),X6),hAPP(hAPP(c_List_Olist__update(X3,X32),X24),X5))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__update__cong2)). 4.46/4.68 fof(fact_list__all2__update__cong, axiom, ![X5, X6, X32, X28, X3, X7, X4, X24]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))=>(c_List_Olist__all2(X4,X3,X28,X7,X32)=>(hBOOL(hAPP(hAPP(X28,X6),X5))=>c_List_Olist__all2(X4,X3,X28,hAPP(hAPP(c_List_Olist__update(X4,X7),X24),X6),hAPP(hAPP(c_List_Olist__update(X3,X32),X24),X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__update__cong)). 4.46/4.68 fof(fact_map__of__zip__is__None, axiom, ![X6, X32, X3, X7, X4]:((~(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7))))<=>c_Option_Ooption_ONone(X3)=hAPP(hAPP(c_Map_Omap__of(X4,X3),hAPP(hAPP(c_List_Ozip(X4,X3),X7),X32)),X6))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__zip__is__None)). 4.46/4.68 fof(fact_inj__image__Compl__subset, axiom, ![X2, X27, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X3,X27),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X3,X27),X2))))<=c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__image__Compl__subset)). 4.46/4.68 fof(fact_posDivAlg__div__mod, axiom, ![X31, X15]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15))=>(hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X15),X31)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,X31))=c_Divides_OposDivAlg(X15,X31)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X31)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_posDivAlg__div__mod)). 4.46/4.68 fof(fact_transfer__int__nat__sum__prod2_I1_J, axiom, ![X27, X2, X4]:(![X42]:(c_Nat__Transfer_Ois__nat(hAPP(X27,X42))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X2)))=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X4),c_Int_Onat),X27)),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Int_Oint),X27),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__sum__prod2_I1_J)). 4.46/4.68 fof(fact_INT__iff, axiom, ![X1, X2, X3, X37, X4]:(![X42]:(hBOOL(hAPP(hAPP(c_member(X3),X42),X2))=>hBOOL(hAPP(hAPP(c_member(X4),X37),hAPP(X1,X42))))<=>hBOOL(hAPP(hAPP(c_member(X4),X37),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__iff)). 4.46/4.68 fof(fact_Max_Ohom__commute, axiom, ![X122, X58, X4]:(class_Orderings_Olinorder(X4)=>(((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X122=>hAPP(X58,c_Big__Operators_Olinorder__class_OMax(X4,X122))=c_Big__Operators_Olinorder__class_OMax(X4,hAPP(c_Set_Oimage(X4,X4,X58),X122)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X122)))<=![X42, X44]:hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(X58,X42)),hAPP(X58,X44))=hAPP(X58,hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X42),X44)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Ohom__commute)). 4.46/4.68 fof(fact_Inf__fin_Ohom__commute, axiom, ![X122, X58, X4]:((((X122!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(X58,c_Big__Operators_Olattice__class_OInf__fin(X4,X122))=c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(c_Set_Oimage(X4,X4,X58),X122)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X122)))<=![X42, X44]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(X58,X42)),hAPP(X58,X44))=hAPP(X58,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X42),X44)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Ohom__commute)). 4.46/4.68 fof(fact_Sup__fin_Ohom__commute, axiom, ![X122, X58, X4]:((((X122!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(X58,c_Big__Operators_Olattice__class_OSup__fin(X4,X122))=c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(c_Set_Oimage(X4,X4,X58),X122)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X122)))<=![X42, X44]:hAPP(X58,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X42),X44))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(X58,X42)),hAPP(X58,X44)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Ohom__commute)). 4.46/4.68 fof(fact_Min_Ohom__commute, axiom, ![X122, X58, X4]:(class_Orderings_Olinorder(X4)=>(![X42, X44]:hAPP(X58,hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X42),X44))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(X58,X42)),hAPP(X58,X44))=>((X122!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(X58,c_Big__Operators_Olinorder__class_OMin(X4,X122))=c_Big__Operators_Olinorder__class_OMin(X4,hAPP(c_Set_Oimage(X4,X4,X58),X122)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X122))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Ohom__commute)). 4.46/4.68 fof(fact_negDivAlg__div__mod, axiom, ![X31, X15]:((hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X15),X31)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,X31))=c_Divides_OnegDivAlg(X15,X31)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X31)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negDivAlg__div__mod)). 4.46/4.68 fof(fact_finite__equiv__class, axiom, ![X173, X16, X2, X4]:(((hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X173),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X2),X16)))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X173)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X2)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__equiv__class)). 4.46/4.68 fof(fact_folding__one__idem_Ounion__idem, axiom, ![X1, X2, X62, X27, X4]:((((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>(hAPP(hAPP(X27,hAPP(X62,X2)),hAPP(X62,X1))=hAPP(X62,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X1))<=X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=c_Finite__Set_Ofolding__one__idem(X4,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Ounion__idem)). 4.46/4.68 fof(fact_times__divide__times__eq, axiom, ![X30, X49, X47, X48, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X47)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X49),X30))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X48),X49)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X47),X30))<=class_Fields_Ofield__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_times__divide__times__eq)). 4.46/4.68 fof(fact_transfer__nat__int__sum__prod_I2_J, axiom, ![X2, X27, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X4),X27),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Int_Oint),X27),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))<=(class_Groups_Ocomm__monoid__add(X4)&class_Groups_Ocomm__monoid__mult(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__sum__prod_I2_J)). 4.46/4.68 fof(fact_transfer__nat__int__sum__prod_I1_J, axiom, ![X2, X27, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X27),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Int_Oint),X27),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))<=(class_Groups_Ocomm__monoid__add(X4)&class_Groups_Ocomm__monoid__mult(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__sum__prod_I1_J)). 4.46/4.68 fof(fact_mod__mult__cong, axiom, ![X91, X11, X163, X10, X12, X4]:(((c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X163),X91),X10)<=c_Divides_Odiv__class_Omod(X4,X11,X10)=c_Divides_Odiv__class_Omod(X4,X91,X10))<=c_Divides_Odiv__class_Omod(X4,X163,X10)=c_Divides_Odiv__class_Omod(X4,X12,X10))<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__cong)). 4.46/4.68 fof(fact_card__inj__on__le, axiom, ![X1, X2, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,X2)=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X2)),hAPP(c_Finite__Set_Ocard(X3),X1))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X3,X27),X2)),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__inj__on__le)). 4.46/4.68 fof(fact_fun__left__comm__idem_Ofold__set, axiom, ![X7, X5, X27, X3, X4]:(c_Finite__Set_Ofun__left__comm__idem(X4,X3,X27)=>hAPP(c_List_Ofoldl(X3,X4,hAPP(c_COMBC(X4,X3,X3),X27),X5),X7)=hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),X5),hAPP(c_List_Oset(X4),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem_Ofold__set)). 4.46/4.68 fof(fact_setprod__pos__nat__iff, axiom, ![X27, X46, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,tc_Nat_Onat),X27),X46)))<=>![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X27,X42)))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X46))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__pos__nat__iff)). 4.46/4.68 fof(fact_ivl__disj__un_I17_J, axiom, ![X23, X22, X67, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X22),X23))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X67),X22)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X22),X23))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X67),X23))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X67),X22)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I17_J)). 4.46/4.68 fof(fact_abs__triangle__ineq2, axiom, ![X11, X12, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),hAPP(c_Groups_Oabs__class_Oabs(X4),X11))),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__triangle__ineq2)). 4.46/4.68 fof(fact_converse__iff, axiom, ![X16, X37, X18, X3, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X18),X37)),hAPP(c_Relation_Oconverse(X3,X4),X16)))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X37),X18)),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__iff)). 4.46/4.68 fof(fact_listrel1__subset__listrel, axiom, ![X93, X16, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool)),c_List_Olistrel1(X4,X16)),c_List_Olistrel(X4,X93)))<=c_Relation_Orefl__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),X93))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),X93))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1__subset__listrel)). 4.46/4.68 fof(fact_abs__triangle__ineq2__sym, axiom, ![X11, X12, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),hAPP(c_Groups_Oabs__class_Oabs(X4),X11))),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X12))))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__triangle__ineq2__sym)). 4.46/4.68 fof(fact_abs__triangle__ineq, axiom, ![X11, X12, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),hAPP(c_Groups_Oabs__class_Oabs(X4),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__triangle__ineq)). 4.46/4.68 fof(fact_abs__triangle__ineq4, axiom, ![X11, X12, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X11))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),hAPP(c_Groups_Oabs__class_Oabs(X4),X11))))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__triangle__ineq4)). 4.46/4.68 fof(fact_in__rtrancl__UnI, axiom, ![X46, X26, X6, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X6),c_Transitive__Closure_Ortrancl(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X26),X46))))<=(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X6),c_Transitive__Closure_Ortrancl(X4,X26)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X6),c_Transitive__Closure_Ortrancl(X4,X46))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__rtrancl__UnI)). 4.46/4.68 fof(fact_list__update__swap, axiom, ![X233, X48, X57, X4, X234, X21]:(hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Olist__update(X4,X57),X21),X48)),X234),X233)=hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Olist__update(X4,X57),X234),X233)),X21),X48)<=X234!=X21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__swap)). 4.46/4.68 fof(fact_mod__add__cong, axiom, ![X91, X11, X163, X10, X12, X4]:((c_Divides_Odiv__class_Omod(X4,X12,X10)=c_Divides_Odiv__class_Omod(X4,X163,X10)=>(c_Divides_Odiv__class_Omod(X4,X91,X10)=c_Divides_Odiv__class_Omod(X4,X11,X10)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X163),X91),X10)))<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__add__cong)). 4.46/4.68 fof(fact_card__Un__disjoint, axiom, ![X1, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X2)),hAPP(c_Finite__Set_Ocard(X4),X1))=hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Un__disjoint)). 4.46/4.68 fof(fact_add__divide__eq__iff, axiom, ![X47, X48, X49, X4]:(class_Fields_Ofield(X4)=>(X49!=c_Groups_Ozero__class_Ozero(X4)=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X49),X48)),X47)),X49)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X48),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X47),X49)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__divide__eq__iff)). 4.46/4.68 fof(fact_map__of__is__SomeD, axiom, ![X5, X6, X70, X4, X3]:(hAPP(c_Option_Ooption_OSome(X4),X5)=hAPP(hAPP(c_Map_Omap__of(X3,X4),X70),X6)=>hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X5)),hAPP(c_List_Oset(tc_prod(X3,X4)),X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__is__SomeD)). 4.46/4.68 fof(fact_abs__eq__mult, axiom, ![X11, X12, X4]:(class_Rings_Oordered__ring__abs(X4)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),c_Groups_Ozero__class_Ozero(X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),c_Groups_Ozero__class_Ozero(X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))))=>hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__eq__mult)). 4.46/4.68 fof(fact_diff__divide__eq__iff, axiom, ![X47, X48, X49, X4]:(class_Fields_Ofield(X4)=>(X49!=c_Groups_Ozero__class_Ozero(X4)=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X49),X48)),X47)),X49)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X48),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X47),X49)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__divide__eq__iff)). 4.46/4.68 fof(fact_mod__diff__cong, axiom, ![X91, X11, X163, X10, X12, X4]:(class_Divides_Oring__div(X4)=>((c_Divides_Odiv__class_Omod(X4,X91,X10)=c_Divides_Odiv__class_Omod(X4,X11,X10)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X11),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X163),X91),X10))<=c_Divides_Odiv__class_Omod(X4,X163,X10)=c_Divides_Odiv__class_Omod(X4,X12,X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__diff__cong)). 4.46/4.68 fof(fact_UN__finite__subset, axiom, ![X52, X2, X4]:(![X199]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X199)),X2)),X52))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2)),X52))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__finite__subset)). 4.46/4.68 fof(fact_add__frac__num, axiom, ![X49, X48, X47, X4]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X47)),X49)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X49),X47))),X47)<=c_Groups_Ozero__class_Ozero(X4)!=X47)<=class_Fields_Ofield__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__frac__num)). 4.46/4.68 fof(fact_list__ball__nth, axiom, ![X28, X7, X4, X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))=>(hBOOL(hAPP(X28,hAPP(hAPP(c_List_Onth(X4),X7),X14)))<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7)))=>hBOOL(hAPP(X28,X42))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ball__nth)). 4.46/4.68 fof(fact_rtrancl__power, axiom, ![X26, X109, X4]:(?[X199]:hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X109),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X199),X26)))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X109),c_Transitive__Closure_Ortrancl(X4,X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__power)). 4.46/4.68 fof(fact_divide__diff__eq__iff, axiom, ![X47, X48, X49, X4]:(class_Fields_Ofield(X4)=>(c_Groups_Ozero__class_Ozero(X4)!=X49=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X49)),X47)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X49),X47))),X49))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__diff__eq__iff)). 4.46/4.68 fof(fact_image__Int, axiom, ![X1, X2, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X3,X27),X2)),hAPP(c_Set_Oimage(X4,X3,X27),X1))=hAPP(c_Set_Oimage(X4,X3,X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Int)). 4.46/4.68 fof(fact_image__set__diff, axiom, ![X1, X2, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>hAPP(c_Set_Oimage(X4,X3,X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X3,X27),X2)),hAPP(c_Set_Oimage(X4,X3,X27),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__set__diff)). 4.46/4.68 fof(fact_order__fun_I1_J, axiom, ![X50, X27, X4, X3]:((class_Orderings_Oorder(X3)&class_Enum_Oenum(X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X3)),X27),X50))<=>hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X4),hAPP(hAPP(c_COMBS(X4,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,tc_HOL_Obool),X4),c_Orderings_Oord__class_Oless__eq(X3)),X27)),X50))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__fun_I1_J)). 4.46/4.68 fof(fact_finite__range__imageI, axiom, ![X27, X29, X50, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X29),hAPP(c_Set_Oimage(X3,X29,hAPP(hAPP(c_COMBB(X4,X29,X3),X27),X50)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Set_Oimage(X3,X4,X50),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__range__imageI)). 4.46/4.68 fof(fact_divide__add__eq__iff, axiom, ![X47, X48, X49, X4]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X49)),X47)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X49),X47))),X49)<=X49!=c_Groups_Ozero__class_Ozero(X4))<=class_Fields_Ofield(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__add__eq__iff)). 4.46/4.68 fof(fact_sort__foldl__insort, axiom, ![X7, X4]:(class_Orderings_Olinorder(X4)=>c_List_Olinorder__class_Osort__key(X4,X4,c_COMBI(X4),X7)=hAPP(c_List_Ofoldl(tc_List_Olist(X4),X4,hAPP(c_COMBC(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4))),c_List_Olist_ONil(X4)),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sort__foldl__insort)). 4.46/4.68 fof(fact_div__mult__self2, axiom, ![X10, X12, X11, X4]:(class_Divides_Osemiring__div(X4)=>(hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10))),X11)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X12),X11))<=c_Groups_Ozero__class_Ozero(X4)!=X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__self2)). 4.46/4.68 fof(fact_power__diff, axiom, ![X19, X17, X12, X4]:(((hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X19)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),X19)))<=X12!=c_Groups_Ozero__class_Ozero(X4))<=class_Fields_Ofield(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__diff)). 4.46/4.68 fof(fact_power__less__power__Suc, axiom, ![X17, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X12)))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__less__power__Suc)). 4.46/4.68 fof(fact_div__mult__self1, axiom, ![X10, X12, X11, X4]:((c_Groups_Ozero__class_Ozero(X4)!=X11=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X12),X11))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11))),X11))<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__self1)). 4.46/4.68 fof(fact_min__max_Ofold__sup__insert, axiom, ![X18, X37, X2, X4]:(class_Orderings_Olinorder(X4)=>(hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omax(X4)),X37),hAPP(hAPP(c_Set_Oinsert(X4),X18),X2))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X18),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omax(X4)),X37),X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofold__sup__insert)). 4.46/4.68 fof(fact_min__max_Ofold__inf__insert, axiom, ![X18, X37, X2, X4]:(class_Orderings_Olinorder(X4)=>(hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omin(X4)),X37),hAPP(hAPP(c_Set_Oinsert(X4),X18),X2))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X18),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omin(X4)),X37),X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofold__inf__insert)). 4.46/4.68 fof(fact_add__num__frac, axiom, ![X48, X49, X47, X4]:((X47!=c_Groups_Ozero__class_Ozero(X4)=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X49),X47))),X47)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X49),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X47)))<=class_Fields_Ofield__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__num__frac)). 4.46/4.68 fof(fact_set__drop__subset__set__drop, axiom, ![X7, X4, X22, X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14),X22))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Odrop(X4),X22),X7))),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Odrop(X4),X14),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__drop__subset__set__drop)). 4.46/4.68 fof(fact_set__take__subset__set__take, axiom, ![X7, X4, X14, X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Otake(X4),X22),X7))),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Otake(X4),X14),X7))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__take__subset__set__take)). 4.46/4.68 fof(fact_fold__sup__insert, axiom, ![X18, X37, X2, X4]:(class_Lattices_Osemilattice__sup(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X18),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4)),X37),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4)),X37),hAPP(hAPP(c_Set_Oinsert(X4),X18),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__sup__insert)). 4.46/4.68 fof(fact_fold__inf__insert, axiom, ![X18, X37, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X18),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),X37),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),X37),hAPP(hAPP(c_Set_Oinsert(X4),X18),X2)))<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__inf__insert)). 4.46/4.68 fof(fact_refl__on__comp__subset, axiom, ![X16, X2, X4]:(c_Relation_Orefl__on(X4,X2,X16)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(c_Relation_Oconverse(X4,X4),X16)),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__comp__subset)). 4.46/4.68 fof(fact_setprod_Oinsert, axiom, ![X50, X6, X2, X4, X3]:(class_Groups_Ocomm__monoid__mult(X3)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(X50,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X50),X2))<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod_Oinsert)). 4.46/4.68 fof(fact_power__minus, axiom, ![X17, X12, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)),X17)<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__minus)). 4.46/4.68 fof(fact_setsum__right__distrib, axiom, ![X2, X27, X3, X16, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),hAPP(hAPP(c_COMBB(X4,X4,X3),hAPP(c_Groups_Otimes__class_Otimes(X4),X16)),X27)),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X16),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X27),X2))<=class_Rings_Osemiring__0(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__right__distrib)). 4.46/4.68 fof(fact_setsum__insert, axiom, ![X27, X18, X62, X4, X3]:(((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),hAPP(hAPP(c_Set_Oinsert(X4),X18),X62))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(X27,X18)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X62))<=~(hBOOL(hAPP(hAPP(c_member(X4),X18),X62))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X62)))<=class_Groups_Ocomm__monoid__add(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__insert)). 4.46/4.68 fof(fact_map__upd__Some__unfold, axiom, ![X5, X6, X37, X18, X22, X4, X3]:(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X4)),X22),X18),hAPP(c_Option_Ooption_OSome(X4),X37)),X6)=hAPP(c_Option_Ooption_OSome(X4),X5)<=>((X6!=X18&hAPP(X22,X6)=hAPP(c_Option_Ooption_OSome(X4),X5))|(X18=X6&X37=X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upd__Some__unfold)). 4.46/4.68 fof(fact_nth__drop_H, axiom, ![X57, X4, X21]:(hAPP(hAPP(c_List_Olist_OCons(X4),hAPP(hAPP(c_List_Onth(X4),X57),X21)),hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_OSuc,X21)),X57))=hAPP(hAPP(c_List_Odrop(X4),X21),X57)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__drop_H)). 4.46/4.68 fof(fact_mlex__less, axiom, ![X26, X4, X5, X6, X27]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X27,X6)),hAPP(X27,X5)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_Wellfounded_Omlex__prod(X4,X27,X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mlex__less)). 4.46/4.68 fof(fact_split__div_H, axiom, ![X14, X22, X28]:(hBOOL(hAPP(X28,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X22),X14)))<=>(?[X144]:((hBOOL(hAPP(X28,X144))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),hAPP(c_Nat_OSuc,X144)))))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X144)),X22)))|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X14&hBOOL(hAPP(X28,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__div_H)). 4.46/4.68 fof(fact_Int__atLeastLessThan, axiom, ![X87, X39, X37, X18, X4]:(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X18),X39)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X37),X87))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X18),X37)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X39),X87))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__atLeastLessThan)). 4.46/4.68 fof(fact_folding__one_Oeq__fold_H, axiom, ![X6, X2, X62, X27, X4]:(((hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,X27),X6),X2)=hAPP(X62,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=c_Finite__Set_Ofolding__one(X4,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Oeq__fold_H)). 4.46/4.68 fof(fact_Image__iff, axiom, ![X2, X16, X3, X37, X4]:(?[X42]:(hBOOL(hAPP(hAPP(c_member(X3),X42),X2))&hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X42),X37)),X16)))<=>hBOOL(hAPP(hAPP(c_member(X4),X37),hAPP(c_Relation_OImage(X3,X4,X16),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__iff)). 4.46/4.68 fof(fact_ImageE, axiom, ![X2, X16, X3, X37, X4]:(~(![X42]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X42),X37)),X16))=>~(hBOOL(hAPP(hAPP(c_member(X3),X42),X2)))))<=hBOOL(hAPP(hAPP(c_member(X4),X37),hAPP(c_Relation_OImage(X3,X4,X16),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ImageE)). 4.46/4.68 fof(fact_fold__graph_H_Ointros_I2_J, axiom, ![X5, X35, X27, X3, X2, X6, X4]:((c_Nitpick_Ofold__graph_H(X4,X3,X27,X35,X2,hAPP(hAPP(X27,X6),X5))<=c_Nitpick_Ofold__graph_H(X4,X3,X27,X35,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X5))<=hBOOL(hAPP(hAPP(c_member(X4),X6),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph_H_Ointros_I2_J)). 4.46/4.68 fof(fact_Max__Un, axiom, ![X1, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X1=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),c_Big__Operators_Olinorder__class_OMax(X4,X2)),c_Big__Operators_Olinorder__class_OMax(X4,X1))=c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__Un)). 4.46/4.68 fof(fact_equiv__class__self, axiom, ![X18, X16, X2, X4]:(c_Equiv__Relations_Oequiv(X4,X2,X16)=>(hBOOL(hAPP(hAPP(c_member(X4),X18),hAPP(c_Relation_OImage(X4,X4,X16),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))<=hBOOL(hAPP(hAPP(c_member(X4),X18),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__class__self)). 4.46/4.68 fof(fact_folding_Ocommute__comp, axiom, ![X6, X5, X62, X27, X3, X4]:(hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X27,X5)),hAPP(X27,X6))=hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X27,X6)),hAPP(X27,X5))<=c_Finite__Set_Ofolding(X4,X3,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ocommute__comp)). 4.46/4.68 fof(fact_list__all2__all__nthI, axiom, ![X28, X37, X3, X18, X4]:((![X199]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X199),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X18)))=>hBOOL(hAPP(hAPP(X28,hAPP(hAPP(c_List_Onth(X4),X18),X199)),hAPP(hAPP(c_List_Onth(X3),X37),X199))))=>c_List_Olist__all2(X4,X3,X28,X18,X37))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X18)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__all__nthI)). 4.46/4.68 fof(fact_list__all2__conv__all__nth, axiom, ![X32, X7, X28, X3, X4]:(c_List_Olist__all2(X4,X3,X28,X7,X32)<=>(![X41]:(hBOOL(hAPP(hAPP(X28,hAPP(hAPP(c_List_Onth(X4),X7),X41)),hAPP(hAPP(c_List_Onth(X3),X32),X41)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))))&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__conv__all__nth)). 4.46/4.68 fof(fact_Inf__fin_Ounion__idem, axiom, ![X1, X2, X4]:(class_Lattices_Olattice(X4)=>(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),c_Big__Operators_Olattice__class_OInf__fin(X4,X2)),c_Big__Operators_Olattice__class_OInf__fin(X4,X1))=c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X1))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Ounion__idem)). 4.46/4.68 fof(fact_mult__strict__right__mono, axiom, ![X10, X11, X12, X4]:(class_Rings_Olinordered__semiring__strict(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__strict__right__mono)). 4.46/4.68 fof(fact_the__inv__into__into, axiom, ![X1, X6, X2, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,X2)=>((hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Fun_Othe__inv__into(X4,X3,X2,X27),X6)),X1))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=hBOOL(hAPP(hAPP(c_member(X3),X6),hAPP(c_Set_Oimage(X4,X3,X27),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__inv__into__into)). 4.46/4.68 fof(fact_wf__union__compatible, axiom, ![X46, X26, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X26),X46)),X26))=>c_Wellfounded_Owf(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X26),X46)))<=c_Wellfounded_Owf(X4,X46))<=c_Wellfounded_Owf(X4,X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__union__compatible)). 4.46/4.68 fof(fact_Min__Un, axiom, ![X1, X2, X4]:(class_Orderings_Olinorder(X4)=>((((c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),c_Big__Operators_Olinorder__class_OMin(X4,X2)),c_Big__Operators_Olinorder__class_OMin(X4,X1))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X1)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1)))<=X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__Un)). 4.46/4.68 fof(fact_mult__less__cancel__right__disj, axiom, ![X37, X39, X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X37),X39)))<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X37),X18)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X39))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),X37)))))<=class_Rings_Olinordered__ring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__cancel__right__disj)). 4.46/4.68 fof(fact_comm__mult__strict__left__mono, axiom, ![X10, X11, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)))))<=class_Rings_Olinordered__comm__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__mult__strict__left__mono)). 4.46/4.68 fof(fact_mult__less__cancel__left__pos, axiom, ![X37, X18, X39, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),X37))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X39),X18)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X39),X37))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X39)))<=class_Rings_Olinordered__ring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__cancel__left__pos)). 4.46/4.68 fof(fact_nonzero__power__divide, axiom, ![X17, X12, X11, X4]:((hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X11)),X17)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X17))<=X11!=c_Groups_Ozero__class_Ozero(X4))<=class_Fields_Ofield(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonzero__power__divide)). 4.46/4.68 fof(fact_mult__strict__left__mono, axiom, ![X10, X11, X12, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11)))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__strict__left__mono)). 4.46/4.68 fof(fact_divide__strict__right__mono, axiom, ![X10, X11, X12, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X10))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11)))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__strict__right__mono)). 4.46/4.68 fof(fact_mult__right__mono, axiom, ![X10, X11, X12, X4]:(class_Rings_Oordered__semiring(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__right__mono)). 4.46/4.68 fof(fact_mult__left__mono, axiom, ![X10, X11, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)))))<=class_Rings_Oordered__semiring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__mono)). 4.46/4.68 fof(fact_Sup__fin_Ounion__idem, axiom, ![X1, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>(X1!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),c_Big__Operators_Olattice__class_OSup__fin(X4,X2)),c_Big__Operators_Olattice__class_OSup__fin(X4,X1))=c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))))))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Ounion__idem)). 4.46/4.68 fof(fact_mult__le__cancel__left__pos, axiom, ![X37, X18, X39, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X39))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X39),X18)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X39),X37)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),X37))))<=class_Rings_Olinordered__ring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__cancel__left__pos)). 4.46/4.68 fof(fact_comm__mult__left__mono, axiom, ![X10, X11, X12, X4]:(class_Rings_Oordered__comm__semiring(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__mult__left__mono)). 4.46/4.68 fof(fact_fold1__eq__fold, axiom, ![X18, X2, X4]:(class_Groups_Oab__semigroup__mult(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(~(hBOOL(hAPP(hAPP(c_member(X4),X18),X2)))=>hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),hAPP(hAPP(c_Set_Oinsert(X4),X18),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Groups_Otimes__class_Otimes(X4)),X18),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__eq__fold)). 4.46/4.68 fof(fact_mult__strict__left__mono__neg, axiom, ![X10, X12, X11, X4]:(class_Rings_Olinordered__ring__strict(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X10),c_Groups_Ozero__class_Ozero(X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__strict__left__mono__neg)). 4.46/4.68 fof(fact_divide__strict__right__mono__neg, axiom, ![X10, X12, X11, X4]:(class_Fields_Olinordered__field(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X10),c_Groups_Ozero__class_Ozero(X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__strict__right__mono__neg)). 4.46/4.68 fof(fact_map__fun__upd, axiom, ![X13, X27, X3, X7, X5, X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(c_List_Oset(X4),X7))))=>hAPP(hAPP(c_List_Omap(X4,X3),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X3),X27),X5),X13)),X7)=hAPP(hAPP(c_List_Omap(X4,X3),X27),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__fun__upd)). 4.46/4.68 fof(fact_rev__ImageI, axiom, ![X16, X37, X3, X2, X18, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X18),X2))=>(hBOOL(hAPP(hAPP(c_member(X3),X37),hAPP(c_Relation_OImage(X4,X3,X16),X2)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X18),X37)),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__ImageI)). 4.46/4.68 fof(fact_fun__left__comm_Ofun__comp__comm, axiom, ![X5, X6, X27, X3, X4]:(hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X27,X6)),hAPP(X27,X5))=hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X27,X5)),hAPP(X27,X6))<=c_Finite__Set_Ofun__left__comm(X4,X3,X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofun__comp__comm)). 4.46/4.68 fof(fact_mult__right__mono__neg, axiom, ![X10, X12, X11, X4]:(class_Rings_Oordered__ring(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X10),c_Groups_Ozero__class_Ozero(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__right__mono__neg)). 4.46/4.68 fof(fact_mult__le__cancel__left__neg, axiom, ![X37, X18, X39, X4]:(class_Rings_Olinordered__ring__strict(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),X18))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X39),X18)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X39),X37))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__cancel__left__neg)). 4.46/4.68 fof(fact_mult__left__mono__neg, axiom, ![X10, X12, X11, X4]:(class_Rings_Oordered__ring(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X10),c_Groups_Ozero__class_Ozero(X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__mono__neg)). 4.46/4.68 fof(fact_single__valued__def, axiom, ![X16, X3, X4]:(![X42, X44]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X42),X44)),X16))=>![X132]:(X132=X44<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X42),X132)),X16))))<=>c_Relation_Osingle__valued(X4,X3,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__def)). 4.46/4.68 fof(fact_map__of__zip__enum__is__Some, axiom, ![X48, X72, X3, X4]:((?[X44]:hAPP(hAPP(c_Map_Omap__of(X4,X3),hAPP(hAPP(c_List_Ozip(X4,X3),c_Enum_Oenum__class_Oenum(X4)),X72)),X48)=hAPP(c_Option_Ooption_OSome(X3),X44)<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X72)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_Enum_Oenum__class_Oenum(X4)))<=class_Enum_Oenum(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__zip__enum__is__Some)). 4.46/4.68 fof(fact_SigmaE, axiom, ![X1, X2, X39, X3, X4]:(~(![X42]:(![X44]:(hBOOL(hAPP(hAPP(c_member(X3),X44),hAPP(X1,X42)))=>X39!=hAPP(hAPP(c_Product__Type_OPair(X4,X3),X42),X44))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X2))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),X39),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SigmaE)). 4.46/4.68 fof(fact_INF__less__iff, axiom, ![X18, X27, X2, X3, X4]:((class_Complete__Lattice_Ocomplete__lattice(X4)&class_Orderings_Olinorder(X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X4),X2),X27)),X18))<=>?[X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(X27,X42)),X18))&hBOOL(hAPP(hAPP(c_member(X3),X42),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__less__iff)). 4.46/4.68 fof(fact_card__Diff__singleton__if, axiom, ![X6, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>((hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))&(hAPP(c_Finite__Set_Ocard(X4),X2)=hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff__singleton__if)). 4.46/4.68 fof(fact_less__SUP__iff, axiom, ![X27, X2, X3, X18, X4]:((class_Complete__Lattice_Ocomplete__lattice(X4)&class_Orderings_Olinorder(X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4),X2),X27)))<=>?[X42]:(hBOOL(hAPP(hAPP(c_member(X3),X42),X2))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),hAPP(X27,X42)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__SUP__iff)). 4.46/4.68 fof(fact_ivl__disj__un_I15_J, axiom, ![X23, X22, X67, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X67),X22))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X22),X23))=>c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X67,X23)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X67,X22)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X22),X23))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I15_J)). 4.46/4.68 fof(fact_ivl__disj__un_I21_J, axiom, ![X23, X22, X67, X4]:(((c_SetInterval_Oord__class_OatLeastAtMost(X4,X67,X23)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X67),X22)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X22,X23))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X22),X23)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X67),X22)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I21_J)). 4.46/4.68 fof(fact_folding__idem_Oidem__left__comp, axiom, ![X50, X6, X29, X62, X27, X3, X4]:(c_Finite__Set_Ofolding__idem(X4,X3,X27,X62)=>hAPP(c_Fun_Ocomp(X3,X3,X29,hAPP(X27,X6)),hAPP(c_Fun_Ocomp(X3,X3,X29,hAPP(X27,X6)),X50))=hAPP(c_Fun_Ocomp(X3,X3,X29,hAPP(X27,X6)),X50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__idem_Oidem__left__comp)). 4.46/4.68 fof(fact_insort__is__Cons, axiom, ![X18, X27, X7, X4, X3]:(class_Orderings_Olinorder(X3)=>(hAPP(hAPP(c_List_Olist_OCons(X4),X18),X7)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X3,X27),X18),X7)<=![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(X27,X18)),hAPP(X27,X42)))<=hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__is__Cons)). 4.46/4.68 fof(fact_wf__eq__minimal, axiom, ![X16, X4]:(![X218]:(?[X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X218))&![X44]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X44),X42)),X16))=>~(hBOOL(hAPP(hAPP(c_member(X4),X44),X218)))))<=?[X42]:hBOOL(hAPP(hAPP(c_member(X4),X42),X218)))<=>c_Wellfounded_Owf(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__eq__minimal)). 4.46/4.68 fof(fact_setsum__eq__1__iff, axiom, ![X27, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(?[X42]:((![X66]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(X27,X66)<=X42!=X66)<=hBOOL(hAPP(hAPP(c_member(X4),X66),X2)))&c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(X27,X42))&hBOOL(hAPP(hAPP(c_member(X4),X42),X2)))<=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X27),X2)=c_Groups_Oone__class_Oone(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__eq__1__iff)). 4.46/4.68 fof(fact_setsum__nonneg__0, axiom, ![X24, X27, X68, X4, X3]:(((((hAPP(X27,X24)=c_Groups_Ozero__class_Ozero(X3)<=hBOOL(hAPP(hAPP(c_member(X4),X24),X68)))<=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X68)=c_Groups_Ozero__class_Ozero(X3))<=![X41]:(hBOOL(hAPP(hAPP(c_member(X4),X41),X68))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(X27,X41)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X68)))<=class_Groups_Oordered__ab__group__add(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__nonneg__0)). 4.46/4.68 fof(fact_folding__idem_Oinsert__idem, axiom, ![X6, X2, X62, X27, X3, X4]:(c_Finite__Set_Ofolding__idem(X4,X3,X27,X62)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(X62,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X62,X2)),hAPP(X27,X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__idem_Oinsert__idem)). 4.46/4.68 fof(fact_ran__map__upd, axiom, ![X37, X3, X4, X18, X22]:(hAPP(hAPP(c_Set_Oinsert(X4),X37),c_Map_Oran(X3,X4,X22))=c_Map_Oran(X3,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X4)),X22),X18),hAPP(c_Option_Ooption_OSome(X4),X37)))<=c_Option_Ooption_ONone(X4)=hAPP(X22,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ran__map__upd)). 4.46/4.68 fof(fact_sorted__list__of__set__remove, axiom, ![X6, X2, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>c_List_Oremove1(X4,X6,c_List_Olinorder__class_Osorted__list__of__set(X4,X2))=c_List_Olinorder__class_Osorted__list__of__set(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__list__of__set__remove)). 4.46/4.68 fof(fact_add__strict__mono, axiom, ![X133, X10, X11, X12, X4]:(class_Groups_Oordered__cancel__ab__semigroup__add(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X10),X133))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X133))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__strict__mono)). 4.46/4.68 fof(fact_add__le__less__mono, axiom, ![X133, X10, X11, X12, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X133)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X10),X133)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11)))<=class_Groups_Oordered__cancel__ab__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__le__less__mono)). 4.46/4.68 fof(fact_all__n__lists__def, axiom, ![X14, X28, X4]:(class_Enum_Oenum(X4)=>(![X42]:(hBOOL(hAPP(X28,X42))<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X42),hAPP(c_List_Oset(tc_List_Olist(X4)),c_Enum_On__lists(X4,X14,c_Enum_Oenum__class_Oenum(X4))))))<=>c_Enum_Oall__n__lists(X4,X28,X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__n__lists__def)). 4.46/4.68 fof(fact_weak__map__of__SomeI, axiom, ![X67, X6, X45, X3, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X45),X6)),hAPP(c_List_Oset(tc_prod(X4,X3)),X67)))=>?[X42]:hAPP(hAPP(c_Map_Omap__of(X4,X3),X67),X45)=hAPP(c_Option_Ooption_OSome(X3),X42)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_weak__map__of__SomeI)). 4.46/4.68 fof(fact_add__less__le__mono, axiom, ![X133, X10, X11, X12, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X10),X133))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X133))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11)))<=class_Groups_Oordered__cancel__ab__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__less__le__mono)). 4.46/4.68 fof(fact_add__mono, axiom, ![X133, X10, X11, X12, X4]:(class_Groups_Oordered__ab__semigroup__add(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X133)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X10),X133)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__mono)). 4.46/4.68 fof(fact_sup__mono, axiom, ![X133, X11, X10, X12, X4]:(class_Lattices_Osemilattice__sup(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X10))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X12),X11)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X10),X133)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X133))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__mono)). 4.46/4.68 fof(fact_inf__mono, axiom, ![X133, X11, X10, X12, X4]:(class_Lattices_Osemilattice__inf(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X12),X11)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X10),X133)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X133)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__mono)). 4.46/4.68 fof(fact_RangeE, axiom, ![X16, X3, X37, X4]:(~(![X42]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X42),X37)),X16))))<=hBOOL(hAPP(hAPP(c_member(X4),X37),hAPP(c_Relation_ORange(X3,X4),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_RangeE)). 4.46/4.68 fof(fact_Range__iff, axiom, ![X16, X3, X18, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X18),hAPP(c_Relation_ORange(X3,X4),X16)))<=>?[X44]:hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X44),X18)),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__iff)). 4.46/4.68 fof(fact_DomainE, axiom, ![X16, X3, X18, X4]:(~(![X44]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X18),X44)),X16))))<=hBOOL(hAPP(hAPP(c_member(X4),X18),hAPP(c_Relation_ODomain(X4,X3),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DomainE)). 4.46/4.68 fof(fact_take__Cons_H, axiom, ![X57, X48, X4, X17]:((hAPP(hAPP(c_List_Olist_OCons(X4),X48),hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X57))=hAPP(hAPP(c_List_Otake(X4),X17),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57))<=X17!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Otake(X4),X17),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57))<=X17=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Cons_H)). 4.46/4.68 fof(fact_zip__rev, axiom, ![X72, X3, X57, X4]:(hAPP(c_List_Orev(tc_prod(X4,X3)),hAPP(hAPP(c_List_Ozip(X4,X3),X57),X72))=hAPP(hAPP(c_List_Ozip(X4,X3),hAPP(c_List_Orev(X4),X57)),hAPP(c_List_Orev(X3),X72))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X72)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__rev)). 4.46/4.68 fof(fact_divide__right__mono, axiom, ![X10, X11, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X10)))))<=class_Fields_Olinordered__field__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__right__mono)). 4.46/4.68 fof(fact_power__mono, axiom, ![X17, X11, X12, X4]:(class_Rings_Olinordered__semidom(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X17)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__mono)). 4.46/4.68 fof(fact_power__strict__increasing__iff, axiom, ![X5, X6, X37, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X37),X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X37),X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X5)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X37)))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__strict__increasing__iff)). 4.46/4.68 fof(fact_INF2__iff, axiom, ![X39, X37, X1, X2, X29, X3, X4]:(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_fun(X29,tc_HOL_Obool))),X2),X1),X37),X39))<=>![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hBOOL(hAPP(hAPP(hAPP(X1,X42),X37),X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF2__iff)). 4.46/4.68 fof(fact_Domain__iff, axiom, ![X16, X3, X18, X4]:(?[X44]:hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X18),X44)),X16))<=>hBOOL(hAPP(hAPP(c_member(X4),X18),hAPP(c_Relation_ODomain(X4,X3),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__iff)). 4.46/4.68 fof(fact_append__in__lists__conv, axiom, ![X2, X32, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),hAPP(hAPP(c_List_Oappend(X4),X7),X32)),c_List_Olists(X4,X2)))<=>(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X32),c_List_Olists(X4,X2)))&hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X7),c_List_Olists(X4,X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__in__lists__conv)). 4.46/4.68 fof(fact_INF2__I, axiom, ![X29, X3, X39, X37, X1, X2, X4]:(![X42]:(hBOOL(hAPP(hAPP(hAPP(X1,X42),X37),X39))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X2)))=>hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_fun(X29,tc_HOL_Obool))),X2),X1),X37),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF2__I)). 4.46/4.68 fof(fact_power__increasing, axiom, ![X12, X152, X17, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),X152))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X152)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Oone__class_Oone(X4)),X12))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__increasing)). 4.46/4.68 fof(fact_power__increasing__iff, axiom, ![X5, X6, X37, X4]:(class_Rings_Olinordered__semidom(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X37),X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X37),X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6),X5)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X37)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__increasing__iff)). 4.46/4.68 fof(fact_divide__right__mono__neg, axiom, ![X10, X11, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X10),c_Groups_Ozero__class_Ozero(X4)))))<=class_Fields_Olinordered__field__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__right__mono__neg)). 4.46/4.68 fof(fact_quotientI, axiom, ![X16, X2, X6, X4]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X16),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X2),X16)))<=hBOOL(hAPP(hAPP(c_member(X4),X6),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotientI)). 4.46/4.68 fof(fact_acc_OaccI, axiom, ![X16, X6, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X6),c_Wellfounded_Oacc(X4,X16)))<=![X44]:(hBOOL(hAPP(hAPP(c_member(X4),X44),c_Wellfounded_Oacc(X4,X16)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X44),X6)),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acc_OaccI)). 4.46/4.68 fof(fact_q__neg__lemma, axiom, ![X177, X178, X91]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X91),X178)),X177)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X178),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X177)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_q__neg__lemma)). 4.46/4.68 fof(fact_not__acc__down, axiom, ![X26, X6, X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X6),c_Wellfounded_Oacc(X4,X26))))=>~(![X132]:(hBOOL(hAPP(hAPP(c_member(X4),X132),c_Wellfounded_Oacc(X4,X26)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X132),X6)),X26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__acc__down)). 4.46/4.68 fof(fact_acc_Osimps, axiom, ![X16, X18, X4]:(![X42]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X18)),X16))=>hBOOL(hAPP(hAPP(c_member(X4),X42),c_Wellfounded_Oacc(X4,X16))))<=>hBOOL(hAPP(hAPP(c_member(X4),X18),c_Wellfounded_Oacc(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acc_Osimps)). 4.46/4.68 fof(fact_ivl__disj__un_I18_J, axiom, ![X23, X22, X67, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X67),X22))=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X67,X22)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X22,X23))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X67),X23)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X22),X23))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I18_J)). 4.46/4.68 fof(fact_insert__fold1SetE, axiom, ![X6, X173, X18, X27, X4]:(hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,X27,hAPP(hAPP(c_Set_Oinsert(X4),X18),X173)),X6))=>~(![X125, X161]:((hBOOL(hAPP(hAPP(c_member(X4),X125),X161))<=hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X4,X27,X125,X161),X6)))<=hAPP(hAPP(c_Set_Oinsert(X4),X125),X161)=hAPP(hAPP(c_Set_Oinsert(X4),X18),X173)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__fold1SetE)). 4.46/4.68 fof(fact_all__nat__less__eq, axiom, ![X28, X14]:(![X42]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X42),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14)))=>hBOOL(hAPP(X28,X42)))<=>![X90]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X14))=>hBOOL(hAPP(X28,X90)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__nat__less__eq)). 4.46/4.68 fof(fact_div__geq, axiom, ![X19, X17]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X17)))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19),X17)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17)),X17)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__geq)). 4.46/4.68 fof(fact_map__eq__conv, axiom, ![X50, X7, X27, X4, X3]:(hAPP(hAPP(c_List_Omap(X3,X4),X27),X7)=hAPP(hAPP(c_List_Omap(X3,X4),X50),X7)<=>![X42]:(hBOOL(hAPP(hAPP(c_member(X3),X42),hAPP(c_List_Oset(X3),X7)))=>hAPP(X50,X42)=hAPP(X27,X42))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__eq__conv)). 4.46/4.68 fof(fact_map__upds__list__update2__drop, axiom, ![X5, X22, X32, X3, X24, X7, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)),X24))=>(c_Map_Omap__upds(X4,X3,X22,X7,X32)=c_Map_Omap__upds(X4,X3,X22,X7,hAPP(hAPP(c_List_Olist__update(X3,X32),X24),X5))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upds__list__update2__drop)). 4.46/4.68 fof(fact_acc__downwards, axiom, ![X37, X16, X18, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X37),c_Wellfounded_Oacc(X4,X16)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X37),X18)),c_Transitive__Closure_Ortrancl(X4,X16))))<=hBOOL(hAPP(hAPP(c_member(X4),X18),c_Wellfounded_Oacc(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acc__downwards)). 4.46/4.68 fof(fact_minus__number__of__mult, axiom, ![X49, X30, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X30))),X49)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30))),X49)<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__number__of__mult)). 4.46/4.68 fof(fact_inj__fun, axiom, ![X29, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>c_Fun_Oinj__on(X4,tc_fun(X29,X3),hAPP(hAPP(c_COMBB(X3,tc_fun(X29,X3),X4),c_COMBK(X3,X29)),X27),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__fun)). 4.46/4.68 fof(fact_takeWhile__append2, axiom, ![X32, X28, X7, X4]:(hAPP(hAPP(c_List_Oappend(X4),X7),c_List_OtakeWhile(X4,X28,X32))=c_List_OtakeWhile(X4,X28,hAPP(hAPP(c_List_Oappend(X4),X7),X32))<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7)))=>hBOOL(hAPP(X28,X42)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__append2)). 4.46/4.68 fof(fact_in__finite__psubset, axiom, ![X1, X2, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X2),X1)),c_Wellfounded_Ofinite__psubset(X4)))<=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__finite__psubset)). 4.46/4.68 fof(fact_nth__drop, axiom, ![X57, X4, X21, X17]:(hAPP(hAPP(c_List_Onth(X4),X57),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X21))=hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Odrop(X4),X17),X57)),X21)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X21)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__drop)). 4.46/4.68 fof(fact_sorted__append, axiom, ![X32, X7, X4]:(class_Orderings_Olinorder(X4)=>(((c_List_Olinorder__class_Osorted(X4,X32)&![X42]:(![X66]:(hBOOL(hAPP(hAPP(c_member(X4),X66),hAPP(c_List_Oset(X4),X32)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X42),X66)))<=hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7)))))&c_List_Olinorder__class_Osorted(X4,X7))<=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Oappend(X4),X7),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__append)). 4.46/4.68 fof(fact_set__update__subsetI, axiom, ![X24, X6, X2, X7, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist__update(X4,X7),X24),X6))),X2)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X7)),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__update__subsetI)). 4.46/4.68 fof(fact_UN__I, axiom, ![X1, X37, X3, X2, X18, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X18),X2))=>(hBOOL(hAPP(hAPP(c_member(X3),X37),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X2),X1)))<=hBOOL(hAPP(hAPP(c_member(X3),X37),hAPP(X1,X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__I)). 4.46/4.68 fof(fact_all__nat__less, axiom, ![X28, X14]:(![X42]:(hBOOL(hAPP(X28,X42))<=hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X42),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14))))<=>![X90]:(hBOOL(hAPP(X28,X90))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__nat__less)). 4.46/4.68 fof(fact_finite__cartesian__product, axiom, ![X1, X3, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1))=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),X1)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__cartesian__product)). 4.46/4.68 fof(fact_card__Diff1__le, axiom, ![X6, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X4),X2)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff1__le)). 4.46/4.68 fof(fact_Int__greaterThanLessThan, axiom, ![X87, X39, X37, X18, X4]:(c_SetInterval_Oord__class_OgreaterThanLessThan(X4,hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X18),X39),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X37),X87))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X18,X37)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X39,X87))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__greaterThanLessThan)). 4.46/4.68 fof(fact_q__pos__lemma, axiom, ![X177, X178, X91]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X178)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X177),X91)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X91),X178)),X177)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_q__pos__lemma)). 4.46/4.68 fof(fact_Int__greaterThanAtMost, axiom, ![X87, X39, X37, X18, X4]:(class_Orderings_Olinorder(X4)=>c_SetInterval_Oord__class_OgreaterThanAtMost(X4,hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X18),X39),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X37),X87))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X18,X37)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X39,X87))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__greaterThanAtMost)). 4.46/4.68 fof(fact_folding__one__idem_Osubset__idem, axiom, ![X1, X2, X62, X27, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(X1!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>(hAPP(hAPP(X27,hAPP(X62,X1)),hAPP(X62,X2))=hAPP(X62,X2)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X2)))))<=c_Finite__Set_Ofolding__one__idem(X4,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Osubset__idem)). 4.46/4.68 fof(fact_min__max_Osup__mono, axiom, ![X133, X11, X10, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X10))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X12),X11)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X10),X133)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X133))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__mono)). 4.46/4.68 fof(fact_min__max_Oinf__mono, axiom, ![X133, X11, X10, X12, X4]:(class_Orderings_Olinorder(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X133))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X12),X11)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X10),X133))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__mono)). 4.46/4.68 fof(fact_Int__atLeastAtMost, axiom, ![X87, X39, X37, X18, X4]:(c_SetInterval_Oord__class_OatLeastAtMost(X4,hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X18),X39),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X37),X87))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X18,X37)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X39,X87))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__atLeastAtMost)). 4.46/4.68 fof(fact_inj__on__fun__updI, axiom, ![X6, X5, X2, X27, X3, X4]:((~(hBOOL(hAPP(hAPP(c_member(X3),X5),hAPP(c_Set_Oimage(X4,X3,X27),X2))))=>c_Fun_Oinj__on(X4,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X3),X27),X6),X5),X2))<=c_Fun_Oinj__on(X4,X3,X27,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__fun__updI)). 4.46/4.68 fof(fact_length__transpose__sorted, axiom, ![X7, X4]:(c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X4))),X7)))=>((c_List_Olist_ONil(tc_List_Olist(X4))!=X7=>hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X4)),X7),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),c_List_Otranspose(X4,X7)))&(X7=c_List_Olist_ONil(tc_List_Olist(X4))=>hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),c_List_Otranspose(X4,X7))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__transpose__sorted)). 4.46/4.68 fof(fact_ivl__disj__un_I19_J, axiom, ![X23, X22, X67, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X22),X23))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X67,X22)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X22,X23))=c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X67,X23))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X67),X22)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I19_J)). 4.46/4.68 fof(fact_max__number__of, axiom, ![X63, X195, X3]:((class_Int_Onumber(X3)&class_Orderings_Oord(X3))=>((hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X195)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63))=hAPP(c_Int_Onumber__class_Onumber__of(X3),X63)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X195)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63))))&(hAPP(c_Int_Onumber__class_Onumber__of(X3),X195)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X195)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X195)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__number__of)). 4.46/4.68 fof(fact_subset__insert__iff, axiom, ![X1, X6, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),X1)))<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X1))<=hBOOL(hAPP(hAPP(c_member(X4),X6),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__insert__iff)). 4.46/4.68 fof(fact_sum__squares__ge__zero, axiom, ![X47, X48, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X48),X48)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X47),X47))))<=class_Rings_Olinordered__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__squares__ge__zero)). 4.46/4.68 fof(fact_ivl__disj__un_I20_J, axiom, ![X23, X22, X67, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X67),X22))=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X67,X22)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X22,X23))=c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X67,X23)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X22),X23))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I20_J)). 4.46/4.68 fof(fact_ivl__disj__un_I22_J, axiom, ![X23, X22, X67, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X22),X23))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X67,X22)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X22,X23))=c_SetInterval_Oord__class_OatLeastAtMost(X4,X67,X23))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X67),X22)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I22_J)). 4.46/4.68 fof(fact_ivl__disj__un_I16_J, axiom, ![X23, X22, X67, X4]:(class_Orderings_Olinorder(X4)=>((c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X67,X23)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X67,X22)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X22,X23))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X22),X23)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X67),X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I16_J)). 4.46/4.68 fof(fact_self__quotient__aux2, axiom, ![X112, X111, X12]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X111))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X112),c_Groups_Oone__class_Oone(tc_Int_Oint))))<=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X111),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X112))=X12)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_self__quotient__aux2)). 4.46/4.68 fof(fact_min__number__of, axiom, ![X63, X195, X3]:((class_Orderings_Oord(X3)&class_Int_Onumber(X3))=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X195)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63))))=>hAPP(c_Int_Onumber__class_Onumber__of(X3),X63)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X195)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X195)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63)))=>hAPP(c_Int_Onumber__class_Onumber__of(X3),X195)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X195)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X63))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__number__of)). 4.46/4.68 fof(fact_diff__add__assoc2, axiom, ![X21, X20, X15]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X21)),X15)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X15)),X21)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__add__assoc2)). 4.46/4.68 fof(fact_Diff__mono, axiom, ![X1, X65, X52, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X52))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X65),X1))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X52),X65))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__mono)). 4.46/4.68 fof(fact_Un__mono, axiom, ![X65, X1, X52, X2, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X52),X65)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X65)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X52))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__mono)). 4.46/4.68 fof(fact_mult__right__le__one__le, axiom, ![X47, X48, X4]:(class_Rings_Olinordered__idom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X48))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X47),c_Groups_Oone__class_Oone(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X48),X47)),X48)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X47))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__right__le__one__le)). 4.46/4.68 fof(fact_mult__left__le__one__le, axiom, ![X47, X48, X4]:(class_Rings_Olinordered__idom(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X47))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X47),c_Groups_Oone__class_Oone(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X47),X48)),X48))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__le__one__le)). 4.46/4.68 fof(fact_setsum__constant, axiom, ![X2, X5, X3, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Finite__Set_Ocard(X3),X2))),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),hAPP(c_COMBK(X4,X3),X5)),X2)<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__constant)). 4.46/4.68 fof(fact_Int__mono, axiom, ![X65, X1, X52, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X52))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X65))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X52),X65))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__mono)). 4.46/4.68 fof(fact_listsum__abs, axiom, ![X7, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(c_List_Omonoid__add__class_Olistsum(X4),X7))),hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X4,X4),c_Groups_Oabs__class_Oabs(X4)),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__abs)). 4.46/4.68 fof(fact_all__nth__imp__all__set, axiom, ![X6, X28, X7, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))=>hBOOL(hAPP(X28,X6)))<=![X41]:(hBOOL(hAPP(X28,hAPP(hAPP(c_List_Onth(X4),X7),X41)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__nth__imp__all__set)). 4.46/4.68 fof(fact_map__of__zip__inject, axiom, ![X88, X7, X3, X32, X4]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X7)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X88)=>(hBOOL(hAPP(c_List_Odistinct(X3),X7))=>(hAPP(c_Map_Omap__of(X3,X4),hAPP(hAPP(c_List_Ozip(X3,X4),X7),X88))=hAPP(c_Map_Omap__of(X3,X4),hAPP(hAPP(c_List_Ozip(X3,X4),X7),X32))=>X88=X32)))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X7)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__zip__inject)). 4.46/4.68 fof(fact_folding__image_Oreindex, axiom, ![X50, X58, X2, X62, X35, X27, X3, X4]:(((c_Fun_Oinj__on(X3,X3,X58,X2)=>hAPP(hAPP(X62,X50),hAPP(c_Set_Oimage(X3,X3,X58),X2))=hAPP(hAPP(X62,hAPP(c_Fun_Ocomp(X3,X4,X3,X50),X58)),X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))<=c_Finite__Set_Ofolding__image(X4,X3,X27,X35,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image_Oreindex)). 4.46/4.68 fof(fact_fold1__set, axiom, ![X7, X4]:(class_Lattices_Oab__semigroup__idem__mult(X4)=>(X7!=c_List_Olist_ONil(X4)=>hAPP(c_List_Ofoldl(X4,X4,c_Groups_Otimes__class_Otimes(X4),hAPP(c_List_Ohd(X4),X7)),hAPP(c_List_Otl(X4),X7))=hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),hAPP(c_List_Oset(X4),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__set)). 4.46/4.68 fof(fact_list__all2__nthD2, axiom, ![X109, X32, X7, X28, X3, X4]:((hBOOL(hAPP(hAPP(X28,hAPP(hAPP(c_List_Onth(X4),X7),X109)),hAPP(hAPP(c_List_Onth(X3),X32),X109)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X109),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32))))<=c_List_Olist__all2(X4,X3,X28,X7,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__nthD2)). 4.46/4.68 fof(fact_fun__left__comm_Ofold__fun__comm, axiom, ![X35, X6, X2, X27, X3, X4]:(c_Finite__Set_Ofun__left__comm(X4,X3,X27)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(hAPP(X27,X6),hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),X35),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),hAPP(hAPP(X27,X6),X35)),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__fun__comm)). 4.46/4.68 fof(fact_Image__singleton__iff, axiom, ![X18, X16, X3, X37, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X37),hAPP(c_Relation_OImage(X3,X4,X16),hAPP(hAPP(c_Set_Oinsert(X3),X18),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X18),X37)),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__singleton__iff)). 4.46/4.68 fof(fact_power__Suc__less__one, axiom, ![X17, X12, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),c_Groups_Oone__class_Oone(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Nat_OSuc,X17))),c_Groups_Oone__class_Oone(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12)))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__Suc__less__one)). 4.46/4.68 fof(fact_set__remove1__eq, axiom, ![X6, X7, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X7))=>hAPP(c_List_Oset(X4),c_List_Oremove1(X4,X6,X7))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X7)),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__remove1__eq)). 4.46/4.68 fof(fact_ex__n__lists__def, axiom, ![X14, X28, X4]:(class_Enum_Oenum(X4)=>(?[X42]:(hBOOL(hAPP(X28,X42))&hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X42),hAPP(c_List_Oset(tc_List_Olist(X4)),c_Enum_On__lists(X4,X14,c_Enum_Oenum__class_Oenum(X4))))))<=>c_Enum_Oex__n__lists(X4,X28,X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__n__lists__def)). 4.46/4.68 fof(fact_Cons__in__lists__iff, axiom, ![X2, X7, X6, X4]:((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X7),c_List_Olists(X4,X2)))&hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))<=>hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)),c_List_Olists(X4,X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cons__in__lists__iff)). 4.46/4.68 fof(fact_min__max_OInf__le__Sup, axiom, ![X2, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X2)),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__le__Sup)). 4.46/4.68 fof(fact_div__add__self2, axiom, ![X12, X11, X4]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X12),X11)),c_Groups_Oone__class_Oone(X4))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)),X11)<=c_Groups_Ozero__class_Ozero(X4)!=X11)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__add__self2)). 4.46/4.68 fof(fact_INF__subset, axiom, ![X27, X1, X2, X4, X3]:(class_Complete__Lattice_Ocomplete__lattice(X3)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X3),X1),X27)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X3),X2),X27))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__subset)). 4.46/4.68 fof(fact_SUP__subset, axiom, ![X27, X1, X2, X4, X3]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X3),X2),X27)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X3),X1),X27)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=class_Complete__Lattice_Ocomplete__lattice(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__subset)). 4.46/4.68 fof(fact_card__Diff__subset, axiom, ![X2, X1, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X2))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X2)),hAPP(c_Finite__Set_Ocard(X4),X1))=hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff__subset)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, axiom, ![X19, X12, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X19)),X19)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),c_Groups_Oone__class_Oone(X4))),X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J)). 4.46/4.68 fof(fact_ex__nat__less__eq, axiom, ![X28, X14]:(?[X90]:(hBOOL(hAPP(X28,X90))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90),X14)))<=>?[X42]:(hBOOL(hAPP(X28,X42))&hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X42),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__nat__less__eq)). 4.46/4.68 fof(fact_of__int__setprod, axiom, ![X2, X27, X3, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X4),hAPP(hAPP(c_COMBB(tc_Int_Oint,X4,X3),c_Int_Oring__1__class_Oof__int(X4)),X27)),X2)=hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Int_Oint),X27),X2))<=(class_Rings_Oring__1(X4)&class_Groups_Ocomm__monoid__mult(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__setprod)). 4.46/4.68 fof(fact_Min_Osubset__idem, axiom, ![X1, X2, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X1=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X2))=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),c_Big__Operators_Olinorder__class_OMin(X4,X1)),c_Big__Operators_Olinorder__class_OMin(X4,X2))=c_Big__Operators_Olinorder__class_OMin(X4,X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Osubset__idem)). 4.46/4.68 fof(fact_Inf__fin_Osubset__idem, axiom, ![X1, X2, X4]:(class_Lattices_Olattice(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X1=>(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),c_Big__Operators_Olattice__class_OInf__fin(X4,X1)),c_Big__Operators_Olattice__class_OInf__fin(X4,X2))=c_Big__Operators_Olattice__class_OInf__fin(X4,X2)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Osubset__idem)). 4.46/4.68 fof(fact_Sup__fin_Osubset__idem, axiom, ![X1, X2, X4]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X2))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),c_Big__Operators_Olattice__class_OSup__fin(X4,X1)),c_Big__Operators_Olattice__class_OSup__fin(X4,X2))=c_Big__Operators_Olattice__class_OSup__fin(X4,X2))<=X1!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Osubset__idem)). 4.46/4.68 fof(fact_Max_Osubset__idem, axiom, ![X1, X2, X4]:(((X1!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X2))=>c_Big__Operators_Olinorder__class_OMax(X4,X2)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),c_Big__Operators_Olinorder__class_OMax(X4,X1)),c_Big__Operators_Olinorder__class_OMax(X4,X2))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Osubset__idem)). 4.46/4.68 fof(fact_of__nat__setprod, axiom, ![X2, X27, X3, X4]:((class_Groups_Ocomm__monoid__mult(X4)&class_Rings_Osemiring__1(X4))=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Nat_Onat),X27),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,X3),c_Nat_Osemiring__1__class_Oof__nat(X4)),X27)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__setprod)). 4.46/4.68 fof(fact_distinct__insort, axiom, ![X7, X6, X27, X4, X3]:((hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X3,X27),X6),X7)))<=>(hBOOL(hAPP(c_List_Odistinct(X4),X7))&~(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7))))))<=class_Orderings_Olinorder(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__insort)). 4.46/4.68 fof(fact_Not__Domain__rtrancl, axiom, ![X5, X26, X6, X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_Relation_ODomain(X4,X4),X26))))=>(X6=X5<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_Transitive__Closure_Ortrancl(X4,X26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Not__Domain__rtrancl)). 4.46/4.68 fof(fact_max__add__distrib__left, axiom, ![X49, X47, X48, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X48),X49)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X47),X49))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X48),X47)),X49)<=class_Groups_Oordered__ab__semigroup__add__imp__le(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__add__distrib__left)). 4.46/4.68 fof(fact_in__set__conv__decomp__first, axiom, ![X7, X6, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))<=>?[X8]:(?[X9]:hAPP(hAPP(c_List_Oappend(X4),X8),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X9))=X7&~(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X8)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__conv__decomp__first)). 4.46/4.68 fof(fact_in__set__conv__decomp__last, axiom, ![X7, X6, X4]:(?[X8, X9]:(~(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X9))))&hAPP(hAPP(c_List_Oappend(X4),X8),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X9))=X7)<=>hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__conv__decomp__last)). 4.46/4.68 fof(fact_div__add__self1, axiom, ![X12, X11, X4]:((hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)),X11)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X12),X11)),c_Groups_Oone__class_Oone(X4))<=X11!=c_Groups_Ozero__class_Ozero(X4))<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__add__self1)). 4.46/4.68 fof(fact_min__add__distrib__left, axiom, ![X49, X47, X48, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X48),X49)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X47),X49))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),X47)),X49)<=class_Groups_Oordered__ab__semigroup__add__imp__le(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__add__distrib__left)). 4.46/4.68 fof(fact_comm__semiring__class_Odistrib, axiom, ![X10, X11, X12, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)),X10)<=class_Rings_Ocomm__semiring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__class_Odistrib)). 4.46/4.68 fof(fact_add__divide__distrib, axiom, ![X10, X11, X12, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X10))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)),X10)<=class_Rings_Odivision__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__divide__distrib)). 4.46/4.68 fof(fact_list__ex1__iff__raw, axiom, ![X7, X28, X4]:(?[X42]:((hBOOL(hAPP(X28,X42))&![X44]:((hBOOL(hAPP(hAPP(c_member(X4),X44),hAPP(c_List_Oset(X4),X7)))&hBOOL(hAPP(X28,X44)))=>X42=X44))&hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7))))<=>c_List_Olist__ex1(X4,X28,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex1__iff__raw)). 4.46/4.68 fof(fact_listsum__triv, axiom, ![X7, X16, X3, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X7))),X16)=hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X3,X4),hAPP(c_COMBK(X4,X3),X16)),X7))<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__triv)). 4.46/4.68 fof(fact_inf__sup__distrib2, axiom, ![X48, X49, X47, X4]:(class_Lattices_Odistrib__lattice(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X47),X48)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X49),X48))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X47),X49)),X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__distrib2)). 4.46/4.68 fof(fact_sup__inf__distrib2, axiom, ![X48, X49, X47, X4]:(class_Lattices_Odistrib__lattice(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X47),X48)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X49),X48))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X47),X49)),X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__inf__distrib2)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, axiom, ![X10, X11, X12, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J)). 4.46/4.68 fof(fact_diff__divide__distrib, axiom, ![X10, X11, X12, X4]:(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X11)),X10)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X10))<=class_Rings_Odivision__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__divide__distrib)). 4.46/4.68 fof(fact_list__ex1__iff, axiom, ![X7, X28, X4]:(c_List_Olist__ex1(X4,X28,X7)<=>?[X42]:((hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7)))&![X44]:((hBOOL(hAPP(hAPP(c_member(X4),X44),hAPP(c_List_Oset(X4),X7)))&hBOOL(hAPP(X28,X44)))=>X44=X42))&hBOOL(hAPP(X28,X42)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex1__iff)). 4.46/4.68 fof(fact_nat__mod__eq__lemma, axiom, ![X47, X17, X48]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X47),X48))=>?[X144]:X48=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X144)))<=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X47,X17)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X48,X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mod__eq__lemma)). 4.46/4.68 fof(fact_max__diff__distrib__left, axiom, ![X49, X47, X48, X4]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X48),X47)),X49)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X48),X49)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X47),X49))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__diff__distrib__left)). 4.46/4.68 fof(fact_min__diff__distrib__left, axiom, ![X49, X47, X48, X4]:(class_Groups_Oordered__ab__group__add(X4)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),X47)),X49)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X48),X49)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X47),X49))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__diff__distrib__left)). 4.46/4.68 fof(fact_finite__quotient, axiom, ![X16, X2, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X2))))=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X2),X16))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__quotient)). 4.46/4.68 fof(fact_folding__idem_Osubset__comp__idem, axiom, ![X1, X2, X62, X27, X3, X4]:(((hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X62,X2)),hAPP(X62,X1))=hAPP(X62,X2)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X2)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=c_Finite__Set_Ofolding__idem(X4,X3,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__idem_Osubset__comp__idem)). 4.46/4.68 fof(fact_setprod__pos__nat, axiom, ![X27, X46, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,tc_Nat_Onat),X27),X46)))<=![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X27,X42)))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X46))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__pos__nat)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, axiom, ![X49, X47, X48, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X48),X47)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X48),X49))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X48),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X47),X49))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J)). 4.46/4.68 fof(fact_SUP2__I, axiom, ![X29, X3, X39, X37, X1, X2, X18, X4]:((hBOOL(hAPP(hAPP(hAPP(X1,X18),X37),X39))=>hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_fun(X29,tc_HOL_Obool))),X2),X1),X37),X39)))<=hBOOL(hAPP(hAPP(c_member(X4),X18),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP2__I)). 4.46/4.68 fof(fact_power__gt1__lemma, axiom, ![X17, X12, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__gt1__lemma)). 4.46/4.68 fof(fact_refl__onI, axiom, ![X2, X16, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X2))))=>(c_Relation_Orefl__on(X4,X2,X16)<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X42)),X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__onI)). 4.46/4.68 fof(fact_refl__on__def, axiom, ![X16, X2, X4]:(c_Relation_Orefl__on(X4,X2,X16)<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X2))))&![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X42)),X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__def)). 4.46/4.68 fof(fact_abs__add__abs, axiom, ![X11, X12, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),hAPP(c_Groups_Oabs__class_Oabs(X4),X11))=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__add__abs)). 4.46/4.68 fof(fact_inf__sup__distrib1, axiom, ![X49, X47, X48, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X47)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X49))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X47),X49))<=class_Lattices_Odistrib__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__distrib1)). 4.46/4.68 fof(fact_mult__less__cancel2, axiom, ![X14, X45, X22]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X45))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X45)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__cancel2)). 4.46/4.68 fof(fact_sup__inf__distrib1, axiom, ![X49, X47, X48, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X47)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X49))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X47),X49))<=class_Lattices_Odistrib__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__inf__distrib1)). 4.46/4.68 fof(fact_nat__mult__less__cancel1, axiom, ![X14, X22, X45]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X22)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X14)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__less__cancel1)). 4.46/4.68 fof(fact_zmult__zless__mono2, axiom, ![X15, X20, X21]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15),X20))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__zless__mono2)). 4.46/4.68 fof(fact_div__le__mono2, axiom, ![X15, X17, X19]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X15),X17)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X15),X19)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X17)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__le__mono2)). 4.46/4.68 fof(fact_hoare__valids__def, axiom, ![X202, X82, X4]:(c_Hoare__Mirabelle_Ohoare__valids(X4,X82,X202)<=>![X199]:(![X42]:(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X4)),X42),X202))=>c_Hoare__Mirabelle_Otriple__valid(X4,X199,X42))<=![X42]:(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X4)),X42),X82))=>c_Hoare__Mirabelle_Otriple__valid(X4,X199,X42)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hoare__valids__def)). 4.46/4.68 fof(fact_mult__less__cancel__left__disj, axiom, ![X37, X18, X39, X4]:(class_Rings_Olinordered__ring__strict(X4)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X37),X18))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),c_Groups_Ozero__class_Ozero(X4))))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),X37))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X39))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X39),X18)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X39),X37))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__cancel__left__disj)). 4.46/4.68 fof(fact_zdiv__mono1, axiom, ![X11, X163, X12]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X163),X11))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),X163))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__mono1)). 4.46/4.68 fof(fact_zdiv__mono1__neg, axiom, ![X11, X163, X12]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X163),X11)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),X163))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__mono1__neg)). 4.46/4.68 fof(fact_listrel1__mono, axiom, ![X68, X16, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),X68))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool)),c_List_Olistrel1(X4,X16)),c_List_Olistrel1(X4,X68)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1__mono)). 4.46/4.68 fof(fact_listrel__mono, axiom, ![X68, X16, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool)),c_List_Olistrel(X4,X16)),c_List_Olistrel(X4,X68)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),X68))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__mono)). 4.46/4.68 fof(fact_finite__subset__induct, axiom, ![X28, X2, X62, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X62))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X62),X2))=>((hBOOL(hAPP(X28,X62))<=![X125, X203]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X203))=>(((hBOOL(hAPP(X28,hAPP(hAPP(c_Set_Oinsert(X4),X125),X203)))<=hBOOL(hAPP(X28,X203)))<=~(hBOOL(hAPP(hAPP(c_member(X4),X125),X203))))<=hBOOL(hAPP(hAPP(c_member(X4),X125),X2)))))<=hBOOL(hAPP(X28,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__subset__induct)). 4.46/4.68 fof(fact_finite__empty__induct, axiom, ![X28, X2, X4]:((hBOOL(hAPP(X28,X2))=>(hBOOL(hAPP(X28,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=![X125, X161]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X161))=>(hBOOL(hAPP(hAPP(c_member(X4),X125),X161))=>(hBOOL(hAPP(X28,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X161),hAPP(hAPP(c_Set_Oinsert(X4),X125),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))<=hBOOL(hAPP(X28,X161)))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__empty__induct)). 4.46/4.68 fof(fact_equiv__type, axiom, ![X16, X2, X4]:(c_Equiv__Relations_Oequiv(X4,X2,X16)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__type)). 4.46/4.68 fof(fact_self__quotient__aux1, axiom, ![X112, X111, X12]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X112))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X111),X12)))<=X12=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X111),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X112)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_self__quotient__aux1)). 4.46/4.68 fof(fact_in__set__butlast__appendI, axiom, ![X32, X7, X6, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),c_List_Obutlast(X4,hAPP(hAPP(c_List_Oappend(X4),X7),X32)))))<=(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),c_List_Obutlast(X4,X7))))|hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),c_List_Obutlast(X4,X32)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__butlast__appendI)). 4.46/4.68 fof(fact_fold1__insert, axiom, ![X6, X2, X4]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),X2))=hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2)<=class_Groups_Oab__semigroup__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__insert)). 4.46/4.68 fof(fact_zdiff__int__split, axiom, ![X5, X6, X28]:(hBOOL(hAPP(X28,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6),X5))))<=>((hBOOL(hAPP(X28,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X6)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X5))=>hBOOL(hAPP(X28,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiff__int__split)). 4.46/4.68 fof(fact_foldl__assoc, axiom, ![X88, X5, X6, X4]:(hAPP(c_List_Ofoldl(X4,X4,c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X6),X5)),X88)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X6),hAPP(c_List_Ofoldl(X4,X4,c_Groups_Oplus__class_Oplus(X4),X5),X88))<=class_Groups_Osemigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__assoc)). 4.46/4.68 fof(fact_folding__idem_Oin__comp__idem, axiom, ![X6, X2, X62, X27, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X62,X2)),hAPP(X27,X6))=hAPP(X62,X2)))<=c_Finite__Set_Ofolding__idem(X4,X3,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__idem_Oin__comp__idem)). 4.46/4.68 fof(fact_ivl__diff, axiom, ![X22, X14, X24, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X24),X14))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X24),X22)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X24),X14))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X14),X22))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__diff)). 4.46/4.68 fof(fact_inj__on__strict__subset, axiom, ![X2, X1, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,X1)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X2),X1))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X3,X27),X2)),hAPP(c_Set_Oimage(X4,X3,X27),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__strict__subset)). 4.46/4.68 fof(fact_atLeastatMost__subset__iff, axiom, ![X87, X39, X37, X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X18,X37)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X39,X87)))<=>(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),X37)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X39),X18))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),X87)))))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastatMost__subset__iff)). 4.46/4.68 fof(fact_crossproduct__eq, axiom, ![X35, X6, X5, X36, X4]:(((X36=X6|X35=X5)<=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X36),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X36),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X35)))<=class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_crossproduct__eq)). 4.46/4.68 fof(fact_power__add, axiom, ![X17, X19, X12, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X19)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17))<=class_Groups_Omonoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__add)). 4.46/4.68 fof(fact_diff__Suc__diff__eq2, axiom, ![X19, X20, X15]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15),X20))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15),X19))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X15))),X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__Suc__diff__eq2)). 4.46/4.68 fof(fact_diff__Suc__diff__eq1, axiom, ![X19, X20, X15]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X15)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X15)),hAPP(c_Nat_OSuc,X20))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__Suc__diff__eq1)). 4.46/4.68 fof(fact_refl__onD, axiom, ![X18, X16, X2, X4]:(c_Relation_Orefl__on(X4,X2,X16)=>(hBOOL(hAPP(hAPP(c_member(X4),X18),X2))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X18)),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__onD)). 4.46/4.68 fof(fact_setsum__negf, axiom, ![X2, X27, X3, X4]:(class_Groups_Oab__group__add(X4)=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X27),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),hAPP(hAPP(c_COMBB(X4,X4,X3),c_Groups_Ouminus__class_Ouminus(X4)),X27)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__negf)). 4.46/4.68 fof(fact_refl__on__Un, axiom, ![X68, X1, X16, X2, X4]:(c_Relation_Orefl__on(X4,X2,X16)=>(c_Relation_Orefl__on(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),X68))<=c_Relation_Orefl__on(X4,X1,X68))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__Un)). 4.46/4.68 fof(fact_refl__on__Int, axiom, ![X68, X1, X16, X2, X4]:((c_Relation_Orefl__on(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),X68))<=c_Relation_Orefl__on(X4,X1,X68))<=c_Relation_Orefl__on(X4,X2,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__Int)). 4.46/4.68 fof(fact_of__nat__setsum, axiom, ![X2, X27, X3, X4]:(class_Rings_Osemiring__1(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,X3),c_Nat_Osemiring__1__class_Oof__nat(X4)),X27)),X2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X27),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__setsum)). 4.46/4.68 fof(fact_append__eq__Cons__conv, axiom, ![X7, X6, X88, X32, X4]:(((hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)=X88&X32=c_List_Olist_ONil(X4))|?[X308]:(X32=hAPP(hAPP(c_List_Olist_OCons(X4),X6),X308)&hAPP(hAPP(c_List_Oappend(X4),X308),X88)=X7))<=>hAPP(hAPP(c_List_Oappend(X4),X32),X88)=hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__eq__Cons__conv)). 4.46/4.68 fof(fact_Cons__eq__append__conv, axiom, ![X88, X32, X7, X6, X4]:(((hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)=X88&c_List_Olist_ONil(X4)=X32)|?[X308]:(X32=hAPP(hAPP(c_List_Olist_OCons(X4),X6),X308)&hAPP(hAPP(c_List_Oappend(X4),X308),X88)=X7))<=>hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)=hAPP(hAPP(c_List_Oappend(X4),X32),X88)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cons__eq__append__conv)). 4.46/4.68 fof(fact_card__Suc__Diff1, axiom, ![X6, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(c_Finite__Set_Ocard(X4),X2)<=hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Suc__Diff1)). 4.46/4.68 fof(fact_min__max_Osup__inf__distrib2, axiom, ![X48, X49, X47, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X47),X48)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X49),X48))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X47),X49)),X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__inf__distrib2)). 4.46/4.68 fof(fact_wf__map__pair__image, axiom, ![X27, X3, X16, X4]:(c_Wellfounded_Owf(X4,X16)=>(c_Wellfounded_Owf(X3,hAPP(c_Set_Oimage(tc_prod(X4,X4),tc_prod(X3,X3),c_Product__Type_Omap__pair(X4,X3,X4,X3,X27,X27)),X16))<=c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__map__pair__image)). 4.46/4.68 fof(fact_setsum__abs__ge__zero, axiom, ![X2, X27, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),hAPP(hAPP(c_COMBB(X4,X4,X3),c_Groups_Oabs__class_Oabs(X4)),X27)),X2)))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__abs__ge__zero)). 4.46/4.68 fof(fact_min__max_Oinf__sup__distrib2, axiom, ![X48, X49, X47, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X47),X49)),X48)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X47),X48)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X49),X48))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__sup__distrib2)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, axiom, ![X112, X47, X48, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X48),X47)),X112)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),X112)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X47),X112))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J)). 4.46/4.68 fof(fact_power__mult__distrib, axiom, ![X17, X11, X12, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11)),X17)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X17))<=class_Groups_Ocomm__monoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__mult__distrib)). 4.46/4.68 fof(fact_power__divide, axiom, ![X17, X11, X12, X4]:(class_Fields_Ofield__inverse__zero(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X11)),X17)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__divide)). 4.46/4.68 fof(fact_Bex__set__replicate, axiom, ![X28, X18, X14, X4]:(?[X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),c_List_Oreplicate(X4,X14,X18))))&hBOOL(hAPP(X28,X42)))<=>(hBOOL(hAPP(X28,X18))&X14!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Bex__set__replicate)). 4.46/4.68 fof(fact_fun__left__comm_Ofold__set__remdups, axiom, ![X7, X5, X27, X3, X4]:(hAPP(c_List_Ofoldl(X3,X4,hAPP(c_COMBC(X4,X3,X3),X27),X5),c_List_Oremdups(X4,X7))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),X5),hAPP(c_List_Oset(X4),X7))<=c_Finite__Set_Ofun__left__comm(X4,X3,X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__set__remdups)). 4.46/4.68 fof(fact_Ball__set__replicate, axiom, ![X28, X18, X14, X4]:(![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),c_List_Oreplicate(X4,X14,X18))))=>hBOOL(hAPP(X28,X42)))<=>(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X14|hBOOL(hAPP(X28,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ball__set__replicate)). 4.46/4.68 fof(fact_min__max_Osup__inf__distrib1, axiom, ![X49, X47, X48, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X48),X47)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X48),X49))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X48),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X47),X49))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__inf__distrib1)). 4.46/4.68 fof(fact_min__max_Oinf__sup__distrib1, axiom, ![X49, X47, X48, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X47),X49))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),X47)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),X49))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__sup__distrib1)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, axiom, ![X112, X236, X48, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X236),X112))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),X236)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),X112))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J)). 4.46/4.68 fof(fact_mod__diff__eq, axiom, ![X10, X11, X12, X4]:(class_Divides_Oring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X11),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),c_Divides_Odiv__class_Omod(X4,X12,X10)),c_Divides_Odiv__class_Omod(X4,X11,X10)),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__diff__eq)). 4.46/4.68 fof(fact_list__size__estimation, axiom, ![X27, X5, X7, X6, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),c_List_Olist_Olist__size(X4,X27,X7)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(X27,X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__size__estimation)). 4.46/4.68 fof(fact_list__size__estimation_H, axiom, ![X27, X5, X7, X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),c_List_Olist_Olist__size(X4,X27,X7)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),hAPP(X27,X6))))<=hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__size__estimation_H)). 4.46/4.68 fof(fact_folding__one_Oinsert, axiom, ![X6, X2, X62, X27, X4]:(((~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))=>(hAPP(X62,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(hAPP(X27,X6),hAPP(X62,X2))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=c_Finite__Set_Ofolding__one(X4,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Oinsert)). 4.46/4.68 fof(fact_le__div__geq, axiom, ![X19, X17]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),X19))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19),X17)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17)),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__div__geq)). 4.46/4.68 fof(fact_takeWhile__append1, axiom, ![X32, X28, X7, X6, X4]:((~(hBOOL(hAPP(X28,X6)))=>c_List_OtakeWhile(X4,X28,hAPP(hAPP(c_List_Oappend(X4),X7),X32))=c_List_OtakeWhile(X4,X28,X7))<=hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__append1)). 4.46/4.68 fof(fact_folding__image__simple__idem_Osubset__idem, axiom, ![X1, X2, X62, X50, X35, X27, X3, X4]:(c_Finite__Set_Ofolding__image__simple__idem(X4,X3,X27,X35,X50,X62)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X2))=>hAPP(hAPP(X27,hAPP(X62,X1)),hAPP(X62,X2))=hAPP(X62,X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple__idem_Osubset__idem)). 4.46/4.68 fof(fact_log_Osimps, axiom, ![X21, X11]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(X11,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X21),X11)))=c_Random_Olog(X11,X21)<=~((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X11),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X21),X11)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X11),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X21),X11)))=>c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=c_Random_Olog(X11,X21))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_log_Osimps)). 4.46/4.68 fof(fact_one__less__power, axiom, ![X17, X12, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__less__power)). 4.46/4.68 fof(fact_INFI__apply, axiom, ![X6, X27, X2, X29, X3, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X4),X2),hAPP(hAPP(c_COMBC(X3,X29,X4),X27),X6))=hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X29,X4)),X2),X27),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INFI__apply)). 4.46/4.68 fof(fact_inj__comp, axiom, ![X50, X29, X27, X3, X4]:((c_Fun_Oinj__on(X29,X3,hAPP(c_Fun_Ocomp(X4,X3,X29,X27),X50),c_Orderings_Otop__class_Otop(tc_fun(X29,tc_HOL_Obool)))<=c_Fun_Oinj__on(X29,X4,X50,c_Orderings_Otop__class_Otop(tc_fun(X29,tc_HOL_Obool))))<=c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__comp)). 4.46/4.68 fof(fact_SUPR__apply, axiom, ![X6, X27, X2, X29, X3, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X29,X4)),X2),X27),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4),X2),hAPP(hAPP(c_COMBC(X3,X29,X4),X27),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUPR__apply)). 4.46/4.68 fof(fact_power__eq__imp__eq__base, axiom, ![X11, X17, X12, X4]:((hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X17)=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))=>X11=X12))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__eq__imp__eq__base)). 4.46/4.68 fof(fact_divmod__int__def, axiom, ![X11, X12]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>c_Divides_OposDivAlg(X12,X11)=c_Divides_Odivmod__int(X12,X11))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11)))=>((hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Divides_Odivmod__int(X12,X11)<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X12)&(X12!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>c_Divides_Odivmod__int(X12,X11)=hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11))))))))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12)))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>c_Divides_Odivmod__int(X12,X11)=c_Divides_OnegDivAlg(X12,X11))&(c_Divides_Odivmod__int(X12,X11)=hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11)))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__def)). 4.46/4.68 fof(fact_neg__divide__less__eq, axiom, ![X18, X37, X39, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),c_Groups_Ozero__class_Ozero(X4)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)),X37))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X37),X39)),X18))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__divide__less__eq)). 4.46/4.68 fof(fact_neg__divide__le__eq, axiom, ![X18, X37, X39, X4]:(class_Fields_Olinordered__field(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X37),X39)),X18))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)),X37)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__divide__le__eq)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, axiom, ![X12, X19, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),c_Groups_Oone__class_Oone(X4))),X19)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J)). 4.46/4.68 fof(fact_mult__imp__less__div__pos, axiom, ![X48, X49, X47, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X47))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X49),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X47)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X49),X47)),X48))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__imp__less__div__pos)). 4.46/4.68 fof(fact_mult__pos__neg, axiom, ![X11, X12, X4]:(class_Rings_Olinordered__semiring__strict(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11)),c_Groups_Ozero__class_Ozero(X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),c_Groups_Ozero__class_Ozero(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__pos__neg)). 4.46/4.68 fof(fact_mult__pos__neg2, axiom, ![X11, X12, X4]:(class_Rings_Olinordered__semiring__strict(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),c_Groups_Ozero__class_Ozero(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)),c_Groups_Ozero__class_Ozero(X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__pos__neg2)). 4.46/4.68 fof(fact_min__max_OInf__fin_Oinsert__idem, axiom, ![X6, X2, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X6),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Oinsert__idem)). 4.46/4.68 fof(fact_mult__imp__le__div__pos, axiom, ![X48, X49, X47, X4]:(class_Fields_Olinordered__field(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X49),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X47)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X49),X47)),X48)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__imp__le__div__pos)). 4.46/4.68 fof(fact_mult__imp__div__pos__less, axiom, ![X49, X48, X47, X4]:(class_Fields_Olinordered__field(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X49),X47)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X47)),X49)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__imp__div__pos__less)). 4.46/4.68 fof(fact_divide__neg__pos, axiom, ![X47, X48, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),c_Groups_Ozero__class_Ozero(X4)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X47))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X47)),c_Groups_Ozero__class_Ozero(X4)))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__neg__pos)). 4.46/4.68 fof(fact_divide__pos__neg, axiom, ![X47, X48, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X47),c_Groups_Ozero__class_Ozero(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X47)),c_Groups_Ozero__class_Ozero(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X48)))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__pos__neg)). 4.46/4.68 fof(fact_min__max_OSup__fin_Oinsert__idem, axiom, ![X6, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X6),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X2))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Oinsert__idem)). 4.46/4.68 fof(fact_mult__imp__div__pos__le, axiom, ![X49, X48, X47, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X47))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X49),X47)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X47)),X49))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__imp__div__pos__le)). 4.46/4.68 fof(fact_neg__less__divide__eq, axiom, ![X37, X18, X39, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),c_Groups_Ozero__class_Ozero(X4)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X37),X39)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__less__divide__eq)). 4.46/4.68 fof(fact_mult__le__0__iff, axiom, ![X37, X18, X4]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X37)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X18))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X37)),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__ring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__0__iff)). 4.46/4.68 fof(fact_split__mult__neg__le, axiom, ![X11, X12, X4]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11)),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Oordered__cancel__semiring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__mult__neg__le)). 4.46/4.68 fof(fact_mult__nonneg__nonpos2, axiom, ![X11, X12, X4]:(class_Rings_Oordered__cancel__semiring(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)),c_Groups_Ozero__class_Ozero(X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),c_Groups_Ozero__class_Ozero(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__nonneg__nonpos2)). 4.46/4.68 fof(fact_neg__le__divide__eq, axiom, ![X37, X18, X39, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X37),X39)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),c_Groups_Ozero__class_Ozero(X4))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__le__divide__eq)). 4.46/4.68 fof(fact_folding__image__simple__idem_Oinsert__idem, axiom, ![X6, X2, X62, X50, X35, X27, X3, X4]:(c_Finite__Set_Ofolding__image__simple__idem(X4,X3,X27,X35,X50,X62)=>(hAPP(X62,hAPP(hAPP(c_Set_Oinsert(X3),X6),X2))=hAPP(hAPP(X27,hAPP(X50,X6)),hAPP(X62,X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple__idem_Oinsert__idem)). 4.46/4.68 fof(fact_divide__nonneg__neg, axiom, ![X47, X48, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X48))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X47),c_Groups_Ozero__class_Ozero(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X47)),c_Groups_Ozero__class_Ozero(X4)))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__nonneg__neg)). 4.46/4.68 fof(fact_divide__nonpos__pos, axiom, ![X47, X48, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X47)),c_Groups_Ozero__class_Ozero(X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X47)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),c_Groups_Ozero__class_Ozero(X4))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__nonpos__pos)). 4.46/4.68 fof(fact_add__neg__neg, axiom, ![X11, X12, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),c_Groups_Ozero__class_Ozero(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)),c_Groups_Ozero__class_Ozero(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),c_Groups_Ozero__class_Ozero(X4))))<=class_Groups_Oordered__comm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__neg__neg)). 4.46/4.68 fof(fact_div__mult__mult2, axiom, ![X11, X12, X10, X4]:(class_Divides_Osemiring__div(X4)=>(hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X12),X11)<=c_Groups_Ozero__class_Ozero(X4)!=X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__mult2)). 4.46/4.68 fof(fact_add__less__mono, axiom, ![X31, X15, X20, X21]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X31)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15),X31)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__less__mono)). 4.46/4.68 fof(fact_diff__less__mono, axiom, ![X10, X11, X12]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X10)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10),X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__less__mono)). 4.46/4.68 fof(fact_diff__less__mono2, axiom, ![X31, X17, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X17))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X31))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31),X17)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31),X19))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__less__mono2)). 4.46/4.68 fof(fact_zadd__zless__mono, axiom, ![X49, X139, X30, X281]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X281),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X139),X49))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X281),X139)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X30),X49))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__zless__mono)). 4.46/4.68 fof(fact_add__nonpos__neg, axiom, ![X11, X12, X4]:(class_Groups_Oordered__comm__monoid__add(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)),c_Groups_Ozero__class_Ozero(X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),c_Groups_Ozero__class_Ozero(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__nonpos__neg)). 4.46/4.68 fof(fact_add__neg__nonpos, axiom, ![X11, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),c_Groups_Ozero__class_Ozero(X4)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)),c_Groups_Ozero__class_Ozero(X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),c_Groups_Ozero__class_Ozero(X4)))))<=class_Groups_Oordered__comm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__neg__nonpos)). 4.46/4.68 fof(fact_add__nonpos__nonpos, axiom, ![X11, X12, X4]:(class_Groups_Oordered__comm__monoid__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),c_Groups_Ozero__class_Ozero(X4)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)),c_Groups_Ozero__class_Ozero(X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),c_Groups_Ozero__class_Ozero(X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__nonpos__nonpos)). 4.46/4.68 fof(fact_less__1__mult, axiom, ![X17, X19, X4]:(class_Rings_Olinordered__semidom(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X17))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X19),X17))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__1__mult)). 4.46/4.68 fof(fact_mult__divide__mult__cancel__left, axiom, ![X11, X12, X10, X4]:((c_Groups_Ozero__class_Ozero(X4)!=X10=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X11))<=class_Fields_Ofield__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__divide__mult__cancel__left)). 4.46/4.68 fof(fact_mult__le__mono, axiom, ![X31, X15, X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15),X31))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X31))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__mono)). 4.46/4.68 fof(fact_add__le__mono, axiom, ![X31, X15, X20, X21]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15),X31))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X31))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__le__mono)). 4.46/4.68 fof(fact_mult__pos__pos, axiom, ![X11, X12, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12)))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__pos__pos)). 4.46/4.68 fof(fact_divide__pos__pos, axiom, ![X47, X48, X4]:(class_Fields_Olinordered__field(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X48))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X47))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X47)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__pos__pos)). 4.46/4.68 fof(fact_add__pos__pos, axiom, ![X11, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)))))<=class_Groups_Oordered__comm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__pos__pos)). 4.46/4.68 fof(fact_divmod__int__rel__div__mod, axiom, ![X12, X11]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X11=>hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,X11),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__div__mod)). 4.46/4.68 fof(fact_INT__D, axiom, ![X18, X1, X2, X3, X37, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X37),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)))=>(hBOOL(hAPP(hAPP(c_member(X4),X37),hAPP(X1,X18)))<=hBOOL(hAPP(hAPP(c_member(X3),X18),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__D)). 4.46/4.68 fof(fact_of__nat__diff, axiom, ![X19, X17, X4]:(class_Rings_Oring__1(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),X19))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X19)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X17))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__diff)). 4.46/4.68 fof(fact_transfer__nat__int__set__relations_I4_J, axiom, ![X1, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__relations_I4_J)). 4.46/4.68 fof(fact_select, axiom, ![X68, X4, X7]:(hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Product__Type_Ofst(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X4,X7),X68))),hAPP(c_List_Oset(X4),X7)))<=X7!=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select)). 4.46/4.68 fof(fact_mult__nonneg__nonneg, axiom, ![X11, X12, X4]:(class_Rings_Oordered__cancel__semiring(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__nonneg__nonneg)). 4.46/4.68 fof(fact_zero__le__mult__iff, axiom, ![X37, X18, X4]:(class_Rings_Olinordered__ring__strict(X4)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),c_Groups_Ozero__class_Ozero(X4))))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X37))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X18))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X37))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__mult__iff)). 4.46/4.68 fof(fact_split__mult__pos__le, axiom, ![X11, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11)))<=((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),c_Groups_Ozero__class_Ozero(X4))))))<=class_Rings_Oordered__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__mult__pos__le)). 4.46/4.68 fof(fact_div__mult__mult1, axiom, ![X11, X12, X10, X4]:((hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X12),X11)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11))<=X10!=c_Groups_Ozero__class_Ozero(X4))<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__mult1)). 4.46/4.68 fof(fact_subset__image__iff, axiom, ![X2, X27, X3, X1, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),hAPP(c_Set_Oimage(X3,X4,X27),X2)))<=>?[X322]:(X1=hAPP(c_Set_Oimage(X3,X4,X27),X322)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X322),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__image__iff)). 4.46/4.68 fof(fact_divide__nonneg__pos, axiom, ![X47, X48, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X48))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X47))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X47)))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__nonneg__pos)). 4.46/4.68 fof(fact_mult__neg__neg, axiom, ![X11, X12, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),c_Groups_Ozero__class_Ozero(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__ring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__neg__neg)). 4.46/4.68 fof(fact_divide__neg__neg, axiom, ![X47, X48, X4]:(class_Fields_Olinordered__field(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X47)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X47),c_Groups_Ozero__class_Ozero(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__neg__neg)). 4.46/4.68 fof(fact_mult__divide__mult__cancel__right, axiom, ![X11, X12, X10, X4]:(class_Fields_Ofield__inverse__zero(X4)=>(X10!=c_Groups_Ozero__class_Ozero(X4)=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X11)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__divide__mult__cancel__right)). 4.46/4.68 fof(fact_quotientE, axiom, ![X16, X2, X173, X4]:(~(![X42]:(~(hBOOL(hAPP(hAPP(c_member(X4),X42),X2)))<=X173=hAPP(c_Relation_OImage(X4,X4,X16),hAPP(hAPP(c_Set_Oinsert(X4),X42),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X173),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X2),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotientE)). 4.46/4.68 fof(fact_Suc__mult__less__cancel1, axiom, ![X14, X22, X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X45)),X22)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X45)),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__mult__less__cancel1)). 4.46/4.68 fof(fact_abs__setprod, axiom, ![X2, X27, X3, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X4),hAPP(hAPP(c_COMBB(X4,X4,X3),c_Groups_Oabs__class_Oabs(X4)),X27)),X2)=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X4),X27),X2))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__setprod)). 4.46/4.68 fof(fact_divide__nonpos__neg, axiom, ![X47, X48, X4]:(class_Fields_Olinordered__field(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X47)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X47),c_Groups_Ozero__class_Ozero(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__nonpos__neg)). 4.46/4.68 fof(fact_of__int__setsum, axiom, ![X2, X27, X3, X4]:(class_Rings_Oring__1(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),hAPP(hAPP(c_COMBB(tc_Int_Oint,X4,X3),c_Int_Oring__1__class_Oof__int(X4)),X27)),X2)=hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Int_Oint),X27),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__setsum)). 4.46/4.68 fof(fact_nat__mult__div__cancel1, axiom, ![X17, X19, X15]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19),X17)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__div__cancel1)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, axiom, ![X141, X142, X143, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X143),X141)),X142)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X143),X142)),X141)<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J)). 4.46/4.68 fof(fact_small__lazy_H_Osimps, axiom, ![X21, X133]:((c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X21),c_Lazy__Sequence_Osmall__lazy_H(X133,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21),c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Lazy__Sequence_Osmall__lazy_H(X133,X21)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X133),X21))))&(c_Lazy__Sequence_Osmall__lazy_H(X133,X21)=c_Lazy__Sequence_Oempty(tc_Int_Oint)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X133),X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__lazy_H_Osimps)). 4.46/4.68 fof(fact_ex__nat__less, axiom, ![X28, X14]:(?[X90]:(hBOOL(hAPP(X28,X90))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X90),X14)))<=>?[X42]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X42),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14)))&hBOOL(hAPP(X28,X42)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__nat__less)). 4.46/4.68 fof(fact_fold1__insert__idem, axiom, ![X6, X2, X4]:(class_Lattices_Oab__semigroup__idem__mult(X4)=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__insert__idem)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, axiom, ![X10, X11, X12, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10)),X11)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J)). 4.46/4.68 fof(fact_transfer__int__nat__set__relations_I4_J, axiom, ![X1, X2]:(c_Nat__Transfer_Onat__set(X2)=>(c_Nat__Transfer_Onat__set(X1)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X2),X1))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__set__relations_I4_J)). 4.46/4.68 fof(fact_set__zip__leftD, axiom, ![X32, X7, X5, X6, X3, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X6),X5)),hAPP(c_List_Oset(tc_prod(X4,X3)),hAPP(hAPP(c_List_Ozip(X4,X3),X7),X32))))=>hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__zip__leftD)). 4.46/4.68 fof(fact_set__zip__rightD, axiom, ![X32, X7, X5, X6, X3, X4]:(hBOOL(hAPP(hAPP(c_member(X3),X5),hAPP(c_List_Oset(X3),X32)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X6),X5)),hAPP(c_List_Oset(tc_prod(X4,X3)),hAPP(hAPP(c_List_Ozip(X4,X3),X7),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__zip__rightD)). 4.46/4.68 fof(fact_sorted_OCons, axiom, ![X6, X7, X4]:(((c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7))<=c_List_Olinorder__class_Osorted(X4,X7))<=![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X42))<=hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7)))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted_OCons)). 4.46/4.68 fof(fact_sorted_Oequations_I2_J, axiom, ![X123, X135, X4]:(((c_List_Olinorder__class_Osorted(X4,X123)&![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X123)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X135),X42))))<=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X135),X123)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted_Oequations_I2_J)). 4.46/4.68 fof(fact_take__Suc, axiom, ![X17, X4, X57]:(hAPP(hAPP(c_List_Olist_OCons(X4),hAPP(c_List_Ohd(X4),X57)),hAPP(hAPP(c_List_Otake(X4),X17),hAPP(c_List_Otl(X4),X57)))=hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_OSuc,X17)),X57)<=c_List_Olist_ONil(X4)!=X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Suc)). 4.46/4.68 fof(fact_sorted__Cons, axiom, ![X7, X6, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7))<=>(c_List_Olinorder__class_Osorted(X4,X7)&![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X42))<=hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__Cons)). 4.46/4.68 fof(fact_mod__mult__eq, axiom, ![X10, X11, X12, X4]:(class_Divides_Osemiring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Divides_Odiv__class_Omod(X4,X12,X10)),c_Divides_Odiv__class_Omod(X4,X11,X10)),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__eq)). 4.46/4.68 fof(fact_mod__add__eq, axiom, ![X10, X11, X12, X4]:(class_Divides_Osemiring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Divides_Odiv__class_Omod(X4,X12,X10)),c_Divides_Odiv__class_Omod(X4,X11,X10)),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__add__eq)). 4.46/4.68 fof(fact_irrefl__def, axiom, ![X16, X4]:(c_Relation_Oirrefl(X4,X16)<=>![X42]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X42)),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_irrefl__def)). 4.46/4.68 fof(fact_nth__Cons_H, axiom, ![X57, X48, X4, X17]:((X48=hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)),X17)<=X17=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(hAPP(hAPP(c_List_Onth(X4),X57),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)),X17)<=X17!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__Cons_H)). 4.46/4.68 fof(fact_Max__mono, axiom, ![X122, X153, X4]:(class_Orderings_Olinorder(X4)=>((X153!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X122))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Big__Operators_Olinorder__class_OMax(X4,X153)),c_Big__Operators_Olinorder__class_OMax(X4,X122)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X153),X122)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__mono)). 4.46/4.68 fof(fact_Min__antimono, axiom, ![X122, X153, X4]:((((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X122))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Big__Operators_Olinorder__class_OMin(X4,X122)),c_Big__Operators_Olinorder__class_OMin(X4,X153))))<=X153!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X153),X122)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__antimono)). 4.46/4.68 fof(fact_card__Plus__conv__if, axiom, ![X1, X3, X2, X4]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X2)),hAPP(c_Finite__Set_Ocard(X3),X1))=hAPP(c_Finite__Set_Ocard(tc_sum(X4,X3)),c_Sum__Type_OPlus(X4,X3,X2,X1))<=(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1))&hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))))&(~((hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1))&hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(tc_sum(X4,X3)),c_Sum__Type_OPlus(X4,X3,X2,X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Plus__conv__if)). 4.46/4.68 fof(fact_folding__image__simple__idem_Oin__idem, axiom, ![X6, X2, X62, X50, X35, X27, X3, X4]:(c_Finite__Set_Ofolding__image__simple__idem(X4,X3,X27,X35,X50,X62)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))=>(hBOOL(hAPP(hAPP(c_member(X3),X6),X2))=>hAPP(hAPP(X27,hAPP(X50,X6)),hAPP(X62,X2))=hAPP(X62,X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple__idem_Oin__idem)). 4.46/4.68 fof(fact_list__all2__map1, axiom, ![X260, X172, X27, X29, X28, X3, X4]:(c_List_Olist__all2(X29,X3,hAPP(hAPP(c_COMBB(X4,tc_fun(X3,tc_HOL_Obool),X29),X28),X27),X172,X260)<=>c_List_Olist__all2(X4,X3,X28,hAPP(hAPP(c_List_Omap(X29,X4),X27),X172),X260)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__map1)). 4.46/4.68 fof(fact_inj__on__Inter, axiom, ![X27, X3, X4, X46]:((c_Fun_Oinj__on(X4,X3,X27,c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X46))<=![X161]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X161),X46))=>c_Fun_Oinj__on(X4,X3,X27,X161)))<=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))!=X46), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__Inter)). 4.46/4.68 fof(fact_subset__card__intvl__is__intvl, axiom, ![X45, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X2)))))=>hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X2)))=X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__card__intvl__is__intvl)). 4.46/4.68 fof(fact_mod__mult__mult2, axiom, ![X11, X10, X12, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Divides_Odiv__class_Omod(X4,X12,X11)),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10))<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__mult2)). 4.46/4.68 fof(fact_mod__mult__mult1, axiom, ![X11, X12, X10, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),c_Divides_Odiv__class_Omod(X4,X12,X11))=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11))<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__mult1)). 4.46/4.68 fof(fact_rtrancl__listrel1__eq__len, axiom, ![X16, X5, X6, X4]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X6)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5)<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X6),X5)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X4),c_List_Olistrel1(X4,X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__listrel1__eq__len)). 4.46/4.68 fof(fact_list__eq__iff__nth__eq, axiom, ![X4, X32, X7]:(X7=X32<=>(![X41]:(hAPP(hAPP(c_List_Onth(X4),X7),X41)=hAPP(hAPP(c_List_Onth(X4),X32),X41)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))))&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__eq__iff__nth__eq)). 4.46/4.68 fof(fact_divide__less__0__iff, axiom, ![X37, X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X18),X37)),c_Groups_Ozero__class_Ozero(X4)))<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X37)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X37),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X18)))))<=class_Fields_Olinordered__field__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__less__0__iff)). 4.46/4.68 fof(fact_simp__from__to, axiom, ![X24, X25]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),X24))=>c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24,X25))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),X24)))=>hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X24),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24),c_Groups_Oone__class_Oone(tc_Int_Oint)),X25))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24,X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_simp__from__to)). 4.46/4.68 fof(fact_listsum__distinct__conv__setsum__set, axiom, ![X27, X7, X4, X3]:((hBOOL(hAPP(c_List_Odistinct(X4),X7))=>hAPP(c_List_Omonoid__add__class_Olistsum(X3),hAPP(hAPP(c_List_Omap(X4,X3),X27),X7))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),hAPP(c_List_Oset(X4),X7)))<=class_Groups_Ocomm__monoid__add(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__distinct__conv__setsum__set)). 4.46/4.68 fof(fact_INT__absorb, axiom, ![X2, X3, X73, X45, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X45),X73))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),hAPP(X2,X45)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X73),X2))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X73),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__absorb)). 4.46/4.68 fof(fact_divide__le__0__iff, axiom, ![X37, X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X18),X37)),c_Groups_Ozero__class_Ozero(X4)))<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X37))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),c_Groups_Ozero__class_Ozero(X4))))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X18))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),c_Groups_Ozero__class_Ozero(X4))))))<=class_Fields_Olinordered__field__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__le__0__iff)). 4.46/4.68 fof(fact_Ints__mult, axiom, ![X37, X18, X4]:(class_Rings_Oring__1(X4)=>((hBOOL(hAPP(hAPP(c_member(X4),X37),c_Int_Oring__1__class_OInts(X4)))=>hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X37)),c_Int_Oring__1__class_OInts(X4))))<=hBOOL(hAPP(hAPP(c_member(X4),X18),c_Int_Oring__1__class_OInts(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__mult)). 4.46/4.68 fof(fact_Nats__mult, axiom, ![X37, X18, X4]:(class_Rings_Osemiring__1(X4)=>((hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X37)),c_Nat_Osemiring__1__class_ONats(X4)))<=hBOOL(hAPP(hAPP(c_member(X4),X37),c_Nat_Osemiring__1__class_ONats(X4))))<=hBOOL(hAPP(hAPP(c_member(X4),X18),c_Nat_Osemiring__1__class_ONats(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nats__mult)). 4.46/4.68 fof(fact_mult__eq__if, axiom, ![X17, X19]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X19=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X17)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X17)))&(X19=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__eq__if)). 4.46/4.68 fof(fact_UN__absorb, axiom, ![X2, X3, X73, X45, X4]:(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X73),X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),hAPP(X2,X45)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X73),X2))<=hBOOL(hAPP(hAPP(c_member(X4),X45),X73))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__absorb)). 4.46/4.68 fof(fact_pred__nat__trancl__eq__le, axiom, ![X14, X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22),X14)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__nat__trancl__eq__le)). 4.46/4.68 fof(fact_rotate1__hd__tl, axiom, ![X4, X57]:(hAPP(hAPP(c_List_Oappend(X4),hAPP(c_List_Otl(X4),X57)),hAPP(hAPP(c_List_Olist_OCons(X4),hAPP(c_List_Ohd(X4),X57)),c_List_Olist_ONil(X4)))=hAPP(c_List_Orotate1(X4),X57)<=X57!=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate1__hd__tl)). 4.46/4.68 fof(fact_Ints__add, axiom, ![X37, X18, X4]:(((hBOOL(hAPP(hAPP(c_member(X4),X37),c_Int_Oring__1__class_OInts(X4)))=>hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X18),X37)),c_Int_Oring__1__class_OInts(X4))))<=hBOOL(hAPP(hAPP(c_member(X4),X18),c_Int_Oring__1__class_OInts(X4))))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__add)). 4.46/4.68 fof(fact_Nats__add, axiom, ![X37, X18, X4]:(class_Rings_Osemiring__1(X4)=>(hBOOL(hAPP(hAPP(c_member(X4),X18),c_Nat_Osemiring__1__class_ONats(X4)))=>(hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X18),X37)),c_Nat_Osemiring__1__class_ONats(X4)))<=hBOOL(hAPP(hAPP(c_member(X4),X37),c_Nat_Osemiring__1__class_ONats(X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nats__add)). 4.46/4.68 fof(fact_Ints__diff, axiom, ![X37, X18, X4]:(((hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X18),X37)),c_Int_Oring__1__class_OInts(X4)))<=hBOOL(hAPP(hAPP(c_member(X4),X37),c_Int_Oring__1__class_OInts(X4))))<=hBOOL(hAPP(hAPP(c_member(X4),X18),c_Int_Oring__1__class_OInts(X4))))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__diff)). 4.46/4.68 fof(fact_zero__less__divide__iff, axiom, ![X37, X18, X4]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X37),c_Groups_Ozero__class_Ozero(X4))))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X18))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X37))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X18),X37))))<=class_Fields_Olinordered__field__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__divide__iff)). 4.46/4.68 fof(fact_mult__le__cancel1, axiom, ![X14, X22, X45]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X45)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X22)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__cancel1)). 4.46/4.68 fof(fact_Int__insert__right__if1, axiom, ![X1, X2, X18, X4]:(hAPP(hAPP(c_Set_Oinsert(X4),X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),X1))<=hBOOL(hAPP(hAPP(c_member(X4),X18),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__insert__right__if1)). 4.46/4.68 fof(fact_inj__image__subset__iff, axiom, ![X1, X2, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X3,X27),X2)),hAPP(c_Set_Oimage(X4,X3,X27),X1)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__image__subset__iff)). 4.46/4.68 fof(fact_mult__le__cancel2, axiom, ![X14, X45, X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X45)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X45)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__cancel2)). 4.46/4.68 fof(fact_zero__le__divide__iff, axiom, ![X37, X18, X4]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X37))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X18)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),c_Groups_Ozero__class_Ozero(X4)))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X18),X37))))<=class_Fields_Olinordered__field__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__divide__iff)). 4.46/4.68 fof(fact_remove1__append, axiom, ![X32, X7, X6, X4]:((hAPP(hAPP(c_List_Oappend(X4),c_List_Oremove1(X4,X6,X7)),X32)=c_List_Oremove1(X4,X6,hAPP(hAPP(c_List_Oappend(X4),X7),X32))<=hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7))))&(~(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7))))=>hAPP(hAPP(c_List_Oappend(X4),X7),c_List_Oremove1(X4,X6,X32))=c_List_Oremove1(X4,X6,hAPP(hAPP(c_List_Oappend(X4),X7),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1__append)). 4.46/4.68 fof(fact_rtrancl__subset__rtrancl, axiom, ![X68, X16, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4,X16)),c_Transitive__Closure_Ortrancl(X4,X68)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),c_Transitive__Closure_Ortrancl(X4,X68)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__subset__rtrancl)). 4.46/4.68 fof(fact_card__insert, axiom, ![X6, X2, X4]:(hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__insert)). 4.46/4.68 fof(fact_inf__Inf__fold__inf, axiom, ![X1, X2, X4]:((hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),X1),X2)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X1),c_Complete__Lattice_OInf__class_OInf(X4,X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__Inf__fold__inf)). 4.46/4.68 fof(fact_nth__map, axiom, ![X27, X3, X7, X4, X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))=>hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Omap(X4,X3),X27),X7)),X14)=hAPP(X27,hAPP(hAPP(c_List_Onth(X4),X7),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__map)). 4.46/4.68 fof(fact_elem__le__sum, axiom, ![X136, X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X136)))<=hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X14),hAPP(c_List_Oset(tc_Nat_Onat),X136)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_elem__le__sum)). 4.46/4.68 fof(fact_wf__Un, axiom, ![X68, X16, X4]:(c_Wellfounded_Owf(X4,X16)=>(c_Wellfounded_Owf(X4,X68)=>(c_Wellfounded_Owf(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),X68))<=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X4,X4),X16)),hAPP(c_Relation_ORange(X4,X4),X68))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__Un)). 4.46/4.68 fof(fact_finite__INT, axiom, ![X2, X3, X73, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X73),X2)))<=?[X42]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X2,X42)))&hBOOL(hAPP(hAPP(c_member(X4),X42),X73)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__INT)). 4.46/4.68 fof(fact_fold1Set_Ointros, axiom, ![X6, X2, X18, X27, X4]:((~(hBOOL(hAPP(hAPP(c_member(X4),X18),X2)))=>hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,X27,hAPP(hAPP(c_Set_Oinsert(X4),X18),X2)),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X4,X27,X18,X2),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1Set_Ointros)). 4.46/4.68 fof(fact_in__rel__def, axiom, ![X5, X6, X26, X3, X4]:(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4,X3,X26),X6),X5))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X6),X5)),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__rel__def)). 4.46/4.68 fof(fact_drop__Cons_H, axiom, ![X57, X48, X4, X17]:((hAPP(hAPP(c_List_Odrop(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X57)=hAPP(hAPP(c_List_Odrop(X4),X17),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57))<=X17!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(X17=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)=hAPP(hAPP(c_List_Odrop(X4),X17),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__Cons_H)). 4.46/4.68 fof(fact_enum__ex__option__def, axiom, ![X28, X4]:(((hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X4),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X4),tc_HOL_Obool,X4),X28),c_Option_Ooption_OSome(X4))))|hBOOL(hAPP(X28,c_Option_Ooption_ONone(X4))))<=>hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X4)),X28)))<=class_Enum_Oenum(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__ex__option__def)). 4.46/4.68 fof(fact_power__inject__base, axiom, ![X11, X17, X12, X4]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11))=>X12=X11)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12)))<=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Nat_OSuc,X17))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(c_Nat_OSuc,X17)))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__inject__base)). 4.46/4.68 fof(fact_less__diff__iff, axiom, ![X14, X22, X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X22))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22),X45)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14),X45)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X14)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__diff__iff)). 4.46/4.68 fof(fact_listsum__setsum__nth, axiom, ![X7, X4]:(hAPP(c_List_Omonoid__add__class_Olistsum(X4),X7)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(c_List_Onth(X4),X7)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__setsum__nth)). 4.46/4.68 fof(fact_le__diff__iff, axiom, ![X14, X22, X45]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X14))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22),X45)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14),X45)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X22))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__diff__iff)). 4.46/4.68 fof(fact_SUP2__E, axiom, ![X39, X37, X1, X2, X29, X3, X4]:(~(![X42]:(~(hBOOL(hAPP(hAPP(hAPP(X1,X42),X37),X39)))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X2))))<=hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_fun(X29,tc_HOL_Obool))),X2),X1),X37),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP2__E)). 4.46/4.68 fof(fact_SUP2__iff, axiom, ![X39, X37, X1, X2, X29, X3, X4]:(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_fun(X29,tc_HOL_Obool))),X2),X1),X37),X39))<=>?[X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))&hBOOL(hAPP(hAPP(hAPP(X1,X42),X37),X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP2__iff)). 4.46/4.68 fof(fact_Un__Int__assoc__eq, axiom, ![X52, X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X52),X2))<=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)),X52)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X1),X52))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Int__assoc__eq)). 4.46/4.68 fof(fact_INF2__D, axiom, ![X18, X39, X37, X1, X2, X29, X3, X4]:(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_fun(X29,tc_HOL_Obool))),X2),X1),X37),X39))=>(hBOOL(hAPP(hAPP(c_member(X4),X18),X2))=>hBOOL(hAPP(hAPP(hAPP(X1,X18),X37),X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF2__D)). 4.46/4.68 fof(fact_power__le__imp__le__base, axiom, ![X11, X17, X12, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Nat_OSuc,X17))),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(c_Nat_OSuc,X17))))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__le__imp__le__base)). 4.46/4.68 fof(fact_UN__iff, axiom, ![X1, X2, X3, X37, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X37),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=>?[X42]:(hBOOL(hAPP(hAPP(c_member(X3),X42),X2))&hBOOL(hAPP(hAPP(c_member(X4),X37),hAPP(X1,X42))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__iff)). 4.46/4.68 fof(fact_add__strict__right__mono, axiom, ![X10, X11, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11)))<=class_Groups_Oordered__cancel__ab__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__strict__right__mono)). 4.46/4.68 fof(fact_add__less__cancel__right, axiom, ![X37, X39, X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),X37))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X18),X39)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X37),X39))))<=class_Groups_Oordered__ab__semigroup__add__imp__le(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__less__cancel__right)). 4.46/4.68 fof(fact_add__strict__left__mono, axiom, ![X10, X11, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X11))))<=class_Groups_Oordered__cancel__ab__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__strict__left__mono)). 4.46/4.68 fof(fact_add__less__cancel__left, axiom, ![X37, X18, X39, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),X37))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X39),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X39),X37))))<=class_Groups_Oordered__ab__semigroup__add__imp__le(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__less__cancel__left)). 4.46/4.68 fof(fact_foldl__absorb0, axiom, ![X88, X6, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X6),hAPP(c_List_Ofoldl(X4,X4,c_Groups_Oplus__class_Oplus(X4),c_Groups_Ozero__class_Ozero(X4)),X88))=hAPP(c_List_Ofoldl(X4,X4,c_Groups_Oplus__class_Oplus(X4),X6),X88)<=class_Groups_Omonoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__absorb0)). 4.46/4.68 fof(fact_add__right__mono, axiom, ![X10, X11, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11)))<=class_Groups_Oordered__ab__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__right__mono)). 4.46/4.68 fof(fact_add__le__cancel__right, axiom, ![X37, X39, X18, X4]:(class_Groups_Oordered__ab__semigroup__add__imp__le(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),X37))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X18),X39)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X37),X39))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__le__cancel__right)). 4.46/4.68 fof(fact_add__left__mono, axiom, ![X10, X11, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11)))<=class_Groups_Oordered__ab__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__left__mono)). 4.46/4.68 fof(fact_add__le__cancel__left, axiom, ![X37, X18, X39, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),X37))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X39),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X39),X37))))<=class_Groups_Oordered__ab__semigroup__add__imp__le(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__le__cancel__left)). 4.46/4.68 fof(fact_power__one__over, axiom, ![X17, X12, X4]:(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),c_Groups_Oone__class_Oone(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),c_Groups_Oone__class_Oone(X4)),X12)),X17)<=class_Fields_Ofield__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__one__over)). 4.46/4.68 fof(fact_list__all2__Cons, axiom, ![X32, X5, X7, X6, X28, X3, X4]:(c_List_Olist__all2(X4,X3,X28,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7),hAPP(hAPP(c_List_Olist_OCons(X3),X5),X32))<=>(hBOOL(hAPP(hAPP(X28,X6),X5))&c_List_Olist__all2(X4,X3,X28,X7,X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__Cons)). 4.46/4.68 fof(fact_folding__image_Oeq__fold, axiom, ![X50, X2, X62, X35, X27, X3, X4]:(c_Finite__Set_Ofolding__image(X4,X3,X27,X35,X62)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))=>hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4,X3,X27),X50),X35),X2)=hAPP(hAPP(X62,X50),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image_Oeq__fold)). 4.46/4.68 fof(fact_comm__monoid__big_OF__eq, axiom, ![X50, X2, X62, X35, X27, X3, X4]:(c_Big__Operators_Ocomm__monoid__big(X4,X3,X27,X35,X62)=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))=>hAPP(hAPP(X62,X50),X2)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4,X3,X27),X50),X35),X2))&(hAPP(hAPP(X62,X50),X2)=X35<=~(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__monoid__big_OF__eq)). 4.46/4.68 fof(fact_set__update__memI, axiom, ![X6, X7, X4, X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))=>hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist__update(X4,X7),X14),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__update__memI)). 4.46/4.68 fof(fact_Sup__fin_Oeq__fold__idem_H, axiom, ![X18, X2, X4]:((hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4)),X18),X2)=c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X18),X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oeq__fold__idem_H)). 4.46/4.68 fof(fact_Inf__fin_Oeq__fold__idem_H, axiom, ![X18, X2, X4]:(class_Lattices_Olattice(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),X18),X2)=c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X18),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oeq__fold__idem_H)). 4.46/4.68 fof(fact_single__valuedD, axiom, ![X35, X5, X6, X16, X3, X4]:(c_Relation_Osingle__valued(X4,X3,X16)=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X6),X5)),X16))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X6),X35)),X16))=>X35=X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valuedD)). 4.46/4.68 fof(fact_range, axiom, ![X198, X15]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X15))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(X15),X198))),X15))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_range)). 4.46/4.68 fof(fact_Inter__subset, axiom, ![X1, X2, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X2)),X1))<=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))!=X2)<=![X207]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X207),X1))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X207),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__subset)). 4.46/4.68 fof(fact_sorted__insort__key, axiom, ![X7, X6, X27, X3, X4]:((c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X27),X7))<=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X27),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3,X4,X27),X6),X7))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__insort__key)). 4.46/4.68 fof(fact_butlast__take, axiom, ![X57, X4, X17]:(c_List_Obutlast(X4,hAPP(hAPP(c_List_Otake(X4),X17),X57))=hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X57)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast__take)). 4.46/4.68 fof(fact_diff__single__insert, axiom, ![X1, X6, X2, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),X1))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__single__insert)). 4.46/4.68 fof(fact_folding__one__idem_Oeq__fold__idem_H, axiom, ![X18, X2, X62, X27, X4]:(c_Finite__Set_Ofolding__one__idem(X4,X27,X62)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,X27),X18),X2)=hAPP(X62,hAPP(hAPP(c_Set_Oinsert(X4),X18),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Oeq__fold__idem_H)). 4.46/4.68 fof(fact_zdiv__zmult2__eq, axiom, ![X11, X12, X10]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X10))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11)),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__zmult2__eq)). 4.46/4.68 fof(fact_list__all2__appendI, axiom, ![X87, X39, X37, X18, X28, X3, X4]:(c_List_Olist__all2(X4,X3,X28,X18,X37)=>(c_List_Olist__all2(X4,X3,X28,X39,X87)=>c_List_Olist__all2(X4,X3,X28,hAPP(hAPP(c_List_Oappend(X4),X18),X39),hAPP(hAPP(c_List_Oappend(X3),X37),X87)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__appendI)). 4.46/4.68 fof(fact_pos__imp__zdiv__neg__iff, axiom, ![X18, X37]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X18),X37)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__imp__zdiv__neg__iff)). 4.46/4.68 fof(fact_neg__imp__zdiv__neg__iff, axiom, ![X18, X37]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X18),X37)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__imp__zdiv__neg__iff)). 4.46/4.68 fof(fact_atLeastLessThan__subset__iff, axiom, ![X87, X39, X37, X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X18),X37)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X39),X87)))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X39),X18))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),X87)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),X18))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__subset__iff)). 4.46/4.68 fof(fact_abs__number__of, axiom, ![X48, X4]:(((hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X48))=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X48))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X48)),c_Groups_Ozero__class_Ozero(X4))))&(hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X48))=hAPP(c_Int_Onumber__class_Onumber__of(X4),X48)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X48)),c_Groups_Ozero__class_Ozero(X4))))))<=(class_Rings_Olinordered__idom(X4)&class_Int_Onumber__ring(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__number__of)). 4.46/4.68 fof(fact_div__nonneg__neg__le0, axiom, ![X11, X12]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__nonneg__neg__le0)). 4.46/4.68 fof(fact_div__nonpos__pos__le0, axiom, ![X11, X12]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__nonpos__pos__le0)). 4.46/4.68 fof(fact_nat__0__less__mult__iff, axiom, ![X14, X22]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__0__less__mult__iff)). 4.46/4.68 fof(fact_pos__imp__zdiv__nonneg__iff, axiom, ![X18, X37]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X18),X37)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__imp__zdiv__nonneg__iff)). 4.46/4.68 fof(fact_insort__insert__insort, axiom, ![X7, X6, X4]:((hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)),X6),X7)=c_List_Olinorder__class_Oinsort__insert__key(X4,X4,c_COMBI(X4),X6,X7)<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__insert__insort)). 4.46/4.68 fof(fact_mod__minus__cong, axiom, ![X163, X11, X12, X4]:(class_Divides_Oring__div(X4)=>(c_Divides_Odiv__class_Omod(X4,X163,X11)=c_Divides_Odiv__class_Omod(X4,X12,X11)=>c_Divides_Odiv__class_Omod(X4,hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12),X11)=c_Divides_Odiv__class_Omod(X4,hAPP(c_Groups_Ouminus__class_Ouminus(X4),X163),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__minus__cong)). 4.46/4.68 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J, axiom, ![X47, X48]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X47))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X48),X47))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X48))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Otransfer__nat__int__function__closures_I1_J)). 4.46/4.68 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, axiom, ![X47, X48]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X48))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X47)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J)). 4.46/4.68 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, axiom, ![X47, X48]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X48))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X47))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X48),X47))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J)). 4.46/4.68 fof(fact_neg__imp__zdiv__nonneg__iff, axiom, ![X18, X37]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X18),X37))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__imp__zdiv__nonneg__iff)). 4.46/4.68 fof(fact_triples__valid__Suc, axiom, ![X14, X202, X4]:(![X42]:(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X4)),X42),X202))=>c_Hoare__Mirabelle_Otriple__valid(X4,X14,X42))<=![X42]:(c_Hoare__Mirabelle_Otriple__valid(X4,hAPP(c_Nat_OSuc,X14),X42)<=hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X4)),X42),X202)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_triples__valid__Suc)). 4.46/4.68 fof(fact_enum__option__def, axiom, ![X4]:(class_Enum_Oenum(X4)=>hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(X4)),c_Option_Ooption_ONone(X4)),hAPP(hAPP(c_List_Omap(X4,tc_Option_Ooption(X4)),c_Option_Ooption_OSome(X4)),c_Enum_Oenum__class_Oenum(X4)))=c_Enum_Oenum__class_Oenum(tc_Option_Ooption(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__option__def)). 4.46/4.68 fof(fact_image__uminus__atLeastLessThan, axiom, ![X5, X6, X4]:(c_SetInterval_Oord__class_OgreaterThanAtMost(X4,hAPP(c_Groups_Ouminus__class_Ouminus(X4),X5),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X6))=hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X6),X5))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__atLeastLessThan)). 4.46/4.68 fof(fact_select__weigth__select, axiom, ![X4, X7]:(X7!=c_List_Olist_ONil(X4)=>c_Random_Oselect__weight(X4,hAPP(hAPP(c_List_Omap(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,X4)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X4),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X7))=c_Random_Oselect(X4,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select__weigth__select)). 4.46/4.68 fof(fact_lists_Osimps, axiom, ![X2, X18, X4]:((c_List_Olist_ONil(X4)=X18|?[X125, X298]:((hAPP(hAPP(c_List_Olist_OCons(X4),X125),X298)=X18&hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X298),c_List_Olists(X4,X2))))&hBOOL(hAPP(hAPP(c_member(X4),X125),X2))))<=>hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X18),c_List_Olists(X4,X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists_Osimps)). 4.46/4.68 fof(fact_setsum__reindex__id, axiom, ![X1, X27, X4, X3]:((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X3),c_Fun_Oid(X3)),hAPP(c_Set_Oimage(X4,X3,X27),X1))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X27),X1)<=c_Fun_Oinj__on(X4,X3,X27,X1))<=class_Groups_Ocomm__monoid__add(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__reindex__id)). 4.46/4.68 fof(fact_setprod__reindex__id, axiom, ![X1, X27, X4, X3]:(class_Groups_Ocomm__monoid__mult(X3)=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),X1)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X3),c_Fun_Oid(X3)),hAPP(c_Set_Oimage(X4,X3,X27),X1))<=c_Fun_Oinj__on(X4,X3,X27,X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__reindex__id)). 4.46/4.68 fof(fact_finite__maxlen, axiom, ![X153, X4]:(?[X199]:![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X42)),X199))<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X42),X153)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X4)),X153))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__maxlen)). 4.46/4.68 fof(fact_sorted__many__eq, axiom, ![X88, X5, X6, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X6),hAPP(hAPP(c_List_Olist_OCons(X4),X5),X88)))<=>(c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X5),X88))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__many__eq)). 4.46/4.68 fof(fact_Int__atLeastAtMostL2, axiom, ![X39, X37, X18, X4]:(class_Orderings_Olinorder(X4)=>c_SetInterval_Oord__class_OatLeastAtMost(X4,hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X18),X39),X37)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X18,X37)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__atLeastAtMostL2)). 4.46/4.68 fof(fact_Domain__mono, axiom, ![X68, X16, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X16),X68))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X4,X3),X16)),hAPP(c_Relation_ODomain(X4,X3),X68)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__mono)). 4.46/4.68 fof(fact_Int__atLeastAtMostL1, axiom, ![X87, X37, X18, X4]:(c_SetInterval_Oord__class_OatLeastAtMost(X4,X18,hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X37),X87))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X18,X37)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X87))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__atLeastAtMostL1)). 4.46/4.68 fof(fact_Int__atLeastAtMostR2, axiom, ![X87, X39, X18, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X18)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X39,X87))=c_SetInterval_Oord__class_OatLeastAtMost(X4,hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X18),X39),X87)<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__atLeastAtMostR2)). 4.46/4.68 fof(fact_dom__minus, axiom, ![X2, X3, X4, X6, X27]:(c_Option_Ooption_ONone(X4)=hAPP(X27,X6)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),c_Map_Odom(X3,X4,X27)),hAPP(hAPP(c_Set_Oinsert(X3),X6),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),c_Map_Odom(X3,X4,X27)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__minus)). 4.46/4.68 fof(fact_zdiff__int, axiom, ![X19, X17]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiff__int)). 4.46/4.68 fof(fact_Int__atLeastAtMostR1, axiom, ![X87, X39, X37, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X37)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X39,X87))=c_SetInterval_Oord__class_OatLeastAtMost(X4,X39,hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X37),X87))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__atLeastAtMostR1)). 4.46/4.68 fof(fact_DomainI, axiom, ![X16, X37, X18, X3, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X18),hAPP(c_Relation_ODomain(X4,X3),X16)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X18),X37)),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DomainI)). 4.46/4.68 fof(fact_RangeI, axiom, ![X16, X37, X18, X3, X4]:(hBOOL(hAPP(hAPP(c_member(X3),X37),hAPP(c_Relation_ORange(X4,X3),X16)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X18),X37)),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_RangeI)). 4.46/4.68 fof(fact_distinct__append, axiom, ![X32, X7, X4]:(((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X7)),hAPP(c_List_Oset(X4),X32))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))&hBOOL(hAPP(c_List_Odistinct(X4),X32)))&hBOOL(hAPP(c_List_Odistinct(X4),X7)))<=>hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Oappend(X4),X7),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__append)). 4.46/4.68 fof(fact_ivl__disj__un_I14_J, axiom, ![X23, X67, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X67),X23))=>hAPP(c_SetInterval_Oord__class_OatLeast(X4),X67)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X67),X23)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I14_J)). 4.46/4.68 fof(fact_ivl__disj__un_I8_J, axiom, ![X23, X67, X4]:(class_Orderings_Olinorder(X4)=>(hAPP(c_SetInterval_Oord__class_OlessThan(X4),X23)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X67)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X67),X23))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X67),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I8_J)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, axiom, ![X19, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X19),X19)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Oone__class_Oone(X4))),X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J)). 4.46/4.68 fof(fact_ivl__disj__un_I12_J, axiom, ![X23, X67, X4]:(class_Orderings_Olinorder(X4)=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X67,X23)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X23))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X67)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X67),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I12_J)). 4.46/4.68 fof(fact_filter_Osimps_I2_J, axiom, ![X7, X4, X6, X28]:((hAPP(c_List_Ofilter(X4,X28),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7))=hAPP(hAPP(c_List_Olist_OCons(X4),X6),hAPP(c_List_Ofilter(X4,X28),X7))<=hBOOL(hAPP(X28,X6)))&(~(hBOOL(hAPP(X28,X6)))=>hAPP(c_List_Ofilter(X4,X28),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7))=hAPP(c_List_Ofilter(X4,X28),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter_Osimps_I2_J)). 4.46/4.68 fof(fact_ivl__disj__un_I11_J, axiom, ![X23, X67, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X67),X23))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X67,X23)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X23))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X67))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I11_J)). 4.46/4.68 fof(fact_ivl__disj__un_I13_J, axiom, ![X23, X67, X4]:((hAPP(c_SetInterval_Oord__class_OatLeast(X4),X67)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X67,X23)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X23))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X67),X23)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I13_J)). 4.46/4.68 fof(fact_ivl__disj__un_I7_J, axiom, ![X23, X67, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X67),X23))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X67)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X67,X23))=hAPP(c_SetInterval_Oord__class_OlessThan(X4),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I7_J)). 4.46/4.68 fof(fact_ivl__disj__un_I10_J, axiom, ![X23, X67, X4]:((hAPP(c_SetInterval_Oord__class_OatMost(X4),X23)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X67)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X67,X23))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X67),X23)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I10_J)). 4.46/4.68 fof(fact_mod__div__equality, axiom, ![X11, X12, X4]:(class_Divides_Osemiring__div(X4)=>X12=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X12),X11)),X11)),c_Divides_Odiv__class_Omod(X4,X12,X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__div__equality)). 4.46/4.68 fof(fact_semiring__div__class_Omod__div__equality_H, axiom, ![X11, X12, X4]:(class_Divides_Osemiring__div(X4)=>X12=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Divides_Odiv__class_Omod(X4,X12,X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X12),X11)),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_semiring__div__class_Omod__div__equality_H)). 4.46/4.68 fof(fact_ivl__disj__un_I9_J, axiom, ![X23, X67, X4]:(class_Orderings_Olinorder(X4)=>(hAPP(c_SetInterval_Oord__class_OatMost(X4),X23)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X67)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X67,X23))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X67),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I9_J)). 4.46/4.68 fof(fact_less__fun__def, axiom, ![X50, X27, X4, X3]:(class_Orderings_Oord(X3)=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X3)),X50),X27)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X3)),X27),X50)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,X3)),X27),X50)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__fun__def)). 4.46/4.68 fof(fact_hd__drop__conv__nth, axiom, ![X17, X4, X57]:((hAPP(c_List_Ohd(X4),hAPP(hAPP(c_List_Odrop(X4),X17),X57))=hAPP(hAPP(c_List_Onth(X4),X57),X17)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57))))<=c_List_Olist_ONil(X4)!=X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__drop__conv__nth)). 4.46/4.68 fof(fact_folding__one__idem_Oinsert__idem, axiom, ![X6, X2, X62, X27, X4]:(c_Finite__Set_Ofolding__one__idem(X4,X27,X62)=>((hAPP(hAPP(X27,X6),hAPP(X62,X2))=hAPP(X62,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Oinsert__idem)). 4.46/4.68 fof(fact_mod__div__equality2, axiom, ![X12, X11, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X12),X11))),c_Divides_Odiv__class_Omod(X4,X12,X11))=X12<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__div__equality2)). 4.46/4.68 fof(fact_min__max_Osup_Oleft__commute, axiom, ![X10, X12, X11, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X11),X10))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X11),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X12),X10))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup_Oleft__commute)). 4.46/4.68 fof(fact_rtrancl__mono, axiom, ![X68, X16, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),X68))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4,X16)),c_Transitive__Closure_Ortrancl(X4,X68)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__mono)). 4.46/4.68 fof(fact_upto_Osimps, axiom, ![X20, X21]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21),X20)))=>c_List_Oupto(X21,X20)=c_List_Olist_ONil(tc_Int_Oint))&(c_List_Oupto(X21,X20)=hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X21),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21),c_Groups_Oone__class_Oone(tc_Int_Oint)),X20))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upto_Osimps)). 4.46/4.68 fof(fact_minus__Max__eq__Min, axiom, ![X46, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X46))=>(hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Big__Operators_Olinorder__class_OMax(X4,X46))=c_Big__Operators_Olinorder__class_OMin(X4,hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),X46))<=X46!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=class_Groups_Olinordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__Max__eq__Min)). 4.46/4.68 fof(fact_insert__Diff__if, axiom, ![X2, X1, X6, X4]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2)),X1)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)<=hBOOL(hAPP(hAPP(c_member(X4),X6),X1)))&(~(hBOOL(hAPP(hAPP(c_member(X4),X6),X1)))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2)),X1)=hAPP(hAPP(c_Set_Oinsert(X4),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__Diff__if)). 4.46/4.68 fof(fact_minus__Min__eq__Max, axiom, ![X46, X4]:(class_Groups_Olinordered__ab__group__add(X4)=>((hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Big__Operators_Olinorder__class_OMin(X4,X46))=c_Big__Operators_Olinorder__class_OMax(X4,hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),X46))<=X46!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X46)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__Min__eq__Max)). 4.46/4.68 fof(fact_add__strict__increasing2, axiom, ![X10, X11, X12, X4]:(class_Groups_Oordered__comm__monoid__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__strict__increasing2)). 4.46/4.68 fof(fact_add__strict__increasing, axiom, ![X10, X11, X12, X4]:(class_Groups_Oordered__comm__monoid__add(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__strict__increasing)). 4.46/4.68 fof(fact_diff__add__assoc, axiom, ![X21, X20, X15]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X15))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20)),X15)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__add__assoc)). 4.46/4.68 fof(fact_diff__diff__right, axiom, ![X21, X20, X15]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15),X20))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X15))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X15)),X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__diff__right)). 4.46/4.68 fof(fact_add__gr__0, axiom, ![X14, X22]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__gr__0)). 4.46/4.68 fof(fact_pos__add__strict, axiom, ![X10, X11, X12, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X10))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__add__strict)). 4.46/4.68 fof(fact_add__increasing, axiom, ![X10, X11, X12, X4]:(class_Groups_Oordered__comm__monoid__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X10))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__increasing)). 4.46/4.68 fof(fact_add__increasing2, axiom, ![X12, X11, X10, X4]:(class_Groups_Oordered__comm__monoid__add(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__increasing2)). 4.46/4.68 fof(fact_fold1__eq__fold__idem, axiom, ![X18, X2, X4]:((hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Groups_Otimes__class_Otimes(X4)),X18),X2)=hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),hAPP(hAPP(c_Set_Oinsert(X4),X18),X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Lattices_Oab__semigroup__idem__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__eq__fold__idem)). 4.46/4.68 fof(fact_UnionI, axiom, ![X2, X52, X173, X4]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X173),X52))=>(hBOOL(hAPP(hAPP(c_member(X4),X2),X173))=>hBOOL(hAPP(hAPP(c_member(X4),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X52))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UnionI)). 4.46/4.68 fof(fact_Times__eq__cancel2, axiom, ![X1, X2, X3, X52, X6, X4]:((X2=X1<=>hAPP(hAPP(c_Product__Type_OSigma(X3,X4),X1),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X3),X52))=hAPP(hAPP(c_Product__Type_OSigma(X3,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X3),X52)))<=hBOOL(hAPP(hAPP(c_member(X4),X6),X52))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Times__eq__cancel2)). 4.46/4.68 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J, axiom, ![X47, X48]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X48,X47)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X47)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X48))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Otransfer__nat__int__function__closures_I2_J)). 4.46/4.68 fof(fact_nat__diff__split__asm, axiom, ![X37, X18, X28]:(hBOOL(hAPP(X28,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18),X37)))<=>~((?[X190]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X37),X190)=X18&~(hBOOL(hAPP(X28,X190))))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),X37))&~(hBOOL(hAPP(X28,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__diff__split__asm)). 4.46/4.68 fof(fact_min__max_Oinf__left__commute, axiom, ![X49, X47, X48, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X47),X49))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X47),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),X49))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__left__commute)). 4.46/4.68 fof(fact_distinct__set__sublists, axiom, ![X7, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X7))=>hBOOL(hAPP(c_List_Odistinct(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool)),c_List_Oset(X4)),c_Enum_Osublists(X4,X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__set__sublists)). 4.46/4.68 fof(fact_setsum__SucD, axiom, ![X14, X2, X27, X4]:(?[X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X27,X42))))<=hAPP(c_Nat_OSuc,X14)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X27),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__SucD)). 4.46/4.68 fof(fact_pos__imp__zdiv__pos__iff, axiom, ![X24, X45]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X45),X24))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24),X45))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__imp__zdiv__pos__iff)). 4.46/4.68 fof(fact_nat__diff__split, axiom, ![X37, X18, X28]:(hBOOL(hAPP(X28,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18),X37)))<=>(![X190]:(X18=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X37),X190)=>hBOOL(hAPP(X28,X190)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),X37))=>hBOOL(hAPP(X28,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__diff__split)). 4.46/4.68 fof(fact_ran__restrictD, axiom, ![X2, X22, X3, X5, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X5),c_Map_Oran(X3,X4,c_Map_Orestrict__map(X3,X4,X22,X2))))=>?[X42]:(hBOOL(hAPP(hAPP(c_member(X3),X42),X2))&hAPP(X22,X42)=hAPP(c_Option_Ooption_OSome(X4),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ran__restrictD)). 4.46/4.68 fof(fact_wfI__pf, axiom, ![X26, X4]:(c_Wellfounded_Owf(X4,X26)<=![X161]:(X161=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X161),hAPP(c_Relation_OImage(X4,X4,X26),X161))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfI__pf)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, axiom, ![X140, X141, X143, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X143),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X141),X140))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X141),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X143),X140))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J)). 4.46/4.68 fof(fact_card__image__le, axiom, ![X27, X3, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X3),hAPP(c_Set_Oimage(X4,X3,X27),X2))),hAPP(c_Finite__Set_Ocard(X4),X2)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__image__le)). 4.46/4.68 fof(fact_in__lists__conv__set, axiom, ![X2, X7, X4]:(![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7)))=>hBOOL(hAPP(hAPP(c_member(X4),X42),X2)))<=>hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X7),c_List_Olists(X4,X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__lists__conv__set)). 4.46/4.68 fof(fact_setsum_OF__eq, axiom, ![X50, X2, X4, X3]:(((~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),X2)=c_Groups_Ozero__class_Ozero(X3))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X50),X2)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,c_Groups_Oplus__class_Oplus(X3)),X50),c_Groups_Ozero__class_Ozero(X3)),X2)))<=class_Groups_Ocomm__monoid__add(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum_OF__eq)). 4.46/4.68 fof(fact_zmod__zminus2__eq__if, axiom, ![X11, X12]:((c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11)),X11)<=c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11))<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zminus2__eq__if)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, axiom, ![X133, X10, X12, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X133))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X133))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J)). 4.46/4.68 fof(fact_DiffI, axiom, ![X1, X2, X39, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X39),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=~(hBOOL(hAPP(hAPP(c_member(X4),X39),X1))))<=hBOOL(hAPP(hAPP(c_member(X4),X39),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DiffI)). 4.46/4.68 fof(fact_map__upds__apply__nontin, axiom, ![X32, X27, X3, X7, X6, X4]:(hAPP(X27,X6)=hAPP(c_Map_Omap__upds(X4,X3,X27,X7,X32),X6)<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upds__apply__nontin)). 4.46/4.68 fof(fact_setprod__constant, axiom, ![X5, X2, X4, X3]:((hAPP(hAPP(c_Power_Opower__class_Opower(X3),X5),hAPP(c_Finite__Set_Ocard(X4),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),hAPP(c_COMBK(X3,X4),X5)),X2)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Groups_Ocomm__monoid__mult(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__constant)). 4.46/4.68 fof(fact_distinct__conv__nth, axiom, ![X7, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X7))<=>![X41]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))=>![X98]:((X41!=X98=>hAPP(hAPP(c_List_Onth(X4),X7),X98)!=hAPP(hAPP(c_List_Onth(X4),X7),X41))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__conv__nth)). 4.46/4.68 fof(fact_listrel1__eq__len, axiom, ![X16, X32, X7, X4]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)),c_List_Olistrel1(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1__eq__len)). 4.46/4.68 fof(fact_sup_Oleft__commute, axiom, ![X10, X12, X11, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X12),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X11),X10))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X11),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X12),X10))<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup_Oleft__commute)). 4.46/4.68 fof(fact_inf__sup__aci_I7_J, axiom, ![X49, X47, X48, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X47),X49))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X47),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X49))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I7_J)). 4.46/4.68 fof(fact_image__mono, axiom, ![X27, X3, X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X3,X27),X2)),hAPP(c_Set_Oimage(X4,X3,X27),X1)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__mono)). 4.46/4.68 fof(fact_pos__divide__less__eq, axiom, ![X18, X37, X39, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X39))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X37),X39)),X18))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__divide__less__eq)). 4.46/4.68 fof(fact_pos__divide__le__eq, axiom, ![X18, X37, X39, X4]:(class_Fields_Olinordered__field(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X39))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X37),X39)),X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__divide__le__eq)). 4.46/4.68 fof(fact_INF__leI, axiom, ![X153, X2, X24, X4, X3]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X3),X2),X153)),hAPP(X153,X24)))<=hBOOL(hAPP(hAPP(c_member(X4),X24),X2)))<=class_Complete__Lattice_Ocomplete__lattice(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__leI)). 4.46/4.68 fof(fact_pos__less__divide__eq, axiom, ![X37, X18, X39, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)),X37))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X37),X39))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X39)))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__less__divide__eq)). 4.46/4.68 fof(fact_pos__le__divide__eq, axiom, ![X37, X18, X39, X4]:(class_Fields_Olinordered__field(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X39))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),X39)),X37))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X37),X39)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__le__divide__eq)). 4.46/4.68 fof(fact_inf__left__commute, axiom, ![X49, X47, X48, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X47),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X49))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X47),X49))<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__left__commute)). 4.46/4.68 fof(fact_elem__le__listsum__nat, axiom, ![X274, X15]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X274)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X274),X15)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X274)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_elem__le__listsum__nat)). 4.46/4.68 fof(fact_le__SUPI, axiom, ![X153, X2, X24, X4, X3]:((hBOOL(hAPP(hAPP(c_member(X4),X24),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(X153,X24)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X3),X2),X153))))<=class_Complete__Lattice_Ocomplete__lattice(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__SUPI)). 4.46/4.68 fof(fact_length__pos__if__in__set, axiom, ![X7, X6, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))<=hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__pos__if__in__set)). 4.46/4.68 fof(fact_INF1__iff, axiom, ![X37, X1, X2, X3, X4]:(![X42]:(hBOOL(hAPP(hAPP(X1,X42),X37))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X2)))<=>hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X2),X1),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF1__iff)). 4.46/4.68 fof(fact_inf__sup__aci_I3_J, axiom, ![X49, X47, X48, X4]:(class_Lattices_Olattice(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X47),X49))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X47),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X49))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I3_J)). 4.46/4.68 fof(fact_power__gt1, axiom, ![X17, X12, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Nat_OSuc,X17)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__gt1)). 4.46/4.68 fof(fact_card__psubset, axiom, ![X2, X1, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X2)),hAPP(c_Finite__Set_Ocard(X4),X1)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X2),X1))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__psubset)). 4.46/4.68 fof(fact_listrelp_OCons, axiom, ![X32, X7, X4, X5, X6, X16]:((c_List_Olistrelp(X4,X16,X7,X32)=>c_List_Olistrelp(X4,X16,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7),hAPP(hAPP(c_List_Olist_OCons(X4),X5),X32)))<=hBOOL(hAPP(hAPP(X16,X6),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrelp_OCons)). 4.46/4.68 fof(fact_inj__mapI, axiom, ![X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>c_Fun_Oinj__on(tc_List_Olist(X4),tc_List_Olist(X3),hAPP(c_List_Omap(X4,X3),X27),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__mapI)). 4.46/4.68 fof(fact_length__remove1, axiom, ![X7, X6, X4]:((~(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7))))=>hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Oremove1(X4,X6,X7)))&(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))=>hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Oremove1(X4,X6,X7))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__remove1)). 4.46/4.68 fof(fact_inf__fun__def, axiom, ![X6, X50, X27, X3, X4]:(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,X4)),X27),X50),X6)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(X27,X6)),hAPP(X50,X6))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__fun__def)). 4.46/4.68 fof(fact_minus__apply, axiom, ![X6, X1, X2, X3, X4]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(X2,X6)),hAPP(X1,X6))=hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,X4)),X2),X1),X6)<=class_Groups_Ominus(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__apply)). 4.46/4.68 fof(fact_sup__fun__def, axiom, ![X6, X50, X27, X3, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(X27,X6)),hAPP(X50,X6))=hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,X4)),X27),X50),X6)<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__fun__def)). 4.46/4.68 fof(fact_le__supI, axiom, ![X11, X48, X12, X4]:(class_Lattices_Osemilattice__sup(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X48))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X12),X11)),X48))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X48))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__supI)). 4.46/4.68 fof(fact_finite__Plus__UNIV__iff, axiom, ![X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X3),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))&hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X4,X3)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X4,X3),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Plus__UNIV__iff)). 4.46/4.68 fof(fact_finite__Prod__UNIV, axiom, ![X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X3)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X4,X3),tc_HOL_Obool))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X3),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Prod__UNIV)). 4.46/4.68 fof(fact_distinct_Osimps_I2_J, axiom, ![X7, X6, X4]:((~(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7))))&hBOOL(hAPP(c_List_Odistinct(X4),X7)))<=>hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct_Osimps_I2_J)). 4.46/4.68 fof(fact_le__inf__iff, axiom, ![X35, X5, X6, X4]:(class_Lattices_Osemilattice__inf(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X5),X35)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X35))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__inf__iff)). 4.46/4.68 fof(fact_abs__mult__pos, axiom, ![X47, X48, X4]:((hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X47),X48))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X47)),X48)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X48)))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__mult__pos)). 4.46/4.68 fof(fact_fun__left__comm_Ofold__graph__fold, axiom, ![X35, X2, X27, X3, X4]:(c_Finite__Set_Ofun__left__comm(X4,X3,X27)=>(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X3,X27,X35,X2),hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),X35),X2)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__graph__fold)). 4.46/4.68 fof(fact_remdups_Osimps_I2_J, axiom, ![X7, X6, X4]:((hAPP(hAPP(c_List_Olist_OCons(X4),X6),c_List_Oremdups(X4,X7))=c_List_Oremdups(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7))<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))))&(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))=>c_List_Oremdups(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7))=c_List_Oremdups(X4,X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups_Osimps_I2_J)). 4.46/4.68 fof(fact_in__set__remove1, axiom, ![X7, X4, X37, X18]:((hBOOL(hAPP(hAPP(c_member(X4),X18),hAPP(c_List_Oset(X4),c_List_Oremove1(X4,X37,X7))))<=>hBOOL(hAPP(hAPP(c_member(X4),X18),hAPP(c_List_Oset(X4),X7))))<=X18!=X37), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__remove1)). 4.46/4.68 fof(fact_less__add__eq__less, axiom, ![X17, X19, X31, X15]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X31)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15),X17)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X17)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__add__eq__less)). 4.46/4.68 fof(fact_semiring__1__class_Oof__nat__code, axiom, ![X14, X4]:(class_Rings_Osemiring__1(X4)=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X14)=c_Nat_Osemiring__1__class_Oof__nat__aux(X4,hAPP(hAPP(c_COMBC(X4,X4,X4),c_Groups_Oplus__class_Oplus(X4)),c_Groups_Oone__class_Oone(X4)),X14,c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_semiring__1__class_Oof__nat__code)). 4.46/4.68 fof(fact_mod__induct__0, axiom, ![X24, X28, X109]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X109))=>hBOOL(hAPP(X28,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))<=hBOOL(hAPP(X28,X24)))<=![X41]:((hBOOL(hAPP(X28,X41))=>hBOOL(hAPP(X28,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X41),X109))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X41),X109)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__induct__0)). 4.46/4.68 fof(fact_drop__Cons__number__of, axiom, ![X57, X48, X4, X63]:((hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)=hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57))<=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>hAPP(hAPP(c_List_Odrop(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X57)=hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__Cons__number__of)). 4.46/4.68 fof(fact_filter__insort__triv, axiom, ![X7, X27, X4, X6, X28, X3]:((~(hBOOL(hAPP(X28,X6)))=>hAPP(c_List_Ofilter(X4,X28),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X3,X27),X6),X7))=hAPP(c_List_Ofilter(X4,X28),X7))<=class_Orderings_Olinorder(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__insort__triv)). 4.46/4.68 fof(fact_nonzero__abs__divide, axiom, ![X12, X11, X4]:((hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),hAPP(c_Groups_Oabs__class_Oabs(X4),X11))=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X11))<=X11!=c_Groups_Ozero__class_Ozero(X4))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonzero__abs__divide)). 4.46/4.68 fof(fact_power__Suc2, axiom, ![X17, X12, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17)),X12)=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Nat_OSuc,X17))<=class_Groups_Omonoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__Suc2)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, axiom, ![X112, X48, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),hAPP(c_Nat_OSuc,X112))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),X112)),X48)<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J)). 4.46/4.68 fof(fact_last__conv__nth, axiom, ![X4, X57]:(c_List_Olist_ONil(X4)!=X57=>c_List_Olast(X4,X57)=hAPP(hAPP(c_List_Onth(X4),X57),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__conv__nth)). 4.46/4.68 fof(fact_Body__triple__valid__Suc, axiom, ![X80, X263, X28, X14, X4]:(c_Hoare__Mirabelle_Otriple__valid(X4,X14,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X28),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X263))),X80))<=>c_Hoare__Mirabelle_Otriple__valid(X4,hAPP(c_Nat_OSuc,X14),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X28),hAPP(c_Com_Ocom_OBODY,X263)),X80))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Body__triple__valid__Suc)). 4.46/4.68 fof(fact_div__less__dividend, axiom, ![X19, X17]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19),X17)),X19)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__less__dividend)). 4.46/4.68 fof(fact_diff__less, axiom, ![X19, X17]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17)),X19))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__less)). 4.46/4.68 fof(fact_int__div__less__self, axiom, ![X15, X48]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X48))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X15))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X48),X15)),X48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__div__less__self)). 4.46/4.68 fof(fact_max__less__iff__conj, axiom, ![X35, X5, X6, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X6),X5)),X35))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),X35))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X5),X35))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__less__iff__conj)). 4.46/4.68 fof(fact_min__max_Ole__sup__iff, axiom, ![X35, X5, X6, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X5),X35))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X35)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X6),X5)),X35)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__sup__iff)). 4.46/4.68 fof(fact_Min__insert, axiom, ![X6, X2, X4]:(class_Orderings_Olinorder(X4)=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X6),c_Big__Operators_Olinorder__class_OMin(X4,X2))=c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__insert)). 4.46/4.68 fof(fact_le__add__diff, axiom, ![X19, X17, X15]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X19)),X15)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__add__diff)). 4.46/4.68 fof(fact_add__less__mono1, axiom, ![X15, X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X15)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__less__mono1)). 4.46/4.68 fof(fact_min__less__iff__conj, axiom, ![X5, X6, X35, X4]:(class_Orderings_Olinorder(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X35),X5))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X35),X6)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X35),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X6),X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__less__iff__conj)). 4.46/4.68 fof(fact_min__max_Ole__inf__iff, axiom, ![X35, X5, X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X5),X35)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X35))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X5))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__inf__iff)). 4.46/4.68 fof(fact_Sup__fin_Oinsert__idem, axiom, ![X6, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X6),c_Big__Operators_Olattice__class_OSup__fin(X4,X2))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oinsert__idem)). 4.46/4.68 fof(fact_nat__add__left__cancel__less, axiom, ![X14, X22, X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X22)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__left__cancel__less)). 4.46/4.68 fof(fact_zadd__strict__right__mono, axiom, ![X15, X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21),X20))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20),X15)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__strict__right__mono)). 4.46/4.68 fof(fact_div__le__mono, axiom, ![X15, X17, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X17))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19),X15)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X17),X15)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__le__mono)). 4.46/4.68 fof(fact_abs__div__pos, axiom, ![X48, X47, X4]:(class_Fields_Olinordered__field__inverse__zero(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X47))=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X48)),X47)=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__div__pos)). 4.46/4.68 fof(fact_less__number__of, axiom, ![X5, X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X6)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X5)))<=(class_Rings_Olinordered__idom(X4)&class_Int_Onumber__ring(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__number__of)). 4.46/4.68 fof(fact_le__number__of, axiom, ![X5, X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X6)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6),X5)))<=(class_Rings_Olinordered__idom(X4)&class_Int_Onumber__ring(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__number__of)). 4.46/4.68 fof(fact_min__max_OInf__fin_Oin__idem, axiom, ![X6, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X2)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X6),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X2))<=hBOOL(hAPP(hAPP(c_member(X4),X6),X2))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Oin__idem)). 4.46/4.68 fof(fact_min__max_OSup__fin_Oin__idem, axiom, ![X6, X2, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X2)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X6),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X2))<=hBOOL(hAPP(hAPP(c_member(X4),X6),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Oin__idem)). 4.46/4.68 fof(fact_Inf__fin_Oinsert__idem, axiom, ![X6, X2, X4]:(class_Lattices_Olattice(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X6),c_Big__Operators_Olattice__class_OInf__fin(X4,X2))=c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oinsert__idem)). 4.46/4.68 fof(fact_mult__le__mono2, axiom, ![X15, X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X20)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__mono2)). 4.46/4.68 fof(fact_add__le__mono1, axiom, ![X15, X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X15)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__le__mono1)). 4.46/4.68 fof(fact_folding__image__simple_Oeq__fold__g, axiom, ![X2, X62, X50, X35, X27, X3, X4]:(c_Finite__Set_Ofolding__image__simple(X4,X3,X27,X35,X50,X62)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))=>hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4,X3,X27),X50),X35),X2)=hAPP(X62,X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Oeq__fold__g)). 4.46/4.68 fof(fact_Max__insert, axiom, ![X6, X2, X4]:(((c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X6),c_Big__Operators_Olinorder__class_OMax(X4,X2))<=X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__insert)). 4.46/4.68 fof(fact_nat__add__left__cancel__le, axiom, ![X14, X22, X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X22)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__left__cancel__le)). 4.46/4.68 fof(fact_diff__le__mono, axiom, ![X31, X17, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X31)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),X31)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__le__mono)). 4.46/4.68 fof(fact_diff__le__mono2, axiom, ![X31, X17, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X17))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31),X17)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31),X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__le__mono2)). 4.46/4.68 fof(fact_zadd__left__mono, axiom, ![X15, X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),X20)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__left__mono)). 4.46/4.68 fof(fact_takeWhile__tail, axiom, ![X67, X7, X4, X6, X28]:(c_List_OtakeWhile(X4,X28,X7)=c_List_OtakeWhile(X4,X28,hAPP(hAPP(c_List_Oappend(X4),X7),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X67)))<=~(hBOOL(hAPP(X28,X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__tail)). 4.46/4.68 fof(fact_setprod__eq__1__iff, axiom, ![X27, X62, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X62))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,tc_Nat_Onat),X27),X62)=c_Groups_Oone__class_Oone(tc_Nat_Onat)<=>![X42]:(hAPP(X27,X42)=c_Groups_Oone__class_Oone(tc_Nat_Onat)<=hBOOL(hAPP(hAPP(c_member(X4),X42),X62))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__eq__1__iff)). 4.46/4.68 fof(fact_setsum__eq__0__iff, axiom, ![X27, X62, X4]:((![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X62))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(X27,X42))<=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X27),X62)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X62))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__eq__0__iff)). 4.46/4.68 fof(fact_Inf__less__iff, axiom, ![X18, X46, X4]:((?[X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X42),X18))&hBOOL(hAPP(hAPP(c_member(X4),X42),X46)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Complete__Lattice_OInf__class_OInf(X4,X46)),X18)))<=(class_Complete__Lattice_Ocomplete__lattice(X4)&class_Orderings_Olinorder(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__less__iff)). 4.46/4.68 fof(fact_less__Sup__iff, axiom, ![X46, X18, X4]:((class_Complete__Lattice_Ocomplete__lattice(X4)&class_Orderings_Olinorder(X4))=>(?[X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X46))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),X42)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),c_Complete__Lattice_OSup__class_OSup(X4,X46))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__Sup__iff)). 4.46/4.68 fof(fact_minus__min__eq__max, axiom, ![X47, X48, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X48)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X47))=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),X47))<=class_Groups_Olinordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__min__eq__max)). 4.46/4.68 fof(fact_minus__max__eq__min, axiom, ![X47, X48, X4]:(class_Groups_Olinordered__ab__group__add(X4)=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X48)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X47))=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X48),X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__max__eq__min)). 4.46/4.68 fof(fact_insort__remove1, axiom, ![X7, X18, X4]:(class_Orderings_Olinorder(X4)=>((c_List_Olinorder__class_Osorted(X4,X7)=>X7=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)),X18),c_List_Oremove1(X4,X18,X7)))<=hBOOL(hAPP(hAPP(c_member(X4),X18),hAPP(c_List_Oset(X4),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__remove1)). 4.46/4.68 fof(fact_minus__add__distrib, axiom, ![X11, X12, X4]:(class_Groups_Oab__group__add(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11))=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__add__distrib)). 4.46/4.68 fof(fact_minus__add, axiom, ![X11, X12, X4]:(class_Groups_Ogroup__add(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12))=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__add)). 4.46/4.68 fof(fact_compl__inf, axiom, ![X47, X48, X4]:(class_Lattices_Oboolean__algebra(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X48)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X47))=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__inf)). 4.46/4.68 fof(fact_compl__sup, axiom, ![X47, X48, X4]:(hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X47))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X48)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X47))<=class_Lattices_Oboolean__algebra(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__sup)). 4.46/4.68 fof(fact_Max__eqI, axiom, ![X6, X2, X4]:((((hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>c_Big__Operators_Olinorder__class_OMax(X4,X2)=X6)<=![X44]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X44),X6))<=hBOOL(hAPP(hAPP(c_member(X4),X44),X2))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__eqI)). 4.46/4.68 fof(fact_SUP1__iff, axiom, ![X37, X1, X2, X3, X4]:(?[X42]:(hBOOL(hAPP(hAPP(X1,X42),X37))&hBOOL(hAPP(hAPP(c_member(X4),X42),X2)))<=>hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X2),X1),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP1__iff)). 4.46/4.68 fof(fact_Min__eqI, axiom, ![X6, X2, X4]:(class_Orderings_Olinorder(X4)=>(((hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>c_Big__Operators_Olinorder__class_OMin(X4,X2)=X6)<=![X44]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X44))<=hBOOL(hAPP(hAPP(c_member(X4),X44),X2))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__eqI)). 4.46/4.68 fof(fact_mod__diff__left__eq, axiom, ![X10, X11, X12, X4]:(class_Divides_Oring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),c_Divides_Odiv__class_Omod(X4,X12,X10)),X11),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X11),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__diff__left__eq)). 4.46/4.68 fof(fact_zmod__zminus1__eq__if, axiom, ![X11, X12]:((c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12),X11)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X11),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11))<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11)=>c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12),X11)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zminus1__eq__if)). 4.46/4.68 fof(fact_InterE, axiom, ![X173, X52, X2, X4]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X173),X52))=>hBOOL(hAPP(hAPP(c_member(X4),X2),X173)))<=hBOOL(hAPP(hAPP(c_member(X4),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X52)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_InterE)). 4.46/4.68 fof(fact_map__add__dom__app__simps_I2_J, axiom, ![X174, X175, X3, X22, X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X22),c_Map_Odom(X4,X3,X175))))=>hAPP(c_Map_Omap__add(X4,X3,X175,X174),X22)=hAPP(X174,X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__dom__app__simps_I2_J)). 4.46/4.68 fof(fact_zmod__simps_I4_J, axiom, ![X11, X10, X12, X4]:(c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Divides_Odiv__class_Omod(X4,X12,X10)),X11),X10)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__simps_I4_J)). 4.46/4.68 fof(fact_mod__add__left__eq, axiom, ![X10, X11, X12, X4]:(c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Divides_Odiv__class_Omod(X4,X12,X10)),X11),X10)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__add__left__eq)). 4.46/4.68 fof(fact_mod__mult__right__eq, axiom, ![X10, X11, X12, X4]:(class_Divides_Osemiring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),c_Divides_Odiv__class_Omod(X4,X11,X10)),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__right__eq)). 4.46/4.68 fof(fact_map__add__dom__app__simps_I3_J, axiom, ![X175, X174, X3, X22, X4]:(hAPP(c_Map_Omap__add(X4,X3,X175,X174),X22)=hAPP(X175,X22)<=~(hBOOL(hAPP(hAPP(c_member(X4),X22),c_Map_Odom(X4,X3,X174))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__dom__app__simps_I3_J)). 4.46/4.68 fof(fact_less__than__iff, axiom, ![X5, X6]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X5)),c_Wellfounded_Oless__than))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__than__iff)). 4.46/4.68 fof(fact_mod__diff__right__eq, axiom, ![X10, X11, X12, X4]:(c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),c_Divides_Odiv__class_Omod(X4,X11,X10)),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X11),X10)<=class_Divides_Oring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__diff__right__eq)). 4.46/4.68 fof(fact_mod__add__right__eq, axiom, ![X10, X11, X12, X4]:(class_Divides_Osemiring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),c_Divides_Odiv__class_Omod(X4,X11,X10)),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__add__right__eq)). 4.46/4.68 fof(fact_psubset__card__mono, axiom, ![X2, X1, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X2),X1))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X2)),hAPP(c_Finite__Set_Ocard(X4),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubset__card__mono)). 4.46/4.68 fof(fact_card__mono, axiom, ![X2, X1, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X2)),hAPP(c_Finite__Set_Ocard(X4),X1))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__mono)). 4.46/4.68 fof(fact_Un__least, axiom, ![X1, X52, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X52))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X52))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)),X52)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__least)). 4.46/4.68 fof(fact_nat__power__less__imp__less, axiom, ![X17, X19, X21]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X17))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X19)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X17))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__power__less__imp__less)). 4.46/4.68 fof(fact_nat__mult__le__cancel1, axiom, ![X14, X22, X45]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X22)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X14))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__le__cancel1)). 4.46/4.68 fof(fact_frac__eq__eq, axiom, ![X36, X6, X35, X5, X4]:((X5!=c_Groups_Ozero__class_Ozero(X4)=>(X35!=c_Groups_Ozero__class_Ozero(X4)=>(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X6),X5)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X36),X35)<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X35)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X36),X5))))<=class_Fields_Ofield(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_frac__eq__eq)). 4.46/4.68 fof(fact_Int__greatest, axiom, ![X1, X2, X52, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X52),X2))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X52),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X52),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__greatest)). 4.46/4.68 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J, axiom, ![X10, X11, X12, X4]:(class_Groups_Oab__semigroup__mult(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11)),X10)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ab__semigroup__mult__class_Omult__ac_I1_J)). 4.46/4.68 fof(fact_times__divide__eq__right, axiom, ![X10, X11, X12, X4]:(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11)),X10)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X10))<=class_Rings_Odivision__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_times__divide__eq__right)). 4.46/4.68 fof(fact_unique__quotient, axiom, ![X177, X178, X111, X112, X11, X12]:((hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,X11),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X178),X177)))=>(X112=X178<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X11))<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,X11),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X112),X111)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_unique__quotient)). 4.46/4.68 fof(fact_unique__remainder, axiom, ![X177, X178, X111, X112, X11, X12]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,X11),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X112),X111)))=>(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,X11),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X178),X177)))=>(X11!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>X177=X111))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_unique__remainder)). 4.46/4.68 fof(fact_inf_Oassoc, axiom, ![X10, X11, X12, X4]:(class_Lattices_Osemilattice__inf(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X12),X11)),X10)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X12),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X11),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf_Oassoc)). 4.46/4.68 fof(fact_div__pos__pos, axiom, ![X11, X12]:((hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11)=hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X12,X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__pos__pos)). 4.46/4.68 fof(fact_div__neg__pos, axiom, ![X11, X12]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X12,X11))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__neg__pos)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, axiom, ![X141, X142, X143, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X143),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X142),X141))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X143),X142)),X141)<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J)). 4.46/4.68 fof(fact_power__commutes, axiom, ![X17, X12, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17)),X12)<=class_Groups_Omonoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__commutes)). 4.46/4.68 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, ![X10, X11, X12, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)),X10)<=class_Groups_Oab__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ab__semigroup__add__class_Oadd__ac_I1_J)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, axiom, ![X10, X11, X12, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J)). 4.46/4.68 fof(fact_setprod__zero, axiom, ![X27, X2, X4, X3]:(class_Rings_Ocomm__semiring__1(X3)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(?[X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))&hAPP(X27,X42)=c_Groups_Ozero__class_Ozero(X3))=>c_Groups_Ozero__class_Ozero(X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__zero)). 4.46/4.68 fof(fact_mult__right__less__imp__less, axiom, ![X11, X10, X12, X4]:(class_Rings_Olinordered__semiring(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__right__less__imp__less)). 4.46/4.68 fof(fact_mult__less__imp__less__right, axiom, ![X11, X10, X12, X4]:(class_Rings_Olinordered__semiring__strict(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__imp__less__right)). 4.46/4.68 fof(fact_mult__left__less__imp__less, axiom, ![X11, X12, X10, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))))<=class_Rings_Olinordered__semiring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__less__imp__less)). 4.46/4.68 fof(fact_sup_Oassoc, axiom, ![X10, X11, X12, X4]:(class_Lattices_Osemilattice__sup(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X12),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X11),X10))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X12),X11)),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup_Oassoc)). 4.46/4.68 fof(fact_inf__sup__aci_I6_J, axiom, ![X49, X47, X48, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X47),X49))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X47)),X49)<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I6_J)). 4.46/4.68 fof(fact_inf__sup__aci_I2_J, axiom, ![X49, X47, X48, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X47),X49))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X47)),X49)<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I2_J)). 4.46/4.68 fof(fact_power__mult, axiom, ![X17, X19, X12, X4]:(class_Groups_Omonoid__mult(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X17))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X19)),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__mult)). 4.46/4.68 fof(fact_mult__less__imp__less__left, axiom, ![X11, X12, X10, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__imp__less__left)). 4.46/4.68 fof(fact_mult__right__le__imp__le, axiom, ![X11, X10, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11))))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__right__le__imp__le)). 4.46/4.68 fof(fact_of__nat__add, axiom, ![X17, X19, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X19)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X17))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17))<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__add)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, axiom, ![X112, X236, X48, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X236),X112))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),X236)),X112)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J)). 4.46/4.68 fof(fact_start__le__sum, axiom, ![X136, X14, X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X136)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_start__le__sum)). 4.46/4.68 fof(fact_mult__left__le__imp__le, axiom, ![X11, X12, X10, X4]:(class_Rings_Olinordered__semiring__strict(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__le__imp__le)). 4.46/4.68 fof(fact_mult__less__cancel__left__neg, axiom, ![X37, X18, X39, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X37),X18))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X39),X18)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X39),X37))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__ring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__cancel__left__neg)). 4.46/4.68 fof(fact_arith__simps_I32_J, axiom, ![X30, X63, X4]:(class_Int_Onumber__ring(X4)=>hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X63),X30))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_arith__simps_I32_J)). 4.46/4.68 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H, axiom, ![X18, X2, X4]:(class_Orderings_Olinorder(X4)=>(c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Set_Oinsert(X4),X18),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omin(X4)),X18),X2)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Oeq__fold__idem_H)). 4.46/4.68 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H, axiom, ![X18, X2, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omax(X4)),X18),X2)=c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Set_Oinsert(X4),X18),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Oeq__fold__idem_H)). 4.46/4.68 fof(fact_mod__mult__self2, axiom, ![X10, X11, X12, X4]:(class_Divides_Osemiring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)),X11)=c_Divides_Odiv__class_Omod(X4,X12,X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__self2)). 4.46/4.68 fof(fact_add__eq__if, axiom, ![X17, X19]:((X19!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X17))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17))&(X19=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17)=X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__eq__if)). 4.46/4.68 fof(fact_add__number__of__eq, axiom, ![X30, X63, X4]:(hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X63),X30))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X30))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__number__of__eq)). 4.46/4.68 fof(fact_finite__Union, axiom, ![X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,tc_HOL_Obool)),X2))=>(![X230]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X230))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X230),X2)))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Union)). 4.46/4.68 fof(fact_even__less__0__iff, axiom, ![X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X18),X18)),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_even__less__0__iff)). 4.46/4.68 fof(fact_double__add__less__zero__iff__single__add__less__zero, axiom, ![X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X18),X18)),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),c_Groups_Ozero__class_Ozero(X4))))<=class_Groups_Olinordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__add__less__zero__iff__single__add__less__zero)). 4.46/4.68 fof(fact_mod__mult__self1, axiom, ![X11, X10, X12, X4]:(class_Divides_Osemiring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)),X11)=c_Divides_Odiv__class_Omod(X4,X12,X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__self1)). 4.46/4.68 fof(fact_list__all2__dropI, axiom, ![X14, X260, X172, X28, X3, X4]:(c_List_Olist__all2(X4,X3,X28,hAPP(hAPP(c_List_Odrop(X4),X14),X172),hAPP(hAPP(c_List_Odrop(X3),X14),X260))<=c_List_Olist__all2(X4,X3,X28,X172,X260)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__dropI)). 4.46/4.68 fof(fact_list__all2__takeI, axiom, ![X14, X32, X7, X28, X3, X4]:(c_List_Olist__all2(X4,X3,X28,X7,X32)=>c_List_Olist__all2(X4,X3,X28,hAPP(hAPP(c_List_Otake(X4),X14),X7),hAPP(hAPP(c_List_Otake(X3),X14),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__takeI)). 4.46/4.68 fof(fact_double__add__le__zero__iff__single__add__le__zero, axiom, ![X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X18),X18)),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),c_Groups_Ozero__class_Ozero(X4))))<=class_Groups_Olinordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__add__le__zero__iff__single__add__le__zero)). 4.46/4.68 fof(fact_zero__less__power, axiom, ![X17, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12)))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__power)). 4.46/4.68 fof(fact_zero__less__double__add__iff__zero__less__single__add, axiom, ![X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X18))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X18),X18))))<=class_Groups_Olinordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__double__add__iff__zero__less__single__add)). 4.46/4.68 fof(fact_one__le__power, axiom, ![X17, X12, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Oone__class_Oone(X4)),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Oone__class_Oone(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__le__power)). 4.46/4.68 fof(fact_number__of__diff, axiom, ![X30, X63, X4]:(class_Int_Onumber__ring(X4)=>hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X63),X30))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X63)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__diff)). 4.46/4.68 fof(fact_zero__le__power, axiom, ![X17, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17))))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__power)). 4.46/4.68 fof(fact_zero__le__double__add__iff__zero__le__single__add, axiom, ![X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X18),X18)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X18)))<=class_Groups_Olinordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__double__add__iff__zero__le__single__add)). 4.46/4.68 fof(fact_atLeastAtMostSuc__conv, axiom, ![X14, X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),hAPP(c_Nat_OSuc,X14)))=>hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X22,X14))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X22,hAPP(c_Nat_OSuc,X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastAtMostSuc__conv)). 4.46/4.68 fof(fact_card__insert__le, axiom, ![X6, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X2)),hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__insert__le)). 4.46/4.68 fof(fact_takeWhile__nth, axiom, ![X7, X28, X4, X25]:(hAPP(hAPP(c_List_Onth(X4),c_List_OtakeWhile(X4,X28,X7)),X25)=hAPP(hAPP(c_List_Onth(X4),X7),X25)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X28,X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__nth)). 4.46/4.68 fof(fact_of__nat__mult, axiom, ![X17, X19, X4]:(class_Rings_Osemiring__1(X4)=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X17))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X19)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__mult)). 4.46/4.68 fof(fact_Inf__le__Sup, axiom, ![X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Big__Operators_Olattice__class_OInf__fin(X4,X2)),c_Big__Operators_Olattice__class_OSup__fin(X4,X2)))))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__le__Sup)). 4.46/4.68 fof(fact_card__insert__disjoint, axiom, ![X6, X2, X4]:((hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X4),X2))=hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__insert__disjoint)). 4.46/4.68 fof(fact_inj__on__diff__nat, axiom, ![X45, X122]:(![X42]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X42),X122))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X42)))=>c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X45),X122)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__diff__nat)). 4.46/4.68 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J, axiom, ![X47, X48]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X48,X47)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X47)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X48))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J)). 4.46/4.68 fof(fact_fun__upds__append__drop, axiom, ![X88, X22, X32, X3, X7, X4]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32)=>c_Map_Omap__upds(X4,X3,X22,hAPP(hAPP(c_List_Oappend(X4),X7),X88),X32)=c_Map_Omap__upds(X4,X3,X22,X7,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upds__append__drop)). 4.46/4.68 fof(fact_minus1__divide, axiom, ![X48, X4]:(hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),c_Groups_Oone__class_Oone(X4)),X48))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin)),X48)<=(class_Fields_Ofield__inverse__zero(X4)&class_Int_Onumber__ring(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus1__divide)). 4.46/4.68 fof(fact_fun__left__comm_Ofun__left__comm, axiom, ![X35, X5, X6, X27, X3, X4]:(hAPP(hAPP(X27,X5),hAPP(hAPP(X27,X6),X35))=hAPP(hAPP(X27,X6),hAPP(hAPP(X27,X5),X35))<=c_Finite__Set_Ofun__left__comm(X4,X3,X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofun__left__comm)). 4.46/4.68 fof(fact_abs__power__minus, axiom, ![X17, X12, X4]:(class_Rings_Olinordered__idom(X4)=>hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)),X17))=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__power__minus)). 4.46/4.68 fof(fact_fun__upds__append2__drop, axiom, ![X88, X22, X32, X3, X7, X4]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)=>c_Map_Omap__upds(X4,X3,X22,X7,hAPP(hAPP(c_List_Oappend(X3),X32),X88))=c_Map_Omap__upds(X4,X3,X22,X7,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upds__append2__drop)). 4.46/4.68 fof(fact_sort__key__simps_I2_J, axiom, ![X7, X6, X27, X4, X3]:(c_List_Olinorder__class_Osort__key(X4,X3,X27,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X3,X27),X6),c_List_Olinorder__class_Osort__key(X4,X3,X27,X7))<=class_Orderings_Olinorder(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sort__key__simps_I2_J)). 4.46/4.68 fof(fact_abs__less__iff, axiom, ![X37, X18, X4]:(class_Rings_Olinordered__idom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X18)),X37))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)),X37))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),X37))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__less__iff)). 4.46/4.68 fof(fact_abs__mult, axiom, ![X11, X12, X4]:(class_Rings_Olinordered__idom(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),hAPP(c_Groups_Oabs__class_Oabs(X4),X11))=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__mult)). 4.46/4.68 fof(fact_Int__insert__left, axiom, ![X1, X52, X18, X4]:((hAPP(hAPP(c_Set_Oinsert(X4),X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X1),X52))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X18),X1)),X52)<=hBOOL(hAPP(hAPP(c_member(X4),X18),X52)))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X1),X52)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X18),X1)),X52)<=~(hBOOL(hAPP(hAPP(c_member(X4),X18),X52))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__insert__left)). 4.46/4.68 fof(fact_Diff__insert__absorb, axiom, ![X2, X6, X4]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2)),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=X2<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__insert__absorb)). 4.46/4.68 fof(fact_listsum__append, axiom, ![X72, X57, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_List_Omonoid__add__class_Olistsum(X4),X57)),hAPP(c_List_Omonoid__add__class_Olistsum(X4),X72))=hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Oappend(X4),X57),X72))<=class_Groups_Omonoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__append)). 4.46/4.68 fof(fact_abs__le__iff, axiom, ![X37, X18, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)),X37))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),X37)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X18)),X37)))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__le__iff)). 4.46/4.68 fof(fact_sublist__singleton, axiom, ![X6, X4, X2]:((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))=>hAPP(hAPP(c_List_Olist_OCons(X4),X6),c_List_Olist_ONil(X4))=c_List_Osublist(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X6),c_List_Olist_ONil(X4)),X2))&(~(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))=>c_List_Osublist(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X6),c_List_Olist_ONil(X4)),X2)=c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__singleton)). 4.46/4.68 fof(fact_abs__divide, axiom, ![X11, X12, X4]:(class_Fields_Olinordered__field__inverse__zero(X4)=>hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X11))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),hAPP(c_Groups_Oabs__class_Oabs(X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__divide)). 4.46/4.68 fof(fact_of__int__mult, axiom, ![X49, X30, X4]:(hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X49))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X30)),hAPP(c_Int_Oring__1__class_Oof__int(X4),X49))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__mult)). 4.46/4.68 fof(fact_min__max_Ofold1__belowI, axiom, ![X18, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hBOOL(hAPP(hAPP(c_member(X4),X18),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omin(X4)),X2)),X18))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofold1__belowI)). 4.46/4.68 fof(fact_fold1__belowI, axiom, ![X18, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hBOOL(hAPP(hAPP(c_member(X4),X18),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Finite__Set_Ofold1(X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),X2)),X18))))<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__belowI)). 4.46/4.68 fof(fact_of__int__add, axiom, ![X49, X30, X4]:(hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X30),X49))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X30)),hAPP(c_Int_Oring__1__class_Oof__int(X4),X49))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__add)). 4.46/4.68 fof(fact_of__int__diff, axiom, ![X49, X30, X4]:(hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X30),X49))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X30)),hAPP(c_Int_Oring__1__class_Oof__int(X4),X49))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__diff)). 4.46/4.68 fof(fact_Id__onE, axiom, ![X2, X39, X4]:(~(![X42]:(X39!=hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X42)<=hBOOL(hAPP(hAPP(c_member(X4),X42),X2))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X39),c_Relation_OId__on(X4,X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__onE)). 4.46/4.68 fof(fact_power__less__imp__less__base, axiom, ![X11, X17, X12, X4]:(class_Rings_Olinordered__semidom(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__less__imp__less__base)). 4.46/4.68 fof(fact_finite__map__freshness, axiom, ![X27, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Map_Odom(X4,X3,X27)))=>(?[X42]:c_Option_Ooption_ONone(X3)=hAPP(X27,X42)<=~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__map__freshness)). 4.46/4.68 fof(fact_InterI, axiom, ![X2, X52, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X52)))<=![X207]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X207),X52))=>hBOOL(hAPP(hAPP(c_member(X4),X2),X207)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_InterI)). 4.46/4.68 fof(fact_finite__cartesian__productD1, axiom, ![X1, X2, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),X1))))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))<=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))!=X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__cartesian__productD1)). 4.46/4.68 fof(fact_finite__cartesian__productD2, axiom, ![X1, X2, X3, X4]:((X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__cartesian__productD2)). 4.46/4.68 fof(fact_lists__accI, axiom, ![X16, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X7),c_List_Olists(X4,c_Wellfounded_Oacc(X4,X16))))<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X7),c_Wellfounded_Oacc(tc_List_Olist(X4),c_List_Olistrel1(X4,X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__accI)). 4.46/4.68 fof(fact_folding_Oeq__fold, axiom, ![X68, X2, X62, X27, X3, X4]:(c_Finite__Set_Ofolding(X4,X3,X27,X62)=>(hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),X68),X2)=hAPP(hAPP(X62,X2),X68)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Oeq__fold)). 4.46/4.68 fof(fact_INTER__UNIV__conv_I2_J, axiom, ![X1, X2, X4, X3]:(![X42]:(hBOOL(hAPP(hAPP(c_member(X3),X42),X2))=>c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(X1,X42))<=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INTER__UNIV__conv_I2_J)). 4.46/4.68 fof(fact_transfer__int__nat__set__relations_I5_J, axiom, ![X1, X2]:((c_Nat__Transfer_Onat__set(X1)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X2),X1))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)))))<=c_Nat__Transfer_Onat__set(X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__set__relations_I5_J)). 4.46/4.68 fof(fact_less__trans__Suc, axiom, ![X15, X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21)),X15))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X15)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__trans__Suc)). 4.46/4.68 fof(fact_INTER__UNIV__conv_I1_J, axiom, ![X1, X2, X3, X4]:(![X42]:(hBOOL(hAPP(hAPP(c_member(X3),X42),X2))=>c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(X1,X42))<=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INTER__UNIV__conv_I1_J)). 4.46/4.68 fof(fact_o__eq__elim, axiom, ![X87, X39, X59, X37, X18, X4, X3, X29]:(hAPP(c_Fun_Ocomp(X59,X3,X4,X39),X87)=hAPP(c_Fun_Ocomp(X29,X3,X4,X18),X37)=>![X160]:hAPP(X39,hAPP(X87,X160))=hAPP(X18,hAPP(X37,X160))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_o__eq__elim)). 4.46/4.68 fof(fact_f__the__inv__into__f, axiom, ![X5, X2, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,X2)=>(hBOOL(hAPP(hAPP(c_member(X3),X5),hAPP(c_Set_Oimage(X4,X3,X27),X2)))=>X5=hAPP(X27,hAPP(c_Fun_Othe__inv__into(X4,X3,X2,X27),X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_f__the__inv__into__f)). 4.46/4.68 fof(fact_zdiv__eq__0__iff, axiom, ![X45, X24]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),X45))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),X24))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X45)<=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24),X45)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__eq__0__iff)). 4.46/4.68 fof(fact_sorted__insort__insert__key, axiom, ![X6, X7, X27, X3, X4]:((c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X27),X7))=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X27),c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X27,X6,X7))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__insort__insert__key)). 4.46/4.68 fof(fact_image__iff, axiom, ![X2, X27, X3, X35, X4]:(?[X42]:(hBOOL(hAPP(hAPP(c_member(X3),X42),X2))&X35=hAPP(X27,X42))<=>hBOOL(hAPP(hAPP(c_member(X4),X35),hAPP(c_Set_Oimage(X3,X4,X27),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__iff)). 4.46/4.68 fof(fact_Int__iff, axiom, ![X1, X2, X39, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X39),X2))&hBOOL(hAPP(hAPP(c_member(X4),X39),X1)))<=>hBOOL(hAPP(hAPP(c_member(X4),X39),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__iff)). 4.46/4.68 fof(fact_Sup__le__iff, axiom, ![X37, X2, X4]:((![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X42),X37))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X2)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Complete__Lattice_OSup__class_OSup(X4,X2)),X37)))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__le__iff)). 4.46/4.68 fof(fact_le__Inf__iff, axiom, ![X2, X37, X4]:((![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),X42)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),c_Complete__Lattice_OInf__class_OInf(X4,X2))))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__Inf__iff)). 4.46/4.68 fof(fact_folding__one__idem_Oin__idem, axiom, ![X6, X2, X62, X27, X4]:(c_Finite__Set_Ofolding__one__idem(X4,X27,X62)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hAPP(hAPP(X27,X6),hAPP(X62,X2))=hAPP(X62,X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Oin__idem)). 4.46/4.68 fof(fact_double__diff, axiom, ![X52, X1, X2, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X52))=>X2=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X52),X2)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__diff)). 4.46/4.68 fof(fact_INT__lower, axiom, ![X1, X3, X2, X18, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X2),X1)),hAPP(X1,X18)))<=hBOOL(hAPP(hAPP(c_member(X4),X18),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__lower)). 4.46/4.68 fof(fact_SigmaD2, axiom, ![X1, X2, X37, X18, X3, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X18),X37)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),X1)))=>hBOOL(hAPP(hAPP(c_member(X3),X37),hAPP(X1,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SigmaD2)). 4.46/4.68 fof(fact_distinct__map, axiom, ![X7, X27, X3, X4]:((c_Fun_Oinj__on(X3,X4,X27,hAPP(c_List_Oset(X3),X7))&hBOOL(hAPP(c_List_Odistinct(X3),X7)))<=>hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(X3,X4),X27),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__map)). 4.46/4.68 fof(fact_setprod__zero__iff, axiom, ![X27, X2, X4, X3]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(?[X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X2))&hAPP(X27,X42)=c_Groups_Ozero__class_Ozero(X3))<=>c_Groups_Ozero__class_Ozero(X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X3),X27),X2)))<=(class_Rings_Ono__zero__divisors(X3)&class_Rings_Ocomm__semiring__1(X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__zero__iff)). 4.46/4.68 fof(fact_UN__upper, axiom, ![X1, X3, X2, X18, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X18),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(X1,X18)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__upper)). 4.46/4.68 fof(fact_wf__not__sym, axiom, ![X6, X18, X16, X4]:((~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X18)),X16)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X6)),X16)))<=c_Wellfounded_Owf(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__not__sym)). 4.46/4.68 fof(fact_refl__onD1, axiom, ![X5, X6, X16, X2, X4]:(c_Relation_Orefl__on(X4,X2,X16)=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),X16))=>hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__onD1)). 4.46/4.68 fof(fact_refl__onD2, axiom, ![X5, X6, X16, X2, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),X16))=>hBOOL(hAPP(hAPP(c_member(X4),X5),X2)))<=c_Relation_Orefl__on(X4,X2,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__onD2)). 4.46/4.68 fof(fact_le__imp__0__less, axiom, ![X49]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X49)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X49))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__imp__0__less)). 4.46/4.68 fof(fact_transpose__empty, axiom, ![X7, X4]:(c_List_Olist_ONil(tc_List_Olist(X4))=c_List_Otranspose(X4,X7)<=>![X42]:(c_List_Olist_ONil(X4)=X42<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X42),hAPP(c_List_Oset(tc_List_Olist(X4)),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__empty)). 4.46/4.68 fof(fact_Nitpick_Orefl_H__def, axiom, ![X16, X4]:(c_Nitpick_Orefl_H(X4,X16)<=>![X42]:hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X42),X42)),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Orefl_H__def)). 4.46/4.68 fof(fact_min__max_Osup_Oassoc, axiom, ![X10, X11, X12, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X11),X10))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X12),X11)),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup_Oassoc)). 4.46/4.68 fof(fact_min__max_Oinf__assoc, axiom, ![X49, X47, X48, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X47),X49))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),X47)),X49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__assoc)). 4.46/4.68 fof(fact_finite__Diff__insert, axiom, ![X1, X18, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Diff__insert)). 4.46/4.68 fof(fact_nonneg1__imp__zdiv__pos__iff, axiom, ![X37, X18]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X18),X37)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X37),X18))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonneg1__imp__zdiv__pos__iff)). 4.46/4.68 fof(fact_List_Oinsert__def, axiom, ![X7, X6, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))=>X7=c_List_Oinsert(X4,X6,X7))&(~(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7))))=>c_List_Oinsert(X4,X6,X7)=hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Oinsert__def)). 4.46/4.68 fof(fact_image__constant, axiom, ![X39, X3, X2, X6, X4]:(hAPP(c_Set_Oimage(X4,X3,hAPP(c_COMBK(X3,X4),X39)),X2)=hAPP(hAPP(c_Set_Oinsert(X3),X39),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))<=hBOOL(hAPP(hAPP(c_member(X4),X6),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__constant)). 4.46/4.68 fof(fact_less__iff__diff__less__0, axiom, ![X37, X18, X4]:(class_Groups_Oordered__ab__group__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X18),X37)),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),X37)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__iff__diff__less__0)). 4.46/4.68 fof(fact_UNION__empty__conv_I2_J, axiom, ![X1, X2, X4, X3]:(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=>![X42]:(hAPP(X1,X42)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=hBOOL(hAPP(hAPP(c_member(X3),X42),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNION__empty__conv_I2_J)). 4.46/4.68 fof(fact_minus__less__iff, axiom, ![X37, X18, X4]:(class_Groups_Oordered__ab__group__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)),X37))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X37)),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__less__iff)). 4.46/4.68 fof(fact_minus__le__iff, axiom, ![X37, X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)),X37))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X37)),X18)))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__le__iff)). 4.46/4.68 fof(fact_UNION__empty__conv_I1_J, axiom, ![X1, X2, X3, X4]:(![X42]:(hAPP(X1,X42)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=hBOOL(hAPP(hAPP(c_member(X3),X42),X2)))<=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNION__empty__conv_I1_J)). 4.46/4.68 fof(fact_le__iff__diff__le__0, axiom, ![X37, X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),X37))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X18),X37)),c_Groups_Ozero__class_Ozero(X4))))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__iff__diff__le__0)). 4.46/4.68 fof(fact_neg__less__iff__less, axiom, ![X18, X37, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X37)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),X37)))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__less__iff__less)). 4.46/4.68 fof(fact_compl__le__compl__iff, axiom, ![X5, X6, X4]:(class_Lattices_Oboolean__algebra(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X6)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X5),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__le__compl__iff)). 4.46/4.68 fof(fact_field__le__mult__one__interval, axiom, ![X47, X48, X4]:(class_Fields_Olinordered__field__inverse__zero(X4)=>(![X132]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X132),X48)),X47))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X132),c_Groups_Oone__class_Oone(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X132)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_field__le__mult__one__interval)). 4.46/4.68 fof(fact_less__minus__iff, axiom, ![X37, X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X37)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X37),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18))))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__minus__iff)). 4.46/4.68 fof(fact_le__minus__iff, axiom, ![X37, X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X37))))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__minus__iff)). 4.46/4.68 fof(fact_field__le__epsilon, axiom, ![X47, X48, X4]:(class_Fields_Olinordered__field(X4)=>(![X316]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X47),X316)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X316)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_field__le__epsilon)). 4.46/4.68 fof(fact_le__imp__neg__le, axiom, ![X11, X12, X4]:(class_Groups_Oordered__ab__group__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__imp__neg__le)). 4.46/4.68 fof(fact_Ints__power, axiom, ![X14, X18, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X18),c_Int_Oring__1__class_OInts(X4)))=>hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X18),X14)),c_Int_Oring__1__class_OInts(X4))))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__power)). 4.46/4.68 fof(fact_listsp__infI, axiom, ![X1, X67, X2, X4]:((hBOOL(hAPP(c_List_Olistsp(X4,X1),X67))=>hBOOL(hAPP(c_List_Olistsp(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)),X67)))<=hBOOL(hAPP(c_List_Olistsp(X4,X2),X67))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp__infI)). 4.46/4.68 fof(fact_map__add__Some__iff, axiom, ![X6, X45, X14, X22, X4, X3]:(hAPP(c_Option_Ooption_OSome(X4),X6)=hAPP(c_Map_Omap__add(X3,X4,X22,X14),X45)<=>(hAPP(X14,X45)=hAPP(c_Option_Ooption_OSome(X4),X6)|(hAPP(X14,X45)=c_Option_Ooption_ONone(X4)&hAPP(c_Option_Ooption_OSome(X4),X6)=hAPP(X22,X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__Some__iff)). 4.46/4.68 fof(fact_length__insort, axiom, ![X7, X6, X27, X4, X3]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X3,X27),X6),X7))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))<=class_Orderings_Olinorder(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__insort)). 4.46/4.68 fof(fact_Int__insert__right, axiom, ![X1, X2, X18, X4]:((hAPP(hAPP(c_Set_Oinsert(X4),X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),X1))<=hBOOL(hAPP(hAPP(c_member(X4),X18),X2)))&(~(hBOOL(hAPP(hAPP(c_member(X4),X18),X2)))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__insert__right)). 4.46/4.68 fof(fact_the__inv__into__onto, axiom, ![X2, X27, X3, X4]:(hAPP(c_Set_Oimage(X3,X4,c_Fun_Othe__inv__into(X4,X3,X2,X27)),hAPP(c_Set_Oimage(X4,X3,X27),X2))=X2<=c_Fun_Oinj__on(X4,X3,X27,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__inv__into__onto)). 4.46/4.68 fof(fact_min__less__iff__disj, axiom, ![X35, X5, X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X6),X5)),X35))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X5),X35))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),X35))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__less__iff__disj)). 4.46/4.68 fof(fact_min__le__iff__disj, axiom, ![X35, X5, X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X6),X5)),X35))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X35))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X5),X35))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__le__iff__disj)). 4.46/4.68 fof(fact_less__max__iff__disj, axiom, ![X5, X6, X35, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X35),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X6),X5)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X35),X5))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X35),X6))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__max__iff__disj)). 4.46/4.68 fof(fact_le__fun__def, axiom, ![X50, X27, X4, X3]:((![X42]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(X27,X42)),hAPP(X50,X42)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X3)),X27),X50)))<=class_Orderings_Oord(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__fun__def)). 4.46/4.68 fof(fact_le__max__iff__disj, axiom, ![X5, X6, X35, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X35),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X6),X5)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X35),X6))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X35),X5))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__max__iff__disj)). 4.46/4.68 fof(fact_image__uminus__greaterThanAtMost, axiom, ![X5, X6, X4]:(class_Groups_Oordered__ab__group__add(X4)=>hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X6,X5))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,hAPP(c_Groups_Ouminus__class_Ouminus(X4),X5)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__greaterThanAtMost)). 4.46/4.68 fof(fact_pred__comp_Oequations, axiom, ![X250, X123, X68, X16, X29, X3, X4]:(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X4,X3,X29,X16,X68),X123),X250))<=>?[X119]:(hBOOL(hAPP(hAPP(X16,X123),X119))&hBOOL(hAPP(hAPP(X68,X119),X250)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__comp_Oequations)). 4.46/4.68 fof(fact_lexn__length, axiom, ![X14, X16, X32, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),X32)),hAPP(c_List_Olexn(X4,X16),X14)))=>(X14=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexn__length)). 4.46/4.68 fof(fact_mono__Field, axiom, ![X68, X16, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OField(X4),X16)),hAPP(c_Relation_OField(X4),X68)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),X68))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mono__Field)). 4.46/4.68 fof(fact_sorted__filter, axiom, ![X28, X7, X27, X3, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X27),hAPP(c_List_Ofilter(X3,X28),X7)))<=c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X27),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__filter)). 4.46/4.68 fof(fact_mod__pos__pos, axiom, ![X11, X12]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))=>(hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X12,X11))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__pos__pos)). 4.46/4.68 fof(fact_lessThan__strict__subset__iff, axiom, ![X14, X22, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X22)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X22),X14)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessThan__strict__subset__iff)). 4.46/4.68 fof(fact_greaterThan__subset__iff, axiom, ![X5, X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X6)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X5),X6)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThan__subset__iff)). 4.46/4.68 fof(fact_lessThan__subset__iff, axiom, ![X5, X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X6)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X5)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessThan__subset__iff)). 4.46/4.68 fof(fact_listsum__0, axiom, ![X7, X3, X4]:(class_Groups_Omonoid__add(X4)=>hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X3,X4),hAPP(c_COMBK(X4,X3),c_Groups_Ozero__class_Ozero(X4))),X7))=c_Groups_Ozero__class_Ozero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__0)). 4.46/4.68 fof(fact_mod__neg__pos, axiom, ![X11, X12]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X12,X11))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__neg__pos)). 4.46/4.68 fof(fact_atMost__subset__iff, axiom, ![X5, X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X6)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X5)))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atMost__subset__iff)). 4.46/4.68 fof(fact_atLeast__subset__iff, axiom, ![X5, X6, X4]:(class_Orderings_Oorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X5),X6))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X6)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast__subset__iff)). 4.46/4.68 fof(fact_listsp__mono, axiom, ![X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),c_List_Olistsp(X4,X2)),c_List_Olistsp(X4,X1)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp__mono)). 4.46/4.68 fof(fact_rel__pow__imp__rtrancl, axiom, ![X26, X14, X109, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X109),c_Transitive__Closure_Ortrancl(X4,X26)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X109),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X14),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__imp__rtrancl)). 4.46/4.68 fof(fact_lists__mono, axiom, ![X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),c_List_Olists(X4,X2)),c_List_Olists(X4,X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__mono)). 4.46/4.68 fof(fact_transfer__nat__int__set__relations_I5_J, axiom, ![X1, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X2),X1))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__relations_I5_J)). 4.46/4.68 fof(fact_divmod__int__rel__0, axiom, ![X11]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X11=>hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__0)). 4.46/4.68 fof(fact_Diff__subset__conv, axiom, ![X52, X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X1),X52)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)),X52))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__subset__conv)). 4.46/4.68 fof(fact_list__all__length, axiom, ![X7, X28, X4]:(c_List_Olist__all(X4,X28,X7)<=>![X199]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X199),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))=>hBOOL(hAPP(X28,hAPP(hAPP(c_List_Onth(X4),X7),X199))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__length)). 4.46/4.68 fof(fact_in__listsp__conv__set, axiom, ![X7, X2, X4]:(hBOOL(hAPP(c_List_Olistsp(X4,X2),X7))<=>![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7)))=>hBOOL(hAPP(X2,X42)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__listsp__conv__set)). 4.46/4.68 fof(fact_UnE, axiom, ![X1, X2, X39, X4]:((~(hBOOL(hAPP(hAPP(c_member(X4),X39),X2)))=>hBOOL(hAPP(hAPP(c_member(X4),X39),X1)))<=hBOOL(hAPP(hAPP(c_member(X4),X39),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UnE)). 4.46/4.68 fof(fact_filter__empty__conv, axiom, ![X7, X28, X4]:(![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7)))=>~(hBOOL(hAPP(X28,X42))))<=>hAPP(c_List_Ofilter(X4,X28),X7)=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__empty__conv)). 4.46/4.68 fof(fact_zero__less__mult__pos2, axiom, ![X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11))))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__mult__pos2)). 4.46/4.68 fof(fact_zero__less__mult__pos, axiom, ![X11, X12, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11))))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__mult__pos)). 4.46/4.68 fof(fact_set__insort, axiom, ![X7, X6, X27, X4, X3]:(class_Orderings_Olinorder(X3)=>hAPP(hAPP(c_Set_Oinsert(X4),X6),hAPP(c_List_Oset(X4),X7))=hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X3,X27),X6),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__insort)). 4.46/4.68 fof(fact_acc__subset, axiom, ![X231, X232, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X232),X231))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_Wellfounded_Oacc(X4,X231)),c_Wellfounded_Oacc(X4,X232)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acc__subset)). 4.46/4.68 fof(fact_nth__list__update__eq, axiom, ![X48, X57, X4, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))=>hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Olist__update(X4,X57),X21),X48)),X21)=X48), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__list__update__eq)). 4.46/4.68 fof(fact_enum__all__option__def, axiom, ![X28, X4]:(class_Enum_Oenum(X4)=>((hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X4),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X4),tc_HOL_Obool,X4),X28),c_Option_Ooption_OSome(X4))))&hBOOL(hAPP(X28,c_Option_Ooption_ONone(X4))))<=>hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X4)),X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__all__option__def)). 4.46/4.68 fof(fact_Suc__mult__le__cancel1, axiom, ![X14, X22, X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X45)),X22)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X45)),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__mult__le__cancel1)). 4.46/4.68 fof(fact_zero__less__two, axiom, ![X4]:(class_Rings_Olinordered__semidom(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Oone__class_Oone(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__two)). 4.46/4.68 fof(fact_comp__inj__on__iff, axiom, ![X282, X29, X2, X27, X3, X4]:((c_Fun_Oinj__on(X4,X29,hAPP(c_Fun_Ocomp(X3,X29,X4,X282),X27),X2)<=>c_Fun_Oinj__on(X3,X29,X282,hAPP(c_Set_Oimage(X4,X3,X27),X2)))<=c_Fun_Oinj__on(X4,X3,X27,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comp__inj__on__iff)). 4.46/4.68 fof(fact_psubset__trans, axiom, ![X52, X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X2),X1))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X1),X52))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X2),X52)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubset__trans)). 4.46/4.68 fof(fact_subset__psubset__trans, axiom, ![X52, X1, X2, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X1),X52))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X2),X52)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__psubset__trans)). 4.46/4.68 fof(fact_psubset__subset__trans, axiom, ![X52, X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X2),X1))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X52))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X2),X52)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubset__subset__trans)). 4.46/4.68 fof(fact_subset__trans, axiom, ![X52, X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X52))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X52)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__trans)). 4.46/4.68 fof(fact_sorted__nth__monoI, axiom, ![X57, X4]:((c_List_Olinorder__class_Osorted(X4,X57)<=![X41, X98]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X41),X98))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_List_Onth(X4),X57),X41)),hAPP(hAPP(c_List_Onth(X4),X57),X98))))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__nth__monoI)). 4.46/4.68 fof(fact_insert__ident, axiom, ![X1, X2, X6, X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))=>(~(hBOOL(hAPP(hAPP(c_member(X4),X6),X1)))=>(X2=X1<=>hAPP(hAPP(c_Set_Oinsert(X4),X6),X2)=hAPP(hAPP(c_Set_Oinsert(X4),X6),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__ident)). 4.46/4.68 fof(fact_insert__image, axiom, ![X27, X3, X2, X6, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hAPP(hAPP(c_Set_Oinsert(X3),hAPP(X27,X6)),hAPP(c_Set_Oimage(X4,X3,X27),X2))=hAPP(c_Set_Oimage(X4,X3,X27),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__image)). 4.46/4.68 fof(fact_congruentD, axiom, ![X35, X5, X27, X16, X3, X4]:(c_Equiv__Relations_Ocongruent(X4,X3,X16,X27)=>(hAPP(X27,X35)=hAPP(X27,X5)<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X5),X35)),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_congruentD)). 4.46/4.68 fof(fact_wf__same__fst, axiom, ![X4, X26, X3, X28]:(c_Wellfounded_Owf(tc_prod(X4,X3),c_Recdef_Osame__fst(X4,X3,X28,X26))<=![X42]:(hBOOL(hAPP(X28,X42))=>c_Wellfounded_Owf(X3,hAPP(X26,X42)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__same__fst)). 4.46/4.68 fof(fact_list__ex__length, axiom, ![X7, X28, X4]:(c_List_Olist__ex(X4,X28,X7)<=>?[X199]:(hBOOL(hAPP(X28,hAPP(hAPP(c_List_Onth(X4),X7),X199)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X199),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__length)). 4.46/4.68 fof(fact_of__int__less__iff, axiom, ![X35, X36, X4]:(class_Rings_Olinordered__idom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),X35))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X36)),hAPP(c_Int_Oring__1__class_Oof__int(X4),X35))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__less__iff)). 4.46/4.68 fof(fact_of__nat__less__iff, axiom, ![X14, X22, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X22)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__less__iff)). 4.46/4.68 fof(fact_of__int__le__iff, axiom, ![X35, X36, X4]:(class_Rings_Olinordered__idom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X36)),hAPP(c_Int_Oring__1__class_Oof__int(X4),X35)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X36),X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__le__iff)). 4.46/4.68 fof(fact_of__nat__le__iff, axiom, ![X14, X22, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X22)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X14))))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__le__iff)). 4.46/4.68 fof(fact_partition__P, axiom, ![X309, X310, X7, X28, X4]:((![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X309)))=>~(hBOOL(hAPP(X28,X42))))&![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X310)))=>hBOOL(hAPP(X28,X42))))<=c_List_Opartition(X4,X28,X7)=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X310),X309)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition__P)). 4.46/4.68 fof(fact_image__uminus__greaterThanLessThan, axiom, ![X5, X6, X4]:(hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X6,X5))=c_SetInterval_Oord__class_OgreaterThanLessThan(X4,hAPP(c_Groups_Ouminus__class_Ouminus(X4),X5),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X6))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__greaterThanLessThan)). 4.46/4.68 fof(fact_image__uminus__atLeastAtMost, axiom, ![X5, X6, X4]:(hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X6,X5))=c_SetInterval_Oord__class_OatLeastAtMost(X4,hAPP(c_Groups_Ouminus__class_Ouminus(X4),X5),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X6))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__atLeastAtMost)). 4.46/4.68 fof(fact_Image__closed__trancl, axiom, ![X173, X16, X4]:(hAPP(c_Relation_OImage(X4,X4,c_Transitive__Closure_Ortrancl(X4,X16)),X173)=X173<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X16),X173)),X173))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__closed__trancl)). 4.46/4.68 fof(fact_inj__image__mem__iff, axiom, ![X2, X18, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>(hBOOL(hAPP(hAPP(c_member(X4),X18),X2))<=>hBOOL(hAPP(hAPP(c_member(X3),hAPP(X27,X18)),hAPP(c_Set_Oimage(X4,X3,X27),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__image__mem__iff)). 4.46/4.68 fof(fact_inf2I, axiom, ![X3, X4, X1, X5, X6, X2]:((hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X3,tc_HOL_Obool))),X2),X1),X6),X5))<=hBOOL(hAPP(hAPP(X1,X6),X5)))<=hBOOL(hAPP(hAPP(X2,X6),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf2I)). 4.46/4.68 fof(fact_INF1__D, axiom, ![X18, X37, X1, X2, X3, X4]:(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X2),X1),X37))=>(hBOOL(hAPP(hAPP(X1,X18),X37))<=hBOOL(hAPP(hAPP(c_member(X4),X18),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF1__D)). 4.46/4.68 fof(fact_mod__pos__neg__trivial, axiom, ![X11, X12]:((c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12),X11)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12),X11)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__pos__neg__trivial)). 4.46/4.68 fof(fact_take__Cons__number__of, axiom, ![X57, X48, X4, X63]:((hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Otake(X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)))&(hAPP(hAPP(c_List_Olist_OCons(X4),X48),hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X57))=hAPP(hAPP(c_List_Otake(X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Cons__number__of)). 4.46/4.68 fof(fact_nth__take, axiom, ![X57, X4, X17, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X17))=>hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Otake(X4),X17),X57)),X21)=hAPP(hAPP(c_List_Onth(X4),X57),X21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__take)). 4.46/4.68 fof(fact_insert__subset, axiom, ![X1, X2, X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))&hBOOL(hAPP(hAPP(c_member(X4),X6),X1)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2)),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__subset)). 4.46/4.68 fof(fact_Max_Oeq__fold__idem_H, axiom, ![X18, X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Set_Oinsert(X4),X18),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omax(X4)),X18),X2))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Oeq__fold__idem_H)). 4.46/4.68 fof(fact_Min_Oeq__fold__idem_H, axiom, ![X18, X2, X4]:((c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X18),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omin(X4)),X18),X2)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Oeq__fold__idem_H)). 4.46/4.68 fof(fact_sup__Sup__fold__sup, axiom, ![X1, X2, X4]:((hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4)),X1),X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X1),c_Complete__Lattice_OSup__class_OSup(X4,X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__Sup__fold__sup)). 4.46/4.68 fof(fact_min__max_Osup__Inf__absorb, axiom, ![X18, X2, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X18),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X2))=X18<=hBOOL(hAPP(hAPP(c_member(X4),X18),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__Inf__absorb)). 4.46/4.68 fof(fact_abs__minus__commute, axiom, ![X11, X12, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X12))=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__minus__commute)). 4.46/4.68 fof(fact_Compl__subset__Compl__iff, axiom, ![X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X2))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__subset__Compl__iff)). 4.46/4.68 fof(fact_insert__mono, axiom, ![X18, X65, X52, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X18),X52)),hAPP(hAPP(c_Set_Oinsert(X4),X18),X65)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X52),X65))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__mono)). 4.46/4.68 fof(fact_nat__zero__less__power__iff, axiom, ![X14, X6]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X6),X14)))<=>(X14=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__zero__less__power__iff)). 4.46/4.68 fof(fact_min__max_Oinf__Sup__absorb, axiom, ![X18, X2, X4]:(((hBOOL(hAPP(hAPP(c_member(X4),X18),X2))=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X18),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X2))=X18)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__Sup__absorb)). 4.46/4.68 fof(fact_of__int__power, axiom, ![X17, X49, X4]:(class_Rings_Oring__1(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X49)),X17)=hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X49),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__power)). 4.46/4.68 fof(fact_zero__le__power__abs, axiom, ![X17, X12, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),X17)))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__power__abs)). 4.46/4.68 fof(fact_of__nat__0__less__iff, axiom, ![X14, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__0__less__iff)). 4.46/4.68 fof(fact_of__nat__power, axiom, ![X17, X19, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X19)),X17)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X19),X17))<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__power)). 4.46/4.68 fof(fact_ord_OatLeastLessThan__iff, axiom, ![X23, X67, X170, X171, X24, X4]:((hBOOL(hAPP(hAPP(X170,X24),X23))&hBOOL(hAPP(hAPP(X171,X67),X24)))<=>hBOOL(hAPP(hAPP(c_member(X4),X24),c_SetInterval_Oord_OatLeastLessThan(X4,X171,X170,X67,X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OatLeastLessThan__iff)). 4.46/4.68 fof(fact_ord_OgreaterThanAtMost__iff, axiom, ![X23, X67, X170, X171, X24, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X24),c_SetInterval_Oord_OgreaterThanAtMost(X4,X171,X170,X67,X23)))<=>(hBOOL(hAPP(hAPP(X170,X67),X24))&hBOOL(hAPP(hAPP(X171,X24),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OgreaterThanAtMost__iff)). 4.46/4.68 fof(fact_filter__id__conv, axiom, ![X7, X28, X4]:(hAPP(c_List_Ofilter(X4,X28),X7)=X7<=>![X42]:(hBOOL(hAPP(X28,X42))<=hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__id__conv)). 4.46/4.68 fof(fact_psubsetD, axiom, ![X39, X1, X2, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X39),X2))=>hBOOL(hAPP(hAPP(c_member(X4),X39),X1)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubsetD)). 4.46/4.68 fof(fact_take__butlast, axiom, ![X57, X4, X17]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))=>hAPP(hAPP(c_List_Otake(X4),X17),X57)=hAPP(hAPP(c_List_Otake(X4),X17),c_List_Obutlast(X4,X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__butlast)). 4.46/4.68 fof(fact_single__Diff__lessThan, axiom, ![X45, X4]:(hAPP(hAPP(c_Set_Oinsert(X4),X45),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X45),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X45))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__Diff__lessThan)). 4.46/4.68 fof(fact_Suc__times__mod__eq, axiom, ![X19, X15]:(c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X19)),X15)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X15))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__times__mod__eq)). 4.46/4.68 fof(fact_Inter__anti__mono, axiom, ![X2, X1, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X1),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__anti__mono)). 4.46/4.68 fof(fact_insort__insert__key__triv, axiom, ![X7, X3, X6, X27, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Oinsort__insert__key(X3,X4,X27,X6,X7)=X7<=hBOOL(hAPP(hAPP(c_member(X4),hAPP(X27,X6)),hAPP(c_Set_Oimage(X3,X4,X27),hAPP(c_List_Oset(X3),X7)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__insert__key__triv)). 4.46/4.68 fof(fact_set__insort__insert, axiom, ![X7, X6, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_Set_Oinsert(X4),X6),hAPP(c_List_Oset(X4),X7))=hAPP(c_List_Oset(X4),c_List_Olinorder__class_Oinsort__insert__key(X4,X4,c_COMBI(X4),X6,X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__insort__insert)). 4.46/4.68 fof(fact_distinct__listsum__conv__Setsum, axiom, ![X7, X4]:((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X4),c_COMBI(X4)),hAPP(c_List_Oset(X4),X7))=hAPP(c_List_Omonoid__add__class_Olistsum(X4),X7)<=hBOOL(hAPP(c_List_Odistinct(X4),X7)))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__listsum__conv__Setsum)). 4.46/4.68 fof(fact_Union__mono, axiom, ![X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X2),X1))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__mono)). 4.46/4.68 fof(fact_accp__subset, axiom, ![X231, X232, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_Wellfounded_Oaccp(X4,X231)),c_Wellfounded_Oaccp(X4,X232)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X232),X231))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_accp__subset)). 4.46/4.68 fof(fact_ivl__disj__int_I11_J, axiom, ![X23, X22, X67, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X67),X22)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X22),X23))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I11_J)). 4.46/4.68 fof(fact_map__upd__triv, axiom, ![X3, X6, X4, X45, X64]:(hAPP(X64,X45)=hAPP(c_Option_Ooption_OSome(X4),X6)=>hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X4)),X64),X45),hAPP(c_Option_Ooption_OSome(X4),X6))=X64), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upd__triv)). 4.46/4.68 fof(fact_power__Suc, axiom, ![X17, X12, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Nat_OSuc,X17))<=class_Power_Opower(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__Suc)). 4.46/4.68 fof(fact_diff__Suc__less, axiom, ![X21, X17]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),hAPP(c_Nat_OSuc,X21))),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__Suc__less)). 4.46/4.68 fof(fact_subset__insert, axiom, ![X1, X2, X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),X1)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__insert)). 4.46/4.68 fof(fact_SigmaD1, axiom, ![X1, X2, X37, X18, X3, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X18),X37)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),X1)))=>hBOOL(hAPP(hAPP(c_member(X4),X18),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SigmaD1)). 4.46/4.68 fof(fact_Pow__mono, axiom, ![X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X4),X2)),hAPP(c_Set_OPow(X4),X1)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__mono)). 4.46/4.68 fof(fact_neg__less__0__iff__less, axiom, ![X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X18))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)),c_Groups_Ozero__class_Ozero(X4))))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__less__0__iff__less)). 4.46/4.68 fof(fact_neg__le__0__iff__le, axiom, ![X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X18)))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__le__0__iff__le)). 4.46/4.68 fof(fact_order__less__trans, axiom, ![X49, X47, X48, X4]:(class_Orderings_Opreorder(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),X49))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X47),X49)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__less__trans)). 4.46/4.68 fof(fact_order__le__less__trans, axiom, ![X49, X47, X48, X4]:(class_Orderings_Opreorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X47))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),X49))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X47),X49))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__le__less__trans)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, axiom, ![X112, X48, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),hAPP(c_Nat_OSuc,X112))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X48),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),X112))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J)). 4.46/4.68 fof(fact_ivl__disj__int_I9_J, axiom, ![X23, X22, X67, X4]:(class_Orderings_Oorder(X4)=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X67,X22)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X22),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I9_J)). 4.46/4.68 fof(fact_ivl__disj__int_I15_J, axiom, ![X23, X22, X67, X4]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X67),X22)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X22,X23))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I15_J)). 4.46/4.68 fof(fact_order__less__le__trans, axiom, ![X49, X47, X48, X4]:(class_Orderings_Opreorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),X47))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),X49))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X47),X49))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__less__le__trans)). 4.46/4.68 fof(fact_xt1_I10_J, axiom, ![X49, X48, X47, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X49),X48))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X49),X47)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X47),X48)))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_xt1_I10_J)). 4.46/4.68 fof(fact_xt1_I8_J, axiom, ![X49, X48, X47, X4]:(class_Orderings_Oorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X47),X48))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X49),X48))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X49),X47))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_xt1_I8_J)). 4.46/4.68 fof(fact_xt1_I7_J, axiom, ![X49, X48, X47, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X47),X48))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X49),X47))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X49),X48))))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_xt1_I7_J)). 4.46/4.68 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, axiom, ![X17, X48]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X48),X17)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X48))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J)). 4.46/4.68 fof(fact_less__diff__conv, axiom, ![X45, X25, X24]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X45)),X25))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__diff__conv)). 4.46/4.68 fof(fact_le__diff__conv, axiom, ![X24, X45, X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X45)),X24))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__diff__conv)). 4.46/4.68 fof(fact_order__trans, axiom, ![X49, X47, X48, X4]:(class_Orderings_Opreorder(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X49))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X47),X49)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__trans)). 4.46/4.68 fof(fact_xt1_I6_J, axiom, ![X49, X48, X47, X4]:(class_Orderings_Oorder(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X49),X47))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X49),X48)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X47),X48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_xt1_I6_J)). 4.46/4.68 fof(fact_neg__0__less__iff__less, axiom, ![X18, X4]:(class_Groups_Oordered__ab__group__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__0__less__iff__less)). 4.46/4.68 fof(fact_neg__0__le__iff__le, axiom, ![X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),c_Groups_Ozero__class_Ozero(X4))))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__0__le__iff__le)). 4.46/4.68 fof(fact_less__infI1, axiom, ![X11, X48, X12, X4]:(class_Lattices_Osemilattice__inf(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X12),X11)),X48))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__infI1)). 4.46/4.68 fof(fact_less__le__not__le, axiom, ![X5, X6, X4]:(((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X5),X6)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),X5)))<=class_Orderings_Opreorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__le__not__le)). 4.46/4.68 fof(fact_transfer__int__nat__quantifiers_I2_J, axiom, ![X28]:(?[X42]:hBOOL(hAPP(X28,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X42)))<=>?[X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X42))&hBOOL(hAPP(X28,X42)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__quantifiers_I2_J)). 4.46/4.68 fof(fact_nonzero__minus__divide__divide, axiom, ![X12, X11, X4]:(class_Rings_Odivision__ring(X4)=>(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X11)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11))<=c_Groups_Ozero__class_Ozero(X4)!=X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonzero__minus__divide__divide)). 4.46/4.68 fof(fact_less__infI2, axiom, ![X12, X48, X11, X4]:(class_Lattices_Osemilattice__inf(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X12),X11)),X48))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__infI2)). 4.46/4.68 fof(fact_le__infI1, axiom, ![X11, X48, X12, X4]:(class_Lattices_Osemilattice__inf(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X48))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X12),X11)),X48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__infI1)). 4.46/4.68 fof(fact_le__infI2, axiom, ![X12, X48, X11, X4]:(class_Lattices_Osemilattice__inf(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X48))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X12),X11)),X48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__infI2)). 4.46/4.68 fof(fact_ivl__disj__int_I10_J, axiom, ![X23, X22, X67, X4]:(class_Orderings_Oorder(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X67,X22)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X22,X23))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I10_J)). 4.46/4.68 fof(fact_map__add__SomeD, axiom, ![X6, X45, X14, X22, X4, X3]:(((hAPP(c_Option_Ooption_OSome(X4),X6)=hAPP(X22,X45)&hAPP(X14,X45)=c_Option_Ooption_ONone(X4))|hAPP(X14,X45)=hAPP(c_Option_Ooption_OSome(X4),X6))<=hAPP(c_Option_Ooption_OSome(X4),X6)=hAPP(c_Map_Omap__add(X3,X4,X22,X14),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__SomeD)). 4.46/4.68 fof(fact_ivl__disj__int_I12_J, axiom, ![X23, X22, X67, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X67,X22)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X22,X23))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I12_J)). 4.46/4.68 fof(fact_ivl__disj__int_I13_J, axiom, ![X23, X22, X67, X4]:(class_Orderings_Oorder(X4)=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X67,X22)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X22,X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I13_J)). 4.46/4.68 fof(fact_ivl__disj__int_I14_J, axiom, ![X23, X22, X67, X4]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X67,X22)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X22,X23))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I14_J)). 4.46/4.68 fof(fact_ivl__disj__int_I16_J, axiom, ![X23, X22, X67, X4]:(class_Orderings_Oorder(X4)=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X67,X22)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X22,X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I16_J)). 4.46/4.68 fof(fact_less__supI1, axiom, ![X11, X12, X48, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X12),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),X12)))<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__supI1)). 4.46/4.68 fof(fact_less__supI2, axiom, ![X12, X11, X48, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X12),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),X11)))<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__supI2)). 4.46/4.68 fof(fact_le__supI1, axiom, ![X11, X12, X48, X4]:(class_Lattices_Osemilattice__sup(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X12),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__supI1)). 4.46/4.68 fof(fact_le__supI2, axiom, ![X12, X11, X48, X4]:(class_Lattices_Osemilattice__sup(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X12),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__supI2)). 4.46/4.68 fof(fact_lists__accD, axiom, ![X16, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X7),c_List_Olists(X4,c_Wellfounded_Oacc(X4,X16))))=>hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X7),c_Wellfounded_Oacc(tc_List_Olist(X4),c_List_Olistrel1(X4,X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__accD)). 4.46/4.68 fof(fact_sgn__times, axiom, ![X11, X12, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Osgn__class_Osgn(X4,X12)),c_Groups_Osgn__class_Osgn(X4,X11))=c_Groups_Osgn__class_Osgn(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__times)). 4.46/4.68 fof(fact_minus__mult__minus, axiom, ![X11, X12, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11)<=class_Rings_Oring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__mult__minus)). 4.46/4.68 fof(fact_nth__Cons__number__of, axiom, ![X57, X48, X4, X63]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)=>X48=hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>hAPP(hAPP(c_List_Onth(X4),X57),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X63)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__Cons__number__of)). 4.46/4.68 fof(fact_Powp__mono, axiom, ![X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X4,X2)),c_Predicate_OPowp(X4,X1)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Powp__mono)). 4.46/4.68 fof(fact_sorted__map__remove1, axiom, ![X6, X7, X27, X3, X4]:((c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X27),X7))=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X27),c_List_Oremove1(X3,X6,X7))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__map__remove1)). 4.46/4.68 fof(fact_append__in__listsp__conv, axiom, ![X32, X7, X2, X4]:(hBOOL(hAPP(c_List_Olistsp(X4,X2),hAPP(hAPP(c_List_Oappend(X4),X7),X32)))<=>(hBOOL(hAPP(c_List_Olistsp(X4,X2),X7))&hBOOL(hAPP(c_List_Olistsp(X4,X2),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__in__listsp__conv)). 4.46/4.68 fof(fact_minus__divide__divide, axiom, ![X11, X12, X4]:(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X11)<=class_Fields_Ofield__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__divide__divide)). 4.46/4.68 fof(fact_less__Suc__eq__0__disj, axiom, ![X14, X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),hAPP(c_Nat_OSuc,X14)))<=>(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X22|?[X98]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X14))&hAPP(c_Nat_OSuc,X98)=X22))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__Suc__eq__0__disj)). 4.46/4.68 fof(fact_le__trans, axiom, ![X15, X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20),X15))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X15)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__trans)). 4.46/4.68 fof(fact_zle__trans, axiom, ![X15, X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21),X20))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21),X15))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20),X15)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__trans)). 4.46/4.68 fof(fact_nonzero__minus__divide__right, axiom, ![X12, X11, X4]:((X11!=c_Groups_Ozero__class_Ozero(X4)=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X11))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)))<=class_Rings_Odivision__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonzero__minus__divide__right)). 4.46/4.68 fof(fact_of__int__less__0__iff, axiom, ![X35, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X35),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X35)),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__less__0__iff)). 4.46/4.68 fof(fact_of__int__le__0__iff, axiom, ![X35, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X35),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X35)),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__le__0__iff)). 4.46/4.68 fof(fact_of__int__0__less__iff, axiom, ![X35, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X35))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Oring__1__class_Oof__int(X4),X35))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__0__less__iff)). 4.46/4.68 fof(fact_of__int__0__le__iff, axiom, ![X35, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Oring__1__class_Oof__int(X4),X35)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X35)))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__0__le__iff)). 4.46/4.68 fof(fact_neg__mod__sign, axiom, ![X12, X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__mod__sign)). 4.46/4.68 fof(fact_takeWhile__eq__all__conv, axiom, ![X7, X28, X4]:(![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7)))=>hBOOL(hAPP(X28,X42)))<=>X7=c_List_OtakeWhile(X4,X28,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__eq__all__conv)). 4.46/4.68 fof(fact_takeWhile_Osimps_I2_J, axiom, ![X7, X4, X6, X28]:((c_List_OtakeWhile(X4,X28,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7))=hAPP(hAPP(c_List_Olist_OCons(X4),X6),c_List_OtakeWhile(X4,X28,X7))<=hBOOL(hAPP(X28,X6)))&(~(hBOOL(hAPP(X28,X6)))=>c_List_Olist_ONil(X4)=c_List_OtakeWhile(X4,X28,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile_Osimps_I2_J)). 4.46/4.68 fof(fact_pos__mod__sign, axiom, ![X12, X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__mod__sign)). 4.46/4.68 fof(fact_insert__Diff1, axiom, ![X2, X1, X6, X4]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2)),X1)<=hBOOL(hAPP(hAPP(c_member(X4),X6),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__Diff1)). 4.46/4.68 fof(fact_Ints__minus, axiom, ![X18, X4]:(class_Rings_Oring__1(X4)=>(hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)),c_Int_Oring__1__class_OInts(X4)))<=hBOOL(hAPP(hAPP(c_member(X4),X18),c_Int_Oring__1__class_OInts(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__minus)). 4.46/4.68 fof(fact_mod__geq, axiom, ![X17, X19]:(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17),X17)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__geq)). 4.46/4.68 fof(fact_linorder__neqE__linordered__idom, axiom, ![X47, X48, X4]:(class_Rings_Olinordered__idom(X4)=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),X47)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X47),X48)))<=X47!=X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__neqE__linordered__idom)). 4.46/4.68 fof(fact_abs__mult__self, axiom, ![X12, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X12)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),hAPP(c_Groups_Oabs__class_Oabs(X4),X12))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__mult__self)). 4.46/4.68 fof(fact_map__upd__eqD1, axiom, ![X5, X14, X6, X18, X22, X3, X4]:(X5=X6<=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),X14),X18),hAPP(c_Option_Ooption_OSome(X3),X5))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),X22),X18),hAPP(c_Option_Ooption_OSome(X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upd__eqD1)). 4.46/4.68 fof(fact_mult__less__cancel1, axiom, ![X14, X22, X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X22)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X14)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X45))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__cancel1)). 4.46/4.68 fof(fact_list__all2__append, axiom, ![X196, X197, X28, X32, X3, X7, X4]:(((c_List_Olist__all2(X4,X3,X28,X7,X32)&c_List_Olist__all2(X4,X3,X28,X197,X196))<=>c_List_Olist__all2(X4,X3,X28,hAPP(hAPP(c_List_Oappend(X4),X7),X197),hAPP(hAPP(c_List_Oappend(X3),X32),X196)))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__append)). 4.46/4.68 fof(fact_inj__on__Int, axiom, ![X1, X2, X27, X3, X4]:((c_Fun_Oinj__on(X4,X3,X27,X1)=>c_Fun_Oinj__on(X4,X3,X27,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=c_Fun_Oinj__on(X4,X3,X27,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__Int)). 4.46/4.68 fof(fact_Ball__set__list__all, axiom, ![X28, X7, X4]:(c_List_Olist__all(X4,X28,X7)<=>![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7)))=>hBOOL(hAPP(X28,X42)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ball__set__list__all)). 4.46/4.68 fof(fact_finite__UNIV__card__ge__0, axiom, ![X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UNIV__card__ge__0)). 4.46/4.68 fof(fact_list__all__iff, axiom, ![X7, X28, X4]:(c_List_Olist__all(X4,X28,X7)<=>![X42]:(hBOOL(hAPP(X28,X42))<=hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__iff)). 4.46/4.68 fof(fact_distinct__zipI1, axiom, ![X72, X3, X57, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X57))=>hBOOL(hAPP(c_List_Odistinct(tc_prod(X4,X3)),hAPP(hAPP(c_List_Ozip(X4,X3),X57),X72)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__zipI1)). 4.46/4.68 fof(fact_distinct__zipI2, axiom, ![X57, X3, X72, X4]:(hBOOL(hAPP(c_List_Odistinct(tc_prod(X3,X4)),hAPP(hAPP(c_List_Ozip(X3,X4),X57),X72)))<=hBOOL(hAPP(c_List_Odistinct(X4),X72))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__zipI2)). 4.46/4.68 fof(fact_finite__induct, axiom, ![X28, X62, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X62))=>((![X42, X203]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X203))=>(~(hBOOL(hAPP(hAPP(c_member(X4),X42),X203)))=>(hBOOL(hAPP(X28,X203))=>hBOOL(hAPP(X28,hAPP(hAPP(c_Set_Oinsert(X4),X42),X203))))))=>hBOOL(hAPP(X28,X62)))<=hBOOL(hAPP(X28,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__induct)). 4.46/4.68 fof(fact_list__all__iff__raw, axiom, ![X7, X28, X4]:(![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7)))=>hBOOL(hAPP(X28,X42)))<=>c_List_Olist__all(X4,X28,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__iff__raw)). 4.46/4.68 fof(fact_congruent2__implies__congruent, axiom, ![X18, X27, X147, X29, X3, X149, X2, X4]:(c_Equiv__Relations_Oequiv(X4,X2,X149)=>(c_Equiv__Relations_Ocongruent2(X4,X3,X29,X149,X147,X27)=>(hBOOL(hAPP(hAPP(c_member(X4),X18),X2))=>c_Equiv__Relations_Ocongruent(X3,X29,X147,hAPP(X27,X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_congruent2__implies__congruent)). 4.46/4.68 fof(fact_linorder__antisym__conv3, axiom, ![X6, X5, X4]:(class_Orderings_Olinorder(X4)=>((X5=X6<=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),X5))))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X5),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__antisym__conv3)). 4.46/4.68 fof(fact_atMost__Int__atLeast, axiom, ![X14, X4]:(hAPP(hAPP(c_Set_Oinsert(X4),X14),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X14)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X14))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atMost__Int__atLeast)). 4.46/4.68 fof(fact_imageI, axiom, ![X27, X3, X2, X6, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hBOOL(hAPP(hAPP(c_member(X3),hAPP(X27,X6)),hAPP(c_Set_Oimage(X4,X3,X27),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_imageI)). 4.46/4.68 fof(fact_finite__compl, axiom, ![X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X2))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__compl)). 4.46/4.68 fof(fact_endo__inj__surj, axiom, ![X27, X2, X4]:(((hAPP(c_Set_Oimage(X4,X4,X27),X2)=X2<=c_Fun_Oinj__on(X4,X4,X27,X2))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X4,X27),X2)),X2)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_endo__inj__surj)). 4.46/4.68 fof(fact_rtrancl__subset, axiom, ![X46, X26, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X26),X46))=>(c_Transitive__Closure_Ortrancl(X4,X26)=c_Transitive__Closure_Ortrancl(X4,X46)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X46),c_Transitive__Closure_Ortrancl(X4,X26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__subset)). 4.46/4.68 fof(fact_inj__on__map__add__dom, axiom, ![X216, X22, X3, X4]:(c_Fun_Oinj__on(X4,tc_Option_Ooption(X3),X216,c_Map_Odom(X4,X3,X216))<=>c_Fun_Oinj__on(X4,tc_Option_Ooption(X3),c_Map_Omap__add(X4,X3,X22,X216),c_Map_Odom(X4,X3,X216))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__map__add__dom)). 4.46/4.68 fof(fact_ord_OatLeastAtMost__iff, axiom, ![X23, X67, X171, X24, X4]:((hBOOL(hAPP(hAPP(X171,X24),X23))&hBOOL(hAPP(hAPP(X171,X67),X24)))<=>hBOOL(hAPP(hAPP(c_member(X4),X24),c_SetInterval_Oord_OatLeastAtMost(X4,X171,X67,X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OatLeastAtMost__iff)). 4.46/4.68 fof(fact_minus__mult__left, axiom, ![X11, X12, X4]:(hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)),X11)<=class_Rings_Oring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__mult__left)). 4.46/4.68 fof(fact_minus__divide__left, axiom, ![X11, X12, X4]:(hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X11))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)),X11)<=class_Rings_Odivision__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__divide__left)). 4.46/4.68 fof(fact_minus__mult__commute, axiom, ![X11, X12, X4]:(class_Rings_Oring(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)),X11)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__mult__commute)). 4.46/4.68 fof(fact_ord_OgreaterThanLessThan__iff, axiom, ![X23, X67, X170, X24, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X24),c_SetInterval_Oord_OgreaterThanLessThan(X4,X170,X67,X23)))<=>(hBOOL(hAPP(hAPP(X170,X67),X24))&hBOOL(hAPP(hAPP(X170,X24),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OgreaterThanLessThan__iff)). 4.46/4.68 fof(fact_Max_Oin__idem, axiom, ![X6, X2, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X6),c_Big__Operators_Olinorder__class_OMax(X4,X2))=c_Big__Operators_Olinorder__class_OMax(X4,X2)<=hBOOL(hAPP(hAPP(c_member(X4),X6),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Oin__idem)). 4.46/4.68 fof(fact_finite__Inter, axiom, ![X153, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X153)))<=?[X42]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X42),X153))&hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X42)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Inter)). 4.46/4.68 fof(fact_the__inv__f__f, axiom, ![X6, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>hAPP(c_Fun_Othe__inv__into(X4,X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),X27),hAPP(X27,X6))=X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__inv__f__f)). 4.46/4.68 fof(fact_Min_Oin__idem, axiom, ![X6, X2, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X6),c_Big__Operators_Olinorder__class_OMin(X4,X2))=c_Big__Operators_Olinorder__class_OMin(X4,X2)<=hBOOL(hAPP(hAPP(c_member(X4),X6),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Oin__idem)). 4.46/4.68 fof(fact_Inf__fin_Oin__idem, axiom, ![X6, X2, X4]:(((hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>c_Big__Operators_Olattice__class_OInf__fin(X4,X2)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X6),c_Big__Operators_Olattice__class_OInf__fin(X4,X2)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oin__idem)). 4.46/4.68 fof(fact_Sup__fin_Oin__idem, axiom, ![X6, X2, X4]:(class_Lattices_Olattice(X4)=>((hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>c_Big__Operators_Olattice__class_OSup__fin(X4,X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X6),c_Big__Operators_Olattice__class_OSup__fin(X4,X2)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oin__idem)). 4.46/4.68 fof(fact_nth__list__update__neq, axiom, ![X48, X57, X4, X20, X21]:(hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Olist__update(X4,X57),X21),X48)),X20)=hAPP(hAPP(c_List_Onth(X4),X57),X20)<=X20!=X21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__list__update__neq)). 4.46/4.68 fof(fact_zless__imp__add1__zle, axiom, ![X49, X30]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X30),c_Groups_Oone__class_Oone(tc_Int_Oint))),X49))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X49))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__imp__add1__zle)). 4.46/4.68 fof(fact_less__bin__lemma, axiom, ![X67, X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),X67))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X45),X67)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__bin__lemma)). 4.46/4.68 fof(fact_linorder__le__cases, axiom, ![X47, X48, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X47),X48))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X47))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__le__cases)). 4.46/4.68 fof(fact_transfer__int__nat__relations_I2_J, axiom, ![X5, X6]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__relations_I2_J)). 4.46/4.68 fof(fact_in__set__dropD, axiom, ![X7, X14, X6, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))<=hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Odrop(X4),X14),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__dropD)). 4.46/4.68 fof(fact_in__set__takeD, axiom, ![X7, X14, X6, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))<=hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Otake(X4),X14),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__takeD)). 4.46/4.68 fof(fact_le__mod__geq, axiom, ![X19, X17]:(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17),X17)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__mod__geq)). 4.46/4.68 fof(fact_z3div__def, axiom, ![X15, X31]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X31))=>c_SMT_Oz3div(X15,X31)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X15),X31))&(c_SMT_Oz3div(X15,X31)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X15),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X31)))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X31))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_z3div__def)). 4.46/4.68 fof(fact_minus__mult__right, axiom, ![X11, X12, X4]:(class_Rings_Oring(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11))=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__mult__right)). 4.46/4.68 fof(fact_transfer__int__nat__relations_I3_J, axiom, ![X5, X6]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6),X5))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__relations_I3_J)). 4.46/4.68 fof(fact_tl__replicate, axiom, ![X48, X4, X17]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X17=>hAPP(c_List_Otl(X4),c_List_Oreplicate(X4,X17,X48))=c_List_Oreplicate(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tl__replicate)). 4.46/4.68 fof(fact_minus__divide__right, axiom, ![X11, X12, X4]:(class_Fields_Ofield__inverse__zero(X4)=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X11))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__divide__right)). 4.46/4.68 fof(fact_zero__less__diff, axiom, ![X22, X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14),X22)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__diff)). 4.46/4.68 fof(fact_zle__add1__eq__le, axiom, ![X35, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X36),X35))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X35),c_Groups_Oone__class_Oone(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__add1__eq__le)). 4.46/4.68 fof(fact_tl__append2, axiom, ![X72, X4, X57]:(c_List_Olist_ONil(X4)!=X57=>hAPP(c_List_Otl(X4),hAPP(hAPP(c_List_Oappend(X4),X57),X72))=hAPP(hAPP(c_List_Oappend(X4),hAPP(c_List_Otl(X4),X57)),X72)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tl__append2)). 4.46/4.68 fof(fact_map__add__comm, axiom, ![X100, X99, X3, X4]:(c_Map_Omap__add(X4,X3,X100,X99)=c_Map_Omap__add(X4,X3,X99,X100)<=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X3,X99)),c_Map_Odom(X4,X3,X100))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__comm)). 4.46/4.68 fof(fact_nth__length__takeWhile, axiom, ![X7, X28, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X28,X7))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))=>~(hBOOL(hAPP(X28,hAPP(hAPP(c_List_Onth(X4),X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X28,X7))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__length__takeWhile)). 4.46/4.68 fof(fact_UnionE, axiom, ![X52, X2, X4]:(~(![X207]:(~(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X207),X52)))<=hBOOL(hAPP(hAPP(c_member(X4),X2),X207))))<=hBOOL(hAPP(hAPP(c_member(X4),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X52)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UnionE)). 4.46/4.68 fof(fact_add__less__imp__less__right, axiom, ![X11, X10, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10))))<=class_Groups_Oordered__ab__semigroup__add__imp__le(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__less__imp__less__right)). 4.46/4.68 fof(fact_add__less__imp__less__left, axiom, ![X11, X12, X10, X4]:(class_Groups_Oordered__ab__semigroup__add__imp__le(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__less__imp__less__left)). 4.46/4.68 fof(fact_card__gt__0__iff, axiom, ![X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))&c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__gt__0__iff)). 4.46/4.68 fof(fact_add__le__imp__le__left, axiom, ![X11, X12, X10, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X11)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11)))<=class_Groups_Oordered__ab__semigroup__add__imp__le(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__le__imp__le__left)). 4.46/4.68 fof(fact_folding__idem_Oidem__comp, axiom, ![X6, X62, X27, X3, X4]:(hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X27,X6)),hAPP(X27,X6))=hAPP(X27,X6)<=c_Finite__Set_Ofolding__idem(X4,X3,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__idem_Oidem__comp)). 4.46/4.68 fof(fact_mod__minus__eq, axiom, ![X11, X12, X4]:(c_Divides_Odiv__class_Omod(X4,hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12),X11)=c_Divides_Odiv__class_Omod(X4,hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Divides_Odiv__class_Omod(X4,X12,X11)),X11)<=class_Divides_Oring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__minus__eq)). 4.46/4.68 fof(fact_wf__no__infinite__down__chainE, axiom, ![X27, X16, X4]:(c_Wellfounded_Owf(X4,X16)=>~(![X266]:hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(X27,hAPP(c_Nat_OSuc,X266))),hAPP(X27,X266))),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__no__infinite__down__chainE)). 4.46/4.68 fof(fact_transfer__int__nat__quantifiers_I1_J, axiom, ![X28]:(![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X42))=>hBOOL(hAPP(X28,X42)))<=>![X42]:hBOOL(hAPP(X28,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X42)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__quantifiers_I1_J)). 4.46/4.68 fof(fact_listsp_Oequations_I2_J, axiom, ![X135, X123, X2, X4]:((hBOOL(hAPP(c_List_Olistsp(X4,X2),X135))&hBOOL(hAPP(X2,X123)))<=>hBOOL(hAPP(c_List_Olistsp(X4,X2),hAPP(hAPP(c_List_Olist_OCons(X4),X123),X135)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp_Oequations_I2_J)). 4.46/4.68 fof(fact_min__max_Ole__infI2, axiom, ![X12, X48, X11, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X48))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X12),X11)),X48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__infI2)). 4.46/4.68 fof(fact_min__max_Oless__supI1, axiom, ![X11, X12, X48, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X12),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),X12)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oless__supI1)). 4.46/4.68 fof(fact_diff__eq__diff__less, axiom, ![X87, X39, X37, X18, X4]:(class_Groups_Oordered__ab__group__add(X4)=>(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X39),X87)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X18),X37)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),X37))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),X87))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__eq__diff__less)). 4.46/4.68 fof(fact_diff__eq__diff__less__eq, axiom, ![X87, X39, X37, X18, X4]:(class_Groups_Oordered__ab__group__add(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X39),X87))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),X37)))<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X18),X37)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X39),X87))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__eq__diff__less__eq)). 4.46/4.68 fof(fact_min__max_Oless__supI2, axiom, ![X12, X11, X48, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X12),X11))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oless__supI2)). 4.46/4.68 fof(fact_min__max_Ole__supI1, axiom, ![X11, X12, X48, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X12),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__supI1)). 4.46/4.68 fof(fact_of__nat__aux_Osimps_I2_J, axiom, ![X24, X14, X116, X4]:(class_Rings_Osemiring__1(X4)=>c_Nat_Osemiring__1__class_Oof__nat__aux(X4,X116,X14,hAPP(X116,X24))=c_Nat_Osemiring__1__class_Oof__nat__aux(X4,X116,hAPP(c_Nat_OSuc,X14),X24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__aux_Osimps_I2_J)). 4.46/4.68 fof(fact_finite__UNIV__surj__inj, axiom, ![X27, X4]:((c_Fun_Oinj__on(X4,X4,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))<=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_Oimage(X4,X4,X27),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UNIV__surj__inj)). 4.46/4.68 fof(fact_map__eq__imp__length__eq, axiom, ![X32, X50, X29, X7, X27, X4, X3]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X7)<=hAPP(hAPP(c_List_Omap(X29,X4),X50),X32)=hAPP(hAPP(c_List_Omap(X3,X4),X27),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__eq__imp__length__eq)). 4.46/4.68 fof(fact_card__insert__if, axiom, ![X6, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>((~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))=>hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X4),X2)))&(hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hAPP(c_Finite__Set_Ocard(X4),X2)=hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__insert__if)). 4.46/4.68 fof(fact_Inf__binary, axiom, ![X37, X18, X4]:(c_Complete__Lattice_OInf__class_OInf(X4,hAPP(hAPP(c_Set_Oinsert(X4),X18),hAPP(hAPP(c_Set_Oinsert(X4),X37),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X18),X37)<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__binary)). 4.46/4.68 fof(fact_list__ex__iff, axiom, ![X7, X28, X4]:(c_List_Olist__ex(X4,X28,X7)<=>?[X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),hAPP(c_List_Oset(X4),X7)))&hBOOL(hAPP(X28,X42)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__iff)). 4.46/4.68 fof(fact_equiv__comp__eq, axiom, ![X16, X2, X4]:(hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(c_Relation_Oconverse(X4,X4),X16)),X16)=X16<=c_Equiv__Relations_Oequiv(X4,X2,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__comp__eq)). 4.46/4.68 fof(fact_image__uminus__lessThan, axiom, ![X6, X4]:(hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X6))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X6))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__lessThan)). 4.46/4.68 fof(fact_compl__unique, axiom, ![X47, X48, X4]:(((X47=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X48)<=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X47)=c_Orderings_Otop__class_Otop(X4))<=c_Orderings_Obot__class_Obot(X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X47))<=class_Lattices_Oboolean__algebra(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__unique)). 4.46/4.68 fof(fact_Sup__binary, axiom, ![X37, X18, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>c_Complete__Lattice_OSup__class_OSup(X4,hAPP(hAPP(c_Set_Oinsert(X4),X18),hAPP(hAPP(c_Set_Oinsert(X4),X37),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X18),X37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__binary)). 4.46/4.68 fof(fact_mult__left__idem, axiom, ![X11, X12, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11)<=class_Lattices_Oab__semigroup__idem__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__idem)). 4.46/4.68 fof(fact_image__uminus__atMost, axiom, ![X6, X4]:(hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X6))=hAPP(c_SetInterval_Oord__class_OatLeast(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X6))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__atMost)). 4.46/4.68 fof(fact_Inf__fold__inf, axiom, ![X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),c_Orderings_Otop__class_Otop(X4)),X2)=c_Complete__Lattice_OInf__class_OInf(X4,X2))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fold__inf)). 4.46/4.68 fof(fact_Sup__fold__sup, axiom, ![X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>c_Complete__Lattice_OSup__class_OSup(X4,X2)=hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4)),c_Orderings_Obot__class_Obot(X4)),X2))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fold__sup)). 4.46/4.68 fof(fact_type__definition_OAbs__inject, axiom, ![X5, X6, X2, X101, X102, X3, X4]:((((X6=X5<=>hAPP(X101,X6)=hAPP(X101,X5))<=hBOOL(hAPP(hAPP(c_member(X3),X5),X2)))<=hBOOL(hAPP(hAPP(c_member(X3),X6),X2)))<=c_Typedef_Otype__definition(X4,X3,X102,X101,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_OAbs__inject)). 4.46/4.68 fof(fact_image__uminus__atLeast, axiom, ![X6, X4]:(hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X6))=hAPP(c_SetInterval_Oord__class_OatMost(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X6))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__atLeast)). 4.46/4.68 fof(fact_inf__sup__aci_I8_J, axiom, ![X47, X48, X4]:(class_Lattices_Olattice(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X47))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I8_J)). 4.46/4.68 fof(fact_inf__sup__aci_I4_J, axiom, ![X47, X48, X4]:(class_Lattices_Olattice(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X47))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I4_J)). 4.46/4.68 fof(fact_image__uminus__greaterThan, axiom, ![X6, X4]:(hAPP(c_SetInterval_Oord__class_OlessThan(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X6))=hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X6))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__greaterThan)). 4.46/4.68 fof(fact_sup__left__idem, axiom, ![X47, X48, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X47)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X47))<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__left__idem)). 4.46/4.68 fof(fact_inf_Oleft__idem, axiom, ![X11, X12, X4]:(class_Lattices_Osemilattice__inf(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X12),X11)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X12),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X12),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf_Oleft__idem)). 4.46/4.68 fof(fact_Min__in, axiom, ![X2, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>hBOOL(hAPP(hAPP(c_member(X4),c_Big__Operators_Olinorder__class_OMin(X4,X2)),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__in)). 4.46/4.68 fof(fact_Max__in, axiom, ![X2, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hBOOL(hAPP(hAPP(c_member(X4),c_Big__Operators_Olinorder__class_OMax(X4,X2)),X2))<=X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__in)). 4.46/4.68 fof(fact_inj__on__the__inv__into, axiom, ![X2, X27, X3, X4]:(c_Fun_Oinj__on(X3,X4,c_Fun_Othe__inv__into(X4,X3,X2,X27),hAPP(c_Set_Oimage(X4,X3,X27),X2))<=c_Fun_Oinj__on(X4,X3,X27,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__the__inv__into)). 4.46/4.68 fof(fact_finite__Plus__iff, axiom, ![X1, X2, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1))&hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X4,X3)),c_Sum__Type_OPlus(X4,X3,X2,X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Plus__iff)). 4.46/4.68 fof(fact_abs__power__minus__one, axiom, ![X17, X4]:(c_Groups_Oone__class_Oone(X4)=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin)),X17))<=(class_Rings_Olinordered__idom(X4)&class_Int_Onumber__ring(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__power__minus__one)). 4.46/4.68 fof(fact_add__minus__cancel, axiom, ![X11, X12, X4]:(class_Groups_Ogroup__add(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)),X11))=X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__minus__cancel)). 4.46/4.68 fof(fact_minus__add__cancel, axiom, ![X11, X12, X4]:(class_Groups_Ogroup__add(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11))=X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__add__cancel)). 4.46/4.68 fof(fact_sup2E, axiom, ![X5, X6, X1, X2, X3, X4]:((hBOOL(hAPP(hAPP(X1,X6),X5))<=~(hBOOL(hAPP(hAPP(X2,X6),X5))))<=hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X3,tc_HOL_Obool))),X2),X1),X6),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup2E)). 4.46/4.68 fof(fact_distinct__product, axiom, ![X72, X3, X57, X4]:((hBOOL(hAPP(c_List_Odistinct(X3),X72))=>hBOOL(hAPP(c_List_Odistinct(tc_prod(X4,X3)),c_Enum_Oproduct(X4,X3,X57,X72))))<=hBOOL(hAPP(c_List_Odistinct(X4),X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__product)). 4.46/4.68 fof(fact_r__into__rtrancl, axiom, ![X16, X109, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X109),X16))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X109),c_Transitive__Closure_Ortrancl(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_r__into__rtrancl)). 4.46/4.68 fof(fact_inj__on__imageI, axiom, ![X2, X27, X50, X29, X3, X4]:(c_Fun_Oinj__on(X29,X3,X50,hAPP(c_Set_Oimage(X4,X29,X27),X2))<=c_Fun_Oinj__on(X4,X3,hAPP(c_Fun_Ocomp(X29,X3,X4,X50),X27),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__imageI)). 4.46/4.68 fof(fact_fun__left__comm__idem_Ofun__comp__idem, axiom, ![X6, X27, X3, X4]:(c_Finite__Set_Ofun__left__comm__idem(X4,X3,X27)=>hAPP(X27,X6)=hAPP(c_Fun_Ocomp(X3,X3,X3,hAPP(X27,X6)),hAPP(X27,X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem_Ofun__comp__idem)). 4.46/4.68 fof(fact_linorder__neqE__nat, axiom, ![X47, X48]:(X47!=X48=>(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),X47)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47),X48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__neqE__nat)). 4.46/4.68 fof(fact_zless__linear, axiom, ![X47, X48]:(X47=X48|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X47),X48))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X48),X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__linear)). 4.46/4.68 fof(fact_rev__predicate2D, axiom, ![X80, X3, X4, X5, X6, X28]:(hBOOL(hAPP(hAPP(X28,X6),X5))=>(hBOOL(hAPP(hAPP(X80,X6),X5))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_fun(X3,tc_HOL_Obool))),X28),X80)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__predicate2D)). 4.46/4.68 fof(fact_div__mult__self1__is__id, axiom, ![X12, X11, X4]:(class_Divides_Osemiring__div(X4)=>(c_Groups_Ozero__class_Ozero(X4)!=X11=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)),X11)=X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__self1__is__id)). 4.46/4.68 fof(fact_div__mult__self2__is__id, axiom, ![X12, X11, X4]:((c_Groups_Ozero__class_Ozero(X4)!=X11=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11)),X11)=X12)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__self2__is__id)). 4.46/4.68 fof(fact_Abs__Integ__induct, axiom, ![X6, X28]:(hBOOL(hAPP(X28,X6))<=![X44]:(hBOOL(hAPP(X28,hAPP(c_Int_OAbs__Integ,X44)))<=hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X44),c_Int_OInteg)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Abs__Integ__induct)). 4.46/4.68 fof(fact_neg__less__nonneg, axiom, ![X18, X4]:(class_Groups_Olinordered__ab__group__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X18))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__less__nonneg)). 4.46/4.68 fof(fact_add__diff__inverse, axiom, ![X17, X19]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X17)))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17))=X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__diff__inverse)). 4.46/4.68 fof(fact_power__abs, axiom, ![X17, X12, X4]:(class_Rings_Olinordered__idom(X4)=>hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__abs)). 4.46/4.68 fof(fact_listsum__simps_I2_J, axiom, ![X57, X48, X4]:(class_Groups_Omonoid__add(X4)=>hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X48),hAPP(c_List_Omonoid__add__class_Olistsum(X4),X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__simps_I2_J)). 4.46/4.68 fof(fact_INF__const, axiom, ![X153, X4, X2, X3]:(class_Complete__Lattice_Ocomplete__lattice(X3)=>(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X3),X2),hAPP(c_COMBK(X3,X4),X153))=X153<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__const)). 4.46/4.68 fof(fact_minus__le__self__iff, axiom, ![X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X18))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)),X18)))<=class_Groups_Olinordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__le__self__iff)). 4.46/4.68 fof(fact_less__minus__self__iff, axiom, ![X18, X4]:(class_Rings_Olinordered__idom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__minus__self__iff)). 4.46/4.68 fof(fact_le__minus__self__iff, axiom, ![X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),c_Groups_Ozero__class_Ozero(X4))))<=class_Groups_Olinordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__minus__self__iff)). 4.46/4.68 fof(fact_sgn__if, axiom, ![X48, X4]:(class_Groups_Osgn__if(X4)=>((X48=c_Groups_Ozero__class_Ozero(X4)=>c_Groups_Osgn__class_Osgn(X4,X48)=c_Groups_Ozero__class_Ozero(X4))&(c_Groups_Ozero__class_Ozero(X4)!=X48=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X48))=>c_Groups_Oone__class_Oone(X4)=c_Groups_Osgn__class_Osgn(X4,X48))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X48)))=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))=c_Groups_Osgn__class_Osgn(X4,X48)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__if)). 4.46/4.68 fof(fact_SUP__const, axiom, ![X153, X4, X2, X3]:((X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>X153=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X3),X2),hAPP(c_COMBK(X3,X4),X153)))<=class_Complete__Lattice_Ocomplete__lattice(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__const)). 4.46/4.68 fof(fact_abs__minus__le__zero, axiom, ![X12, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12))),c_Groups_Ozero__class_Ozero(X4)))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__minus__le__zero)). 4.46/4.68 fof(fact_ivl__disj__int_I8_J, axiom, ![X23, X67, X4]:(class_Orderings_Oorder(X4)=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X67),X23)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I8_J)). 4.46/4.68 fof(fact_ivl__disj__int_I2_J, axiom, ![X23, X67, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X67)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X67),X23))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I2_J)). 4.46/4.68 fof(fact_append1__eq__conv, axiom, ![X5, X32, X6, X7, X4]:(hAPP(hAPP(c_List_Oappend(X4),X32),hAPP(hAPP(c_List_Olist_OCons(X4),X5),c_List_Olist_ONil(X4)))=hAPP(hAPP(c_List_Oappend(X4),X7),hAPP(hAPP(c_List_Olist_OCons(X4),X6),c_List_Olist_ONil(X4)))<=>(X32=X7&X5=X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append1__eq__conv)). 4.46/4.68 fof(fact_divmod__int__rel__div, axiom, ![X111, X112, X11, X12]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X11=>X112=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11))<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,X11),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X112),X111)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__div)). 4.46/4.68 fof(fact_posDivAlg__correct, axiom, ![X11, X12]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,X11),c_Divides_OposDivAlg(X12,X11))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_posDivAlg__correct)). 4.46/4.68 fof(fact_equivp__def, axiom, ![X26, X4]:(c_Equiv__Relations_Oequivp(X4,X26)<=>![X42, X44]:(hAPP(X26,X42)=hAPP(X26,X44)<=>hBOOL(hAPP(hAPP(X26,X42),X44)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equivp__def)). 4.46/4.68 fof(fact_union__fold__insert, axiom, ![X1, X2, X4]:(hAPP(hAPP(c_Finite__Set_Ofold(X4,tc_fun(X4,tc_HOL_Obool),c_Set_Oinsert(X4)),X1),X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_union__fold__insert)). 4.46/4.68 fof(fact_negDivAlg__correct, axiom, ![X11, X12]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,X11),c_Divides_OnegDivAlg(X12,X11))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negDivAlg__correct)). 4.46/4.68 fof(fact_rel__pow__0__E, axiom, ![X26, X5, X6, X4]:(X6=X5<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__0__E)). 4.46/4.68 fof(fact_ivl__disj__int_I7_J, axiom, ![X23, X67, X4]:(class_Orderings_Oorder(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X67,X23)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X23))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I7_J)). 4.46/4.68 fof(fact_ivl__disj__int_I6_J, axiom, ![X23, X67, X4]:(class_Orderings_Oorder(X4)=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X67,X23)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I6_J)). 4.46/4.68 fof(fact_ivl__disj__int_I5_J, axiom, ![X23, X67, X4]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X67,X23)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X23))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I5_J)). 4.46/4.68 fof(fact_ivl__disj__int_I4_J, axiom, ![X23, X67, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X67)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X67,X23))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I4_J)). 4.46/4.68 fof(fact_ivl__disj__int_I3_J, axiom, ![X23, X67, X4]:(class_Orderings_Oorder(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X67)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X67,X23))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I3_J)). 4.46/4.68 fof(fact_ivl__disj__int_I1_J, axiom, ![X23, X67, X4]:(class_Orderings_Oorder(X4)=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X67)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X67,X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I1_J)). 4.46/4.68 fof(fact_comm__monoid__big_Oinfinite, axiom, ![X50, X2, X62, X35, X27, X3, X4]:(c_Big__Operators_Ocomm__monoid__big(X4,X3,X27,X35,X62)=>(~(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))=>hAPP(hAPP(X62,X50),X2)=X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__monoid__big_Oinfinite)). 4.46/4.68 fof(fact_last__drop, axiom, ![X57, X4, X17]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)))=>c_List_Olast(X4,X57)=c_List_Olast(X4,hAPP(hAPP(c_List_Odrop(X4),X17),X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__drop)). 4.46/4.68 fof(fact_Min__le, axiom, ![X6, X2, X4]:(class_Orderings_Olinorder(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Big__Operators_Olinorder__class_OMin(X4,X2)),X6))<=hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__le)). 4.46/4.68 fof(fact_finite__Un, axiom, ![X82, X62, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X82))&hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X62)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X62),X82)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Un)). 4.46/4.68 fof(fact_image__constant__conv, axiom, ![X39, X3, X4, X2]:((hAPP(hAPP(c_Set_Oinsert(X3),X39),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))=hAPP(c_Set_Oimage(X4,X3,hAPP(c_COMBK(X3,X4),X39)),X2)<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2)&(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))=hAPP(c_Set_Oimage(X4,X3,hAPP(c_COMBK(X3,X4),X39)),X2)<=X2=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__constant__conv)). 4.46/4.68 fof(fact_Max__ge, axiom, ![X6, X2, X4]:(class_Orderings_Olinorder(X4)=>((hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),c_Big__Operators_Olinorder__class_OMax(X4,X2))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__ge)). 4.46/4.68 fof(fact_transfer__nat__int__set__relations_I2_J, axiom, ![X2, X6]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X6),X2))<=>hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__relations_I2_J)). 4.46/4.68 fof(fact_hd__map, axiom, ![X27, X3, X4, X7]:(c_List_Olist_ONil(X4)!=X7=>hAPP(c_List_Ohd(X3),hAPP(hAPP(c_List_Omap(X4,X3),X27),X7))=hAPP(X27,hAPP(c_List_Ohd(X4),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__map)). 4.46/4.68 fof(fact_inj__on__contraD, axiom, ![X5, X6, X2, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,X2)=>((hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>(hBOOL(hAPP(hAPP(c_member(X4),X5),X2))=>hAPP(X27,X5)!=hAPP(X27,X6)))<=X5!=X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__contraD)). 4.46/4.68 fof(fact_Suc__diff__le, axiom, ![X19, X17]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),X19))=>hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19)),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__diff__le)). 4.46/4.68 fof(fact_listrel__Nil1, axiom, ![X16, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_ONil(X4)),X7)),c_List_Olistrel(X4,X16)))=>X7=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__Nil1)). 4.46/4.68 fof(fact_listrel__Nil2, axiom, ![X16, X7, X4]:(X7=c_List_Olist_ONil(X4)<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),c_List_Olist_ONil(X4))),c_List_Olistrel(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__Nil2)). 4.46/4.68 fof(fact_filter__sort, axiom, ![X7, X27, X28, X4, X3]:(c_List_Olinorder__class_Osort__key(X4,X3,X27,hAPP(c_List_Ofilter(X4,X28),X7))=hAPP(c_List_Ofilter(X4,X28),c_List_Olinorder__class_Osort__key(X4,X3,X27,X7))<=class_Orderings_Olinorder(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__sort)). 4.46/4.68 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J, axiom, ![X6, X2]:(c_Nat__Transfer_Onat__set(X2)=>(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X6),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J)). 4.46/4.68 fof(fact_zero__less__int__conv, axiom, ![X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__int__conv)). 4.46/4.68 fof(fact_sgn__less, axiom, ![X18, X4]:(class_Rings_Olinordered__idom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Osgn__class_Osgn(X4,X18)),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__less)). 4.46/4.68 fof(fact_sgn__greater, axiom, ![X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),c_Groups_Osgn__class_Osgn(X4,X18)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X18)))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__greater)). 4.46/4.68 fof(fact_butlast__append, axiom, ![X57, X4, X72]:((hAPP(hAPP(c_List_Oappend(X4),X57),c_List_Obutlast(X4,X72))=c_List_Obutlast(X4,hAPP(hAPP(c_List_Oappend(X4),X57),X72))<=c_List_Olist_ONil(X4)!=X72)&(c_List_Obutlast(X4,hAPP(hAPP(c_List_Oappend(X4),X57),X72))=c_List_Obutlast(X4,X57)<=c_List_Olist_ONil(X4)=X72)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast__append)). 4.46/4.68 fof(fact_finite__UNIV__inj__surj, axiom, ![X27, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))=>(hAPP(c_Set_Oimage(X4,X4,X27),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))<=c_Fun_Oinj__on(X4,X4,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UNIV__inj__surj)). 4.46/4.68 fof(fact_sup__Inf__absorb, axiom, ![X18, X2, X4]:(((hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X18),c_Big__Operators_Olattice__class_OInf__fin(X4,X2))=X18<=hBOOL(hAPP(hAPP(c_member(X4),X18),X2)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__Inf__absorb)). 4.46/4.68 fof(fact_inf__Sup__absorb, axiom, ![X18, X2, X4]:(class_Lattices_Olattice(X4)=>((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X18),c_Big__Operators_Olattice__class_OSup__fin(X4,X2))=X18<=hBOOL(hAPP(hAPP(c_member(X4),X18),X2)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__Sup__absorb)). 4.46/4.68 fof(fact_min__max_Oinf_Oleft__idem, axiom, ![X11, X12, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X12),X11))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X12),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf_Oleft__idem)). 4.46/4.68 fof(fact_min__max_Osup_Oleft__idem, axiom, ![X11, X12, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X12),X11)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X12),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup_Oleft__idem)). 4.46/4.68 fof(fact_inj__on__def, axiom, ![X2, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,X2)<=>![X42]:(![X66]:(hBOOL(hAPP(hAPP(c_member(X4),X66),X2))=>(hAPP(X27,X42)=hAPP(X27,X66)=>X42=X66))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__def)). 4.46/4.68 fof(fact_of__nat__Suc, axiom, ![X19, X4]:(class_Rings_Osemiring__1(X4)=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Nat_OSuc,X19))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__Suc)). 4.46/4.68 fof(fact_ComplI, axiom, ![X2, X39, X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X39),X2)))=>hBOOL(hAPP(hAPP(c_member(X4),X39),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ComplI)). 4.46/4.68 fof(fact_mod__less__divisor, axiom, ![X19, X17]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17)),X17))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__less__divisor)). 4.46/4.68 fof(fact_pos__mod__bound, axiom, ![X12, X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11)),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__mod__bound)). 4.46/4.68 fof(fact_mod__le__divisor, axiom, ![X19, X17]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17)),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__le__divisor)). 4.46/4.68 fof(fact_zmod__le__nonneg__dividend, axiom, ![X15, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X15)),X19))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__le__nonneg__dividend)). 4.46/4.68 fof(fact_ranI, axiom, ![X3, X37, X4, X18, X22]:(hAPP(X22,X18)=hAPP(c_Option_Ooption_OSome(X4),X37)=>hBOOL(hAPP(hAPP(c_member(X4),X37),c_Map_Oran(X3,X4,X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ranI)). 4.46/4.68 fof(fact_insort__key_Osimps_I1_J, axiom, ![X6, X27, X4, X3]:(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X3,X27),X6),c_List_Olist_ONil(X4))=hAPP(hAPP(c_List_Olist_OCons(X4),X6),c_List_Olist_ONil(X4))<=class_Orderings_Olinorder(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__key_Osimps_I1_J)). 4.46/4.68 fof(fact_fun__left__comm_Ofun__left__comm__apply, axiom, ![X50, X29, X27, X3, X4]:(c_Finite__Set_Ofun__left__comm(X29,X3,hAPP(hAPP(c_COMBB(X4,tc_fun(X3,X3),X29),X27),X50))<=c_Finite__Set_Ofun__left__comm(X4,X3,X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofun__left__comm__apply)). 4.46/4.68 fof(fact_remove1__idem, axiom, ![X7, X6, X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7))))=>c_List_Oremove1(X4,X6,X7)=X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1__idem)). 4.46/4.68 fof(fact_neg__mod__bound, axiom, ![X12, X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__mod__bound)). 4.46/4.68 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply, axiom, ![X50, X29, X27, X3, X4]:(c_Finite__Set_Ofun__left__comm__idem(X4,X3,X27)=>c_Finite__Set_Ofun__left__comm__idem(X29,X3,hAPP(hAPP(c_COMBB(X4,tc_fun(X3,X3),X29),X27),X50))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem_Ofun__left__comm__idem__apply)). 4.46/4.68 fof(fact_finite__converse, axiom, ![X16, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X3,X4)),X16))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X3)),hAPP(c_Relation_Oconverse(X3,X4),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__converse)). 4.46/4.68 fof(fact_exists1__code, axiom, ![X28, X4]:(class_Enum_Oenum(X4)=>(c_List_Olist__ex1(X4,X28,c_Enum_Oenum__class_Oenum(X4))<=>?[X42]:(hBOOL(hAPP(X28,X42))&![X44]:(X44=X42<=hBOOL(hAPP(X28,X44)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_exists1__code)). 4.46/4.68 fof(fact_UnCI, axiom, ![X2, X1, X39, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X39),X2))<=~(hBOOL(hAPP(hAPP(c_member(X4),X39),X1))))=>hBOOL(hAPP(hAPP(c_member(X4),X39),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UnCI)). 4.46/4.68 fof(fact_override__on__def, axiom, ![X50, X27, X3, X2, X18, X4]:((~(hBOOL(hAPP(hAPP(c_member(X4),X18),X2)))=>hAPP(X27,X18)=hAPP(c_Fun_Ooverride__on(X4,X3,X27,X50,X2),X18))&(hBOOL(hAPP(hAPP(c_member(X4),X18),X2))=>hAPP(X50,X18)=hAPP(c_Fun_Ooverride__on(X4,X3,X27,X50,X2),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_override__on__def)). 4.46/4.68 fof(fact_in__set__sublistD, axiom, ![X73, X7, X6, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),c_List_Osublist(X4,X7,X73))))=>hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__sublistD)). 4.46/4.68 fof(fact_notin__set__remove1, axiom, ![X5, X7, X6, X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),c_List_Oremove1(X4,X5,X7)))))<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_notin__set__remove1)). 4.46/4.68 fof(fact_setprod__1, axiom, ![X2, X3, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X4),hAPP(c_COMBK(X4,X3),c_Groups_Oone__class_Oone(X4))),X2)=c_Groups_Oone__class_Oone(X4)<=class_Groups_Ocomm__monoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__1)). 4.46/4.68 fof(fact_setsum__0, axiom, ![X2, X3, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),hAPP(c_COMBK(X4,X3),c_Groups_Ozero__class_Ozero(X4))),X2)=c_Groups_Ozero__class_Ozero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__0)). 4.46/4.68 fof(fact_set__takeWhileD, axiom, ![X7, X28, X6, X4]:((hBOOL(hAPP(X28,X6))&hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7))))<=hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),c_List_OtakeWhile(X4,X28,X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__takeWhileD)). 4.46/4.68 fof(fact_hd__in__set, axiom, ![X4, X7]:(X7!=c_List_Olist_ONil(X4)=>hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_List_Ohd(X4),X7)),hAPP(c_List_Oset(X4),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__in__set)). 4.46/4.68 fof(fact_sgn__neg, axiom, ![X12, X4]:((c_Groups_Osgn__class_Osgn(X4,X12)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__neg)). 4.46/4.68 fof(fact_Id__on__iff, axiom, ![X2, X5, X6, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_Relation_OId__on(X4,X2)))<=>(X5=X6&hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__on__iff)). 4.46/4.68 fof(fact_card__seteq, axiom, ![X2, X1, X4]:(((X2=X1<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X1)),hAPP(c_Finite__Set_Ocard(X4),X2))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__seteq)). 4.46/4.68 fof(fact_insert__dom, axiom, ![X3, X5, X4, X6, X27]:(hAPP(X27,X6)=hAPP(c_Option_Ooption_OSome(X4),X5)=>hAPP(hAPP(c_Set_Oinsert(X3),X6),c_Map_Odom(X3,X4,X27))=c_Map_Odom(X3,X4,X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__dom)). 4.46/4.68 fof(fact_INT__constant, axiom, ![X39, X3, X4, X2]:((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X2=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),X39))=c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))&(X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),X39))=X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__constant)). 4.46/4.68 fof(fact_map__add__dom__app__simps_I1_J, axiom, ![X175, X174, X3, X22, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X22),c_Map_Odom(X4,X3,X174)))=>hAPP(X174,X22)=hAPP(c_Map_Omap__add(X4,X3,X175,X174),X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__dom__app__simps_I1_J)). 4.46/4.68 fof(fact_split__paired__All, axiom, ![X3, X4, X28]:(![X125, X119]:hBOOL(hAPP(X28,hAPP(hAPP(c_Product__Type_OPair(X4,X3),X125),X119)))<=>![X138]:hBOOL(hAPP(X28,X138))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__paired__All)). 4.46/4.68 fof(fact_div__mult__self__is__m, axiom, ![X19, X17]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X17)),X17)=X19<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__self__is__m)). 4.46/4.68 fof(fact_div__mult__self1__is__m, axiom, ![X19, X17]:(X19=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X19)),X17)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__self1__is__m)). 4.46/4.68 fof(fact_equivp__transp, axiom, ![X35, X5, X6, X26, X4]:(c_Equiv__Relations_Oequivp(X4,X26)=>((hBOOL(hAPP(hAPP(X26,X5),X35))=>hBOOL(hAPP(hAPP(X26,X6),X35)))<=hBOOL(hAPP(hAPP(X26,X6),X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equivp__transp)). 4.46/4.68 fof(fact_sgn__1__neg, axiom, ![X18, X4]:((hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))=c_Groups_Osgn__class_Osgn(X4,X18)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__1__neg)). 4.46/4.68 fof(fact_abs__ge__minus__self, axiom, ![X12, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__ge__minus__self)). 4.46/4.68 fof(fact_zero__le__square, axiom, ![X12, X4]:(class_Rings_Olinordered__ring(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__square)). 4.46/4.68 fof(fact_less__add__one, axiom, ![X12, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),c_Groups_Oone__class_Oone(X4))))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__add__one)). 4.46/4.68 fof(fact_list__all2__rev, axiom, ![X32, X7, X28, X3, X4]:(c_List_Olist__all2(X4,X3,X28,hAPP(c_List_Orev(X4),X7),hAPP(c_List_Orev(X3),X32))<=>c_List_Olist__all2(X4,X3,X28,X7,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__rev)). 4.46/4.68 fof(fact_domI, axiom, ![X3, X37, X4, X18, X22]:(hAPP(c_Option_Ooption_OSome(X4),X37)=hAPP(X22,X18)=>hBOOL(hAPP(hAPP(c_member(X3),X18),c_Map_Odom(X3,X4,X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_domI)). 4.46/4.68 fof(fact_less__imp__diff__less, axiom, ![X17, X15, X20]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X15))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X17)),X15))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__imp__diff__less)). 4.46/4.68 fof(fact_mod__Suc, axiom, ![X17, X19]:((hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17))!=X17=>hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X19),X17))&(hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17))=X17=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X19),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__Suc)). 4.46/4.68 fof(fact_the__inv__into__f__f, axiom, ![X6, X2, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,X2)=>(hAPP(c_Fun_Othe__inv__into(X4,X3,X2,X27),hAPP(X27,X6))=X6<=hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__inv__into__f__f)). 4.46/4.68 fof(fact_remove1__insort, axiom, ![X7, X6, X4]:(X7=c_List_Oremove1(X4,X6,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)),X6),X7))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1__insort)). 4.46/4.68 fof(fact_termination__basic__simps_I1_J, axiom, ![X49, X47, X48]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),X49)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_termination__basic__simps_I1_J)). 4.46/4.68 fof(fact_Powp__def, axiom, ![X1, X2, X4]:(![X42]:(hBOOL(hAPP(X2,X42))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X1)))<=>hBOOL(hAPP(c_Predicate_OPowp(X4,X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Powp__def)). 4.46/4.68 fof(fact_eq__diff__iff, axiom, ![X14, X22, X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X22))=>((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22),X45)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14),X45)<=>X14=X22)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__diff__iff)). 4.46/4.68 fof(fact_option__map__eq__Some, axiom, ![X5, X192, X27, X4, X3]:(hAPP(hAPP(c_Option_Omap(X3,X4),X27),X192)=hAPP(c_Option_Ooption_OSome(X4),X5)<=>?[X132]:(X5=hAPP(X27,X132)&hAPP(c_Option_Ooption_OSome(X3),X132)=X192)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option__map__eq__Some)). 4.46/4.68 fof(fact_trans__less__add2, axiom, ![X19, X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X20)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trans__less__add2)). 4.46/4.68 fof(fact_termination__basic__simps_I3_J, axiom, ![X49, X47, X48]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X48),X47))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X48),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),X49)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_termination__basic__simps_I3_J)). 4.46/4.68 fof(fact_trans__le__add2, axiom, ![X19, X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X20)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trans__le__add2)). 4.46/4.68 fof(fact_single__valued__rel__pow, axiom, ![X14, X26, X4]:(c_Relation_Osingle__valued(X4,X4,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X14),X26))<=c_Relation_Osingle__valued(X4,X4,X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__rel__pow)). 4.46/4.68 fof(fact_Suc__lessI, axiom, ![X17, X19]:((hAPP(c_Nat_OSuc,X19)!=X17=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19)),X17)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__lessI)). 4.46/4.68 fof(fact_negD, axiom, ![X48]:(?[X199]:X48=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X199)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X48),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negD)). 4.46/4.68 fof(fact_inj__mapD, axiom, ![X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))<=c_Fun_Oinj__on(tc_List_Olist(X4),tc_List_Olist(X3),hAPP(c_List_Omap(X4,X3),X27),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__mapD)). 4.46/4.68 fof(fact_abs__le__D2, axiom, ![X11, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),X11)))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__le__D2)). 4.46/4.68 fof(fact_in__set__butlastD, axiom, ![X7, X6, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),c_List_Obutlast(X4,X7))))=>hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__butlastD)). 4.46/4.68 fof(fact_inj__on__diff, axiom, ![X1, X2, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,X2)=>c_Fun_Oinj__on(X4,X3,X27,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__diff)). 4.46/4.68 fof(fact_sorted__sort__key, axiom, ![X7, X27, X3, X4]:(c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X27),c_List_Olinorder__class_Osort__key(X3,X4,X27,X7)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__sort__key)). 4.46/4.68 fof(fact_Sup__set__fold, axiom, ![X7, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>hAPP(c_List_Ofoldl(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4),c_Orderings_Obot__class_Obot(X4)),X7)=c_Complete__Lattice_OSup__class_OSup(X4,hAPP(c_List_Oset(X4),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__set__fold)). 4.46/4.68 fof(fact_Inf__set__fold, axiom, ![X7, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>hAPP(c_List_Ofoldl(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4),c_Orderings_Otop__class_Otop(X4)),X7)=c_Complete__Lattice_OInf__class_OInf(X4,hAPP(c_List_Oset(X4),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__set__fold)). 4.46/4.68 fof(fact_not__sum__squares__lt__zero, axiom, ![X47, X48, X4]:(class_Rings_Olinordered__ring(X4)=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X48),X48)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X47),X47))),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__sum__squares__lt__zero)). 4.46/4.68 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J, axiom, ![X48, X4]:(class_Rings_Ocomm__ring__1(X4)=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),X48)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))),X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J)). 4.46/4.68 fof(fact_sup2CI, axiom, ![X3, X4, X2, X5, X6, X1]:(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X3,tc_HOL_Obool))),X2),X1),X6),X5))<=(hBOOL(hAPP(hAPP(X2,X6),X5))<=~(hBOOL(hAPP(hAPP(X1,X6),X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup2CI)). 4.46/4.68 fof(fact_listsum__eq__0__nat__iff__nat, axiom, ![X136]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X136)<=>![X42]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X42),hAPP(c_List_Oset(tc_Nat_Onat),X136)))=>X42=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__eq__0__nat__iff__nat)). 4.46/4.68 fof(fact_power__inject__exp, axiom, ![X14, X22, X18, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X18))=>(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X18),X14)=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X18),X22)<=>X22=X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__inject__exp)). 4.46/4.68 fof(fact_div__neg__neg__trivial, axiom, ![X11, X12]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),X12))=>c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__neg__neg__trivial)). 4.46/4.68 fof(fact_lessThan__iff, axiom, ![X45, X24, X4]:(class_Orderings_Oord(X4)=>(hBOOL(hAPP(hAPP(c_member(X4),X24),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X45)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessThan__iff)). 4.46/4.68 fof(fact_list__update__same__conv, axiom, ![X6, X7, X4, X24]:((X7=hAPP(hAPP(c_List_Olist__update(X4,X7),X24),X6)<=>X6=hAPP(hAPP(c_List_Onth(X4),X7),X24))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__same__conv)). 4.46/4.68 fof(fact_last__map, axiom, ![X27, X3, X4, X7]:(X7!=c_List_Olist_ONil(X4)=>hAPP(X27,c_List_Olast(X4,X7))=c_List_Olast(X3,hAPP(hAPP(c_List_Omap(X4,X3),X27),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__map)). 4.46/4.68 fof(fact_atMost__iff, axiom, ![X45, X24, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X24),X45))<=>hBOOL(hAPP(hAPP(c_member(X4),X24),hAPP(c_SetInterval_Oord__class_OatMost(X4),X45))))<=class_Orderings_Oord(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atMost__iff)). 4.46/4.68 fof(fact_greaterThan__iff, axiom, ![X45, X24, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X24),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X45)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X45),X24)))<=class_Orderings_Oord(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThan__iff)). 4.46/4.68 fof(fact_atLeast__iff, axiom, ![X45, X24, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X24),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X45)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X45),X24)))<=class_Orderings_Oord(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast__iff)). 4.46/4.68 fof(fact_card__image, axiom, ![X2, X27, X3, X4]:(hAPP(c_Finite__Set_Ocard(X3),hAPP(c_Set_Oimage(X4,X3,X27),X2))=hAPP(c_Finite__Set_Ocard(X4),X2)<=c_Fun_Oinj__on(X4,X3,X27,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__image)). 4.46/4.68 fof(fact_single__valued__rel__comp, axiom, ![X68, X29, X16, X3, X4]:((c_Relation_Osingle__valued(X4,X29,hAPP(hAPP(c_Relation_Orel__comp(X4,X3,X29),X16),X68))<=c_Relation_Osingle__valued(X3,X29,X68))<=c_Relation_Osingle__valued(X4,X3,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__rel__comp)). 4.46/4.68 fof(fact_Inf__insert, axiom, ![X2, X18, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X18),c_Complete__Lattice_OInf__class_OInf(X4,X2))=c_Complete__Lattice_OInf__class_OInf(X4,hAPP(hAPP(c_Set_Oinsert(X4),X18),X2))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__insert)). 4.46/4.68 fof(fact_Sup__insert, axiom, ![X2, X18, X4]:(c_Complete__Lattice_OSup__class_OSup(X4,hAPP(hAPP(c_Set_Oinsert(X4),X18),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X18),c_Complete__Lattice_OSup__class_OSup(X4,X2))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__insert)). 4.46/4.68 fof(fact_doubleton__eq__iff, axiom, ![X87, X39, X37, X18, X4]:(((X37=X87&X18=X39)|(X87=X18&X39=X37))<=>hAPP(hAPP(c_Set_Oinsert(X4),X39),hAPP(hAPP(c_Set_Oinsert(X4),X87),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=hAPP(hAPP(c_Set_Oinsert(X4),X18),hAPP(hAPP(c_Set_Oinsert(X4),X37),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_doubleton__eq__iff)). 4.46/4.68 fof(fact_nat__mult__eq__cancel1, axiom, ![X14, X22, X45]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X45))=>(X22=X14<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X14)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X22))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__eq__cancel1)). 4.46/4.68 fof(fact_minus__shift__def, axiom, ![X111, X31, X15]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X15),X31)))=>c_Random_Ominus__shift(X111,X15,X31)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X15),X31))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X15),X31))=>c_Random_Ominus__shift(X111,X15,X31)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X111),X15)),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__shift__def)). 4.46/4.68 fof(fact_small__lazy__prod__def, axiom, ![X133, X3, X4]:(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X4,X3),X133)=c_Lazy__Sequence_Oproduct(X4,X3,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X4,X133),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X3,X133))<=(class_Lazy__Sequence_Osmall__lazy(X3)&class_Lazy__Sequence_Osmall__lazy(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__lazy__prod__def)). 4.46/4.68 fof(fact_last__in__set, axiom, ![X4, X172]:(hBOOL(hAPP(hAPP(c_member(X4),c_List_Olast(X4,X172)),hAPP(c_List_Oset(X4),X172)))<=c_List_Olist_ONil(X4)!=X172), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__in__set)). 4.46/4.68 fof(fact_sorted__distinct__set__unique, axiom, ![X32, X7, X4]:(class_Orderings_Olinorder(X4)=>(((c_List_Olinorder__class_Osorted(X4,X32)=>((hAPP(c_List_Oset(X4),X32)=hAPP(c_List_Oset(X4),X7)=>X32=X7)<=hBOOL(hAPP(c_List_Odistinct(X4),X32))))<=hBOOL(hAPP(c_List_Odistinct(X4),X7)))<=c_List_Olinorder__class_Osorted(X4,X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__distinct__set__unique)). 4.46/4.68 fof(fact_THE__default__def, axiom, ![X87, X4, X28]:((~(?[X42]:(![X44]:(X44=X42<=hBOOL(hAPP(X28,X44)))&hBOOL(hAPP(X28,X42))))=>X87=c_FunDef_OTHE__default(X4,X87,X28))&(c_FunDef_OTHE__default(X4,X87,X28)=c_HOL_OThe(X4,X28)<=?[X42]:(![X44]:(hBOOL(hAPP(X28,X44))=>X42=X44)&hBOOL(hAPP(X28,X42))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_THE__default__def)). 4.46/4.68 fof(fact_length__greater__0__conv, axiom, ![X7, X4]:(X7!=c_List_Olist_ONil(X4)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__greater__0__conv)). 4.46/4.68 fof(fact_length__sort, axiom, ![X7, X27, X4, X3]:(class_Orderings_Olinorder(X3)=>hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Olinorder__class_Osort__key(X4,X3,X27,X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__sort)). 4.46/4.68 fof(fact_list__all2__rev1, axiom, ![X32, X7, X28, X3, X4]:(c_List_Olist__all2(X4,X3,X28,hAPP(c_List_Orev(X4),X7),X32)<=>c_List_Olist__all2(X4,X3,X28,X7,hAPP(c_List_Orev(X3),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__rev1)). 4.46/4.68 fof(fact_minus__diff__eq, axiom, ![X11, X12, X4]:(class_Groups_Oab__group__add(X4)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X12)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__diff__eq)). 4.46/4.68 fof(fact_finite__nat__set__iff__bounded, axiom, ![X122]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X122))<=>?[X90]:![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X90))<=hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X42),X122)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__nat__set__iff__bounded)). 4.46/4.68 fof(fact_finite__nat__set__iff__bounded__le, axiom, ![X122]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X122))<=>?[X90]:![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X90))<=hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X42),X122)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__nat__set__iff__bounded__le)). 4.46/4.68 fof(fact_type__definition_ORep__range, axiom, ![X2, X101, X102, X3, X4]:(hAPP(c_Set_Oimage(X4,X3,X102),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=X2<=c_Typedef_Otype__definition(X4,X3,X102,X101,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_ORep__range)). 4.46/4.68 fof(fact_divmod__int__rel__neg, axiom, ![X97, X11, X12]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,X11),hAPP(c_Divides_OnegateSnd,X97)))<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11)),X97))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__neg)). 4.46/4.68 fof(fact_diff__diff__cancel, axiom, ![X17, X21]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),X21))=X21<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__diff__cancel)). 4.46/4.68 fof(fact_le__add__diff__inverse, axiom, ![X19, X17]:(X19=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__add__diff__inverse)). 4.46/4.68 fof(fact_neg__le__iff__le, axiom, ![X18, X37, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X37)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),X37)))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__le__iff__le)). 4.46/4.68 fof(fact_nat__le__linear, axiom, ![X17, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),X19))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__le__linear)). 4.46/4.68 fof(fact_zle__linear, axiom, ![X30, X49]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),X49))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X49),X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__linear)). 4.46/4.68 fof(fact_map__injective, axiom, ![X32, X7, X27, X4, X3]:(hAPP(hAPP(c_List_Omap(X3,X4),X27),X32)=hAPP(hAPP(c_List_Omap(X3,X4),X27),X7)=>(X32=X7<=c_Fun_Oinj__on(X3,X4,X27,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__injective)). 4.46/4.68 fof(fact_divmod__int__rel__mod, axiom, ![X111, X112, X11, X12]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X11=>c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11)=X111)<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,X11),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X112),X111)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__mod)). 4.46/4.68 fof(fact_of__nat__less__imp__less, axiom, ![X17, X19, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X19)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X17)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X17)))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__less__imp__less)). 4.46/4.68 fof(fact_ab__diff__minus, axiom, ![X11, X12, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X11)<=class_Groups_Oab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ab__diff__minus)). 4.46/4.68 fof(fact_fun__left__comm__idem_Ofun__left__idem, axiom, ![X35, X6, X27, X3, X4]:(c_Finite__Set_Ofun__left__comm__idem(X4,X3,X27)=>hAPP(hAPP(X27,X6),hAPP(hAPP(X27,X6),X35))=hAPP(hAPP(X27,X6),X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem_Ofun__left__idem)). 4.46/4.68 fof(fact_Times__empty, axiom, ![X1, X2, X3, X4]:(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X3),tc_HOL_Obool))=hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),X1))<=>(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))=X1|c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Times__empty)). 4.46/4.68 fof(fact_set__replicate__conv__if, axiom, ![X6, X4, X14]:((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(c_List_Oset(X4),c_List_Oreplicate(X4,X14,X6))<=X14=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(X14!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>hAPP(c_List_Oset(X4),c_List_Oreplicate(X4,X14,X6))=hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__replicate__conv__if)). 4.46/4.68 fof(fact_diff__def, axiom, ![X11, X12, X4]:(class_Groups_Ogroup__add(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__def)). 4.46/4.68 fof(fact_fun__left__comm_Ofold__graph__determ, axiom, ![X5, X6, X2, X35, X27, X3, X4]:(c_Finite__Set_Ofun__left__comm(X4,X3,X27)=>((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X3,X27,X35,X2),X5))=>X6=X5)<=hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X3,X27,X35,X2),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__graph__determ)). 4.46/4.68 fof(fact_diff__minus__eq__add, axiom, ![X11, X12, X4]:(class_Groups_Ogroup__add(X4)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__minus__eq__add)). 4.46/4.68 fof(fact_subset__insertI2, axiom, ![X37, X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X37),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__insertI2)). 4.46/4.68 fof(fact_finite__surj, axiom, ![X27, X1, X3, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_Set_Oimage(X4,X3,X27),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__surj)). 4.46/4.68 fof(fact_sorted__insort, axiom, ![X7, X6, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Osorted(X4,X7)<=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)),X6),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__insort)). 4.46/4.68 fof(fact_diff__eq, axiom, ![X47, X48, X4]:(class_Lattices_Oboolean__algebra(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X47))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X48),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__eq)). 4.46/4.68 fof(fact_leI, axiom, ![X47, X48, X4]:(class_Orderings_Olinorder(X4)=>(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),X47)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X47),X48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_leI)). 4.46/4.68 fof(fact_disjoint__eq__subset__Compl, axiom, ![X1, X2, X4]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_disjoint__eq__subset__Compl)). 4.46/4.68 fof(fact_nth__replicate, axiom, ![X48, X4, X17, X21]:(hAPP(hAPP(c_List_Onth(X4),c_List_Oreplicate(X4,X17,X48)),X21)=X48<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__replicate)). 4.46/4.68 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J, axiom, ![X47, X48, X4]:(class_Rings_Ocomm__ring__1(X4)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X48),X47)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X48),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J)). 4.46/4.68 fof(fact_Inter__lower, axiom, ![X2, X1, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X2)),X1))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X1),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__lower)). 4.46/4.68 fof(fact_Union__upper, axiom, ![X2, X1, X4]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X1),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__upper)). 4.46/4.68 fof(fact_zero__less__imp__eq__int, axiom, ![X15]:(?[X199]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X199))&hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X199)=X15)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__imp__eq__int)). 4.46/4.68 fof(fact_Inf__lower, axiom, ![X2, X6, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Complete__Lattice_OInf__class_OInf(X4,X2)),X6)))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__lower)). 4.46/4.68 fof(fact_Sup__upper, axiom, ![X2, X6, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>(hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),c_Complete__Lattice_OSup__class_OSup(X4,X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__upper)). 4.46/4.68 fof(fact_length__n__lists__elem, axiom, ![X7, X14, X32, X4]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X32),hAPP(c_List_Oset(tc_List_Olist(X4)),c_Enum_On__lists(X4,X14,X7))))=>X14=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__n__lists__elem)). 4.46/4.68 fof(fact_abs__if, axiom, ![X12, X4]:(class_Groups_Oabs__if(X4)=>((hAPP(c_Groups_Oabs__class_Oabs(X4),X12)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),c_Groups_Ozero__class_Ozero(X4))))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),c_Groups_Ozero__class_Ozero(X4))))=>hAPP(c_Groups_Oabs__class_Oabs(X4),X12)=X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__if)). 4.46/4.68 fof(fact_PowI, axiom, ![X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))=>hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X4),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_PowI)). 4.46/4.68 fof(fact_subset__singletonD, axiom, ![X6, X2, X4]:((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X2|hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=X2)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__singletonD)). 4.46/4.68 fof(fact_mod__add__self2, axiom, ![X11, X12, X4]:(c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11),X11)=c_Divides_Odiv__class_Omod(X4,X12,X11)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__add__self2)). 4.46/4.68 fof(fact_mod__add__self1, axiom, ![X12, X11, X4]:(class_Divides_Osemiring__div(X4)=>c_Divides_Odiv__class_Omod(X4,X12,X11)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__add__self1)). 4.46/4.68 fof(fact_peek__and__def, axiom, ![X68, X117, X109, X28, X4]:(hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X4,X28,X109),X117),X68))<=>(hBOOL(hAPP(hAPP(X28,X117),X68))&hBOOL(hAPP(X109,X68)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_peek__and__def)). 4.46/4.68 fof(fact_accp_Osimps, axiom, ![X18, X16, X4]:(![X42]:(hBOOL(hAPP(c_Wellfounded_Oaccp(X4,X16),X42))<=hBOOL(hAPP(hAPP(X16,X42),X18)))<=>hBOOL(hAPP(c_Wellfounded_Oaccp(X4,X16),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_accp_Osimps)). 4.46/4.68 fof(fact_insert__iff, axiom, ![X2, X37, X18, X4]:((X37=X18|hBOOL(hAPP(hAPP(c_member(X4),X18),X2)))<=>hBOOL(hAPP(hAPP(c_member(X4),X18),hAPP(hAPP(c_Set_Oinsert(X4),X37),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__iff)). 4.46/4.68 fof(fact_accp_Oequations, axiom, ![X18, X16, X4]:(![X42]:(hBOOL(hAPP(hAPP(X16,X42),X18))=>hBOOL(hAPP(c_Wellfounded_Oaccp(X4,X16),X42)))<=>hBOOL(hAPP(c_Wellfounded_Oaccp(X4,X16),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_accp_Oequations)). 4.46/4.68 fof(fact_atLeastLessThan__empty__iff2, axiom, ![X37, X18, X4]:((hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X18),X37)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),X37))))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__empty__iff2)). 4.46/4.68 fof(fact_inf__le1, axiom, ![X47, X48, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X47)),X48))<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__le1)). 4.46/4.68 fof(fact_inf__sup__ord_I1_J, axiom, ![X47, X48, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X47)),X48))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__ord_I1_J)). 4.46/4.68 fof(fact_z3mod__def, axiom, ![X15, X31]:((c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X31))=c_SMT_Oz3mod(X15,X31)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X31))))&(c_SMT_Oz3mod(X15,X31)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,X31)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X31)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_z3mod__def)). 4.46/4.68 fof(fact_linorder__antisym__conv2, axiom, ![X5, X6, X4]:(class_Orderings_Olinorder(X4)=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),X5)))<=>X5=X6)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__antisym__conv2)). 4.46/4.68 fof(fact_xt1_I12_J, axiom, ![X11, X12, X4]:(class_Orderings_Oorder(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12)))<=X12!=X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_xt1_I12_J)). 4.46/4.68 fof(fact_inf__le2, axiom, ![X47, X48, X4]:(class_Lattices_Osemilattice__inf(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X47)),X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__le2)). 4.46/4.68 fof(fact_inf__sup__ord_I2_J, axiom, ![X47, X48, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X47)),X47))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__ord_I2_J)). 4.46/4.68 fof(fact_sup__ge1, axiom, ![X47, X48, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X47)))<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__ge1)). 4.46/4.68 fof(fact_inf__sup__ord_I3_J, axiom, ![X47, X48, X4]:(class_Lattices_Olattice(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__ord_I3_J)). 4.46/4.68 fof(fact_atLeastLessThan__inj_I1_J, axiom, ![X87, X39, X37, X18, X4]:((hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X18),X37)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X39),X87)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),X87))=>X18=X39)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),X37))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__inj_I1_J)). 4.46/4.68 fof(fact_atLeastLessThan__inj_I2_J, axiom, ![X87, X39, X37, X18, X4]:(class_Orderings_Olinorder(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X18),X37))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X39),X87))=>X87=X37))<=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X18),X37)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X39),X87))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__inj_I2_J)). 4.46/4.68 fof(fact_sup__ge2, axiom, ![X48, X47, X4]:(class_Lattices_Osemilattice__sup(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X47),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__ge2)). 4.46/4.68 fof(fact_inf__sup__ord_I4_J, axiom, ![X48, X47, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X47),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X47)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__ord_I4_J)). 4.46/4.68 fof(fact_wf__Int1, axiom, ![X93, X16, X4]:(c_Wellfounded_Owf(X4,X16)=>c_Wellfounded_Owf(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),X93))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__Int1)). 4.46/4.68 fof(fact_wf__Int2, axiom, ![X93, X16, X4]:(c_Wellfounded_Owf(X4,X16)=>c_Wellfounded_Owf(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X93),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__Int2)). 4.46/4.68 fof(fact_fun__left__comm_Ofold__equality, axiom, ![X5, X2, X35, X27, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X3,X27,X35,X2),X5))=>X5=hAPP(hAPP(c_Finite__Set_Ofold(X4,X3,X27),X35),X2))<=c_Finite__Set_Ofun__left__comm(X4,X3,X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__equality)). 4.46/4.68 fof(fact_distinct__insort__insert, axiom, ![X6, X27, X7, X4, X3]:(class_Orderings_Olinorder(X3)=>(hBOOL(hAPP(c_List_Odistinct(X4),c_List_Olinorder__class_Oinsort__insert__key(X4,X3,X27,X6,X7)))<=hBOOL(hAPP(c_List_Odistinct(X4),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__insort__insert)). 4.46/4.68 fof(fact_add1__zle__eq, axiom, ![X35, X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X36),c_Groups_Oone__class_Oone(tc_Int_Oint))),X35))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add1__zle__eq)). 4.46/4.68 fof(fact_type__definition_OAbs__inverse, axiom, ![X5, X2, X101, X102, X3, X4]:((hBOOL(hAPP(hAPP(c_member(X3),X5),X2))=>X5=hAPP(X102,hAPP(X101,X5)))<=c_Typedef_Otype__definition(X4,X3,X102,X101,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_OAbs__inverse)). 4.46/4.68 fof(fact_le__supE, axiom, ![X48, X11, X12, X4]:(class_Lattices_Osemilattice__sup(X4)=>(~((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X48)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X48))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X12),X11)),X48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__supE)). 4.46/4.68 fof(fact_le__infE, axiom, ![X11, X12, X48, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X12),X11)))=>~((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X12)))))<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__infE)). 4.46/4.68 fof(fact_restrict__out, axiom, ![X22, X3, X2, X6, X4]:(c_Option_Ooption_ONone(X3)=hAPP(c_Map_Orestrict__map(X4,X3,X22,X2),X6)<=~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__out)). 4.46/4.68 fof(fact_ord_OlessThan__iff, axiom, ![X45, X170, X24, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X24),c_SetInterval_Oord_OlessThan(X4,X170,X45)))<=>hBOOL(hAPP(hAPP(X170,X24),X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OlessThan__iff)). 4.46/4.68 fof(fact_ord_OatMost__iff, axiom, ![X45, X171, X24, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X24),c_SetInterval_Oord_OatMost(X4,X171,X45)))<=>hBOOL(hAPP(hAPP(X171,X24),X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OatMost__iff)). 4.46/4.68 fof(fact_ord_OgreaterThan__iff, axiom, ![X45, X170, X24, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X24),c_SetInterval_Oord_OgreaterThan(X4,X170,X45)))<=>hBOOL(hAPP(hAPP(X170,X45),X24))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OgreaterThan__iff)). 4.46/4.68 fof(fact_not__less__eq, axiom, ![X14, X22]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),hAPP(c_Nat_OSuc,X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__less__eq)). 4.46/4.68 fof(fact_ord_OatLeast__iff, axiom, ![X45, X171, X24, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X24),c_SetInterval_Oord_OatLeast(X4,X171,X45)))<=>hBOOL(hAPP(hAPP(X171,X45),X24))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OatLeast__iff)). 4.46/4.68 fof(fact_le__Suc__eq, axiom, ![X14, X22]:((hAPP(c_Nat_OSuc,X14)=X22|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),hAPP(c_Nat_OSuc,X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__Suc__eq)). 4.46/4.68 fof(fact_fun__upd__def, axiom, ![X37, X27, X3, X4, X18, X6]:((X37=hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X3),X27),X18),X37),X6)<=X18=X6)&(X6!=X18=>hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X3),X27),X18),X37),X6)=hAPP(X27,X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__def)). 4.46/4.68 fof(fact_less__code__numeral__def, axiom, ![X22, X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X14),X22))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X14)),hAPP(c_Code__Numeral_Onat__of,X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__code__numeral__def)). 4.46/4.68 fof(fact_Suc__mono, axiom, ![X17, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19)),hAPP(c_Nat_OSuc,X17)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__mono)). 4.46/4.68 fof(fact_less__eq__code__numeral__def, axiom, ![X22, X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X14)),hAPP(c_Code__Numeral_Onat__of,X22)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X14),X22))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__code__numeral__def)). 4.46/4.68 fof(fact_finite__surj__inj, axiom, ![X27, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Fun_Oinj__on(X4,X4,X27,X2)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X4,X4,X27),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__surj__inj)). 4.46/4.68 fof(fact_Ints__odd__nonzero, axiom, ![X18, X4]:((c_Groups_Ozero__class_Ozero(X4)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),X18)),X18)<=hBOOL(hAPP(hAPP(c_member(X4),X18),c_Int_Oring__1__class_OInts(X4))))<=class_Int_Oring__char__0(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__odd__nonzero)). 4.46/4.68 fof(fact_sorted__list__of__set__sort__remdups, axiom, ![X7, X4]:(class_Orderings_Olinorder(X4)=>c_List_Olinorder__class_Osorted__list__of__set(X4,hAPP(c_List_Oset(X4),X7))=c_List_Olinorder__class_Osort__key(X4,X4,c_COMBI(X4),c_List_Oremdups(X4,X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__list__of__set__sort__remdups)). 4.46/4.68 fof(fact_distinct__card, axiom, ![X7, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X7))=>hAPP(c_Finite__Set_Ocard(X4),hAPP(c_List_Oset(X4),X7))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__card)). 4.46/4.68 fof(fact_atLeastatMost__empty__iff, axiom, ![X37, X18, X4]:(class_Orderings_Oorder(X4)=>(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X18),X37)))<=>c_SetInterval_Oord__class_OatLeastAtMost(X4,X18,X37)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastatMost__empty__iff)). 4.46/4.68 fof(fact_finite__option__UNIV, axiom, ![X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X4)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X4),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__option__UNIV)). 4.46/4.68 fof(fact_type__definition_ORep, axiom, ![X6, X2, X101, X102, X3, X4]:(c_Typedef_Otype__definition(X4,X3,X102,X101,X2)=>hBOOL(hAPP(hAPP(c_member(X3),hAPP(X102,X6)),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_ORep)). 4.46/4.68 fof(fact_divide__minus1, axiom, ![X48, X4]:((class_Fields_Ofield__inverse__zero(X4)&class_Int_Onumber__ring(X4))=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X48),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin))=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__minus1)). 4.46/4.68 fof(fact_Suc__pred_H, axiom, ![X17]:(X17=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),c_Groups_Oone__class_Oone(tc_Nat_Onat)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__pred_H)). 4.46/4.68 fof(fact_abs__ge__zero, axiom, ![X12, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__ge__zero)). 4.46/4.68 fof(fact_of__nat__0__le__iff, axiom, ![X17, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X17)))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__0__le__iff)). 4.46/4.68 fof(fact_mult__minus1, axiom, ![X49, X4]:(hAPP(c_Groups_Ouminus__class_Ouminus(X4),X49)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin)),X49)<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__minus1)). 4.46/4.68 fof(fact_domIff, axiom, ![X22, X3, X18, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X18),c_Map_Odom(X4,X3,X22)))<=>hAPP(X22,X18)!=c_Option_Ooption_ONone(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_domIff)). 4.46/4.68 fof(fact_of__int__minus, axiom, ![X49, X4]:(class_Rings_Oring__1(X4)=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X49))=hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X49))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__minus)). 4.46/4.68 fof(fact_arith__simps_I30_J, axiom, ![X30, X4]:(class_Int_Onumber__ring(X4)=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X30))=hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_arith__simps_I30_J)). 4.46/4.68 fof(fact_abs__of__neg, axiom, ![X12, X4]:((hAPP(c_Groups_Oabs__class_Oabs(X4),X12)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),c_Groups_Ozero__class_Ozero(X4))))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__of__neg)). 4.46/4.68 fof(fact_abs__of__nonpos, axiom, ![X12, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),c_Groups_Ozero__class_Ozero(X4)))=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)=hAPP(c_Groups_Oabs__class_Oabs(X4),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__of__nonpos)). 4.46/4.68 fof(fact_dom__eq__empty__conv, axiom, ![X27, X3, X4]:(X27=hAPP(c_COMBK(tc_Option_Ooption(X3),X4),c_Option_Ooption_ONone(X3))<=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=c_Map_Odom(X4,X3,X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__eq__empty__conv)). 4.46/4.68 fof(fact_int__zle__neg, axiom, ![X22, X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22))))<=>(X14=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&X22=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__zle__neg)). 4.46/4.68 fof(fact_semilattice__big_OF__eq, axiom, ![X2, X62, X27, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(c_Finite__Set_Ofold1(X4,X27),X2)=hAPP(X62,X2))<=c_Big__Operators_Osemilattice__big(X4,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_semilattice__big_OF__eq)). 4.46/4.68 fof(fact_folding__one_Oeq__fold, axiom, ![X2, X62, X27, X4]:(c_Finite__Set_Ofolding__one(X4,X27,X62)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(c_Finite__Set_Ofold1(X4,X27),X2)=hAPP(X62,X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Oeq__fold)). 4.46/4.68 fof(fact_mult__minus1__right, axiom, ![X49, X4]:(hAPP(c_Groups_Ouminus__class_Ouminus(X4),X49)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X49),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__minus1__right)). 4.46/4.68 fof(fact_list__update__beyond, axiom, ![X48, X21, X57, X4]:(X57=hAPP(hAPP(c_List_Olist__update(X4,X57),X21),X48)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),X21))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__beyond)). 4.46/4.68 fof(fact_min__max_Ole__supE, axiom, ![X48, X11, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X12),X11)),X48))=>~((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X48)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X48)))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__supE)). 4.46/4.68 fof(fact_hd__append2, axiom, ![X72, X4, X57]:(hAPP(c_List_Ohd(X4),hAPP(hAPP(c_List_Oappend(X4),X57),X72))=hAPP(c_List_Ohd(X4),X57)<=X57!=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__append2)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, axiom, ![X11, X12, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, axiom, ![X10, X12, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X12)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)). 4.46/4.68 fof(fact_fun__Compl__def, axiom, ![X6, X2, X3, X4]:(class_Groups_Ouminus(X4)=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(X2,X6))=hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,X4)),X2),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__Compl__def)). 4.46/4.68 fof(fact_mult__sgn__abs, axiom, ![X48, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Osgn__class_Osgn(X4,X48)),hAPP(c_Groups_Oabs__class_Oabs(X4),X48))=X48<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__sgn__abs)). 4.46/4.68 fof(fact_card__eq__UNIV__imp__eq__UNIV, axiom, ![X2, X4]:((hAPP(c_Finite__Set_Ocard(X4),X2)=hAPP(c_Finite__Set_Ocard(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>X2=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__eq__UNIV__imp__eq__UNIV)). 4.46/4.68 fof(fact_diff__add__cancel, axiom, ![X11, X12, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X11)),X11)=X12<=class_Groups_Ogroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__add__cancel)). 4.46/4.68 fof(fact_add__diff__cancel, axiom, ![X11, X12, X4]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)),X11)=X12<=class_Groups_Ogroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__diff__cancel)). 4.46/4.68 fof(fact_sup__inf__absorb, axiom, ![X47, X48, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X47))=X48<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__inf__absorb)). 4.46/4.68 fof(fact_inf__sup__absorb, axiom, ![X47, X48, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X47))=X48<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__absorb)). 4.46/4.68 fof(fact_finite__Diff, axiom, ![X1, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Diff)). 4.46/4.68 fof(fact_finite__Int, axiom, ![X82, X62, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X62),X82)))<=(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X82))|hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X62)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Int)). 4.46/4.68 fof(fact_sup__commute, axiom, ![X47, X48, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X47)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X47),X48)<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__commute)). 4.46/4.68 fof(fact_min__max_Oinf__le1, axiom, ![X47, X48, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),X47)),X48))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__le1)). 4.46/4.68 fof(fact_min__max_Oinf__le2, axiom, ![X47, X48, X4]:(class_Orderings_Olinorder(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),X47)),X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__le2)). 4.46/4.68 fof(fact_inf__sup__aci_I5_J, axiom, ![X47, X48, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X47),X48)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X47)<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I5_J)). 4.46/4.68 fof(fact_le__maxI1, axiom, ![X47, X48, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X48),X47)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__maxI1)). 4.46/4.68 fof(fact_le__maxI2, axiom, ![X48, X47, X4]:(class_Orderings_Olinorder(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X47),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X48),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__maxI2)). 4.46/4.68 fof(fact_inf1I, axiom, ![X4, X1, X6, X2]:(hBOOL(hAPP(X2,X6))=>(hBOOL(hAPP(X1,X6))=>hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf1I)). 4.46/4.68 fof(fact_finite__Diff2, axiom, ![X2, X1, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Diff2)). 4.46/4.68 fof(fact_div__eq, axiom, ![X111, X112, X17, X19]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19),X17)=X112<=hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X19,X17),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X112),X111)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__eq)). 4.46/4.68 fof(fact_map__add__None, axiom, ![X45, X14, X22, X4, X3]:(hAPP(c_Map_Omap__add(X3,X4,X22,X14),X45)=c_Option_Ooption_ONone(X4)<=>(c_Option_Ooption_ONone(X4)=hAPP(X14,X45)&c_Option_Ooption_ONone(X4)=hAPP(X22,X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__None)). 4.46/4.68 fof(fact_min__max_Osup__commute, axiom, ![X47, X48, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X48),X47)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X47),X48)<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__commute)). 4.46/4.68 fof(fact_finite__Domain, axiom, ![X16, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X3)),X16))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Relation_ODomain(X4,X3),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Domain)). 4.46/4.68 fof(fact_finite__Range, axiom, ![X16, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Relation_ORange(X4,X3),X16)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X3)),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Range)). 4.46/4.68 fof(fact_insort__insert__triv, axiom, ![X7, X6, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_member(X4),X6),hAPP(c_List_Oset(X4),X7)))=>X7=c_List_Olinorder__class_Oinsort__insert__key(X4,X4,c_COMBI(X4),X6,X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__insert__triv)). 4.46/4.68 fof(fact_min__max_Oinf__commute, axiom, ![X47, X48, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X47),X48)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),X47)<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__commute)). 4.46/4.68 fof(fact_inf__commute, axiom, ![X47, X48, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X47)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X47),X48)<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__commute)). 4.46/4.68 fof(fact_self__quotient, axiom, ![X111, X112, X12]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,X12),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X112),X111)))=>(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X12=>X112=c_Groups_Oone__class_Oone(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_self__quotient)). 4.46/4.68 fof(fact_inf__sup__aci_I1_J, axiom, ![X47, X48, X4]:(class_Lattices_Olattice(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X47),X48)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I1_J)). 4.46/4.68 fof(fact_DiffD1, axiom, ![X1, X2, X39, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X39),X2))<=hBOOL(hAPP(hAPP(c_member(X4),X39),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DiffD1)). 4.46/4.68 fof(fact_IntE, axiom, ![X1, X2, X39, X4]:(~((~(hBOOL(hAPP(hAPP(c_member(X4),X39),X1)))<=hBOOL(hAPP(hAPP(c_member(X4),X39),X2))))<=hBOOL(hAPP(hAPP(c_member(X4),X39),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_IntE)). 4.46/4.68 fof(fact_greaterThanAtMost__empty__iff2, axiom, ![X67, X45, X4]:(class_Orderings_Oorder(X4)=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X45,X67)<=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X45),X67))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThanAtMost__empty__iff2)). 4.46/4.68 fof(fact_self__remainder, axiom, ![X111, X112, X12]:((X111=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<=X12!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,X12),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X112),X111)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_self__remainder)). 4.46/4.68 fof(fact_IntD2, axiom, ![X1, X2, X39, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X39),X1))<=hBOOL(hAPP(hAPP(c_member(X4),X39),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_IntD2)). 4.46/4.68 fof(fact_Ints__of__int, axiom, ![X35, X4]:(class_Rings_Oring__1(X4)=>hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X35)),c_Int_Oring__1__class_OInts(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__of__int)). 4.46/4.68 fof(fact_Ints__number__of, axiom, ![X36, X4]:(class_Int_Onumber__ring(X4)=>hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X36)),c_Int_Oring__1__class_OInts(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__number__of)). 4.46/4.68 fof(fact_Ints__of__nat, axiom, ![X14, X4]:(hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X14)),c_Int_Oring__1__class_OInts(X4)))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__of__nat)). 4.46/4.68 fof(fact_of__nat__in__Nats, axiom, ![X14, X4]:(class_Rings_Osemiring__1(X4)=>hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X14)),c_Nat_Osemiring__1__class_ONats(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__in__Nats)). 4.46/4.68 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J, axiom, ![X2]:(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2))=hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X2)<=c_Nat__Transfer_Onat__set(X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J)). 4.46/4.68 fof(fact_wfE__pf, axiom, ![X2, X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_Relation_OImage(X4,X4,X26),X2)))=>X2=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=c_Wellfounded_Owf(X4,X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfE__pf)). 4.46/4.68 fof(fact_inj__on__Un__image__eq__iff, axiom, ![X1, X2, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))=>(X2=X1<=>hAPP(c_Set_Oimage(X4,X3,X27),X2)=hAPP(c_Set_Oimage(X4,X3,X27),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__Un__image__eq__iff)). 4.46/4.68 fof(fact_subset__inj__on, axiom, ![X2, X1, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,X1)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))=>c_Fun_Oinj__on(X4,X3,X27,X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__inj__on)). 4.46/4.68 fof(fact_listrelp_Oequations_I2_J, axiom, ![X253, X135, X250, X123, X16, X4]:((c_List_Olistrelp(X4,X16,X250,X253)&hBOOL(hAPP(hAPP(X16,X123),X135)))<=>c_List_Olistrelp(X4,X16,hAPP(hAPP(c_List_Olist_OCons(X4),X123),X250),hAPP(hAPP(c_List_Olist_OCons(X4),X135),X253))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrelp_Oequations_I2_J)). 4.46/4.68 fof(fact_filter__replicate, axiom, ![X14, X4, X6, X28]:((hAPP(c_List_Ofilter(X4,X28),c_List_Oreplicate(X4,X14,X6))=c_List_Olist_ONil(X4)<=~(hBOOL(hAPP(X28,X6))))&(hBOOL(hAPP(X28,X6))=>hAPP(c_List_Ofilter(X4,X28),c_List_Oreplicate(X4,X14,X6))=c_List_Oreplicate(X4,X14,X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__replicate)). 4.46/4.68 fof(fact_drop__eq__Nil, axiom, ![X7, X14, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)),X14))<=>c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Odrop(X4),X14),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__eq__Nil)). 4.46/4.68 fof(fact_RangeP_Oequations, axiom, ![X135, X16, X3, X4]:(?[X125]:hBOOL(hAPP(hAPP(X16,X125),X135))<=>hBOOL(hAPP(c_Predicate_ORangeP(X4,X3,X16),X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_RangeP_Oequations)). 4.46/4.68 fof(fact_DomainP_Oequations, axiom, ![X123, X16, X3, X4]:(hBOOL(hAPP(c_Predicate_ODomainP(X4,X3,X16),X123))<=>?[X138]:hBOOL(hAPP(hAPP(X16,X123),X138))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DomainP_Oequations)). 4.46/4.68 fof(fact_mod__div__trivial, axiom, ![X11, X12, X4]:(class_Divides_Osemiring__div(X4)=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),c_Divides_Odiv__class_Omod(X4,X12,X11)),X11)=c_Groups_Ozero__class_Ozero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__div__trivial)). 4.46/4.68 fof(fact_mod__mult__self2__is__0, axiom, ![X11, X12, X4]:(class_Divides_Osemiring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11),X11)=c_Groups_Ozero__class_Ozero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__self2__is__0)). 4.46/4.68 fof(fact_mod__mult__self1__is__0, axiom, ![X12, X11, X4]:(class_Divides_Osemiring__div(X4)=>c_Groups_Ozero__class_Ozero(X4)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__self1__is__0)). 4.46/4.68 fof(fact_inj__image__eq__iff, axiom, ![X1, X2, X27, X3, X4]:(c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>(X1=X2<=>hAPP(c_Set_Oimage(X4,X3,X27),X2)=hAPP(c_Set_Oimage(X4,X3,X27),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__image__eq__iff)). 4.46/4.68 fof(fact_finite__imageI, axiom, ![X58, X3, X62, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X4,X3,X58),X62)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X62))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__imageI)). 4.46/4.68 fof(fact_distinct__drop, axiom, ![X21, X57, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Odrop(X4),X21),X57)))<=hBOOL(hAPP(c_List_Odistinct(X4),X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__drop)). 4.46/4.68 fof(fact_distinct__take, axiom, ![X21, X57, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X57))=>hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Otake(X4),X21),X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__take)). 4.46/4.68 fof(fact_le__iff__add, axiom, ![X14, X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))<=>?[X266]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X266)=X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__iff__add)). 4.46/4.68 fof(fact_list__all__simps_I1_J, axiom, ![X7, X6, X28, X4]:((c_List_Olist__all(X4,X28,X7)&hBOOL(hAPP(X28,X6)))<=>c_List_Olist__all(X4,X28,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__simps_I1_J)). 4.46/4.68 fof(fact_power__0__Suc, axiom, ![X17, X4]:((class_Power_Opower(X4)&class_Rings_Osemiring__0(X4))=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Nat_OSuc,X17))=c_Groups_Ozero__class_Ozero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__0__Suc)). 4.46/4.68 fof(fact_min__max_OInf__fin_Osingleton, axiom, ![X6, X4]:(c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=X6<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Osingleton)). 4.46/4.68 fof(fact_min__max_OSup__fin_Osingleton, axiom, ![X6, X4]:(class_Orderings_Olinorder(X4)=>c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Osingleton)). 4.46/4.68 fof(fact_sgn__1__pos, axiom, ![X18, X4]:(class_Rings_Olinordered__idom(X4)=>(c_Groups_Osgn__class_Osgn(X4,X18)=c_Groups_Oone__class_Oone(X4)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__1__pos)). 4.46/4.68 fof(fact_pos__zmult__eq__1__iff, axiom, ![X14, X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))=>(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22),X14)=c_Groups_Oone__class_Oone(tc_Int_Oint)<=>(c_Groups_Oone__class_Oone(tc_Int_Oint)=X14&c_Groups_Oone__class_Oone(tc_Int_Oint)=X22))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__zmult__eq__1__iff)). 4.46/4.68 fof(fact_add__lessD1, axiom, ![X15, X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20)),X15))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X15))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__lessD1)). 4.46/4.68 fof(fact_single__valued__subset, axiom, ![X68, X16, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X16),X68))=>(c_Relation_Osingle__valued(X4,X3,X68)=>c_Relation_Osingle__valued(X4,X3,X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__subset)). 4.46/4.68 fof(fact_distinct__sort, axiom, ![X7, X27, X4, X3]:(class_Orderings_Olinorder(X3)=>(hBOOL(hAPP(c_List_Odistinct(X4),X7))<=>hBOOL(hAPP(c_List_Odistinct(X4),c_List_Olinorder__class_Osort__key(X4,X3,X27,X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__sort)). 4.46/4.68 fof(fact_add__leD1, axiom, ![X17, X15, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X15)),X17))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__leD1)). 4.46/4.68 fof(fact_list__all__append, axiom, ![X32, X7, X28, X4]:(c_List_Olist__all(X4,X28,hAPP(hAPP(c_List_Oappend(X4),X7),X32))<=>(c_List_Olist__all(X4,X28,X32)&c_List_Olist__all(X4,X28,X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__append)). 4.46/4.68 fof(fact_distinct__butlast, axiom, ![X4, X57]:((hBOOL(hAPP(c_List_Odistinct(X4),c_List_Obutlast(X4,X57)))<=hBOOL(hAPP(c_List_Odistinct(X4),X57)))<=c_List_Olist_ONil(X4)!=X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__butlast)). 4.46/4.68 fof(fact_Rep__Integ__induct, axiom, ![X28, X5]:(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X5),c_Int_OInteg))=>(hBOOL(hAPP(X28,X5))<=![X42]:hBOOL(hAPP(X28,hAPP(c_Int_ORep__Integ,X42))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Rep__Integ__induct)). 4.46/4.68 fof(fact_not__less__less__Suc__eq, axiom, ![X22, X14]:((X14=X22<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),hAPP(c_Nat_OSuc,X22))))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__less__less__Suc__eq)). 4.46/4.68 fof(fact_nth__via__drop, axiom, ![X72, X47, X57, X17, X4]:(hAPP(hAPP(c_List_Onth(X4),X57),X17)=X47<=hAPP(hAPP(c_List_Olist_OCons(X4),X47),X72)=hAPP(hAPP(c_List_Odrop(X4),X17),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__via__drop)). 4.46/4.68 fof(fact_Sup__fin__Sup, axiom, ![X2, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2=>c_Big__Operators_Olattice__class_OSup__fin(X4,X2)=c_Complete__Lattice_OSup__class_OSup(X4,X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin__Sup)). 4.46/4.68 fof(fact_int__one__le__iff__zero__less, axiom, ![X35]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X35))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X35))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__one__le__iff__zero__less)). 4.46/4.68 fof(fact_compl__sup__top, axiom, ![X48, X4]:(c_Orderings_Otop__class_Otop(X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X48)),X48)<=class_Lattices_Oboolean__algebra(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__sup__top)). 4.46/4.68 fof(fact_ab__left__minus, axiom, ![X12, X4]:(class_Groups_Oab__group__add(X4)=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ab__left__minus)). 4.46/4.68 fof(fact_Inf__fin__Inf, axiom, ![X2, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>((c_Complete__Lattice_OInf__class_OInf(X4,X2)=c_Big__Operators_Olattice__class_OInf__fin(X4,X2)<=X2!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin__Inf)). 4.46/4.68 fof(fact_right__minus, axiom, ![X12, X4]:(class_Groups_Ogroup__add(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12))=c_Groups_Ozero__class_Ozero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_right__minus)). 4.46/4.68 fof(fact_sup__compl__top, axiom, ![X48, X4]:(class_Lattices_Oboolean__algebra(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X48))=c_Orderings_Otop__class_Otop(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__compl__top)). 4.46/4.68 fof(fact_min__max_Osup__inf__absorb, axiom, ![X47, X48, X4]:(class_Orderings_Olinorder(X4)=>X48=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X48),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__inf__absorb)). 4.46/4.68 fof(fact_min__max_Oinf__sup__absorb, axiom, ![X47, X48, X4]:(class_Orderings_Olinorder(X4)=>X48=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X48),X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__sup__absorb)). 4.46/4.68 fof(fact_atLeastAtMost__singleton, axiom, ![X18, X4]:(class_Orderings_Oorder(X4)=>hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=c_SetInterval_Oord__class_OatLeastAtMost(X4,X18,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastAtMost__singleton)). 4.46/4.68 fof(fact_abs__le__D1, axiom, ![X11, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),X11)))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__le__D1)). 4.46/4.68 fof(fact_last__append, axiom, ![X57, X4, X72]:((c_List_Olist_ONil(X4)=X72=>c_List_Olast(X4,X57)=c_List_Olast(X4,hAPP(hAPP(c_List_Oappend(X4),X57),X72)))&(X72!=c_List_Olist_ONil(X4)=>c_List_Olast(X4,X72)=c_List_Olast(X4,hAPP(hAPP(c_List_Oappend(X4),X57),X72)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__append)). 4.46/4.68 fof(fact_last__ConsR, axiom, ![X48, X4, X57]:(X57!=c_List_Olist_ONil(X4)=>c_List_Olast(X4,X57)=c_List_Olast(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__ConsR)). 4.46/4.68 fof(fact_Nitpick_Owf_H__def, axiom, ![X16, X4]:((c_Wellfounded_Oacyclic(X4,X16)&(c_Nitpick_Ounknown(tc_HOL_Obool)|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X4)),X16))))<=>c_Nitpick_Owf_H(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Owf_H__def)). 4.46/4.68 fof(fact_dual__min, axiom, ![X4]:(class_Orderings_Olinorder(X4)=>c_Orderings_Oord_Omin(X4,hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X4)))=c_Orderings_Oord__class_Omax(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dual__min)). 4.46/4.68 fof(fact_nat__less__le, axiom, ![X14, X22]:((X14!=X22&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__less__le)). 4.46/4.68 fof(fact_dual__max, axiom, ![X4]:(c_Orderings_Oord_Omax(X4,hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X4)))=c_Orderings_Oord__class_Omin(X4)<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dual__max)). 4.46/4.68 fof(fact_distinct__n__lists, axiom, ![X17, X57, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X57))=>hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X4)),c_Enum_On__lists(X4,X17,X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__n__lists)). 4.46/4.68 fof(fact_distinct__filter, axiom, ![X28, X7, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),hAPP(c_List_Ofilter(X4,X28),X7)))<=hBOOL(hAPP(c_List_Odistinct(X4),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__filter)). 4.46/4.68 fof(fact_pigeonhole, axiom, ![X2, X27, X3, X4]:(~(c_Fun_Oinj__on(X3,X4,X27,X2))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),hAPP(c_Set_Oimage(X3,X4,X27),X2))),hAPP(c_Finite__Set_Ocard(X3),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pigeonhole)). 4.46/4.68 fof(fact_abs__sgn, axiom, ![X15, X4]:(class_Rings_Olinordered__idom(X4)=>hAPP(c_Groups_Oabs__class_Oabs(X4),X15)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X15),c_Groups_Osgn__class_Osgn(X4,X15))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__sgn)). 4.46/4.68 fof(fact_set__sort, axiom, ![X7, X27, X4, X3]:(hAPP(c_List_Oset(X4),c_List_Olinorder__class_Osort__key(X4,X3,X27,X7))=hAPP(c_List_Oset(X4),X7)<=class_Orderings_Olinorder(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__sort)). 4.46/4.68 fof(fact_weaken, axiom, ![X202, X283, X82, X4]:(c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,X283)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool)),X202),X283))=>c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,X202))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_weaken)). 4.46/4.68 fof(fact_thin, axiom, ![X82, X202, X208, X4]:((c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,X202)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool)),X208),X82)))<=c_Hoare__Mirabelle_Ohoare__derivs(X4,X208,X202)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_thin)). 4.46/4.68 fof(fact_Union__quotient, axiom, ![X16, X2, X4]:(c_Equiv__Relations_Oequiv(X4,X2,X16)=>c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X2),X16))=X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__quotient)). 4.46/4.68 fof(fact_restrict__map__def, axiom, ![X22, X3, X2, X6, X4]:((~(hBOOL(hAPP(hAPP(c_member(X4),X6),X2)))=>hAPP(c_Map_Orestrict__map(X4,X3,X22,X2),X6)=c_Option_Ooption_ONone(X3))&(hBOOL(hAPP(hAPP(c_member(X4),X6),X2))=>hAPP(X22,X6)=hAPP(c_Map_Orestrict__map(X4,X3,X22,X2),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__map__def)). 4.46/4.68 fof(fact_conversep_Ointros, axiom, ![X3, X4, X37, X18, X16]:(hBOOL(hAPP(hAPP(X16,X18),X37))=>hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4,X3,X16),X37),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conversep_Ointros)). 4.46/4.68 fof(fact_rev__predicate1D, axiom, ![X80, X4, X6, X28]:((hBOOL(hAPP(X80,X6))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X28),X80)))<=hBOOL(hAPP(X28,X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__predicate1D)). 4.46/4.68 fof(fact_finite__Field, axiom, ![X16, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Relation_OField(X4),X16)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X4)),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Field)). 4.46/4.68 fof(fact_min__max_OInf__fin_OF__eq, axiom, ![X2, X4]:((c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X2)=hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omin(X4)),X2)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_OF__eq)). 4.46/4.68 fof(fact_min__max_OSup__fin_OF__eq, axiom, ![X2, X4]:((c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X2)=hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omax(X4)),X2)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_OF__eq)). 4.46/4.68 fof(fact_enum__prod__def, axiom, ![X3, X4]:(c_Enum_Oenum__class_Oenum(tc_prod(X4,X3))=c_Enum_Oproduct(X4,X3,c_Enum_Oenum__class_Oenum(X4),c_Enum_Oenum__class_Oenum(X3))<=(class_Enum_Oenum(X3)&class_Enum_Oenum(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__prod__def)). 4.46/4.68 fof(fact_remove1__remdups, axiom, ![X48, X57, X4]:(c_List_Oremdups(X4,c_List_Oremove1(X4,X48,X57))=c_List_Oremove1(X4,X48,c_List_Oremdups(X4,X57))<=hBOOL(hAPP(c_List_Odistinct(X4),X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1__remdups)). 4.46/4.68 fof(fact_abs__ge__self, axiom, ![X12, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__ge__self)). 4.46/4.68 fof(fact_mult__cancel2, axiom, ![X14, X45, X22]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X45)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X45)<=>(X22=X14|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__cancel2)). 4.46/4.68 fof(fact_nat__mult__eq__cancel__disj, axiom, ![X14, X22, X45]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X14)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X22)<=>(X22=X14|X45=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__eq__cancel__disj)). 4.46/4.68 fof(fact_less__Suc__eq, axiom, ![X14, X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),hAPP(c_Nat_OSuc,X14)))<=>(X14=X22|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__Suc__eq)). 4.46/4.68 fof(fact_less__Suc__eq__le, axiom, ![X14, X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22),hAPP(c_Nat_OSuc,X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__Suc__eq__le)). 4.46/4.68 fof(fact_inf2D1, axiom, ![X5, X6, X1, X2, X3, X4]:(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X3,tc_HOL_Obool))),X2),X1),X6),X5))=>hBOOL(hAPP(hAPP(X2,X6),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf2D1)). 4.46/4.68 fof(fact_mod__pos__pos__trivial, axiom, ![X11, X12]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),X11))=>c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11)=X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__pos__pos__trivial)). 4.46/4.68 fof(fact_mod__neg__neg__trivial, axiom, ![X11, X12]:((c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11)=X12<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__neg__neg__trivial)). 4.46/4.68 fof(fact_inf2D2, axiom, ![X5, X6, X1, X2, X3, X4]:(hBOOL(hAPP(hAPP(X1,X6),X5))<=hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X3,tc_HOL_Obool))),X2),X1),X6),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf2D2)). 4.46/4.68 fof(fact_transfer__int__nat__set__relations_I3_J, axiom, ![X1, X2]:(c_Nat__Transfer_Onat__set(X2)=>(c_Nat__Transfer_Onat__set(X1)=>(hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)<=>X2=X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__set__relations_I3_J)). 4.46/4.68 fof(fact_wf__comp__self, axiom, ![X26, X4]:(c_Wellfounded_Owf(X4,X26)<=>c_Wellfounded_Owf(X4,hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X26),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__comp__self)). 4.46/4.68 fof(fact_ex__in__conv, axiom, ![X2, X4]:(?[X42]:hBOOL(hAPP(hAPP(c_member(X4),X42),X2))<=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__in__conv)). 4.46/4.68 fof(fact_Pow__iff, axiom, ![X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))<=>hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X4),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__iff)). 4.46/4.68 fof(fact_atLeastLessThan__empty, axiom, ![X18, X37, X4]:((hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X18),X37)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),X18)))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__empty)). 4.46/4.68 fof(fact_all__not__in__conv, axiom, ![X2, X4]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X2<=>![X42]:~(hBOOL(hAPP(hAPP(c_member(X4),X42),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__not__in__conv)). 4.46/4.68 fof(fact_listsum__foldl, axiom, ![X4]:(class_Groups_Omonoid__add(X4)=>c_List_Ofoldl(X4,X4,c_Groups_Oplus__class_Oplus(X4),c_Groups_Ozero__class_Ozero(X4))=c_List_Omonoid__add__class_Olistsum(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__foldl)). 4.46/4.68 fof(fact_set__eq__subset, axiom, ![X4, X1, X2]:(X2=X1<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X2))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__eq__subset)). 4.46/4.68 fof(fact_finite__fun__UNIVD2, axiom, ![X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,X3)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X4,X3),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__fun__UNIVD2)). 4.46/4.68 fof(fact_equivp__symp, axiom, ![X5, X6, X26, X4]:(c_Equiv__Relations_Oequivp(X4,X26)=>(hBOOL(hAPP(hAPP(X26,X6),X5))=>hBOOL(hAPP(hAPP(X26,X5),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equivp__symp)). 4.46/4.68 fof(fact_Max_OF__eq, axiom, ![X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omax(X4)),X2)=c_Big__Operators_Olinorder__class_OMax(X4,X2))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_OF__eq)). 4.46/4.68 fof(fact_Sup__fin_OF__eq, axiom, ![X2, X4]:(class_Lattices_Olattice(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(c_Finite__Set_Ofold1(X4,c_Lattices_Osemilattice__sup__class_Osup(X4)),X2)=c_Big__Operators_Olattice__class_OSup__fin(X4,X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_OF__eq)). 4.46/4.68 fof(fact_sup1E, axiom, ![X6, X1, X2, X4]:((~(hBOOL(hAPP(X2,X6)))=>hBOOL(hAPP(X1,X6)))<=hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup1E)). 4.46/4.68 fof(fact_take__all, axiom, ![X17, X57, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),X17))=>X57=hAPP(hAPP(c_List_Otake(X4),X17),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__all)). 4.46/4.68 fof(fact_Inf__fin_OF__eq, axiom, ![X2, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>hAPP(c_Finite__Set_Ofold1(X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),X2)=c_Big__Operators_Olattice__class_OInf__fin(X4,X2))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_OF__eq)). 4.46/4.68 fof(fact_Min_OF__eq, axiom, ![X2, X4]:((c_Big__Operators_Olinorder__class_OMin(X4,X2)=hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omin(X4)),X2)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_OF__eq)). 4.46/4.68 fof(fact_eq__card__imp__inj__on, axiom, ![X27, X3, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>(hAPP(c_Finite__Set_Ocard(X4),X2)=hAPP(c_Finite__Set_Ocard(X3),hAPP(c_Set_Oimage(X4,X3,X27),X2))=>c_Fun_Oinj__on(X4,X3,X27,X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__card__imp__inj__on)). 4.46/4.68 fof(fact_zero__less__one, axiom, ![X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),c_Groups_Oone__class_Oone(X4)))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__one)). 4.46/4.68 fof(fact_inf__absorb1, axiom, ![X47, X48, X4]:((X48=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X47)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X47)))<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__absorb1)). 4.46/4.68 fof(fact_inf__absorb2, axiom, ![X48, X47, X4]:(class_Lattices_Osemilattice__inf(X4)=>(X47=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X47)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X47),X48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__absorb2)). 4.46/4.68 fof(fact_le__iff__sup, axiom, ![X5, X6, X4]:(class_Lattices_Osemilattice__sup(X4)=>(X5=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X6),X5)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__iff__sup)). 4.46/4.68 fof(fact_zero__le__one, axiom, ![X4]:(class_Rings_Olinordered__semidom(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),c_Groups_Oone__class_Oone(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__one)). 4.46/4.68 fof(fact_wf__lex__prod, axiom, ![X193, X3, X194, X4]:((c_Wellfounded_Owf(tc_prod(X4,X3),c_Wellfounded_Olex__prod(X4,X3,X194,X193))<=c_Wellfounded_Owf(X3,X193))<=c_Wellfounded_Owf(X4,X194)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__lex__prod)). 4.46/4.68 fof(fact_transfer__int__nat__set__relations_I1_J, axiom, ![X2]:(c_Nat__Transfer_Onat__set(X2)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__set__relations_I1_J)). 4.46/4.68 fof(fact_sup__absorb1, axiom, ![X48, X47, X4]:((X48=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X47)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X47),X48)))<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__absorb1)). 4.46/4.68 fof(fact_abs__of__nonneg, axiom, ![X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>hAPP(c_Groups_Oabs__class_Oabs(X4),X12)=X12)<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__of__nonneg)). 4.46/4.68 fof(fact_abs__of__pos, axiom, ![X12, X4]:((X12=hAPP(c_Groups_Oabs__class_Oabs(X4),X12)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12)))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__of__pos)). 4.46/4.68 fof(fact_minus__unique, axiom, ![X11, X12, X4]:((hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)=X11<=c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11))<=class_Groups_Ogroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__unique)). 4.46/4.68 fof(fact_Suc__less__SucD, axiom, ![X17, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19)),hAPP(c_Nat_OSuc,X17)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__less__SucD)). 4.46/4.68 fof(fact_finite__acyclic__wf__converse, axiom, ![X16, X4]:((c_Wellfounded_Oacyclic(X4,X16)=>c_Wellfounded_Owf(X4,hAPP(c_Relation_Oconverse(X4,X4),X16)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X4)),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__acyclic__wf__converse)). 4.46/4.68 fof(fact_WT_Oequations_I5_J, axiom, ![X135, X123, X250]:((hBOOL(hAPP(c_Com_OWT,X123))&hBOOL(hAPP(c_Com_OWT,X135)))<=>hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X250,X123,X135)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WT_Oequations_I5_J)). 4.46/4.68 fof(fact_diff__0, axiom, ![X12, X4]:(class_Groups_Ogroup__add(X4)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),c_Groups_Ozero__class_Ozero(X4)),X12)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__0)). 4.46/4.68 fof(fact_list__ex__simps_I1_J, axiom, ![X7, X6, X28, X4]:((hBOOL(hAPP(X28,X6))|c_List_Olist__ex(X4,X28,X7))<=>c_List_Olist__ex(X4,X28,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__simps_I1_J)). 4.46/4.68 fof(fact_acc__wfD, axiom, ![X6, X16, X4]:(c_Wellfounded_Owf(X4,X16)=>hBOOL(hAPP(hAPP(c_member(X4),X6),c_Wellfounded_Oacc(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acc__wfD)). 4.46/4.68 fof(fact_sorted__insort__insert, axiom, ![X6, X7, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Osorted(X4,c_List_Olinorder__class_Oinsort__insert__key(X4,X4,c_COMBI(X4),X6,X7))<=c_List_Olinorder__class_Osorted(X4,X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__insort__insert)). 4.46/4.68 fof(fact_acyclic__subset, axiom, ![X16, X68, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),X68))=>c_Wellfounded_Oacyclic(X4,X16))<=c_Wellfounded_Oacyclic(X4,X68)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclic__subset)). 4.46/4.68 fof(fact_wf__subset, axiom, ![X109, X16, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X109),X16))=>c_Wellfounded_Owf(X4,X109))<=c_Wellfounded_Owf(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__subset)). 4.46/4.68 fof(fact_wfP__subset, axiom, ![X109, X16, X4]:(c_Wellfounded_OwfP(X4,X16)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X109),X16))=>c_Wellfounded_OwfP(X4,X109))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__subset)). 4.46/4.68 fof(fact_mod__eq, axiom, ![X111, X112, X17, X19]:(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X19,X17),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X112),X111)))=>c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17)=X111), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__eq)). 4.46/4.68 fof(fact_power__0__left, axiom, ![X17, X4]:(((hAPP(hAPP(c_Power_Opower__class_Opower(X4),c_Groups_Ozero__class_Ozero(X4)),X17)=c_Groups_Ozero__class_Ozero(X4)<=X17!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X17=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),c_Groups_Ozero__class_Ozero(X4)),X17)=c_Groups_Oone__class_Oone(X4)))<=(class_Rings_Osemiring__0(X4)&class_Power_Opower(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__0__left)). 4.46/4.68 fof(fact_compl__inf__bot, axiom, ![X48, X4]:(class_Lattices_Oboolean__algebra(X4)=>c_Orderings_Obot__class_Obot(X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X48)),X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__inf__bot)). 4.46/4.68 fof(fact_inf__compl__bot, axiom, ![X48, X4]:(class_Lattices_Oboolean__algebra(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X48))=c_Orderings_Obot__class_Obot(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__compl__bot)). 4.46/4.68 fof(fact_Suc__mult__cancel1, axiom, ![X14, X22, X45]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X45)),X14)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X45)),X22)<=>X22=X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__mult__cancel1)). 4.46/4.68 fof(fact_list__ex__append, axiom, ![X32, X7, X28, X4]:((c_List_Olist__ex(X4,X28,X7)|c_List_Olist__ex(X4,X28,X32))<=>c_List_Olist__ex(X4,X28,hAPP(hAPP(c_List_Oappend(X4),X7),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__append)). 4.46/4.68 fof(fact_abs__minus__cancel, axiom, ![X12, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12))=hAPP(c_Groups_Oabs__class_Oabs(X4),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__minus__cancel)). 4.46/4.68 fof(fact_Compl__atMost, axiom, ![X45, X4]:(class_Orderings_Olinorder(X4)=>hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X45))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__atMost)). 4.46/4.68 fof(fact_Compl__atLeast, axiom, ![X45, X4]:(class_Orderings_Olinorder(X4)=>hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X45))=hAPP(c_SetInterval_Oord__class_OlessThan(X4),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__atLeast)). 4.46/4.68 fof(fact_Compl__greaterThan, axiom, ![X45, X4]:(hAPP(c_SetInterval_Oord__class_OatMost(X4),X45)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X45))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__greaterThan)). 4.46/4.68 fof(fact_Compl__lessThan, axiom, ![X45, X4]:(class_Orderings_Olinorder(X4)=>hAPP(c_SetInterval_Oord__class_OatLeast(X4),X45)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__lessThan)). 4.46/4.68 fof(fact_equiv__listrel, axiom, ![X16, X2, X4]:(c_Equiv__Relations_Oequiv(tc_List_Olist(X4),c_List_Olists(X4,X2),c_List_Olistrel(X4,X16))<=c_Equiv__Relations_Oequiv(X4,X2,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__listrel)). 4.46/4.68 fof(fact_transfer__nat__int__set__relations_I1_J, axiom, ![X2]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__relations_I1_J)). 4.46/4.68 fof(fact_listrel__refl__on, axiom, ![X16, X2, X4]:(c_Relation_Orefl__on(X4,X2,X16)=>c_Relation_Orefl__on(tc_List_Olist(X4),c_List_Olists(X4,X2),c_List_Olistrel(X4,X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__refl__on)). 4.46/4.68 fof(fact_Pair__fst__snd__eq, axiom, ![X3, X4, X64, X68]:(X64=X68<=>(hAPP(c_Product__Type_Osnd(X4,X3),X64)=hAPP(c_Product__Type_Osnd(X4,X3),X68)&hAPP(c_Product__Type_Ofst(X4,X3),X68)=hAPP(c_Product__Type_Ofst(X4,X3),X64))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pair__fst__snd__eq)). 4.46/4.68 fof(fact_list__all2__lengthD, axiom, ![X32, X7, X28, X3, X4]:(c_List_Olist__all2(X4,X3,X28,X7,X32)=>hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__lengthD)). 4.46/4.68 fof(fact_finite__imageD, axiom, ![X2, X27, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Set_Oimage(X3,X4,X27),X2)))=>(c_Fun_Oinj__on(X3,X4,X27,X2)=>hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__imageD)). 4.46/4.68 fof(fact_finite_OinsertI, axiom, ![X18, X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Set_Oinsert(X4),X18),X2)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite_OinsertI)). 4.46/4.68 fof(fact_finite__Pow__iff, axiom, ![X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_OPow(X4),X2)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Pow__iff)). 4.46/4.68 fof(fact_rev__finite__subset, axiom, ![X2, X1, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__finite__subset)). 4.46/4.68 fof(fact_hd__rev, axiom, ![X4, X57]:(c_List_Olast(X4,X57)=hAPP(c_List_Ohd(X4),hAPP(c_List_Orev(X4),X57))<=c_List_Olist_ONil(X4)!=X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__rev)). 4.46/4.68 fof(fact_setsum_Oempty, axiom, ![X50, X3, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X50),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum_Oempty)). 4.46/4.68 fof(fact_inj__of__nat, axiom, ![X4]:(c_Fun_Oinj__on(tc_Nat_Onat,X4,c_Nat_Osemiring__1__class_Oof__nat(X4),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))<=class_Nat_Osemiring__char__0(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__of__nat)). 4.46/4.68 fof(fact_Ints__1, axiom, ![X4]:(class_Rings_Oring__1(X4)=>hBOOL(hAPP(hAPP(c_member(X4),c_Groups_Oone__class_Oone(X4)),c_Int_Oring__1__class_OInts(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__1)). 4.46/4.68 fof(fact_Nats__1, axiom, ![X4]:(class_Rings_Osemiring__1(X4)=>hBOOL(hAPP(hAPP(c_member(X4),c_Groups_Oone__class_Oone(X4)),c_Nat_Osemiring__1__class_ONats(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nats__1)). 4.46/4.68 fof(fact_atLeastatMost__empty, axiom, ![X18, X37, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X37),X18))=>c_SetInterval_Oord__class_OatLeastAtMost(X4,X18,X37)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastatMost__empty)). 4.46/4.68 fof(fact_mod__mod__trivial, axiom, ![X11, X12, X4]:(c_Divides_Odiv__class_Omod(X4,c_Divides_Odiv__class_Omod(X4,X12,X11),X11)=c_Divides_Odiv__class_Omod(X4,X12,X11)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mod__trivial)). 4.46/4.68 fof(fact_transfer__nat__int__set__relations_I3_J, axiom, ![X1, X2]:(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)<=>X2=X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__relations_I3_J)). 4.46/4.68 fof(fact_Ints__0, axiom, ![X4]:(hBOOL(hAPP(hAPP(c_member(X4),c_Groups_Ozero__class_Ozero(X4)),c_Int_Oring__1__class_OInts(X4)))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__0)). 4.46/4.68 fof(fact_Nats__0, axiom, ![X4]:(class_Rings_Osemiring__1(X4)=>hBOOL(hAPP(hAPP(c_member(X4),c_Groups_Ozero__class_Ozero(X4)),c_Nat_Osemiring__1__class_ONats(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nats__0)). 4.46/4.68 fof(fact_sorted__single, axiom, ![X48, X4]:(c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X48),c_List_Olist_ONil(X4)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__single)). 4.46/4.68 fof(fact_listsum__rev, axiom, ![X57, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(c_List_Omonoid__add__class_Olistsum(X4),X57)=hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(c_List_Orev(X4),X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__rev)). 4.46/4.68 fof(fact_triple_Oinject, axiom, ![X275, X164, X276, X182, X33, X183, X4]:(((X164=X33&X275=X182)&X276=X183)<=>hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X276),X164),X275)=hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X183),X33),X182)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_triple_Oinject)). 4.46/4.68 fof(fact_distinct__sublistI, axiom, ![X73, X7, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X7))=>hBOOL(hAPP(c_List_Odistinct(X4),c_List_Osublist(X4,X7,X73)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__sublistI)). 4.46/4.68 fof(fact_abs__idempotent, axiom, ![X12, X4]:(hAPP(c_Groups_Oabs__class_Oabs(X4),X12)=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__idempotent)). 4.46/4.68 fof(fact_abs__of__nat, axiom, ![X17, X4]:(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X17)=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X17))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__of__nat)). 4.46/4.68 fof(fact_of__int__of__nat__eq, axiom, ![X17, X4]:(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X17)=hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__of__nat__eq)). 4.46/4.68 fof(fact_distinct__remove1, axiom, ![X48, X57, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),c_List_Oremove1(X4,X48,X57)))<=hBOOL(hAPP(c_List_Odistinct(X4),X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__remove1)). 4.46/4.68 fof(fact_distinct__takeWhile, axiom, ![X28, X7, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X7))=>hBOOL(hAPP(c_List_Odistinct(X4),c_List_OtakeWhile(X4,X28,X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__takeWhile)). 4.46/4.68 fof(fact_distinct__insert, axiom, ![X48, X57, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),c_List_Oinsert(X4,X48,X57)))<=hBOOL(hAPP(c_List_Odistinct(X4),X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__insert)). 4.46/4.68 fof(fact_rp__inv__image__rp, axiom, ![X27, X3, X28, X4]:(c_FunDef_Oreduction__pair(X4,X28)=>c_FunDef_Oreduction__pair(X3,hAPP(hAPP(c_FunDef_Orp__inv__image(X4,X3),X28),X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rp__inv__image__rp)). 4.46/4.68 fof(fact_wf__inv__image, axiom, ![X27, X3, X16, X4]:(c_Wellfounded_Owf(X4,X16)=>c_Wellfounded_Owf(X3,hAPP(hAPP(c_Relation_Oinv__image(X4,X3),X16),X27))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__inv__image)). 4.46/4.68 fof(fact_abs__minus__one, axiom, ![X4]:(hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin))=c_Groups_Oone__class_Oone(X4)<=(class_Rings_Olinordered__idom(X4)&class_Int_Onumber__ring(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__minus__one)). 4.46/4.68 fof(fact_type__definition_OAbs__image, axiom, ![X2, X101, X102, X3, X4]:(hAPP(c_Set_Oimage(X3,X4,X101),X2)=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))<=c_Typedef_Otype__definition(X4,X3,X102,X101,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_OAbs__image)). 4.46/4.68 fof(fact_divmod__int__correct, axiom, ![X12, X11]:(X11!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,X11),c_Divides_Odivmod__int(X12,X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__correct)). 4.46/4.68 fof(fact_min__max_Oinf__absorb1, axiom, ![X47, X48, X4]:((X48=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),X47)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X47)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__absorb1)). 4.46/4.68 fof(fact_order__antisym, axiom, ![X47, X48, X4]:(((X47=X48<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X47),X48)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X47)))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__antisym)). 4.46/4.68 fof(fact_card__ge__0__finite, axiom, ![X2, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__ge__0__finite)). 4.46/4.68 fof(fact_min__max_Oinf__absorb2, axiom, ![X48, X47, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X47),X48))=>X47=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X48),X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__absorb2)). 4.46/4.68 fof(fact_min__max_Osup__absorb2, axiom, ![X47, X48, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X47))=>X47=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X48),X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__absorb2)). 4.46/4.68 fof(fact_min__max_Osup__absorb1, axiom, ![X48, X47, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X47),X48))=>X48=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X48),X47))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__absorb1)). 4.46/4.68 fof(fact_diffs0__imp__equal, axiom, ![X17, X19]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),X19)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>X17=X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diffs0__imp__equal)). 4.46/4.68 fof(fact_DiffD2, axiom, ![X1, X2, X39, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X39),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)))=>~(hBOOL(hAPP(hAPP(c_member(X4),X39),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DiffD2)). 4.46/4.68 fof(fact_distinct1__rotate, axiom, ![X7, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X7))<=>hBOOL(hAPP(c_List_Odistinct(X4),hAPP(c_List_Orotate1(X4),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct1__rotate)). 4.46/4.68 fof(fact_distinct__tl, axiom, ![X57, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),hAPP(c_List_Otl(X4),X57)))<=hBOOL(hAPP(c_List_Odistinct(X4),X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__tl)). 4.46/4.68 fof(fact_last__rev, axiom, ![X4, X57]:(hAPP(c_List_Ohd(X4),X57)=c_List_Olast(X4,hAPP(c_List_Orev(X4),X57))<=c_List_Olist_ONil(X4)!=X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__rev)). 4.46/4.68 fof(fact_sorted__list__of__set, axiom, ![X2, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))=>((hAPP(c_List_Oset(X4),c_List_Olinorder__class_Osorted__list__of__set(X4,X2))=X2&hBOOL(hAPP(c_List_Odistinct(X4),c_List_Olinorder__class_Osorted__list__of__set(X4,X2))))&c_List_Olinorder__class_Osorted(X4,c_List_Olinorder__class_Osorted__list__of__set(X4,X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__list__of__set)). 4.46/4.68 fof(fact_sorted__drop, axiom, ![X17, X57, X4]:((c_List_Olinorder__class_Osorted(X4,X57)=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Odrop(X4),X17),X57)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__drop)). 4.46/4.68 fof(fact_distinct__rev, axiom, ![X7, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X7))<=>hBOOL(hAPP(c_List_Odistinct(X4),hAPP(c_List_Orev(X4),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__rev)). 4.46/4.68 fof(fact_folding__one_Osingleton, axiom, ![X6, X62, X27, X4]:(hAPP(X62,hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=X6<=c_Finite__Set_Ofolding__one(X4,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Osingleton)). 4.46/4.68 fof(fact_sorted__take, axiom, ![X17, X57, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Osorted(X4,X57)=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Otake(X4),X17),X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__take)). 4.46/4.68 fof(fact_abs__zmult__eq__1, axiom, ![X17, X19]:(c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19),X17))=>c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__zmult__eq__1)). 4.46/4.68 fof(fact_greaterThanLessThan__empty, axiom, ![X45, X67, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X67),X45))=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X45,X67))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThanLessThan__empty)). 4.46/4.68 fof(fact_greaterThanAtMost__empty, axiom, ![X45, X67, X4]:(class_Orderings_Oorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X67),X45))=>c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X45,X67)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThanAtMost__empty)). 4.46/4.68 fof(fact_fun__left__comm__insort, axiom, ![X4]:(c_Finite__Set_Ofun__left__comm(X4,tc_List_Olist(X4),c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__insort)). 4.46/4.68 fof(fact_sup1I1, axiom, ![X1, X4, X6, X2]:(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1),X6))<=hBOOL(hAPP(X2,X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup1I1)). 4.46/4.68 fof(fact_sup1CI, axiom, ![X4, X2, X6, X1]:(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1),X6))<=(~(hBOOL(hAPP(X1,X6)))=>hBOOL(hAPP(X2,X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup1CI)). 4.46/4.68 fof(fact_zabs__def, axiom, ![X21]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X21)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))=>hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X21)=X21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zabs__def)). 4.46/4.68 fof(fact_rotate1__length01, axiom, ![X57, X4]:(X57=hAPP(c_List_Orotate1(X4),X57)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate1__length01)). 4.46/4.68 fof(fact_div__0, axiom, ![X12, X4]:(class_Divides_Osemiring__div(X4)=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),c_Groups_Ozero__class_Ozero(X4)),X12)=c_Groups_Ozero__class_Ozero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__0)). 4.46/4.68 fof(fact_order__less__imp__le, axiom, ![X47, X48, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X47))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),X47)))<=class_Orderings_Opreorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__less__imp__le)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, axiom, ![X12, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ozero__class_Ozero(X4)),X12)=c_Groups_Ozero__class_Ozero(X4)<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J)). 4.46/4.68 fof(fact_power__one, axiom, ![X17, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),c_Groups_Oone__class_Oone(X4)),X17)=c_Groups_Oone__class_Oone(X4)<=class_Groups_Omonoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__one)). 4.46/4.68 fof(fact_sup__top__left, axiom, ![X48, X4]:(class_Lattices_Obounded__lattice__top(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),c_Orderings_Otop__class_Otop(X4)),X48)=c_Orderings_Otop__class_Otop(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__top__left)). 4.46/4.68 fof(fact_mult__zero__left, axiom, ![X12, X4]:(class_Rings_Omult__zero(X4)=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ozero__class_Ozero(X4)),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__zero__left)). 4.46/4.68 fof(fact_div__less, axiom, ![X17, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X17))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19),X17)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__less)). 4.46/4.68 fof(fact_divide__zero__left, axiom, ![X12, X4]:(c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),c_Groups_Ozero__class_Ozero(X4)),X12)<=class_Rings_Odivision__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__zero__left)). 4.46/4.68 fof(fact_hd__conv__nth, axiom, ![X4, X57]:(hAPP(hAPP(c_List_Onth(X4),X57),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_List_Ohd(X4),X57)<=c_List_Olist_ONil(X4)!=X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__conv__nth)). 4.46/4.68 fof(fact_diff__is__0__eq, axiom, ![X14, X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))<=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22),X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__is__0__eq)). 4.46/4.68 fof(fact_WT_OSemi, axiom, ![X226, X227]:(hBOOL(hAPP(c_Com_OWT,X227))=>(hBOOL(hAPP(c_Com_OWT,X226))=>hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X227,X226))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WT_OSemi)). 4.46/4.68 fof(fact_no__zero__divisors, axiom, ![X11, X12, X4]:(((X11!=c_Groups_Ozero__class_Ozero(X4)=>c_Groups_Ozero__class_Ozero(X4)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11))<=X12!=c_Groups_Ozero__class_Ozero(X4))<=class_Rings_Ono__zero__divisors(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_no__zero__divisors)). 4.46/4.68 fof(fact_le__iff__inf, axiom, ![X5, X6, X4]:(class_Lattices_Osemilattice__inf(X4)=>(X6=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X6),X5)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__iff__inf)). 4.46/4.68 fof(fact_atLeastAtMost__singleton__iff, axiom, ![X39, X37, X18, X4]:(class_Orderings_Oorder(X4)=>(c_SetInterval_Oord__class_OatLeastAtMost(X4,X18,X37)=hAPP(hAPP(c_Set_Oinsert(X4),X39),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=>(X37=X39&X18=X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastAtMost__singleton__iff)). 4.46/4.68 fof(fact_sgn__pos, axiom, ![X12, X4]:(class_Rings_Olinordered__idom(X4)=>(c_Groups_Oone__class_Oone(X4)=c_Groups_Osgn__class_Osgn(X4,X12)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__pos)). 4.46/4.68 fof(fact_Suc__lessD, axiom, ![X17, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X17))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19)),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__lessD)). 4.46/4.68 fof(fact_tsub__def, axiom, ![X48, X47]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Nat__Transfer_Otsub(X48,X47)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X47),X48))))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X48),X47)=c_Nat__Transfer_Otsub(X48,X47)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X47),X48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tsub__def)). 4.46/4.68 fof(fact_le__antisym, axiom, ![X17, X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X17))=>(X19=X17<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__antisym)). 4.46/4.68 fof(fact_setprod_Oempty, axiom, ![X50, X3, X4]:(c_Groups_Oone__class_Oone(X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X4),X50),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))<=class_Groups_Ocomm__monoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod_Oempty)). 4.46/4.68 fof(fact_zle__antisym, axiom, ![X30, X49]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X49),X30))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),X49))=>X49=X30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__antisym)). 4.46/4.68 fof(fact_equal__int__def, axiom, ![X67, X45]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X45),X67)<=>hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X45),X67))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equal__int__def)). 4.46/4.68 fof(fact_wf__not__refl, axiom, ![X18, X16, X4]:(c_Wellfounded_Owf(X4,X16)=>~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X18)),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__not__refl)). 4.46/4.68 fof(fact_divide__zero, axiom, ![X12, X4]:(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),c_Groups_Ozero__class_Ozero(X4))=c_Groups_Ozero__class_Ozero(X4)<=class_Rings_Odivision__ring__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__zero)). 4.46/4.68 fof(fact_mult__is__0, axiom, ![X14, X22]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X14)<=>(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X14|X22=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__is__0)). 4.46/4.68 fof(fact_sup__top__right, axiom, ![X48, X4]:(c_Orderings_Otop__class_Otop(X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),c_Orderings_Otop__class_Otop(X4))<=class_Lattices_Obounded__lattice__top(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__top__right)). 4.46/4.68 fof(fact_top__greatest, axiom, ![X48, X4]:(class_Orderings_Otop(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),c_Orderings_Otop__class_Otop(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_top__greatest)). 4.46/4.68 fof(fact_le__less__Suc__eq, axiom, ![X14, X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22),X14))=>(X14=X22<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),hAPP(c_Nat_OSuc,X22))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__less__Suc__eq)). 4.46/4.68 fof(fact_min__max_Ole__iff__sup, axiom, ![X5, X6, X4]:(class_Orderings_Olinorder(X4)=>(hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X6),X5)=X5<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__iff__sup)). 4.46/4.68 fof(fact_div__by__0, axiom, ![X12, X4]:(class_Divides_Osemiring__div(X4)=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X12),c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__by__0)). 4.46/4.68 fof(fact_min__max_Ole__iff__inf, axiom, ![X5, X6, X4]:(class_Orderings_Olinorder(X4)=>(hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X6),X5)=X6<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__iff__inf)). 4.46/4.68 fof(fact_int__le__0__conv, axiom, ![X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__le__0__conv)). 4.46/4.68 fof(fact_hd__replicate, axiom, ![X48, X4, X17]:(X48=hAPP(c_List_Ohd(X4),c_List_Oreplicate(X4,X17,X48))<=X17!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__replicate)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, axiom, ![X12, X4]:(c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),c_Groups_Ozero__class_Ozero(X4))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J)). 4.46/4.68 fof(fact_wf__lexn, axiom, ![X14, X16, X4]:(c_Wellfounded_Owf(X4,X16)=>c_Wellfounded_Owf(tc_List_Olist(X4),hAPP(c_List_Olexn(X4,X16),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__lexn)). 4.46/4.68 fof(fact_negative__eq__positive, axiom, ![X22, X14]:((X14=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&X22=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negative__eq__positive)). 4.46/4.68 fof(fact_mult__zero__right, axiom, ![X12, X4]:(class_Rings_Omult__zero(X4)=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__zero__right)). 4.46/4.68 fof(fact_finite__PlusD_I1_J, axiom, ![X1, X2, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X4,X3)),c_Sum__Type_OPlus(X4,X3,X2,X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__PlusD_I1_J)). 4.46/4.68 fof(fact_Un__absorb1, axiom, ![X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)=X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__absorb1)). 4.46/4.68 fof(fact_Un__absorb2, axiom, ![X2, X1, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X2))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)=X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__absorb2)). 4.46/4.68 fof(fact_Int__absorb1, axiom, ![X2, X1, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),X2))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)=X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__absorb1)). 4.46/4.68 fof(fact_n__lists__Nil, axiom, ![X4, X17]:((c_List_Olist_ONil(tc_List_Olist(X4))=c_Enum_On__lists(X4,X17,c_List_Olist_ONil(X4))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X17)&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X17=>c_Enum_On__lists(X4,X17,c_List_Olist_ONil(X4))=hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_List_Olist_ONil(tc_List_Olist(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_n__lists__Nil)). 4.46/4.68 fof(fact_finite__PlusD_I2_J, axiom, ![X1, X2, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X4,X3)),c_Sum__Type_OPlus(X4,X3,X2,X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__PlusD_I2_J)). 4.46/4.68 fof(fact_folding__image__simple__idem_Oidem, axiom, ![X6, X62, X50, X35, X27, X3, X4]:(c_Finite__Set_Ofolding__image__simple__idem(X4,X3,X27,X35,X50,X62)=>hAPP(hAPP(X27,X6),X6)=X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple__idem_Oidem)). 4.46/4.68 fof(fact_total__on__converse, axiom, ![X16, X2, X4]:(c_Relation_Ototal__on(X4,X2,X16)<=>c_Relation_Ototal__on(X4,X2,hAPP(c_Relation_Oconverse(X4,X4),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_total__on__converse)). 4.46/4.68 fof(fact_refl__on__converse, axiom, ![X16, X2, X4]:(c_Relation_Orefl__on(X4,X2,X16)<=>c_Relation_Orefl__on(X4,X2,hAPP(c_Relation_Oconverse(X4,X4),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__converse)). 4.46/4.68 fof(fact_divide__self__if, axiom, ![X12, X4]:(((c_Groups_Ozero__class_Ozero(X4)!=X12=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X12)=c_Groups_Oone__class_Oone(X4))&(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X12)=c_Groups_Ozero__class_Ozero(X4)<=c_Groups_Ozero__class_Ozero(X4)=X12))<=class_Rings_Odivision__ring__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__self__if)). 4.46/4.68 fof(fact_Int__absorb2, axiom, ![X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))=>X2=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__absorb2)). 4.46/4.68 fof(fact_ComplE, axiom, ![X2, X39, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X39),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X2)))=>~(hBOOL(hAPP(hAPP(c_member(X4),X39),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ComplE)). 4.46/4.68 fof(fact_nat__set__def, axiom, ![X46]:(![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X42))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X42),X46)))<=>c_Nat__Transfer_Onat__set(X46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__set__def)). 4.46/4.68 fof(fact_add__right__cancel, axiom, ![X39, X18, X37, X4]:(class_Groups_Ocancel__semigroup__add(X4)=>(X39=X37<=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X37),X18)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X39),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__right__cancel)). 4.46/4.68 fof(fact_div__self, axiom, ![X12, X4]:(class_Divides_Osemiring__div(X4)=>(c_Groups_Ozero__class_Ozero(X4)!=X12=>c_Groups_Oone__class_Oone(X4)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X12),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__self)). 4.46/4.68 fof(fact_add__imp__eq, axiom, ![X10, X11, X12, X4]:((X11=X10<=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11))<=class_Groups_Ocancel__ab__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__imp__eq)). 4.46/4.68 fof(fact_add__left__cancel, axiom, ![X39, X37, X18, X4]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X18),X37)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X18),X39)<=>X37=X39)<=class_Groups_Ocancel__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__left__cancel)). 4.46/4.68 fof(fact_divide__self, axiom, ![X12, X4]:(class_Rings_Odivision__ring(X4)=>(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X12)=c_Groups_Oone__class_Oone(X4)<=X12!=c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__self)). 4.46/4.68 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J, axiom, ![X1, X2]:((c_Nat__Transfer_Onat__set(X1)=>c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X2),X1)))<=c_Nat__Transfer_Onat__set(X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J)). 4.46/4.68 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J, axiom, ![X1, X2]:((c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X2),X1))<=c_Nat__Transfer_Onat__set(X1))<=c_Nat__Transfer_Onat__set(X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J)). 4.46/4.68 fof(fact_not__neg__eq__ge__0, axiom, ![X6]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))<=>~(hBOOL(hAPP(c_Nat__Numeral_Oneg,X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__neg__eq__ge__0)). 4.46/4.68 fof(fact_WT_Oequations_I3_J, axiom, ![X123, X250, X135]:(hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X135,X250,X123)))<=>hBOOL(hAPP(c_Com_OWT,X123))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WT_Oequations_I3_J)). 4.46/4.68 fof(fact_card__distinct, axiom, ![X7, X4]:(hAPP(c_Finite__Set_Ocard(X4),hAPP(c_List_Oset(X4),X7))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)=>hBOOL(hAPP(c_List_Odistinct(X4),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__distinct)). 4.46/4.68 fof(fact_sorted__butlast, axiom, ![X57, X4]:((c_List_Olist_ONil(X4)!=X57=>(c_List_Olinorder__class_Osorted(X4,c_List_Obutlast(X4,X57))<=c_List_Olinorder__class_Osorted(X4,X57)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__butlast)). 4.46/4.68 fof(fact_last__replicate, axiom, ![X48, X4, X17]:(c_List_Olast(X4,c_List_Oreplicate(X4,X17,X48))=X48<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__replicate)). 4.46/4.68 fof(fact_take__eq__Nil, axiom, ![X7, X14, X4]:((c_List_Olist_ONil(X4)=X7|X14=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=>c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Otake(X4),X14),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__eq__Nil)). 4.46/4.68 fof(fact_injD, axiom, ![X5, X6, X27, X3, X4]:((hAPP(X27,X6)=hAPP(X27,X5)=>X5=X6)<=c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_injD)). 4.46/4.68 fof(fact_power__0, axiom, ![X12, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X4)<=class_Power_Opower(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__0)). 4.46/4.68 fof(fact_mult__eq__self__implies__10, axiom, ![X17, X19]:((X17=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X19=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X17)=X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__eq__self__implies__10)). 4.46/4.68 fof(fact_mult__1__left, axiom, ![X12, X4]:(class_Groups_Omonoid__mult(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oone__class_Oone(X4)),X12)=X12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__1__left)). 4.46/4.68 fof(fact_mult__1, axiom, ![X12, X4]:(class_Groups_Ocomm__monoid__mult(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oone__class_Oone(X4)),X12)=X12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__1)). 4.46/4.68 fof(fact_add__0__left, axiom, ![X12, X4]:(class_Groups_Omonoid__add(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Ozero__class_Ozero(X4)),X12)=X12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__0__left)). 4.46/4.68 fof(fact_Pair__eq, axiom, ![X278, X223, X37, X18, X3, X4]:(hAPP(hAPP(c_Product__Type_OPair(X4,X3),X18),X37)=hAPP(hAPP(c_Product__Type_OPair(X4,X3),X223),X278)<=>(X278=X37&X223=X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pair__eq)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, axiom, ![X48, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X4)<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J)). 4.46/4.68 fof(fact_add__0, axiom, ![X12, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Ozero__class_Ozero(X4)),X12)=X12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__0)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, axiom, ![X12, X4]:(X12=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oone__class_Oone(X4)),X12)<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, axiom, ![X12, X4]:(class_Rings_Ocomm__semiring__1(X4)=>X12=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Ozero__class_Ozero(X4)),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J)). 4.46/4.68 fof(fact_inf__top__left, axiom, ![X48, X4]:(class_Lattices_Obounded__lattice__top(X4)=>X48=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),c_Orderings_Otop__class_Otop(X4)),X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__top__left)). 4.46/4.68 fof(fact_div__by__1, axiom, ![X12, X4]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X12),c_Groups_Oone__class_Oone(X4))=X12<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__by__1)). 4.46/4.68 fof(fact_mult_Ocomm__neutral, axiom, ![X12, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),c_Groups_Oone__class_Oone(X4))=X12<=class_Groups_Ocomm__monoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult_Ocomm__neutral)). 4.46/4.68 fof(fact_add__0__right, axiom, ![X12, X4]:(class_Groups_Omonoid__add(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),c_Groups_Ozero__class_Ozero(X4))=X12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__0__right)). 4.46/4.68 fof(fact_diff__0__right, axiom, ![X12, X4]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),c_Groups_Ozero__class_Ozero(X4))=X12<=class_Groups_Ogroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__0__right)). 4.46/4.68 fof(fact_inf__top__right, axiom, ![X48, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),c_Orderings_Otop__class_Otop(X4))=X48<=class_Lattices_Obounded__lattice__top(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__top__right)). 4.46/4.68 fof(fact_right__inverse__eq, axiom, ![X18, X37, X4]:(class_Rings_Odivision__ring(X4)=>(c_Groups_Ozero__class_Ozero(X4)!=X37=>(X18=X37<=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X18),X37)=c_Groups_Oone__class_Oone(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_right__inverse__eq)). 4.46/4.68 fof(fact_wf__no__loop, axiom, ![X26, X4]:(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X26),X26)=>c_Wellfounded_Owf(X4,X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__no__loop)). 4.46/4.68 fof(fact_mult__1__right, axiom, ![X12, X4]:(X12=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),c_Groups_Oone__class_Oone(X4))<=class_Groups_Omonoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__1__right)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, axiom, ![X12, X4]:(class_Rings_Ocomm__semiring__1(X4)=>X12=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),c_Groups_Oone__class_Oone(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J)). 4.46/4.68 fof(fact_divide__1, axiom, ![X12, X4]:(class_Rings_Odivision__ring(X4)=>X12=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),c_Groups_Oone__class_Oone(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__1)). 4.46/4.68 fof(fact_type__definition_ORep__inverse, axiom, ![X6, X2, X101, X102, X3, X4]:(c_Typedef_Otype__definition(X4,X3,X102,X101,X2)=>X6=hAPP(X101,hAPP(X102,X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_ORep__inverse)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, axiom, ![X12, X4]:(X12=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),c_Groups_Ozero__class_Ozero(X4))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J)). 4.46/4.68 fof(fact_add_Ocomm__neutral, axiom, ![X12, X4]:(class_Groups_Ocomm__monoid__add(X4)=>X12=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add_Ocomm__neutral)). 4.46/4.68 fof(fact_double__compl, axiom, ![X48, X4]:(class_Lattices_Oboolean__algebra(X4)=>X48=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X48))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__compl)). 4.46/4.68 fof(fact_power__one__right, axiom, ![X12, X4]:(X12=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),c_Groups_Oone__class_Oone(tc_Nat_Onat))<=class_Groups_Omonoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__one__right)). 4.46/4.68 fof(fact_conversepD, axiom, ![X37, X18, X16, X3, X4]:(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4,X3,X16),X18),X37))=>hBOOL(hAPP(hAPP(X16,X37),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conversepD)). 4.46/4.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, axiom, ![X48, X4]:(X48=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X48),c_Groups_Oone__class_Oone(tc_Nat_Onat))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)). 4.46/4.68 fof(fact_exists__code, axiom, ![X28, X4]:(class_Enum_Oenum(X4)=>(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X4),X28))<=>?[X138]:hBOOL(hAPP(X28,X138)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_exists__code)). 4.46/4.68 fof(fact_enum__ex, axiom, ![X28, X4]:(class_Enum_Oenum(X4)=>(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X4),X28))<=>?[X138]:hBOOL(hAPP(X28,X138)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__ex)). 4.46/4.68 fof(fact_Inf__singleton, axiom, ![X18, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>c_Complete__Lattice_OInf__class_OInf(X4,hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__singleton)). 4.46/4.68 fof(fact_sorted__sort, axiom, ![X7, X4]:(class_Orderings_Olinorder(X4)=>c_List_Olinorder__class_Osorted(X4,c_List_Olinorder__class_Osort__key(X4,X4,c_COMBI(X4),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__sort)). 4.46/4.68 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures, axiom, ![X5, X6]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))=>c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X6,X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SetInterval_Otransfer__nat__int__set__function__closures)). 4.46/4.68 fof(fact_Max_Osingleton, axiom, ![X6, X4]:(class_Orderings_Olinorder(X4)=>c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Osingleton)). 4.46/4.68 fof(fact_Sup__singleton, axiom, ![X18, X4]:(c_Complete__Lattice_OSup__class_OSup(X4,hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=X18<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__singleton)). 4.46/4.68 fof(fact_Sup__fin_Osingleton, axiom, ![X6, X4]:(c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=X6<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Osingleton)). 4.46/4.68 fof(fact_Inf__fin_Osingleton, axiom, ![X6, X4]:(X6=c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Osingleton)). 4.46/4.68 fof(fact_power__power__power, axiom, ![X4]:(c_Power_Opower_Opower(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Otimes__class_Otimes(X4))=c_Power_Opower__class_Opower(X4)<=class_Power_Opower(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__power__power)). 4.46/4.68 fof(fact_Min_Osingleton, axiom, ![X6, X4]:(class_Orderings_Olinorder(X4)=>X6=c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Osingleton)). 4.46/4.68 fof(fact_order__less__asym_H, axiom, ![X11, X12, X4]:(class_Orderings_Opreorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11))=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__less__asym_H)). 4.46/4.68 fof(fact_xt1_I9_J, axiom, ![X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11))))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_xt1_I9_J)). 4.46/4.68 fof(fact_not__less__iff__gr__or__eq, axiom, ![X5, X6, X4]:(((X5=X6|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X5),X6)))<=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),X5))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__less__iff__gr__or__eq)). 4.46/4.68 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J, axiom, ![X47, X48]:(c_Nat__Transfer_Ois__nat(X48)=>(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X48),X47))<=c_Nat__Transfer_Ois__nat(X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Otransfer__int__nat__function__closures_I1_J)). 4.46/4.68 fof(fact_elem__set, axiom, ![X192, X6, X4]:(X192=hAPP(c_Option_Ooption_OSome(X4),X6)<=>hBOOL(hAPP(hAPP(c_member(X4),X6),c_Option_Oset(X4,X192)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_elem__set)). 4.46/4.68 fof(fact_divmod__nat__rel__unique, axiom, ![X321, X97, X17, X19]:(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X19,X17),X97))=>(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X19,X17),X321))=>X97=X321)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel__unique)). 4.46/4.68 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J, axiom, ![X47, X48]:((c_Nat__Transfer_Ois__nat(X47)=>c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X47)))<=c_Nat__Transfer_Ois__nat(X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J)). 4.46/4.68 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J, axiom, ![X47, X48]:((c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X48),X47))<=c_Nat__Transfer_Ois__nat(X47))<=c_Nat__Transfer_Ois__nat(X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J)). 4.46/4.68 fof(fact_finite__insert, axiom, ![X2, X18, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Set_Oinsert(X4),X18),X2)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__insert)). 4.46/4.68 fof(fact_Rep__Integ__cases, axiom, ![X5]:(~(![X42]:X5!=hAPP(c_Int_ORep__Integ,X42))<=hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X5),c_Int_OInteg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Rep__Integ__cases)). 4.46/4.68 fof(fact_subset__Un__eq, axiom, ![X1, X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X1))<=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)=X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__Un__eq)). 4.46/4.68 fof(fact_some__eq__ex, axiom, ![X4, X28]:(?[X138]:hBOOL(hAPP(X28,X138))<=>hBOOL(hAPP(X28,c_Hilbert__Choice_OEps(X4,X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_some__eq__ex)). 4.46/4.68 fof(fact_list__ex__rev, axiom, ![X7, X28, X4]:(c_List_Olist__ex(X4,X28,X7)<=>c_List_Olist__ex(X4,X28,hAPP(c_List_Orev(X4),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__rev)). 4.46/4.68 fof(fact_list__all__rev, axiom, ![X7, X28, X4]:(c_List_Olist__all(X4,X28,hAPP(c_List_Orev(X4),X7))<=>c_List_Olist__all(X4,X28,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__rev)). 4.46/4.68 fof(fact_folding__image__simple_Oempty, axiom, ![X62, X50, X35, X27, X3, X4]:(hAPP(X62,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))=X35<=c_Finite__Set_Ofolding__image__simple(X4,X3,X27,X35,X50,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Oempty)). 4.46/4.68 fof(fact_inj__on__imageI2, axiom, ![X2, X27, X282, X29, X3, X4]:(c_Fun_Oinj__on(X4,X29,X27,X2)<=c_Fun_Oinj__on(X4,X3,hAPP(c_Fun_Ocomp(X29,X3,X4,X282),X27),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__imageI2)). 4.46/4.68 fof(fact_nat__add__right__cancel, axiom, ![X14, X45, X22]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X45)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X45)<=>X14=X22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__right__cancel)). 4.46/4.68 fof(fact_nat__add__left__cancel, axiom, ![X14, X22, X45]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X22)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X14)<=>X14=X22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__left__cancel)). 4.46/4.68 fof(fact_top__apply, axiom, ![X6, X3, X4]:(c_Orderings_Otop__class_Otop(X4)=hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3,X4)),X6)<=class_Orderings_Otop(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_top__apply)). 4.46/4.68 fof(fact_diff__self, axiom, ![X12, X4]:(class_Groups_Ogroup__add(X4)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X12)=c_Groups_Ozero__class_Ozero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__self)). 4.46/4.68 fof(fact_Diff__triv, axiom, ![X1, X2, X4]:(X2=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__triv)). 4.46/4.68 fof(fact_replicate__eq__replicate, axiom, ![X5, X14, X6, X22, X4]:(((X6=X5<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X22)&X22=X14)<=>c_List_Oreplicate(X4,X22,X6)=c_List_Oreplicate(X4,X14,X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__eq__replicate)). 4.46/4.68 fof(fact_sort__key__simps_I1_J, axiom, ![X27, X4, X3]:(class_Orderings_Olinorder(X3)=>c_List_Olist_ONil(X4)=c_List_Olinorder__class_Osort__key(X4,X3,X27,c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sort__key__simps_I1_J)). 4.46/4.68 fof(fact_not__square__less__zero, axiom, ![X12, X4]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X12)),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__square__less__zero)). 4.46/4.68 fof(fact_bot__least, axiom, ![X48, X4]:(class_Orderings_Obot(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Orderings_Obot__class_Obot(X4)),X48))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bot__least)). 4.46/4.68 fof(fact_subset__Compl__self__eq, axiom, ![X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X2)))<=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__Compl__self__eq)). 4.46/4.68 fof(fact_list_Oinject, axiom, ![X222, X223, X85, X18, X4]:((X18=X223&X85=X222)<=>hAPP(hAPP(c_List_Olist_OCons(X4),X223),X222)=hAPP(hAPP(c_List_Olist_OCons(X4),X18),X85)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Oinject)). 4.46/4.68 fof(fact_append__same__eq, axiom, ![X88, X7, X32, X4]:(X88=X32<=>hAPP(hAPP(c_List_Oappend(X4),X88),X7)=hAPP(hAPP(c_List_Oappend(X4),X32),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__same__eq)). 4.46/4.68 fof(fact_mem__def, axiom, ![X2, X6, X4]:(hBOOL(hAPP(X2,X6))<=>hBOOL(hAPP(hAPP(c_member(X4),X6),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mem__def)). 4.46/4.68 fof(fact_same__append__eq, axiom, ![X88, X32, X7, X4]:(hAPP(hAPP(c_List_Oappend(X4),X7),X88)=hAPP(hAPP(c_List_Oappend(X4),X7),X32)<=>X32=X88), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_same__append__eq)). 4.46/4.68 fof(fact_equal__refl, axiom, ![X48, X4]:(class_HOL_Oequal(X4)=>hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X4),X48),X48))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equal__refl)). 4.46/4.68 fof(fact_order__refl, axiom, ![X48, X4]:(class_Orderings_Opreorder(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X48),X48))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__refl)). 4.46/4.68 fof(fact_min__ext__wf, axiom, ![X16, X4]:(c_Wellfounded_Owf(tc_fun(X4,tc_HOL_Obool),c_Wellfounded_Omin__ext(X4,X16))<=c_Wellfounded_Owf(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__ext__wf)). 4.46/4.68 fof(fact_max__ext__wf, axiom, ![X16, X4]:(c_Wellfounded_Owf(X4,X16)=>c_Wellfounded_Owf(tc_fun(X4,tc_HOL_Obool),c_Wellfounded_Omax__ext(X4,X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__ext__wf)). 4.46/4.68 fof(fact_acyclic__converse, axiom, ![X16, X4]:(c_Wellfounded_Oacyclic(X4,X16)<=>c_Wellfounded_Oacyclic(X4,hAPP(c_Relation_Oconverse(X4,X4),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclic__converse)). 4.46/4.68 fof(fact_fun__upd__idem__iff, axiom, ![X5, X6, X27, X3, X4]:(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X3),X27),X6),X5)=X27<=>hAPP(X27,X6)=X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__idem__iff)). 4.46/4.68 fof(fact_singletonE, axiom, ![X18, X37, X4]:(X37=X18<=hBOOL(hAPP(hAPP(c_member(X4),X37),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_singletonE)). 4.46/4.68 fof(fact_fold__graph__imp__finite, axiom, ![X6, X2, X35, X27, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X3,X27,X35,X2),X6))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph__imp__finite)). 4.46/4.68 fof(fact_of__nat__aux_Osimps_I1_J, axiom, ![X24, X116, X4]:(class_Rings_Osemiring__1(X4)=>X24=c_Nat_Osemiring__1__class_Oof__nat__aux(X4,X116,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__aux_Osimps_I1_J)). 4.46/4.68 fof(fact_WT_Oequations_I6_J, axiom, ![X123, X135]:(hBOOL(hAPP(c_Com_OWT,X123))<=>hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X135,X123)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WT_Oequations_I6_J)). 4.46/4.68 fof(fact_gr0__conv__Suc, axiom, ![X14]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14))<=>?[X90]:hAPP(c_Nat_OSuc,X90)=X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_gr0__conv__Suc)). 4.46/4.68 fof(fact_inf1D1, axiom, ![X6, X1, X2, X4]:(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1),X6))=>hBOOL(hAPP(X2,X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf1D1)). 4.46/4.68 fof(fact_inf1D2, axiom, ![X6, X1, X2, X4]:(hBOOL(hAPP(X1,X6))<=hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf1D2)). 4.46/4.68 fof(fact_folding__one__idem_Oidem, axiom, ![X6, X62, X27, X4]:(X6=hAPP(hAPP(X27,X6),X6)<=c_Finite__Set_Ofolding__one__idem(X4,X27,X62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Oidem)). 4.46/4.68 fof(fact_sorted__tl, axiom, ![X57, X4]:((c_List_Olinorder__class_Osorted(X4,X57)=>c_List_Olinorder__class_Osorted(X4,hAPP(c_List_Otl(X4),X57)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__tl)). 4.46/4.68 fof(fact_enum__UNIV, axiom, ![X4]:(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(c_List_Oset(X4),c_Enum_Oenum__class_Oenum(X4))<=class_Enum_Oenum(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__UNIV)). 4.46/4.68 fof(fact_inf__eq__top__iff, axiom, ![X5, X6, X4]:(((X6=c_Orderings_Otop__class_Otop(X4)&X5=c_Orderings_Otop__class_Otop(X4))<=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X6),X5)=c_Orderings_Otop__class_Otop(X4))<=class_Lattices_Obounded__lattice__top(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__eq__top__iff)). 4.46/4.68 fof(fact_Sup__UNIV, axiom, ![X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>c_Complete__Lattice_OSup__class_OSup(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__UNIV)). 4.46/4.68 fof(fact_inf__bot__left, axiom, ![X48, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),c_Orderings_Obot__class_Obot(X4)),X48)=c_Orderings_Obot__class_Obot(X4)<=class_Lattices_Obounded__lattice__bot(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__bot__left)). 4.46/4.68 fof(fact_inf__bot__right, axiom, ![X48, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),c_Orderings_Obot__class_Obot(X4))=c_Orderings_Obot__class_Obot(X4)<=class_Lattices_Obounded__lattice__bot(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__bot__right)). 4.46/4.68 fof(fact_mod__if, axiom, ![X17, X19]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X17)))=>c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17),X17))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X17))=>X19=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__if)). 4.46/4.68 fof(fact_empty__fold__graphE, axiom, ![X6, X35, X27, X3, X4]:(X35=X6<=hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X3,X27,X35,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__fold__graphE)). 4.46/4.68 fof(fact_wf__exp, axiom, ![X26, X14, X4]:(c_Wellfounded_Owf(X4,X26)<=c_Wellfounded_Owf(X4,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X14),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__exp)). 4.46/4.68 fof(fact_wf__acc__iff, axiom, ![X16, X4]:(c_Wellfounded_Owf(X4,X16)<=>![X42]:hBOOL(hAPP(hAPP(c_member(X4),X42),c_Wellfounded_Oacc(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__acc__iff)). 4.46/4.68 fof(fact_sgn__sgn, axiom, ![X12, X4]:(class_Rings_Olinordered__idom(X4)=>c_Groups_Osgn__class_Osgn(X4,c_Groups_Osgn__class_Osgn(X4,X12))=c_Groups_Osgn__class_Osgn(X4,X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__sgn)). 4.46/4.68 fof(fact_eq__number__of, axiom, ![X5, X6, X4]:((hAPP(c_Int_Onumber__class_Onumber__of(X4),X6)=hAPP(c_Int_Onumber__class_Onumber__of(X4),X5)<=>X5=X6)<=(class_Int_Oring__char__0(X4)&class_Int_Onumber__ring(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__number__of)). 4.46/4.68 fof(fact_sup__bot__left, axiom, ![X48, X4]:(class_Lattices_Obounded__lattice__bot(X4)=>X48=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),c_Orderings_Obot__class_Obot(X4)),X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__bot__left)). 4.46/4.68 fof(fact_accp__wfPD, axiom, ![X6, X16, X4]:(hBOOL(hAPP(c_Wellfounded_Oaccp(X4,X16),X6))<=c_Wellfounded_OwfP(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_accp__wfPD)). 4.46/4.68 fof(fact_mod__0, axiom, ![X12, X4]:(class_Divides_Osemiring__div(X4)=>c_Groups_Ozero__class_Ozero(X4)=c_Divides_Odiv__class_Omod(X4,c_Groups_Ozero__class_Ozero(X4),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__0)). 4.46/4.68 fof(fact_sup__bot__right, axiom, ![X48, X4]:(X48=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),c_Orderings_Obot__class_Obot(X4))<=class_Lattices_Obounded__lattice__bot(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__bot__right)). 4.46/4.68 fof(fact_card__eq__0__iff, axiom, ![X2, X4]:((~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))|c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X2)<=>hAPP(c_Finite__Set_Ocard(X4),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__eq__0__iff)). 4.46/4.68 fof(fact_folding_Oempty, axiom, ![X62, X27, X3, X4]:(c_Finite__Set_Ofolding(X4,X3,X27,X62)=>c_Fun_Oid(X3)=hAPP(X62,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Oempty)). 4.46/4.68 fof(fact_mod__by__1, axiom, ![X12, X4]:(c_Groups_Ozero__class_Ozero(X4)=c_Divides_Odiv__class_Omod(X4,X12,c_Groups_Oone__class_Oone(X4))<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__by__1)). 4.46/4.68 fof(fact_zdiv__self, axiom, ![X12]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X12=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X12)=c_Groups_Oone__class_Oone(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__self)). 4.46/4.68 fof(fact_reflpE, axiom, ![X6, X16, X4]:(hBOOL(hAPP(hAPP(X16,X6),X6))<=c_Predicate_Oreflp(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_reflpE)). 4.46/4.68 fof(fact_equivp__reflp, axiom, ![X6, X26, X4]:(c_Equiv__Relations_Oequivp(X4,X26)=>hBOOL(hAPP(hAPP(X26,X6),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equivp__reflp)). 4.46/4.68 fof(fact_insert__absorb, axiom, ![X2, X18, X4]:(hAPP(hAPP(c_Set_Oinsert(X4),X18),X2)=X2<=hBOOL(hAPP(hAPP(c_member(X4),X18),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__absorb)). 4.46/4.68 fof(fact_neg__def, axiom, ![X117]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X117),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>hBOOL(hAPP(c_Nat__Numeral_Oneg,X117))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__def)). 4.46/4.68 fof(fact_all__code, axiom, ![X28, X4]:(class_Enum_Oenum(X4)=>(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X4),X28))<=>![X138]:hBOOL(hAPP(X28,X138)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__code)). 4.46/4.68 fof(fact_not__Some__eq, axiom, ![X4, X6]:(c_Option_Ooption_ONone(X4)=X6<=>![X44]:hAPP(c_Option_Ooption_OSome(X4),X44)!=X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__Some__eq)). 4.46/4.68 fof(fact_cut, axiom, ![X82, X202, X208, X4]:((c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,X208)=>c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,X202))<=c_Hoare__Mirabelle_Ohoare__derivs(X4,X208,X202)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_cut)). 4.46/4.68 fof(fact_not__None__eq, axiom, ![X4, X6]:(c_Option_Ooption_ONone(X4)!=X6<=>?[X44]:X6=hAPP(c_Option_Ooption_OSome(X4),X44)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__None__eq)). 4.46/4.68 fof(fact_sorted__remove1, axiom, ![X12, X57, X4]:((c_List_Olinorder__class_Osorted(X4,c_List_Oremove1(X4,X12,X57))<=c_List_Olinorder__class_Osorted(X4,X57))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__remove1)). 4.46/4.68 fof(fact_sorted__takeWhile, axiom, ![X28, X7, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Osorted(X4,c_List_OtakeWhile(X4,X28,X7))<=c_List_Olinorder__class_Osorted(X4,X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__takeWhile)). 4.46/4.68 fof(fact_type__definition_ORep__inject, axiom, ![X5, X6, X2, X101, X102, X3, X4]:(c_Typedef_Otype__definition(X4,X3,X102,X101,X2)=>(hAPP(X102,X5)=hAPP(X102,X6)<=>X5=X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_ORep__inject)). 4.46/4.68 fof(fact_enum__all, axiom, ![X28, X4]:((hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X4),X28))<=>![X138]:hBOOL(hAPP(X28,X138)))<=class_Enum_Oenum(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__all)). 4.46/4.68 fof(fact_upto__empty, axiom, ![X21, X20]:(c_List_Olist_ONil(tc_Int_Oint)=c_List_Oupto(X21,X20)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X21))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upto__empty)). 4.46/4.68 fof(fact_arith__simps_I31_J, axiom, ![X4]:(hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_arith__simps_I31_J)). 4.46/4.68 fof(fact_field__power__not__zero, axiom, ![X17, X12, X4]:((c_Groups_Ozero__class_Ozero(X4)!=X12=>c_Groups_Ozero__class_Ozero(X4)!=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X17))<=class_Rings_Oring__1__no__zero__divisors(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_field__power__not__zero)). 4.46/4.68 fof(fact_linorder__not__le, axiom, ![X5, X6, X4]:(class_Orderings_Olinorder(X4)=>(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X5)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X5),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__not__le)). 4.46/4.68 fof(fact_wf__lex, axiom, ![X16, X4]:(c_Wellfounded_Owf(tc_List_Olist(X4),c_List_Olex(X4,X16))<=c_Wellfounded_Owf(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__lex)). 4.46/4.68 fof(fact_Inf__fin_Oidem, axiom, ![X48, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X48)=X48<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oidem)). 4.46/4.68 fof(fact_times_Oidem, axiom, ![X12, X4]:(class_Lattices_Oab__semigroup__idem__mult(X4)=>X12=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_times_Oidem)). 4.46/4.68 fof(fact_sup__idem, axiom, ![X48, X4]:(class_Lattices_Osemilattice__sup(X4)=>X48=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__idem)). 4.46/4.68 fof(fact_wf__lenlex, axiom, ![X16, X4]:(c_Wellfounded_Owf(tc_List_Olist(X4),c_List_Olenlex(X4,X16))<=c_Wellfounded_Owf(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__lenlex)). 4.46/4.68 fof(fact_wf__iff__acyclic__if__finite, axiom, ![X16, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X4)),X16))=>(c_Wellfounded_Oacyclic(X4,X16)<=>c_Wellfounded_Owf(X4,X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__iff__acyclic__if__finite)). 4.46/4.68 fof(fact_Sup__fin_Oidem, axiom, ![X48, X4]:(class_Lattices_Olattice(X4)=>X48=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X48),X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oidem)). 4.46/4.68 fof(fact_inf__idem, axiom, ![X48, X4]:(X48=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X48),X48)<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__idem)). 4.46/4.68 fof(fact_abs__not__less__zero, axiom, ![X12, X4]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),c_Groups_Ozero__class_Ozero(X4))))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__not__less__zero)). 4.46/4.68 fof(fact_of__nat__less__0__iff, axiom, ![X19, X4]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X19)),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__less__0__iff)). 4.46/4.68 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J, axiom, ![X17, X48]:(c_Nat__Transfer_Ois__nat(X48)=>c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X48),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J)). 4.46/4.68 fof(fact_mod__by__0, axiom, ![X12, X4]:(c_Divides_Odiv__class_Omod(X4,X12,c_Groups_Ozero__class_Ozero(X4))=X12<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__by__0)). 4.46/4.68 fof(fact_le__0__eq, axiom, ![X14]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X14<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__0__eq)). 4.46/4.68 fof(fact_of__int__eq__iff, axiom, ![X35, X36, X4]:((hAPP(c_Int_Oring__1__class_Oof__int(X4),X36)=hAPP(c_Int_Oring__1__class_Oof__int(X4),X35)<=>X35=X36)<=class_Int_Oring__char__0(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__eq__iff)). 4.46/4.68 fof(fact_compl__eq__compl__iff, axiom, ![X5, X6, X4]:((X6=X5<=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),X5)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X6))<=class_Lattices_Oboolean__algebra(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__eq__compl__iff)). 4.46/4.68 fof(fact_singleton__inject, axiom, ![X37, X18, X4]:(X37=X18<=hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(X4),X37),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_singleton__inject)). 4.46/4.68 fof(fact_neg__equal__iff__equal, axiom, ![X37, X18, X4]:(class_Groups_Ogroup__add(X4)=>(hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X37)<=>X18=X37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__equal__iff__equal)). 4.46/4.68 fof(fact_of__nat__eq__iff, axiom, ![X14, X22, X4]:(class_Nat_Osemiring__char__0(X4)=>(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X22)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X14)<=>X14=X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__eq__iff)). 4.46/4.68 fof(help_c__fconj__1, axiom, ![X80, X28]:(~(hBOOL(X28))|~(hBOOL(X80))|hBOOL(hAPP(hAPP(c_fconj,X28),X80))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fconj__1)). 4.46/4.68 fof(fact_enum__distinct, axiom, ![X4]:(class_Enum_Oenum(X4)=>hBOOL(hAPP(c_List_Odistinct(X4),c_Enum_Oenum__class_Oenum(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__distinct)). 4.46/4.68 fof(fact_inj__uminus, axiom, ![X2, X4]:(class_Groups_Oordered__ab__group__add(X4)=>c_Fun_Oinj__on(X4,X4,c_Groups_Ouminus__class_Ouminus(X4),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__uminus)). 4.46/4.68 fof(fact_ext, axiom, ![X50, X27]:(![X42]:hAPP(X50,X42)=hAPP(X27,X42)=>X50=X27), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ext)). 4.46/4.68 fof(fact_number__of__eq, axiom, ![X15, X4]:(hAPP(c_Int_Oring__1__class_Oof__int(X4),X15)=hAPP(c_Int_Onumber__class_Onumber__of(X4),X15)<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__eq)). 4.46/4.68 fof(fact_sup__eq__bot__iff, axiom, ![X5, X6, X4]:(((c_Orderings_Obot__class_Obot(X4)=X5&X6=c_Orderings_Obot__class_Obot(X4))<=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X6),X5)=c_Orderings_Obot__class_Obot(X4))<=class_Lattices_Obounded__lattice__bot(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__eq__bot__iff)). 4.46/4.68 fof(fact_WTs__elim__cases_I3_J, axiom, ![X39, X18, X76]:(hBOOL(hAPP(c_Com_OWT,X39))<=hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X76,X18,X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WTs__elim__cases_I3_J)). 4.46/4.68 fof(fact_abs__one, axiom, ![X4]:(class_Rings_Olinordered__idom(X4)=>c_Groups_Oone__class_Oone(X4)=hAPP(c_Groups_Oabs__class_Oabs(X4),c_Groups_Oone__class_Oone(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__one)). 4.46/4.68 fof(fact_listsum__simps_I1_J, axiom, ![X4]:(class_Groups_Omonoid__add(X4)=>c_Groups_Ozero__class_Ozero(X4)=hAPP(c_List_Omonoid__add__class_Olistsum(X4),c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__simps_I1_J)). 4.46/4.68 fof(fact_compl__bot__eq, axiom, ![X4]:(c_Orderings_Otop__class_Otop(X4)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Orderings_Obot__class_Obot(X4))<=class_Lattices_Oboolean__algebra(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__bot__eq)). 4.46/4.68 fof(fact_Inf__UNIV, axiom, ![X4]:(c_Orderings_Obot__class_Obot(X4)=c_Complete__Lattice_OInf__class_OInf(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__UNIV)). 4.46/4.68 fof(fact_wf__in__rel, axiom, ![X26, X4]:(c_Wellfounded_Owf(X4,X26)=>c_Wellfounded_OwfP(X4,c_FunDef_Oin__rel(X4,X4,X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__in__rel)). 4.46/4.68 fof(fact_wf__mlex, axiom, ![X27, X26, X4]:(c_Wellfounded_Owf(X4,X26)=>c_Wellfounded_Owf(X4,c_Wellfounded_Omlex__prod(X4,X27,X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__mlex)). 4.46/4.68 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J, axiom, ![X47, X48]:(c_Nat__Transfer_Ois__nat(X48)=>(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X48,X47))<=c_Nat__Transfer_Ois__nat(X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Otransfer__int__nat__function__closures_I2_J)). 4.46/4.68 fof(fact_abs__zero, axiom, ![X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>c_Groups_Ozero__class_Ozero(X4)=hAPP(c_Groups_Oabs__class_Oabs(X4),c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__zero)). 4.46/4.68 fof(fact_min__max_Osup_Oidem, axiom, ![X12, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X12),X12)=X12<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup_Oidem)). 4.46/4.68 fof(fact_map__is__Nil__conv, axiom, ![X7, X27, X4, X3]:(c_List_Olist_ONil(X3)=X7<=>hAPP(hAPP(c_List_Omap(X3,X4),X27),X7)=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__is__Nil__conv)). 4.46/4.68 fof(fact_list__update__nonempty, axiom, ![X6, X45, X7, X4]:(c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Olist__update(X4,X7),X45),X6)<=>c_List_Olist_ONil(X4)=X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__nonempty)). 4.46/4.68 fof(fact_minus__zero, axiom, ![X4]:(class_Groups_Ogroup__add(X4)=>c_Groups_Ozero__class_Ozero(X4)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__zero)). 4.46/4.68 fof(fact_min__max_Oinf_Oidem, axiom, ![X12, X4]:(X12=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X12),X12)<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf_Oidem)). 4.46/4.68 fof(fact_Compl__eq__Compl__iff, axiom, ![X1, X2, X4]:(X2=X1<=>hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X1)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__eq__Compl__iff)). 4.46/4.68 fof(fact_add__is__0, axiom, ![X14, X22]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X14)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=>(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X22&c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__is__0)). 4.46/4.68 fof(fact_option__map__is__None, axiom, ![X165, X27, X4, X3]:(X165=c_Option_Ooption_ONone(X3)<=>hAPP(hAPP(c_Option_Omap(X3,X4),X27),X165)=c_Option_Ooption_ONone(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option__map__is__None)). 4.46/4.68 fof(fact_greaterThan__eq__iff, axiom, ![X5, X6, X4]:(class_Orderings_Olinorder(X4)=>(X6=X5<=>hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X6)=hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThan__eq__iff)). 4.46/4.68 fof(fact_compl__top__eq, axiom, ![X4]:(class_Lattices_Oboolean__algebra(X4)=>c_Orderings_Obot__class_Obot(X4)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Orderings_Otop__class_Otop(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__top__eq)). 4.46/4.68 fof(fact_nat__mult__eq__1__iff, axiom, ![X14, X22]:((c_Groups_Oone__class_Oone(tc_Nat_Onat)=X14&c_Groups_Oone__class_Oone(tc_Nat_Onat)=X22)<=>c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__eq__1__iff)). 4.46/4.68 fof(fact_lessThan__eq__iff, axiom, ![X5, X6, X4]:((hAPP(c_SetInterval_Oord__class_OlessThan(X4),X5)=hAPP(c_SetInterval_Oord__class_OlessThan(X4),X6)<=>X5=X6)<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessThan__eq__iff)). 4.46/4.68 fof(fact_atMost__eq__iff, axiom, ![X5, X6, X4]:((X5=X6<=>hAPP(c_SetInterval_Oord__class_OatMost(X4),X5)=hAPP(c_SetInterval_Oord__class_OatMost(X4),X6))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atMost__eq__iff)). 4.46/4.68 fof(fact_atLeast__eq__iff, axiom, ![X5, X6, X4]:(class_Orderings_Olinorder(X4)=>(hAPP(c_SetInterval_Oord__class_OatLeast(X4),X6)=hAPP(c_SetInterval_Oord__class_OatLeast(X4),X5)<=>X6=X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast__eq__iff)). 4.46/4.68 fof(fact_sorted__remdups, axiom, ![X31, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Osorted(X4,X31)=>c_List_Olinorder__class_Osorted(X4,c_List_Oremdups(X4,X31)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__remdups)). 4.46/4.68 fof(fact_nat__1__eq__mult__iff, axiom, ![X14, X22]:(c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X14)<=>(c_Groups_Oone__class_Oone(tc_Nat_Onat)=X14&X22=c_Groups_Oone__class_Oone(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__1__eq__mult__iff)). 4.46/4.68 fof(help_c__fimplies__1, axiom, ![X80, X28]:(hBOOL(X28)|hBOOL(hAPP(hAPP(c_fimplies,X28),X80))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fimplies__1)). 4.46/4.68 fof(fact_asm, axiom, ![X82, X202, X4]:(c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,X202)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool)),X202),X82))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_asm)). 4.46/4.68 fof(fact_WT_Oequations_I7_J, axiom, ![X18]:(hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X18)))<=>?[X44]:hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X44)=hAPP(c_Com_Obody,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WT_Oequations_I7_J)). 4.46/4.68 fof(fact_right__minus__eq, axiom, ![X37, X18, X4]:((X37=X18<=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X18),X37))<=class_Groups_Ogroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_right__minus__eq)). 4.46/4.68 fof(fact_mod__self, axiom, ![X12, X4]:(c_Groups_Ozero__class_Ozero(X4)=c_Divides_Odiv__class_Omod(X4,X12,X12)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__self)). 4.46/4.68 fof(fact_pair__box_Oinject, axiom, ![X278, X223, X37, X18, X3, X4]:(c_Nitpick_Opair__box_OPairBox(X4,X3,X18,X37)=c_Nitpick_Opair__box_OPairBox(X4,X3,X223,X278)<=>(X18=X223&X37=X278)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__box_Oinject)). 4.46/4.68 fof(fact_WTs__elim__cases_I4_J, axiom, ![X290, X226]:(~((hBOOL(hAPP(c_Com_OWT,X226))=>~(hBOOL(hAPP(c_Com_OWT,X290)))))<=hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X226,X290)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WTs__elim__cases_I4_J)). 4.46/4.68 fof(fact_equal__eq, axiom, ![X5, X6, X4]:(class_HOL_Oequal(X4)=>(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X4),X6),X5))<=>X5=X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equal__eq)). 4.46/4.68 fof(fact_is__nat__def, axiom, ![X6]:(c_Nat__Transfer_Ois__nat(X6)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_is__nat__def)). 4.46/4.68 fof(fact_sorted__list__of__set__empty, axiom, ![X4]:(class_Orderings_Olinorder(X4)=>c_List_Olinorder__class_Osorted__list__of__set(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__list__of__set__empty)). 4.46/4.68 fof(fact_Nil__is__append__conv, axiom, ![X32, X7, X4]:(c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Oappend(X4),X7),X32)<=>(c_List_Olist_ONil(X4)=X7&X32=c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nil__is__append__conv)). 4.46/4.68 fof(fact_Inf__empty, axiom, ![X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>c_Complete__Lattice_OInf__class_OInf(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__empty)). 4.46/4.68 fof(fact_finite__code, axiom, ![X2, X4]:(class_Finite__Set_Ofinite(X4)=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__code)). 4.46/4.68 fof(fact_neg__equal__0__iff__equal, axiom, ![X18, X4]:((X18=c_Groups_Ozero__class_Ozero(X4)<=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),X18)=c_Groups_Ozero__class_Ozero(X4))<=class_Groups_Ogroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__equal__0__iff__equal)). 4.46/4.68 fof(fact_abs__eq__0, axiom, ![X18, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>(c_Groups_Ozero__class_Ozero(X4)=hAPP(c_Groups_Oabs__class_Oabs(X4),X18)<=>X18=c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__eq__0)). 4.46/4.68 fof(fact_wfP__accp__iff, axiom, ![X16, X4]:(![X138]:hBOOL(hAPP(c_Wellfounded_Oaccp(X4,X16),X138))<=>c_Wellfounded_OwfP(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__accp__iff)). 4.46/4.68 fof(fact_WTs__elim__cases_I7_J, axiom, ![X159]:(hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X159)))=>~(![X44]:hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X44)!=hAPP(c_Com_Obody,X159))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WTs__elim__cases_I7_J)). 4.46/4.68 fof(help_c__fdisj__3, axiom, ![X80, X28]:(~(hBOOL(hAPP(hAPP(c_fdisj,X28),X80)))|hBOOL(X28)|hBOOL(X80)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fdisj__3)). 4.46/4.68 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures, axiom, ![X5, X6]:(c_Nat__Transfer_Ois__nat(X6)=>c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X6,X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SetInterval_Otransfer__int__nat__set__function__closures)). 4.46/4.68 fof(fact_int__int__eq, axiom, ![X14, X22]:(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14)<=>X14=X22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__int__eq)). 4.46/4.68 fof(fact_not__one__less__zero, axiom, ![X4]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__one__less__zero)). 4.46/4.68 fof(fact_bot__fun__def, axiom, ![X6, X3, X4]:(class_Orderings_Obot(X4)=>hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3,X4)),X6)=c_Orderings_Obot__class_Obot(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bot__fun__def)). 4.46/4.68 fof(fact_subset__empty, axiom, ![X2, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__empty)). 4.46/4.68 fof(fact_not__one__le__zero, axiom, ![X4]:(class_Rings_Olinordered__semidom(X4)=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__one__le__zero)). 4.46/4.68 fof(fact_option_Oinject, axiom, ![X223, X18, X4]:(hAPP(c_Option_Ooption_OSome(X4),X18)=hAPP(c_Option_Ooption_OSome(X4),X223)<=>X18=X223), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Oinject)). 4.46/4.68 fof(fact_rev__is__rev__conv, axiom, ![X32, X7, X4]:(hAPP(c_List_Orev(X4),X32)=hAPP(c_List_Orev(X4),X7)<=>X7=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__is__rev__conv)). 4.46/4.68 fof(fact_length__0__conv, axiom, ![X7, X4]:(X7=c_List_Olist_ONil(X4)<=>hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__0__conv)). 4.46/4.68 fof(fact_distinct__remdups__id, axiom, ![X57, X4]:(X57=c_List_Oremdups(X4,X57)<=hBOOL(hAPP(c_List_Odistinct(X4),X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__remdups__id)). 4.46/4.68 fof(fact_list__all2__Nil, axiom, ![X32, X28, X3, X4]:(X32=c_List_Olist_ONil(X3)<=>c_List_Olist__all2(X4,X3,X28,c_List_Olist_ONil(X4),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__Nil)). 4.46/4.68 fof(fact_fun__left__comm, axiom, ![X4]:(class_Groups_Oab__semigroup__mult(X4)=>c_Finite__Set_Ofun__left__comm(X4,X4,c_Groups_Otimes__class_Otimes(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm)). 4.46/4.68 fof(fact_min__max_Ofun__left__comm__idem__sup, axiom, ![X4]:(class_Orderings_Olinorder(X4)=>c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Orderings_Oord__class_Omax(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofun__left__comm__idem__sup)). 4.46/4.68 fof(fact_min__max_Ofun__left__comm__idem__inf, axiom, ![X4]:(c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Orderings_Oord__class_Omin(X4))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofun__left__comm__idem__inf)). 4.46/4.68 fof(fact_fun__left__comm__idem, axiom, ![X4]:(c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Groups_Otimes__class_Otimes(X4))<=class_Lattices_Oab__semigroup__idem__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem)). 4.46/4.68 fof(fact_fun__left__comm__idem__sup, axiom, ![X4]:(c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4))<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem__sup)). 4.46/4.68 fof(fact_min__ord__min, axiom, ![X4]:(class_Orderings_Oord(X4)=>c_Orderings_Oord_Omin(X4,c_Orderings_Oord__class_Oless__eq(X4))=c_Orderings_Oord__class_Omin(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__ord__min)). 4.46/4.68 fof(fact_self__append__conv2, axiom, ![X7, X4, X32]:(X7=c_List_Olist_ONil(X4)<=>hAPP(hAPP(c_List_Oappend(X4),X7),X32)=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_self__append__conv2)). 4.46/4.68 fof(fact_fun__left__comm__idem__inf, axiom, ![X4]:(c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4))<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem__inf)). 4.46/4.68 fof(fact_triple__valid__Suc, axiom, ![X251, X17, X4]:(c_Hoare__Mirabelle_Otriple__valid(X4,hAPP(c_Nat_OSuc,X17),X251)=>c_Hoare__Mirabelle_Otriple__valid(X4,X17,X251)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_triple__valid__Suc)). 4.46/4.68 fof(fact_max__ord__max, axiom, ![X4]:(c_Orderings_Oord_Omax(X4,c_Orderings_Oord__class_Oless__eq(X4))=c_Orderings_Oord__class_Omax(X4)<=class_Orderings_Oord(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__ord__max)). 4.46/4.68 fof(fact_append__self__conv, axiom, ![X32, X7, X4]:(X32=c_List_Olist_ONil(X4)<=>X7=hAPP(hAPP(c_List_Oappend(X4),X7),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__self__conv)). 4.46/4.68 fof(fact_add__eq__self__zero, axiom, ![X17, X19]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17)=X19=>X17=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__eq__self__zero)). 4.46/4.68 fof(help_c__fdisj__1, axiom, ![X80, X28]:(hBOOL(hAPP(hAPP(c_fdisj,X28),X80))|~(hBOOL(X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fdisj__1)). 4.46/4.68 fof(fact_lazy__sequence_Oinject, axiom, ![X280, X223, X242, X18, X4]:(c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X223,X280)=c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X18,X242)<=>(X18=X223&X280=X242)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Oinject)). 4.46/4.68 fof(fact_com_Osimps_I4_J, axiom, ![X53, X54, X55, X77, X78, X34]:(((X78=X54&X53=X77)&X55=X34)<=>c_Com_Ocom_OCond(X34,X78,X77)=c_Com_Ocom_OCond(X55,X54,X53)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I4_J)). 4.46/4.68 fof(fact_sgn0, axiom, ![X4]:(class_Groups_Osgn__if(X4)=>c_Groups_Ozero__class_Ozero(X4)=c_Groups_Osgn__class_Osgn(X4,c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn0)). 4.46/4.68 fof(help_c__fdisj__2, axiom, ![X28, X80]:(~(hBOOL(X80))|hBOOL(hAPP(hAPP(c_fdisj,X28),X80))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fdisj__2)). 4.46/4.68 fof(help_c__fimplies__2, axiom, ![X28, X80]:(~(hBOOL(X80))|hBOOL(hAPP(hAPP(c_fimplies,X28),X80))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fimplies__2)). 4.46/4.68 fof(fact_com_Osimps_I2_J, axiom, ![X164, X55, X214, X33, X34, X56]:(c_Com_Ocom_OLocal(X56,X34,X33)=c_Com_Ocom_OLocal(X214,X55,X164)<=>((X56=X214&X34=X55)&X33=X164)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I2_J)). 4.46/4.68 fof(fact_remdups__id__iff__distinct, axiom, ![X7, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X7))<=>X7=c_List_Oremdups(X4,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups__id__iff__distinct)). 4.46/4.68 fof(fact_Un__empty, axiom, ![X1, X2, X4]:((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X1&X2=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__empty)). 4.46/4.68 fof(fact_quotient__is__empty, axiom, ![X16, X2, X4]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X2<=>c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))=hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X2),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotient__is__empty)). 4.46/4.68 fof(fact_of__int__0, axiom, ![X4]:(hAPP(c_Int_Oring__1__class_Oof__int(X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(X4)<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__0)). 4.46/4.68 fof(fact_of__int__1, axiom, ![X4]:(c_Groups_Oone__class_Oone(X4)=hAPP(c_Int_Oring__1__class_Oof__int(X4),c_Groups_Oone__class_Oone(tc_Int_Oint))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__1)). 4.46/4.68 fof(fact_of__nat__1, axiom, ![X4]:(class_Rings_Osemiring__1(X4)=>c_Groups_Oone__class_Oone(X4)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),c_Groups_Oone__class_Oone(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__1)). 4.46/4.68 fof(fact_of__nat__0, axiom, ![X4]:(c_Groups_Ozero__class_Ozero(X4)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__0)). 4.46/4.68 fof(arity_prod__Lazy__Sequence_Osmall__lazy, axiom, ![X128, X129]:(class_Lazy__Sequence_Osmall__lazy(tc_prod(X129,X128))<=(class_Lazy__Sequence_Osmall__lazy(X128)&class_Lazy__Sequence_Osmall__lazy(X129))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_prod__Lazy__Sequence_Osmall__lazy)). 4.46/4.68 fof(arity_fun__HOL_Oequal, axiom, ![X128, X129]:((class_Enum_Oenum(X129)&class_HOL_Oequal(X128))=>class_HOL_Oequal(tc_fun(X129,X128))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__HOL_Oequal)). 4.46/4.68 fof(fact_int__eq__0__conv, axiom, ![X14]:(X14=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__eq__0__conv)). 4.46/4.68 fof(fact_Sup__empty, axiom, ![X4]:(c_Orderings_Obot__class_Obot(X4)=c_Complete__Lattice_OSup__class_OSup(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__empty)). 4.46/4.68 fof(arity_sum__Finite__Set_Ofinite, axiom, ![X128, X129]:(class_Finite__Set_Ofinite(tc_sum(X129,X128))<=(class_Finite__Set_Ofinite(X128)&class_Finite__Set_Ofinite(X129))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_sum__Finite__Set_Ofinite)). 4.46/4.68 fof(arity_prod__Finite__Set_Ofinite, axiom, ![X128, X129]:(class_Finite__Set_Ofinite(tc_prod(X129,X128))<=(class_Finite__Set_Ofinite(X128)&class_Finite__Set_Ofinite(X129))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_prod__Finite__Set_Ofinite)). 4.46/4.68 fof(arity_fun__Finite__Set_Ofinite, axiom, ![X128, X129]:(class_Finite__Set_Ofinite(tc_fun(X129,X128))<=(class_Finite__Set_Ofinite(X128)&class_Finite__Set_Ofinite(X129))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Finite__Set_Ofinite)). 4.46/4.68 fof(arity_prod__Smallcheck_Osmall, axiom, ![X128, X129]:((class_Smallcheck_Osmall(X129)&class_Smallcheck_Osmall(X128))=>class_Smallcheck_Osmall(tc_prod(X129,X128))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_prod__Smallcheck_Osmall)). 4.46/4.68 fof(fact_image__is__empty, axiom, ![X2, X27, X4, X3]:(X2=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))<=>hAPP(c_Set_Oimage(X3,X4,X27),X2)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__is__empty)). 4.46/4.68 fof(fact_WT_OBody, axiom, ![X249]:(hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X249)))<=hAPP(c_Com_Obody,X249)!=c_Option_Ooption_ONone(tc_Com_Ocom)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WT_OBody)). 4.46/4.68 fof(arity_sum__Enum_Oenum, axiom, ![X128, X129]:(class_Enum_Oenum(tc_sum(X129,X128))<=(class_Enum_Oenum(X129)&class_Enum_Oenum(X128))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_sum__Enum_Oenum)). 4.46/4.68 fof(arity_prod__Enum_Oenum, axiom, ![X128, X129]:(class_Enum_Oenum(tc_prod(X129,X128))<=(class_Enum_Oenum(X129)&class_Enum_Oenum(X128))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_prod__Enum_Oenum)). 4.46/4.68 fof(arity_fun__Enum_Oenum, axiom, ![X128, X129]:((class_Enum_Oenum(X128)&class_Enum_Oenum(X129))=>class_Enum_Oenum(tc_fun(X129,X128))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Enum_Oenum)). 4.46/4.68 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J, axiom, ![X47, X48]:(c_Nat__Transfer_Ois__nat(X48)=>(c_Nat__Transfer_Ois__nat(X47)=>c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X48,X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J)). 4.46/4.68 fof(fact_insort__not__Nil, axiom, ![X7, X18, X27, X4, X3]:(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X3,X27),X18),X7)!=c_List_Olist_ONil(X4)<=class_Orderings_Olinorder(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__not__Nil)). 4.46/4.68 fof(help_c__fimplies__3, axiom, ![X80, X28]:(hBOOL(X80)|~(hBOOL(X28))|~(hBOOL(hAPP(hAPP(c_fimplies,X28),X80)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fimplies__3)). 4.46/4.68 fof(fact_empty__replicate, axiom, ![X6, X14, X4]:(c_List_Oreplicate(X4,X14,X6)=c_List_Olist_ONil(X4)<=>X14=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__replicate)). 4.46/4.68 fof(fact_set__empty2, axiom, ![X7, X4]:(hAPP(c_List_Oset(X4),X7)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=>X7=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__empty2)). 4.46/4.68 fof(fact_set__empty__eq, axiom, ![X192, X4]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=c_Option_Oset(X4,X192)<=>c_Option_Ooption_ONone(X4)=X192), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__empty__eq)). 4.46/4.68 fof(help_c__fNot__2, axiom, ![X28]:(~(~(hBOOL(X28)))|hBOOL(hAPP(c_fNot,X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fNot__2)). 4.46/4.68 fof(fact_rotate1__is__Nil__conv, axiom, ![X7, X4]:(X7=c_List_Olist_ONil(X4)<=>hAPP(c_List_Orotate1(X4),X7)=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate1__is__Nil__conv)). 4.46/4.68 fof(fact_rev__is__Nil__conv, axiom, ![X7, X4]:(hAPP(c_List_Orev(X4),X7)=c_List_Olist_ONil(X4)<=>X7=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__is__Nil__conv)). 4.46/4.68 fof(fact_hoare__sound, axiom, ![X202, X82, X4]:(c_Hoare__Mirabelle_Ohoare__valids(X4,X82,X202)<=c_Hoare__Mirabelle_Ohoare__derivs(X4,X82,X202)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hoare__sound)). 4.46/4.68 fof(fact_iszero__0, axiom, ![X4]:(c_Int_Oiszero(X4,c_Groups_Ozero__class_Ozero(X4))<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_iszero__0)). 4.46/4.68 fof(fact_order__less__irrefl, axiom, ![X48, X4]:(class_Orderings_Opreorder(X4)=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X48),X48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__less__irrefl)). 4.46/4.68 fof(help_c__fequal__1, axiom, ![X5, X6]:(~(hBOOL(hAPP(hAPP(c_fequal,X6),X5)))|X6=X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fequal__1)). 4.46/4.68 fof(fact_com_Osimps_I3_J, axiom, ![X53, X54, X77, X78]:(c_Com_Ocom_OSemi(X78,X77)=c_Com_Ocom_OSemi(X54,X53)<=>(X54=X78&X77=X53)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I3_J)). 4.46/4.68 fof(fact_nat__list__def, axiom, ![X67]:(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X67))<=>c_List_Onat__list(X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__list__def)). 4.46/4.68 fof(fact_Code__Numeral_Onat__of__inject, axiom, ![X67, X45]:(X67=X45<=>hAPP(c_Code__Numeral_Onat__of,X45)=hAPP(c_Code__Numeral_Onat__of,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Code__Numeral_Onat__of__inject)). 4.46/4.68 fof(fact_Rep__Integ__inject, axiom, ![X5, X6]:(hAPP(c_Int_ORep__Integ,X5)=hAPP(c_Int_ORep__Integ,X6)<=>X5=X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Rep__Integ__inject)). 4.46/4.68 fof(fact_com_Osimps_I5_J, axiom, ![X164, X55, X33, X34]:(c_Com_Ocom_OWhile(X55,X164)=c_Com_Ocom_OWhile(X34,X33)<=>(X55=X34&X164=X33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I5_J)). 4.46/4.68 fof(fact_nat_Oinject, axiom, ![X244, X201]:(hAPP(c_Nat_OSuc,X244)=hAPP(c_Nat_OSuc,X201)<=>X201=X244), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat_Oinject)). 4.46/4.68 fof(arity_fun__Orderings_Otop, axiom, ![X129, X128]:(class_Orderings_Otop(X128)=>class_Orderings_Otop(tc_fun(X129,X128))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Orderings_Otop)). 4.46/4.68 fof(arity_fun__Groups_Ouminus, axiom, ![X129, X128]:(class_Groups_Ouminus(X128)=>class_Groups_Ouminus(tc_fun(X129,X128))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Groups_Ouminus)). 4.46/4.68 fof(arity_fun__Lattices_Odistrib__lattice, axiom, ![X129, X128]:(class_Lattices_Odistrib__lattice(X128)=>class_Lattices_Odistrib__lattice(tc_fun(X129,X128))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Odistrib__lattice)). 4.46/4.68 fof(arity_fun__Orderings_Oord, axiom, ![X129, X128]:(class_Orderings_Oord(tc_fun(X129,X128))<=class_Orderings_Oord(X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Orderings_Oord)). 4.46/4.68 fof(arity_fun__Lattices_Oboolean__algebra, axiom, ![X129, X128]:(class_Lattices_Oboolean__algebra(tc_fun(X129,X128))<=class_Lattices_Oboolean__algebra(X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Oboolean__algebra)). 4.46/4.68 fof(arity_fun__Orderings_Opreorder, axiom, ![X129, X128]:(class_Orderings_Opreorder(tc_fun(X129,X128))<=class_Orderings_Opreorder(X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Orderings_Opreorder)). 4.46/4.68 fof(arity_fun__Lattices_Obounded__lattice__top, axiom, ![X129, X128]:(class_Lattices_Obounded__lattice__top(tc_fun(X129,X128))<=class_Lattices_Obounded__lattice(X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Obounded__lattice__top)). 4.46/4.68 fof(arity_fun__Lattices_Obounded__lattice, axiom, ![X129, X128]:(class_Lattices_Obounded__lattice(X128)=>class_Lattices_Obounded__lattice(tc_fun(X129,X128))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Obounded__lattice)). 4.46/4.68 fof(arity_fun__Complete__Lattice_Ocomplete__lattice, axiom, ![X129, X128]:(class_Complete__Lattice_Ocomplete__lattice(tc_fun(X129,X128))<=class_Complete__Lattice_Ocomplete__lattice(X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Complete__Lattice_Ocomplete__lattice)). 4.46/4.68 fof(help_c__fconj__2, axiom, ![X80, X28]:(~(hBOOL(hAPP(hAPP(c_fconj,X28),X80)))|hBOOL(X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fconj__2)). 4.46/4.68 fof(help_c__fconj__3, axiom, ![X80, X28]:(~(hBOOL(hAPP(hAPP(c_fconj,X28),X80)))|hBOOL(X80)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fconj__3)). 4.46/4.68 fof(arity_fun__Lattices_Osemilattice__sup, axiom, ![X129, X128]:(class_Lattices_Olattice(X128)=>class_Lattices_Osemilattice__sup(tc_fun(X129,X128))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Osemilattice__sup)). 4.46/4.68 fof(arity_fun__Lattices_Osemilattice__inf, axiom, ![X129, X128]:(class_Lattices_Osemilattice__inf(tc_fun(X129,X128))<=class_Lattices_Olattice(X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Osemilattice__inf)). 4.46/4.68 fof(arity_fun__Lattices_Olattice, axiom, ![X129, X128]:(class_Lattices_Olattice(tc_fun(X129,X128))<=class_Lattices_Olattice(X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Olattice)). 4.46/4.68 fof(arity_fun__Orderings_Obot, axiom, ![X129, X128]:(class_Orderings_Obot(X128)=>class_Orderings_Obot(tc_fun(X129,X128))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Orderings_Obot)). 4.46/4.68 fof(fact_remdups__eq__nil__right__iff, axiom, ![X6, X4]:(X6=c_List_Olist_ONil(X4)<=>c_List_Oremdups(X4,X6)=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups__eq__nil__right__iff)). 4.46/4.68 fof(arity_fun__Orderings_Oorder, axiom, ![X129, X128]:(class_Orderings_Oorder(X128)=>class_Orderings_Oorder(tc_fun(X129,X128))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Orderings_Oorder)). 4.46/4.68 fof(arity_fun__Lattices_Obounded__lattice__bot, axiom, ![X129, X128]:(class_Lattices_Obounded__lattice(X128)=>class_Lattices_Obounded__lattice__bot(tc_fun(X129,X128))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Obounded__lattice__bot)). 4.46/4.68 fof(arity_fun__Groups_Ominus, axiom, ![X129, X128]:(class_Groups_Ominus(X128)=>class_Groups_Ominus(tc_fun(X129,X128))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Groups_Ominus)). 4.46/4.68 fof(fact_iszero__def, axiom, ![X35, X4]:(class_Rings_Osemiring__1(X4)=>(c_Int_Oiszero(X4,X35)<=>c_Groups_Ozero__class_Ozero(X4)=X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_iszero__def)). 4.46/4.68 fof(fact_sup__max, axiom, ![X4]:(c_Orderings_Oord__class_Omax(X4)=c_Lattices_Osemilattice__sup__class_Osup(X4)<=(class_Lattices_Osemilattice__sup(X4)&class_Orderings_Olinorder(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__max)). 4.46/4.68 fof(fact_inf__min, axiom, ![X4]:(c_Lattices_Osemilattice__inf__class_Oinf(X4)=c_Orderings_Oord__class_Omin(X4)<=(class_Lattices_Osemilattice__inf(X4)&class_Orderings_Olinorder(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__min)). 4.46/4.68 fof(fact_nonzero__number__of__Min, axiom, ![X4]:(class_Int_Onumber__ring(X4)=>~(c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonzero__number__of__Min)). 4.46/4.68 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy, axiom, ![X128]:(class_Lazy__Sequence_Osmall__lazy(X128)=>class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X128))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_List__Olist__Lazy__Sequence_Osmall__lazy)). 4.46/4.68 fof(fact_wf__acyclic, axiom, ![X16, X4]:(c_Wellfounded_Owf(X4,X16)=>c_Wellfounded_Oacyclic(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__acyclic)). 4.46/4.68 fof(arity_Option__Ooption__Finite__Set_Ofinite, axiom, ![X128]:(class_Finite__Set_Ofinite(X128)=>class_Finite__Set_Ofinite(tc_Option_Ooption(X128))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Option__Ooption__Finite__Set_Ofinite)). 4.46/4.68 fof(arity_Option__Ooption__Enum_Oenum, axiom, ![X128]:(class_Enum_Oenum(X128)=>class_Enum_Oenum(tc_Option_Ooption(X128))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Option__Ooption__Enum_Oenum)). 4.46/4.68 fof(fact_com_Osimps_I6_J, axiom, ![X79, X319]:(hAPP(c_Com_Ocom_OBODY,X79)=hAPP(c_Com_Ocom_OBODY,X319)<=>X319=X79), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I6_J)). 4.46/4.68 fof(fact_eq__equal, axiom, ![X4]:(c_fequal=c_HOL_Oequal__class_Oequal(X4)<=class_HOL_Oequal(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__equal)). 4.46/4.68 fof(help_c__fNot__1, axiom, ![X28]:(~(hBOOL(hAPP(c_fNot,X28)))|~(hBOOL(X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fNot__1)). 4.46/4.68 fof(fact_not__iszero__1, axiom, ![X4]:(~(c_Int_Oiszero(X4,c_Groups_Oone__class_Oone(X4)))<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__iszero__1)). 4.46/4.68 fof(fact_one__neq__zero, axiom, ![X4]:(c_Groups_Ozero__class_Ozero(X4)!=c_Groups_Oone__class_Oone(X4)<=class_Rings_Ozero__neq__one(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__neq__zero)). 4.46/4.68 fof(fact_Nil__notin__lex, axiom, ![X16, X32, X4]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_ONil(X4)),X32)),c_List_Olex(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nil__notin__lex)). 4.46/4.68 fof(fact_not__Nil__listrel1, axiom, ![X16, X7, X4]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_ONil(X4)),X7)),c_List_Olistrel1(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__Nil__listrel1)). 4.46/4.68 fof(fact_Nil2__notin__lex, axiom, ![X16, X7, X4]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),c_List_Olist_ONil(X4))),c_List_Olex(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nil2__notin__lex)). 4.46/4.68 fof(fact_lexord__Nil__right, axiom, ![X16, X6, X4]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X6),c_List_Olist_ONil(X4))),c_List_Olexord(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__Nil__right)). 4.46/4.68 fof(fact_not__listrel1__Nil, axiom, ![X16, X7, X4]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X7),c_List_Olist_ONil(X4))),c_List_Olistrel1(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__listrel1__Nil)). 4.46/4.68 fof(fact_in__measures_I1_J, axiom, ![X5, X6, X4]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X5)),c_List_Omeasures(X4,c_List_Olist_ONil(tc_fun(X4,tc_Nat_Onat)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__measures_I1_J)). 4.46/4.68 fof(fact_not__zle__0__negative, axiom, ![X17]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X17)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__zle__0__negative)). 4.46/4.69 fof(fact_not__int__zless__negative, axiom, ![X19, X17]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__int__zless__negative)). 4.46/4.69 fof(fact_map__upd__nonempty, axiom, ![X6, X45, X64, X3, X4]:hAPP(c_COMBK(tc_Option_Ooption(X3),X4),c_Option_Ooption_ONone(X3))!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),X64),X45),hAPP(c_Option_Ooption_OSome(X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upd__nonempty)). 4.46/4.69 fof(fact_not__add__less1, axiom, ![X20, X21]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20)),X21))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__add__less1)). 4.46/4.69 fof(fact_not__add__less2, axiom, ![X21, X20]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X21)),X21))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__add__less2)). 4.46/4.69 fof(fact_int__less__0__conv, axiom, ![X15]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X15)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__less__0__conv)). 4.46/4.69 fof(fact_Cantors__paradox, axiom, ![X2, X4]:~(?[X40]:hAPP(c_Set_OPow(X4),X2)=hAPP(c_Set_Oimage(X4,tc_fun(X4,tc_HOL_Obool),X40),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cantors__paradox)). 4.46/4.69 fof(fact_infinite__UNIV__listI, axiom, ![X4]:~(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X4)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X4),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_infinite__UNIV__listI)). 4.46/4.69 fof(fact_empty__fold1SetE, axiom, ![X6, X27, X4]:~(hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,X27,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__fold1SetE)). 4.46/4.69 fof(fact_less__nat__zero__code, axiom, ![X17]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__nat__zero__code)). 4.46/4.69 fof(fact_not__psubset__empty, axiom, ![X2, X4]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__psubset__empty)). 4.46/4.69 fof(fact_bot2E, axiom, ![X5, X6, X3, X4]:~(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_fun(X3,tc_HOL_Obool))),X6),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bot2E)). 4.46/4.69 fof(fact_infinite__UNIV__nat, axiom, ~(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_infinite__UNIV__nat)). 4.46/4.69 fof(fact_infinite__UNIV__int, axiom, ~(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_infinite__UNIV__int)). 4.46/4.69 fof(fact_com_Osimps_I36_J, axiom, ![X53, X54, X55, X33, X34, X56]:c_Com_Ocom_OLocal(X56,X34,X33)!=c_Com_Ocom_OCond(X55,X54,X53), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I36_J)). 4.46/4.69 fof(fact_not__neg__int, axiom, ![X17]:~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__neg__int)). 4.46/4.69 fof(fact_less__irrefl__nat, axiom, ![X17]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__irrefl__nat)). 4.46/4.69 fof(fact_list_Osimps_I3_J, axiom, ![X162, X163, X4]:c_List_Olist_ONil(X4)!=hAPP(hAPP(c_List_Olist_OCons(X4),X163),X162), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osimps_I3_J)). 4.46/4.69 fof(fact_rel__simps_I7_J, axiom, ~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I7_J)). 4.46/4.69 fof(fact_com_Osimps_I39_J, axiom, ![X33, X34, X56, X164, X55]:c_Com_Ocom_OLocal(X56,X34,X33)!=c_Com_Ocom_OWhile(X55,X164), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I39_J)). 4.46/4.69 fof(fact_com_Osimps_I45_J, axiom, ![X77, X78, X53, X54, X55]:c_Com_Ocom_OSemi(X78,X77)!=c_Com_Ocom_OCond(X55,X54,X53), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I45_J)). 4.46/4.69 fof(fact_com_Osimps_I34_J, axiom, ![X53, X54, X33, X34, X56]:c_Com_Ocom_OSemi(X54,X53)!=c_Com_Ocom_OLocal(X56,X34,X33), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I34_J)). 4.46/4.69 fof(fact_com_Osimps_I41_J, axiom, ![X33, X34, X56, X79]:c_Com_Ocom_OLocal(X56,X34,X33)!=hAPP(c_Com_Ocom_OBODY,X79), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I41_J)). 4.46/4.69 fof(fact_com_Osimps_I54_J, axiom, ![X79, X77, X78, X34]:hAPP(c_Com_Ocom_OBODY,X79)!=c_Com_Ocom_OCond(X34,X78,X77), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I54_J)). 4.46/4.69 fof(fact_com_Osimps_I53_J, axiom, ![X77, X78, X34, X164, X55]:c_Com_Ocom_OWhile(X55,X164)!=c_Com_Ocom_OCond(X34,X78,X77), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I53_J)). 4.46/4.69 fof(fact_not__Cons__self, axiom, ![X48, X4, X57]:X57!=hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__Cons__self)). 4.46/4.69 fof(fact_option_Osimps_I3_J, axiom, ![X163, X4]:c_Option_Ooption_ONone(X4)!=hAPP(c_Option_Ooption_OSome(X4),X163), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Osimps_I3_J)). 4.46/4.69 fof(fact_com_Osimps_I48_J, axiom, ![X166, X167, X168]:c_Com_Ocom_OSemi(X168,X167)!=hAPP(c_Com_Ocom_OBODY,X166), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I48_J)). 4.46/4.69 fof(fact_lazy__sequence_Osimps_I3_J, axiom, ![X279, X163, X4]:c_Lazy__Sequence_Olazy__sequence_OEmpty(X4)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X163,X279), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Osimps_I3_J)). 4.46/4.69 fof(fact_com_Osimps_I58_J, axiom, ![X79, X33, X34]:c_Com_Ocom_OWhile(X34,X33)!=hAPP(c_Com_Ocom_OBODY,X79), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I58_J)). 4.46/4.69 fof(fact_empty__not__insert, axiom, ![X2, X18, X4]:c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Set_Oinsert(X4),X18),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__not__insert)). 4.46/4.69 fof(fact_com_Osimps_I47_J, axiom, ![X77, X78, X164, X55]:c_Com_Ocom_OWhile(X55,X164)!=c_Com_Ocom_OSemi(X78,X77), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I47_J)). 4.46/4.69 fof(fact_not__neg__1, axiom, ~(hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__neg__1)). 4.46/4.69 fof(fact_not__neg__0, axiom, ~(hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__neg__0)). 4.46/4.69 fof(fact_Pow__not__empty, axiom, ![X2, X4]:c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))!=hAPP(c_Set_OPow(X4),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__not__empty)). 4.46/4.69 fof(fact_com_Osimps_I15_J, axiom, ![X53, X54, X55]:c_Com_Ocom_OSKIP!=c_Com_Ocom_OCond(X55,X54,X53), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I15_J)). 4.46/4.69 fof(fact_com_Osimps_I10_J, axiom, ![X164, X55, X214]:c_Com_Ocom_OSKIP!=c_Com_Ocom_OLocal(X214,X55,X164), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I10_J)). 4.46/4.69 fof(conj_3, hypothesis, ~(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,v_y)),v_F))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_3)). 4.46/4.69 fof(fact_Suc__not__Zero, axiom, ![X19]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__not__Zero)). 4.46/4.69 fof(fact_list__ex__simps_I2_J, axiom, ![X28, X4]:~(c_List_Olist__ex(X4,X28,c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__simps_I2_J)). 4.46/4.69 fof(fact_list__ex1__simps_I1_J, axiom, ![X28, X4]:~(c_List_Olist__ex1(X4,X28,c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex1__simps_I1_J)). 4.46/4.69 fof(fact_UNIV__not__empty, axiom, ![X4]:c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__not__empty)). 4.46/4.69 fof(fact_com_Osimps_I18_J, axiom, ![X166]:c_Com_Ocom_OSKIP!=hAPP(c_Com_Ocom_OBODY,X166), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I18_J)). 4.46/4.69 fof(fact_com_Osimps_I13_J, axiom, ![X270, X271]:c_Com_Ocom_OSKIP!=c_Com_Ocom_OSemi(X271,X270), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I13_J)). 4.46/4.69 fof(fact_com_Osimps_I16_J, axiom, ![X164, X55]:c_Com_Ocom_OSKIP!=c_Com_Ocom_OWhile(X55,X164), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I16_J)). 4.46/4.69 fof(fact_Suc__n__not__n, axiom, ![X17]:X17!=hAPP(c_Nat_OSuc,X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__n__not__n)). 4.46/4.69 fof(fact_rel__simps_I40_J, axiom, c_Int_OPls!=c_Int_OMin, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I40_J)). 4.46/4.69 fof(help_c__fFalse__1, axiom, ~(hBOOL(c_fFalse)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fFalse__1)). 4.46/4.69 fof(fact_image__split__eq__Sigma, axiom, ![X2, X50, X27, X3, X4, X29]:hAPP(c_Set_Oimage(X29,tc_prod(X4,X3),hAPP(hAPP(c_COMBS(X29,X3,tc_prod(X4,X3)),hAPP(hAPP(c_COMBB(X4,tc_fun(X3,tc_prod(X4,X3)),X29),c_Product__Type_OPair(X4,X3)),X27)),X50)),X2)=hAPP(hAPP(c_Product__Type_OSigma(X4,X3),hAPP(c_Set_Oimage(X29,X4,X27),X2)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X4),c_Set_Oimage(X29,X3,X50)),hAPP(hAPP(c_COMBC(X4,tc_fun(X29,tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_HOL_Obool),tc_fun(tc_fun(X29,tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool),X4),c_Set_Ovimage(X29,X4,X27)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Set_Oinsert(X4)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__split__eq__Sigma)). 4.46/4.69 fof(fact_sublist__shift__lemma__Suc, axiom, ![X217, X7, X28, X4]:hAPP(hAPP(c_List_Omap(tc_prod(X4,tc_Nat_Onat),X4),c_Product__Type_Ofst(X4,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X4,tc_Nat_Onat)),X28),c_Product__Type_Osnd(X4,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X4,tc_Nat_Onat),X7),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X217))))=hAPP(hAPP(c_List_Omap(tc_prod(X4,tc_Nat_Onat),X4),c_Product__Type_Ofst(X4,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X4,tc_Nat_Onat)),X28),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X4,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X4,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X4,tc_Nat_Onat),X7),X217))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__shift__lemma__Suc)). 4.46/4.69 fof(fact_scomp__scomp, axiom, ![X58, X50, X27, X60, X61, X3, X59, X29, X4]:hAPP(hAPP(c_Product__Type_Oscomp(X4,X61,X60,X3),X27),hAPP(hAPP(c_COMBC(X61,tc_fun(X29,tc_fun(X59,X3)),tc_fun(X60,X3)),hAPP(hAPP(c_COMBB(tc_fun(X60,tc_prod(X29,X59)),tc_fun(tc_fun(X29,tc_fun(X59,X3)),tc_fun(X60,X3)),X61),c_Product__Type_Oscomp(X60,X29,X59,X3)),X50)),X58))=hAPP(hAPP(c_Product__Type_Oscomp(X4,X29,X59,X3),hAPP(hAPP(c_Product__Type_Oscomp(X4,X61,X60,tc_prod(X29,X59)),X27),X50)),X58), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_scomp__scomp)). 4.46/4.69 fof(fact_option__map__o__map__upd, axiom, ![X37, X18, X22, X27, X4, X3, X29]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X29),tc_Option_Ooption(X3),X4,hAPP(c_Option_Omap(X29,X3),X27)),X22)),X18),hAPP(c_Option_Ooption_OSome(X3),hAPP(X27,X37)))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X29),tc_Option_Ooption(X3),X4,hAPP(c_Option_Omap(X29,X3),X27)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X29)),X22),X18),hAPP(c_Option_Ooption_OSome(X29),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option__map__o__map__upd)). 4.46/4.69 fof(fact_Sigma__Diff__distrib2, axiom, ![X1, X2, X73, X3, X4]:hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X73),hAPP(hAPP(c_COMBS(X4,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool))),X2)),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X73),X2)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X73),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Diff__distrib2)). 4.46/4.69 fof(fact_Sigma__Un__distrib2, axiom, ![X1, X2, X73, X3, X4]:hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X73),hAPP(hAPP(c_COMBS(X4,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool))),X2)),X1))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X73),X2)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X73),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Un__distrib2)). 4.46/4.69 fof(fact_Sigma__Int__distrib2, axiom, ![X1, X2, X73, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X73),X2)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X73),X1))=hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X73),hAPP(hAPP(c_COMBS(X4,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool))),X2)),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Int__distrib2)). 4.46/4.69 fof(fact_UN__Un__distrib, axiom, ![X1, X2, X73, X4, X3]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X73),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X73),X1))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X73),hAPP(hAPP(c_COMBS(X3,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X3),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool))),X2)),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__Un__distrib)). 4.46/4.69 fof(fact_INT__Int__distrib, axiom, ![X1, X2, X73, X4, X3]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X73),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X73),X1))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X73),hAPP(hAPP(c_COMBS(X3,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X3),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool))),X2)),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__Int__distrib)). 4.46/4.69 fof(fact_map__of__map__restrict, axiom, ![X215, X27, X3, X4]:hAPP(c_Map_Omap__of(X4,X3),hAPP(hAPP(c_List_Omap(X4,tc_prod(X4,X3)),hAPP(hAPP(c_COMBS(X4,X3,tc_prod(X4,X3)),c_Product__Type_OPair(X4,X3)),X27)),X215))=c_Map_Orestrict__map(X4,X3,hAPP(c_Fun_Ocomp(X3,tc_Option_Ooption(X3),X4,c_Option_Ooption_OSome(X3)),X27),hAPP(c_List_Oset(X4),X215)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__map__restrict)). 4.46/4.69 fof(fact_map__pair_Ocompositionality, axiom, ![X315, X24, X58, X60, X61, X50, X27, X3, X59, X4, X29]:hAPP(c_Product__Type_Omap__pair(X61,X4,X60,X3,hAPP(c_Fun_Ocomp(X29,X4,X61,X27),X58),hAPP(c_Fun_Ocomp(X59,X3,X60,X50),X24)),X315)=hAPP(c_Product__Type_Omap__pair(X29,X4,X59,X3,X27,X50),hAPP(c_Product__Type_Omap__pair(X61,X29,X60,X59,X58,X24),X315)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair_Ocompositionality)). 4.46/4.69 fof(fact_zip__update, axiom, ![X47, X72, X48, X21, X57, X3, X4]:hAPP(hAPP(c_List_Ozip(X4,X3),hAPP(hAPP(c_List_Olist__update(X4,X57),X21),X48)),hAPP(hAPP(c_List_Olist__update(X3,X72),X21),X47))=hAPP(hAPP(c_List_Olist__update(tc_prod(X4,X3),hAPP(hAPP(c_List_Ozip(X4,X3),X57),X72)),X21),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X48),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__update)). 4.46/4.69 fof(fact_zip__Cons__Cons, axiom, ![X72, X47, X57, X48, X3, X4]:hAPP(hAPP(c_List_Olist_OCons(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X48),X47)),hAPP(hAPP(c_List_Ozip(X4,X3),X57),X72))=hAPP(hAPP(c_List_Ozip(X4,X3),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)),hAPP(hAPP(c_List_Olist_OCons(X3),X47),X72)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__Cons__Cons)). 4.46/4.69 fof(fact_image__add__atLeastLessThan, axiom, ![X25, X24, X45]:hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X45)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24),X25))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X45)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__add__atLeastLessThan)). 4.46/4.69 fof(fact_fun__upd__comp, axiom, ![X5, X6, X50, X27, X4, X3, X29]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X3),hAPP(c_Fun_Ocomp(X29,X3,X4,X27),X50)),X6),hAPP(X27,X5))=hAPP(c_Fun_Ocomp(X29,X3,X4,X27),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X29),X50),X6),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__comp)). 4.46/4.69 fof(fact_fst__comp__map__pair, axiom, ![X50, X27, X3, X4, X59, X29]:hAPP(c_Fun_Ocomp(X4,X29,tc_prod(X4,X3),X27),c_Product__Type_Ofst(X4,X3))=hAPP(c_Fun_Ocomp(tc_prod(X29,X59),X29,tc_prod(X4,X3),c_Product__Type_Ofst(X29,X59)),c_Product__Type_Omap__pair(X4,X29,X3,X59,X27,X50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fst__comp__map__pair)). 4.46/4.69 fof(fact_snd__comp__map__pair, axiom, ![X50, X27, X3, X4, X29, X59]:hAPP(c_Fun_Ocomp(X3,X29,tc_prod(X4,X3),X50),c_Product__Type_Osnd(X4,X3))=hAPP(c_Fun_Ocomp(tc_prod(X59,X29),X29,tc_prod(X4,X3),c_Product__Type_Osnd(X59,X29)),c_Product__Type_Omap__pair(X4,X59,X3,X29,X27,X50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snd__comp__map__pair)). 4.46/4.69 fof(fact_image__add__atLeastAtMost, axiom, ![X25, X24, X45]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X45),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X45))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X45)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24,X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__add__atLeastAtMost)). 4.46/4.69 fof(fact_transpose__map__map, axiom, ![X7, X27, X3, X4]:c_List_Otranspose(X4,hAPP(hAPP(c_List_Omap(tc_List_Olist(X3),tc_List_Olist(X4)),hAPP(c_List_Omap(X3,X4),X27)),X7))=hAPP(hAPP(c_List_Omap(tc_List_Olist(X3),tc_List_Olist(X4)),hAPP(c_List_Omap(X3,X4),X27)),c_List_Otranspose(X3,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__map__map)). 4.46/4.69 fof(fact_split__comp, axiom, ![X6, X50, X27, X59, X4, X29, X3]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3,X29,X4),hAPP(c_Fun_Ocomp(X59,tc_fun(X29,X4),X3,X27),X50)),X6)=hAPP(hAPP(X27,hAPP(X50,hAPP(c_Product__Type_Ofst(X3,X29),X6))),hAPP(c_Product__Type_Osnd(X3,X29),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__comp)). 4.46/4.69 fof(fact_length__filter__map, axiom, ![X7, X27, X3, X28, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Ofilter(X4,X28),hAPP(hAPP(c_List_Omap(X3,X4),X27),X7)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),hAPP(c_List_Ofilter(X3,hAPP(c_Fun_Ocomp(X4,tc_HOL_Obool,X3,X28),X27)),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__filter__map)). 4.46/4.69 fof(fact_zip__same__conv__map, axiom, ![X7, X4]:hAPP(hAPP(c_List_Omap(X4,tc_prod(X4,X4)),hAPP(hAPP(c_COMBS(X4,X4,tc_prod(X4,X4)),c_Product__Type_OPair(X4,X4)),c_COMBI(X4))),X7)=hAPP(hAPP(c_List_Ozip(X4,X4),X7),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__same__conv__map)). 4.46/4.69 fof(fact_UN__o, axiom, ![X27, X50, X29, X2, X4, X3]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_Fun_Ocomp(X29,tc_fun(X4,tc_HOL_Obool),X3,X50),X27))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29,tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X29,X27),X2)),X50), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__o)). 4.46/4.69 fof(fact_o__assoc, axiom, ![X58, X50, X59, X27, X4, X3, X29]:hAPP(c_Fun_Ocomp(X59,X3,X4,hAPP(c_Fun_Ocomp(X29,X3,X59,X27),X50)),X58)=hAPP(c_Fun_Ocomp(X29,X3,X4,X27),hAPP(c_Fun_Ocomp(X59,X29,X4,X50),X58)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_o__assoc)). 4.46/4.69 fof(fact_map__update, axiom, ![X5, X45, X7, X27, X4, X3]:hAPP(hAPP(c_List_Omap(X3,X4),X27),hAPP(hAPP(c_List_Olist__update(X3,X7),X45),X5))=hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Omap(X3,X4),X27),X7)),X45),hAPP(X27,X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__update)). 4.46/4.69 fof(fact_UN__simps_I10_J, axiom, ![X1, X2, X27, X29, X4, X3]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29,tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(X3,tc_fun(X4,tc_HOL_Obool),X29),X1),X27))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X29,X3,X27),X2)),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I10_J)). 4.46/4.69 fof(fact_INT__simps_I10_J, axiom, ![X1, X2, X27, X29, X4, X3]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X29,X3,X27),X2)),X1)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29,tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(X3,tc_fun(X4,tc_HOL_Obool),X29),X1),X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__simps_I10_J)). 4.46/4.69 fof(fact_restrict__complement__singleton__eq, axiom, ![X6, X27, X3, X4]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),X27),X6),c_Option_Ooption_ONone(X3))=c_Map_Orestrict__map(X4,X3,X27,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__complement__singleton__eq)). 4.46/4.69 fof(fact_option__map__comp, axiom, ![X165, X50, X29, X27, X4, X3]:hAPP(hAPP(c_Option_Omap(X29,X4),hAPP(c_Fun_Ocomp(X3,X4,X29,X27),X50)),X165)=hAPP(hAPP(c_Option_Omap(X3,X4),X27),hAPP(hAPP(c_Option_Omap(X29,X3),X50),X165)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option__map__comp)). 4.46/4.69 fof(fact_INT__insert, axiom, ![X1, X2, X18, X4, X3]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X3),X18),X2)),X1)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(X1,X18)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__insert)). 4.46/4.69 fof(fact_UN__insert, axiom, ![X1, X2, X18, X4, X3]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X3),X18),X2)),X1)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(X1,X18)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__insert)). 4.46/4.69 fof(fact_Range__Union, axiom, ![X46, X4, X3]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X46),c_Relation_ORange(X3,X4))=hAPP(c_Relation_ORange(X3,X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),X46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__Union)). 4.46/4.69 fof(fact_Domain__Union, axiom, ![X46, X3, X4]:hAPP(c_Relation_ODomain(X4,X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),X46))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X46),c_Relation_ODomain(X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__Union)). 4.46/4.69 fof(fact_map_Osimps_I2_J, axiom, ![X7, X6, X27, X4, X3]:hAPP(hAPP(c_List_Omap(X3,X4),X27),hAPP(hAPP(c_List_Olist_OCons(X3),X6),X7))=hAPP(hAPP(c_List_Olist_OCons(X4),hAPP(X27,X6)),hAPP(hAPP(c_List_Omap(X3,X4),X27),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map_Osimps_I2_J)). 4.46/4.69 fof(fact_foldl__Cons, axiom, ![X7, X6, X18, X27, X3, X4]:hAPP(c_List_Ofoldl(X4,X3,X27,X18),hAPP(hAPP(c_List_Olist_OCons(X3),X6),X7))=hAPP(c_List_Ofoldl(X4,X3,X27,hAPP(hAPP(X27,X18),X6)),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__Cons)). 4.46/4.69 fof(fact_take__map, axiom, ![X7, X27, X3, X14, X4]:hAPP(hAPP(c_List_Omap(X3,X4),X27),hAPP(hAPP(c_List_Otake(X3),X14),X7))=hAPP(hAPP(c_List_Otake(X4),X14),hAPP(hAPP(c_List_Omap(X3,X4),X27),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__map)). 4.46/4.69 fof(fact_drop__map, axiom, ![X7, X27, X3, X14, X4]:hAPP(hAPP(c_List_Odrop(X4),X14),hAPP(hAPP(c_List_Omap(X3,X4),X27),X7))=hAPP(hAPP(c_List_Omap(X3,X4),X27),hAPP(hAPP(c_List_Odrop(X3),X14),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__map)). 4.46/4.69 fof(fact_image__compose, axiom, ![X16, X50, X27, X29, X4, X3]:hAPP(c_Set_Oimage(X3,X4,hAPP(c_Fun_Ocomp(X29,X4,X3,X27),X50)),X16)=hAPP(c_Set_Oimage(X29,X4,X27),hAPP(c_Set_Oimage(X3,X29,X50),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__compose)). 4.46/4.69 fof(fact_maps__simps_I1_J, axiom, ![X7, X6, X27, X4, X3]:c_List_Omaps(X3,X4,X27,hAPP(hAPP(c_List_Olist_OCons(X3),X6),X7))=hAPP(hAPP(c_List_Oappend(X4),hAPP(X27,X6)),c_List_Omaps(X3,X4,X27,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_maps__simps_I1_J)). 4.46/4.69 fof(fact_Un__left__commute, axiom, ![X52, X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X52))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X1),X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__left__commute)). 4.46/4.69 fof(fact_Int__left__commute, axiom, ![X52, X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X52))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X1),X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__left__commute)). 4.46/4.69 fof(fact_converse__inv__image, axiom, ![X27, X26, X3, X4]:hAPP(c_Relation_Oconverse(X4,X4),hAPP(hAPP(c_Relation_Oinv__image(X3,X4),X26),X27))=hAPP(hAPP(c_Relation_Oinv__image(X3,X4),hAPP(c_Relation_Oconverse(X3,X3),X26)),X27), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__inv__image)). 4.46/4.69 fof(fact_list__size__map, axiom, ![X7, X50, X3, X27, X4]:c_List_Olist_Olist__size(X3,hAPP(c_Fun_Ocomp(X4,tc_Nat_Onat,X3,X27),X50),X7)=c_List_Olist_Olist__size(X4,X27,hAPP(hAPP(c_List_Omap(X3,X4),X50),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__size__map)). 4.46/4.69 fof(fact_power_Opower_Opower__Suc, axiom, ![X14, X18, X285, X286, X4]:hAPP(hAPP(X285,X18),hAPP(hAPP(c_Power_Opower_Opower(X4,X286,X285),X18),X14))=hAPP(hAPP(c_Power_Opower_Opower(X4,X286,X285),X18),hAPP(c_Nat_OSuc,X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power_Opower_Opower__Suc)). 4.46/4.69 fof(fact_Un__Inter, axiom, ![X1, X2, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X1),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Inter)). 4.46/4.69 fof(fact_Int__Union, axiom, ![X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X1))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X1),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Union)). 4.46/4.69 fof(fact_map__add__def, axiom, ![X6, X100, X99, X4, X3]:hAPP(c_Map_Omap__add(X3,X4,X99,X100),X6)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X4),X4,hAPP(X99,X6),c_Option_Ooption_OSome(X4)),hAPP(X100,X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__def)). 4.46/4.69 fof(fact_prod__case__beta, axiom, ![X109, X27, X4, X29, X3]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3,X29,X4),X27),X109)=hAPP(hAPP(X27,hAPP(c_Product__Type_Ofst(X3,X29),X109)),hAPP(c_Product__Type_Osnd(X3,X29),X109)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_prod__case__beta)). 4.46/4.69 fof(fact_image__Union, axiom, ![X46, X27, X4, X3]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X3,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X46),c_Set_Oimage(X3,X4,X27))=hAPP(c_Set_Oimage(X3,X4,X27),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Union)). 4.46/4.69 fof(fact_image__insert, axiom, ![X1, X18, X27, X4, X3]:hAPP(c_Set_Oimage(X3,X4,X27),hAPP(hAPP(c_Set_Oinsert(X3),X18),X1))=hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X27,X18)),hAPP(c_Set_Oimage(X3,X4,X27),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__insert)). 4.46/4.69 fof(fact_rotate__simps, axiom, ![X57, X48, X3, X4]:(c_List_Olist_ONil(X4)=hAPP(c_List_Orotate1(X4),c_List_Olist_ONil(X4))&hAPP(c_List_Orotate1(X3),hAPP(hAPP(c_List_Olist_OCons(X3),X48),X57))=hAPP(hAPP(c_List_Oappend(X3),X57),hAPP(hAPP(c_List_Olist_OCons(X3),X48),c_List_Olist_ONil(X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__simps)). 4.46/4.69 fof(fact_map__replicate__const, axiom, ![X306, X45, X4, X3]:hAPP(hAPP(c_List_Omap(X3,X4),hAPP(c_COMBK(X4,X3),X45)),X306)=c_List_Oreplicate(X4,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X306),X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__replicate__const)). 4.46/4.69 fof(fact_map__tl, axiom, ![X7, X27, X4, X3]:hAPP(hAPP(c_List_Omap(X3,X4),X27),hAPP(c_List_Otl(X3),X7))=hAPP(c_List_Otl(X4),hAPP(hAPP(c_List_Omap(X3,X4),X27),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__tl)). 4.46/4.69 fof(fact_mult__div__cancel, axiom, ![X19, X17]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19),X17))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__div__cancel)). 4.46/4.69 fof(fact_zmult__div__cancel, axiom, ![X19, X17]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19),X17))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__div__cancel)). 4.46/4.69 fof(fact_set__map, axiom, ![X7, X27, X3, X4]:hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Omap(X3,X4),X27),X7))=hAPP(c_Set_Oimage(X3,X4,X27),hAPP(c_List_Oset(X3),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__map)). 4.46/4.69 fof(fact_map__butlast, axiom, ![X7, X27, X4, X3]:c_List_Obutlast(X4,hAPP(hAPP(c_List_Omap(X3,X4),X27),X7))=hAPP(hAPP(c_List_Omap(X3,X4),X27),c_List_Obutlast(X3,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__butlast)). 4.46/4.69 fof(fact_nat__add__left__commute, axiom, ![X49, X47, X48]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),X49))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__left__commute)). 4.46/4.69 fof(fact_nat__rec__Suc, axiom, ![X201, X169, X38, X4]:hAPP(c_Nat_Onat_Onat__rec(X4,X38,X169),hAPP(c_Nat_OSuc,X201))=hAPP(hAPP(X169,X201),hAPP(c_Nat_Onat_Onat__rec(X4,X38,X169),X201)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__rec__Suc)). 4.46/4.69 fof(fact_mult__Suc, axiom, ![X17, X19]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X17))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19)),X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__Suc)). 4.46/4.69 fof(fact_partition_Osimps_I1_J, axiom, ![X28, X4]:hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_List_Olist_ONil(X4))=c_List_Opartition(X4,X28,c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition_Osimps_I1_J)). 4.46/4.69 fof(fact_mult__Suc__right, axiom, ![X17, X19]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X17))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),hAPP(c_Nat_OSuc,X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__Suc__right)). 4.46/4.69 fof(help_c__COMBS__1, axiom, ![X26, X80, X28, X4, X29, X3]:hAPP(hAPP(hAPP(c_COMBS(X3,X29,X4),X28),X80),X26)=hAPP(hAPP(X28,X26),hAPP(X80,X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBS__1)). 4.46/4.69 fof(fact_rev__filter, axiom, ![X7, X28, X4]:hAPP(c_List_Ofilter(X4,X28),hAPP(c_List_Orev(X4),X7))=hAPP(c_List_Orev(X4),hAPP(c_List_Ofilter(X4,X28),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__filter)). 4.46/4.69 fof(fact_insert__commute, axiom, ![X2, X5, X6, X4]:hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2))=hAPP(hAPP(c_Set_Oinsert(X4),X6),hAPP(hAPP(c_Set_Oinsert(X4),X5),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__commute)). 4.46/4.69 fof(fact_n__lists_Osimps_I1_J, axiom, ![X57, X4]:hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_List_Olist_ONil(tc_List_Olist(X4)))=c_Enum_On__lists(X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_n__lists_Osimps_I1_J)). 4.46/4.69 fof(fact_split__Pair, axiom, ![X3, X4]:c_Fun_Oid(tc_prod(X4,X3))=hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_prod(X4,X3)),c_Product__Type_OPair(X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__Pair)). 4.46/4.69 fof(fact_remove1__commute, axiom, ![X191, X47, X48, X4]:c_List_Oremove1(X4,X48,c_List_Oremove1(X4,X47,X191))=c_List_Oremove1(X4,X47,c_List_Oremove1(X4,X48,X191)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1__commute)). 4.46/4.69 fof(fact_New__DSequence_Opos__union__def, axiom, ![X24, X257, X107, X4]:hAPP(c_New__DSequence_Opos__union(X4,X107,X257),X24)=c_Lazy__Sequence_Oappend(X4,hAPP(X107,X24),hAPP(X257,X24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Opos__union__def)). 4.46/4.69 fof(fact_sublists_Osimps_I1_J, axiom, ![X4]:c_Enum_Osublists(X4,c_List_Olist_ONil(X4))=hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_List_Olist_ONil(tc_List_Olist(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublists_Osimps_I1_J)). 4.46/4.69 fof(fact_lexn_Osimps_I1_J, axiom, ![X16, X4]:hAPP(c_List_Olexn(X4,X16),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexn_Osimps_I1_J)). 4.46/4.69 fof(fact_rp__inv__image__def, axiom, ![X3, X4]:hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X3,X4),tc_prod(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(tc_prod(X3,X3),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X3,X4),tc_fun(tc_prod(X3,X3),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X3,X4),tc_prod(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(tc_prod(X3,X3),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X3,X4),tc_fun(tc_prod(X3,X3),tc_HOL_Obool)),tc_fun(tc_fun(X3,X4),tc_prod(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(tc_prod(X3,X3),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X3,X4),tc_fun(tc_prod(X3,X3),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X3,X4),tc_prod(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(tc_prod(X3,X3),tc_HOL_Obool))))),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X3,X4),tc_fun(tc_prod(X3,X3),tc_HOL_Obool)),tc_fun(tc_fun(X3,X4),tc_prod(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(tc_prod(X3,X3),tc_HOL_Obool))),tc_fun(tc_prod(X4,X4),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,X4),tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(tc_prod(X3,X3),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X3,X4),tc_fun(tc_prod(X3,X3),tc_HOL_Obool)),tc_fun(tc_fun(X3,X4),tc_prod(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(tc_prod(X3,X3),tc_HOL_Obool)))),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_COMBS(tc_fun(X3,X4),tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(tc_prod(X3,X3),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,X4),tc_fun(tc_prod(X3,X3),tc_HOL_Obool)),tc_fun(tc_fun(X3,X4),tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(tc_prod(X3,X3),tc_HOL_Obool)))),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(tc_prod(X3,X3),tc_HOL_Obool))),tc_fun(X3,X4)),c_Product__Type_OPair(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(tc_prod(X3,X3),tc_HOL_Obool)))),c_Relation_Oinv__image(X4,X3))))),c_Relation_Oinv__image(X4,X3)))=c_FunDef_Orp__inv__image(X4,X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rp__inv__image__def)). 4.46/4.69 fof(fact_partition_Osimps_I2_J, axiom, ![X7, X6, X28, X4]:c_List_Opartition(X4,X28,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7))=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X4),tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))),tc_fun(tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))),tc_List_Olist(X4)),c_COMBS(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),tc_fun(tc_List_Olist(X4),tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))),tc_List_Olist(X4)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),tc_List_Olist(X4)),hAPP(c_If(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(X28,X6)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),tc_List_Olist(X4)),c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(c_List_Olist_OCons(X4),X6))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),tc_fun(tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))),tc_List_Olist(X4)),c_COMBB(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_List_Olist(X4))),c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)))),hAPP(c_List_Olist_OCons(X4),X6)))),c_List_Opartition(X4,X28,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition_Osimps_I2_J)). 4.46/4.69 fof(fact_minus__int__def, axiom, ![X35]:hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X35)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X35), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__int__def)). 4.46/4.69 fof(fact_map__upds__fold__map__upd, axiom, ![X196, X215, X22, X3, X4]:c_Map_Omap__upds(X4,X3,X22,X215,X196)=hAPP(c_List_Ofoldl(tc_fun(X4,tc_Option_Ooption(X3)),tc_prod(X4,X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X3,tc_fun(X4,tc_Option_Ooption(X3)))),tc_fun(tc_prod(X4,X3),tc_fun(X4,tc_Option_Ooption(X3))),tc_fun(X4,tc_Option_Ooption(X3))),c_Product__Type_Oprod_Oprod__case(X4,X3,tc_fun(X4,tc_Option_Ooption(X3)))),hAPP(hAPP(c_COMBC(tc_fun(X4,tc_Option_Ooption(X3)),tc_fun(X3,tc_Option_Ooption(X3)),tc_fun(X4,tc_fun(X3,tc_fun(X4,tc_Option_Ooption(X3))))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(X3,tc_Option_Ooption(X3)),tc_fun(X3,tc_fun(X4,tc_Option_Ooption(X3))))),tc_fun(tc_fun(X3,tc_Option_Ooption(X3)),tc_fun(X4,tc_fun(X3,tc_fun(X4,tc_Option_Ooption(X3))))),tc_fun(X4,tc_Option_Ooption(X3))),c_COMBC(X4,tc_fun(X3,tc_Option_Ooption(X3)),tc_fun(X3,tc_fun(X4,tc_Option_Ooption(X3))))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_Option_Ooption(X3),tc_fun(X4,tc_Option_Ooption(X3)))),tc_fun(X4,tc_fun(tc_fun(X3,tc_Option_Ooption(X3)),tc_fun(X3,tc_fun(X4,tc_Option_Ooption(X3))))),tc_fun(X4,tc_Option_Ooption(X3))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X3),tc_fun(X4,tc_Option_Ooption(X3))),tc_fun(tc_fun(X3,tc_Option_Ooption(X3)),tc_fun(X3,tc_fun(X4,tc_Option_Ooption(X3)))),X4),c_COMBB(tc_Option_Ooption(X3),tc_fun(X4,tc_Option_Ooption(X3)),X3))),c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3))))),c_Option_Ooption_OSome(X3))),X22),hAPP(hAPP(c_List_Ozip(X4,X3),X215),X196)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upds__fold__map__upd)). 4.46/4.69 fof(fact_Sigma__def, axiom, ![X1, X2, X3, X4]:hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),X1)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBS(X4,tc_fun(X3,tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(tc_prod(X4,X3),tc_HOL_Obool))),X1)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_fun(tc_prod(X4,X3),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(tc_prod(X4,X3),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X3,tc_fun(tc_prod(X4,X3),tc_HOL_Obool))),X4),c_COMBC(X3,tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(tc_prod(X4,X3),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(tc_prod(X4,X3),tc_HOL_Obool))),X4),hAPP(c_COMBB(tc_prod(X4,X3),tc_fun(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X3),c_Set_Oinsert(tc_prod(X4,X3)))),c_Product__Type_OPair(X4,X3)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X3),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__def)). 4.46/4.69 fof(fact_UN__Times__distrib, axiom, ![X62, X254, X1, X2, X3, X4, X59, X29]:hAPP(hAPP(c_Product__Type_OSigma(X4,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29,tc_fun(X4,tc_HOL_Obool)),X2),X254)),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X59,tc_fun(X3,tc_HOL_Obool)),X1),X62)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X29,X59),tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X29,X59),X2),hAPP(c_COMBK(tc_fun(X59,tc_HOL_Obool),X29),X1))),hAPP(c_Product__Type_Oprod_Oprod__case(X29,X59,tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X29,tc_fun(X59,tc_fun(X4,tc_fun(X3,tc_HOL_Obool))),tc_fun(X59,tc_fun(tc_prod(X4,X3),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_fun(X3,tc_HOL_Obool)),tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),tc_fun(tc_fun(X59,tc_fun(X4,tc_fun(X3,tc_HOL_Obool))),tc_fun(X59,tc_fun(tc_prod(X4,X3),tc_HOL_Obool))),X29),c_COMBB(tc_fun(X4,tc_fun(X3,tc_HOL_Obool)),tc_fun(tc_prod(X4,X3),tc_HOL_Obool),X59)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_fun(X3,tc_HOL_Obool)),tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X29),c_Product__Type_OSigma(X4,X3)),X254))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X4,tc_fun(X3,tc_HOL_Obool)),X59),c_COMBK(tc_fun(X3,tc_HOL_Obool),X4)),X62)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__Times__distrib)). 4.46/4.69 fof(fact_zip__Cons, axiom, ![X32, X5, X7, X3, X4]:hAPP(hAPP(c_List_Ozip(X4,X3),X7),hAPP(hAPP(c_List_Olist_OCons(X3),X5),X32))=hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X4,X3)),X4,c_List_Olist_ONil(tc_prod(X4,X3)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_List_Olist(X4),tc_List_Olist(tc_prod(X4,X3))),tc_fun(tc_List_Olist(X4),tc_List_Olist(tc_prod(X4,X3)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X4,X3)),tc_List_Olist(tc_prod(X4,X3))),tc_fun(tc_fun(tc_List_Olist(X4),tc_List_Olist(tc_prod(X4,X3))),tc_fun(tc_List_Olist(X4),tc_List_Olist(tc_prod(X4,X3)))),X4),c_COMBB(tc_List_Olist(tc_prod(X4,X3)),tc_List_Olist(tc_prod(X4,X3)),tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_prod(X4,X3),tc_fun(tc_List_Olist(tc_prod(X4,X3)),tc_List_Olist(tc_prod(X4,X3))),X4),c_List_Olist_OCons(tc_prod(X4,X3))),hAPP(hAPP(c_COMBC(X4,X3,tc_prod(X4,X3)),c_Product__Type_OPair(X4,X3)),X5)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(X3),tc_List_Olist(tc_prod(X4,X3))),c_List_Ozip(X4,X3)),X32))),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__Cons)). 4.46/4.69 fof(fact_zip__Cons1, axiom, ![X32, X7, X6, X3, X4]:hAPP(hAPP(c_List_Ozip(X4,X3),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)),X32)=hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X4,X3)),X3,c_List_Olist_ONil(tc_prod(X4,X3)),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_List_Olist(X3),tc_List_Olist(tc_prod(X4,X3))),tc_fun(tc_List_Olist(X3),tc_List_Olist(tc_prod(X4,X3)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X4,X3)),tc_List_Olist(tc_prod(X4,X3))),tc_fun(tc_fun(tc_List_Olist(X3),tc_List_Olist(tc_prod(X4,X3))),tc_fun(tc_List_Olist(X3),tc_List_Olist(tc_prod(X4,X3)))),X3),c_COMBB(tc_List_Olist(tc_prod(X4,X3)),tc_List_Olist(tc_prod(X4,X3)),tc_List_Olist(X3))),hAPP(hAPP(c_COMBB(tc_prod(X4,X3),tc_fun(tc_List_Olist(tc_prod(X4,X3)),tc_List_Olist(tc_prod(X4,X3))),X3),c_List_Olist_OCons(tc_prod(X4,X3))),hAPP(c_Product__Type_OPair(X4,X3),X6)))),hAPP(c_List_Ozip(X4,X3),X7))),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__Cons1)). 4.46/4.69 fof(fact_map__zip__map2, axiom, ![X32, X50, X59, X7, X27, X4, X29, X3]:hAPP(hAPP(c_List_Omap(tc_prod(X3,X59),X4),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X59,X4),hAPP(hAPP(c_COMBB(tc_fun(X59,tc_prod(X3,X29)),tc_fun(X59,X4),X3),hAPP(c_COMBB(tc_prod(X3,X29),X4,X59),X27)),hAPP(hAPP(c_COMBC(X3,tc_fun(X59,X29),tc_fun(X59,tc_prod(X3,X29))),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_prod(X3,X29)),tc_fun(tc_fun(X59,X29),tc_fun(X59,tc_prod(X3,X29))),X3),c_COMBB(X29,tc_prod(X3,X29),X59)),c_Product__Type_OPair(X3,X29))),X50)))),hAPP(hAPP(c_List_Ozip(X3,X59),X7),X32))=hAPP(hAPP(c_List_Omap(tc_prod(X3,X29),X4),X27),hAPP(hAPP(c_List_Ozip(X3,X29),X7),hAPP(hAPP(c_List_Omap(X59,X29),X50),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__zip__map2)). 4.46/4.69 fof(fact_Int__UN__distrib2, axiom, ![X1, X114, X29, X2, X73, X3, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X73),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool),X3),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29,tc_fun(X4,tc_HOL_Obool)),X114)),hAPP(hAPP(c_COMBC(X3,tc_fun(X29,tc_fun(X4,tc_HOL_Obool)),tc_fun(X29,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_fun(X29,tc_fun(X4,tc_HOL_Obool)),tc_fun(X29,tc_fun(X4,tc_HOL_Obool))),X3),c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X29)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X3),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool))),X2))),X1)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X73),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29,tc_fun(X4,tc_HOL_Obool)),X114),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__UN__distrib2)). 4.46/4.69 fof(fact_Un__INT__distrib2, axiom, ![X1, X114, X29, X2, X73, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X73),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29,tc_fun(X4,tc_HOL_Obool)),X114),X1))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X73),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool),X3),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29,tc_fun(X4,tc_HOL_Obool)),X114)),hAPP(hAPP(c_COMBC(X3,tc_fun(X29,tc_fun(X4,tc_HOL_Obool)),tc_fun(X29,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_fun(X29,tc_fun(X4,tc_HOL_Obool)),tc_fun(X29,tc_fun(X4,tc_HOL_Obool))),X3),c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X29)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X3),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool))),X2))),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__INT__distrib2)). 4.46/4.69 fof(fact_map__of__map, axiom, ![X7, X27, X29, X3, X4]:hAPP(c_Map_Omap__of(X4,X3),hAPP(hAPP(c_List_Omap(tc_prod(X4,X29),tc_prod(X4,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X29,tc_prod(X4,X3)),hAPP(hAPP(c_COMBC(X4,tc_fun(X29,X3),tc_fun(X29,tc_prod(X4,X3))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(tc_fun(X29,X3),tc_fun(X29,tc_prod(X4,X3))),X4),c_COMBB(X3,tc_prod(X4,X3),X29)),c_Product__Type_OPair(X4,X3))),X27))),X7))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X29),tc_Option_Ooption(X3),X4,hAPP(c_Option_Omap(X29,X3),X27)),hAPP(c_Map_Omap__of(X4,X29),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__map)). 4.46/4.69 fof(fact_zip__map2, axiom, ![X32, X27, X29, X7, X3, X4]:hAPP(hAPP(c_List_Omap(tc_prod(X4,X29),tc_prod(X4,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X29,tc_prod(X4,X3)),hAPP(hAPP(c_COMBC(X4,tc_fun(X29,X3),tc_fun(X29,tc_prod(X4,X3))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(tc_fun(X29,X3),tc_fun(X29,tc_prod(X4,X3))),X4),c_COMBB(X3,tc_prod(X4,X3),X29)),c_Product__Type_OPair(X4,X3))),X27))),hAPP(hAPP(c_List_Ozip(X4,X29),X7),X32))=hAPP(hAPP(c_List_Ozip(X4,X3),X7),hAPP(hAPP(c_List_Omap(X29,X3),X27),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__map2)). 4.46/4.69 fof(fact_neg__bind__def, axiom, ![X103, X104, X105, X27, X26, X4, X3]:c_New__DSequence_Oneg__bind(X3,X4,hAPP(hAPP(hAPP(X26,X105),X104),X103),hAPP(hAPP(c_COMBC(X3,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4)))),hAPP(hAPP(c_COMBC(X3,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4))))),hAPP(hAPP(c_COMBC(X3,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4)))))),X27),X105)),X104)),X103))=hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X3,X4,X26,X27),X105),X104),X103), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__bind__def)). 4.46/4.69 fof(fact_min__weak__def, axiom, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool))))=c_FunDef_Omin__weak, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__weak__def)). 4.46/4.69 fof(fact_max__weak__def, axiom, c_FunDef_Omax__weak=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__weak__def)). 4.46/4.69 fof(fact_sublists_Osimps_I2_J, axiom, ![X7, X6, X4]:c_Enum_Osublists(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7))=hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(X4)),tc_List_Olist(tc_List_Olist(X4))),c_Enum_Osublists(X4,X7)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(X4)),tc_List_Olist(tc_List_Olist(X4)),tc_List_Olist(tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(X4)),tc_fun(tc_List_Olist(tc_List_Olist(X4)),tc_List_Olist(tc_List_Olist(X4))),tc_List_Olist(tc_List_Olist(X4))),c_List_Oappend(tc_List_Olist(X4))),hAPP(c_List_Omap(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(c_List_Olist_OCons(X4),X6)))),c_COMBI(tc_List_Olist(tc_List_Olist(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublists_Osimps_I2_J)). 4.46/4.69 fof(fact_New__Random__Sequence_Oneg__decr__bind__def, axiom, ![X103, X104, X105, X27, X26, X4, X3]:c_New__Random__Sequence_Oneg__decr__bind(X3,X4,X26,X27,X105,X104,X103)=c_New__DSequence_Oneg__decr__bind(X3,X4,hAPP(hAPP(hAPP(X26,X105),X104),X103),hAPP(hAPP(c_COMBC(X3,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4)))),hAPP(hAPP(c_COMBC(X3,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4))))),hAPP(hAPP(c_COMBC(X3,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4)))))),X27),X105)),X104)),X103)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__Random__Sequence_Oneg__decr__bind__def)). 4.46/4.69 fof(fact_map__zip__map, axiom, ![X32, X7, X50, X59, X27, X4, X29, X3]:hAPP(hAPP(c_List_Omap(tc_prod(X3,X29),X4),X27),hAPP(hAPP(c_List_Ozip(X3,X29),hAPP(hAPP(c_List_Omap(X59,X3),X50),X7)),X32))=hAPP(hAPP(c_List_Omap(tc_prod(X59,X29),X4),hAPP(c_Product__Type_Oprod_Oprod__case(X59,X29,X4),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_prod(X3,X29)),tc_fun(X29,X4),X59),hAPP(c_COMBB(tc_prod(X3,X29),X4,X29),X27)),hAPP(hAPP(c_COMBB(X3,tc_fun(X29,tc_prod(X3,X29)),X59),c_Product__Type_OPair(X3,X29)),X50)))),hAPP(hAPP(c_List_Ozip(X59,X29),X7),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__zip__map)). 4.46/4.69 fof(fact__02, axiom, ![X288, X289, X3, X4]:c_Lazy__Sequence_Oproduct(X4,X3,X289,X288)=hAPP(c_Lazy__Sequence_Obind(X4,tc_prod(X4,X3),X289),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X4,X3))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X4,X3)),X4),c_Lazy__Sequence_Obind(X3,tc_prod(X4,X3),X288)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(X3,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X4,X3))),X4),hAPP(c_COMBB(tc_prod(X4,X3),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X4,X3)),X3),c_Lazy__Sequence_Osingle(tc_prod(X4,X3)))),c_Product__Type_OPair(X4,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact__02)). 4.46/4.69 fof(fact_pos__bind__def, axiom, ![X103, X104, X105, X27, X26, X4, X3]:c_New__DSequence_Opos__bind(X3,X4,hAPP(hAPP(hAPP(X26,X105),X104),X103),hAPP(hAPP(c_COMBC(X3,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4))),hAPP(hAPP(c_COMBC(X3,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4)))),hAPP(hAPP(c_COMBC(X3,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4))))),X27),X105)),X104)),X103))=hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X3,X4,X26,X27),X105),X104),X103), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__bind__def)). 4.46/4.69 fof(fact_New__Random__Sequence_Opos__decr__bind__def, axiom, ![X103, X104, X105, X27, X26, X4, X3]:c_New__DSequence_Opos__decr__bind(X3,X4,hAPP(hAPP(hAPP(X26,X105),X104),X103),hAPP(hAPP(c_COMBC(X3,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4))),hAPP(hAPP(c_COMBC(X3,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4)))),hAPP(hAPP(c_COMBC(X3,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4))))),X27),X105)),X104)),X103))=c_New__Random__Sequence_Opos__decr__bind(X3,X4,X26,X27,X105,X104,X103), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__Random__Sequence_Opos__decr__bind__def)). 4.46/4.69 fof(fact_insert__times__insert, axiom, ![X1, X37, X2, X18, X3, X4]:hAPP(hAPP(c_Product__Type_OSigma(X4,X3),hAPP(hAPP(c_Set_Oinsert(X4),X18),X2)),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),hAPP(hAPP(c_Set_Oinsert(X3),X37),X1)))=hAPP(hAPP(c_Set_Oinsert(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X18),X37)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),hAPP(hAPP(c_Set_Oinsert(X3),X37),X1)))),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),hAPP(hAPP(c_Set_Oinsert(X4),X18),X2)),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__times__insert)). 4.46/4.69 fof(fact_inj__graph, axiom, ![X3, X4]:c_Fun_Oinj__on(tc_fun(X4,X3),tc_fun(tc_prod(X4,X3),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X4,X3)),c_Set_OCollect(tc_prod(X4,X3))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X3,tc_HOL_Obool)),tc_fun(tc_prod(X4,X3),tc_HOL_Obool),tc_fun(X4,X3)),c_Product__Type_Oprod_Oprod__case(X4,X3,tc_HOL_Obool)),hAPP(c_COMBB(X3,tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_COMBC(X3,X3,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X4,X3),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__graph)). 4.46/4.69 fof(fact_rel__comp__UNION__distrib2, axiom, ![X68, X16, X73, X59, X3, X29, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X59,tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X73),hAPP(hAPP(c_COMBC(X59,tc_fun(tc_prod(X29,X3),tc_HOL_Obool),tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X4,X29),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X29,X3),tc_HOL_Obool),tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X59),c_Relation_Orel__comp(X4,X29,X3)),X16)),X68))=hAPP(hAPP(c_Relation_Orel__comp(X4,X29,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X59,tc_fun(tc_prod(X4,X29),tc_HOL_Obool)),X73),X16)),X68), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__UNION__distrib2)). 4.46/4.69 fof(fact_select__weight__def, axiom, ![X7, X4]:c_Random_Oselect__weight(X4,X7)=hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X4),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X4)),X7)))),hAPP(hAPP(c_COMBB(X4,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X4,X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select__weight__def)). 4.46/4.69 fof(fact_map__filter__map__filter, axiom, ![X7, X28, X27, X4, X3]:c_List_Omap__filter(X3,X4,hAPP(hAPP(c_COMBC(X3,tc_Option_Ooption(X4),tc_Option_Ooption(X4)),hAPP(hAPP(c_COMBS(X3,tc_Option_Ooption(X4),tc_fun(tc_Option_Ooption(X4),tc_Option_Ooption(X4))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X4),tc_fun(tc_Option_Ooption(X4),tc_Option_Ooption(X4))),X3),c_If(tc_Option_Ooption(X4))),X28)),hAPP(hAPP(c_COMBB(X4,tc_Option_Ooption(X4),X3),c_Option_Ooption_OSome(X4)),X27))),c_Option_Ooption_ONone(X4)),X7)=hAPP(hAPP(c_List_Omap(X3,X4),X27),hAPP(c_List_Ofilter(X3,X28),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__filter__map__filter)). 4.46/4.69 fof(fact_measures__def, axiom, ![X115, X4]:c_List_Omeasures(X4,X115)=hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),X4),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(X4,tc_List_Olist(tc_fun(X4,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(X4,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),X4),c_List_Omap(tc_fun(X4,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(X4,tc_Nat_Onat),X4,tc_Nat_Onat),c_COMBI(tc_fun(X4,tc_Nat_Onat))))),X115)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_measures__def)). 4.46/4.69 fof(fact_zip__map1, axiom, ![X32, X7, X27, X29, X3, X4]:hAPP(hAPP(c_List_Omap(tc_prod(X29,X3),tc_prod(X4,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X29,X3,tc_prod(X4,X3)),hAPP(hAPP(c_COMBB(X4,tc_fun(X3,tc_prod(X4,X3)),X29),c_Product__Type_OPair(X4,X3)),X27))),hAPP(hAPP(c_List_Ozip(X29,X3),X7),X32))=hAPP(hAPP(c_List_Ozip(X4,X3),hAPP(hAPP(c_List_Omap(X29,X4),X27),X7)),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__map1)). 4.46/4.69 fof(fact_swap__product, axiom, ![X1, X2, X4, X3]:hAPP(c_Set_Oimage(tc_prod(X3,X4),tc_prod(X4,X3),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X4,tc_prod(X4,X3)),hAPP(c_COMBC(X4,X3,tc_prod(X4,X3)),c_Product__Type_OPair(X4,X3)))),hAPP(hAPP(c_Product__Type_OSigma(X3,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X3),X1)))=hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_swap__product)). 4.46/4.69 fof(fact_rotate1__def, axiom, ![X7, X4]:hAPP(c_List_Olist_Olist__case(tc_List_Olist(X4),X4,c_List_Olist_ONil(X4),hAPP(hAPP(c_COMBB(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),X4),hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Oappend(X4))),hAPP(hAPP(c_COMBC(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_OCons(X4)),c_List_Olist_ONil(X4)))),X7)=hAPP(c_List_Orotate1(X4),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate1__def)). 4.46/4.69 fof(fact_zip__append2, axiom, ![X191, X72, X57, X3, X4]:hAPP(hAPP(c_List_Ozip(X4,X3),X57),hAPP(hAPP(c_List_Oappend(X3),X72),X191))=hAPP(hAPP(c_List_Oappend(tc_prod(X4,X3)),hAPP(hAPP(c_List_Ozip(X4,X3),hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X72)),X57)),X72)),hAPP(hAPP(c_List_Ozip(X4,X3),hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X72)),X57)),X191)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__append2)). 4.46/4.69 fof(fact_zip__append1, axiom, ![X191, X72, X57, X3, X4]:hAPP(hAPP(c_List_Oappend(tc_prod(X4,X3)),hAPP(hAPP(c_List_Ozip(X4,X3),X57),hAPP(hAPP(c_List_Otake(X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),X191))),hAPP(hAPP(c_List_Ozip(X4,X3),X72),hAPP(hAPP(c_List_Odrop(X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),X191)))=hAPP(hAPP(c_List_Ozip(X4,X3),hAPP(hAPP(c_List_Oappend(X4),X57),X72)),X191), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__append1)). 4.46/4.69 fof(fact_split__twice, axiom, ![X109, X50, X61, X59, X27, X4, X29, X3]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3,X29,X4),X27),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X59,X61,tc_prod(X3,X29)),X50),X109))=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X59,X61,X4),hAPP(hAPP(c_COMBB(tc_fun(X61,tc_prod(X3,X29)),tc_fun(X61,X4),X59),hAPP(c_COMBB(tc_prod(X3,X29),X4,X61),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X29,X4),X27))),X50)),X109), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__twice)). 4.46/4.69 fof(fact_split__comp__eq, axiom, ![X50, X27, X59, X29, X3, X4]:hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,X29),hAPP(hAPP(c_COMBB(X59,tc_fun(X3,X29),X4),X27),X50))=hAPP(hAPP(c_COMBS(tc_prod(X4,X3),X3,X29),hAPP(hAPP(c_COMBB(X59,tc_fun(X3,X29),tc_prod(X4,X3)),X27),hAPP(hAPP(c_COMBB(X4,X59,tc_prod(X4,X3)),X50),c_Product__Type_Ofst(X4,X3)))),c_Product__Type_Osnd(X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__comp__eq)). 4.46/4.69 fof(fact_foldl__map, axiom, ![X7, X27, X29, X18, X50, X3, X4]:hAPP(c_List_Ofoldl(X4,X3,X50,X18),hAPP(hAPP(c_List_Omap(X29,X3),X27),X7))=hAPP(c_List_Ofoldl(X4,X29,hAPP(hAPP(c_COMBC(X4,tc_fun(X29,X3),tc_fun(X29,X4)),hAPP(hAPP(c_COMBB(tc_fun(X3,X4),tc_fun(tc_fun(X29,X3),tc_fun(X29,X4)),X4),c_COMBB(X3,X4,X29)),X50)),X27),X18),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__map)). 4.46/4.69 fof(fact_INT__extend__simps_I9_J, axiom, ![X52, X1, X29, X2, X4, X3]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29,tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X29,tc_HOL_Obool)),X2),X1)),X52)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X3,tc_fun(X29,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_HOL_Obool),tc_fun(tc_fun(X29,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),X3),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29,tc_fun(X4,tc_HOL_Obool))),X1)),X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__extend__simps_I9_J)). 4.46/4.69 fof(fact_list__update_Osimps_I2_J, axiom, ![X13, X24, X7, X6, X4]:hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)),X24),X13)=c_Nat_Onat_Onat__case(tc_List_Olist(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X7),hAPP(hAPP(c_COMBB(tc_List_Olist(X4),tc_List_Olist(X4),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X4),X6)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X4,tc_List_Olist(X4)),c_List_Olist__update(X4,X7)),X13)),X24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update_Osimps_I2_J)). 4.46/4.69 fof(fact_rel__comp__UNION__distrib, axiom, ![X16, X73, X59, X68, X3, X29, X4]:hAPP(hAPP(c_Relation_Orel__comp(X4,X29,X3),X68),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X59,tc_fun(tc_prod(X29,X3),tc_HOL_Obool)),X73),X16))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X59,tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X73),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X29,X3),tc_HOL_Obool),tc_fun(tc_prod(X4,X3),tc_HOL_Obool),X59),hAPP(c_Relation_Orel__comp(X4,X29,X3),X68)),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__UNION__distrib)). 4.46/4.69 fof(fact_Image__INT__subset, axiom, ![X1, X2, X29, X16, X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3,X4,X16),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29,tc_fun(X3,tc_HOL_Obool)),X2),X1))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29,tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X29),c_Relation_OImage(X3,X4,X16)),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__INT__subset)). 4.46/4.69 fof(fact_map__filter__simps_I1_J, axiom, ![X7, X6, X27, X4, X3]:hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(X4),X4,c_List_Omap__filter(X3,X4,X27,X7),hAPP(hAPP(c_COMBC(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_OCons(X4)),c_List_Omap__filter(X3,X4,X27,X7))),hAPP(X27,X6))=c_List_Omap__filter(X3,X4,X27,hAPP(hAPP(c_List_Olist_OCons(X3),X6),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__filter__simps_I1_J)). 4.46/4.69 fof(fact_tl__append, axiom, ![X32, X7, X4]:hAPP(c_List_Otl(X4),hAPP(hAPP(c_List_Oappend(X4),X7),X32))=hAPP(c_List_Olist_Olist__case(tc_List_Olist(X4),X4,hAPP(c_List_Otl(X4),X32),hAPP(c_COMBK(tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),X4),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Oappend(X4)),X32))),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tl__append)). 4.46/4.69 fof(fact_take__Cons, axiom, ![X7, X6, X14, X4]:hAPP(hAPP(c_List_Otake(X4),X14),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7))=c_Nat_Onat_Onat__case(tc_List_Olist(X4),c_List_Olist_ONil(X4),hAPP(hAPP(c_COMBB(tc_List_Olist(X4),tc_List_Olist(X4),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X4),X6)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Otake(X4)),X7)),X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Cons)). 4.46/4.69 fof(fact_map__pair_Ocomp, axiom, ![X24, X58, X50, X27, X3, X4, X59, X29, X60, X61]:c_Product__Type_Omap__pair(X4,X29,X3,X59,hAPP(c_Fun_Ocomp(X61,X29,X4,X27),X58),hAPP(c_Fun_Ocomp(X60,X59,X3,X50),X24))=hAPP(c_Fun_Ocomp(tc_prod(X61,X60),tc_prod(X29,X59),tc_prod(X4,X3),c_Product__Type_Omap__pair(X61,X29,X60,X59,X27,X50)),c_Product__Type_Omap__pair(X4,X61,X3,X60,X58,X24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair_Ocomp)). 4.46/4.69 fof(fact_update__zip, axiom, ![X134, X21, X72, X57, X3, X4]:hAPP(hAPP(c_List_Olist__update(tc_prod(X4,X3),hAPP(hAPP(c_List_Ozip(X4,X3),X57),X72)),X21),X134)=hAPP(hAPP(c_List_Ozip(X4,X3),hAPP(hAPP(c_List_Olist__update(X4,X57),X21),hAPP(c_Product__Type_Ofst(X4,X3),X134))),hAPP(hAPP(c_List_Olist__update(X3,X72),X21),hAPP(c_Product__Type_Osnd(X4,X3),X134))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_update__zip)). 4.46/4.69 fof(fact_Eps__split, axiom, ![X28, X3, X4]:c_Hilbert__Choice_OEps(tc_prod(X4,X3),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_HOL_Obool),X28))=c_Hilbert__Choice_OEps(tc_prod(X4,X3),hAPP(hAPP(c_COMBS(tc_prod(X4,X3),X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X4,tc_fun(X3,tc_HOL_Obool),tc_prod(X4,X3)),X28),c_Product__Type_Ofst(X4,X3))),c_Product__Type_Osnd(X4,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Eps__split)). 4.46/4.69 fof(fact_restrict__upd__same, axiom, ![X5, X6, X22, X3, X4]:c_Map_Orestrict__map(X4,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),X22),X6),hAPP(c_Option_Ooption_OSome(X3),X5)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=c_Map_Orestrict__map(X4,X3,X22,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__upd__same)). 4.46/4.69 fof(fact_The__split, axiom, ![X28, X3, X4]:c_HOL_OThe(tc_prod(X4,X3),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_HOL_Obool),X28))=c_HOL_OThe(tc_prod(X4,X3),hAPP(hAPP(c_COMBS(tc_prod(X4,X3),X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X4,tc_fun(X3,tc_HOL_Obool),tc_prod(X4,X3)),X28),c_Product__Type_Ofst(X4,X3))),c_Product__Type_Osnd(X4,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_The__split)). 4.46/4.69 fof(fact_Image__Int__subset, axiom, ![X1, X2, X26, X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3,X4,X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X2),X1))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3,X4,X26),X2)),hAPP(c_Relation_OImage(X3,X4,X26),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__Int__subset)). 4.46/4.69 fof(fact_converse__INTER, axiom, ![X16, X46, X29, X4, X3]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29,tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X46),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X3),tc_HOL_Obool),X29),c_Relation_Oconverse(X3,X4)),X16))=hAPP(c_Relation_Oconverse(X3,X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29,tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),X46),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__INTER)). 4.46/4.69 fof(fact_converse__UNION, axiom, ![X16, X46, X29, X4, X3]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29,tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X46),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X3),tc_HOL_Obool),X29),c_Relation_Oconverse(X3,X4)),X16))=hAPP(c_Relation_Oconverse(X3,X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29,tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),X46),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__UNION)). 4.46/4.69 fof(fact_Ex__inj__on__UNION__Sigma, axiom, ![X2, X73, X3, X4]:?[X40]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,tc_prod(X3,X4),X40),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X73),X2))),hAPP(hAPP(c_Product__Type_OSigma(X3,X4),X73),X2)))&c_Fun_Oinj__on(X4,tc_prod(X3,X4),X40,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X73),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ex__inj__on__UNION__Sigma)). 4.46/4.69 fof(fact_div__mult1__eq, axiom, ![X10, X11, X12]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X11)),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X11),X10))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X11,X10))),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult1__eq)). 4.46/4.69 fof(fact_UN__simps_I6_J, axiom, ![X1, X2, X52, X4, X3]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBC(X3,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X3),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool))),X2)),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X52),X2)),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I6_J)). 4.46/4.69 fof(fact_zdiv__zmult1__eq, axiom, ![X10, X11, X12]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X11)),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X10))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X10))),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__zmult1__eq)). 4.46/4.69 fof(fact_UN__simps_I4_J, axiom, ![X1, X2, X52, X4, X3]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBC(X3,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X3),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool))),X2)),X1))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X52),X2)),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I4_J)). 4.46/4.69 fof(fact_INT__simps_I6_J, axiom, ![X1, X2, X52, X4, X3]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X52),X2)),X1)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBC(X3,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X3),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool))),X2)),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__simps_I6_J)). 4.46/4.69 fof(fact_rtrancl__Un__subset, axiom, ![X46, X26, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4,X26)),c_Transitive__Closure_Ortrancl(X4,X46))),c_Transitive__Closure_Ortrancl(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X26),X46)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__Un__subset)). 4.46/4.69 fof(fact_rel__comp__distrib2, axiom, ![X26, X110, X46, X3, X29, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X29,X3),X46),X26)),hAPP(hAPP(c_Relation_Orel__comp(X4,X29,X3),X110),X26))=hAPP(hAPP(c_Relation_Orel__comp(X4,X29,X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X29),tc_HOL_Obool)),X46),X110)),X26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__distrib2)). 4.46/4.69 fof(fact_rel__comp__distrib, axiom, ![X110, X46, X26, X3, X29, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X29,X3),X26),X46)),hAPP(hAPP(c_Relation_Orel__comp(X4,X29,X3),X26),X110))=hAPP(hAPP(c_Relation_Orel__comp(X4,X29,X3),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29,X3),tc_HOL_Obool)),X46),X110)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__distrib)). 4.46/4.69 fof(fact_Range__Int__subset, axiom, ![X1, X2, X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ORange(X3,X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),X2),X1))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ORange(X3,X4),X2)),hAPP(c_Relation_ORange(X3,X4),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__Int__subset)). 4.46/4.69 fof(fact_Domain__Int__subset, axiom, ![X1, X2, X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X4,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X2),X1))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X4,X3),X2)),hAPP(c_Relation_ODomain(X4,X3),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__Int__subset)). 4.46/4.69 fof(fact_Range__Diff__subset, axiom, ![X1, X2, X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ORange(X3,X4),X2)),hAPP(c_Relation_ORange(X3,X4),X1))),hAPP(c_Relation_ORange(X3,X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__Diff__subset)). 4.46/4.69 fof(fact_Domain__Diff__subset, axiom, ![X1, X2, X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X4,X3),X2)),hAPP(c_Relation_ODomain(X4,X3),X1))),hAPP(c_Relation_ODomain(X4,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__Diff__subset)). 4.46/4.69 fof(fact_Id__on__def_H, axiom, ![X2, X4]:hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X4,tc_HOL_Obool)),X4),c_COMBC(X4,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj)),c_fequal))),X2))=c_Relation_OId__on(X4,X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__on__def_H)). 4.46/4.69 fof(fact_Sigma__Union, axiom, ![X1, X173, X3, X4]:hAPP(hAPP(c_Product__Type_OSigma(X4,X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X173)),X1)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X173),hAPP(hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(X3,tc_HOL_Obool)),tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),c_Product__Type_OSigma(X4,X3)),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Union)). 4.46/4.69 fof(fact_map__of_Osimps_I2_J, axiom, ![X108, X109, X3, X4]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),hAPP(c_Map_Omap__of(X4,X3),X108)),hAPP(c_Product__Type_Ofst(X4,X3),X109)),hAPP(c_Option_Ooption_OSome(X3),hAPP(c_Product__Type_Osnd(X4,X3),X109)))=hAPP(c_Map_Omap__of(X4,X3),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X4,X3)),X109),X108)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of_Osimps_I2_J)). 4.46/4.69 fof(fact_rtrancl__is__UN__rel__pow, axiom, ![X26, X4]:c_Transitive__Closure_Ortrancl(X4,X26)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool)),X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__is__UN__rel__pow)). 4.46/4.69 fof(fact_rel__pow__add, axiom, ![X26, X14, X22, X4]:hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X14)),X26)=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X22),X26)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X14),X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__add)). 4.46/4.69 fof(fact_UN__Pow__subset, axiom, ![X1, X2, X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),X3),c_Set_OPow(X4)),X1))),hAPP(c_Set_OPow(X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__Pow__subset)). 4.46/4.69 fof(fact_wmin__emptyI, axiom, ![X173]:hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X173),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wmin__emptyI)). 4.46/4.69 fof(fact_product_Osimps_I2_J, axiom, ![X32, X7, X6, X3, X4]:c_Enum_Oproduct(X4,X3,hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7),X32)=hAPP(hAPP(c_List_Oappend(tc_prod(X4,X3)),hAPP(hAPP(c_List_Omap(X3,tc_prod(X4,X3)),hAPP(c_Product__Type_OPair(X4,X3),X6)),X32)),c_Enum_Oproduct(X4,X3,X7,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_product_Osimps_I2_J)). 4.46/4.69 fof(fact_fun__left__comm__idem__remove, axiom, ![X4]:c_Finite__Set_Ofun__left__comm__idem(X4,tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Set_Oinsert(X4)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem__remove)). 4.46/4.69 fof(fact_Compl__Times__UNIV1, axiom, ![X2, X3, X4]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),X2)))=hAPP(hAPP(c_Product__Type_OSigma(X4,X3),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__Times__UNIV1)). 4.46/4.69 fof(fact_Compl__Times__UNIV2, axiom, ![X2, X3, X4]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))))=hAPP(hAPP(c_Product__Type_OSigma(X4,X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X2)),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__Times__UNIV2)). 4.46/4.69 fof(fact_image__diff__subset, axiom, ![X1, X2, X27, X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X4,X27),X2)),hAPP(c_Set_Oimage(X3,X4,X27),X1))),hAPP(c_Set_Oimage(X3,X4,X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__diff__subset)). 4.46/4.69 fof(fact_image__Int__subset, axiom, ![X1, X2, X27, X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X4,X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X2),X1))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X4,X27),X2)),hAPP(c_Set_Oimage(X3,X4,X27),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Int__subset)). 4.46/4.69 fof(fact_drop__append, axiom, ![X72, X57, X17, X4]:hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Odrop(X4),X17),X57)),hAPP(hAPP(c_List_Odrop(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57))),X72))=hAPP(hAPP(c_List_Odrop(X4),X17),hAPP(hAPP(c_List_Oappend(X4),X57),X72)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__append)). 4.46/4.69 fof(fact_take__append, axiom, ![X72, X57, X17, X4]:hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Otake(X4),X17),X57)),hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57))),X72))=hAPP(hAPP(c_List_Otake(X4),X17),hAPP(hAPP(c_List_Oappend(X4),X57),X72)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__append)). 4.46/4.69 fof(fact_dom__option__map, axiom, ![X22, X27, X29, X3, X4]:c_Map_Odom(X4,X29,X22)=c_Map_Odom(X4,X3,hAPP(hAPP(c_COMBS(X4,tc_Option_Ooption(X29),tc_Option_Ooption(X3)),hAPP(hAPP(c_COMBB(tc_fun(X29,X3),tc_fun(tc_Option_Ooption(X29),tc_Option_Ooption(X3)),X4),c_Option_Omap(X29,X3)),X27)),X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__option__map)). 4.46/4.69 fof(fact_hb__flat_Osimps_I2_J, axiom, ![X284, X107, X4]:c_Lazy__Sequence_Ohb__flat(X4,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4))),X107,X284))=c_Lazy__Sequence_Oappend(tc_Option_Ooption(X4),hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4)),tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4)),c_Lazy__Sequence_Ohit__bound(X4),c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4)))),X107),c_Lazy__Sequence_Ohb__flat(X4,X284)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hb__flat_Osimps_I2_J)). 4.46/4.69 fof(fact_pick__drop__zero, axiom, ![X7, X4]:c_Random_Opick(X4,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X4),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X4)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X7))=c_Random_Opick(X4,X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pick__drop__zero)). 4.46/4.69 fof(fact_select__weigth__drop__zero, axiom, ![X7, X4]:c_Random_Oselect__weight(X4,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X4),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X4)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X7))=c_Random_Oselect__weight(X4,X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select__weigth__drop__zero)). 4.46/4.69 fof(fact_zip__takeWhile__fst, axiom, ![X32, X7, X28, X3, X4]:c_List_OtakeWhile(tc_prod(X4,X3),hAPP(c_Fun_Ocomp(X4,tc_HOL_Obool,tc_prod(X4,X3),X28),c_Product__Type_Ofst(X4,X3)),hAPP(hAPP(c_List_Ozip(X4,X3),X7),X32))=hAPP(hAPP(c_List_Ozip(X4,X3),c_List_OtakeWhile(X4,X28,X7)),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__takeWhile__fst)). 4.46/4.69 fof(fact_zip__takeWhile__snd, axiom, ![X32, X28, X7, X3, X4]:c_List_OtakeWhile(tc_prod(X4,X3),hAPP(c_Fun_Ocomp(X3,tc_HOL_Obool,tc_prod(X4,X3),X28),c_Product__Type_Osnd(X4,X3)),hAPP(hAPP(c_List_Ozip(X4,X3),X7),X32))=hAPP(hAPP(c_List_Ozip(X4,X3),X7),c_List_OtakeWhile(X3,X28,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__takeWhile__snd)). 4.46/4.69 fof(fact_Sigma__Int__distrib1, axiom, ![X52, X114, X73, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X73),X52)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X114),X52))=hAPP(hAPP(c_Product__Type_OSigma(X4,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X73),X114)),X52), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Int__distrib1)). 4.46/4.69 fof(fact_Sigma__Diff__distrib1, axiom, ![X52, X114, X73, X3, X4]:hAPP(hAPP(c_Product__Type_OSigma(X4,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X73),X114)),X52)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X73),X52)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X114),X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Diff__distrib1)). 4.46/4.69 fof(fact_Sigma__Un__distrib1, axiom, ![X52, X114, X73, X3, X4]:hAPP(hAPP(c_Product__Type_OSigma(X4,X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X73),X114)),X52)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X73),X52)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X114),X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Un__distrib1)). 4.46/4.69 fof(fact_drop__Cons, axiom, ![X7, X6, X14, X4]:hAPP(hAPP(c_List_Odrop(X4),X14),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7))=c_Nat_Onat_Onat__case(tc_List_Olist(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Odrop(X4)),X7),X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__Cons)). 4.46/4.69 fof(fact_neg__map__def, axiom, ![X28, X27, X4, X3]:c_New__Random__Sequence_Oneg__map(X3,X4,X27,X28)=c_New__Random__Sequence_Oneg__bind(X3,X4,X28,hAPP(c_Fun_Ocomp(X4,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4)))))),X3,c_New__Random__Sequence_Oneg__single(X4)),X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__map__def)). 4.46/4.69 fof(fact_map__add__upd, axiom, ![X5, X6, X50, X27, X3, X4]:c_Map_Omap__add(X4,X3,X27,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),X50),X6),hAPP(c_Option_Ooption_OSome(X3),X5)))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),c_Map_Omap__add(X4,X3,X27,X50)),X6),hAPP(c_Option_Ooption_OSome(X3),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__upd)). 4.46/4.69 fof(fact_split__eta, axiom, ![X27, X29, X3, X4]:hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,X29),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(X3,X29),X4),hAPP(c_COMBB(tc_prod(X4,X3),X29,X3),X27)),c_Product__Type_OPair(X4,X3)))=X27, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__eta)). 4.46/4.69 fof(fact_INT__extend__simps_I8_J, axiom, ![X1, X2, X4, X3]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2)),X1)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X3,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool))),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__extend__simps_I8_J)). 4.46/4.69 fof(fact_UN__simps_I8_J, axiom, ![X1, X2, X4, X3]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2)),X1)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X3,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool))),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I8_J)). 4.46/4.69 fof(fact_dom__map__upds, axiom, ![X32, X7, X22, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X32)),X7))),c_Map_Odom(X4,X3,X22))=c_Map_Odom(X4,X3,c_Map_Omap__upds(X4,X3,X22,X7,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__map__upds)). 4.46/4.69 fof(fact_pair__leq__def, axiom, c_FunDef_Opair__leq=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__leq__def)). 4.46/4.69 fof(fact_Image__UN, axiom, ![X1, X2, X29, X16, X4, X3]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29,tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X29),c_Relation_OImage(X3,X4,X16)),X1))=hAPP(c_Relation_OImage(X3,X4,X16),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29,tc_fun(X3,tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__UN)). 4.46/4.69 fof(fact_pos__map__def, axiom, ![X28, X27, X4, X3]:c_New__Random__Sequence_Opos__map(X3,X4,X27,X28)=c_New__Random__Sequence_Opos__bind(X3,X4,X28,hAPP(c_Fun_Ocomp(X4,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4))))),X3,c_New__Random__Sequence_Opos__single(X4)),X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__map__def)). 4.46/4.69 fof(fact_Union__Int__subset, axiom, ![X1, X2, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X2),X1))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__Int__subset)). 4.46/4.69 fof(fact_Inter__Un__subset, axiom, ![X1, X2, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X1))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__Un__subset)). 4.46/4.69 fof(fact_UN__Un, axiom, ![X153, X1, X2, X4, X3]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),X153)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X1),X153))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1)),X153), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__Un)). 4.46/4.69 fof(fact_INT__Un, axiom, ![X153, X1, X2, X4, X3]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1)),X153)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X2),X153)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X1),X153)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__Un)). 4.46/4.69 fof(fact_list__update__length, axiom, ![X47, X72, X48, X57, X4]:hAPP(hAPP(c_List_Oappend(X4),X57),hAPP(hAPP(c_List_Olist_OCons(X4),X47),X72))=hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Oappend(X4),X57),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X72))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),X47), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__length)). 4.46/4.69 fof(fact_image__add__int__atLeastLessThan, axiom, ![X23, X67]:hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),X67)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23),X67)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X67),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__add__int__atLeastLessThan)). 4.46/4.69 fof(fact_Un__Pow__subset, axiom, ![X1, X2, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X4),X2)),hAPP(c_Set_OPow(X4),X1))),hAPP(c_Set_OPow(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Pow__subset)). 4.46/4.69 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J, axiom, ![X1, X2]:hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X2),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J)). 4.46/4.69 fof(fact_Un__Image, axiom, ![X2, X46, X26, X4, X3]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3,X4,X26),X2)),hAPP(c_Relation_OImage(X3,X4,X46),X2))=hAPP(c_Relation_OImage(X3,X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),X26),X46)),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Image)). 4.46/4.69 fof(fact_swap__inj__on, axiom, ![X2, X3, X4]:c_Fun_Oinj__on(tc_prod(X4,X3),tc_prod(X3,X4),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,tc_prod(X3,X4)),hAPP(c_COMBC(X3,X4,tc_prod(X3,X4)),c_Product__Type_OPair(X3,X4))),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_swap__inj__on)). 4.46/4.69 fof(fact_funpow__add, axiom, ![X27, X14, X22, X4]:hAPP(c_Fun_Ocomp(X4,X4,X4,hAPP(hAPP(c_Nat_Ocompow(X4,X4),X22),X27)),hAPP(hAPP(c_Nat_Ocompow(X4,X4),X14),X27))=hAPP(hAPP(c_Nat_Ocompow(X4,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X14)),X27), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_funpow__add)). 4.46/4.69 fof(fact_Un__INT__distrib, axiom, ![X2, X73, X3, X1, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X73),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X3),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X1)),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X73),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__INT__distrib)). 4.46/4.69 fof(fact_UN__extend__simps_I7_J, axiom, ![X1, X52, X3, X2, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X52),X1))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X3),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2)),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__extend__simps_I7_J)). 4.46/4.69 fof(fact_UN__extend__simps_I5_J, axiom, ![X1, X52, X3, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X52),X1))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X3),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2)),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__extend__simps_I5_J)). 4.46/4.69 fof(fact_Option_Omap_Ocomp, axiom, ![X50, X27, X4, X3, X29]:hAPP(c_Option_Omap(X4,X3),hAPP(c_Fun_Ocomp(X29,X3,X4,X27),X50))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X29),tc_Option_Ooption(X3),tc_Option_Ooption(X4),hAPP(c_Option_Omap(X29,X3),X27)),hAPP(c_Option_Omap(X4,X29),X50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Option_Omap_Ocomp)). 4.46/4.69 fof(fact_map__comp__map, axiom, ![X50, X27, X4, X3, X29]:hAPP(c_List_Omap(X4,X3),hAPP(c_Fun_Ocomp(X29,X3,X4,X27),X50))=hAPP(c_Fun_Ocomp(tc_List_Olist(X29),tc_List_Olist(X3),tc_List_Olist(X4),hAPP(c_List_Omap(X29,X3),X27)),hAPP(c_List_Omap(X4,X29),X50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__comp__map)). 4.46/4.69 fof(fact_converse__Un, axiom, ![X68, X16, X4, X3]:hAPP(c_Relation_Oconverse(X3,X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),X16),X68))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X3,X4),X16)),hAPP(c_Relation_Oconverse(X3,X4),X68)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__Un)). 4.46/4.69 fof(fact_converse__Int, axiom, ![X68, X16, X4, X3]:hAPP(c_Relation_Oconverse(X3,X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),X16),X68))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X3,X4),X16)),hAPP(c_Relation_Oconverse(X3,X4),X68)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__Int)). 4.46/4.69 fof(fact_partition__filter__conv, axiom, ![X7, X27, X4]:c_List_Opartition(X4,X27,X7)=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(c_List_Ofilter(X4,X27),X7)),hAPP(c_List_Ofilter(X4,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X4,c_fNot),X27)),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition__filter__conv)). 4.46/4.69 fof(fact_image__UN, axiom, ![X1, X2, X29, X27, X4, X3]:hAPP(c_Set_Oimage(X3,X4,X27),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29,tc_fun(X3,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29,tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X29),c_Set_Oimage(X3,X4,X27)),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__UN)). 4.46/4.69 fof(fact_Image__Un, axiom, ![X1, X2, X26, X4, X3]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3,X4,X26),X2)),hAPP(c_Relation_OImage(X3,X4,X26),X1))=hAPP(c_Relation_OImage(X3,X4,X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__Un)). 4.46/4.69 fof(fact_map__upds__def, axiom, ![X32, X7, X22, X3, X4]:c_Map_Omap__upds(X4,X3,X22,X7,X32)=c_Map_Omap__add(X4,X3,X22,hAPP(c_Map_Omap__of(X4,X3),hAPP(c_List_Orev(tc_prod(X4,X3)),hAPP(hAPP(c_List_Ozip(X4,X3),X7),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upds__def)). 4.46/4.69 fof(fact_drop__zip, axiom, ![X72, X57, X17, X3, X4]:hAPP(hAPP(c_List_Odrop(tc_prod(X4,X3)),X17),hAPP(hAPP(c_List_Ozip(X4,X3),X57),X72))=hAPP(hAPP(c_List_Ozip(X4,X3),hAPP(hAPP(c_List_Odrop(X4),X17),X57)),hAPP(hAPP(c_List_Odrop(X3),X17),X72)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__zip)). 4.46/4.69 fof(fact_product__list__set, axiom, ![X32, X7, X3, X4]:hAPP(c_List_Oset(tc_prod(X4,X3)),c_Enum_Oproduct(X4,X3,X7,X32))=hAPP(hAPP(c_Product__Type_OSigma(X4,X3),hAPP(c_List_Oset(X4),X7)),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_List_Oset(X3),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_product__list__set)). 4.46/4.69 fof(fact_zadd__int__left, axiom, ![X49, X17, X19]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17))),X49)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17)),X49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__int__left)). 4.46/4.69 fof(fact_card__cartesian__product, axiom, ![X1, X2, X3, X4]:hAPP(c_Finite__Set_Ocard(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),X1)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X2)),hAPP(c_Finite__Set_Ocard(X3),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__cartesian__product)). 4.46/4.69 fof(fact_Pow__insert, axiom, ![X2, X18, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X4),X2)),hAPP(c_Set_Oimage(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),hAPP(c_Set_Oinsert(X4),X18)),hAPP(c_Set_OPow(X4),X2)))=hAPP(c_Set_OPow(X4),hAPP(hAPP(c_Set_Oinsert(X4),X18),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__insert)). 4.46/4.69 fof(fact_listrel_ONil, axiom, ![X16, X4]:hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_List_Olist_ONil(X4))),c_List_Olistrel(X4,X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel_ONil)). 4.46/4.69 fof(fact_Int__Union2, axiom, ![X2, X1, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X1)),X2)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool))),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Union2)). 4.46/4.69 fof(fact_converse__rel__comp, axiom, ![X68, X16, X29, X4, X3]:hAPP(c_Relation_Oconverse(X3,X4),hAPP(hAPP(c_Relation_Orel__comp(X3,X29,X4),X16),X68))=hAPP(hAPP(c_Relation_Orel__comp(X4,X29,X3),hAPP(c_Relation_Oconverse(X29,X4),X68)),hAPP(c_Relation_Oconverse(X3,X29),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__rel__comp)). 4.46/4.69 fof(fact_filter__map, axiom, ![X7, X27, X3, X28, X4]:hAPP(c_List_Ofilter(X4,X28),hAPP(hAPP(c_List_Omap(X3,X4),X27),X7))=hAPP(hAPP(c_List_Omap(X3,X4),X27),hAPP(c_List_Ofilter(X3,hAPP(c_Fun_Ocomp(X4,tc_HOL_Obool,X3,X28),X27)),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__map)). 4.46/4.69 fof(fact_Id__on__subset__Times, axiom, ![X2, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Relation_OId__on(X4,X2)),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__on__subset__Times)). 4.46/4.69 fof(fact_rel__pow__0__I, axiom, ![X26, X6, X4]:hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X6),X6)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__0__I)). 4.46/4.69 fof(fact_rtrancl__Un__rtrancl, axiom, ![X46, X26, X4]:c_Transitive__Closure_Ortrancl(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X26),X46))=c_Transitive__Closure_Ortrancl(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4,X26)),c_Transitive__Closure_Ortrancl(X4,X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__Un__rtrancl)). 4.46/4.69 fof(fact_Range__Un__eq, axiom, ![X1, X2, X4, X3]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ORange(X3,X4),X2)),hAPP(c_Relation_ORange(X3,X4),X1))=hAPP(c_Relation_ORange(X3,X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__Un__eq)). 4.46/4.69 fof(fact_Domain__Un__eq, axiom, ![X1, X2, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X4,X3),X2)),hAPP(c_Relation_ODomain(X4,X3),X1))=hAPP(c_Relation_ODomain(X4,X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__Un__eq)). 4.46/4.69 fof(fact_pred__nat__def, axiom, hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc)))=c_Wellfounded_Opred__nat, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__nat__def)). 4.46/4.69 fof(fact_converse__meet, axiom, ![X68, X16, X4, X3]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X3,tc_HOL_Obool))),c_Predicate_Oconversep(X3,X4,X16)),c_Predicate_Oconversep(X3,X4,X68))=c_Predicate_Oconversep(X3,X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_fun(X4,tc_HOL_Obool))),X16),X68)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__meet)). 4.46/4.69 fof(fact_Pow__INT__eq, axiom, ![X1, X2, X3, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),X3),c_Set_OPow(X4)),X1))=hAPP(c_Set_OPow(X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__INT__eq)). 4.46/4.69 fof(fact_converse__join, axiom, ![X68, X16, X4, X3]:c_Predicate_Oconversep(X3,X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_fun(X4,tc_HOL_Obool))),X16),X68))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X3,tc_HOL_Obool))),c_Predicate_Oconversep(X3,X4,X16)),c_Predicate_Oconversep(X3,X4,X68)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__join)). 4.46/4.69 fof(fact_Compl__UN, axiom, ![X1, X2, X3, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X3),c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool))),X1))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__UN)). 4.46/4.69 fof(fact_Compl__INT, axiom, ![X1, X2, X3, X4]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X3),c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool))),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__INT)). 4.46/4.69 fof(fact_INT__simps_I5_J, axiom, ![X1, X18, X52, X4, X3]:hAPP(hAPP(c_Set_Oinsert(X4),X18),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X52),X1))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X52),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X3),hAPP(c_Set_Oinsert(X4),X18)),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__simps_I5_J)). 4.46/4.69 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1, axiom, ![X16, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool)),c_List_Olistrel1(X4,c_Transitive__Closure_Ortrancl(X4,X16))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X4),c_List_Olistrel1(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1__rtrancl__subset__rtrancl__listrel1)). 4.46/4.69 fof(fact_Range__insert, axiom, ![X16, X37, X18, X4, X3]:hAPP(c_Relation_ORange(X3,X4),hAPP(hAPP(c_Set_Oinsert(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X18),X37)),X16))=hAPP(hAPP(c_Set_Oinsert(X4),X37),hAPP(c_Relation_ORange(X3,X4),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__insert)). 4.46/4.69 fof(fact_Un__Diff, axiom, ![X52, X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X52)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X1),X52))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)),X52), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Diff)). 4.46/4.69 fof(fact_Domain__insert, axiom, ![X16, X37, X18, X3, X4]:hAPP(c_Relation_ODomain(X4,X3),hAPP(hAPP(c_Set_Oinsert(tc_prod(X4,X3)),hAPP(hAPP(c_Product__Type_OPair(X4,X3),X18),X37)),X16))=hAPP(hAPP(c_Set_Oinsert(X4),X18),hAPP(c_Relation_ODomain(X4,X3),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__insert)). 4.46/4.69 fof(fact_Un__Int__distrib2, axiom, ![X2, X52, X1, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X1),X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X52),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X1),X52)),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Int__distrib2)). 4.46/4.69 fof(fact_Int__Un__distrib2, axiom, ![X2, X52, X1, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X1),X52)),X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X1),X2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X52),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Un__distrib2)). 4.46/4.69 fof(fact_Diff__Int, axiom, ![X52, X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X52))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X1),X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__Int)). 4.46/4.69 fof(fact_Un__Int__distrib, axiom, ![X52, X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X1),X52))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Int__distrib)). 4.46/4.69 fof(fact_Int__Un__distrib, axiom, ![X52, X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X1),X52))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Un__distrib)). 4.46/4.69 fof(fact_takeWhile__map, axiom, ![X7, X27, X3, X28, X4]:c_List_OtakeWhile(X4,X28,hAPP(hAPP(c_List_Omap(X3,X4),X27),X7))=hAPP(hAPP(c_List_Omap(X3,X4),X27),c_List_OtakeWhile(X3,hAPP(c_Fun_Ocomp(X4,tc_HOL_Obool,X3,X28),X27),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__map)). 4.46/4.69 fof(fact_replicate__app__Cons__same, axiom, ![X57, X48, X17, X4]:hAPP(hAPP(c_List_Olist_OCons(X4),X48),hAPP(hAPP(c_List_Oappend(X4),c_List_Oreplicate(X4,X17,X48)),X57))=hAPP(hAPP(c_List_Oappend(X4),c_List_Oreplicate(X4,X17,X48)),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__app__Cons__same)). 4.46/4.69 fof(fact_rev__drop, axiom, ![X57, X21, X4]:hAPP(c_List_Orev(X4),hAPP(hAPP(c_List_Odrop(X4),X21),X57))=hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),X21)),hAPP(c_List_Orev(X4),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__drop)). 4.46/4.69 fof(fact_rev__take, axiom, ![X57, X21, X4]:hAPP(c_List_Orev(X4),hAPP(hAPP(c_List_Otake(X4),X21),X57))=hAPP(hAPP(c_List_Odrop(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),X21)),hAPP(c_List_Orev(X4),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__take)). 4.46/4.69 fof(fact_splice_Osimps_I3_J, axiom, ![X72, X47, X57, X48, X4]:c_List_Osplice(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57),hAPP(hAPP(c_List_Olist_OCons(X4),X47),X72))=hAPP(hAPP(c_List_Olist_OCons(X4),X48),hAPP(hAPP(c_List_Olist_OCons(X4),X47),c_List_Osplice(X4,X57,X72))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_splice_Osimps_I3_J)). 4.46/4.69 fof(fact_nth__append__length__plus, axiom, ![X17, X72, X57, X4]:hAPP(hAPP(c_List_Onth(X4),X72),X17)=hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Oappend(X4),X57),X72)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__append__length__plus)). 4.46/4.69 fof(fact_restrict__map__insert, axiom, ![X2, X18, X27, X3, X4]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X3)),c_Map_Orestrict__map(X4,X3,X27,X2)),X18),hAPP(X27,X18))=c_Map_Orestrict__map(X4,X3,X27,hAPP(hAPP(c_Set_Oinsert(X4),X18),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__map__insert)). 4.46/4.69 fof(fact_set__update__subset__insert, axiom, ![X6, X24, X7, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist__update(X4,X7),X24),X6))),hAPP(hAPP(c_Set_Oinsert(X4),X6),hAPP(c_List_Oset(X4),X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__update__subset__insert)). 4.46/4.69 fof(fact_comp__funpow, axiom, ![X27, X14, X3, X4]:c_Fun_Ocomp(X3,X3,X4,hAPP(hAPP(c_Nat_Ocompow(X3,X3),X14),X27))=hAPP(hAPP(c_Nat_Ocompow(tc_fun(X4,X3),tc_fun(X4,X3)),X14),c_Fun_Ocomp(X3,X3,X4,X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comp__funpow)). 4.46/4.69 fof(fact_map__pair__simp, axiom, ![X37, X18, X50, X27, X3, X59, X4, X29]:hAPP(c_Product__Type_Omap__pair(X29,X4,X59,X3,X27,X50),hAPP(hAPP(c_Product__Type_OPair(X29,X59),X18),X37))=hAPP(hAPP(c_Product__Type_OPair(X4,X3),hAPP(X27,X18)),hAPP(X50,X37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair__simp)). 4.46/4.69 fof(conj_4, hypothesis, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),v_F),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_4)). 4.46/4.69 fof(conj_6, hypothesis, c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)),v_F), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_6)). 4.46/4.69 fof(fact_the__elem__def, axiom, ![X173, X4]:c_HOL_OThe(X4,hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),hAPP(c_fequal,X173)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Set_Oinsert(X4)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=c_Set_Othe__elem(X4,X173), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__elem__def)). 4.46/4.69 fof(fact_fun__upd__upd, axiom, ![X35, X5, X6, X27, X3, X4]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X3),X27),X6),X35)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X3),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X3),X27),X6),X5)),X6),X35), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__upd)). 4.46/4.69 fof(fact_take__drop, axiom, ![X57, X19, X17, X4]:hAPP(hAPP(c_List_Odrop(X4),X19),hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X19)),X57))=hAPP(hAPP(c_List_Otake(X4),X17),hAPP(hAPP(c_List_Odrop(X4),X19),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__drop)). 4.46/4.69 fof(fact_diff__mult__distrib, axiom, ![X15, X17, X19]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X15))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17)),X15), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__mult__distrib)). 4.46/4.69 fof(fact_zdiff__zmult__distrib, axiom, ![X30, X74, X75]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X75),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X74),X30))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X75),X74)),X30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiff__zmult__distrib)). 4.46/4.69 fof(fact_add__mult__distrib, axiom, ![X15, X17, X19]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17)),X15)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X15)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__mult__distrib)). 4.46/4.69 fof(fact_zadd__zmult__distrib, axiom, ![X30, X74, X75]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X75),X74)),X30)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X75),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X74),X30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__zmult__distrib)). 4.46/4.69 fof(fact_drop__take, axiom, ![X57, X19, X17, X4]:hAPP(hAPP(c_List_Odrop(X4),X17),hAPP(hAPP(c_List_Otake(X4),X19),X57))=hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17)),hAPP(hAPP(c_List_Odrop(X4),X17),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__take)). 4.46/4.69 fof(fact_zdiff__zmult__distrib2, axiom, ![X74, X75, X30]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X75)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X74))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X75),X74)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiff__zmult__distrib2)). 4.46/4.69 fof(fact_add__mult__distrib2, axiom, ![X17, X19, X15]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__mult__distrib2)). 4.46/4.69 fof(fact_diff__mult__distrib2, axiom, ![X17, X19, X15]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__mult__distrib2)). 4.46/4.69 fof(fact_zpower__zadd__distrib, axiom, ![X49, X47, X48]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X48),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),X49))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X48),X47)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X48),X49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zpower__zadd__distrib)). 4.46/4.69 fof(fact_hb__map_Osimps_I2_J, axiom, ![X107, X6, X27, X4, X3]:c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X4),hAPP(hAPP(c_Option_Omap(X3,X4),X27),X6),c_Lazy__Sequence_Ohb__map(X3,X4,X27,X107))=c_Lazy__Sequence_Ohb__map(X3,X4,X27,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X3),X6,X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hb__map_Osimps_I2_J)). 4.46/4.69 fof(fact_map__of__append, axiom, ![X32, X7, X3, X4]:hAPP(c_Map_Omap__of(X4,X3),hAPP(hAPP(c_List_Oappend(tc_prod(X4,X3)),X7),X32))=c_Map_Omap__add(X4,X3,hAPP(c_Map_Omap__of(X4,X3),X32),hAPP(c_Map_Omap__of(X4,X3),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__append)). 4.46/4.69 fof(fact_listrel__subset__rtrancl__listrel1, axiom, ![X16, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool)),c_List_Olistrel(X4,X16)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X4),c_List_Olistrel1(X4,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__subset__rtrancl__listrel1)). 4.46/4.69 fof(fact_New__DSequence_Opos__bind__def, axiom, ![X24, X27, X6, X4, X3]:hAPP(c_Lazy__Sequence_Obind(X3,X4,hAPP(X6,X24)),hAPP(hAPP(c_COMBC(X3,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4)),X27),X24))=hAPP(c_New__DSequence_Opos__bind(X3,X4,X6,X27),X24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Opos__bind__def)). 4.46/4.69 fof(fact_rev__foldl__cons, axiom, ![X7, X4]:hAPP(c_List_Ofoldl(tc_List_Olist(X4),X4,hAPP(c_COMBC(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_OCons(X4)),c_List_Olist_ONil(X4)),X7)=hAPP(c_List_Orev(X4),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__foldl__cons)). 4.46/4.69 fof(fact_Diff__insert, axiom, ![X1, X18, X2, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__insert)). 4.46/4.69 fof(fact_int__setprod, axiom, ![X2, X27, X4]:hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X4),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X27)),X2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,tc_Nat_Onat),X27),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__setprod)). 4.46/4.69 fof(fact_int__setsum, axiom, ![X2, X27, X4]:hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X4),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X27)),X2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X27),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__setsum)). 4.46/4.69 fof(fact_list__update__code_I3_J, axiom, ![X47, X21, X57, X48, X4]:hAPP(hAPP(c_List_Olist_OCons(X4),X48),hAPP(hAPP(c_List_Olist__update(X4,X57),X21),X47))=hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)),hAPP(c_Nat_OSuc,X21)),X47), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__code_I3_J)). 4.46/4.69 fof(fact_foldl__append, axiom, ![X32, X7, X18, X27, X3, X4]:hAPP(c_List_Ofoldl(X4,X3,X27,X18),hAPP(hAPP(c_List_Oappend(X3),X7),X32))=hAPP(c_List_Ofoldl(X4,X3,X27,hAPP(c_List_Ofoldl(X4,X3,X27,X18),X7)),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__append)). 4.46/4.69 fof(fact_divmod__nat__rel, axiom, ![X17, X19]:hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X19,X17),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19),X17)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel)). 4.46/4.69 fof(fact_Field__Un, axiom, ![X68, X16, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OField(X4),X16)),hAPP(c_Relation_OField(X4),X68))=hAPP(c_Relation_OField(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X16),X68)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Field__Un)). 4.46/4.69 fof(fact_empty__upd__none, axiom, ![X235, X6, X4, X3]:hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X4)),hAPP(c_COMBK(tc_Option_Ooption(X4),X3),c_Option_Ooption_ONone(X4))),X6),c_Option_Ooption_ONone(X4)),X235)=c_Option_Ooption_ONone(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__upd__none)). 4.46/4.69 fof(fact_funpow__mult, axiom, ![X27, X22, X14, X4]:hAPP(hAPP(c_Nat_Ocompow(X4,X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X14)),X27)=hAPP(hAPP(c_Nat_Ocompow(X4,X4),X14),hAPP(hAPP(c_Nat_Ocompow(X4,X4),X22),X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_funpow__mult)). 4.46/4.69 fof(fact_filter__append, axiom, ![X32, X7, X28, X4]:hAPP(hAPP(c_List_Oappend(X4),hAPP(c_List_Ofilter(X4,X28),X7)),hAPP(c_List_Ofilter(X4,X28),X32))=hAPP(c_List_Ofilter(X4,X28),hAPP(hAPP(c_List_Oappend(X4),X7),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__append)). 4.46/4.69 fof(fact_Option_Omap__def, axiom, ![X27, X3, X4]:hAPP(c_Option_Omap(X4,X3),X27)=c_Option_Ooption_Ooption__case(tc_Option_Ooption(X3),X4,c_Option_Ooption_ONone(X3),hAPP(hAPP(c_COMBB(X3,tc_Option_Ooption(X3),X4),c_Option_Ooption_OSome(X3)),X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Option_Omap__def)). 4.46/4.69 fof(fact_tl__take, axiom, ![X57, X17, X4]:hAPP(c_List_Otl(X4),hAPP(hAPP(c_List_Otake(X4),X17),X57))=hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X4),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tl__take)). 4.46/4.69 fof(fact_sublists__powset, axiom, ![X7, X4]:hAPP(c_Set_OPow(X4),hAPP(c_List_Oset(X4),X7))=hAPP(c_Set_Oimage(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool),c_List_Oset(X4)),hAPP(c_List_Oset(tc_List_Olist(X4)),c_Enum_Osublists(X4,X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublists__powset)). 4.46/4.69 fof(fact_mod__mult__distrib, axiom, ![X15, X17, X19]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X15))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17)),X15), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__distrib)). 4.46/4.69 fof(fact_mod__mult__distrib2, axiom, ![X17, X19, X15]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__distrib2)). 4.46/4.69 fof(fact_mod__mult__self4, axiom, ![X19, X17, X15]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X19),X17)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X17)),X19)),X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__self4)). 4.46/4.69 fof(fact_nth__append__length, axiom, ![X72, X48, X57, X4]:X48=hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Oappend(X4),X57),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X72))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__append__length)). 4.46/4.69 fof(fact_select__weight__cons__zero, axiom, ![X7, X6, X4]:c_Random_Oselect__weight(X4,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X4)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X4),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X6)),X7))=c_Random_Oselect__weight(X4,X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select__weight__cons__zero)). 4.46/4.69 fof(fact_UNIV__option__conv, axiom, ![X4]:c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X4),tc_HOL_Obool))=hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(X4)),c_Option_Ooption_ONone(X4)),hAPP(c_Set_Oimage(X4,tc_Option_Ooption(X4),c_Option_Ooption_OSome(X4)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__option__conv)). 4.46/4.69 fof(fact_lex__def, axiom, ![X16, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X4,X16))=c_List_Olex(X4,X16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lex__def)). 4.46/4.69 fof(fact_length__filter__le, axiom, ![X7, X28, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Ofilter(X4,X28),X7))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__filter__le)). 4.46/4.69 fof(fact_UNIV__Times__UNIV, axiom, ![X3, X4]:c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X4,X3),tc_HOL_Obool))=hAPP(hAPP(c_Product__Type_OSigma(X4,X3),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__Times__UNIV)). 4.46/4.69 fof(fact__01, axiom, ![X269, X48, X4]:hAPP(c_Lazy__Sequence_Oyield(X4),c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X48,X269))=hAPP(c_Option_Ooption_OSome(tc_prod(X4,tc_Lazy__Sequence_Olazy__sequence(X4))),hAPP(hAPP(c_Product__Type_OPair(X4,tc_Lazy__Sequence_Olazy__sequence(X4)),X48),X269)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact__01)). 4.46/4.69 fof(fact_funpow_Osimps_I2_J, axiom, ![X27, X14, X4]:hAPP(hAPP(c_Nat_Ocompow(X4,X4),hAPP(c_Nat_OSuc,X14)),X27)=hAPP(c_Fun_Ocomp(X4,X4,X4,X27),hAPP(hAPP(c_Nat_Ocompow(X4,X4),X14),X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_funpow_Osimps_I2_J)). 4.46/4.69 fof(fact_insert__inter__insert, axiom, ![X1, X2, X18, X4]:hAPP(hAPP(c_Set_Oinsert(X4),X18),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X18),X2)),hAPP(hAPP(c_Set_Oinsert(X4),X18),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__inter__insert)). 4.46/4.69 fof(fact_replicate__length__filter, axiom, ![X7, X6, X4]:hAPP(c_List_Ofilter(X4,hAPP(c_fequal,X6)),X7)=c_List_Oreplicate(X4,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Ofilter(X4,hAPP(c_fequal,X6)),X7)),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__length__filter)). 4.46/4.69 fof(fact_take__Suc__Cons, axiom, ![X57, X48, X17, X4]:hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_OSuc,X17)),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57))=hAPP(hAPP(c_List_Olist_OCons(X4),X48),hAPP(hAPP(c_List_Otake(X4),X17),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Suc__Cons)). 4.46/4.69 fof(fact_finite__range__map__of, axiom, ![X70, X3, X4]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X4)),hAPP(c_Set_Oimage(X3,tc_Option_Ooption(X4),hAPP(c_Map_Omap__of(X3,X4),X70)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__range__map__of)). 4.46/4.69 fof(fact_length__takeWhile__le, axiom, ![X7, X28, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X28,X7))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__takeWhile__le)). 4.46/4.69 fof(fact_zpower__zmod, axiom, ![X47, X19, X48]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X48,X19)),X47),X19)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X48),X47),X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zpower__zmod)). 4.46/4.69 fof(fact_zdiff__zmod__left, axiom, ![X47, X19, X48]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X48),X47),X19)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X48,X19)),X47),X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiff__zmod__left)). 4.46/4.69 fof(fact_listsp__inf__eq, axiom, ![X1, X2, X4]:c_List_Olistsp(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),c_List_Olistsp(X4,X2)),c_List_Olistsp(X4,X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp__inf__eq)). 4.46/4.69 fof(fact_replicate__add, axiom, ![X48, X19, X17, X4]:hAPP(hAPP(c_List_Oappend(X4),c_List_Oreplicate(X4,X17,X48)),c_List_Oreplicate(X4,X19,X48))=c_List_Oreplicate(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X19),X48), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__add)). 4.46/4.69 fof(fact_zmod__zmult1__eq, axiom, ![X10, X11, X12]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X11),X10)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X10)),X10), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zmult1__eq)). 4.46/4.69 fof(fact_zdiff__zmod__right, axiom, ![X19, X47, X48]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X48),X47),X19)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X48),c_Divides_Odiv__class_Omod(tc_Int_Oint,X47,X19)),X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiff__zmod__right)). 4.46/4.69 fof(fact_diff__cancel2, axiom, ![X17, X15, X19]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X15)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__cancel2)). 4.46/4.69 fof(fact_diff__cancel, axiom, ![X17, X19, X15]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15),X19)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__cancel)). 4.46/4.69 fof(fact_Pow__Int__eq, axiom, ![X1, X2, X4]:hAPP(c_Set_OPow(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X4),X2)),hAPP(c_Set_OPow(X4),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__Int__eq)). 4.46/4.69 fof(fact_dom__map__add, axiom, ![X14, X22, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X3,X14)),c_Map_Odom(X4,X3,X22))=c_Map_Odom(X4,X3,c_Map_Omap__add(X4,X3,X22,X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__map__add)). 4.46/4.69 fof(fact_snd__def, axiom, ![X109, X4, X3]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3,X4,X4),hAPP(c_COMBK(tc_fun(X4,X4),X3),c_COMBI(X4))),X109)=hAPP(c_Product__Type_Osnd(X3,X4),X109), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snd__def)). 4.46/4.69 fof(fact_sorted__transpose, axiom, ![X7, X4]:c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X4))),c_List_Otranspose(X4,X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__transpose)). 4.46/4.69 fof(fact_set__drop__subset, axiom, ![X7, X14, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Odrop(X4),X14),X7))),hAPP(c_List_Oset(X4),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__drop__subset)). 4.46/4.69 fof(fact_set__take__subset, axiom, ![X7, X14, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Otake(X4),X14),X7))),hAPP(c_List_Oset(X4),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__take__subset)). 4.46/4.69 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J, axiom, ![X14, X22]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X22,X14)=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X22),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SetInterval_Otransfer__nat__int__set__functions_I2_J)). 4.46/4.69 fof(fact_fst__map__pair, axiom, ![X6, X50, X27, X59, X29, X3, X4]:hAPP(c_Product__Type_Ofst(X4,X3),hAPP(c_Product__Type_Omap__pair(X29,X4,X59,X3,X27,X50),X6))=hAPP(X27,hAPP(c_Product__Type_Ofst(X29,X59),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fst__map__pair)). 4.46/4.69 fof(fact_snd__prod__fun, axiom, ![X6, X50, X27, X59, X29, X4, X3]:hAPP(c_Product__Type_Osnd(X3,X4),hAPP(c_Product__Type_Omap__pair(X29,X3,X59,X4,X27,X50),X6))=hAPP(X50,hAPP(c_Product__Type_Osnd(X29,X59),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snd__prod__fun)). 4.46/4.69 fof(fact_partition__filter2, axiom, ![X7, X28, X4]:hAPP(c_Product__Type_Osnd(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Opartition(X4,X28,X7))=hAPP(c_List_Ofilter(X4,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X4,c_fNot),X28)),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition__filter2)). 4.46/4.69 fof(fact_butlast__conv__take, axiom, ![X57, X4]:hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X57)=c_List_Obutlast(X4,X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast__conv__take)). 4.46/4.69 fof(fact_set__sublist__subset, axiom, ![X73, X7, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),c_List_Osublist(X4,X7,X73))),hAPP(c_List_Oset(X4),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__sublist__subset)). 4.46/4.69 fof(fact_set__remove1__subset, axiom, ![X7, X6, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),c_List_Oremove1(X4,X6,X7))),hAPP(c_List_Oset(X4),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__remove1__subset)). 4.46/4.69 fof(fact_rtrancl_Ortrancl__refl, axiom, ![X16, X18, X4]:hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X18),X18)),c_Transitive__Closure_Ortrancl(X4,X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl_Ortrancl__refl)). 4.46/4.69 fof(fact_negative__zless, axiom, ![X19, X17]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X17)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negative__zless)). 4.46/4.69 fof(fact_inj__singleton, axiom, ![X4]:c_Fun_Oinj__on(X4,tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Set_Oinsert(X4)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__singleton)). 4.46/4.69 fof(fact_remdups__map__remdups, axiom, ![X7, X27, X3, X4]:c_List_Oremdups(X4,hAPP(hAPP(c_List_Omap(X3,X4),X27),X7))=c_List_Oremdups(X4,hAPP(hAPP(c_List_Omap(X3,X4),X27),c_List_Oremdups(X3,X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups__map__remdups)). 4.46/4.69 fof(fact_diff__Suc, axiom, ![X14, X22]:c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22),X14))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22),hAPP(c_Nat_OSuc,X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__Suc)). 4.46/4.69 fof(fact_Field__def, axiom, ![X16, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X4,X4),X16)),hAPP(c_Relation_ORange(X4,X4),X16))=hAPP(c_Relation_OField(X4),X16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Field__def)). 4.46/4.69 fof(fact_scomp__apply, axiom, ![X6, X50, X27, X4, X59, X29, X3]:hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X3,X29,X59,X4),X27),X50),X6)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29,X59,X4),X50),hAPP(X27,X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_scomp__apply)). 4.46/4.69 fof(fact_list__update__overwrite, axiom, ![X47, X48, X21, X57, X4]:hAPP(hAPP(c_List_Olist__update(X4,X57),X21),X47)=hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Olist__update(X4,X57),X21),X48)),X21),X47), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__overwrite)). 4.46/4.69 fof(fact_converse__pred__comp, axiom, ![X68, X16, X29, X4, X3]:c_Predicate_Opred__comp(X4,X29,X3,c_Predicate_Oconversep(X29,X4,X68),c_Predicate_Oconversep(X3,X29,X16))=c_Predicate_Oconversep(X3,X4,c_Predicate_Opred__comp(X3,X29,X4,X16,X68)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__pred__comp)). 4.46/4.69 fof(fact_funpow__swap1, axiom, ![X6, X14, X4, X27]:hAPP(X27,hAPP(hAPP(hAPP(c_Nat_Ocompow(X4,X4),X14),X27),X6))=hAPP(hAPP(hAPP(c_Nat_Ocompow(X4,X4),X14),X27),hAPP(X27,X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_funpow__swap1)). 4.46/4.69 fof(fact_append__assoc, axiom, ![X191, X72, X57, X4]:hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Oappend(X4),X57),X72)),X191)=hAPP(hAPP(c_List_Oappend(X4),X57),hAPP(hAPP(c_List_Oappend(X4),X72),X191)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__assoc)). 4.46/4.69 fof(fact_append__Cons, axiom, ![X72, X57, X48, X4]:hAPP(hAPP(c_List_Olist_OCons(X4),X48),hAPP(hAPP(c_List_Oappend(X4),X57),X72))=hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)),X72), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__Cons)). 4.46/4.69 fof(fact_drop__drop, axiom, ![X57, X19, X17, X4]:hAPP(hAPP(c_List_Odrop(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X19)),X57)=hAPP(hAPP(c_List_Odrop(X4),X17),hAPP(hAPP(c_List_Odrop(X4),X19),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__drop)). 4.46/4.69 fof(fact_div__mod__code__numeral__def, axiom, ![X19, X17]:hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X17),X19)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X17,X19))=c_Code__Numeral_Odiv__mod__code__numeral(X17,X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mod__code__numeral__def)). 4.46/4.69 fof(fact_nat__mult__assoc, axiom, ![X15, X17, X19]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X17)),X15)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__assoc)). 4.46/4.69 fof(fact_zmult__assoc, axiom, ![X89, X74, X75]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X75),X74)),X89)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X75),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X74),X89)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__assoc)). 4.46/4.69 fof(fact_zpower__zpower, axiom, ![X49, X47, X48]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X48),X47)),X49)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X47),X49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zpower__zpower)). 4.46/4.69 fof(fact_div__mult2__eq, axiom, ![X10, X11, X12]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X10))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X12),X11)),X10), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult2__eq)). 4.46/4.69 fof(fact_rev__append, axiom, ![X72, X57, X4]:hAPP(c_List_Orev(X4),hAPP(hAPP(c_List_Oappend(X4),X57),X72))=hAPP(hAPP(c_List_Oappend(X4),hAPP(c_List_Orev(X4),X72)),hAPP(c_List_Orev(X4),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__append)). 4.46/4.69 fof(fact_Divides_Otransfer__int__nat__functions_I1_J, axiom, ![X47, X48]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X48)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X47))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X48),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Otransfer__int__nat__functions_I1_J)). 4.46/4.69 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J, axiom, ![X47, X48]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X47))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X48)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J)). 4.46/4.69 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J, axiom, ![X47, X48]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X47))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X48)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J)). 4.46/4.69 fof(fact_UN__singleton, axiom, ![X2, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Set_Oinsert(X4)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=X2, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__singleton)). 4.46/4.69 fof(fact_card__length, axiom, ![X7, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),hAPP(c_List_Oset(X4),X7))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__length)). 4.46/4.69 fof(fact_mod__mult__self3, axiom, ![X19, X17, X15]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X17)),X19),X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__self3)). 4.46/4.69 fof(fact_Un__Diff__Int, axiom, ![X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1))=X2, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Diff__Int)). 4.46/4.69 fof(fact_split__conv, axiom, ![X37, X18, X27, X4, X29, X3]:hAPP(hAPP(X27,X18),X37)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3,X29,X4),X27),hAPP(hAPP(c_Product__Type_OPair(X3,X29),X18),X37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__conv)). 4.46/4.69 fof(fact_restrict__restrict, axiom, ![X1, X2, X22, X3, X4]:c_Map_Orestrict__map(X4,X3,c_Map_Orestrict__map(X4,X3,X22,X2),X1)=c_Map_Orestrict__map(X4,X3,X22,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__restrict)). 4.46/4.69 fof(fact_list__update__code_I2_J, axiom, ![X47, X57, X48, X4]:hAPP(hAPP(c_List_Olist_OCons(X4),X47),X57)=hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X47), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__code_I2_J)). 4.46/4.69 fof(fact_takeWhile__eq__take, axiom, ![X7, X28, X4]:c_List_OtakeWhile(X4,X28,X7)=hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X28,X7))),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__eq__take)). 4.46/4.69 fof(fact_triple_Osimps_I2_J, axiom, ![X182, X33, X183, X38, X4, X3]:c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X38,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X183),X33),X182))=hAPP(hAPP(hAPP(X38,X183),X33),X182), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_triple_Osimps_I2_J)). 4.46/4.69 fof(fact_triple_Orecs, axiom, ![X182, X33, X183, X38, X4, X3]:hAPP(hAPP(hAPP(X38,X183),X33),X182)=c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X38,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X183),X33),X182)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_triple_Orecs)). 4.46/4.69 fof(fact_length__n__lists, axiom, ![X57, X17, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),c_Enum_On__lists(X4,X17,X57))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__n__lists)). 4.46/4.69 fof(fact_le__cube, axiom, ![X19]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__cube)). 4.46/4.69 fof(fact_take__tl, axiom, ![X57, X17, X4]:hAPP(c_List_Otl(X4),hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_OSuc,X17)),X57))=hAPP(hAPP(c_List_Otake(X4),X17),hAPP(c_List_Otl(X4),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__tl)). 4.46/4.69 fof(fact_take__1__Cons, axiom, ![X57, X48, X4]:hAPP(hAPP(c_List_Olist_OCons(X4),X48),c_List_Olist_ONil(X4))=hAPP(hAPP(c_List_Otake(X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__1__Cons)). 4.46/4.69 fof(fact_insert__Diff__single, axiom, ![X2, X18, X4]:hAPP(hAPP(c_Set_Oinsert(X4),X18),X2)=hAPP(hAPP(c_Set_Oinsert(X4),X18),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__Diff__single)). 4.46/4.69 fof(fact_negative__zless__0, axiom, ![X17]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X17)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negative__zless__0)). 4.46/4.69 fof(fact_negative__zle, axiom, ![X19, X17]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negative__zle)). 4.46/4.69 fof(fact_zero__le__zpower__abs, axiom, ![X17, X48]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X48)),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__zpower__abs)). 4.46/4.69 fof(fact_zminus__zmod, axiom, ![X19, X48]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X48,X19)),X19)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X48),X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zminus__zmod)). 4.46/4.69 fof(fact_nth__Cons__Suc, axiom, ![X17, X57, X48, X4]:hAPP(hAPP(c_List_Onth(X4),X57),X17)=hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)),hAPP(c_Nat_OSuc,X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__Cons__Suc)). 4.46/4.69 fof(fact_drop__Suc__Cons, axiom, ![X57, X48, X17, X4]:hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_OSuc,X17)),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57))=hAPP(hAPP(c_List_Odrop(X4),X17),X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__Suc__Cons)). 4.46/4.69 fof(fact_prod_Orecs, axiom, ![X37, X18, X38, X4, X29, X3]:c_Product__Type_Oprod_Oprod__rec(X3,X29,X4,X38,hAPP(hAPP(c_Product__Type_OPair(X3,X29),X18),X37))=hAPP(hAPP(X38,X18),X37), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_prod_Orecs)). 4.46/4.69 fof(fact_append__take__drop__id, axiom, ![X57, X17, X4]:X57=hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Otake(X4),X17),X57)),hAPP(hAPP(c_List_Odrop(X4),X17),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__take__drop__id)). 4.46/4.69 fof(fact_surjective__pairing, axiom, ![X3, X4, X251]:hAPP(hAPP(c_Product__Type_OPair(X4,X3),hAPP(c_Product__Type_Ofst(X4,X3),X251)),hAPP(c_Product__Type_Osnd(X4,X3),X251))=X251, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_surjective__pairing)). 4.46/4.69 fof(fact_map__add__upds, axiom, ![X32, X7, X100, X99, X3, X4]:c_Map_Omap__upds(X4,X3,c_Map_Omap__add(X4,X3,X99,X100),X7,X32)=c_Map_Omap__add(X4,X3,X99,c_Map_Omap__upds(X4,X3,X100,X7,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__upds)). 4.46/4.69 fof(fact_nth_Osimps, axiom, ![X14, X7, X6, X4]:hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X6),X7)),X14)=c_Nat_Onat_Onat__case(X4,X6,hAPP(c_List_Onth(X4),X7),X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth_Osimps)). 4.46/4.69 fof(fact_restrict__map__empty, axiom, ![X6, X65, X4, X3]:hAPP(c_Map_Orestrict__map(X3,X4,hAPP(c_COMBK(tc_Option_Ooption(X4),X3),c_Option_Ooption_ONone(X4)),X65),X6)=c_Option_Ooption_ONone(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__map__empty)). 4.46/4.69 fof(fact_Sigma__empty2, axiom, ![X2, X3, X4]:c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X3),tc_HOL_Obool))=hAPP(hAPP(c_Product__Type_OSigma(X4,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__empty2)). 4.46/4.69 fof(fact_drop__replicate, axiom, ![X48, X15, X21, X4]:hAPP(hAPP(c_List_Odrop(X4),X21),c_List_Oreplicate(X4,X15,X48))=c_List_Oreplicate(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15),X21),X48), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__replicate)). 4.46/4.69 fof(fact_zmod__zminus2, axiom, ![X11, X12]:c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zminus2)). 4.46/4.69 fof(fact_length__tl, axiom, ![X57, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Otl(X4),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__tl)). 4.46/4.69 fof(fact_Divides_Otransfer__int__nat__functions_I2_J, axiom, ![X47, X48]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X48),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X47))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X48,X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Otransfer__int__nat__functions_I2_J)). 4.46/4.69 fof(fact_zmod__zminus__zminus, axiom, ![X11, X12]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zminus__zminus)). 4.46/4.69 fof(fact_Pair__scomp, axiom, ![X27, X6, X3, X29, X4]:hAPP(hAPP(c_Product__Type_Oscomp(X4,X29,X4,X3),hAPP(c_Product__Type_OPair(X29,X4),X6)),X27)=hAPP(X27,X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pair__scomp)). 4.46/4.69 fof(fact_dom__restrict, axiom, ![X2, X22, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X3,X22)),X2)=c_Map_Odom(X4,X3,c_Map_Orestrict__map(X4,X3,X22,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__restrict)). 4.46/4.69 fof(fact_list_Osimps_I5_J, axiom, ![X85, X18, X169, X38, X3, X4]:hAPP(c_List_Olist_Olist__case(X4,X3,X38,X169),hAPP(hAPP(c_List_Olist_OCons(X3),X18),X85))=hAPP(hAPP(X169,X18),X85), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osimps_I5_J)). 4.46/4.69 fof(fact_Diff__idemp, axiom, ![X1, X2, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__idemp)). 4.46/4.69 fof(fact_Un__Diff__cancel, axiom, ![X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X1),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Diff__cancel)). 4.46/4.69 fof(fact_Int__left__absorb, axiom, ![X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__left__absorb)). 4.46/4.69 fof(fact_Un__left__absorb, axiom, ![X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__left__absorb)). 4.46/4.69 fof(fact_rel__comp__empty1, axiom, ![X26, X3, X29, X4]:hAPP(hAPP(c_Relation_Orel__comp(X4,X29,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X29),tc_HOL_Obool))),X26)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X3),tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__empty1)). 4.46/4.69 fof(fact_rel__comp__empty2, axiom, ![X26, X3, X29, X4]:c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X3),tc_HOL_Obool))=hAPP(hAPP(c_Relation_Orel__comp(X4,X29,X3),X26),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X29,X3),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__empty2)). 4.46/4.69 fof(fact_dom__const, axiom, ![X27, X3, X4]:c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=c_Map_Odom(X4,X3,hAPP(hAPP(c_COMBB(X3,tc_Option_Ooption(X3),X4),c_Option_Ooption_OSome(X3)),X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__const)). 4.46/4.69 fof(fact_rtrancl__idemp__self__comp, axiom, ![X26, X4]:hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),c_Transitive__Closure_Ortrancl(X4,X26)),c_Transitive__Closure_Ortrancl(X4,X26))=c_Transitive__Closure_Ortrancl(X4,X26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__idemp__self__comp)). 4.46/4.69 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J, axiom, ![X47, X48]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X48),X47))=c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X48),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J)). 4.46/4.69 fof(fact_wf__less, axiom, c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__less)). 4.46/4.69 fof(fact_card__eq__setsum, axiom, ![X2, X4]:hAPP(c_Finite__Set_Ocard(X4),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X4),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__eq__setsum)). 4.46/4.69 fof(fact_length__butlast, axiom, ![X57, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Obutlast(X4,X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__butlast)). 4.46/4.69 fof(fact_small__int__def, axiom, ![X87, X27]:c_Smallcheck_Osmall_H(X27,hAPP(c_Code__Numeral_Oint__of,X87),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X87)))=hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),X27),X87), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__int__def)). 4.46/4.69 fof(fact_listrel1__converse, axiom, ![X16, X4]:c_List_Olistrel1(X4,hAPP(c_Relation_Oconverse(X4,X4),X16))=hAPP(c_Relation_Oconverse(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel1(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1__converse)). 4.46/4.69 fof(fact_map__add__assoc, axiom, ![X294, X100, X99, X3, X4]:c_Map_Omap__add(X4,X3,c_Map_Omap__add(X4,X3,X99,X100),X294)=c_Map_Omap__add(X4,X3,X99,c_Map_Omap__add(X4,X3,X100,X294)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__assoc)). 4.46/4.69 fof(fact_scomp__Pair, axiom, ![X6, X29, X3, X4]:hAPP(hAPP(c_Product__Type_Oscomp(X4,X3,X29,tc_prod(X3,X29)),X6),c_Product__Type_OPair(X3,X29))=X6, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_scomp__Pair)). 4.46/4.69 fof(fact_image__Suc__atLeastAtMost, axiom, ![X25, X24]:hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24,X25))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24),hAPP(c_Nat_OSuc,X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Suc__atLeastAtMost)). 4.46/4.69 fof(fact_map__replicate, axiom, ![X6, X14, X27, X4, X3]:c_List_Oreplicate(X4,X14,hAPP(X27,X6))=hAPP(hAPP(c_List_Omap(X3,X4),X27),c_List_Oreplicate(X3,X14,X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__replicate)). 4.46/4.69 fof(fact_length__list__update, axiom, ![X48, X21, X57, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist__update(X4,X57),X21),X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__list__update)). 4.46/4.69 fof(fact_Inter__image__eq, axiom, ![X2, X1, X3, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)=c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),hAPP(c_Set_Oimage(X3,tc_fun(X4,tc_HOL_Obool),X1),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__image__eq)). 4.46/4.69 fof(fact_zmult__zminus, axiom, ![X30, X49]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X49),X30))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X49)),X30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__zminus)). 4.46/4.69 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J, axiom, ![X17, X48]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X48),X17))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X48)),X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J)). 4.46/4.69 fof(fact_partition__filter1, axiom, ![X7, X28, X4]:hAPP(c_Product__Type_Ofst(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Opartition(X4,X28,X7))=hAPP(c_List_Ofilter(X4,X28),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition__filter1)). 4.46/4.69 fof(fact_zdiv__zminus2, axiom, ![X11, X12]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12)),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__zminus2)). 4.46/4.69 fof(fact_inj__on__add__nat, axiom, ![X122, X45]:c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X45),X122), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__add__nat)). 4.46/4.69 fof(fact_negative__zle__0, axiom, ![X17]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negative__zle__0)). 4.46/4.69 fof(fact_UNIV__Plus__UNIV, axiom, ![X3, X4]:c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X4,X3),tc_HOL_Obool))=c_Sum__Type_OPlus(X4,X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__Plus__UNIV)). 4.46/4.69 fof(fact_subset__Pow__Union, axiom, ![X2, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__Pow__Union)). 4.46/4.69 fof(fact_UN__empty2, axiom, ![X2, X4, X3]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__empty2)). 4.46/4.69 fof(fact_mod__Suc__eq__Suc__mod, axiom, ![X17, X19]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X19),X17)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17)),X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__Suc__eq__Suc__mod)). 4.46/4.69 fof(fact_full__small__int__def, axiom, ![X87, X27]:c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,X27,X87)=c_Smallcheck_Ofull__small_H(X27,hAPP(c_Code__Numeral_Oint__of,X87),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X87))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_full__small__int__def)). 4.46/4.69 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int, axiom, ![X23, X67]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X67),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23),c_Groups_Oone__class_Oone(tc_Int_Oint)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X67,X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThanPlusOne__atLeastAtMost__int)). 4.46/4.69 fof(fact_fst__def, axiom, ![X109, X3, X4]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X3,X4),c_COMBK(X4,X3)),X109)=hAPP(c_Product__Type_Ofst(X4,X3),X109), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fst__def)). 4.46/4.69 fof(fact_pair__box_Osimps_I2_J, axiom, ![X37, X18, X38, X4, X29, X3]:c_Nitpick_Opair__box_Opair__box__case(X3,X29,X4,X38,c_Nitpick_Opair__box_OPairBox(X3,X29,X18,X37))=hAPP(hAPP(X38,X18),X37), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__box_Osimps_I2_J)). 4.46/4.69 fof(fact_pair__box_Orecs, axiom, ![X37, X18, X38, X4, X29, X3]:c_Nitpick_Opair__box_Opair__box__rec(X3,X29,X4,X38,c_Nitpick_Opair__box_OPairBox(X3,X29,X18,X37))=hAPP(hAPP(X38,X18),X37), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__box_Orecs)). 4.46/4.69 fof(fact_Diff__Compl, axiom, ![X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__Compl)). 4.46/4.69 fof(fact_set__replicate__Suc, axiom, ![X6, X14, X4]:hAPP(c_List_Oset(X4),c_List_Oreplicate(X4,hAPP(c_Nat_OSuc,X14),X6))=hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__replicate__Suc)). 4.46/4.69 fof(fact_option__map__Some, axiom, ![X6, X27, X4, X3]:hAPP(hAPP(c_Option_Omap(X3,X4),X27),hAPP(c_Option_Ooption_OSome(X3),X6))=hAPP(c_Option_Ooption_OSome(X4),hAPP(X27,X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option__map__Some)). 4.46/4.69 fof(fact_diff__less__Suc, axiom, ![X17, X19]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17)),hAPP(c_Nat_OSuc,X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__less__Suc)). 4.46/4.69 fof(fact_less__add__Suc2, axiom, ![X19, X21]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__add__Suc2)). 4.46/4.69 fof(fact_Body__triple__valid__0, axiom, ![X80, X263, X28, X4]:c_Hoare__Mirabelle_Otriple__valid(X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X28),hAPP(c_Com_Ocom_OBODY,X263)),X80)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Body__triple__valid__0)). 4.46/4.69 fof(fact_int__Suc, axiom, ![X19]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X19))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__Suc)). 4.46/4.69 fof(fact_replicate__Suc, axiom, ![X48, X17, X4]:c_List_Oreplicate(X4,hAPP(c_Nat_OSuc,X17),X48)=hAPP(hAPP(c_List_Olist_OCons(X4),X48),c_List_Oreplicate(X4,X17,X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__Suc)). 4.46/4.69 fof(fact_New__DSequence_Oneg__union__def, axiom, ![X24, X5, X6, X4]:hAPP(c_New__DSequence_Oneg__union(X4,X6,X5),X24)=c_Lazy__Sequence_Oappend(tc_Option_Ooption(X4),hAPP(X6,X24),hAPP(X5,X24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Oneg__union__def)). 4.46/4.69 fof(fact_drop__butlast, axiom, ![X57, X17, X4]:c_List_Obutlast(X4,hAPP(hAPP(c_List_Odrop(X4),X17),X57))=hAPP(hAPP(c_List_Odrop(X4),X17),c_List_Obutlast(X4,X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__butlast)). 4.46/4.69 fof(fact_fold__def, axiom, ![X2, X35, X27, X4, X3]:c_HOL_OThe(X4,c_Finite__Set_Ofold__graph(X3,X4,X27,X35,X2))=hAPP(hAPP(c_Finite__Set_Ofold(X3,X4,X27),X35),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__def)). 4.46/4.69 fof(fact_Image__Id__on, axiom, ![X1, X2, X4]:hAPP(c_Relation_OImage(X4,X4,c_Relation_OId__on(X4,X2)),X1)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__Id__on)). 4.46/4.69 fof(fact_eq__comp__r, axiom, ![X26, X4]:X26=c_Predicate_Opred__comp(X4,X4,X4,c_fequal,c_Predicate_Opred__comp(X4,X4,X4,X26,c_fequal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__comp__r)). 4.46/4.69 fof(fact_listset_Osimps_I2_J, axiom, ![X69, X2, X4]:c_List_Olistset(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_HOL_Obool)),X2),X69))=c_List_Oset__Cons(X4,X2,c_List_Olistset(X4,X69)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listset_Osimps_I2_J)). 4.46/4.69 fof(help_c__COMBC__1, axiom, ![X26, X80, X28, X4, X29, X3]:hAPP(hAPP(X28,X26),X80)=hAPP(hAPP(hAPP(c_COMBC(X3,X29,X4),X28),X80),X26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBC__1)). 4.46/4.69 fof(fact_empty__map__add, axiom, ![X22, X3, X4]:c_Map_Omap__add(X4,X3,hAPP(c_COMBK(tc_Option_Ooption(X3),X4),c_Option_Ooption_ONone(X3)),X22)=X22, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__map__add)). 4.46/4.69 fof(fact_map__add__empty, axiom, ![X22, X3, X4]:X22=c_Map_Omap__add(X4,X3,X22,hAPP(c_COMBK(tc_Option_Ooption(X3),X4),c_Option_Ooption_ONone(X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__empty)). 4.46/4.69 fof(fact_List_Oset__insert, axiom, ![X7, X6, X4]:hAPP(hAPP(c_Set_Oinsert(X4),X6),hAPP(c_List_Oset(X4),X7))=hAPP(c_List_Oset(X4),c_List_Oinsert(X4,X6,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Oset__insert)). 4.46/4.69 fof(fact_ran__empty, axiom, ![X4, X3]:c_Map_Oran(X3,X4,hAPP(c_COMBK(tc_Option_Ooption(X4),X3),c_Option_Ooption_ONone(X4)))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ran__empty)). 4.46/4.69 fof(fact_transpose_Osimps_I2_J, axiom, ![X262, X4]:c_List_Otranspose(X4,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),X262))=c_List_Otranspose(X4,X262), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose_Osimps_I2_J)). 4.46/4.69 fof(fact_Range__converse, axiom, ![X16, X4, X3]:hAPP(c_Relation_ORange(X3,X4),hAPP(c_Relation_Oconverse(X4,X3),X16))=hAPP(c_Relation_ODomain(X4,X3),X16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__converse)). 4.46/4.69 fof(fact_Domain__converse, axiom, ![X16, X3, X4]:hAPP(c_Relation_ORange(X3,X4),X16)=hAPP(c_Relation_ODomain(X4,X3),hAPP(c_Relation_Oconverse(X3,X4),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__converse)). 4.46/4.69 fof(fact_map__pair_Oidentity, axiom, ![X3, X4]:c_Product__Type_Omap__pair(X4,X4,X3,X3,c_COMBI(X4),c_COMBI(X3))=c_Fun_Oid(tc_prod(X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair_Oidentity)). 4.46/4.69 fof(fact_map__pair_Oid, axiom, ![X3, X4]:c_Fun_Oid(tc_prod(X4,X3))=c_Product__Type_Omap__pair(X4,X4,X3,X3,c_Fun_Oid(X4),c_Fun_Oid(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair_Oid)). 4.46/4.69 fof(fact_lazy__sequence_Osimps_I5_J, axiom, ![X242, X18, X169, X38, X3, X4]:hAPP(hAPP(X169,X18),X242)=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X4,X3,X38,X169,c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X18,X242)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Osimps_I5_J)). 4.46/4.69 fof(fact_Inter__def, axiom, ![X46, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X46),c_COMBI(tc_fun(X4,tc_HOL_Obool)))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X46), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__def)). 4.46/4.69 fof(fact_Union__def, axiom, ![X46, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X46),c_COMBI(tc_fun(X4,tc_HOL_Obool)))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X46), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__def)). 4.46/4.69 fof(fact_subtract__code__numeral__def, axiom, c_Code__Numeral_Osubtract__code__numeral=c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subtract__code__numeral__def)). 4.46/4.69 fof(fact_pair__box_Osize_I2_J, axiom, ![X11, X12, X3, X4]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X4,X3)),c_Nitpick_Opair__box_OPairBox(X4,X3,X12,X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__box_Osize_I2_J)). 4.46/4.69 fof(fact_Diff__subset, axiom, ![X1, X2, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X1)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__subset)). 4.46/4.69 fof(fact_Int__lower1, axiom, ![X1, X2, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__lower1)). 4.46/4.69 fof(fact_triple_Osize_I1_J, axiom, ![X182, X33, X183, X86, X4]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Hoare__Mirabelle_Otriple_Otriple__size(X4,X86,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X183),X33),X182)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_triple_Osize_I1_J)). 4.46/4.69 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J, axiom, ![X2]:hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J)). 4.46/4.69 fof(fact_Int__lower2, axiom, ![X1, X2, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X1)),X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__lower2)). 4.46/4.69 fof(fact_Un__upper1, axiom, ![X1, X2, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__upper1)). 4.46/4.69 fof(fact_Un__upper2, axiom, ![X2, X1, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__upper2)). 4.46/4.69 fof(fact_triple_Osize_I2_J, axiom, ![X182, X33, X183, X4]:hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(X4)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X183),X33),X182))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_triple_Osize_I2_J)). 4.46/4.69 fof(fact_remdups__filter, axiom, ![X7, X28, X4]:hAPP(c_List_Ofilter(X4,X28),c_List_Oremdups(X4,X7))=c_List_Oremdups(X4,hAPP(c_List_Ofilter(X4,X28),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups__filter)). 4.46/4.69 fof(fact_rtrancl__converse, axiom, ![X16, X4]:hAPP(c_Relation_Oconverse(X4,X4),c_Transitive__Closure_Ortrancl(X4,X16))=c_Transitive__Closure_Ortrancl(X4,hAPP(c_Relation_Oconverse(X4,X4),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__converse)). 4.46/4.69 fof(fact_option_Osimps_I5_J, axiom, ![X18, X169, X38, X3, X4]:hAPP(c_Option_Ooption_Ooption__case(X4,X3,X38,X169),hAPP(c_Option_Ooption_OSome(X3),X18))=hAPP(X169,X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Osimps_I5_J)). 4.46/4.69 fof(fact_nth__Cons__0, axiom, ![X57, X48, X4]:hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X48, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__Cons__0)). 4.46/4.69 fof(fact_Diff__disjoint, axiom, ![X1, X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X1),X2))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__disjoint)). 4.46/4.69 fof(fact_dom__empty, axiom, ![X3, X4]:c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=c_Map_Odom(X4,X3,hAPP(c_COMBK(tc_Option_Ooption(X3),X4),c_Option_Ooption_ONone(X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__empty)). 4.46/4.69 fof(fact_list__update__id, axiom, ![X21, X57, X4]:hAPP(hAPP(c_List_Olist__update(X4,X57),X21),hAPP(hAPP(c_List_Onth(X4),X57),X21))=X57, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__id)). 4.46/4.69 fof(fact_drop__1__Cons, axiom, ![X57, X48, X4]:X57=hAPP(hAPP(c_List_Odrop(X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__1__Cons)). 4.46/4.69 fof(fact_Rep__Integ, axiom, ![X6]:hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X6)),c_Int_OInteg)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Rep__Integ)). 4.46/4.69 fof(help_c__COMBB__1, axiom, ![X26, X80, X28, X29, X4, X3]:hAPP(X28,hAPP(X80,X26))=hAPP(hAPP(hAPP(c_COMBB(X3,X4,X29),X28),X80),X26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBB__1)). 4.46/4.69 fof(fact__03, axiom, ![X268, X269, X48, X4]:c_Lazy__Sequence_Oappend(X4,c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X48,X269),X268)=c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X48,c_Lazy__Sequence_Oappend(X4,X269,X268)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact__03)). 4.46/4.69 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int, axiom, ![X23, X67]:c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X67,X23)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X67),c_Groups_Oone__class_Oone(tc_Int_Oint))),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastPlusOneLessThan__greaterThanLessThan__int)). 4.46/4.69 fof(fact_lists_ONil, axiom, ![X2, X4]:hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_List_Olists(X4,X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists_ONil)). 4.46/4.69 fof(fact_map__of__Cons__code_I1_J, axiom, ![X15, X4, X3]:c_Option_Ooption_ONone(X4)=hAPP(hAPP(c_Map_Omap__of(X3,X4),c_List_Olist_ONil(tc_prod(X3,X4))),X15), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__Cons__code_I1_J)). 4.46/4.69 fof(fact_diff__add__0, axiom, ![X19, X17]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__add__0)). 4.46/4.69 fof(fact_card__atLeastLessThan, axiom, ![X23, X67]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23),X67)=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X67),X23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__atLeastLessThan)). 4.46/4.69 fof(fact_fold__graph_OemptyI, axiom, ![X35, X27, X3, X4]:hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X3,X27,X35,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph_OemptyI)). 4.46/4.69 fof(fact_Abs__Integ__cases, axiom, ![X6]:~(![X44]:(~(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X44),c_Int_OInteg)))<=hAPP(c_Int_OAbs__Integ,X44)=X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Abs__Integ__cases)). 4.46/4.69 fof(fact_div__le__dividend, axiom, ![X17, X19]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19),X17)),X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__le__dividend)). 4.46/4.69 fof(fact_diff__le__self, axiom, ![X17, X19]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X17)),X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__le__self)). 4.46/4.69 fof(fact_neg__zminus__int, axiom, ![X17]:hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__zminus__int)). 4.46/4.69 fof(fact_le__square, axiom, ![X19]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__square)). 4.46/4.69 fof(fact_le__add1, axiom, ![X19, X17]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__add1)). 4.46/4.69 fof(fact_option_Orecs_I2_J, axiom, ![X18, X169, X38, X3, X4]:c_Option_Ooption_Ooption__rec(X4,X3,X38,X169,hAPP(c_Option_Ooption_OSome(X3),X18))=hAPP(X169,X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Orecs_I2_J)). 4.46/4.69 fof(fact_le__add2, axiom, ![X19, X17]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__add2)). 4.46/4.69 fof(fact_neg__single__def, axiom, ![X103, X104, X105, X6, X4]:hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X4),X6),X105),X104),X103)=c_New__DSequence_Oneg__single(X4,X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__single__def)). 4.46/4.69 fof(fact_pos__single__def, axiom, ![X103, X104, X105, X6, X4]:c_New__DSequence_Opos__single(X4,X6)=hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X4),X6),X105),X104),X103), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__single__def)). 4.46/4.69 fof(fact_length__rotate1, axiom, ![X57, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Orotate1(X4),X57))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__rotate1)). 4.46/4.69 fof(fact_length__rev, axiom, ![X57, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X57)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Orev(X4),X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__rev)). 4.46/4.69 fof(fact_fold__image__empty, axiom, ![X35, X50, X27, X3, X4]:X35=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4,X3,X27),X50),X35),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__empty)). 4.46/4.69 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J, axiom, ![X49]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X49))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J)). 4.46/4.69 fof(fact_Compl__partition, axiom, ![X2, X4]:c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__partition)). 4.46/4.69 fof(fact_div__int__def, axiom, ![X11, X12]:hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X12,X11))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__int__def)). 4.46/4.69 fof(fact_negateSnd__def, axiom, c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))=c_Divides_OnegateSnd, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negateSnd__def)). 4.46/4.69 fof(fact_less__than__def, axiom, c_Wellfounded_Oless__than=c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__than__def)). 4.46/4.69 fof(fact_zip__Nil, axiom, ![X72, X3, X4]:hAPP(hAPP(c_List_Ozip(X4,X3),c_List_Olist_ONil(X4)),X72)=c_List_Olist_ONil(tc_prod(X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__Nil)). 4.46/4.69 fof(fact_fun__upd__same, axiom, ![X5, X6, X27, X4, X3]:X5=hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X27),X6),X5),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__same)). 4.46/4.69 fof(fact_diff__add__inverse, axiom, ![X19, X17]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X19)),X17)=X19, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__add__inverse)). 4.46/4.69 fof(fact_diff__add__inverse2, axiom, ![X17, X19]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X17)),X17)=X19, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__add__inverse2)). 4.46/4.69 fof(fact_fun__upd__triv, axiom, ![X6, X27, X3, X4]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X3),X27),X6),hAPP(X27,X6))=X27, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__triv)). 4.46/4.69 fof(fact_zip_Osimps_I1_J, axiom, ![X57, X3, X4]:c_List_Olist_ONil(tc_prod(X4,X3))=hAPP(hAPP(c_List_Ozip(X4,X3),X57),c_List_Olist_ONil(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip_Osimps_I1_J)). 4.46/4.69 fof(fact_Pow__bottom, axiom, ![X1, X4]:hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),hAPP(c_Set_OPow(X4),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__bottom)). 4.46/4.69 fof(fact_mod__less__eq__dividend, axiom, ![X17, X19]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X17)),X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__less__eq__dividend)). 4.46/4.69 fof(fact_Compl__eq__Diff__UNIV, axiom, ![X2, X4]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__eq__Diff__UNIV)). 4.46/4.69 fof(fact_transfer__morphism__int__nat, axiom, c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__morphism__int__nat)). 4.46/4.69 fof(fact_zmod__zdiv__trivial, axiom, ![X11, X12]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11)),X11)=c_Groups_Ozero__class_Ozero(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zdiv__trivial)). 4.46/4.69 fof(fact_insert__absorb2, axiom, ![X2, X6, X4]:hAPP(hAPP(c_Set_Oinsert(X4),X6),X2)=hAPP(hAPP(c_Set_Oinsert(X4),X6),hAPP(hAPP(c_Set_Oinsert(X4),X6),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__absorb2)). 4.46/4.69 fof(fact_subset__insertI, axiom, ![X18, X1, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(X4),X18),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__insertI)). 4.46/4.69 fof(fact_Field__converse, axiom, ![X16, X4]:hAPP(c_Relation_OField(X4),X16)=hAPP(c_Relation_OField(X4),hAPP(c_Relation_Oconverse(X4,X4),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Field__converse)). 4.46/4.69 fof(fact_posDivAlg__0, axiom, ![X11]:hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_posDivAlg__0)). 4.46/4.69 fof(fact_restrict__map__to__empty, axiom, ![X6, X22, X4, X3]:c_Option_Ooption_ONone(X4)=hAPP(c_Map_Orestrict__map(X3,X4,X22,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__map__to__empty)). 4.46/4.69 fof(fact_Sigma__empty1, axiom, ![X1, X3, X4]:c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X3),tc_HOL_Obool))=hAPP(hAPP(c_Product__Type_OSigma(X4,X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__empty1)). 4.46/4.69 fof(fact_rel__pow__1, axiom, ![X26, X4]:X26=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__1)). 4.46/4.69 fof(fact_insert__remdups, axiom, ![X57, X48, X4]:c_List_Oinsert(X4,X48,c_List_Oremdups(X4,X57))=c_List_Oremdups(X4,c_List_Oinsert(X4,X48,X57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__remdups)). 4.46/4.69 fof(fact_rev__replicate, axiom, ![X48, X17, X4]:hAPP(c_List_Orev(X4),c_List_Oreplicate(X4,X17,X48))=c_List_Oreplicate(X4,X17,X48), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__replicate)). 4.46/4.69 fof(fact_Pow__top, axiom, ![X2, X4]:hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X4),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__top)). 4.46/4.69 fof(fact_insertI1, axiom, ![X1, X18, X4]:hBOOL(hAPP(hAPP(c_member(X4),X18),hAPP(hAPP(c_Set_Oinsert(X4),X18),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insertI1)). 4.46/4.69 fof(fact_mod__int__def, axiom, ![X11, X12]:c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X11)=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X12,X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__int__def)). 4.46/4.69 fof(fact_hb__map_Osimps_I1_J, axiom, ![X27, X4, X3]:c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(X4))=c_Lazy__Sequence_Ohb__map(X3,X4,X27,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hb__map_Osimps_I1_J)). 4.46/4.69 fof(fact_Option_Oset_Osimps_I2_J, axiom, ![X6, X4]:hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=c_Option_Oset(X4,hAPP(c_Option_Ooption_OSome(X4),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Option_Oset_Osimps_I2_J)). 4.46/4.69 fof(fact_insert__Nil, axiom, ![X48, X4]:c_List_Oinsert(X4,X48,c_List_Olist_ONil(X4))=hAPP(hAPP(c_List_Olist_OCons(X4),X48),c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__Nil)). 4.46/4.69 fof(fact_fold__graph_H_Ointros_I1_J, axiom, ![X35, X27, X3, X4]:c_Nitpick_Ofold__graph_H(X4,X3,X27,X35,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),X35), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph_H_Ointros_I1_J)). 4.46/4.69 fof(fact_fold1__singleton, axiom, ![X18, X27, X4]:hAPP(c_Finite__Set_Ofold1(X4,X27),hAPP(hAPP(c_Set_Oinsert(X4),X18),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=X18, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__singleton)). 4.46/4.69 fof(fact_zero__less__Suc, axiom, ![X17]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__Suc)). 4.46/4.69 fof(fact_power_Opower_Opower__0, axiom, ![X18, X285, X286, X4]:X286=hAPP(hAPP(c_Power_Opower_Opower(X4,X286,X285),X18),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power_Opower_Opower__0)). 4.46/4.69 fof(fact_converse__converse, axiom, ![X16, X4, X3]:X16=hAPP(c_Relation_Oconverse(X3,X4),hAPP(c_Relation_Oconverse(X4,X3),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__converse)). 4.46/4.69 fof(fact_fold1__def, axiom, ![X2, X27, X4]:c_HOL_OThe(X4,c_Finite__Set_Ofold1Set(X4,X27,X2))=hAPP(c_Finite__Set_Ofold1(X4,X27),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__def)). 4.46/4.69 fof(fact_Range__rtrancl, axiom, ![X26, X4]:hAPP(c_Relation_ORange(X4,X4),c_Transitive__Closure_Ortrancl(X4,X26))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__rtrancl)). 4.46/4.69 fof(fact_Domain__rtrancl, axiom, ![X26, X4]:c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Relation_ODomain(X4,X4),c_Transitive__Closure_Ortrancl(X4,X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__rtrancl)). 4.46/4.69 fof(fact_converse__Id__on, axiom, ![X2, X4]:c_Relation_OId__on(X4,X2)=hAPP(c_Relation_Oconverse(X4,X4),c_Relation_OId__on(X4,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__Id__on)). 4.46/4.69 fof(fact_type__definition__code__numeral, axiom, c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition__code__numeral)). 4.46/4.69 fof(fact_finite__atLeastLessThan, axiom, ![X23, X67]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X67),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__atLeastLessThan)). 4.46/4.69 fof(fact_finite__atLeastLessThan__int, axiom, ![X23, X67]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X67),X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__atLeastLessThan__int)). 4.46/4.69 fof(fact_refl__rtrancl, axiom, ![X16, X4]:c_Relation_Orefl__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__rtrancl)). 4.46/4.69 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1, axiom, ![X16, X4]:c_List_Olistrel(X4,c_Transitive__Closure_Ortrancl(X4,X16))=c_Transitive__Closure_Ortrancl(tc_List_Olist(X4),c_List_Olistrel1(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__rtrancl__eq__rtrancl__listrel1)). 4.46/4.69 fof(fact_list__update__code_I1_J, axiom, ![X47, X21, X4]:c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Olist__update(X4,c_List_Olist_ONil(X4)),X21),X47), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__code_I1_J)). 4.46/4.69 fof(fact_INT__empty, axiom, ![X1, X4, X3]:c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__empty)). 4.46/4.69 fof(fact_fold__empty, axiom, ![X35, X27, X4, X3]:X35=hAPP(hAPP(c_Finite__Set_Ofold(X3,X4,X27),X35),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__empty)). 4.46/4.69 fof(fact_funpow_Osimps_I1_J, axiom, ![X27, X4]:hAPP(hAPP(c_Nat_Ocompow(X4,X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27)=c_Fun_Oid(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_funpow_Osimps_I1_J)). 4.46/4.69 fof(fact_product_Osimps_I1_J, axiom, ![X255, X3, X4]:c_Enum_Oproduct(X4,X3,c_List_Olist_ONil(X4),X255)=c_List_Olist_ONil(tc_prod(X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_product_Osimps_I1_J)). 4.46/4.69 fof(fact_option__map__None, axiom, ![X27, X4, X3]:hAPP(hAPP(c_Option_Omap(X3,X4),X27),c_Option_Ooption_ONone(X3))=c_Option_Ooption_ONone(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option__map__None)). 4.46/4.69 fof(fact_Nitpick_Ofrac__def, axiom, ![X11, X12, X4]:c_Nitpick_OAbs__Frac(X4,c_Nitpick_Onorm__frac(X12,X11))=hAPP(hAPP(c_Nitpick_Ofrac(X4),X12),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Ofrac__def)). 4.46/4.69 fof(fact_set__rotate1, axiom, ![X7, X4]:hAPP(c_List_Oset(X4),hAPP(c_List_Orotate1(X4),X7))=hAPP(c_List_Oset(X4),X7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__rotate1)). 4.46/4.69 fof(fact_set__rev, axiom, ![X7, X4]:hAPP(c_List_Oset(X4),X7)=hAPP(c_List_Oset(X4),hAPP(c_List_Orev(X4),X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__rev)). 4.46/4.69 fof(fact_option_Osize_I4_J, axiom, ![X12, X4]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X4)),hAPP(c_Option_Ooption_OSome(X4),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Osize_I4_J)). 4.46/4.69 fof(fact_Un__UNIV__left, axiom, ![X1, X4]:c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__UNIV__left)). 4.46/4.69 fof(fact_Un__UNIV__right, axiom, ![X2, X4]:c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__UNIV__right)). 4.46/4.69 fof(fact_inj__on__rev, axiom, ![X2, X4]:c_Fun_Oinj__on(tc_List_Olist(X4),tc_List_Olist(X4),c_List_Orev(X4),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__rev)). 4.46/4.69 fof(fact_abs__int__eq, axiom, ![X19]:hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__int__eq)). 4.46/4.69 fof(fact_id__o, axiom, ![X50, X4, X3]:X50=hAPP(c_Fun_Ocomp(X3,X3,X4,c_Fun_Oid(X3)),X50), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_id__o)). 4.46/4.69 fof(fact_list_Osimps_I4_J, axiom, ![X169, X38, X3, X4]:hAPP(c_List_Olist_Olist__case(X4,X3,X38,X169),c_List_Olist_ONil(X3))=X38, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osimps_I4_J)). 4.46/4.69 fof(fact_o__id, axiom, ![X27, X3, X4]:hAPP(c_Fun_Ocomp(X4,X3,X4,X27),c_Fun_Oid(X4))=X27, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_o__id)). 4.46/4.69 fof(fact_override__on__emptyset, axiom, ![X50, X27, X3, X4]:c_Fun_Ooverride__on(X4,X3,X27,X50,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=X27, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_override__on__emptyset)). 4.46/4.69 fof(fact_option_Osimps_I4_J, axiom, ![X169, X38, X3, X4]:X38=hAPP(c_Option_Ooption_Ooption__case(X4,X3,X38,X169),c_Option_Ooption_ONone(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Osimps_I4_J)). 4.46/4.69 fof(fact_foldl__Nil, axiom, ![X18, X27, X3, X4]:X18=hAPP(c_List_Ofoldl(X4,X3,X27,X18),c_List_Olist_ONil(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__Nil)). 4.46/4.69 fof(fact_nat__case__Suc, axiom, ![X201, X169, X38, X4]:c_Nat_Onat_Onat__case(X4,X38,X169,hAPP(c_Nat_OSuc,X201))=hAPP(X169,X201), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__case__Suc)). 4.46/4.69 fof(fact_length__replicate, axiom, ![X48, X17, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Oreplicate(X4,X17,X48))=X17, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__replicate)). 4.46/4.69 fof(fact_hd_Osimps, axiom, ![X57, X48, X4]:hAPP(c_List_Ohd(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57))=X48, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd_Osimps)). 4.46/4.69 fof(fact_tl_Osimps_I2_J, axiom, ![X57, X48, X4]:hAPP(c_List_Otl(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X48),X57))=X57, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tl_Osimps_I2_J)). 4.46/4.69 fof(fact_diff__Suc__1, axiom, ![X17]:X17=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17)),c_Groups_Oone__class_Oone(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__Suc__1)). 4.46/4.69 fof(fact_subset__UNIV, axiom, ![X2, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__UNIV)). 4.46/4.69 fof(fact_refl__on__empty, axiom, ![X4]:c_Relation_Orefl__on(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__empty)). 4.46/4.69 fof(fact_atLeastSucLessThan__greaterThanLessThan, axiom, ![X23, X67]:c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X67,X23)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X67)),X23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastSucLessThan__greaterThanLessThan)). 4.46/4.69 fof(fact_number__of__code__numeral__def, axiom, c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral)=hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__code__numeral__def)). 4.46/4.69 fof(fact_finite__atLeastAtMost, axiom, ![X23, X67]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X67,X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__atLeastAtMost)). 4.46/4.69 fof(fact_Diff__UNIV, axiom, ![X2, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__UNIV)). 4.46/4.69 fof(fact_finite__atLeastAtMost__int, axiom, ![X23, X67]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X67,X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__atLeastAtMost__int)). 4.46/4.69 fof(fact_UNIV__I, axiom, ![X6, X4]:hBOOL(hAPP(hAPP(c_member(X4),X6),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__I)). 4.46/4.69 fof(fact_set__remdups, axiom, ![X7, X4]:hAPP(c_List_Oset(X4),X7)=hAPP(c_List_Oset(X4),c_List_Oremdups(X4,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__remdups)). 4.46/4.69 fof(fact_lessI, axiom, ![X17]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_OSuc,X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessI)). 4.46/4.69 fof(fact_option_Orecs_I1_J, axiom, ![X169, X38, X3, X4]:c_Option_Ooption_Ooption__rec(X4,X3,X38,X169,c_Option_Ooption_ONone(X3))=X38, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Orecs_I1_J)). 4.46/4.69 fof(fact_map__upds__Nil2, axiom, ![X172, X22, X3, X4]:c_Map_Omap__upds(X4,X3,X22,X172,c_List_Olist_ONil(X3))=X22, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upds__Nil2)). 4.46/4.69 fof(fact_map__upds__Nil1, axiom, ![X260, X22, X3, X4]:X22=c_Map_Omap__upds(X4,X3,X22,c_List_Olist_ONil(X4),X260), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upds__Nil1)). 4.46/4.69 fof(fact_conversep__conversep, axiom, ![X16, X4, X3]:X16=c_Predicate_Oconversep(X3,X4,c_Predicate_Oconversep(X4,X3,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conversep__conversep)). 4.46/4.69 fof(fact_lists__UNIV, axiom, ![X4]:c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X4),tc_HOL_Obool))=c_List_Olists(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__UNIV)). 4.46/4.69 fof(fact_small__lazy__int__def, axiom, ![X133]:c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X133)=c_Lazy__Sequence_Osmall__lazy_H(X133,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X133)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__lazy__int__def)). 4.46/4.69 fof(fact_Option_Omap_Oidentity, axiom, ![X4]:hAPP(c_Option_Omap(X4,X4),c_COMBI(X4))=c_Fun_Oid(tc_Option_Ooption(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Option_Omap_Oidentity)). 4.46/4.69 fof(fact_List_Omap_Oid, axiom, ![X4]:hAPP(c_List_Omap(X4,X4),c_Fun_Oid(X4))=c_Fun_Oid(tc_List_Olist(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Omap_Oid)). 4.46/4.69 fof(fact_Option_Omap_Oid, axiom, ![X4]:c_Fun_Oid(tc_Option_Ooption(X4))=hAPP(c_Option_Omap(X4,X4),c_Fun_Oid(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Option_Omap_Oid)). 4.46/4.69 fof(fact_Int__UNIV__left, axiom, ![X1, X4]:X1=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__UNIV__left)). 4.46/4.69 fof(fact_the__elem__eq, axiom, ![X6, X4]:X6=c_Set_Othe__elem(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__elem__eq)). 4.46/4.69 fof(fact_Field__empty, axiom, ![X4]:hAPP(c_Relation_OField(X4),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Field__empty)). 4.46/4.69 fof(fact_Image__empty, axiom, ![X26, X4, X3]:hAPP(c_Relation_OImage(X3,X4,X26),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__empty)). 4.46/4.69 fof(fact_List_Omap_Oidentity, axiom, ![X4]:c_Fun_Oid(tc_List_Olist(X4))=hAPP(c_List_Omap(X4,X4),c_COMBI(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Omap_Oidentity)). 4.46/4.69 fof(fact_map__filter__simps_I2_J, axiom, ![X27, X4, X3]:c_List_Omap__filter(X3,X4,X27,c_List_Olist_ONil(X3))=c_List_Olist_ONil(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__filter__simps_I2_J)). 4.46/4.69 fof(fact_maps__simps_I2_J, axiom, ![X27, X4, X3]:c_List_Olist_ONil(X4)=c_List_Omaps(X3,X4,X27,c_List_Olist_ONil(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_maps__simps_I2_J)). 4.46/4.69 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J, axiom, ![X52]:c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J)). 4.46/4.69 fof(fact_double__complement, axiom, ![X2, X4]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X2))=X2, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__complement)). 4.46/4.69 fof(fact_Int__UNIV__right, axiom, ![X2, X4]:X2=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__UNIV__right)). 4.46/4.69 fof(fact_take__0, axiom, ![X57, X4]:c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Otake(X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__0)). 4.46/4.69 fof(fact_drop__Nil, axiom, ![X17, X4]:c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Odrop(X4),X17),c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__Nil)). 4.46/4.69 fof(fact_take__Nil, axiom, ![X17, X4]:c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Otake(X4),X17),c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Nil)). 4.46/4.69 fof(fact_nat__of__number, axiom, ![X15]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15)=hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__of__number)). 4.46/4.69 fof(fact_diff__0__eq__0, axiom, ![X17]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__0__eq__0)). 4.46/4.69 fof(fact_zdiv__zero, axiom, ![X11]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__zero)). 4.46/4.69 fof(fact_DIVISION__BY__ZERO, axiom, ![X12]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint))&c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=X12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DIVISION__BY__ZERO)). 4.46/4.69 fof(fact_nat__rec__0, axiom, ![X169, X38, X4]:hAPP(c_Nat_Onat_Onat__rec(X4,X38,X169),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X38, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__rec__0)). 4.46/4.69 fof(fact_inj__Some, axiom, ![X2, X4]:c_Fun_Oinj__on(X4,tc_Option_Ooption(X4),c_Option_Ooption_OSome(X4),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__Some)). 4.46/4.69 fof(fact_Range__Id__on, axiom, ![X2, X4]:hAPP(c_Relation_ORange(X4,X4),c_Relation_OId__on(X4,X2))=X2, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__Id__on)). 4.46/4.69 fof(fact_Domain__Id__on, axiom, ![X2, X4]:X2=hAPP(c_Relation_ODomain(X4,X4),c_Relation_OId__on(X4,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__Id__on)). 4.46/4.69 fof(fact_listrelp_ONil, axiom, ![X16, X4]:c_List_Olistrelp(X4,X16,c_List_Olist_ONil(X4),c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrelp_ONil)). 4.46/4.69 fof(fact_remdups__remdups, axiom, ![X57, X4]:c_List_Oremdups(X4,c_List_Oremdups(X4,X57))=c_List_Oremdups(X4,X57), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups__remdups)). 4.46/4.69 fof(fact_rtrancl__idemp, axiom, ![X16, X4]:c_Transitive__Closure_Ortrancl(X4,X16)=c_Transitive__Closure_Ortrancl(X4,c_Transitive__Closure_Ortrancl(X4,X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__idemp)). 4.46/4.69 fof(fact_transpose_Osimps_I1_J, axiom, ![X4]:c_List_Olist_ONil(tc_List_Olist(X4))=c_List_Otranspose(X4,c_List_Olist_ONil(tc_List_Olist(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose_Osimps_I1_J)). 4.46/4.69 fof(fact_listsp_ONil, axiom, ![X2, X4]:hBOOL(hAPP(c_List_Olistsp(X4,X2),c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp_ONil)). 4.46/4.69 fof(fact_distinct__remdups, axiom, ![X57, X4]:hBOOL(hAPP(c_List_Odistinct(X4),c_List_Oremdups(X4,X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__remdups)). 4.46/4.69 fof(fact_distinct__upto, axiom, ![X20, X21]:hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X21,X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__upto)). 4.46/4.69 fof(fact_Union__UNIV, axiom, ![X4]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__UNIV)). 4.46/4.69 fof(fact_New__DSequence_Opos__single__def, axiom, ![X189, X48, X4]:hAPP(c_New__DSequence_Opos__single(X4,X48),X189)=hAPP(c_Lazy__Sequence_Osingle(X4),X48), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Opos__single__def)). 4.46/4.69 fof(fact_filter_Osimps_I1_J, axiom, ![X28, X4]:hAPP(c_List_Ofilter(X4,X28),c_List_Olist_ONil(X4))=c_List_Olist_ONil(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter_Osimps_I1_J)). 4.46/4.69 fof(fact_option_Osize_I3_J, axiom, ![X4]:hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X4)),c_Option_Ooption_ONone(X4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Osize_I3_J)). 4.46/4.69 fof(fact_Union__Pow__eq, axiom, ![X2, X4]:X2=c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(c_Set_OPow(X4),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__Pow__eq)). 4.46/4.69 fof(fact_list_Osize_I3_J, axiom, ![X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Olist_ONil(X4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osize_I3_J)). 4.46/4.69 fof(fact_lazy__sequence_Osize_I3_J, axiom, ![X4]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X4)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Osize_I3_J)). 4.46/4.69 fof(fact_Pow__UNIV, axiom, ![X4]:hAPP(c_Set_OPow(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__UNIV)). 4.46/4.69 fof(fact_code__numeral_Osimps_I4_J, axiom, ![X169, X38, X4]:c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X4,X38,X169,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=X38, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Osimps_I4_J)). 4.46/4.69 fof(fact_nat__case__0, axiom, ![X169, X38, X4]:c_Nat_Onat_Onat__case(X4,X38,X169,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X38, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__case__0)). 4.46/4.69 fof(fact_image__ident, axiom, ![X76, X4]:hAPP(c_Set_Oimage(X4,X4,c_COMBI(X4)),X76)=X76, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__ident)). 4.46/4.69 fof(fact_image__id, axiom, ![X76, X4]:hAPP(c_Set_Oimage(X4,X4,c_Fun_Oid(X4)),X76)=X76, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__id)). 4.46/4.69 fof(fact_empty__subsetI, axiom, ![X2, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__subsetI)). 4.46/4.69 fof(help_c__COMBK__1, axiom, ![X158, X159, X3, X4]:X159=hAPP(hAPP(c_COMBK(X4,X3),X159),X158), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBK__1)). 4.46/4.69 fof(fact_append__Nil, axiom, ![X72, X4]:hAPP(hAPP(c_List_Oappend(X4),c_List_Olist_ONil(X4)),X72)=X72, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__Nil)). 4.46/4.69 fof(fact_drop__0, axiom, ![X57, X4]:hAPP(hAPP(c_List_Odrop(X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57)=X57, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__0)). 4.46/4.69 fof(fact_sublist__empty, axiom, ![X7, X4]:c_List_Osublist(X4,X7,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=c_List_Olist_ONil(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__empty)). 4.46/4.69 fof(fact_append__Nil2, axiom, ![X57, X4]:X57=hAPP(hAPP(c_List_Oappend(X4),X57),c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__Nil2)). 4.46/4.69 fof(fact_empty__Diff, axiom, ![X2, X4]:c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__Diff)). 4.46/4.69 fof(fact_the_Osimps, axiom, ![X48, X4]:X48=hAPP(c_Option_Othe(X4),hAPP(c_Option_Ooption_OSome(X4),X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the_Osimps)). 4.46/4.69 fof(fact_Int__empty__left, axiom, ![X1, X4]:c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__empty__left)). 4.46/4.69 fof(fact_Int__empty__right, axiom, ![X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__empty__right)). 4.46/4.69 fof(fact_nat__mult__1, axiom, ![X17]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X17)=X17, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__1)). 4.46/4.69 fof(fact_zmult__1, axiom, ![X49]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X49)=X49, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__1)). 4.46/4.69 fof(fact_plus__nat_Oadd__0, axiom, ![X17]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)=X17, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_plus__nat_Oadd__0)). 4.46/4.69 fof(fact_quotient__empty, axiom, ![X16, X4]:c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))=hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotient__empty)). 4.46/4.69 fof(fact_Id__on__empty, axiom, ![X4]:c_Relation_OId__on(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__on__empty)). 4.46/4.69 fof(fact_minus__nat_Odiff__0, axiom, ![X19]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X19, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__nat_Odiff__0)). 4.46/4.69 fof(fact_subset__refl, axiom, ![X2, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__refl)). 4.46/4.69 fof(fact_Inter__UNIV, axiom, ![X4]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__UNIV)). 4.46/4.69 fof(fact_nat__mult__1__right, axiom, ![X17]:X17=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),c_Groups_Oone__class_Oone(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__1__right)). 4.46/4.69 fof(fact_zmult__1__right, axiom, ![X49]:X49=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X49),c_Groups_Oone__class_Oone(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__1__right)). 4.46/4.69 fof(fact_inj__on__empty, axiom, ![X27, X3, X4]:c_Fun_Oinj__on(X4,X3,X27,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__empty)). 4.46/4.69 fof(fact_image__empty, axiom, ![X27, X4, X3]:hAPP(c_Set_Oimage(X3,X4,X27),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__empty)). 4.46/4.69 fof(fact_Diff__empty, axiom, ![X2, X4]:X2=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__empty)). 4.46/4.69 fof(fact_zminus__zminus, axiom, ![X49]:X49=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zminus__zminus)). 4.46/4.69 fof(fact_New__DSequence_Oneg__single__def, axiom, ![X189, X48, X4]:c_Lazy__Sequence_Ohb__single(X4,X48)=hAPP(c_New__DSequence_Oneg__single(X4,X48),X189), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Oneg__single__def)). 4.46/4.69 fof(fact_wf__empty, axiom, ![X4]:c_Wellfounded_Owf(X4,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__empty)). 4.46/4.69 fof(fact_Compl__UNIV__eq, axiom, ![X4]:c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__UNIV__eq)). 4.46/4.69 fof(fact_inj__on__id2, axiom, ![X2, X4]:c_Fun_Oinj__on(X4,X4,c_COMBI(X4),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__id2)). 4.46/4.69 fof(fact_Diff__cancel, axiom, ![X2, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X2),X2)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__cancel)). 4.46/4.69 fof(fact_eq__int__refl, axiom, ![X15]:hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X15),X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__refl)). 4.46/4.69 fof(fact_inj__on__id, axiom, ![X2, X4]:c_Fun_Oinj__on(X4,X4,c_Fun_Oid(X4),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__id)). 4.46/4.69 fof(fact_single__valued__Id__on, axiom, ![X2, X4]:c_Relation_Osingle__valued(X4,X4,c_Relation_OId__on(X4,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__Id__on)). 4.46/4.69 fof(fact_refl__on__Id__on, axiom, ![X2, X4]:c_Relation_Orefl__on(X4,X2,c_Relation_OId__on(X4,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__Id__on)). 4.46/4.69 fof(fact_le__refl, axiom, ![X17]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__refl)). 4.46/4.69 fof(fact_zle__refl, axiom, ![X30]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X30),X30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__refl)). 4.46/4.69 fof(fact_takeWhile_Osimps_I1_J, axiom, ![X28, X4]:c_List_OtakeWhile(X4,X28,c_List_Olist_ONil(X4))=c_List_Olist_ONil(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile_Osimps_I1_J)). 4.46/4.69 fof(fact_sublist__nil, axiom, ![X2, X4]:c_List_Olist_ONil(X4)=c_List_Osublist(X4,c_List_Olist_ONil(X4),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__nil)). 4.46/4.69 fof(fact_rel__simps_I6_J, axiom, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I6_J)). 4.46/4.69 fof(fact_rel__simps_I23_J, axiom, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I23_J)). 4.46/4.69 fof(fact_remove1_Osimps_I1_J, axiom, ![X48, X4]:c_List_Olist_ONil(X4)=c_List_Oremove1(X4,X48,c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1_Osimps_I1_J)). 4.46/4.69 fof(fact_option_Osize_I1_J, axiom, ![X86, X4]:c_Option_Ooption_Ooption__size(X4,X86,c_Option_Ooption_ONone(X4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Osize_I1_J)). 4.46/4.69 fof(fact_neg__number__of__Min, axiom, hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__number__of__Min)). 4.46/4.69 fof(fact_list_Osize_I1_J, axiom, ![X86, X4]:c_List_Olist_Olist__size(X4,X86,c_List_Olist_ONil(X4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osize_I1_J)). 4.46/4.69 fof(fact_replicate__0, axiom, ![X48, X4]:c_List_Olist_ONil(X4)=c_List_Oreplicate(X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__0)). 4.46/4.69 fof(fact_zmod__zero, axiom, ![X11]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zero)). 4.46/4.69 fof(fact_diff__self__eq__0, axiom, ![X19]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19),X19)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__self__eq__0)). 4.46/4.69 fof(fact_Inter__empty, axiom, ![X4]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__empty)). 4.46/4.69 fof(fact_Compl__empty__eq, axiom, ![X4]:c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__empty__eq)). 4.46/4.69 fof(fact_Un__absorb, axiom, ![X2, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X2),X2)=X2, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__absorb)). 4.46/4.69 fof(fact_Int__absorb, axiom, ![X2, X4]:X2=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X2),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__absorb)). 4.46/4.69 fof(fact_distinct_Osimps_I1_J, axiom, ![X4]:hBOOL(hAPP(c_List_Odistinct(X4),c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct_Osimps_I1_J)). 4.46/4.69 fof(fact_rev_Osimps_I1_J, axiom, ![X4]:hAPP(c_List_Orev(X4),c_List_Olist_ONil(X4))=c_List_Olist_ONil(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev_Osimps_I1_J)). 4.46/4.69 fof(fact_tl_Osimps_I1_J, axiom, ![X4]:c_List_Olist_ONil(X4)=hAPP(c_List_Otl(X4),c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tl_Osimps_I1_J)). 4.46/4.69 fof(fact_List_Oset_Osimps_I1_J, axiom, ![X4]:c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(c_List_Oset(X4),c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Oset_Osimps_I1_J)). 4.46/4.69 fof(fact__04, axiom, ![X268, X4]:X268=c_Lazy__Sequence_Oappend(X4,c_Lazy__Sequence_Olazy__sequence_OEmpty(X4),X268), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact__04)). 4.46/4.69 fof(fact_splice_Osimps_I1_J, axiom, ![X72, X4]:X72=c_List_Osplice(X4,c_List_Olist_ONil(X4),X72), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_splice_Osimps_I1_J)). 4.46/4.69 fof(fact_splice__Nil2, axiom, ![X57, X4]:X57=c_List_Osplice(X4,X57,c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_splice__Nil2)). 4.46/4.69 fof(fact_Option_Oset_Osimps_I1_J, axiom, ![X4]:c_Option_Oset(X4,c_Option_Ooption_ONone(X4))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Option_Oset_Osimps_I1_J)). 4.46/4.69 fof(fact_Union__empty, axiom, ![X4]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__empty)). 4.46/4.69 fof(fact_finite_Oequations_I1_J, axiom, ![X4]:hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite_Oequations_I1_J)). 4.46/4.69 fof(fact_inj__Suc, axiom, ![X122]:c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X122), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__Suc)). 4.46/4.69 fof(fact_zmod__self, axiom, ![X12]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__self)). 4.46/4.69 fof(fact_top1I, axiom, ![X6, X4]:hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_top1I)). 4.46/4.69 fof(fact_total__on__empty, axiom, ![X16, X4]:c_Relation_Ototal__on(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),X16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_total__on__empty)). 4.46/4.69 fof(fact_fun__left__comm__idem__insert, axiom, ![X4]:c_Finite__Set_Ofun__left__comm__idem(X4,tc_fun(X4,tc_HOL_Obool),c_Set_Oinsert(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem__insert)). 4.46/4.69 fof(fact_sorted__upto, axiom, ![X20, X21]:c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X21,X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__upto)). 4.46/4.69 fof(fact_list__all__simps_I2_J, axiom, ![X28, X4]:c_List_Olist__all(X4,X28,c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__simps_I2_J)). 4.46/4.69 fof(fact_wf__measures, axiom, ![X115, X4]:c_Wellfounded_Owf(X4,c_List_Omeasures(X4,X115)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__measures)). 4.46/4.69 fof(fact_wf__finite__psubset, axiom, ![X4]:c_Wellfounded_Owf(tc_fun(X4,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__finite__psubset)). 4.46/4.69 fof(fact_butlast_Osimps_I1_J, axiom, ![X4]:c_List_Olist_ONil(X4)=c_List_Obutlast(X4,c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast_Osimps_I1_J)). 4.46/4.69 fof(fact_remdups_Osimps_I1_J, axiom, ![X4]:c_List_Olist_ONil(X4)=c_List_Oremdups(X4,c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups_Osimps_I1_J)). 4.46/4.69 fof(fact_some__sym__eq__trivial, axiom, ![X6, X4]:c_Hilbert__Choice_OEps(X4,hAPP(c_fequal,X6))=X6, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_some__sym__eq__trivial)). 4.46/4.69 fof(fact_the__sym__eq__trivial, axiom, ![X6, X4]:X6=c_HOL_OThe(X4,hAPP(c_fequal,X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__sym__eq__trivial)). 4.46/4.69 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J, axiom, ![X49]:c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J)). 4.46/4.69 fof(fact_New__DSequence_Opos__empty__def, axiom, ![X189, X4]:hAPP(c_New__DSequence_Opos__empty(X4),X189)=c_Lazy__Sequence_Oempty(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Opos__empty__def)). 4.46/4.69 fof(fact_zero__code__numeral__code, axiom, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls)=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__code__numeral__code)). 4.46/4.69 fof(fact_one__code__numeral__def, axiom, hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__code__numeral__def)). 4.46/4.69 fof(fact_conversep__eq, axiom, ![X4]:c_Predicate_Oconversep(X4,X4,c_fequal)=c_fequal, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conversep__eq)). 4.46/4.69 fof(fact_Rep__Integ__inverse, axiom, ![X6]:X6=hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Rep__Integ__inverse)). 4.46/4.69 fof(fact_com_Osize_I15_J, axiom, ![X118]:hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,X118))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I15_J)). 4.46/4.69 fof(arity_Nitpick__Opair____box__HOL_Oequal, axiom, ![X128, X129]:class_HOL_Oequal(tc_Nitpick_Opair__box(X129,X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nitpick__Opair____box__HOL_Oequal)). 4.46/4.69 fof(arity_sum__HOL_Oequal, axiom, ![X128, X129]:class_HOL_Oequal(tc_sum(X129,X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_sum__HOL_Oequal)). 4.46/4.69 fof(arity_prod__HOL_Oequal, axiom, ![X128, X129]:class_HOL_Oequal(tc_prod(X129,X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_prod__HOL_Oequal)). 4.46/4.69 fof(arity_Nitpick__Opair____box__Nat_Osize, axiom, ![X128, X129]:class_Nat_Osize(tc_Nitpick_Opair__box(X129,X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nitpick__Opair____box__Nat_Osize)). 4.46/4.69 fof(arity_sum__Nat_Osize, axiom, ![X128, X129]:class_Nat_Osize(tc_sum(X129,X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_sum__Nat_Osize)). 4.46/4.69 fof(arity_prod__Nat_Osize, axiom, ![X128, X129]:class_Nat_Osize(tc_prod(X129,X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_prod__Nat_Osize)). 4.46/4.69 fof(fact_hoare__derivs_Oequations_I1_J, axiom, ![X18, X4]:c_Hoare__Mirabelle_Ohoare__derivs(X4,X18,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hoare__derivs_Oequations_I1_J)). 4.46/4.69 fof(fact_com_Osize_I7_J, axiom, ![X118]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,X118)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I7_J)). 4.46/4.69 fof(fact_wf__int__ge__less__than2, axiom, ![X87]:c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__int__ge__less__than2)). 4.46/4.69 fof(fact_wf__int__ge__less__than, axiom, ![X87]:c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__int__ge__less__than)). 4.46/4.69 fof(help_c__COMBI__1, axiom, ![X159, X4]:hAPP(c_COMBI(X4),X159)=X159, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBI__1)). 4.46/4.69 fof(fact_id__apply, axiom, ![X48, X4]:X48=hAPP(c_Fun_Oid(X4),X48), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_id__apply)). 4.46/4.69 fof(fact_nat__size, axiom, ![X17]:X17=hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__size)). 4.46/4.69 fof(fact_identity__equivp, axiom, ![X4]:c_Equiv__Relations_Oequivp(X4,c_fequal), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_identity__equivp)). 4.46/4.69 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal, axiom, ![X128]:class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal)). 4.46/4.69 fof(arity_Option__Ooption__HOL_Oequal, axiom, ![X128]:class_HOL_Oequal(tc_Option_Ooption(X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Option__Ooption__HOL_Oequal)). 4.46/4.69 fof(arity_List__Olist__HOL_Oequal, axiom, ![X128]:class_HOL_Oequal(tc_List_Olist(X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_List__Olist__HOL_Oequal)). 4.46/4.69 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize, axiom, ![X128]:class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Lazy____Sequence__Olazy____sequence__Nat_Osize)). 4.46/4.69 fof(arity_Option__Ooption__Nat_Osize, axiom, ![X128]:class_Nat_Osize(tc_Option_Ooption(X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Option__Ooption__Nat_Osize)). 4.46/4.69 fof(arity_List__Olist__Nat_Osize, axiom, ![X128]:class_Nat_Osize(tc_List_Olist(X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_List__Olist__Nat_Osize)). 4.46/4.69 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal, axiom, ![X128]:class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Hoare____Mirabelle__Otriple__HOL_Oequal)). 4.46/4.69 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize, axiom, ![X128]:class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Hoare____Mirabelle__Otriple__Nat_Osize)). 4.46/4.69 fof(fact_int__0__neq__1, axiom, c_Groups_Oone__class_Oone(tc_Int_Oint)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__0__neq__1)). 4.46/4.69 fof(fact_Nitpick_OFrac__def, axiom, hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Nitpick_OFrac, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_OFrac__def)). 4.46/4.69 fof(fact_max__rpair__set, axiom, c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__rpair__set)). 4.46/4.69 fof(fact_min__rpair__set, axiom, c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__rpair__set)). 4.46/4.69 fof(fact_Integ__def, axiom, hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel)=c_Int_OInteg, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Integ__def)). 4.46/4.69 fof(fact_UN__atMost__UNIV, axiom, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat))=c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__atMost__UNIV)). 4.46/4.69 fof(fact_UN__lessThan__UNIV, axiom, c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__lessThan__UNIV)). 4.46/4.69 fof(fact_UN__atLeast__UNIV, axiom, c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__atLeast__UNIV)). 4.46/4.69 fof(fact_equiv__intrel, axiom, c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__intrel)). 4.46/4.69 fof(fact_INT__greaterThan__UNIV, axiom, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__greaterThan__UNIV)). 4.46/4.69 fof(fact_type__definition__Integ, axiom, c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition__Integ)). 4.46/4.69 fof(fact_greaterThan__0, axiom, hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThan__0)). 4.46/4.69 fof(fact_transfer__morphism__nat__int, axiom, c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__morphism__nat__int)). 4.46/4.69 fof(fact_inj__int, axiom, c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__int)). 4.46/4.69 fof(fact_int__0__less__1, axiom, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__0__less__1)). 4.46/4.69 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, axiom, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J)). 4.46/4.69 fof(fact_int__of__def, axiom, hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of)=c_Code__Numeral_Oint__of, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__of__def)). 4.46/4.69 fof(fact_code__numeral__zero__minus__one, axiom, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral__zero__minus__one)). 4.46/4.69 fof(fact_card__UNIV__unit, axiom, hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__UNIV__unit)). 4.46/4.69 fof(fact_atLeast__0, axiom, c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast__0)). 4.46/4.69 fof(fact_pair__less__def, axiom, c_FunDef_Opair__less=c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__less__def)). 4.46/4.69 fof(fact_int__1, axiom, c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__1)). 4.46/4.69 fof(fact_code__numeral_Osize_I3_J, axiom, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Osize_I3_J)). 4.46/4.69 fof(fact_max__strict__def, axiom, c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)=c_FunDef_Omax__strict, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__strict__def)). 4.46/4.69 fof(fact_int__0, axiom, c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__0)). 4.46/4.69 fof(fact_min__strict__def, axiom, c_FunDef_Omin__strict=c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__strict__def)). 4.46/4.69 fof(fact_wf__pair__less, axiom, c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__pair__less)). 4.46/4.69 fof(fact_com_Osize_I9_J, axiom, hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I9_J)). 4.46/4.69 fof(fact_bool_Osize_I4_J, axiom, hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bool_Osize_I4_J)). 4.46/4.69 fof(fact_bool_Osize_I3_J, axiom, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bool_Osize_I3_J)). 4.46/4.69 fof(conj_2, hypothesis, hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),v_F)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_2)). 4.46/4.69 fof(fact_WT_OSkip, axiom, hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WT_OSkip)). 4.46/4.69 fof(fact_wf__less__than, axiom, c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__less__than)). 4.46/4.69 fof(fact_wf__pred__nat, axiom, c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__pred__nat)). 4.46/4.69 fof(fact_code__numeral_Osize_I1_J, axiom, c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Osize_I1_J)). 4.46/4.69 fof(fact_nat_Osize_I1_J, axiom, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat_Osize_I1_J)). 4.46/4.69 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J, axiom, c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J)). 4.46/4.69 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J, axiom, c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J)). 4.46/4.69 fof(fact_finite__dom__body, axiom, hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__dom__body)). 4.46/4.69 fof(fact_bool_Osize_I1_J, axiom, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_HOL_Obool_Obool__size(c_fTrue), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bool_Osize_I1_J)). 4.46/4.69 fof(fact_bool_Osize_I2_J, axiom, c_HOL_Obool_Obool__size(c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bool_Osize_I2_J)). 4.46/4.69 fof(fact_of__int__eq__id, axiom, c_Int_Oring__1__class_Oof__int(tc_Int_Oint)=c_Fun_Oid(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__eq__id)). 4.46/4.69 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J, axiom, c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J)). 4.46/4.69 fof(fact_body__def, axiom, hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies)=c_Com_Obody, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_body__def)). 4.46/4.69 fof(fact_com_Osize_I1_J, axiom, c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I1_J)). 4.46/4.69 fof(conj_5, hypothesis, hAPP(c_Com_Obody,v_pn)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_5)). 4.46/4.69 fof(fact_bot__nat__def, axiom, c_Orderings_Obot__class_Obot(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bot__nat__def)). 4.46/4.69 fof(arity_Int__Oint__Rings_Oidom, axiom, class_Rings_Oidom(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oidom)). 4.46/4.69 fof(arity_Int__Oint__Rings_Olinordered__ring, axiom, class_Rings_Olinordered__ring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__ring)). 4.46/4.69 fof(arity_Int__Oint__Rings_Oordered__ring__abs, axiom, class_Rings_Oordered__ring__abs(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oordered__ring__abs)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add, axiom, class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add)). 4.46/4.69 fof(arity_Nat__Onat__Groups_Oab__semigroup__add, axiom, class_Groups_Oab__semigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oab__semigroup__add)). 4.46/4.69 fof(arity_Int__Oint__Groups_Oab__semigroup__add, axiom, class_Groups_Oab__semigroup__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oab__semigroup__add)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring, axiom, class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring)). 4.46/4.69 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring, axiom, class_Rings_Oordered__cancel__semiring(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Oordered__cancel__semiring)). 4.46/4.69 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring, axiom, class_Rings_Oordered__cancel__semiring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oordered__cancel__semiring)). 4.46/4.69 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy, axiom, class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy)). 4.46/4.69 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy, axiom, class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Lazy__Sequence_Osmall__lazy)). 4.46/4.69 fof(arity_Int__Oint__Rings_Olinordered__semiring__1, axiom, class_Rings_Olinordered__semiring__1(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__semiring__1)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring, axiom, class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring)). 4.46/4.69 fof(arity_Nat__Onat__Rings_Olinordered__semiring, axiom, class_Rings_Olinordered__semiring(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Olinordered__semiring)). 4.46/4.69 fof(arity_Int__Oint__Rings_Olinordered__semiring, axiom, class_Rings_Olinordered__semiring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__semiring)). 4.46/4.69 fof(arity_Int__Oint__Rings_Ocomm__ring__1, axiom, class_Rings_Ocomm__ring__1(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Ocomm__ring__1)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add, axiom, class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add)). 4.46/4.69 fof(arity_Nat__Onat__Groups_Osemigroup__add, axiom, class_Groups_Osemigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Osemigroup__add)). 4.46/4.69 fof(arity_Int__Oint__Groups_Osemigroup__add, axiom, class_Groups_Osemigroup__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Osemigroup__add)). 4.46/4.69 fof(arity_Int__Oint__Groups_Oabs__if, axiom, class_Groups_Oabs__if(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oabs__if)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring, axiom, class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring)). 4.46/4.69 fof(arity_Nat__Onat__Rings_Ocomm__semiring, axiom, class_Rings_Ocomm__semiring(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Ocomm__semiring)). 4.46/4.69 fof(arity_Int__Oint__Rings_Ocomm__semiring, axiom, class_Rings_Ocomm__semiring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Ocomm__semiring)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower, axiom, class_Power_Opower(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Power_Opower)). 4.46/4.69 fof(arity_Nat__Onat__Power_Opower, axiom, class_Power_Opower(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Power_Opower)). 4.46/4.69 fof(arity_Int__Oint__Power_Opower, axiom, class_Power_Opower(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Power_Opower)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors, axiom, class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors)). 4.46/4.69 fof(arity_Nat__Onat__Rings_Ono__zero__divisors, axiom, class_Rings_Ono__zero__divisors(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Ono__zero__divisors)). 4.46/4.69 fof(arity_Int__Oint__Rings_Ono__zero__divisors, axiom, class_Rings_Ono__zero__divisors(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Ono__zero__divisors)). 4.46/4.69 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors, axiom, class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oring__1__no__zero__divisors)). 4.46/4.69 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors, axiom, class_Rings_Oring__no__zero__divisors(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oring__no__zero__divisors)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict, axiom, class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict)). 4.46/4.69 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict, axiom, class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict)). 4.46/4.69 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, axiom, class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__comm__semiring__strict)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring, axiom, class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Osemiring)). 4.46/4.69 fof(arity_Nat__Onat__Rings_Osemiring, axiom, class_Rings_Osemiring(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Osemiring)). 4.46/4.69 fof(arity_Int__Oint__Rings_Osemiring, axiom, class_Rings_Osemiring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Osemiring)). 4.46/4.69 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict, axiom, class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__semiring__1__strict)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one, axiom, class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one)). 4.46/4.69 fof(arity_Nat__Onat__Rings_Ozero__neq__one, axiom, class_Rings_Ozero__neq__one(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Ozero__neq__one)). 4.46/4.69 fof(arity_Int__Oint__Rings_Ozero__neq__one, axiom, class_Rings_Ozero__neq__one(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Ozero__neq__one)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring, axiom, class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring)). 4.46/4.69 fof(arity_Nat__Onat__Rings_Oordered__semiring, axiom, class_Rings_Oordered__semiring(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Oordered__semiring)). 4.46/4.69 fof(arity_Int__Oint__Rings_Oordered__semiring, axiom, class_Rings_Oordered__semiring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oordered__semiring)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add, axiom, class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add)). 4.46/4.69 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, axiom, class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add)). 4.46/4.69 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add, axiom, class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ocancel__ab__semigroup__add)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add, axiom, class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add)). 4.46/4.69 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add, axiom, class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add)). 4.46/4.69 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add, axiom, class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0, axiom, class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0)). 4.46/4.69 fof(arity_Nat__Onat__Rings_Osemiring__0, axiom, class_Rings_Osemiring__0(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Osemiring__0)). 4.46/4.69 fof(arity_Int__Oint__Rings_Osemiring__0, axiom, class_Rings_Osemiring__0(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Osemiring__0)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone, axiom, class_Groups_Oone(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Oone)). 4.46/4.69 fof(arity_Nat__Onat__Groups_Oone, axiom, class_Groups_Oone(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oone)). 4.46/4.69 fof(arity_Int__Oint__Groups_Oone, axiom, class_Groups_Oone(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oone)). 4.46/4.69 fof(arity_Product____Type__Ounit__HOL_Oequal, axiom, class_HOL_Oequal(tc_Product__Type_Ounit), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Product____Type__Ounit__HOL_Oequal)). 4.46/4.69 fof(arity_Code____Evaluation__Oterm__HOL_Oequal, axiom, class_HOL_Oequal(tc_Code__Evaluation_Oterm), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Evaluation__Oterm__HOL_Oequal)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal, axiom, class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__HOL_Oequal)). 4.46/4.69 fof(arity_Nat__Onat__HOL_Oequal, axiom, class_HOL_Oequal(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__HOL_Oequal)). 4.46/4.69 fof(arity_Int__Oint__HOL_Oequal, axiom, class_HOL_Oequal(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__HOL_Oequal)). 4.46/4.69 fof(arity_Nat__Onat__Orderings_Owellorder, axiom, class_Orderings_Owellorder(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Orderings_Owellorder)). 4.46/4.69 fof(arity_Int__Oint__Groups_Ouminus, axiom, class_Groups_Ouminus(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ouminus)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add, axiom, class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add)). 4.46/4.69 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add, axiom, class_Groups_Ocancel__semigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ocancel__semigroup__add)). 4.46/4.69 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add, axiom, class_Groups_Ocancel__semigroup__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ocancel__semigroup__add)). 4.46/4.69 fof(arity_Int__Oint__Rings_Olinordered__ring__strict, axiom, class_Rings_Olinordered__ring__strict(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__ring__strict)). 4.46/4.69 fof(arity_Nat__Onat__Lattices_Odistrib__lattice, axiom, class_Lattices_Odistrib__lattice(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Lattices_Odistrib__lattice)). 4.46/4.69 fof(arity_Int__Oint__Lattices_Odistrib__lattice, axiom, class_Lattices_Odistrib__lattice(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Lattices_Odistrib__lattice)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero, axiom, class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Ozero)). 4.46/4.69 fof(arity_Nat__Onat__Groups_Ozero, axiom, class_Groups_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ozero)). 4.46/4.69 fof(arity_Int__Oint__Groups_Ozero, axiom, class_Groups_Ozero(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ozero)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0, axiom, class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0)). 4.46/4.69 fof(arity_Nat__Onat__Nat_Osemiring__char__0, axiom, class_Nat_Osemiring__char__0(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Nat_Osemiring__char__0)). 4.46/4.69 fof(arity_Int__Oint__Nat_Osemiring__char__0, axiom, class_Nat_Osemiring__char__0(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Nat_Osemiring__char__0)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add, axiom, class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add)). 4.46/4.69 fof(arity_Nat__Onat__Groups_Omonoid__add, axiom, class_Groups_Omonoid__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Omonoid__add)). 4.46/4.69 fof(arity_Int__Oint__Groups_Omonoid__add, axiom, class_Groups_Omonoid__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Omonoid__add)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring, axiom, class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring)). 4.46/4.69 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring, axiom, class_Rings_Oordered__comm__semiring(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Oordered__comm__semiring)). 4.46/4.69 fof(arity_Int__Oint__Rings_Oordered__comm__semiring, axiom, class_Rings_Oordered__comm__semiring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oordered__comm__semiring)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord, axiom, class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Orderings_Oord)). 4.46/4.69 fof(arity_Nat__Onat__Orderings_Oord, axiom, class_Orderings_Oord(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Orderings_Oord)). 4.46/4.69 fof(arity_Int__Oint__Orderings_Oord, axiom, class_Orderings_Oord(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Orderings_Oord)). 4.46/4.69 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite, axiom, class_Finite__Set_Ofinite(tc_Product__Type_Ounit), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Product____Type__Ounit__Finite__Set_Ofinite)). 4.46/4.69 fof(arity_Int__Oint__Groups_Osgn__if, axiom, class_Groups_Osgn__if(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Osgn__if)). 4.46/4.69 fof(arity_Product____Type__Ounit__Nat_Osize, axiom, class_Nat_Osize(tc_Product__Type_Ounit), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Product____Type__Ounit__Nat_Osize)). 4.46/4.69 fof(arity_Code____Evaluation__Oterm__Nat_Osize, axiom, class_Nat_Osize(tc_Code__Evaluation_Oterm), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Evaluation__Oterm__Nat_Osize)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize, axiom, class_Nat_Osize(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Nat_Osize)). 4.46/4.69 fof(arity_Nat__Onat__Nat_Osize, axiom, class_Nat_Osize(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Nat_Osize)). 4.46/4.69 fof(arity_Int__Oint__Rings_Oring__1, axiom, class_Rings_Oring__1(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oring__1)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add, axiom, class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add)). 4.46/4.69 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add, axiom, class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add)). 4.46/4.69 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add, axiom, class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Olinordered__ab__semigroup__add)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder)). 4.46/4.69 fof(arity_Nat__Onat__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Orderings_Opreorder)). 4.46/4.69 fof(arity_Int__Oint__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Orderings_Opreorder)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add, axiom, class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add)). 4.46/4.69 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add, axiom, class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oordered__ab__semigroup__add)). 4.46/4.69 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add, axiom, class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oordered__ab__semigroup__add)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le, axiom, class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le)). 4.46/4.69 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le, axiom, class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le)). 4.46/4.69 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, axiom, class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le)). 4.46/4.69 fof(arity_Product____Type__Ounit__Smallcheck_Osmall, axiom, class_Smallcheck_Osmall(tc_Product__Type_Ounit), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Product____Type__Ounit__Smallcheck_Osmall)). 4.46/4.69 fof(arity_Int__Oint__Smallcheck_Osmall, axiom, class_Smallcheck_Osmall(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Smallcheck_Osmall)). 4.46/4.69 fof(arity_Int__Oint__Groups_Oab__group__add, axiom, class_Groups_Oab__group__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oab__group__add)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict, axiom, class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict)). 4.46/4.69 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict, axiom, class_Rings_Olinordered__semiring__strict(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Olinordered__semiring__strict)). 4.46/4.69 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict, axiom, class_Rings_Olinordered__semiring__strict(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__semiring__strict)). 4.46/4.69 fof(arity_Nat__Onat__Lattices_Osemilattice__sup, axiom, class_Lattices_Osemilattice__sup(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Lattices_Osemilattice__sup)). 4.46/4.69 fof(arity_Int__Oint__Lattices_Osemilattice__sup, axiom, class_Lattices_Osemilattice__sup(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Lattices_Osemilattice__sup)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber, axiom, class_Int_Onumber(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Int_Onumber)). 4.46/4.69 fof(arity_Nat__Onat__Int_Onumber, axiom, class_Int_Onumber(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Int_Onumber)). 4.46/4.69 fof(arity_Int__Oint__Int_Onumber, axiom, class_Int_Onumber(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Int_Onumber)). 4.46/4.69 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, axiom, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct)). 4.46/4.69 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, axiom, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult, axiom, class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult)). 4.46/4.69 fof(arity_Nat__Onat__Groups_Omonoid__mult, axiom, class_Groups_Omonoid__mult(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Omonoid__mult)). 4.46/4.69 fof(arity_Int__Oint__Groups_Omonoid__mult, axiom, class_Groups_Omonoid__mult(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Omonoid__mult)). 4.46/4.69 fof(arity_Int__Oint__Rings_Olinordered__idom, axiom, class_Rings_Olinordered__idom(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__idom)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1, axiom, class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1)). 4.46/4.69 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1, axiom, class_Rings_Ocomm__semiring__1(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Ocomm__semiring__1)). 4.46/4.69 fof(arity_Int__Oint__Rings_Ocomm__semiring__1, axiom, class_Rings_Ocomm__semiring__1(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Ocomm__semiring__1)). 4.46/4.69 fof(arity_Int__Oint__Rings_Oordered__ring, axiom, class_Rings_Oordered__ring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oordered__ring)). 4.46/4.69 fof(arity_Nat__Onat__Lattices_Osemilattice__inf, axiom, class_Lattices_Osemilattice__inf(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Lattices_Osemilattice__inf)). 4.46/4.69 fof(arity_Int__Oint__Lattices_Osemilattice__inf, axiom, class_Lattices_Osemilattice__inf(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Lattices_Osemilattice__inf)). 4.46/4.69 fof(arity_Nat__Onat__Lattices_Olattice, axiom, class_Lattices_Olattice(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Lattices_Olattice)). 4.46/4.69 fof(arity_Int__Oint__Lattices_Olattice, axiom, class_Lattices_Olattice(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Lattices_Olattice)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult, axiom, class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult)). 4.46/4.69 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult, axiom, class_Groups_Oab__semigroup__mult(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oab__semigroup__mult)). 4.46/4.69 fof(arity_Int__Oint__Groups_Oab__semigroup__mult, axiom, class_Groups_Oab__semigroup__mult(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oab__semigroup__mult)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero, axiom, class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero)). 4.46/4.69 fof(arity_Nat__Onat__Rings_Omult__zero, axiom, class_Rings_Omult__zero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Omult__zero)). 4.46/4.69 fof(arity_Int__Oint__Rings_Omult__zero, axiom, class_Rings_Omult__zero(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Omult__zero)). 4.46/4.69 fof(arity_Int__Oint__Int_Oring__char__0, axiom, class_Int_Oring__char__0(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Int_Oring__char__0)). 4.46/4.69 fof(arity_Nat__Onat__Orderings_Obot, axiom, class_Orderings_Obot(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Orderings_Obot)). 4.46/4.69 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs, axiom, class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oordered__ab__group__add__abs)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder, axiom, class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Orderings_Oorder)). 4.46/4.69 fof(arity_Nat__Onat__Orderings_Oorder, axiom, class_Orderings_Oorder(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Orderings_Oorder)). 4.46/4.69 fof(arity_Int__Oint__Orderings_Oorder, axiom, class_Orderings_Oorder(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Orderings_Oorder)). 4.46/4.69 fof(arity_Int__Oint__Groups_Oordered__ab__group__add, axiom, class_Groups_Oordered__ab__group__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oordered__ab__group__add)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1, axiom, class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1)). 4.46/4.69 fof(arity_Nat__Onat__Rings_Osemiring__1, axiom, class_Rings_Osemiring__1(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Osemiring__1)). 4.46/4.69 fof(arity_Int__Oint__Rings_Osemiring__1, axiom, class_Rings_Osemiring__1(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Osemiring__1)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus, axiom, class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Ominus)). 4.46/4.69 fof(arity_Nat__Onat__Groups_Ominus, axiom, class_Groups_Ominus(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ominus)). 4.46/4.69 fof(arity_Int__Oint__Groups_Ominus, axiom, class_Groups_Ominus(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ominus)). 4.46/4.69 fof(arity_Product____Type__Ounit__Enum_Oenum, axiom, class_Enum_Oenum(tc_Product__Type_Ounit), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Product____Type__Ounit__Enum_Oenum)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add, axiom, class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add)). 4.46/4.69 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add, axiom, class_Groups_Ocomm__monoid__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ocomm__monoid__add)). 4.46/4.69 fof(arity_Int__Oint__Groups_Ocomm__monoid__add, axiom, class_Groups_Ocomm__monoid__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ocomm__monoid__add)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult, axiom, class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult)). 4.46/4.69 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult, axiom, class_Groups_Ocomm__monoid__mult(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ocomm__monoid__mult)). 4.46/4.69 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult, axiom, class_Groups_Ocomm__monoid__mult(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ocomm__monoid__mult)). 4.46/4.69 fof(arity_Int__Oint__Rings_Oring, axiom, class_Rings_Oring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oring)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div, axiom, class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div)). 4.46/4.69 fof(arity_Nat__Onat__Divides_Osemiring__div, axiom, class_Divides_Osemiring__div(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Divides_Osemiring__div)). 4.46/4.69 fof(arity_Int__Oint__Divides_Osemiring__div, axiom, class_Divides_Osemiring__div(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Divides_Osemiring__div)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder, axiom, class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder)). 4.46/4.69 fof(arity_Nat__Onat__Orderings_Olinorder, axiom, class_Orderings_Olinorder(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Orderings_Olinorder)). 4.46/4.69 fof(arity_Int__Oint__Orderings_Olinorder, axiom, class_Orderings_Olinorder(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Orderings_Olinorder)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add, axiom, class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add)). 4.46/4.69 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add, axiom, class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oordered__comm__monoid__add)). 4.46/4.69 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add, axiom, class_Groups_Oordered__comm__monoid__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oordered__comm__monoid__add)). 4.46/4.69 fof(arity_Int__Oint__Groups_Ogroup__add, axiom, class_Groups_Ogroup__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ogroup__add)). 4.46/4.69 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add, axiom, class_Groups_Olinordered__ab__group__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Olinordered__ab__group__add)). 4.46/4.69 fof(arity_HOL__Obool__Orderings_Otop, axiom, class_Orderings_Otop(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Orderings_Otop)). 4.46/4.69 fof(arity_Com__Ostate__HOL_Oequal, axiom, class_HOL_Oequal(tc_Com_Ostate), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Com__Ostate__HOL_Oequal)). 4.46/4.69 fof(arity_Com__Ocom__HOL_Oequal, axiom, class_HOL_Oequal(tc_Com_Ocom), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Com__Ocom__HOL_Oequal)). 4.46/4.69 fof(arity_HOL__Obool__HOL_Oequal, axiom, class_HOL_Oequal(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__HOL_Oequal)). 4.46/4.69 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom, axiom, class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom)). 4.46/4.69 fof(arity_Nat__Onat__Rings_Olinordered__semidom, axiom, class_Rings_Olinordered__semidom(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Olinordered__semidom)). 4.46/4.69 fof(arity_Int__Oint__Rings_Olinordered__semidom, axiom, class_Rings_Olinordered__semidom(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__semidom)). 4.46/4.69 fof(arity_Int__Oint__Divides_Oring__div, axiom, class_Divides_Oring__div(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Divides_Oring__div)). 4.46/4.69 fof(arity_HOL__Obool__Groups_Ouminus, axiom, class_Groups_Ouminus(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Groups_Ouminus)). 4.46/4.69 fof(arity_Int__Oint__Int_Onumber__ring, axiom, class_Int_Onumber__ring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Int_Onumber__ring)). 4.46/4.69 fof(arity_HOL__Obool__Lattices_Odistrib__lattice, axiom, class_Lattices_Odistrib__lattice(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Lattices_Odistrib__lattice)). 4.46/4.69 fof(arity_HOL__Obool__Orderings_Oord, axiom, class_Orderings_Oord(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Orderings_Oord)). 4.46/4.69 fof(arity_HOL__Obool__Lattices_Oboolean__algebra, axiom, class_Lattices_Oboolean__algebra(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Lattices_Oboolean__algebra)). 4.46/4.69 fof(arity_HOL__Obool__Finite__Set_Ofinite, axiom, class_Finite__Set_Ofinite(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Finite__Set_Ofinite)). 4.46/4.69 fof(arity_Com__Ostate__Nat_Osize, axiom, class_Nat_Osize(tc_Com_Ostate), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Com__Ostate__Nat_Osize)). 4.46/4.69 fof(help_c__fTrue__1, axiom, hBOOL(c_fTrue), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fTrue__1)). 4.46/4.69 fof(arity_Com__Ocom__Nat_Osize, axiom, class_Nat_Osize(tc_Com_Ocom), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Com__Ocom__Nat_Osize)). 4.46/4.69 fof(arity_HOL__Obool__Nat_Osize, axiom, class_Nat_Osize(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Nat_Osize)). 4.46/4.69 fof(arity_HOL__Obool__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Orderings_Opreorder)). 4.46/4.69 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top, axiom, class_Lattices_Obounded__lattice__top(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Lattices_Obounded__lattice__top)). 4.46/4.69 fof(arity_HOL__Obool__Lattices_Obounded__lattice, axiom, class_Lattices_Obounded__lattice(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Lattices_Obounded__lattice)). 4.46/4.69 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice, axiom, class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice)). 4.46/4.69 fof(arity_HOL__Obool__Lattices_Osemilattice__sup, axiom, class_Lattices_Osemilattice__sup(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Lattices_Osemilattice__sup)). 4.46/4.69 fof(arity_HOL__Obool__Lattices_Osemilattice__inf, axiom, class_Lattices_Osemilattice__inf(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Lattices_Osemilattice__inf)). 4.46/4.69 fof(arity_HOL__Obool__Lattices_Olattice, axiom, class_Lattices_Olattice(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Lattices_Olattice)). 4.46/4.69 fof(arity_HOL__Obool__Orderings_Obot, axiom, class_Orderings_Obot(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Orderings_Obot)). 4.46/4.69 fof(arity_HOL__Obool__Orderings_Oorder, axiom, class_Orderings_Oorder(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Orderings_Oorder)). 4.46/4.69 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot, axiom, class_Lattices_Obounded__lattice__bot(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Lattices_Obounded__lattice__bot)). 4.46/4.69 fof(arity_HOL__Obool__Groups_Ominus, axiom, class_Groups_Ominus(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Groups_Ominus)). 4.46/4.69 fof(arity_HOL__Obool__Enum_Oenum, axiom, class_Enum_Oenum(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Enum_Oenum)). 4.46/4.69 fof(c_0_4429, plain, ![X9964]:c_Int_Osucc(X9964)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9964),c_Int_OMin), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I2_J])). 4.46/4.69 cnf(c_0_4430, plain, (c_Int_OPls=c_Int_Osucc(c_Int_OMin)), inference(split_conjunct,[status(thm)],[fact_succ__Min])). 4.46/4.69 cnf(c_0_4431, plain, (c_Int_Osucc(X1)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)), inference(split_conjunct,[status(thm)],[c_0_4429])). 4.46/4.69 fof(c_0_4432, plain, ![X5437]:c_Int_Osucc(X5437)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5437),c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(variable_rename,[status(thm)],[fact_succ__def])). 4.46/4.69 fof(c_0_4433, plain, ![X8542]:X8542=c_Int_Osucc(c_Int_Opred(X8542)), inference(variable_rename,[status(thm)],[fact_succ__pred])). 4.46/4.69 fof(c_0_4434, plain, ![X11969]:c_Int_Opred(X11969)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11969),c_Int_OMin), inference(variable_rename,[status(thm)],[fact_add__Min__right])). 4.46/4.69 cnf(c_0_4435, plain, (c_Int_OPls=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)), inference(rw,[status(thm)],[c_0_4430, c_0_4431])). 4.46/4.69 cnf(c_0_4436, plain, (c_Int_OPls=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[fact_Pls__def]), ['final']). 4.46/4.69 cnf(c_0_4437, plain, (c_Int_Osucc(X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_4432])). 4.46/4.69 fof(c_0_4438, plain, ![X345]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X345)=c_Int_Opred(X345), inference(variable_rename,[status(thm)],[fact_add__Min])). 4.46/4.69 fof(c_0_4439, plain, ![X7004]:c_Int_OMin!=c_Int_OBit0(X7004), inference(variable_rename,[status(thm)],[fact_rel__simps_I42_J])). 4.46/4.69 fof(c_0_4440, plain, ![X7965]:c_Int_OBit0(X7965)=c_Int_Opred(c_Int_OBit1(X7965)), inference(variable_rename,[status(thm)],[fact_pred__Bit1])). 4.46/4.69 fof(c_0_4441, plain, ![X9098]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X9098)),X9098)=c_Int_OBit1(X9098), inference(variable_rename,[status(thm)],[fact_Bit1__def])). 4.46/4.69 cnf(c_0_4442, plain, (X1=c_Int_Osucc(c_Int_Opred(X1))), inference(split_conjunct,[status(thm)],[c_0_4433])). 4.46/4.69 cnf(c_0_4443, plain, (c_Int_Opred(X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)), inference(split_conjunct,[status(thm)],[c_0_4434])). 4.46/4.69 fof(c_0_4444, plain, ![X400]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X400))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X400)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I4_J])). 4.46/4.69 fof(c_0_4445, plain, ![X11999]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11999),X11999)=c_Int_OBit0(X11999), inference(variable_rename,[status(thm)],[fact_Bit0__def])). 4.46/4.69 fof(c_0_4446, plain, ![X4356]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4356),c_Int_OPls)=X4356, inference(variable_rename,[status(thm)],[fact_add__Pls__right])). 4.46/4.69 cnf(c_0_4447, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_4435, c_0_4436])). 4.46/4.69 cnf(c_0_4448, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(rw,[status(thm)],[c_0_4437, c_0_4431]), ['final']). 4.46/4.69 cnf(c_0_4449, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X1)=c_Int_Opred(X1)), inference(split_conjunct,[status(thm)],[c_0_4438])). 4.46/4.69 fof(c_0_4450, plain, ![X7987]:c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X7987,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_upt__0])). 4.46/4.69 fof(c_0_4451, plain, ![X3150, X3151]:c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3151),X3150))=c_List_Oupt(X3151,X3150), inference(variable_rename,[status(thm)],[fact_sorted__list__of__set__range])). 4.46/4.69 fof(c_0_4452, plain, ![X12887, X12888, X12889, X12890]:hAPP(c_Set_OCollect(X12890),hAPP(hAPP(c_COMBB(X12889,tc_HOL_Obool,X12890),X12887),X12888))=hAPP(c_Set_Ovimage(X12890,X12889,X12888),hAPP(c_Set_OCollect(X12889),X12887)), inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq])). 4.46/4.69 fof(c_0_4453, plain, ![X3665, X3666]:X3665=hAPP(c_Set_OCollect(X3666),X3665), inference(variable_rename,[status(thm)],[fact_Collect__def])). 4.46/4.69 fof(c_0_4454, plain, ![X12536, X12537]:hAPP(c_Set_OCollect(X12537),hAPP(hAPP(c_COMBC(X12537,tc_fun(X12537,tc_HOL_Obool),tc_HOL_Obool),c_member(X12537)),X12536))=X12536, inference(variable_rename,[status(thm)],[fact_Collect__mem__eq])). 4.46/4.69 fof(c_0_4455, plain, ![X6108, X6109, X6110, X6111]:hAPP(hAPP(c_Product__Type_OSigma(X6111,X6110),hAPP(c_Set_OCollect(X6111),X6109)),hAPP(c_COMBK(tc_fun(X6110,tc_HOL_Obool),X6111),hAPP(c_Set_OCollect(X6110),X6108)))=hAPP(c_Set_OCollect(tc_prod(X6111,X6110)),hAPP(c_Product__Type_Oprod_Oprod__case(X6111,X6110,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X6111,tc_fun(X6110,tc_HOL_Obool),tc_fun(X6110,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X6110,tc_HOL_Obool),tc_fun(X6110,tc_HOL_Obool)),X6111),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X6110)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6111),c_fconj),X6109))),X6108))), inference(variable_rename,[status(thm)],[fact_Collect__split])). 4.46/4.69 fof(c_0_4456, plain, ![X4127, X4128]:((c_Groups_Oone__class_Oone(X4128)!=hAPP(hAPP(c_Power_Opower__class_Opower(X4128),X4127),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|(X4127=c_Groups_Oone__class_Oone(X4128)|X4127=hAPP(c_Groups_Ouminus__class_Ouminus(X4128),c_Groups_Oone__class_Oone(X4128)))|~class_Rings_Oring__1__no__zero__divisors(X4128))&((X4127!=c_Groups_Oone__class_Oone(X4128)|c_Groups_Oone__class_Oone(X4128)=hAPP(hAPP(c_Power_Opower__class_Opower(X4128),X4127),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|~class_Rings_Oring__1__no__zero__divisors(X4128))&(X4127!=hAPP(c_Groups_Ouminus__class_Ouminus(X4128),c_Groups_Oone__class_Oone(X4128))|c_Groups_Oone__class_Oone(X4128)=hAPP(hAPP(c_Power_Opower__class_Opower(X4128),X4127),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|~class_Rings_Oring__1__no__zero__divisors(X4128)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power2__eq__1__iff])])])])). 4.46/4.69 fof(c_0_4457, plain, ![X14412, X14413]:((c_Groups_Ozero__class_Ozero(X14413)=X14412|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14413),c_Groups_Ozero__class_Ozero(X14413)),hAPP(hAPP(c_Power_Opower__class_Opower(X14413),X14412),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|~class_Rings_Olinordered__idom(X14413))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14413),c_Groups_Ozero__class_Ozero(X14413)),hAPP(hAPP(c_Power_Opower__class_Opower(X14413),X14412),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|c_Groups_Ozero__class_Ozero(X14413)!=X14412|~class_Rings_Olinordered__idom(X14413))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power2])])])). 4.46/4.69 fof(c_0_4458, plain, ![X2125]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2125),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))|(X2125=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X2125=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__2__cases])])). 4.46/4.69 fof(c_0_4459, plain, ![X7856, X7857]:(~class_Rings_Olinordered__idom(X7857)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7857),hAPP(hAPP(c_Power_Opower__class_Opower(X7857),X7856),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X7857)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power2__less__0])])])). 4.46/4.69 fof(c_0_4460, plain, ![X10232]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X10232)=hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X10232)), inference(variable_rename,[status(thm)],[fact_nat__number__of__def])). 4.46/4.69 fof(c_0_4461, plain, ![X5431]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5431)=X5431, inference(variable_rename,[status(thm)],[fact_number__of__is__id])). 4.46/4.69 fof(c_0_4462, plain, ![X16246]:c_Int_Opred(X16246)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X16246),c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(variable_rename,[status(thm)],[fact_pred__def])). 4.46/4.69 fof(c_0_4463, plain, ![X13598, X13599, X13600]:hAPP(c_Set_OCollect(X13600),hAPP(hAPP(c_COMBS(X13600,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X13600),c_fconj),X13599)),X13598))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13600,tc_HOL_Obool)),hAPP(c_Set_OCollect(X13600),X13599)),hAPP(c_Set_OCollect(X13600),X13598)), inference(variable_rename,[status(thm)],[fact_Collect__conj__eq])). 4.46/4.69 fof(c_0_4464, plain, ![X8389]:((c_Int_OPls!=c_Int_OBit0(X8389)|X8389=c_Int_OPls)&(X8389!=c_Int_OPls|c_Int_OPls=c_Int_OBit0(X8389))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I38_J])])). 4.46/4.69 fof(c_0_4465, negated_conjecture, ~(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,v_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))), inference(assume_negation,[status(cth)],[conj_7])). 4.46/4.69 fof(c_0_4466, plain, ![X14554, X14555]:hAPP(c_Set_OCollect(X14555),hAPP(c_fequal,X14554))=hAPP(hAPP(c_Set_Oinsert(X14555),X14554),c_Orderings_Obot__class_Obot(tc_fun(X14555,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_singleton__conv2])). 4.46/4.69 fof(c_0_4467, plain, ![X6406]:~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X6406))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__int__code_I7_J])])). 4.46/4.69 fof(c_0_4468, plain, ![X10886]:~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X10886)),c_Int_OMin)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__int__code_I11_J])])). 4.46/4.69 cnf(c_0_4469, plain, (c_Int_OMin!=c_Int_OBit0(X1)), inference(split_conjunct,[status(thm)],[c_0_4439])). 4.46/4.69 cnf(c_0_4470, plain, (c_Int_OBit0(X1)=c_Int_Opred(c_Int_OBit1(X1))), inference(split_conjunct,[status(thm)],[c_0_4440])). 4.46/4.69 cnf(c_0_4471, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)=c_Int_OBit1(X1)), inference(split_conjunct,[status(thm)],[c_0_4441])). 4.46/4.69 fof(c_0_4472, plain, ![X13355]:c_Int_OPls!=c_Int_OBit1(X13355), inference(variable_rename,[status(thm)],[fact_rel__simps_I46_J])). 4.46/4.69 fof(c_0_4473, plain, ![X11095, X11096]:c_List_Ofoldr(tc_List_Olist(X11096),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X11096)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X11096))),X11095,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X11096))),c_List_Otranspose(X11096,X11095)), inference(variable_rename,[status(thm)],[fact_length__transpose])). 4.46/4.69 fof(c_0_4474, plain, ![X16344, X16345, X16346, X16347, X16348]:c_List_Ofoldr(X16348,X16347,X16346,X16345,X16344)=hAPP(c_List_Ofoldl(X16347,X16348,hAPP(c_COMBC(X16348,X16347,X16347),X16346),X16344),hAPP(c_List_Orev(X16348),X16345)), inference(variable_rename,[status(thm)],[fact_foldr__foldl])). 4.46/4.69 fof(c_0_4475, plain, ![X17453, X17454]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17454)),X17453)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17454),X17453)), inference(variable_rename,[status(thm)],[fact_add__Suc])). 4.46/4.69 fof(c_0_4476, plain, ![X2238, X2239]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2239),hAPP(c_Nat_OSuc,X2238))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2239)),X2238), inference(variable_rename,[status(thm)],[fact_add__Suc__shift])). 4.46/4.69 fof(c_0_4477, plain, ![X14067, X14068]:c_List_Oconcat(X14068,hAPP(hAPP(c_List_Omap(tc_List_Olist(X14068),tc_List_Olist(X14068)),c_List_Olist_Olist__case(tc_List_Olist(X14068),X14068,c_List_Olist_ONil(X14068),hAPP(hAPP(c_COMBB(tc_List_Olist(X14068),tc_fun(tc_List_Olist(X14068),tc_List_Olist(X14068)),X14068),c_COMBK(tc_List_Olist(X14068),tc_List_Olist(X14068))),hAPP(hAPP(c_COMBC(X14068,tc_List_Olist(X14068),tc_List_Olist(X14068)),c_List_Olist_OCons(X14068)),c_List_Olist_ONil(X14068))))),X14067))=hAPP(hAPP(c_List_Omap(tc_List_Olist(X14068),X14068),c_List_Ohd(X14068)),hAPP(c_List_Ofilter(tc_List_Olist(X14068),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X14068)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X14068),tc_List_Olist(X14068),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X14068)))),X14067)), inference(variable_rename,[status(thm)],[fact_transpose__aux__filter__head])). 4.46/4.69 fof(c_0_4478, plain, ![X15423, X15424]:c_List_Oconcat(X15424,X15423)=hAPP(c_List_Ofoldl(tc_List_Olist(X15424),tc_List_Olist(X15424),c_List_Oappend(X15424),c_List_Olist_ONil(X15424)),X15423), inference(variable_rename,[status(thm)],[fact_concat__conv__foldl])). 4.46/4.69 fof(c_0_4479, plain, ![X949, X950, X951, X952]:c_List_Omaps(X952,X951,X950,X949)=c_List_Oconcat(X951,hAPP(hAPP(c_List_Omap(X952,tc_List_Olist(X951)),X950),X949)), inference(variable_rename,[status(thm)],[fact_maps__def])). 4.46/4.69 fof(c_0_4480, plain, ![X11560, X11561]:hAPP(c_Set_OCollect(X11561),hAPP(hAPP(c_COMBC(X11561,X11561,tc_HOL_Obool),c_fequal),X11560))=hAPP(hAPP(c_Set_Oinsert(X11561),X11560),c_Orderings_Obot__class_Obot(tc_fun(X11561,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_singleton__conv])). 4.46/4.69 fof(c_0_4481, plain, ![X16779, X16780]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16780,tc_HOL_Obool)),hAPP(c_Set_OCollect(X16780),X16779))=hAPP(c_Set_OCollect(X16780),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X16780),c_fNot),X16779)), inference(variable_rename,[status(thm)],[fact_Collect__neg__eq])). 4.46/4.69 fof(c_0_4482, plain, ![X16737, X16738]:hAPP(hAPP(c_List_Omap(tc_List_Olist(X16738),tc_List_Olist(X16738)),c_List_Otl(X16738)),hAPP(c_List_Ofilter(tc_List_Olist(X16738),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X16738)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X16738),tc_List_Olist(X16738),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X16738)))),X16737))=c_List_Oconcat(tc_List_Olist(X16738),hAPP(hAPP(c_List_Omap(tc_List_Olist(X16738),tc_List_Olist(tc_List_Olist(X16738))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X16738)),X16738,c_List_Olist_ONil(tc_List_Olist(X16738)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X16738),tc_List_Olist(tc_List_Olist(X16738))),X16738),hAPP(hAPP(c_COMBC(tc_List_Olist(X16738),tc_List_Olist(tc_List_Olist(X16738)),tc_List_Olist(tc_List_Olist(X16738))),c_List_Olist_OCons(tc_List_Olist(X16738))),c_List_Olist_ONil(tc_List_Olist(X16738)))))),X16737)), inference(variable_rename,[status(thm)],[fact_transpose__aux__filter__tail])). 4.46/4.69 fof(c_0_4483, plain, ![X10432, X10433]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10433),X10432))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X10433)),c_Int_OBit0(X10432)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I9_J])). 4.46/4.69 cnf(c_0_4484, plain, (X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),c_Int_OMin)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4442, c_0_4443]), c_0_4431])). 4.46/4.69 fof(c_0_4485, plain, ![X13505, X13506]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13505),X13506)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13506),X13505), inference(variable_rename,[status(thm)],[fact_zadd__commute])). 4.46/4.69 fof(c_0_4486, plain, ![X5934]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X5934))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X5934)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I5_J])). 4.46/4.69 cnf(c_0_4487, plain, (c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1))), inference(split_conjunct,[status(thm)],[c_0_4444])). 4.46/4.69 fof(c_0_4488, plain, ![X9486, X9487, X9488]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9488),X9487)),X9486)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9488),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9487),X9486)), inference(variable_rename,[status(thm)],[fact_zadd__assoc])). 4.46/4.69 cnf(c_0_4489, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)=c_Int_OBit0(X1)), inference(split_conjunct,[status(thm)],[c_0_4445])). 4.46/4.69 fof(c_0_4490, plain, ![X12257, X12258, X12259, X12260]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12260,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12260,tc_HOL_Obool)),X12259),X12258)),X12257)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12260,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12260,tc_HOL_Obool)),X12259),X12258)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12260,tc_HOL_Obool)),X12257),X12258)), inference(variable_rename,[status(thm)],[fact_Diff__Int2])). 4.46/4.69 fof(c_0_4491, plain, ![X9470, X9471, X9472, X9473]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9473,tc_HOL_Obool)),X9472),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9473,tc_HOL_Obool)),X9471),X9470))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9473,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9473,tc_HOL_Obool)),X9472),X9471)),X9470), inference(variable_rename,[status(thm)],[fact_Int__Diff])). 4.46/4.69 fof(c_0_4492, plain, ![X4679, X4680]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X4680|hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Divides_Odivmod__int(X4680,X4679))&((X4679!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4680)=c_Divides_Odivmod__int(X4680,X4679)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X4680)&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X4679|hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X4679))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4679)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4680))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4679),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4680),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X4680,X4679)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X4679))))),c_Divides_Opdivmod(X4680,X4679))))=c_Divides_Odivmod__int(X4680,X4679)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X4680))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__pdivmod])])])])). 4.46/4.69 fof(c_0_4493, plain, ![X11946, X11947, X11948, X11949]:c_Product__Type_Oapsnd(X11949,X11948,X11947,X11946)=c_Product__Type_Omap__pair(X11947,X11947,X11949,X11948,c_Fun_Oid(X11947),X11946), inference(variable_rename,[status(thm)],[fact_apsnd__def])). 4.46/4.69 fof(c_0_4494, plain, ![X15208, X15209]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X15209|hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Divides_Odivmod__int(X15209,X15208))&((X15208=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X15208))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,X15209)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X15208))),c_Divides_Opdivmod(X15209,X15208)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X15208))))),c_Divides_Opdivmod(X15209,X15208))))=c_Divides_Odivmod__int(X15209,X15208)|X15209=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(X15208!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odivmod__int(X15209,X15208)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15209)|X15209=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__code])])])])). 4.46/4.69 fof(c_0_4495, plain, ![X5597, X5598]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X5597|c_Groups_Ozero__class_Ozero(X5598)=hAPP(c_Int_Oring__1__class_Oof__int(X5598),X5597)|~class_Rings_Oring__1(X5598))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5597),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Groups_Ouminus__class_Ouminus(X5598),hAPP(c_Int_Oring__1__class_Oof__int(X5598),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X5597)))=hAPP(c_Int_Oring__1__class_Oof__int(X5598),X5597)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X5597|~class_Rings_Oring__1(X5598))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5597),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Oring__1__class_Oof__int(X5598),X5597)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X5598),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X5598,X5598)),tc_fun(tc_Int_Oint,X5598)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5598,X5598),X5598),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X5598,X5598)),tc_fun(tc_Int_Oint,X5598)),tc_Int_Oint),c_COMBB(tc_fun(X5598,X5598),X5598,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X5598,tc_fun(tc_fun(X5598,X5598),X5598),tc_Int_Oint),c_HOL_OLet(X5598,X5598)),c_Int_Oring__1__class_Oof__int(X5598)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X5598,X5598),tc_fun(X5598,X5598)),hAPP(hAPP(c_COMBB(tc_fun(X5598,tc_fun(X5598,X5598)),tc_fun(tc_fun(X5598,X5598),tc_fun(X5598,X5598)),tc_Int_Oint),c_COMBS(X5598,X5598,X5598)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X5598,X5598),tc_fun(X5598,tc_fun(X5598,X5598))),hAPP(hAPP(c_COMBB(tc_fun(X5598,tc_fun(X5598,X5598)),tc_fun(tc_fun(X5598,X5598),tc_fun(X5598,tc_fun(X5598,X5598))),tc_Int_Oint),c_COMBB(X5598,tc_fun(X5598,X5598),X5598)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5598,tc_fun(X5598,X5598)),tc_Int_Oint),c_If(X5598)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(X5598,X5598,X5598),c_Groups_Oplus__class_Oplus(X5598)),c_COMBI(X5598))))),hAPP(hAPP(c_COMBC(X5598,X5598,X5598),hAPP(hAPP(c_COMBB(X5598,tc_fun(X5598,X5598),X5598),c_Groups_Oplus__class_Oplus(X5598)),hAPP(hAPP(c_COMBS(X5598,X5598,X5598),c_Groups_Oplus__class_Oplus(X5598)),c_COMBI(X5598)))),c_Groups_Oone__class_Oone(X5598))))),c_Divides_Odivmod__int(X5597,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X5597|~class_Rings_Oring__1(X5598)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__num])])])])). 4.46/4.69 fof(c_0_4496, plain, ![X8890, X8891, X8892]:(~class_Int_Onumber__ring(X8892)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8892),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8892),hAPP(hAPP(c_Power_Opower__class_Opower(X8892),X8891),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X8892),X8890),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8892),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8892),hAPP(c_Int_Onumber__class_Onumber__of(X8892),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X8891)),X8890))=hAPP(hAPP(c_Power_Opower__class_Opower(X8892),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8892),X8891),X8890)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power2__diff])])])). 4.46/4.69 cnf(c_0_4497, plain, (hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), inference(split_conjunct,[status(thm)],[fact_numeral__2__eq__2])). 4.46/4.69 cnf(c_0_4498, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OPls)=X1), inference(split_conjunct,[status(thm)],[c_0_4446])). 4.46/4.69 cnf(c_0_4499, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_4447, c_0_4448])). 4.46/4.69 cnf(c_0_4500, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)), inference(rw,[status(thm)],[c_0_4449, c_0_4443])). 4.46/4.69 fof(c_0_4501, plain, ![X9467, X9468, X9469]:(~class_Int_Onumber__ring(X9469)|hAPP(hAPP(c_Power_Opower__class_Opower(X9469),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9469),X9468),X9467)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9469),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9469),hAPP(hAPP(c_Power_Opower__class_Opower(X9469),X9468),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X9469),X9467),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9469),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9469),hAPP(c_Int_Onumber__class_Onumber__of(X9469),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X9468)),X9467))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__sum])])). 4.46/4.69 fof(c_0_4502, plain, ![X16491, X16492]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16492),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16491),c_Groups_Oone__class_Oone(tc_Int_Oint)),X16492))),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X16491)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X16492))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__zmod__mult__2])])). 4.46/4.69 fof(c_0_4503, plain, ![X8738]:(((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X8738,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X8738),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))=hAPP(c_Code__Numeral_Oint__of,X8738)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X8738)&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X8738,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|hAPP(c_Code__Numeral_Oint__of,X8738)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X8738),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X8738))&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X8738|hAPP(c_Code__Numeral_Oint__of,X8738)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__of__code])])])])). 4.46/4.69 fof(c_0_4504, plain, ![X7023, X7024]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7024))|c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X7023)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X7024))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X7023,X7024)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__zmod__mult__2])])])). 4.46/4.69 fof(c_0_4505, plain, ![X8304, X8305]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8305),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X8304))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X8305))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8304),c_Groups_Oone__class_Oone(tc_Int_Oint))),X8305)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__zdiv__mult__2])])). 4.46/4.69 fof(c_0_4506, plain, ![X3255, X3256, X3257]:((X3256!=c_Groups_Ozero__class_Ozero(X3257)|X3255!=c_Groups_Ozero__class_Ozero(X3257)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3257),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3257),hAPP(hAPP(c_Power_Opower__class_Opower(X3257),X3256),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X3257),X3255),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X3257)))|~class_Rings_Olinordered__idom(X3257))&((X3256=c_Groups_Ozero__class_Ozero(X3257)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3257),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3257),hAPP(hAPP(c_Power_Opower__class_Opower(X3257),X3256),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X3257),X3255),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X3257)))|~class_Rings_Olinordered__idom(X3257))&(X3255=c_Groups_Ozero__class_Ozero(X3257)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3257),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3257),hAPP(hAPP(c_Power_Opower__class_Opower(X3257),X3256),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X3257),X3255),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X3257)))|~class_Rings_Olinordered__idom(X3257)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sum__power2__le__zero__iff])])])])). 4.46/4.69 fof(c_0_4507, plain, ![X16445, X16446]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X16446)))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X16445)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X16446)))),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X16445)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X16446))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X16446)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X16445),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X16446)))),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X16445)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X16446))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmod__number__of__Bit1])])])). 4.46/4.69 fof(c_0_4508, plain, ![X1178, X1179]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1179))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1178),X1179)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1178))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1179))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__zdiv__mult__2])])])). 4.46/4.69 fof(c_0_4509, plain, ![X13314, X13315, X13316]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13316),c_Groups_Ozero__class_Ozero(X13316)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13316),hAPP(hAPP(c_Power_Opower__class_Opower(X13316),X13315),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X13316),X13314),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))|(c_Groups_Ozero__class_Ozero(X13316)!=X13314|X13315!=c_Groups_Ozero__class_Ozero(X13316))|~class_Rings_Olinordered__idom(X13316))&((c_Groups_Ozero__class_Ozero(X13316)=X13314|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13316),c_Groups_Ozero__class_Ozero(X13316)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13316),hAPP(hAPP(c_Power_Opower__class_Opower(X13316),X13315),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X13316),X13314),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))|~class_Rings_Olinordered__idom(X13316))&(X13315=c_Groups_Ozero__class_Ozero(X13316)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13316),c_Groups_Ozero__class_Ozero(X13316)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13316),hAPP(hAPP(c_Power_Opower__class_Opower(X13316),X13315),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X13316),X13314),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))|~class_Rings_Olinordered__idom(X13316)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sum__power2__gt__zero__iff])])])])). 4.46/4.69 fof(c_0_4510, plain, ![X15159, X15160, X15161]:(((c_Groups_Ozero__class_Ozero(X15161)=X15159|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15161),hAPP(hAPP(c_Power_Opower__class_Opower(X15161),X15160),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X15161),X15159),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))!=c_Groups_Ozero__class_Ozero(X15161)|~class_Rings_Olinordered__idom(X15161))&(c_Groups_Ozero__class_Ozero(X15161)=X15160|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15161),hAPP(hAPP(c_Power_Opower__class_Opower(X15161),X15160),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X15161),X15159),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))!=c_Groups_Ozero__class_Ozero(X15161)|~class_Rings_Olinordered__idom(X15161)))&(c_Groups_Ozero__class_Ozero(X15161)!=X15159|c_Groups_Ozero__class_Ozero(X15161)!=X15160|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15161),hAPP(hAPP(c_Power_Opower__class_Opower(X15161),X15160),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X15161),X15159),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_Groups_Ozero__class_Ozero(X15161)|~class_Rings_Olinordered__idom(X15161))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sum__power2__eq__zero__iff])])])])). 4.46/4.69 fof(c_0_4511, plain, ![X3558, X3559, X3560]:(~class_Rings_Olinordered__idom(X3560)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3560),c_Groups_Ozero__class_Ozero(X3560)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3560),hAPP(hAPP(c_Power_Opower__class_Opower(X3560),X3559),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X3560),X3558),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__ge__zero])])). 4.46/4.69 fof(c_0_4512, plain, ![X11314, X11315, X11316]:(~class_Groups_Omonoid__mult(X11316)|hAPP(hAPP(c_Power_Opower__class_Opower(X11316),X11315),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X11314)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11316),X11315),hAPP(hAPP(c_Power_Opower__class_Opower(X11316),hAPP(hAPP(c_Power_Opower__class_Opower(X11316),X11315),X11314)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__odd__eq])])). 4.46/4.69 fof(c_0_4513, plain, ![X14135, X14136, X14137]:((hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk409_3(X14135,X14136,X14137)),esk410_3(X14135,X14136,X14137))))|hBOOL(hAPP(hAPP(X14135,X14137),X14136))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X14137),X14136))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk409_3(X14135,X14136,X14137)),esk410_3(X14135,X14136,X14137))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk410_3(X14135,X14136,X14137)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X14135,esk409_3(X14135,X14136,X14137)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),esk410_3(X14135,X14136,X14137))))|hBOOL(hAPP(hAPP(X14135,X14137),X14136))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X14137),X14136))))&(~hBOOL(hAPP(hAPP(X14135,esk409_3(X14135,X14136,X14137)),esk410_3(X14135,X14136,X14137)))|hBOOL(hAPP(hAPP(X14135,X14137),X14136))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X14137),X14136)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_negDivAlg_Opinduct])])])])])). 4.46/4.69 fof(c_0_4514, plain, ![X5805, X5806, X5807]:(~class_Rings_Oring__1(X5807)|hAPP(hAPP(c_Power_Opower__class_Opower(X5807),X5806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X5805))=hAPP(hAPP(c_Power_Opower__class_Opower(X5807),hAPP(c_Groups_Ouminus__class_Ouminus(X5807),X5806)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X5805))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus__even])])). 4.46/4.69 fof(c_0_4515, plain, ![X16279, X16280, X16281]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk474_3(X16279,X16280,X16281)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X16280))),X16281)))|hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X16280)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X16280)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X16280),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X16280)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X16280)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X16280),hAPP(hAPP(c_COMBB(tc_List_Olist(X16280),tc_fun(tc_Nat_Onat,X16280),tc_Nat_Onat),c_List_Onth(X16280)),hAPP(c_List_Onth(tc_List_Olist(X16280)),X16281))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X16280))),X16281)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X16279))=c_List_Otranspose(X16280,X16281)|c_List_Olist_ONil(tc_List_Olist(X16280))=X16281)&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16280)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X16280)),X16281),esk474_3(X16279,X16280,X16281)))!=X16279|hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X16280)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X16280)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X16280),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X16280)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X16280)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X16280),hAPP(hAPP(c_COMBB(tc_List_Olist(X16280),tc_fun(tc_Nat_Onat,X16280),tc_Nat_Onat),c_List_Onth(X16280)),hAPP(c_List_Onth(tc_List_Olist(X16280)),X16281))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X16280))),X16281)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X16279))=c_List_Otranspose(X16280,X16281)|c_List_Olist_ONil(tc_List_Olist(X16280))=X16281))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk474_3(X16279,X16280,X16281)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X16280))),X16281)))|hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X16280)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X16280)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X16280),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X16280)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X16280)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X16280),hAPP(hAPP(c_COMBB(tc_List_Olist(X16280),tc_fun(tc_Nat_Onat,X16280),tc_Nat_Onat),c_List_Onth(X16280)),hAPP(c_List_Onth(tc_List_Olist(X16280)),X16281))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X16280))),X16281)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X16279))=c_List_Otranspose(X16280,X16281)|X16279!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16280)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X16280)),X16281),esk474_3(X16279,X16280,X16281)))!=X16279|hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X16280)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X16280)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X16280),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X16280)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X16280)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X16280),hAPP(hAPP(c_COMBB(tc_List_Olist(X16280),tc_fun(tc_Nat_Onat,X16280),tc_Nat_Onat),c_List_Onth(X16280)),hAPP(c_List_Onth(tc_List_Olist(X16280)),X16281))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X16280))),X16281)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X16279))=c_List_Otranspose(X16280,X16281)|X16279!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transpose__rectangle])])])])])). 4.46/4.69 cnf(c_0_4516, plain, (c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_4450])). 4.46/4.69 cnf(c_0_4517, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))=c_List_Oupt(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4451])). 4.46/4.69 fof(c_0_4518, plain, ![X1515]:c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1515),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_atLeastLessThan0])). 4.46/4.69 fof(c_0_4519, plain, ![X8086, X8087, X8088]:((hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk229_3(X8086,X8087,X8088)),esk230_3(X8086,X8087,X8088))))|hBOOL(hAPP(hAPP(X8086,X8088),X8087))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X8088),X8087))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk229_3(X8086,X8087,X8088)),esk230_3(X8086,X8087,X8088)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk230_3(X8086,X8087,X8088)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X8086,esk229_3(X8086,X8087,X8088)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),esk230_3(X8086,X8087,X8088))))|hBOOL(hAPP(hAPP(X8086,X8088),X8087))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X8088),X8087))))&(~hBOOL(hAPP(hAPP(X8086,esk229_3(X8086,X8087,X8088)),esk230_3(X8086,X8087,X8088)))|hBOOL(hAPP(hAPP(X8086,X8088),X8087))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X8088),X8087)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_posDivAlg_Opinduct])])])])])). 4.46/4.69 fof(c_0_4520, plain, ![X2869, X2870, X2871]:(~class_Groups_Omonoid__mult(X2871)|hAPP(hAPP(c_Power_Opower__class_Opower(X2871),hAPP(hAPP(c_Power_Opower__class_Opower(X2871),X2870),X2869)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Power_Opower__class_Opower(X2871),X2870),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2869))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__even__eq])])])). 4.46/4.69 fof(c_0_4521, plain, ![X8155, X8156]:(~class_Rings_Olinordered__idom(X8156)|hAPP(c_Groups_Oabs__class_Oabs(X8156),hAPP(hAPP(c_Power_Opower__class_Opower(X8156),X8155),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=hAPP(hAPP(c_Power_Opower__class_Opower(X8156),X8155),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__power2])])])). 4.46/4.69 fof(c_0_4522, plain, ![X1329, X1330]:(~class_Rings_Olinordered__idom(X1330)|hAPP(hAPP(c_Power_Opower__class_Opower(X1330),X1329),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Power_Opower__class_Opower(X1330),hAPP(c_Groups_Oabs__class_Oabs(X1330),X1329)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power2__abs])])])). 4.46/4.69 fof(c_0_4523, plain, ![X4943, X4944]:(~class_Rings_Oring__1(X4944)|hAPP(hAPP(c_Power_Opower__class_Opower(X4944),X4943),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Power_Opower__class_Opower(X4944),hAPP(c_Groups_Ouminus__class_Ouminus(X4944),X4943)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__minus])])). 4.46/4.69 fof(c_0_4524, plain, ![X8791]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X8791,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X8791,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))&(c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X8791,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X8791,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod2__gr__0])])). 4.46/4.69 fof(c_0_4525, plain, ![X8600, X8601, X8602]:(~class_Rings_Ocomm__semiring__1(X8602)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8602),X8601),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8602),hAPP(hAPP(c_Power_Opower__class_Opower(X8602),X8601),X8600)),hAPP(hAPP(c_Power_Opower__class_Opower(X8602),X8601),X8600)))=hAPP(hAPP(c_Power_Opower__class_Opower(X8602),X8601),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X8600)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J])])])). 4.46/4.69 fof(c_0_4526, plain, ![X16840, X16841]:(~class_Rings_Osemiring__1(X16841)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16840))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16841),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X16841),hAPP(c_Int_Onat,X16840))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X16841),hAPP(c_Int_Onat,X16840)))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X16841),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X16840))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__double])])])). 4.46/4.69 fof(c_0_4527, plain, ![X2674, X2675]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2674),X2675)))|c_Divides_OnegDivAlg(X2674,X2675)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2674),X2675))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2675)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2674),X2675)))|c_Divides_OnegDivAlg(X2674,X2675)=hAPP(c_Divides_Oadjust(X2675),c_Divides_OnegDivAlg(X2674,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2675)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2675)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn])])])])). 4.46/4.69 fof(c_0_4528, plain, ![X4357, X4358]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4358),X4357)))|hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4358),X4357))=c_Divides_OnegDivAlg(X4358,X4357))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4357),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4358),X4357))=c_Divides_OnegDivAlg(X4358,X4357)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4357),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4358),X4357)))|hAPP(c_Divides_Oadjust(X4357),c_Divides_OnegDivAlg(X4358,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X4357)))=c_Divides_OnegDivAlg(X4358,X4357))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_negDivAlg_Osimps])])])])). 4.46/4.69 fof(c_0_4529, plain, ![X1757, X1758, X1759, X1760]:hAPP(c_Set_OCollect(X1760),hAPP(hAPP(c_COMBC(X1760,tc_fun(X1759,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1759,tc_fun(tc_fun(X1759,tc_HOL_Obool),tc_HOL_Obool),X1760),c_member(X1759)),X1758)),X1757))=hAPP(c_Set_Ovimage(X1760,X1759,X1758),X1757), inference(variable_rename,[status(thm)],[fact_vimage__def])). 4.46/4.69 cnf(c_0_4530, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4))=hAPP(c_Set_Ovimage(X1,X2,X4),hAPP(c_Set_OCollect(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4452])). 4.46/4.69 cnf(c_0_4531, plain, (X1=hAPP(c_Set_OCollect(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_4453]), ['final']). 4.46/4.69 fof(c_0_4532, plain, ![X16688, X16689, X16690]:(~class_Rings_Ocomm__semiring__1(X16690)|hAPP(hAPP(c_Power_Opower__class_Opower(X16690),X16689),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X16688))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16690),hAPP(hAPP(c_Power_Opower__class_Opower(X16690),X16689),X16688)),hAPP(hAPP(c_Power_Opower__class_Opower(X16690),X16689),X16688))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J])])])). 4.46/4.69 fof(c_0_4533, plain, ![X8339, X8340]:hAPP(c_Set_OCollect(tc_List_Olist(X8340)),hAPP(hAPP(c_COMBC(tc_List_Olist(X8340),tc_fun(X8340,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X8340,tc_HOL_Obool),tc_fun(tc_fun(X8340,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X8340)),c_Orderings_Oord__class_Oless__eq(tc_fun(X8340,tc_HOL_Obool))),c_List_Oset(X8340))),X8339))=c_List_Olists(X8340,X8339), inference(variable_rename,[status(thm)],[fact_lists__eq__set])). 4.46/4.69 fof(c_0_4534, plain, ![X10316, X10317, X10318]:(~class_Rings_Olinordered__idom(X10318)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10318),X10317),c_Groups_Ozero__class_Ozero(X10318)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10318),hAPP(hAPP(c_Power_Opower__class_Opower(X10318),X10317),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X10316)))),c_Groups_Ozero__class_Ozero(X10318))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_odd__power__less__zero])])])). 4.46/4.69 fof(c_0_4535, plain, ![X584, X585]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X585),X584))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X584),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Divides_Oadjust(X584),c_Divides_OposDivAlg(X585,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X584)))=c_Divides_OposDivAlg(X585,X584))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X584),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Divides_OposDivAlg(X585,X584)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X585))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X585),X584))|c_Divides_OposDivAlg(X585,X584)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X585)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg_Osimps])])])). 4.46/4.69 fof(c_0_4536, plain, ![X391, X392]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X391),X392))|hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X391)=c_Divides_OposDivAlg(X391,X392)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X392)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X391),X392))|hAPP(c_Divides_Oadjust(X392),c_Divides_OposDivAlg(X391,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X392)))=c_Divides_OposDivAlg(X391,X392)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X392)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn])])])])). 4.46/4.69 fof(c_0_4537, plain, ![X15001]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15001))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15001),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__n__div__2__gt__zero])])). 4.46/4.69 fof(c_0_4538, plain, ![X2864, X2865]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2865)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2864))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2865),X2864)), inference(variable_rename,[status(thm)],[fact_zminus__zadd__distrib])). 4.46/4.69 fof(c_0_4539, plain, ![X11696, X11697]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X11697),X11696)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11697),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11696)), inference(variable_rename,[status(thm)],[fact_diff__int__def])). 4.46/4.69 fof(c_0_4540, plain, ![X2358, X2359, X2360]:(~class_Rings_Olinordered__idom(X2360)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2360),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2360),hAPP(hAPP(c_Power_Opower__class_Opower(X2360),X2359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2360),X2358),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X2360)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__sum__power2__lt__zero])])])). 4.46/4.69 fof(c_0_4541, plain, ![X12221, X12222, X12223]:(~hBOOL(hAPP(c_List_Odistinct(X12223),X12222))|(~hBOOL(hAPP(hAPP(c_member(X12223),X12221),hAPP(c_List_Oset(X12223),X12222)))|hAPP(hAPP(c_List_Olist_OCons(X12223),X12221),hAPP(c_List_Orev(X12223),c_List_OtakeWhile(X12223,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12223),c_fNot),hAPP(hAPP(c_COMBC(X12223,X12223,tc_HOL_Obool),c_fequal),X12221)),X12222)))=c_List_OdropWhile(X12223,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12223),c_fNot),hAPP(hAPP(c_COMBC(X12223,X12223,tc_HOL_Obool),c_fequal),X12221)),hAPP(c_List_Orev(X12223),X12222)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dropWhile__neq__rev])])])). 4.46/4.69 fof(c_0_4542, plain, ![X10283, X10284, X10285]:hAPP(hAPP(c_List_Odrop(X10285),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10285)),c_List_OtakeWhile(X10285,X10284,X10283))),X10283)=c_List_OdropWhile(X10285,X10284,X10283), inference(variable_rename,[status(thm)],[fact_dropWhile__eq__drop])). 4.46/4.69 fof(c_0_4543, plain, ![X13228, X13229]:(~class_Rings_Oring__1(X13229)|hAPP(hAPP(c_Power_Opower__class_Opower(X13229),hAPP(c_Groups_Ouminus__class_Ouminus(X13229),c_Groups_Oone__class_Oone(X13229))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X13228)))=hAPP(c_Groups_Ouminus__class_Ouminus(X13229),c_Groups_Oone__class_Oone(X13229))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__minus1__odd])])])). 4.46/4.69 fof(c_0_4544, plain, ![X6943, X6944]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6944),c_Groups_Ozero__class_Ozero(X6944)),X6943))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6944),c_Groups_Ozero__class_Ozero(X6944)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6944),X6943),hAPP(c_Int_Onumber__class_Onumber__of(X6944),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|(~class_Int_Onumber__ring(X6944)|~class_Fields_Olinordered__field__inverse__zero(X6944)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6944),c_Groups_Ozero__class_Ozero(X6944)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6944),X6943),hAPP(c_Int_Onumber__class_Onumber__of(X6944),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6944),c_Groups_Ozero__class_Ozero(X6944)),X6943))|(~class_Int_Onumber__ring(X6944)|~class_Fields_Olinordered__field__inverse__zero(X6944)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff])])])). 4.46/4.69 fof(c_0_4545, plain, ![X10360, X10361, X10362]:(~class_Rings_Olinordered__idom(X10362)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10362),c_Groups_Ozero__class_Ozero(X10362)),hAPP(hAPP(c_Power_Opower__class_Opower(X10362),X10361),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X10360))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__even__power_H])])). 4.46/4.69 fof(c_0_4546, plain, ![X3104, X3105]:(~class_Int_Onumber__ring(X3105)|hAPP(hAPP(c_Power_Opower__class_Opower(X3105),hAPP(c_Int_Onumber__class_Onumber__of(X3105),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3104)))=hAPP(c_Int_Onumber__class_Onumber__of(X3105),c_Int_OMin)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__m1__odd])])])). 4.46/4.69 fof(c_0_4547, plain, ![X5227, X5228]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5228)))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5227)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5228))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X5227))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X5228))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5228)))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X5227))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X5228)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5227)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5228)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__number__of__Bit1])])])). 4.46/4.69 fof(c_0_4548, plain, ![X5252, X5253]:(~class_Rings_Oring__1(X5253)|c_Groups_Oone__class_Oone(X5253)=hAPP(hAPP(c_Power_Opower__class_Opower(X5253),hAPP(c_Groups_Ouminus__class_Ouminus(X5253),c_Groups_Oone__class_Oone(X5253))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X5252))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__minus1__even])])])). 4.46/4.69 fof(c_0_4549, plain, ![X8564]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X8564))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X8564),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__2__gt__zero])])])). 4.46/4.69 fof(c_0_4550, plain, ![X16875, X16876]:((hAPP(c_Nat_OSuc,X16875)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X16876)|hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X16876))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X16875))))))&(~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X16876))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X16875)))))|hAPP(c_Nat_OSuc,X16875)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X16876))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__Suc])])). 4.46/4.69 fof(c_0_4551, plain, ![X4482, X4483, X4484]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4484,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4484,tc_HOL_Obool)),hAPP(c_Set_OCollect(X4484),X4483))),hAPP(c_Set_OCollect(X4484),X4482))=hAPP(c_Set_OCollect(X4484),hAPP(hAPP(c_COMBS(X4484,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4484),c_fimplies),X4483)),X4482)), inference(variable_rename,[status(thm)],[fact_Collect__imp__eq])). 4.46/4.69 fof(c_0_4552, plain, ![X4794, X4795, X4796]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4796,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4796,tc_HOL_Obool)),X4795),X4794))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4796,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4796,tc_HOL_Obool)),X4795)),X4794), inference(variable_rename,[status(thm)],[fact_Compl__Diff__eq])). 4.46/4.69 fof(c_0_4553, plain, ![X13560, X13561]:(~class_Int_Onumber__ring(X13561)|c_Groups_Oone__class_Oone(X13561)=hAPP(hAPP(c_Power_Opower__class_Opower(X13561),hAPP(c_Int_Onumber__class_Onumber__of(X13561),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X13560))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__m1__even])])])). 4.46/4.69 fof(c_0_4554, plain, ![X2980, X2981]:(~class_Rings_Olinordered__idom(X2981)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2981),c_Groups_Ozero__class_Ozero(X2981)),hAPP(hAPP(c_Power_Opower__class_Opower(X2981),X2980),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__power2])])])). 4.46/4.69 fof(c_0_4555, plain, ![X13273, X13274]:(~class_Complete__Lattice_Ocomplete__lattice(X13274)|c_Complete__Lattice_OSup__class_OSup(X13274,hAPP(c_Set_OCollect(X13274),hAPP(hAPP(c_COMBB(tc_fun(X13274,tc_HOL_Obool),tc_HOL_Obool,X13274),c_HOL_OAll(X13274)),hAPP(hAPP(c_COMBB(tc_fun(X13274,tc_HOL_Obool),tc_fun(X13274,tc_HOL_Obool),X13274),hAPP(c_COMBS(X13274,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X13274),c_fimplies),hAPP(hAPP(c_COMBC(X13274,tc_fun(X13274,tc_HOL_Obool),tc_HOL_Obool),c_member(X13274)),X13273)))),c_Orderings_Oord__class_Oless__eq(X13274)))))=c_Complete__Lattice_OInf__class_OInf(X13274,X13273)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__Sup])])). 4.46/4.69 cnf(c_0_4556, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))=X2), inference(split_conjunct,[status(thm)],[c_0_4454])). 4.46/4.69 fof(c_0_4557, plain, ![X2624, X2625, X2626, X2627]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2626,tc_fun(X2627,tc_HOL_Obool)),X2625),hAPP(hAPP(c_COMBB(tc_fun(X2627,tc_HOL_Obool),tc_fun(X2627,tc_HOL_Obool),X2626),c_Set_OCollect(X2627)),hAPP(c_COMBC(X2627,X2626,tc_HOL_Obool),X2624)))=hAPP(c_Set_OCollect(X2627),hAPP(hAPP(c_COMBB(tc_fun(X2626,tc_HOL_Obool),tc_HOL_Obool,X2627),c_HOL_OAll(X2626)),hAPP(hAPP(c_COMBB(tc_fun(X2626,tc_HOL_Obool),tc_fun(X2626,tc_HOL_Obool),X2627),hAPP(c_COMBS(X2626,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2626),c_fimplies),hAPP(hAPP(c_COMBC(X2626,tc_fun(X2626,tc_HOL_Obool),tc_HOL_Obool),c_member(X2626)),X2625)))),X2624))), inference(variable_rename,[status(thm)],[fact_Collect__ball__eq])). 4.46/4.69 fof(c_0_4558, plain, ![X13421, X13422]:(~class_Complete__Lattice_Ocomplete__lattice(X13422)|c_Complete__Lattice_OInf__class_OInf(X13422,hAPP(c_Set_OCollect(X13422),hAPP(hAPP(c_COMBB(tc_fun(X13422,tc_HOL_Obool),tc_HOL_Obool,X13422),c_HOL_OAll(X13422)),hAPP(hAPP(c_COMBB(tc_fun(X13422,tc_HOL_Obool),tc_fun(X13422,tc_HOL_Obool),X13422),hAPP(c_COMBS(X13422,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X13422),c_fimplies),hAPP(hAPP(c_COMBC(X13422,tc_fun(X13422,tc_HOL_Obool),tc_HOL_Obool),c_member(X13422)),X13421)))),hAPP(c_COMBC(X13422,X13422,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X13422))))))=c_Complete__Lattice_OSup__class_OSup(X13422,X13421)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__Inf])])). 4.46/4.69 fof(c_0_4559, plain, ![X8448, X8449]:((~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X8448))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8449)),c_Int_Onat)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X8449)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8448))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X8449)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8448)))|hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X8448))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8449)),c_Int_Onat))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__number__of])])). 4.46/4.69 fof(c_0_4560, plain, ![X341, X342]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X342)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X341)))|hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X341))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X342)),c_Int_Onat))))))&(~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X341))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X342)),c_Int_Onat)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X342)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X341))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__number__of])])). 4.46/4.69 fof(c_0_4561, plain, ![X4753, X4754]:(~class_Int_Onumber__ring(X4754)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4754),X4753),X4753)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4754),hAPP(c_Int_Onumber__class_Onumber__of(X4754),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X4753)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2])])). 4.46/4.69 fof(c_0_4562, plain, ![X11642, X11643]:(~class_Int_Onumber__ring(X11643)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11643),X11642),X11642)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11643),X11642),hAPP(c_Int_Onumber__class_Onumber__of(X11643),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])])). 4.46/4.69 fof(c_0_4563, plain, ![X858, X859]:(~class_Groups_Omonoid__mult(X859)|hAPP(hAPP(c_Power_Opower__class_Opower(X859),X858),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X859),X858),X858)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power2__eq__square])])])). 4.46/4.69 fof(c_0_4564, plain, ![X4563, X4564]:(~class_Rings_Ocomm__semiring__1(X4564)|hAPP(hAPP(c_Power_Opower__class_Opower(X4564),X4563),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4564),X4563),X4563)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J])])])). 4.46/4.69 fof(c_0_4565, plain, ![X6303, X6304]:(~class_Groups_Omonoid__mult(X6304)|hAPP(hAPP(c_Power_Opower__class_Opower(X6304),X6303),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6304),X6303),X6303)),X6303)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power3__eq__cube])])])). 4.46/4.69 cnf(c_0_4566, plain, (hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), inference(split_conjunct,[status(thm)],[fact_numeral__3__eq__3])). 4.46/4.69 fof(c_0_4567, plain, ![X1953, X1954, X1955]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1954)))|hAPP(hAPP(c_HOL_OLet(X1955,X1955),hAPP(hAPP(c_Power_Opower__class_Opower(X1955),X1953),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1954))),hAPP(hAPP(c_COMBS(X1955,X1955,X1955),hAPP(hAPP(c_COMBB(X1955,tc_fun(X1955,X1955),X1955),c_Groups_Otimes__class_Otimes(X1955)),hAPP(c_Groups_Otimes__class_Otimes(X1955),X1953))),c_COMBI(X1955)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1955),X1953),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1954)))|~class_Int_Onumber__ring(X1955))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1954)))|hAPP(hAPP(c_Power_Opower__class_Opower(X1955),X1953),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1954)))=c_Groups_Oone__class_Oone(X1955)|~class_Int_Onumber__ring(X1955))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__number__of__odd])])])])). 4.46/4.69 fof(c_0_4568, plain, ![X5701, X5702, X5703, X5704]:c_Nitpick_Oprod(X5704,X5703,X5702,X5701)=hAPP(c_Set_OCollect(tc_prod(X5704,X5703)),hAPP(c_Product__Type_Oprod_Oprod__case(X5704,X5703,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5704,tc_fun(X5703,tc_HOL_Obool),tc_fun(X5703,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5703,tc_HOL_Obool),tc_fun(X5703,tc_HOL_Obool)),X5704),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5703)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5704),c_fconj),hAPP(hAPP(c_COMBC(X5704,tc_fun(X5704,tc_HOL_Obool),tc_HOL_Obool),c_member(X5704)),X5702)))),hAPP(hAPP(c_COMBC(X5703,tc_fun(X5703,tc_HOL_Obool),tc_HOL_Obool),c_member(X5703)),X5701)))), inference(variable_rename,[status(thm)],[fact_Nitpick_Oprod__def])). 4.46/4.69 cnf(c_0_4569, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_Set_OCollect(X1),X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_OCollect(X2),X4)))=hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X3))),X4)))), inference(split_conjunct,[status(thm)],[c_0_4455])). 4.46/4.69 fof(c_0_4570, plain, ![X16340, X16341]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X16341)))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X16340),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X16341)))=c_Groups_Oone__class_Oone(tc_Int_Oint))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X16341)))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X16340),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X16341)))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X16340),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X16341))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16340))),c_COMBI(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zpower__number__of__odd])])])). 4.46/4.69 fof(c_0_4571, plain, ![X3398]:(~class_Int_Onumber__ring(X3398)|hAPP(c_Int_Onumber__class_Onumber__of(X3398),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3398),c_Groups_Oone__class_Oone(X3398)),c_Groups_Oone__class_Oone(X3398))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_one__add__one__is__two])])])). 4.46/4.69 fof(c_0_4572, plain, ![X4086, X4087]:((c_Groups_Ozero__class_Ozero(X4087)!=X4086|c_Groups_Ozero__class_Ozero(X4087)=hAPP(hAPP(c_Power_Opower__class_Opower(X4087),X4086),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|~class_Rings_Oring__1__no__zero__divisors(X4087))&(c_Groups_Ozero__class_Ozero(X4087)!=hAPP(hAPP(c_Power_Opower__class_Opower(X4087),X4086),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|c_Groups_Ozero__class_Ozero(X4087)=X4086|~class_Rings_Oring__1__no__zero__divisors(X4087))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__eq__power2])])])). 4.46/4.69 fof(c_0_4573, plain, ![X5229, X5230, X5231]:(~hBOOL(hAPP(c_List_Odistinct(X5231),X5230))|(~hBOOL(hAPP(hAPP(c_member(X5231),X5229),hAPP(c_List_Oset(X5231),X5230)))|c_List_OtakeWhile(X5231,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5231),c_fNot),hAPP(hAPP(c_COMBC(X5231,X5231,tc_HOL_Obool),c_fequal),X5229)),hAPP(c_List_Orev(X5231),X5230))=hAPP(c_List_Orev(X5231),hAPP(c_List_Otl(X5231),c_List_OdropWhile(X5231,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5231),c_fNot),hAPP(hAPP(c_COMBC(X5231,X5231,tc_HOL_Obool),c_fequal),X5229)),X5230))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__neq__rev])])). 4.46/4.69 fof(c_0_4574, plain, ![X10511, X10512, X10513]:hAPP(hAPP(c_List_Odrop(X10513),X10512),hAPP(c_List_Otl(X10513),X10511))=hAPP(c_List_Otl(X10513),hAPP(hAPP(c_List_Odrop(X10513),X10512),X10511)), inference(variable_rename,[status(thm)],[fact_drop__tl])). 4.46/4.69 fof(c_0_4575, plain, ![X511, X512, X513]:hAPP(hAPP(c_List_Odrop(X513),hAPP(c_Nat_OSuc,X512)),X511)=hAPP(hAPP(c_List_Odrop(X513),X512),hAPP(c_List_Otl(X513),X511)), inference(variable_rename,[status(thm)],[fact_drop__Suc])). 4.46/4.69 fof(c_0_4576, plain, ![X4399, X4400, X4401]:(~class_Int_Onumber__ring(X4401)|hAPP(hAPP(c_HOL_OLet(X4401,X4401),hAPP(hAPP(c_Power_Opower__class_Opower(X4401),X4400),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4399))),hAPP(hAPP(c_COMBS(X4401,X4401,X4401),c_Groups_Otimes__class_Otimes(X4401)),c_COMBI(X4401)))=hAPP(hAPP(c_Power_Opower__class_Opower(X4401),X4400),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X4399)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__number__of__even])])])). 4.46/4.69 fof(c_0_4577, plain, ![X6297]:(~class_Rings_Osemiring__1(X6297)|hAPP(hAPP(c_Power_Opower__class_Opower(X6297),c_Groups_Oone__class_Oone(X6297)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Oone__class_Oone(X6297)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_one__power2])])])). 4.46/4.69 fof(c_0_4578, plain, ![X4542]:(~class_Rings_Osemiring__1(X4542)|hAPP(hAPP(c_Power_Opower__class_Opower(X4542),c_Groups_Ozero__class_Ozero(X4542)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Ozero__class_Ozero(X4542)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__power2])])])). 4.46/4.69 fof(c_0_4579, plain, ![X1168, X1169, X1170]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1170)),X1168)),X1169)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1170)),hAPP(hAPP(c_List_Otake(X1170),X1169),X1168)), inference(variable_rename,[status(thm)],[fact_length__take])). 4.46/4.69 fof(c_0_4580, plain, ![X5786, X5787]:((~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X5787))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X5786))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5787)),hAPP(c_Nat_OSuc,X5786))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5787)),hAPP(c_Nat_OSuc,X5786)))|hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X5787))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X5786)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__Suc])])). 4.46/4.69 fof(c_0_4581, plain, ![X16493, X16494, X16495]:(~class_Rings_Oring__1(X16495)|~class_Rings_Oinverse(X16495)|c_Nitpick_Oof__frac(X16494,X16495,X16493)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16495),hAPP(c_Int_Oring__1__class_Oof__int(X16495),hAPP(c_Nitpick_Onum(X16494),X16493))),hAPP(c_Int_Oring__1__class_Oof__int(X16495),hAPP(c_Nitpick_Odenom(X16494),X16493)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oof__frac__def])])). 4.46/4.69 fof(c_0_4582, plain, ![X14420]:c_Nitpick_Onum(X14420)=hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X14420,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X14420)), inference(variable_rename,[status(thm)],[fact_Nitpick_Onum__def])). 4.46/4.69 fof(c_0_4583, plain, ![X15229]:hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X15229,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X15229))=c_Nitpick_Odenom(X15229), inference(variable_rename,[status(thm)],[fact_Nitpick_Odenom__def])). 4.46/4.69 fof(c_0_4584, plain, ![X10969, X10970]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X10970)),hAPP(c_Nat_OSuc,X10969)))|hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X10970))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X10969)))))&(~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X10970))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X10969))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X10970)),hAPP(c_Nat_OSuc,X10969))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of__Suc])])). 4.46/4.69 fof(c_0_4585, plain, ![X11790, X11791, X11792]:(~class_Rings_Olinordered__idom(X11792)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11792),c_Groups_Ozero__class_Ozero(X11792)),hAPP(hAPP(c_Power_Opower__class_Opower(X11792),X11791),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X11790)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11792),c_Groups_Ozero__class_Ozero(X11792)),X11791)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_odd__0__le__power__imp__0__le])])])). 4.46/4.69 cnf(c_0_4586, plain, (X2=c_Groups_Oone__class_Oone(X1)|X2=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))|c_Groups_Oone__class_Oone(X1)!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_4456])). 4.46/4.69 cnf(c_0_4587, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4457])). 4.46/4.69 cnf(c_0_4588, plain, (X1=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), inference(split_conjunct,[status(thm)],[c_0_4458])). 4.46/4.69 cnf(c_0_4589, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_4459])). 4.46/4.69 fof(c_0_4590, plain, ![X5977, X5978, X5979, X5980, X5981]:(~c_Fun_Oinj__on(X5981,X5980,X5979,hAPP(hAPP(c_Set_Oinsert(X5981),X5978),hAPP(c_List_Oset(X5981),X5977)))|hAPP(c_List_OremoveAll(X5980,hAPP(X5979,X5978)),hAPP(hAPP(c_List_Omap(X5981,X5980),X5979),X5977))=hAPP(hAPP(c_List_Omap(X5981,X5980),X5979),hAPP(c_List_OremoveAll(X5981,X5978),X5977))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__removeAll__inj__on])])). 4.46/4.69 fof(c_0_4591, plain, ![X12273, X12274]:c_List_Ofilter(X12274,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12274),c_fNot),hAPP(c_fequal,X12273)))=c_List_OremoveAll(X12274,X12273), inference(variable_rename,[status(thm)],[fact_removeAll__filter__not__eq])). 4.46/4.69 fof(c_0_4592, plain, ![X15068, X15069]:((~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X15069)),c_Int_OBit0(X15068)))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X15069),X15068)))&(~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X15069),X15068))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X15069)),c_Int_OBit0(X15068))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I13_J])])). 4.46/4.69 fof(c_0_4593, plain, ![X12362, X12363]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12363),X12362))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X12363)),c_Int_OBit0(X12362))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X12363)),c_Int_OBit0(X12362)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12363),X12362)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I14_J])])). 4.46/4.69 fof(c_0_4594, plain, ![X7253, X7254]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7254),X7253))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X7254)),c_Int_OBit0(X7253))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X7254)),c_Int_OBit0(X7253)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7254),X7253)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I31_J])])). 4.46/4.69 fof(c_0_4595, plain, ![X15836, X15837, X15838, X15839]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15839),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15838)),c_List_OdropWhile(X15838,X15837,X15836))))|hAPP(hAPP(c_List_Onth(X15838),c_List_OdropWhile(X15838,X15837,X15836)),X15839)=hAPP(hAPP(c_List_Onth(X15838),X15836),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15839),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15838)),c_List_OtakeWhile(X15838,X15837,X15836))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dropWhile__nth])])])). 4.46/4.69 fof(c_0_4596, plain, ![X14543]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X14543)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X14543)))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X14543)))|hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14543)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X14543)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__number__of__Bit1])])])). 4.46/4.69 fof(c_0_4597, plain, ![X2072, X2073, X2074, X2075, X2076]:(~c_Fun_Oinj__on(X2076,X2075,X2074,c_Orderings_Otop__class_Otop(tc_fun(X2076,tc_HOL_Obool)))|hAPP(c_List_OremoveAll(X2075,hAPP(X2074,X2073)),hAPP(hAPP(c_List_Omap(X2076,X2075),X2074),X2072))=hAPP(hAPP(c_List_Omap(X2076,X2075),X2074),hAPP(c_List_OremoveAll(X2076,X2073),X2072))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__removeAll__inj])])])). 4.46/4.69 fof(c_0_4598, plain, ![X5494, X5495]:(~class_Int_Onumber__ring(X5495)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5495),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5495),c_Groups_Ozero__class_Ozero(X5495)),hAPP(c_Int_Onumber__class_Onumber__of(X5495),X5494))),hAPP(c_Int_Onumber__class_Onumber__of(X5495),X5494))=hAPP(c_Int_Onumber__class_Onumber__of(X5495),c_Int_OBit0(X5494))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_number__of__Bit0])])])). 4.46/4.69 fof(c_0_4599, plain, ![X16337, X16338]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16338),X16337))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X16338)),c_Int_OBit1(X16337))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X16338)),c_Int_OBit1(X16337)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16338),X16337)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I14_J])])). 4.46/4.69 fof(c_0_4600, plain, ![X4275, X4276]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4276),X4275))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X4276)),c_Int_OBit1(X4275))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X4276)),c_Int_OBit1(X4275)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4276),X4275)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I14_J])])). 4.46/4.69 fof(c_0_4601, plain, ![X4945, X4946]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4946),X4945))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X4946)),c_Int_OBit0(X4945))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X4946)),c_Int_OBit0(X4945)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4946),X4945)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I16_J])])). 4.46/4.69 fof(c_0_4602, plain, ![X4273, X4274]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X4274)),c_Int_OBit0(X4273)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4274),X4273)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4274),X4273))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X4274)),c_Int_OBit0(X4273))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I15_J])])). 4.46/4.69 fof(c_0_4603, plain, ![X16808, X16809]:(~class_Int_Onumber__ring(X16809)|hAPP(c_Int_Onumber__class_Onumber__of(X16809),c_Int_OBit0(X16808))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16809),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16809),c_Groups_Oone__class_Oone(X16809)),c_Groups_Oone__class_Oone(X16809))),hAPP(c_Int_Onumber__class_Onumber__of(X16809),X16808))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_double__number__of__Bit0])])])). 4.46/4.69 fof(c_0_4604, plain, ![X14, X45, X28]:(epred1_3(X28,X45,X14)<=>(((X45=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>hBOOL(hAPP(X28,X14)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>![X41, X98]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),X98))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X45),X41)),X98)=X14)=>hBOOL(hAPP(X28,X98)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))=>![X41, X98]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),X45))&hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X45),X41)),X98)=X14)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98)))=>hBOOL(hAPP(X28,X98)))))), introduced(definition)). 4.46/4.69 fof(c_0_4605, plain, ![X8429, X8430]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8430),X8429)),X8429)=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X8430),X8429), inference(variable_rename,[status(thm)],[fact_nat__minus__add__max])). 4.46/4.69 fof(c_0_4606, plain, ![X9576, X9577]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9577),X9576)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9576),X9577), inference(variable_rename,[status(thm)],[fact_nat__add__commute])). 4.46/4.69 fof(c_0_4607, plain, ![X916, X917]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X917))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X916),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X917),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X916)),X917)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__diff__eq__diff__pred])])])). 4.46/4.69 cnf(c_0_4608, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))), inference(split_conjunct,[status(thm)],[c_0_4460])). 4.46/4.69 cnf(c_0_4609, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)=X1), inference(split_conjunct,[status(thm)],[c_0_4461]), ['final']). 4.46/4.69 fof(c_0_4610, plain, ![X13918, X13919]:(~class_Int_Onumber__ring(X13919)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13919),hAPP(c_Int_Onumber__class_Onumber__of(X13919),X13918)),c_Groups_Oone__class_Oone(X13919))=hAPP(c_Int_Onumber__class_Onumber__of(X13919),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13918),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__special_I2_J])])). 4.46/4.69 fof(c_0_4611, plain, ![X3987, X3988]:(~class_Int_Onumber__ring(X3988)|hAPP(c_Int_Onumber__class_Onumber__of(X3988),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3987)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3988),c_Groups_Oone__class_Oone(X3988)),hAPP(c_Int_Onumber__class_Onumber__of(X3988),X3987))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__special_I1_J])])])). 4.46/4.69 fof(c_0_4612, plain, ![X14, X45, X28]:(epred2_3(X28,X45,X14)<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))=>![X41]:(?[X98]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))&X14=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X45),X41)),X98))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),X45)))=>hBOOL(hAPP(X28,X41))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>![X41]:(?[X98]:((X14=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X45),X41)),X98)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X45),X98)))=>hBOOL(hAPP(X28,X41)))))), introduced(definition)). 4.46/4.69 fof(c_0_4613, plain, ![X11698, X11699, X11700, X11701]:((X11701=X11700|hAPP(c_List_OremoveAll(X11699,X11701),hAPP(hAPP(c_List_Olist_OCons(X11699),X11700),X11698))=hAPP(hAPP(c_List_Olist_OCons(X11699),X11700),hAPP(c_List_OremoveAll(X11699,X11701),X11698)))&(X11701!=X11700|hAPP(c_List_OremoveAll(X11699,X11701),hAPP(hAPP(c_List_Olist_OCons(X11699),X11700),X11698))=hAPP(c_List_OremoveAll(X11699,X11701),X11698))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_removeAll_Osimps_I2_J])])). 4.46/4.69 fof(c_0_4614, plain, ![X15033]:hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X15033),c_Groups_Oone__class_Oone(tc_Int_Oint)))=c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X15033), inference(variable_rename,[status(thm)],[fact_negDivAlg__minus1])). 4.46/4.69 cnf(c_0_4615, plain, (c_Int_Opred(X1)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_4462])). 4.46/4.69 fof(c_0_4616, plain, ![X879, X880, X881, X882, X883]:(X879!=hAPP(c_Product__Type_Ofst(X883,X882),hAPP(hAPP(c_Product__Type_OPair(X883,X882),X881),X880))|X881=X879), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fst__eqD])])). 4.46/4.69 fof(c_0_4617, plain, ![X8046, X8047, X8048, X8049, X8050]:(X8046!=hAPP(c_Product__Type_Osnd(X8050,X8049),hAPP(hAPP(c_Product__Type_OPair(X8050,X8049),X8048),X8047))|X8046=X8047), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snd__eqD])])). 4.46/4.69 fof(c_0_4618, plain, ![X1656, X1657]:((~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1657),X1656))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1657)),c_Int_OBit1(X1656))))&(~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1657)),c_Int_OBit1(X1656)))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1657),X1656)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I16_J])])). 4.46/4.69 fof(c_0_4619, plain, ![X9628, X9629]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X9629)),c_Int_OBit1(X9628)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9629),X9628)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9629),X9628))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X9629)),c_Int_OBit1(X9628))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I16_J])])). 4.46/4.69 fof(c_0_4620, plain, ![X3140, X3141]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X3141)),c_Int_OBit1(X3140)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3141),X3140)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3141),X3140))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X3141)),c_Int_OBit1(X3140))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I16_J])])). 4.46/4.69 fof(c_0_4621, plain, ![X494, X495, X496]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X496),c_Nitpick_Oplus__frac(X496,X495,c_Nitpick_Ouminus__frac(X496,X494)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Nitpick_Oless__frac(X496,X495,X494))&(~c_Nitpick_Oless__frac(X496,X495,X494)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X496),c_Nitpick_Oplus__frac(X496,X495,c_Nitpick_Ouminus__frac(X496,X494)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__frac__def])])). 4.46/4.69 fof(c_0_4622, plain, ![X14458, X14459, X14460]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X14460),c_Nitpick_Oplus__frac(X14460,X14459,c_Nitpick_Ouminus__frac(X14460,X14458)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Nitpick_Oless__eq__frac(X14460,X14459,X14458))&(~c_Nitpick_Oless__eq__frac(X14460,X14459,X14458)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X14460),c_Nitpick_Oplus__frac(X14460,X14459,c_Nitpick_Ouminus__frac(X14460,X14458)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__eq__frac__def])])). 4.46/4.69 fof(c_0_4623, plain, ![X5473, X5474]:(~class_Int_Onumber__ring(X5474)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5474),c_Groups_Oone__class_Oone(X5474)),hAPP(c_Int_Onumber__class_Onumber__of(X5474),X5473))=hAPP(c_Int_Onumber__class_Onumber__of(X5474),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X5473))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__special_I2_J])])])). 4.46/4.69 fof(c_0_4624, plain, ![X12149, X12150]:(~class_Int_Onumber__ring(X12150)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12150),hAPP(c_Int_Onumber__class_Onumber__of(X12150),X12149)),c_Groups_Oone__class_Oone(X12150))=hAPP(c_Int_Onumber__class_Onumber__of(X12150),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12149),c_Int_OBit1(c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I3_J])])). 4.46/4.69 fof(c_0_4625, plain, ![X807, X808]:(~class_Int_Onumber__ring(X808)|hAPP(c_Int_Onumber__class_Onumber__of(X808),c_Int_OBit1(X807))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X808),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X808),c_Groups_Oone__class_Oone(X808)),hAPP(c_Int_Onumber__class_Onumber__of(X808),X807))),hAPP(c_Int_Onumber__class_Onumber__of(X808),X807))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_number__of__Bit1])])])). 4.46/4.69 fof(c_0_4626, plain, ![X1349, X1350]:((~c_Int_Oiszero(X1350,hAPP(c_Int_Onumber__class_Onumber__of(X1350),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1349))))|hAPP(c_Int_Onumber__class_Onumber__of(X1350),X1349)=c_Groups_Oone__class_Oone(X1350)|~class_Int_Onumber__ring(X1350))&(hAPP(c_Int_Onumber__class_Onumber__of(X1350),X1349)!=c_Groups_Oone__class_Oone(X1350)|c_Int_Oiszero(X1350,hAPP(c_Int_Onumber__class_Onumber__of(X1350),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1349))))|~class_Int_Onumber__ring(X1350))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I2_J])])])). 4.46/4.69 fof(c_0_4627, plain, ![X8642, X8643]:((hAPP(c_Int_Onumber__class_Onumber__of(X8643),X8642)!=c_Groups_Oone__class_Oone(X8643)|c_Int_Oiszero(X8643,hAPP(c_Int_Onumber__class_Onumber__of(X8643),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8642),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))|~class_Int_Onumber__ring(X8643))&(~c_Int_Oiszero(X8643,hAPP(c_Int_Onumber__class_Onumber__of(X8643),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8642),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))|hAPP(c_Int_Onumber__class_Onumber__of(X8643),X8642)=c_Groups_Oone__class_Oone(X8643)|~class_Int_Onumber__ring(X8643))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__special_I4_J])])])])). 4.46/4.69 fof(c_0_4628, plain, ![X10655, X10656]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10656),c_Groups_Oone__class_Oone(X10656)),hAPP(c_Int_Onumber__class_Onumber__of(X10656),X10655)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X10655))|(~class_Rings_Olinordered__idom(X10656)|~class_Int_Onumber__ring(X10656)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X10655))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10656),c_Groups_Oone__class_Oone(X10656)),hAPP(c_Int_Onumber__class_Onumber__of(X10656),X10655)))|(~class_Rings_Olinordered__idom(X10656)|~class_Int_Onumber__ring(X10656)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__special_I2_J])])])])). 4.46/4.69 fof(c_0_4629, plain, ![X4480, X4481]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X4480))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4481),c_Groups_Oone__class_Oone(X4481)),hAPP(c_Int_Onumber__class_Onumber__of(X4481),X4480)))|(~class_Rings_Olinordered__idom(X4481)|~class_Int_Onumber__ring(X4481)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4481),c_Groups_Oone__class_Oone(X4481)),hAPP(c_Int_Onumber__class_Onumber__of(X4481),X4480)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X4480))|(~class_Rings_Olinordered__idom(X4481)|~class_Int_Onumber__ring(X4481)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__special_I2_J])])])])). 4.46/4.69 fof(c_0_4630, plain, ![X5583, X5584]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5584),X5583))|c_List_Oupt(X5584,hAPP(c_Nat_OSuc,X5583))=c_List_Olist_ONil(tc_Nat_Onat))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5584),X5583))|hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X5584,X5583)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X5583),c_List_Olist_ONil(tc_Nat_Onat)))=c_List_Oupt(X5584,hAPP(c_Nat_OSuc,X5583)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_upt__Suc])])])). 4.46/4.69 fof(c_0_4631, plain, ![X10286, X10287]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10286),c_Int_OBit1(c_Int_OPls)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10287),hAPP(c_Int_Onumber__class_Onumber__of(X10287),X10286)),c_Groups_Oone__class_Oone(X10287)))|(~class_Rings_Olinordered__idom(X10287)|~class_Int_Onumber__ring(X10287)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10287),hAPP(c_Int_Onumber__class_Onumber__of(X10287),X10286)),c_Groups_Oone__class_Oone(X10287)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10286),c_Int_OBit1(c_Int_OPls)))|(~class_Rings_Olinordered__idom(X10287)|~class_Int_Onumber__ring(X10287)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__special_I4_J])])])])). 4.46/4.69 fof(c_0_4632, plain, ![X11690, X11691]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11690),c_Int_OBit1(c_Int_OPls)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11691),hAPP(c_Int_Onumber__class_Onumber__of(X11691),X11690)),c_Groups_Oone__class_Oone(X11691)))|(~class_Rings_Olinordered__idom(X11691)|~class_Int_Onumber__ring(X11691)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11691),hAPP(c_Int_Onumber__class_Onumber__of(X11691),X11690)),c_Groups_Oone__class_Oone(X11691)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11690),c_Int_OBit1(c_Int_OPls)))|(~class_Rings_Olinordered__idom(X11691)|~class_Int_Onumber__ring(X11691)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I4_J])])])). 4.46/4.69 fof(c_0_4633, plain, ![X1484, X1485, X1486, X1487]:(~class_Groups_Ocomm__monoid__add(X1487)|hAPP(c_List_Omonoid__add__class_Olistsum(X1487),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1487),X1486),c_List_Oupt(X1485,X1484)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1487),X1486),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X1485,X1484)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__nat])])). 4.46/4.69 fof(c_0_4634, plain, ![X4972, X4973]:hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X4973,X4972))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X4973),X4972), inference(variable_rename,[status(thm)],[fact_atLeastLessThan__upt])). 4.46/4.69 fof(c_0_4635, plain, ![X8079, X8080]:((~c_Int_Oiszero(X8080,hAPP(c_Int_Onumber__class_Onumber__of(X8080),X8079))|c_Int_Oiszero(X8080,hAPP(c_Int_Onumber__class_Onumber__of(X8080),c_Int_OBit0(X8079)))|(~class_Int_Onumber__ring(X8080)|~class_Int_Oring__char__0(X8080)))&(~c_Int_Oiszero(X8080,hAPP(c_Int_Onumber__class_Onumber__of(X8080),c_Int_OBit0(X8079)))|c_Int_Oiszero(X8080,hAPP(c_Int_Onumber__class_Onumber__of(X8080),X8079))|(~class_Int_Onumber__ring(X8080)|~class_Int_Oring__char__0(X8080)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_iszero__number__of__Bit0])])])])). 4.46/4.69 fof(c_0_4636, plain, ![X15107, X15108]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15108)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X15107)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15108)),X15107)))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15108)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X15108))),X15107)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15108)),X15107)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of__add])])])). 4.46/4.69 fof(c_0_4637, plain, ![X5337, X5338, X5339]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5339,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5339),X5338)),hAPP(c_Set_OCollect(X5339),X5337))=hAPP(c_Set_OCollect(X5339),hAPP(hAPP(c_COMBS(X5339,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5339),c_fdisj),X5338)),X5337)), inference(variable_rename,[status(thm)],[fact_Collect__disj__eq])). 4.46/4.69 fof(c_0_4638, plain, ![X17379]:((~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X17379),c_Int_OPls))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X17379)),c_Int_OPls)))&(~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X17379)),c_Int_OPls))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X17379),c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I9_J])])). 4.46/4.69 fof(c_0_4639, plain, ![X10135]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X10135)),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10135),c_Int_OMin)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10135),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X10135)),c_Int_OMin)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I11_J])])). 4.46/4.69 fof(c_0_4640, plain, ![X7353]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X7353)),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7353),c_Int_OPls)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7353),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X7353)),c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I10_J])])). 4.46/4.69 fof(c_0_4641, plain, ![X2176]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X2176)),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2176),c_Int_OMin)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2176),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X2176)),c_Int_OMin)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I28_J])])). 4.46/4.69 fof(c_0_4642, plain, ![X6805]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6805),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X6805)),c_Int_OPls)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X6805)),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6805),c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I27_J])])). 4.46/4.69 fof(c_0_4643, plain, ![X8072]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X8072))))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8072))))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8072)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X8072)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit0])])). 4.46/4.69 fof(c_0_4644, plain, ![X6399]:((~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X6399)))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X6399)))&(~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X6399))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X6399))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I3_J])])). 4.46/4.69 fof(c_0_4645, plain, ![X12448]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X12448))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X12448))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X12448)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X12448)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I8_J])])). 4.46/4.69 fof(c_0_4646, plain, ![X15739]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X15739))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X15739))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X15739)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X15739)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I4_J])])). 4.46/4.69 fof(c_0_4647, plain, ![X13656]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X13656)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X13656)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X13656))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X13656))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I25_J])])). 4.46/4.69 fof(c_0_4648, plain, ![X4839]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X4839))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X4839))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X4839)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X4839)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I21_J])])). 4.46/4.69 fof(c_0_4649, plain, ![X3221, X3222, X3223, X3224]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3224),X3223))|X3221!=c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3224),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3223)|X3224!=X3222|c_List_Oupt(X3224,X3223)=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3222),X3221))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3224),X3223))|c_List_Oupt(X3224,X3223)!=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3222),X3221))&(X3221=c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3224),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3223)|c_List_Oupt(X3224,X3223)!=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3222),X3221)))&(X3224=X3222|c_List_Oupt(X3224,X3223)!=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3222),X3221)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__eq__Cons__conv])])])). 4.46/4.69 fof(c_0_4650, plain, ![X7043, X7044, X7045, X7046]:((((~hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7043))|hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7043))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),hAPP(hAPP(c_Set_Oinsert(X7046),X7044),X7043))))&(((~hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7045))|hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7045))|hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7043))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),hAPP(hAPP(c_Set_Oinsert(X7046),X7044),X7043))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7046,tc_HOL_Obool)),X7045),X7043))|hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7045))|hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7043))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),hAPP(hAPP(c_Set_Oinsert(X7046),X7044),X7043)))))&((~hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7045))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7046,tc_HOL_Obool)),X7045),hAPP(hAPP(c_Set_Oinsert(X7046),X7044),c_Orderings_Obot__class_Obot(tc_fun(X7046,tc_HOL_Obool))))),X7043))|hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7043))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),hAPP(hAPP(c_Set_Oinsert(X7046),X7044),X7043))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7046,tc_HOL_Obool)),X7045),X7043))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7046,tc_HOL_Obool)),X7045),hAPP(hAPP(c_Set_Oinsert(X7046),X7044),c_Orderings_Obot__class_Obot(tc_fun(X7046,tc_HOL_Obool))))),X7043))|hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7043))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),hAPP(hAPP(c_Set_Oinsert(X7046),X7044),X7043)))))))&((~hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7043))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),X7043))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),hAPP(hAPP(c_Set_Oinsert(X7046),X7044),X7043))))&(((~hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7045))|hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7045))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),X7043))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),hAPP(hAPP(c_Set_Oinsert(X7046),X7044),X7043))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7046,tc_HOL_Obool)),X7045),X7043))|hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7045))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),X7043))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),hAPP(hAPP(c_Set_Oinsert(X7046),X7044),X7043)))))&((~hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7045))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7046,tc_HOL_Obool)),X7045),hAPP(hAPP(c_Set_Oinsert(X7046),X7044),c_Orderings_Obot__class_Obot(tc_fun(X7046,tc_HOL_Obool))))),X7043))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),X7043))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),hAPP(hAPP(c_Set_Oinsert(X7046),X7044),X7043))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7046,tc_HOL_Obool)),X7045),X7043))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7046,tc_HOL_Obool)),X7045),hAPP(hAPP(c_Set_Oinsert(X7046),X7044),c_Orderings_Obot__class_Obot(tc_fun(X7046,tc_HOL_Obool))))),X7043))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),X7043))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),hAPP(hAPP(c_Set_Oinsert(X7046),X7044),X7043))))))))&((~hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7043))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),X7043))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),hAPP(hAPP(c_Set_Oinsert(X7046),X7044),X7043))))&((~hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7045))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7046,tc_HOL_Obool)),X7045),hAPP(hAPP(c_Set_Oinsert(X7046),X7044),c_Orderings_Obot__class_Obot(tc_fun(X7046,tc_HOL_Obool))))),X7043))|hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7043))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),hAPP(hAPP(c_Set_Oinsert(X7046),X7044),X7043))))&(hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7045))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7046,tc_HOL_Obool)),X7045),X7043))|hBOOL(hAPP(hAPP(c_member(X7046),X7044),X7043))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7046,tc_HOL_Obool)),X7045),hAPP(hAPP(c_Set_Oinsert(X7046),X7044),X7043))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_psubset__insert__iff])])])])). 4.46/4.69 fof(c_0_4651, plain, ![X5130, X5131, X5132]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5132,tc_HOL_Obool)),X5131),X5130))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5132,tc_HOL_Obool)),X5131),X5130))|X5131=X5130))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5132,tc_HOL_Obool)),X5131),X5130))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5132,tc_HOL_Obool)),X5131),X5130)))&(X5131!=X5130|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5132,tc_HOL_Obool)),X5131),X5130))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])])). 4.46/4.69 fof(c_0_4652, plain, ![X16614, X16615, X16616]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X16616,X16616),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X16616,X16616),X16615)),c_Transitive__Closure_Ortrancl(X16616,X16615))!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X16616,X16616),tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16616,X16616)),hAPP(hAPP(c_Product__Type_OPair(X16616,X16616),X16614),X16614)),c_Transitive__Closure_Otrancl(X16616,X16615)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_irrefl__tranclI])])])). 4.46/4.69 fof(c_0_4653, plain, ![X8654, X8655]:hAPP(hAPP(c_Relation_Orel__comp(X8655,X8655,X8655),X8654),c_Transitive__Closure_Ortrancl(X8655,X8654))=c_Transitive__Closure_Otrancl(X8655,X8654), inference(variable_rename,[status(thm)],[fact_trancl__unfold__left])). 4.46/4.69 fof(c_0_4654, plain, ![X15721, X15722, X15723]:hAPP(c_Set_Oimage(tc_prod(X15723,X15722),X15723,c_Product__Type_Ofst(X15723,X15722)),hAPP(c_List_Oset(tc_prod(X15723,X15722)),X15721))=c_Map_Odom(X15723,X15722,hAPP(c_Map_Omap__of(X15723,X15722),X15721)), inference(variable_rename,[status(thm)],[fact_dom__map__of__conv__image__fst])). 4.46/4.69 fof(c_0_4655, plain, ![X3879, X3880, X3881]:hAPP(c_Set_Oimage(tc_prod(X3881,X3880),X3881,c_Product__Type_Ofst(X3881,X3880)),X3879)=hAPP(c_Relation_ODomain(X3881,X3880),X3879), inference(variable_rename,[status(thm)],[fact_fst__eq__Domain])). 4.46/4.69 fof(c_0_4656, plain, ![X15781, X15782]:((c_Int_OBit0(X15782)!=c_Int_OBit0(X15781)|X15781=X15782)&(X15781!=X15782|c_Int_OBit0(X15782)=c_Int_OBit0(X15781))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I48_J])])). 4.46/4.69 fof(c_0_4657, plain, ![X8543, X8544]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X8544))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8543),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X8544)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X8543)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8544))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__diff__number__of])])])). 4.46/4.69 fof(c_0_4658, plain, ![X7998, X7999]:(~class_Int_Onumber__ring(X7999)|~class_Fields_Ofield(X7999)|X7998=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7999),X7998),hAPP(c_Int_Onumber__class_Onumber__of(X7999),c_Int_OBit1(c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__Numeral1])])])). 4.46/4.69 fof(c_0_4659, plain, ![X17359, X17360]:((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X17360|c_Code__Numeral_Onat__of__aux(X17360,X17359)=X17359)&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X17360|c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X17360),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X17359))=c_Code__Numeral_Onat__of__aux(X17360,X17359))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__of__aux__code])])])). 4.46/4.69 fof(c_0_4660, plain, ![X4649, X4650]:c_Code__Numeral_Onat__of__aux(X4650,X4649)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X4650)),X4649), inference(variable_rename,[status(thm)],[fact_nat__of__aux__def])). 4.46/4.69 fof(c_0_4661, plain, ![X17293, X17294, X17295, X17296]:(hBOOL(hAPP(X17296,X17295))|hAPP(c_List_Ofilter(X17294,X17296),X17293)=hAPP(c_List_OremoveAll(X17294,X17295),hAPP(c_List_Ofilter(X17294,X17296),X17293))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_removeAll__filter__not])])])). 4.46/4.69 fof(c_0_4662, plain, ![X14923, X14924, X14925, X14926]:hAPP(c_List_Ofilter(X14926,hAPP(hAPP(c_COMBS(X14926,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X14926),c_fconj),X14924)),X14925)),X14923)=hAPP(c_List_Ofilter(X14926,X14925),hAPP(c_List_Ofilter(X14926,X14924),X14923)), inference(variable_rename,[status(thm)],[fact_filter__filter])). 4.46/4.69 cnf(c_0_4663, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2)),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2)),hAPP(c_Set_OCollect(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_4463])). 4.46/4.69 fof(c_0_4664, plain, ![X6706, X6707]:(~class_Int_Onumber__ring(X6707)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6707),hAPP(c_Int_Onumber__class_Onumber__of(X6707),c_Int_OBit1(c_Int_OPls))),X6706)=X6706), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__numeral__1])])])). 4.46/4.69 fof(c_0_4665, plain, ![X7617, X7618]:(~class_Int_Onumber__ring(X7618)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7618),X7617),hAPP(c_Int_Onumber__class_Onumber__of(X7618),c_Int_OBit1(c_Int_OPls)))=X7617), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__numeral__1__right])])])). 4.46/4.69 fof(c_0_4666, plain, ![X9251]:((~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X9251),c_Int_OMin))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X9251)),c_Int_OMin)))&(~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X9251)),c_Int_OMin))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X9251),c_Int_OMin)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I12_J])])). 4.46/4.69 fof(c_0_4667, plain, ![X8985]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8985),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X8985)),c_Int_OMin)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X8985)),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8985),c_Int_OMin)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I13_J])])). 4.46/4.69 fof(c_0_4668, plain, ![X5022]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5022),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X5022)),c_Int_OPls)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X5022)),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5022),c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I12_J])])). 4.46/4.69 fof(c_0_4669, plain, ![X10950]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X10950)),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10950),c_Int_OMin)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10950),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X10950)),c_Int_OMin)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I30_J])])). 4.46/4.69 fof(c_0_4670, plain, ![X7754]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7754),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X7754)),c_Int_OPls)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X7754)),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7754),c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I29_J])])). 4.46/4.69 fof(c_0_4671, plain, ![X13075]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X13075))))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X13075))))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X13075)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X13075)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit1])])). 4.46/4.69 fof(c_0_4672, plain, ![X2753]:((~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X2753)))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X2753)))&(~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X2753))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X2753))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I8_J])])). 4.46/4.69 fof(c_0_4673, plain, ![X14487]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X14487))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X14487))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X14487)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X14487)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I9_J])])). 4.46/4.69 fof(c_0_4674, plain, ![X17365]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X17365))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X17365))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X17365)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X17365)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I5_J])])). 4.46/4.69 fof(c_0_4675, plain, ![X16230]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X16230)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X16230)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X16230))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X16230))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I26_J])])). 4.46/4.69 fof(c_0_4676, plain, ![X15894]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X15894)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X15894)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X15894))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X15894))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I22_J])])). 4.46/4.69 fof(c_0_4677, plain, ![X1036, X1037, X1038]:((hBOOL(hAPP(X1038,X1037))|c_Orderings_Obot__class_Obot(tc_fun(X1036,tc_HOL_Obool))=hAPP(c_Set_OCollect(X1036),hAPP(hAPP(c_COMBS(X1036,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1036),c_fconj),hAPP(c_fequal,X1037))),X1038)))&(~hBOOL(hAPP(X1038,X1037))|hAPP(hAPP(c_Set_Oinsert(X1036),X1037),c_Orderings_Obot__class_Obot(tc_fun(X1036,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X1036),hAPP(hAPP(c_COMBS(X1036,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1036),c_fconj),hAPP(c_fequal,X1037))),X1038)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Collect__conv__if2])])])). 4.46/4.69 fof(c_0_4678, plain, ![X13223]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13223),c_Int_OPls))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13223)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13223),c_Int_OPls))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13223)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X13223)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__number__of__diff__1])])])). 4.46/4.69 cnf(c_0_4679, plain, (X1=c_Int_OPls|c_Int_OPls!=c_Int_OBit0(X1)), inference(split_conjunct,[status(thm)],[c_0_4464])). 4.46/4.69 fof(c_0_4680, plain, ![X6799]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6799),c_Int_OPls))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X6799))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6799)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6799),c_Int_OPls))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6799))=c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__1__add__number__of])])])). 4.46/4.69 fof(c_0_4681, plain, ![X12607]:X12607=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X12607), inference(variable_rename,[status(thm)],[fact_add__Pls])). 4.46/4.69 fof(c_0_4682, plain, ![X3798, X3799, X3800]:(hBOOL(hAPP(hAPP(c_member(X3800),X3799),hAPP(c_List_Oset(X3800),X3798)))|X3798=hAPP(c_List_OremoveAll(X3800,X3799),X3798)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_removeAll__id])])])). 4.46/4.69 fof(c_0_4683, plain, ![X11278]:(~class_Int_Onumber__ring(X11278)|c_Groups_Oone__class_Oone(X11278)=hAPP(c_Int_Onumber__class_Onumber__of(X11278),c_Int_OBit1(c_Int_OPls))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J])])). 4.46/4.69 fof(c_0_4684, plain, ![X2936, X2937, X2938]:(~hBOOL(hAPP(c_List_Odistinct(X2938),X2937))|hAPP(c_List_OremoveAll(X2938,X2936),X2937)=c_List_Oremove1(X2938,X2936,X2937)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__remove1__removeAll])])])). 4.46/4.69 fof(c_0_4685, plain, ![X10705, X10706]:((c_Int_OBit1(X10706)!=c_Int_OBit1(X10705)|X10706=X10705)&(X10706!=X10705|c_Int_OBit1(X10706)=c_Int_OBit1(X10705))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J])])). 4.46/4.69 fof(c_0_4686, plain, ![X1311, X1312]:(~class_Int_Onumber__ring(X1312)|hAPP(c_Int_Onumber__class_Onumber__of(X1312),c_Int_Osucc(X1311))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1312),c_Groups_Oone__class_Oone(X1312)),hAPP(c_Int_Onumber__class_Onumber__of(X1312),X1311))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_number__of__succ])])])). 4.46/4.69 fof(c_0_4687, plain, ![X4085]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4085)))|c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4085)))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4085)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X4085))=hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4085)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of])])])). 4.46/4.69 fof(c_0_4688, plain, ![X6661]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X6661))))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6661)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6661)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X6661)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__pred__iff__0])])). 4.46/4.69 fof(c_0_4689, plain, ![X12498, X12499]:(~class_Int_Oring__char__0(X12499)|~class_Int_Onumber__ring(X12499)|~c_Int_Oiszero(X12499,hAPP(c_Int_Onumber__class_Onumber__of(X12499),c_Int_OBit1(X12498)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_iszero__number__of__Bit1])])])). 4.46/4.69 fof(c_0_4690, plain, ![X331]:(~class_Int_Onumber__ring(X331)|~c_Int_Oiszero(X331,hAPP(c_Int_Onumber__class_Onumber__of(X331),c_Int_OBit1(c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__iszero__Numeral1])])])). 4.46/4.69 fof(c_0_4691, plain, ![X7261]:((X7261!=c_Int_OMin|c_Int_OBit1(X7261)=c_Int_OMin)&(c_Int_OBit1(X7261)!=c_Int_OMin|X7261=c_Int_OMin)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I47_J])])). 4.46/4.69 fof(c_0_4692, plain, ![X957]:(~c_Hoare__Mirabelle_Ostate__not__singleton|(~c_Com_OWT__bodies|(~hBOOL(hAPP(c_Com_OWT,X957))|c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X957)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_MGF])])])). 4.46/4.69 fof(c_0_4693, plain, ![X13564, X13565]:((c_Code__Numeral_OSuc__code__numeral(X13564)!=c_Code__Numeral_OSuc__code__numeral(X13565)|X13564=X13565)&(X13564!=X13565|c_Code__Numeral_OSuc__code__numeral(X13564)=c_Code__Numeral_OSuc__code__numeral(X13565))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Oinject])])). 4.46/4.69 fof(c_0_4694, plain, ![X13536]:hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X13536)))=c_Code__Numeral_OSuc__code__numeral(X13536), inference(variable_rename,[status(thm)],[fact_Suc__code__numeral__def])). 4.46/4.69 fof(c_0_4695, negated_conjecture, ~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,v_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))), inference(fof_simplification,[status(thm)],[c_0_4465])). 4.46/4.69 cnf(c_0_4696, plain, (hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X2))=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_4466])). 4.46/4.69 fof(c_0_4697, plain, ![X6643, X6644]:~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X6644)),c_Int_OBit1(X6643))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__int__code_I14_J])])). 4.46/4.69 fof(c_0_4698, plain, ![X1730, X1731]:~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1731)),c_Int_OBit0(X1730))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__int__code_I15_J])])). 4.46/4.69 cnf(c_0_4699, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1)))), inference(split_conjunct,[status(thm)],[c_0_4467])). 4.46/4.69 cnf(c_0_4700, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_4468])). 4.46/4.69 cnf(c_0_4701, plain, (c_Int_OMin!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4469, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.69 fof(c_0_4702, plain, ![X7158, X7159]:c_Int_OBit1(X7159)!=c_Int_OBit0(X7158), inference(variable_rename,[status(thm)],[fact_rel__simps_I50_J])). 4.46/4.69 fof(c_0_4703, plain, ![X5104]:~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X5104)),c_Int_OPls)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__int__code_I10_J])])). 4.46/4.69 fof(c_0_4704, plain, ![X8901]:~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X8901))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__int__code_I4_J])])). 4.46/4.69 cnf(c_0_4705, plain, (c_Int_OPls!=c_Int_OBit1(X1)), inference(split_conjunct,[status(thm)],[c_0_4472])). 4.46/4.69 fof(c_0_4706, plain, ![X9202]:c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=c_Code__Numeral_OSuc__code__numeral(X9202), inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I3_J])). 4.46/4.69 fof(c_0_4707, plain, ![X5827, X5828, X5829, X5830]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5830,X5830),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5830,X5827)),hAPP(c_Set_OCollect(tc_prod(X5830,X5830)),hAPP(c_Product__Type_Oprod_Oprod__case(X5830,X5830,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5830,tc_fun(X5830,tc_HOL_Obool),tc_fun(X5830,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5830,tc_HOL_Obool),tc_fun(X5830,tc_HOL_Obool)),X5830),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5830)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5830),c_fconj),hAPP(hAPP(c_COMBC(X5830,tc_fun(tc_prod(X5830,X5830),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X5830,X5830),tc_fun(tc_fun(tc_prod(X5830,X5830),tc_HOL_Obool),tc_HOL_Obool),X5830),c_member(tc_prod(X5830,X5830))),hAPP(hAPP(c_COMBC(X5830,X5830,tc_prod(X5830,X5830)),c_Product__Type_OPair(X5830,X5830)),X5829))),c_Transitive__Closure_Ortrancl(X5830,X5827))))),hAPP(hAPP(c_COMBC(X5830,tc_fun(tc_prod(X5830,X5830),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X5830,X5830),tc_fun(tc_fun(tc_prod(X5830,X5830),tc_HOL_Obool),tc_HOL_Obool),X5830),c_member(tc_prod(X5830,X5830))),hAPP(c_Product__Type_OPair(X5830,X5830),X5828))),c_Transitive__Closure_Ortrancl(X5830,X5827))))))=c_Transitive__Closure_Otrancl(X5830,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5830,X5830)),hAPP(hAPP(c_Product__Type_OPair(X5830,X5830),X5829),X5828)),X5827)), inference(variable_rename,[status(thm)],[fact_trancl__insert])). 4.46/4.69 fof(c_0_4708, plain, ![X6185, X6186, X6187, X6188]:hAPP(hAPP(c_List_Omap(tc_prod(X6188,tc_Nat_Onat),X6188),c_Product__Type_Ofst(X6188,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X6188,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X6188,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X6188,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X6188,tc_Nat_Onat))),X6187)),hAPP(hAPP(c_List_Ozip(X6188,tc_Nat_Onat),X6186),c_List_Oupt(X6185,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6185),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6188)),X6186))))))=hAPP(hAPP(c_List_Omap(tc_prod(X6188,tc_Nat_Onat),X6188),c_Product__Type_Ofst(X6188,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X6188,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X6188,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X6188,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X6188,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(X6188,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X6188,tc_Nat_Onat))),X6185))),X6187)),hAPP(hAPP(c_List_Ozip(X6188,tc_Nat_Onat),X6186),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6188)),X6186))))), inference(variable_rename,[status(thm)],[fact_sublist__shift__lemma])). 4.46/4.69 fof(c_0_4709, plain, ![X3704, X3705, X3706]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3706)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X3705))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3704)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3704)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3706),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3704),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X3705)))), inference(variable_rename,[status(thm)],[fact_arith__series__int])). 4.46/4.69 fof(c_0_4710, plain, ![X538, X539]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X539),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X538)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X539)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X538))), inference(variable_rename,[status(thm)],[fact_zmod__number__of__Bit0])). 4.46/4.69 fof(c_0_4711, plain, ![X10984, X10985]:c_List_Ofoldr(tc_List_Olist(X10985),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X10985)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X10985))),c_List_Otranspose(X10985,X10984),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10985))),hAPP(c_List_Ofilter(tc_List_Olist(X10985),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X10985)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X10985),tc_List_Olist(X10985),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X10985)))),X10984)), inference(variable_rename,[status(thm)],[fact_transpose__max__length])). 4.46/4.69 cnf(c_0_4712, plain, (c_List_Ofoldr(tc_List_Olist(X1),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X1)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_4473])). 4.46/4.69 cnf(c_0_4713, plain, (c_List_Ofoldr(X1,X2,X3,X4,X5)=hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X5),hAPP(c_List_Orev(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_4474])). 4.46/4.69 fof(c_0_4714, plain, ![X3601, X3602]:c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3602),c_Int_Osucc(X3601)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X3602)),c_Int_OBit1(X3601)), inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit1])). 4.46/4.69 fof(c_0_4715, plain, ![X6557]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X6557)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6557),X6557), inference(variable_rename,[status(thm)],[fact_nat__mult__2])). 4.46/4.69 fof(c_0_4716, plain, ![X8132]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8132),X8132)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8132),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), inference(variable_rename,[status(thm)],[fact_nat__mult__2__right])). 4.46/4.69 fof(c_0_4717, plain, ![X12795, X12796]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X12796),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X12795)))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X12796),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12795))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))), inference(variable_rename,[status(thm)],[fact_zpower__number__of__even])). 4.46/4.69 fof(c_0_4718, plain, ![X5640, X5641]:c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5641),X5640))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X5641)),c_Int_OBit1(X5640)), inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit1])). 4.46/4.69 fof(c_0_4719, plain, ![X5691, X5692]:c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5692),X5691))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X5692)),c_Int_OBit0(X5691)), inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit0])). 4.46/4.69 fof(c_0_4720, plain, ![X7961, X7962, X7963, X7964]:c_List_Oconcat(X7963,hAPP(hAPP(c_List_Omap(tc_List_Olist(X7964),tc_List_Olist(X7963)),hAPP(c_List_Omap(X7964,X7963),X7962)),X7961))=hAPP(hAPP(c_List_Omap(X7964,X7963),X7962),c_List_Oconcat(X7964,X7961)), inference(variable_rename,[status(thm)],[fact_map__concat])). 4.46/4.69 fof(c_0_4721, plain, ![X8744, X8745]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X8745)),X8744)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8745),X8744))),X8744), inference(variable_rename,[status(thm)],[fact_mult__Bit1])). 4.46/4.69 fof(c_0_4722, plain, ![X2556, X2557]:c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2557),X2556))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X2557)),X2556), inference(variable_rename,[status(thm)],[fact_mult__Bit0])). 4.46/4.69 fof(c_0_4723, plain, ![X16835]:hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X16835)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X16835)), inference(variable_rename,[status(thm)],[fact_nat__number__of__Bit0])). 4.46/4.69 fof(c_0_4724, plain, ![X7889]:c_Int_OBit0(c_Int_Osucc(X7889))=c_Int_Osucc(c_Int_OBit1(X7889)), inference(variable_rename,[status(thm)],[fact_succ__Bit1])). 4.46/4.69 fof(c_0_4725, plain, ![X15930, X15931]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X15931)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X15930))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X15931,X15930)), inference(variable_rename,[status(thm)],[fact_com_Osize_I12_J])). 4.46/4.69 fof(c_0_4726, plain, ![X10253, X10254, X10255]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10255),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10254),X10253))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10255),X10254)),X10253), inference(variable_rename,[status(thm)],[fact_nat__add__assoc])). 4.46/4.69 fof(c_0_4727, plain, ![X3787]:hAPP(c_Nat_OSuc,X3787)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3787),c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1])). 4.46/4.69 cnf(c_0_4728, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4475])). 4.46/4.69 cnf(c_0_4729, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_4476]), ['final']). 4.46/4.69 fof(c_0_4730, plain, ![X7790, X7791]:c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X7791,X7790))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X7791)),c_Com_Ocom_Ocom__size(X7790))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_com_Osize_I4_J])). 4.46/4.69 fof(c_0_4731, plain, ![X10773]:hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X10773))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X10773))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))=c_Divides_Oadjust(X10773), inference(variable_rename,[status(thm)],[fact_adjust__def])). 4.46/4.69 fof(c_0_4732, plain, ![X12131, X12132, X12133]:hAPP(c_Divides_Oadjust(X12133),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X12132),X12131))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X12131),X12133)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X12132)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X12132)),X12131))), inference(variable_rename,[status(thm)],[fact_adjust__eq])). 4.46/4.69 fof(c_0_4733, plain, ![X6911, X6912, X6913]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X6913),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X6913),X6912),hAPP(c_Nitpick_Odenom(X6913),X6911))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X6913),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X6913),tc_Int_Oint),c_Nitpick_Ofrac(X6913)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X6913),X6912))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X6913),X6912))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X6913),X6911))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X6913),X6911)))))),c_COMBI(tc_Int_Oint)))=c_Nitpick_Oplus__frac(X6913,X6912,X6911), inference(variable_rename,[status(thm)],[fact_Nitpick_Oplus__frac__def])). 4.46/4.69 fof(c_0_4734, plain, ![X9884, X9885, X9886, X9887]:hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X9887)),hAPP(hAPP(c_List_Olist_OCons(X9887),X9886),c_List_Oconcat(X9887,hAPP(hAPP(c_List_Omap(tc_List_Olist(X9887),tc_List_Olist(X9887)),c_List_Olist_Olist__case(tc_List_Olist(X9887),X9887,c_List_Olist_ONil(X9887),hAPP(hAPP(c_COMBB(tc_List_Olist(X9887),tc_fun(tc_List_Olist(X9887),tc_List_Olist(X9887)),X9887),c_COMBK(tc_List_Olist(X9887),tc_List_Olist(X9887))),hAPP(hAPP(c_COMBC(X9887,tc_List_Olist(X9887),tc_List_Olist(X9887)),c_List_Olist_OCons(X9887)),c_List_Olist_ONil(X9887))))),X9884)))),c_List_Otranspose(X9887,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X9887)),X9885),c_List_Oconcat(tc_List_Olist(X9887),hAPP(hAPP(c_List_Omap(tc_List_Olist(X9887),tc_List_Olist(tc_List_Olist(X9887))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X9887)),X9887,c_List_Olist_ONil(tc_List_Olist(X9887)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X9887),tc_List_Olist(tc_List_Olist(X9887))),X9887),hAPP(hAPP(c_COMBC(tc_List_Olist(X9887),tc_List_Olist(tc_List_Olist(X9887)),tc_List_Olist(tc_List_Olist(X9887))),c_List_Olist_OCons(tc_List_Olist(X9887))),c_List_Olist_ONil(tc_List_Olist(X9887)))))),X9884)))))=c_List_Otranspose(X9887,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X9887)),hAPP(hAPP(c_List_Olist_OCons(X9887),X9886),X9885)),X9884)), inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I3_J])). 4.46/4.69 cnf(c_0_4735, plain, (c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))))),X2))=hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),c_List_Ohd(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1)))),X2))), inference(split_conjunct,[status(thm)],[c_0_4477])). 4.46/4.69 cnf(c_0_4736, plain, (c_List_Oconcat(X1,X2)=hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_4478])). 4.46/4.69 cnf(c_0_4737, plain, (c_List_Omaps(X1,X2,X3,X4)=c_List_Oconcat(X2,hAPP(hAPP(c_List_Omap(X1,tc_List_Olist(X2)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_4479])). 4.46/4.69 cnf(c_0_4738, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_4480])). 4.46/4.69 cnf(c_0_4739, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2))=hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2))), inference(split_conjunct,[status(thm)],[c_0_4481])). 4.46/4.69 cnf(c_0_4740, plain, (hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Otl(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1)))),X2))=c_List_Oconcat(tc_List_Olist(X1),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1)))))),X2))), inference(split_conjunct,[status(thm)],[c_0_4482])). 4.46/4.69 fof(c_0_4741, plain, ![X1345, X1346, X1347, X1348]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1348)),X1347))),c_List_Ofoldr(tc_List_Olist(X1346),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X1346)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1346))),X1345,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1348)),X1347)),c_List_Ofoldr(tc_List_Olist(X1346),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X1346)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1346),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X1346)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1346)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X1346),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1346)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1346),tc_List_Olist(X1346),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1346)))),X1345),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(variable_rename,[status(thm)],[fact_transpose__aux__max])). 4.46/4.69 fof(c_0_4742, plain, ![X2982, X2983, X2984, X2985, X2986]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X2986),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2983))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X2986,X2986),hAPP(hAPP(c_COMBC(tc_Int_Oint,X2986,tc_fun(X2986,X2986)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2986,tc_fun(X2986,X2986)),tc_Int_Oint),c_If(X2986)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X2986,X2985,X2984),X2982))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X2986,X2986),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X2986,X2986),tc_Int_Oint),X2984),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X2982))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X2986,tc_Int_Oint),c_Nat_Onat_Onat__rec(X2986,X2985,X2984)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X2982)))))=hAPP(c_Nat_Onat_Onat__rec(X2986,X2985,X2984),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2983)),X2982)), inference(variable_rename,[status(thm)],[fact_nat__rec__add__eq__if])). 4.46/4.69 fof(c_0_4743, plain, ![X8951]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X8951))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X8951),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), inference(variable_rename,[status(thm)],[fact_div2__Suc__Suc])). 4.46/4.69 fof(c_0_4744, plain, ![X12248, X12249, X12250, X12251, X12252]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X12252),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X12249))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X12252,X12252),hAPP(hAPP(c_COMBC(tc_Int_Oint,X12252,tc_fun(X12252,X12252)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X12252,tc_fun(X12252,X12252)),tc_Int_Oint),c_If(X12252)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X12252,X12251,X12250,X12248))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X12252,tc_Int_Oint),X12250),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X12248))))=c_Nat_Onat_Onat__case(X12252,X12251,X12250,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12249)),X12248)), inference(variable_rename,[status(thm)],[fact_nat__case__add__eq__if])). 4.46/4.69 fof(c_0_4745, plain, ![X6871]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X6871)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X6871,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), inference(variable_rename,[status(thm)],[fact_mod2__Suc__Suc])). 4.46/4.69 fof(c_0_4746, plain, ![X15432, X15433, X15434]:hAPP(hAPP(c_Nitpick_Ofrac(X15434),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X15434),X15433)),hAPP(c_Nitpick_Onum(X15434),X15432))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X15434),X15433)),hAPP(c_Nitpick_Odenom(X15434),X15432)))=c_Nitpick_Otimes__frac(X15434,X15433,X15432), inference(variable_rename,[status(thm)],[fact_Nitpick_Otimes__frac__def])). 4.46/4.69 fof(c_0_4747, plain, ![X3342, X3343]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3343)),hAPP(c_Nat_OSuc,X3342))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X3343))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X3342))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),X3342)))), inference(variable_rename,[status(thm)],[fact_max__Suc__number__of])). 4.46/4.69 fof(c_0_4748, plain, ![X11996]:c_Relation_OId(X11996)=hAPP(c_Set_OCollect(tc_prod(X11996,X11996)),hAPP(hAPP(c_COMBB(tc_fun(X11996,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X11996,X11996)),c_HOL_OEx(X11996)),hAPP(hAPP(c_COMBC(tc_prod(X11996,X11996),tc_fun(X11996,tc_prod(X11996,X11996)),tc_fun(X11996,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X11996,X11996),tc_HOL_Obool),tc_fun(tc_fun(X11996,tc_prod(X11996,X11996)),tc_fun(X11996,tc_HOL_Obool)),tc_prod(X11996,X11996)),c_COMBB(tc_prod(X11996,X11996),tc_HOL_Obool,X11996)),c_fequal)),hAPP(hAPP(c_COMBS(X11996,X11996,tc_prod(X11996,X11996)),c_Product__Type_OPair(X11996,X11996)),c_COMBI(X11996))))), inference(variable_rename,[status(thm)],[fact_Id__def])). 4.46/4.69 fof(c_0_4749, plain, ![X16551]:c_Transitive__Closure_Ortrancl(X16551,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X16551,X16551),tc_HOL_Obool)))=c_Relation_OId(X16551), inference(variable_rename,[status(thm)],[fact_rtrancl__empty])). 4.46/4.69 fof(c_0_4750, plain, ![X15500, X15501, X15502, X15503]:hAPP(c_Nat_Onat_Onat__rec(X15503,X15502,X15501),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15500))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X15503),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X15500))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X15503,X15503),hAPP(hAPP(c_COMBC(tc_Int_Oint,X15503,tc_fun(X15503,X15503)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X15503,tc_fun(X15503,X15503)),tc_Int_Oint),c_If(X15503)),c_Nat__Numeral_Oneg)),X15502)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X15503,X15503),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X15503,X15503),tc_Int_Oint),X15501),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X15503,tc_Int_Oint),c_Nat_Onat_Onat__rec(X15503,X15502,X15501)),c_Int_Onat)))), inference(variable_rename,[status(thm)],[fact_nat__rec__number__of])). 4.46/4.69 fof(c_0_4751, plain, ![X11098, X11099]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X11099))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),X11098))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X11099)),hAPP(c_Nat_OSuc,X11098)), inference(variable_rename,[status(thm)],[fact_min__Suc__number__of])). 4.46/4.69 fof(c_0_4752, plain, ![X17069, X17070, X17071]:c_List_Oconcat(tc_List_Olist(X17071),hAPP(hAPP(c_List_Omap(tc_List_Olist(X17071),tc_List_Olist(tc_List_Olist(X17071))),hAPP(hAPP(c_COMBC(tc_List_Olist(X17071),tc_List_Olist(X17071),tc_List_Olist(tc_List_Olist(X17071))),hAPP(hAPP(c_COMBB(tc_fun(X17071,tc_List_Olist(X17071)),tc_fun(tc_List_Olist(X17071),tc_List_Olist(tc_List_Olist(X17071))),tc_List_Olist(X17071)),c_List_Omap(X17071,tc_List_Olist(X17071))),hAPP(c_COMBC(X17071,tc_List_Olist(X17071),tc_List_Olist(X17071)),c_List_Olist_OCons(X17071)))),X17069)),c_Enum_On__lists(X17071,X17070,X17069)))=c_Enum_On__lists(X17071,hAPP(c_Nat_OSuc,X17070),X17069), inference(variable_rename,[status(thm)],[fact_n__lists_Osimps_I2_J])). 4.46/4.69 fof(c_0_4753, plain, ![X8393, X8394]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X8394)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8393))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X8393))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X8394))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X8394)),c_Int_Onat)))), inference(variable_rename,[status(thm)],[fact_max__number__of__Suc])). 4.46/4.69 fof(c_0_4754, plain, ![X15049, X15050]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X15049))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X15050)),c_Int_Onat))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X15050)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15049)), inference(variable_rename,[status(thm)],[fact_min__number__of__Suc])). 4.46/4.69 fof(c_0_4755, plain, ![X13913, X13914, X13915]:hAPP(hAPP(c_List_Omap(tc_prod(X13915,tc_Nat_Onat),X13915),c_Product__Type_Ofst(X13915,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X13915,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X13915,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X13915,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X13915,tc_Nat_Onat))),X13913)),hAPP(hAPP(c_List_Ozip(X13915,tc_Nat_Onat),X13914),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13915)),X13914)))))=c_List_Osublist(X13915,X13914,X13913), inference(variable_rename,[status(thm)],[fact_sublist__def])). 4.46/4.69 fof(c_0_4756, plain, ![X8450, X8451]:c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8451),X8450))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X8451)),c_Int_OBit0(X8450)), inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit0])). 4.46/4.69 fof(c_0_4757, plain, ![X12190, X12191]:c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X12191),X12190))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X12191)),c_Int_OBit0(X12190)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I7_J])). 4.46/4.69 cnf(c_0_4758, plain, (c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2))), inference(split_conjunct,[status(thm)],[c_0_4483])). 4.46/4.69 cnf(c_0_4759, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),c_Groups_Oone__class_Oone(tc_Int_Oint))=X1), inference(rw,[status(thm)],[c_0_4484, c_0_4448])). 4.46/4.69 cnf(c_0_4760, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_4485]), ['final']). 4.46/4.69 fof(c_0_4761, plain, ![X11470, X11471]:hAPP(c_Set_OCollect(X11471),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X11471,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X11471),c_HOL_OAll(tc_fun(X11471,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X11471,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X11471,tc_HOL_Obool),tc_HOL_Obool),X11471),hAPP(c_COMBS(tc_fun(X11471,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X11471,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X11471,tc_HOL_Obool),tc_fun(tc_fun(X11471,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X11471,tc_HOL_Obool))),X11470)))),c_member(X11471))))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X11471,tc_HOL_Obool),X11470), inference(variable_rename,[status(thm)],[fact_Inter__eq])). 4.46/4.69 fof(c_0_4762, plain, ![X8521, X8522, X8523, X8524]:c_Nat_Onat_Onat__case(X8524,X8523,X8522,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8521))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X8524),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X8521))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X8524,X8524),hAPP(hAPP(c_COMBC(tc_Int_Oint,X8524,tc_fun(X8524,X8524)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8524,tc_fun(X8524,X8524)),tc_Int_Oint),c_If(X8524)),c_Nat__Numeral_Oneg)),X8523)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X8524,tc_Int_Oint),X8522),c_Int_Onat))), inference(variable_rename,[status(thm)],[fact_nat__case__number__of])). 4.46/4.69 fof(c_0_4763, plain, ![X8787, X8788]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X8788)),X8787))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X8788)),c_Int_OBit1(X8787)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I8_J])). 4.46/4.69 fof(c_0_4764, plain, ![X15573]:X15573=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15573),X15573)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), inference(variable_rename,[status(thm)],[fact_add__self__div__2])). 4.46/4.69 fof(c_0_4765, plain, ![X987, X988]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X988)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X987))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X988))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X987))), inference(variable_rename,[status(thm)],[fact_zdiv__number__of__Bit0])). 4.46/4.69 fof(c_0_4766, plain, ![X10467]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10467),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X10467)), inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc_H])). 4.46/4.69 fof(c_0_4767, plain, ![X11977, X11978, X11979]:c_Map_Odom(X11979,X11978,X11977)=hAPP(c_Set_OCollect(X11979),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11979),c_fNot),hAPP(hAPP(c_COMBC(X11979,tc_Option_Ooption(X11978),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X11978),tc_fun(tc_Option_Ooption(X11978),tc_HOL_Obool),X11979),c_fequal),X11977)),c_Option_Ooption_ONone(X11978)))), inference(variable_rename,[status(thm)],[fact_dom__def])). 4.46/4.69 fof(c_0_4768, plain, ![X6221, X6222, X6223, X6224]:hAPP(hAPP(c_List_Omap(X6223,X6224),X6222),X6221)=c_List_Oconcat(X6224,hAPP(hAPP(c_List_Omap(X6223,tc_List_Olist(X6224)),hAPP(hAPP(c_COMBC(X6223,tc_List_Olist(X6224),tc_List_Olist(X6224)),hAPP(hAPP(c_COMBB(X6224,tc_fun(tc_List_Olist(X6224),tc_List_Olist(X6224)),X6223),c_List_Olist_OCons(X6224)),X6222)),c_List_Olist_ONil(X6224))),X6221)), inference(variable_rename,[status(thm)],[fact_concat__map__singleton])). 4.46/4.69 fof(c_0_4769, plain, ![X1210, X1211]:hAPP(c_New__DSequence_Opos__not__seq(X1211),X1210)=c_Lazy__Sequence_Ohb__not__seq(hAPP(X1211,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X1210))), inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__not__seq__def])). 4.46/4.69 fof(c_0_4770, plain, ![X16699]:hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16699)))),c_Orderings_Oord__class_Oless(tc_Int_Oint))))=c_Int_Oint__ge__less__than(X16699), inference(variable_rename,[status(thm)],[fact_int__ge__less__than__def])). 4.46/4.69 fof(c_0_4771, plain, ![X2515, X2516, X2517, X2518]:hAPP(c_Set_OCollect(tc_prod(X2518,X2517)),hAPP(c_Product__Type_Oprod_Oprod__case(X2518,X2517,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X2518,tc_fun(X2517,tc_HOL_Obool),tc_fun(X2517,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2517,tc_HOL_Obool),tc_fun(X2517,tc_HOL_Obool)),X2518),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2517)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2518),c_fconj),X2516))),X2515)))=hAPP(hAPP(c_Product__Type_OSigma(X2518,X2517),hAPP(c_Set_OCollect(X2518),X2516)),hAPP(hAPP(c_COMBB(tc_fun(X2517,tc_HOL_Obool),tc_fun(X2517,tc_HOL_Obool),X2518),c_Set_OCollect(X2517)),X2515)), inference(variable_rename,[status(thm)],[fact_SetCompr__Sigma__eq])). 4.46/4.69 cnf(c_0_4772, plain, (hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), inference(split_conjunct,[status(thm)],[fact_card__UNIV__bool])). 4.46/4.69 fof(c_0_4773, plain, ![X5492, X5493]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X5493)),c_Int_OBit1(X5492))=c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X5493),X5492)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I10_J])). 4.46/4.69 fof(c_0_4774, plain, ![X8179, X8180]:c_Nitpick_OAbs__Frac(X8180,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(X8180),X8179))),hAPP(c_Nitpick_Odenom(X8180),X8179)))=c_Nitpick_Ouminus__frac(X8180,X8179), inference(variable_rename,[status(thm)],[fact_Nitpick_Ouminus__frac__def])). 4.46/4.69 fof(c_0_4775, plain, ![X536, X537]:c_Transitive__Closure_Ortrancl(X537,X536)=c_Transitive__Closure_Otrancl(X537,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X537,X537),tc_HOL_Obool)),X536),c_Relation_OId(X537))), inference(variable_rename,[status(thm)],[fact_trancl__reflcl])). 4.46/4.69 fof(c_0_4776, plain, ![X372, X373]:c_Transitive__Closure_Ortrancl(X373,X372)=c_Transitive__Closure_Ortrancl(X373,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X373,X373),tc_HOL_Obool)),X372),c_Relation_OId(X373))), inference(variable_rename,[status(thm)],[fact_rtrancl__reflcl])). 4.46/4.69 fof(c_0_4777, plain, ![X8814]:c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X8814))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X8814)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I3_J])). 4.46/4.69 fof(c_0_4778, plain, ![X9437, X9438]:c_Nitpick_Oint__lcm(X9438,X9437)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X9438)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X9437)))), inference(variable_rename,[status(thm)],[fact_Nitpick_Oint__lcm__def])). 4.46/4.69 fof(c_0_4779, plain, ![X4685, X4686]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4686),X4685)),c_Nitpick_Onat__gcd(X4686,X4685))=c_Nitpick_Onat__lcm(X4686,X4685), inference(variable_rename,[status(thm)],[fact_Nitpick_Onat__lcm__def])). 4.46/4.69 fof(c_0_4780, plain, ![X1434, X1435]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1435))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1434)))=hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1435),X1434))), inference(variable_rename,[status(thm)],[fact_nat__abs__mult__distrib])). 4.46/4.69 fof(c_0_4781, plain, ![X2858]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X2858))=c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X2858)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I6_J])). 4.46/4.69 cnf(c_0_4782, plain, (c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1))), inference(split_conjunct,[status(thm)],[c_0_4486])). 4.46/4.69 cnf(c_0_4783, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4487, c_0_4471]), c_0_4471])). 4.46/4.69 cnf(c_0_4784, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4488]), ['final']). 4.46/4.69 cnf(c_0_4785, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4489, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.69 fof(c_0_4786, plain, ![X6657]:c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6657)))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X6657)), inference(variable_rename,[status(thm)],[fact_minus__Bit1])). 4.46/4.69 fof(c_0_4787, plain, ![X3702, X3703]:c_List_Oconcat(X3703,hAPP(hAPP(c_List_Omap(tc_List_Olist(X3703),tc_List_Olist(X3703)),c_List_Orev(X3703)),hAPP(c_List_Orev(tc_List_Olist(X3703)),X3702)))=hAPP(c_List_Orev(X3703),c_List_Oconcat(X3703,X3702)), inference(variable_rename,[status(thm)],[fact_rev__concat])). 4.46/4.69 fof(c_0_4788, plain, ![X9267]:c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X9267))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X9267)), inference(variable_rename,[status(thm)],[fact_minus__Bit0])). 4.46/4.69 fof(c_0_4789, plain, ![X14874, X14875, X14876]:c_List_Oconcat(X14876,hAPP(hAPP(c_List_Omap(tc_List_Olist(X14876),tc_List_Olist(X14876)),c_List_Ofilter(X14876,X14875)),X14874))=hAPP(c_List_Ofilter(X14876,X14875),c_List_Oconcat(X14876,X14874)), inference(variable_rename,[status(thm)],[fact_filter__concat])). 4.46/4.69 fof(c_0_4790, plain, ![X9160, X9161]:c_Transitive__Closure_Otrancl(X9161,X9160)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X9161,X9161),tc_HOL_Obool)),X9160),hAPP(hAPP(c_Relation_Orel__comp(X9161,X9161,X9161),c_Transitive__Closure_Otrancl(X9161,X9160)),X9160)), inference(variable_rename,[status(thm)],[fact_trancl__unfold])). 4.46/4.69 fof(c_0_4791, plain, ![X877, X878]:hAPP(hAPP(c_Relation_Orel__comp(X878,X878,X878),c_Transitive__Closure_Ortrancl(X878,X877)),X877)=c_Transitive__Closure_Otrancl(X878,X877), inference(variable_rename,[status(thm)],[fact_trancl__unfold__right])). 4.46/4.69 fof(c_0_4792, plain, ![X3118, X3119]:c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(X3119)),c_List_Oembed__list(X3118)))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X3119),X3118), inference(variable_rename,[status(thm)],[fact_transfer__nat__int__list__functions_I1_J])). 4.46/4.69 fof(c_0_4793, plain, ![X12125]:c_List_Oreturn__list(X12125)=hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X12125), inference(variable_rename,[status(thm)],[fact_return__list__def])). 4.46/4.69 fof(c_0_4794, plain, ![X15308]:c_List_Oembed__list(X15308)=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X15308), inference(variable_rename,[status(thm)],[fact_embed__list__def])). 4.46/4.69 fof(c_0_4795, plain, ![X11492, X11493, X11494]:hAPP(c_Set_OCollect(X11494),hAPP(hAPP(c_COMBS(X11494,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X11494),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11494),c_fNot),hAPP(hAPP(c_COMBC(X11494,X11494,tc_HOL_Obool),c_fequal),X11493)))),X11492))=hAPP(hAPP(c_Set_Oinsert(X11494),X11493),hAPP(c_Set_OCollect(X11494),X11492)), inference(variable_rename,[status(thm)],[fact_insert__Collect])). 4.46/4.69 fof(c_0_4796, plain, ![X11448, X11449, X11450, X11451, X11452]:c_List_Ofoldr(X11451,X11452,hAPP(c_COMBC(X11452,X11451,X11452),X11450),hAPP(c_List_Orev(X11451),X11448),X11449)=hAPP(c_List_Ofoldl(X11452,X11451,X11450,X11449),X11448), inference(variable_rename,[status(thm)],[fact_foldl__foldr])). 4.46/4.69 fof(c_0_4797, plain, ![X11865, X11866]:c_Transitive__Closure_Ortrancl(X11866,X11865)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X11866,X11866),tc_HOL_Obool)),c_Relation_OId(X11866)),hAPP(hAPP(c_Relation_Orel__comp(X11866,X11866,X11866),c_Transitive__Closure_Ortrancl(X11866,X11865)),X11865)), inference(variable_rename,[status(thm)],[fact_rtrancl__unfold])). 4.46/4.69 fof(c_0_4798, plain, ![X643, X644, X645, X646]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X646,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X646,tc_HOL_Obool)),X645),X643)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X646,tc_HOL_Obool)),X644),X643))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X646,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X646,tc_HOL_Obool)),X645),X644)),X643), inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib2])). 4.46/4.69 cnf(c_0_4799, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_4490])). 4.46/4.69 cnf(c_0_4800, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)), inference(split_conjunct,[status(thm)],[c_0_4491]), ['final']). 4.46/4.69 fof(c_0_4801, plain, ![X11457]:c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X11457))), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J])). 4.46/4.69 fof(c_0_4802, plain, ![X11329, X11330]:hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X11330,X11329))=c_List_Oupt(hAPP(c_Nat_OSuc,X11330),hAPP(c_Nat_OSuc,X11329)), inference(variable_rename,[status(thm)],[fact_map__Suc__upt])). 4.46/4.69 fof(c_0_4803, plain, ![X8699, X8700, X8701, X8702, X8703]:((X8699!=hAPP(X8700,X8702)|hBOOL(hAPP(hAPP(c_member(X8703),X8702),hAPP(c_Set_Ovimage(X8703,X8701,X8700),hAPP(hAPP(c_Set_Oinsert(X8701),X8699),c_Orderings_Obot__class_Obot(tc_fun(X8701,tc_HOL_Obool)))))))&(~hBOOL(hAPP(hAPP(c_member(X8703),X8702),hAPP(c_Set_Ovimage(X8703,X8701,X8700),hAPP(hAPP(c_Set_Oinsert(X8701),X8699),c_Orderings_Obot__class_Obot(tc_fun(X8701,tc_HOL_Obool))))))|X8699=hAPP(X8700,X8702))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__singleton__eq])])). 4.46/4.69 fof(c_0_4804, plain, ![X15227, X15228]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X15228)),hAPP(c_Nat_OSuc,X15227))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X15228),X15227)), inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastLessThan])). 4.46/4.69 fof(c_0_4805, plain, ![X13431, X13432]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X13432,X13431)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X13432),hAPP(c_Nat_OSuc,X13431)), inference(variable_rename,[status(thm)],[fact_atLeastLessThanSuc__atLeastAtMost])). 4.46/4.69 fof(c_0_4806, plain, ![X13552]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X13552)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X13552)), inference(variable_rename,[status(thm)],[fact_code__numeral_Osize_I4_J])). 4.46/4.69 fof(c_0_4807, plain, ![X6741, X6742]:hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X6741),X6742))=hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X6742,X6741)), inference(variable_rename,[status(thm)],[fact_card__greaterThanAtMost__int])). 4.46/4.69 fof(c_0_4808, plain, ![X14676, X14677]:c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X14677,X14676)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X14677),c_Groups_Oone__class_Oone(tc_Int_Oint)),X14676), inference(variable_rename,[status(thm)],[fact_atLeastPlusOneAtMost__greaterThanAtMost__int])). 4.46/4.69 fof(c_0_4809, plain, ![X1358, X1359]:hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1358),X1359)),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1359,X1358)), inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost__int])). 4.46/4.69 fof(c_0_4810, plain, ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)), inference(fof_simplification,[status(thm)],[fact_rel__simps_I2_J])). 4.46/4.69 fof(c_0_4811, plain, ![X12426, X12427, X12428]:((c_List_Olist_ONil(X12428)!=X12426|hAPP(c_List_Orotate(X12428,X12427),X12426)=c_List_Olist_ONil(X12428))&(hAPP(c_List_Orotate(X12428,X12427),X12426)!=c_List_Olist_ONil(X12428)|c_List_Olist_ONil(X12428)=X12426)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__is__Nil__conv])])). 4.46/4.69 fof(c_0_4812, plain, ![X13689, X13690]:hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X13690),tc_List_Olist(X13690)),X13689),c_List_Orotate1(X13690))=c_List_Orotate(X13690,X13689), inference(variable_rename,[status(thm)],[fact_rotate__def])). 4.46/4.69 fof(c_0_4813, plain, ![X3340, X3341]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3341,X3340)=hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X3341,hAPP(c_Nat_OSuc,X3340))), inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upt])). 4.46/4.69 fof(c_0_4814, plain, ![X3142]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X3142)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X3142)), inference(variable_rename,[status(thm)],[fact_code__numeral_Osize_I2_J])). 4.46/4.69 fof(c_0_4815, plain, ![X7054, X7055, X7056, X7057]:hAPP(X7055,X7054)=c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X7057,X7056,X7055,c_Code__Numeral_OSuc__code__numeral(X7054)), inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I5_J])). 4.46/4.69 fof(c_0_4816, plain, ![X12880]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X12880)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))=X12880, inference(variable_rename,[status(thm)],[fact_Suc__code__numeral__minus__one])). 4.46/4.69 fof(c_0_4817, plain, ![X12472, X12473]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12472),X12473)=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X12473,X12472)), inference(variable_rename,[status(thm)],[fact_card__greaterThanAtMost])). 4.46/4.69 fof(c_0_4818, plain, ![X6896, X6897]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X6897),X6896)=c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X6897,X6896), inference(variable_rename,[status(thm)],[fact_atLeastSucAtMost__greaterThanAtMost])). 4.46/4.69 fof(c_0_4819, plain, ![X4228]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4228)),X4228)=c_Groups_Ozero__class_Ozero(tc_Int_Oint), inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2])). 4.46/4.69 fof(c_0_4820, plain, ![X16375]:c_Orderings_Obot__class_Obot(tc_fun(X16375,tc_HOL_Obool))=hAPP(c_Set_OCollect(X16375),hAPP(c_COMBK(tc_HOL_Obool,X16375),c_fFalse)), inference(variable_rename,[status(thm)],[fact_empty__def])). 4.46/4.69 fof(c_0_4821, plain, ![X6872]:hAPP(c_Set_OCollect(X6872),hAPP(c_COMBK(tc_HOL_Obool,X6872),c_fTrue))=c_Orderings_Otop__class_Otop(tc_fun(X6872,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_UNIV__def])). 4.46/4.69 fof(c_0_4822, plain, ![X11793]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X11793),hAPP(c_Nat_OSuc,X11793))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X11793),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_atLeastLessThan__singleton])). 4.46/4.69 fof(c_0_4823, plain, ![X3409, X3410, X3411, X3412, X3413, X3414, X3415]:(~class_Rings_Osemiring__0(X3415)|(~c_Fun_Oinj__on(tc_prod(X3414,X3413),X3415,hAPP(c_Product__Type_Oprod_Oprod__case(X3414,X3413,X3415),hAPP(hAPP(c_COMBC(X3414,tc_fun(X3413,X3415),tc_fun(X3413,X3415)),hAPP(hAPP(c_COMBB(tc_fun(X3415,X3415),tc_fun(tc_fun(X3413,X3415),tc_fun(X3413,X3415)),X3414),c_COMBB(X3415,X3415,X3413)),hAPP(hAPP(c_COMBB(X3415,tc_fun(X3415,X3415),X3414),c_Groups_Otimes__class_Otimes(X3415)),X3412))),X3411)),hAPP(hAPP(c_Product__Type_OSigma(X3414,X3413),X3410),hAPP(c_COMBK(tc_fun(X3413,tc_HOL_Obool),X3414),X3409)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3415,X3415),c_Fun_Oid(X3415)),hAPP(c_Set_OCollect(X3415),hAPP(hAPP(c_COMBB(tc_fun(X3414,tc_HOL_Obool),tc_HOL_Obool,X3415),c_HOL_OEx(X3414)),hAPP(hAPP(c_COMBB(tc_fun(X3414,tc_fun(X3413,tc_HOL_Obool)),tc_fun(X3414,tc_HOL_Obool),X3415),hAPP(c_COMBB(tc_fun(X3413,tc_HOL_Obool),tc_HOL_Obool,X3414),c_HOL_OEx(X3413))),hAPP(hAPP(c_COMBC(X3415,tc_fun(X3414,tc_fun(X3413,tc_HOL_Obool)),tc_fun(X3414,tc_fun(X3413,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X3414,tc_fun(tc_fun(X3413,tc_HOL_Obool),tc_fun(X3413,tc_HOL_Obool))),tc_fun(tc_fun(X3414,tc_fun(X3413,tc_HOL_Obool)),tc_fun(X3414,tc_fun(X3413,tc_HOL_Obool))),X3415),c_COMBS(X3414,tc_fun(X3413,tc_HOL_Obool),tc_fun(X3413,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X3414,tc_fun(X3413,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X3414,tc_fun(tc_fun(X3413,tc_HOL_Obool),tc_fun(X3413,tc_HOL_Obool))),X3415),hAPP(c_COMBB(tc_fun(X3413,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X3413,tc_HOL_Obool),tc_fun(X3413,tc_HOL_Obool)),X3414),c_COMBS(X3413,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X3414,tc_fun(X3413,tc_HOL_Obool)),tc_fun(X3414,tc_fun(X3413,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X3415),hAPP(c_COMBB(tc_fun(X3413,tc_HOL_Obool),tc_fun(X3413,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X3414),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3413),c_fconj))),hAPP(hAPP(c_COMBC(X3415,tc_fun(X3414,tc_fun(X3413,X3415)),tc_fun(X3414,tc_fun(X3413,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3413,X3415),tc_fun(X3413,tc_HOL_Obool)),tc_fun(tc_fun(X3414,tc_fun(X3413,X3415)),tc_fun(X3414,tc_fun(X3413,tc_HOL_Obool))),X3415),c_COMBB(tc_fun(X3413,X3415),tc_fun(X3413,tc_HOL_Obool),X3414)),hAPP(hAPP(c_COMBB(tc_fun(X3415,tc_HOL_Obool),tc_fun(tc_fun(X3413,X3415),tc_fun(X3413,tc_HOL_Obool)),X3415),c_COMBB(X3415,tc_HOL_Obool,X3413)),c_fequal))),hAPP(hAPP(c_COMBC(X3414,tc_fun(X3413,X3415),tc_fun(X3413,X3415)),hAPP(hAPP(c_COMBB(tc_fun(X3415,X3415),tc_fun(tc_fun(X3413,X3415),tc_fun(X3413,X3415)),X3414),c_COMBB(X3415,X3415,X3413)),hAPP(hAPP(c_COMBB(X3415,tc_fun(X3415,X3415),X3414),c_Groups_Otimes__class_Otimes(X3415)),X3412))),X3411)))))),hAPP(hAPP(c_COMBC(X3414,tc_fun(X3413,tc_HOL_Obool),tc_fun(X3413,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X3413,tc_HOL_Obool),tc_fun(X3413,tc_HOL_Obool)),X3414),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3413)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3414),c_fconj),hAPP(hAPP(c_COMBC(X3414,tc_fun(X3414,tc_HOL_Obool),tc_HOL_Obool),c_member(X3414)),X3410)))),hAPP(hAPP(c_COMBC(X3413,tc_fun(X3413,tc_HOL_Obool),tc_HOL_Obool),c_member(X3413)),X3409)))))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3415),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3414,X3415),X3412),X3410)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3413,X3415),X3411),X3409)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__mult__setsum__if__inj])])])). 4.46/4.69 cnf(c_0_4824, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1))))=c_Divides_Odivmod__int(X2,X1)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2), inference(split_conjunct,[status(thm)],[c_0_4492])). 4.46/4.69 cnf(c_0_4825, plain, (c_Product__Type_Oapsnd(X1,X2,X3,X4)=c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X4)), inference(split_conjunct,[status(thm)],[c_0_4493])). 4.46/4.69 cnf(c_0_4826, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,X2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1))))=c_Divides_Odivmod__int(X2,X1)|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_4494])). 4.46/4.69 fof(c_0_4827, plain, ![X7520, X7521, X7522]:(~class_Orderings_Olinorder(X7522)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7522),X7521))|(c_Orderings_Obot__class_Obot(tc_fun(X7522,tc_HOL_Obool))=X7521|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7522),X7520))|(c_Orderings_Obot__class_Obot(tc_fun(X7522,tc_HOL_Obool))=X7520|c_Big__Operators_Olattice_OInf__fin(X7522,c_Orderings_Oord__class_Omin(X7522),hAPP(c_Set_OCollect(X7522),hAPP(hAPP(c_COMBB(tc_fun(X7522,tc_HOL_Obool),tc_HOL_Obool,X7522),c_HOL_OEx(X7522)),hAPP(hAPP(c_COMBB(tc_fun(X7522,tc_fun(X7522,tc_HOL_Obool)),tc_fun(X7522,tc_HOL_Obool),X7522),hAPP(c_COMBB(tc_fun(X7522,tc_HOL_Obool),tc_HOL_Obool,X7522),c_HOL_OEx(X7522))),hAPP(hAPP(c_COMBC(X7522,tc_fun(X7522,tc_fun(X7522,tc_HOL_Obool)),tc_fun(X7522,tc_fun(X7522,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7522,tc_fun(tc_fun(X7522,tc_HOL_Obool),tc_fun(X7522,tc_HOL_Obool))),tc_fun(tc_fun(X7522,tc_fun(X7522,tc_HOL_Obool)),tc_fun(X7522,tc_fun(X7522,tc_HOL_Obool))),X7522),c_COMBS(X7522,tc_fun(X7522,tc_HOL_Obool),tc_fun(X7522,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7522,tc_fun(X7522,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X7522,tc_fun(tc_fun(X7522,tc_HOL_Obool),tc_fun(X7522,tc_HOL_Obool))),X7522),hAPP(c_COMBB(tc_fun(X7522,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X7522,tc_HOL_Obool),tc_fun(X7522,tc_HOL_Obool)),X7522),c_COMBS(X7522,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7522,tc_fun(X7522,tc_HOL_Obool)),tc_fun(X7522,tc_fun(X7522,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X7522),hAPP(c_COMBB(tc_fun(X7522,tc_HOL_Obool),tc_fun(X7522,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7522),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7522),c_fconj))),hAPP(hAPP(c_COMBC(X7522,tc_fun(X7522,tc_fun(X7522,X7522)),tc_fun(X7522,tc_fun(X7522,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7522,X7522),tc_fun(X7522,tc_HOL_Obool)),tc_fun(tc_fun(X7522,tc_fun(X7522,X7522)),tc_fun(X7522,tc_fun(X7522,tc_HOL_Obool))),X7522),c_COMBB(tc_fun(X7522,X7522),tc_fun(X7522,tc_HOL_Obool),X7522)),hAPP(hAPP(c_COMBB(tc_fun(X7522,tc_HOL_Obool),tc_fun(tc_fun(X7522,X7522),tc_fun(X7522,tc_HOL_Obool)),X7522),c_COMBB(X7522,tc_HOL_Obool,X7522)),c_fequal))),c_Orderings_Oord__class_Omax(X7522)))))),hAPP(hAPP(c_COMBC(X7522,tc_fun(X7522,tc_HOL_Obool),tc_fun(X7522,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X7522,tc_HOL_Obool),tc_fun(X7522,tc_HOL_Obool)),X7522),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7522)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7522),c_fconj),hAPP(hAPP(c_COMBC(X7522,tc_fun(X7522,tc_HOL_Obool),tc_HOL_Obool),c_member(X7522)),X7521)))),hAPP(hAPP(c_COMBC(X7522,tc_fun(X7522,tc_HOL_Obool),tc_HOL_Obool),c_member(X7522)),X7520)))))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X7522),c_Big__Operators_Olattice_OInf__fin(X7522,c_Orderings_Oord__class_Omin(X7522),X7521)),c_Big__Operators_Olattice_OInf__fin(X7522,c_Orderings_Oord__class_Omin(X7522),X7520))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__Inf2__distrib])])])). 4.46/4.69 fof(c_0_4828, plain, ![X9208, X9209, X9210]:(~class_Orderings_Olinorder(X9210)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9210),X9209))|(c_Orderings_Obot__class_Obot(tc_fun(X9210,tc_HOL_Obool))=X9209|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9210),X9208))|(c_Orderings_Obot__class_Obot(tc_fun(X9210,tc_HOL_Obool))=X9208|c_Big__Operators_Olattice_OSup__fin(X9210,c_Orderings_Oord__class_Omax(X9210),hAPP(c_Set_OCollect(X9210),hAPP(hAPP(c_COMBB(tc_fun(X9210,tc_HOL_Obool),tc_HOL_Obool,X9210),c_HOL_OEx(X9210)),hAPP(hAPP(c_COMBB(tc_fun(X9210,tc_fun(X9210,tc_HOL_Obool)),tc_fun(X9210,tc_HOL_Obool),X9210),hAPP(c_COMBB(tc_fun(X9210,tc_HOL_Obool),tc_HOL_Obool,X9210),c_HOL_OEx(X9210))),hAPP(hAPP(c_COMBC(X9210,tc_fun(X9210,tc_fun(X9210,tc_HOL_Obool)),tc_fun(X9210,tc_fun(X9210,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X9210,tc_fun(tc_fun(X9210,tc_HOL_Obool),tc_fun(X9210,tc_HOL_Obool))),tc_fun(tc_fun(X9210,tc_fun(X9210,tc_HOL_Obool)),tc_fun(X9210,tc_fun(X9210,tc_HOL_Obool))),X9210),c_COMBS(X9210,tc_fun(X9210,tc_HOL_Obool),tc_fun(X9210,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X9210,tc_fun(X9210,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X9210,tc_fun(tc_fun(X9210,tc_HOL_Obool),tc_fun(X9210,tc_HOL_Obool))),X9210),hAPP(c_COMBB(tc_fun(X9210,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X9210,tc_HOL_Obool),tc_fun(X9210,tc_HOL_Obool)),X9210),c_COMBS(X9210,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X9210,tc_fun(X9210,tc_HOL_Obool)),tc_fun(X9210,tc_fun(X9210,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X9210),hAPP(c_COMBB(tc_fun(X9210,tc_HOL_Obool),tc_fun(X9210,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X9210),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X9210),c_fconj))),hAPP(hAPP(c_COMBC(X9210,tc_fun(X9210,tc_fun(X9210,X9210)),tc_fun(X9210,tc_fun(X9210,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X9210,X9210),tc_fun(X9210,tc_HOL_Obool)),tc_fun(tc_fun(X9210,tc_fun(X9210,X9210)),tc_fun(X9210,tc_fun(X9210,tc_HOL_Obool))),X9210),c_COMBB(tc_fun(X9210,X9210),tc_fun(X9210,tc_HOL_Obool),X9210)),hAPP(hAPP(c_COMBB(tc_fun(X9210,tc_HOL_Obool),tc_fun(tc_fun(X9210,X9210),tc_fun(X9210,tc_HOL_Obool)),X9210),c_COMBB(X9210,tc_HOL_Obool,X9210)),c_fequal))),c_Orderings_Oord__class_Omin(X9210)))))),hAPP(hAPP(c_COMBC(X9210,tc_fun(X9210,tc_HOL_Obool),tc_fun(X9210,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X9210,tc_HOL_Obool),tc_fun(X9210,tc_HOL_Obool)),X9210),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X9210)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X9210),c_fconj),hAPP(hAPP(c_COMBC(X9210,tc_fun(X9210,tc_HOL_Obool),tc_HOL_Obool),c_member(X9210)),X9209)))),hAPP(hAPP(c_COMBC(X9210,tc_fun(X9210,tc_HOL_Obool),tc_HOL_Obool),c_member(X9210)),X9208)))))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X9210),c_Big__Operators_Olattice_OSup__fin(X9210,c_Orderings_Oord__class_Omax(X9210),X9209)),c_Big__Operators_Olattice_OSup__fin(X9210,c_Orderings_Oord__class_Omax(X9210),X9208))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__Sup2__distrib])])])). 4.46/4.69 fof(c_0_4829, plain, ![X14379, X14380, X14381]:(~class_Lattices_Odistrib__lattice(X14381)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14381),X14380))|(c_Orderings_Obot__class_Obot(tc_fun(X14381,tc_HOL_Obool))=X14380|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14381),X14379))|(X14379=c_Orderings_Obot__class_Obot(tc_fun(X14381,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X14381),c_Big__Operators_Olattice__class_OSup__fin(X14381,X14380)),c_Big__Operators_Olattice__class_OSup__fin(X14381,X14379))=c_Big__Operators_Olattice__class_OSup__fin(X14381,hAPP(c_Set_OCollect(X14381),hAPP(hAPP(c_COMBB(tc_fun(X14381,tc_HOL_Obool),tc_HOL_Obool,X14381),c_HOL_OEx(X14381)),hAPP(hAPP(c_COMBB(tc_fun(X14381,tc_fun(X14381,tc_HOL_Obool)),tc_fun(X14381,tc_HOL_Obool),X14381),hAPP(c_COMBB(tc_fun(X14381,tc_HOL_Obool),tc_HOL_Obool,X14381),c_HOL_OEx(X14381))),hAPP(hAPP(c_COMBC(X14381,tc_fun(X14381,tc_fun(X14381,tc_HOL_Obool)),tc_fun(X14381,tc_fun(X14381,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X14381,tc_fun(tc_fun(X14381,tc_HOL_Obool),tc_fun(X14381,tc_HOL_Obool))),tc_fun(tc_fun(X14381,tc_fun(X14381,tc_HOL_Obool)),tc_fun(X14381,tc_fun(X14381,tc_HOL_Obool))),X14381),c_COMBS(X14381,tc_fun(X14381,tc_HOL_Obool),tc_fun(X14381,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X14381,tc_fun(X14381,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X14381,tc_fun(tc_fun(X14381,tc_HOL_Obool),tc_fun(X14381,tc_HOL_Obool))),X14381),hAPP(c_COMBB(tc_fun(X14381,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X14381,tc_HOL_Obool),tc_fun(X14381,tc_HOL_Obool)),X14381),c_COMBS(X14381,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X14381,tc_fun(X14381,tc_HOL_Obool)),tc_fun(X14381,tc_fun(X14381,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X14381),hAPP(c_COMBB(tc_fun(X14381,tc_HOL_Obool),tc_fun(X14381,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X14381),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X14381),c_fconj))),hAPP(hAPP(c_COMBC(X14381,tc_fun(X14381,tc_fun(X14381,X14381)),tc_fun(X14381,tc_fun(X14381,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X14381,X14381),tc_fun(X14381,tc_HOL_Obool)),tc_fun(tc_fun(X14381,tc_fun(X14381,X14381)),tc_fun(X14381,tc_fun(X14381,tc_HOL_Obool))),X14381),c_COMBB(tc_fun(X14381,X14381),tc_fun(X14381,tc_HOL_Obool),X14381)),hAPP(hAPP(c_COMBB(tc_fun(X14381,tc_HOL_Obool),tc_fun(tc_fun(X14381,X14381),tc_fun(X14381,tc_HOL_Obool)),X14381),c_COMBB(X14381,tc_HOL_Obool,X14381)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X14381)))))),hAPP(hAPP(c_COMBC(X14381,tc_fun(X14381,tc_HOL_Obool),tc_fun(X14381,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X14381,tc_HOL_Obool),tc_fun(X14381,tc_HOL_Obool)),X14381),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X14381)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X14381),c_fconj),hAPP(hAPP(c_COMBC(X14381,tc_fun(X14381,tc_HOL_Obool),tc_HOL_Obool),c_member(X14381)),X14380)))),hAPP(hAPP(c_COMBC(X14381,tc_fun(X14381,tc_HOL_Obool),tc_HOL_Obool),c_member(X14381)),X14379)))))))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__Sup2__distrib])])])). 4.46/4.69 fof(c_0_4830, plain, ![X11216, X11217, X11218]:(~class_Lattices_Odistrib__lattice(X11218)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11218),X11217))|(X11217=c_Orderings_Obot__class_Obot(tc_fun(X11218,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11218),X11216))|(X11216=c_Orderings_Obot__class_Obot(tc_fun(X11218,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X11218),c_Big__Operators_Olattice__class_OInf__fin(X11218,X11217)),c_Big__Operators_Olattice__class_OInf__fin(X11218,X11216))=c_Big__Operators_Olattice__class_OInf__fin(X11218,hAPP(c_Set_OCollect(X11218),hAPP(hAPP(c_COMBB(tc_fun(X11218,tc_HOL_Obool),tc_HOL_Obool,X11218),c_HOL_OEx(X11218)),hAPP(hAPP(c_COMBB(tc_fun(X11218,tc_fun(X11218,tc_HOL_Obool)),tc_fun(X11218,tc_HOL_Obool),X11218),hAPP(c_COMBB(tc_fun(X11218,tc_HOL_Obool),tc_HOL_Obool,X11218),c_HOL_OEx(X11218))),hAPP(hAPP(c_COMBC(X11218,tc_fun(X11218,tc_fun(X11218,tc_HOL_Obool)),tc_fun(X11218,tc_fun(X11218,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X11218,tc_fun(tc_fun(X11218,tc_HOL_Obool),tc_fun(X11218,tc_HOL_Obool))),tc_fun(tc_fun(X11218,tc_fun(X11218,tc_HOL_Obool)),tc_fun(X11218,tc_fun(X11218,tc_HOL_Obool))),X11218),c_COMBS(X11218,tc_fun(X11218,tc_HOL_Obool),tc_fun(X11218,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X11218,tc_fun(X11218,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X11218,tc_fun(tc_fun(X11218,tc_HOL_Obool),tc_fun(X11218,tc_HOL_Obool))),X11218),hAPP(c_COMBB(tc_fun(X11218,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X11218,tc_HOL_Obool),tc_fun(X11218,tc_HOL_Obool)),X11218),c_COMBS(X11218,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X11218,tc_fun(X11218,tc_HOL_Obool)),tc_fun(X11218,tc_fun(X11218,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X11218),hAPP(c_COMBB(tc_fun(X11218,tc_HOL_Obool),tc_fun(X11218,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X11218),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X11218),c_fconj))),hAPP(hAPP(c_COMBC(X11218,tc_fun(X11218,tc_fun(X11218,X11218)),tc_fun(X11218,tc_fun(X11218,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X11218,X11218),tc_fun(X11218,tc_HOL_Obool)),tc_fun(tc_fun(X11218,tc_fun(X11218,X11218)),tc_fun(X11218,tc_fun(X11218,tc_HOL_Obool))),X11218),c_COMBB(tc_fun(X11218,X11218),tc_fun(X11218,tc_HOL_Obool),X11218)),hAPP(hAPP(c_COMBB(tc_fun(X11218,tc_HOL_Obool),tc_fun(tc_fun(X11218,X11218),tc_fun(X11218,tc_HOL_Obool)),X11218),c_COMBB(X11218,tc_HOL_Obool,X11218)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X11218)))))),hAPP(hAPP(c_COMBC(X11218,tc_fun(X11218,tc_HOL_Obool),tc_fun(X11218,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X11218,tc_HOL_Obool),tc_fun(X11218,tc_HOL_Obool)),X11218),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11218)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X11218),c_fconj),hAPP(hAPP(c_COMBC(X11218,tc_fun(X11218,tc_HOL_Obool),tc_HOL_Obool),c_member(X11218)),X11217)))),hAPP(hAPP(c_COMBC(X11218,tc_fun(X11218,tc_HOL_Obool),tc_HOL_Obool),c_member(X11218)),X11216)))))))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__Inf2__distrib])])])). 4.46/4.69 cnf(c_0_4831, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X2,X2)),tc_fun(tc_Int_Oint,X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X2),X2),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X2,X2)),tc_fun(tc_Int_Oint,X2)),tc_Int_Oint),c_COMBB(tc_fun(X2,X2),X2,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,X2),X2),tc_Int_Oint),c_HOL_OLet(X2,X2)),c_Int_Oring__1__class_Oof__int(X2)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X2,X2),tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X2,X2)),tc_fun(tc_fun(X2,X2),tc_fun(X2,X2)),tc_Int_Oint),c_COMBS(X2,X2,X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X2,X2),tc_fun(X2,tc_fun(X2,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X2,X2)),tc_fun(tc_fun(X2,X2),tc_fun(X2,tc_fun(X2,X2))),tc_Int_Oint),c_COMBB(X2,tc_fun(X2,X2),X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),tc_Int_Oint),c_If(X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(X2,X2,X2),c_Groups_Oplus__class_Oplus(X2)),c_COMBI(X2))))),hAPP(hAPP(c_COMBC(X2,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X2),c_Groups_Oplus__class_Oplus(X2)),hAPP(hAPP(c_COMBS(X2,X2,X2),c_Groups_Oplus__class_Oplus(X2)),c_COMBI(X2)))),c_Groups_Oone__class_Oone(X2))))),c_Divides_Odivmod__int(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|~class_Rings_Oring__1(X2)), inference(split_conjunct,[status(thm)],[c_0_4495])). 4.46/4.69 cnf(c_0_4832, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4496])). 4.46/4.69 cnf(c_0_4833, plain, (hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4497, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.69 cnf(c_0_4834, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=X1), inference(rw,[status(thm)],[c_0_4498, c_0_4436]), ['final']). 4.46/4.69 cnf(c_0_4835, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_4499, c_0_4500]), ['final']). 4.46/4.69 cnf(c_0_4836, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[fact_One__nat__def]), ['final']). 4.46/4.69 cnf(c_0_4837, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),X3))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4501])). 4.46/4.69 cnf(c_0_4838, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_4502])). 4.46/4.69 fof(c_0_4839, plain, ![X17565, X17566, X17567, X17568, X17569, X17570, X17571]:(~class_Groups_Ocomm__monoid__add(X17571)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17570),X17569))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17568),X17567))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17568,X17571),hAPP(hAPP(c_COMBS(X17568,tc_fun(X17570,tc_HOL_Obool),X17571),hAPP(hAPP(c_COMBB(tc_fun(X17570,X17571),tc_fun(tc_fun(X17570,tc_HOL_Obool),X17571),X17568),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17570,X17571)),hAPP(c_COMBC(X17570,X17568,X17571),X17566))),hAPP(hAPP(c_COMBB(tc_fun(X17570,tc_HOL_Obool),tc_fun(X17570,tc_HOL_Obool),X17568),c_Set_OCollect(X17570)),hAPP(hAPP(c_COMBB(tc_fun(X17570,tc_HOL_Obool),tc_fun(X17570,tc_HOL_Obool),X17568),hAPP(c_COMBS(X17570,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17570),c_fconj),hAPP(hAPP(c_COMBC(X17570,tc_fun(X17570,tc_HOL_Obool),tc_HOL_Obool),c_member(X17570)),X17569)))),hAPP(c_COMBC(X17570,X17568,tc_HOL_Obool),X17565))))),X17567)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17570,X17571),hAPP(hAPP(c_COMBS(X17570,tc_fun(X17568,tc_HOL_Obool),X17571),hAPP(hAPP(c_COMBB(tc_fun(X17568,X17571),tc_fun(tc_fun(X17568,tc_HOL_Obool),X17571),X17570),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17568,X17571)),X17566)),hAPP(hAPP(c_COMBB(tc_fun(X17568,tc_HOL_Obool),tc_fun(X17568,tc_HOL_Obool),X17570),c_Set_OCollect(X17568)),hAPP(hAPP(c_COMBB(tc_fun(X17568,tc_HOL_Obool),tc_fun(X17568,tc_HOL_Obool),X17570),hAPP(c_COMBS(X17568,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17568),c_fconj),hAPP(hAPP(c_COMBC(X17568,tc_fun(X17568,tc_HOL_Obool),tc_HOL_Obool),c_member(X17568)),X17567)))),X17565)))),X17569)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__setsum__restrict])])])). 4.46/4.69 cnf(c_0_4840, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|hAPP(c_Code__Numeral_Oint__of,X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1), inference(split_conjunct,[status(thm)],[c_0_4503])). 4.46/4.69 cnf(c_0_4841, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_4504])). 4.46/4.69 fof(c_0_4842, plain, ![X4503, X4504, X4505, X4506, X4507, X4508, X4509, X4510, X4511]:((c_Hoare__Mirabelle_Ohoare__derivs(X4509,X4508,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4509)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4509),hAPP(X4507,esk123_9(X4503,X4504,X4505,X4506,X4507,X4508,X4509,X4510,X4511))),hAPP(X4506,esk123_9(X4503,X4504,X4505,X4506,X4507,X4508,X4509,X4510,X4511))),hAPP(X4505,esk123_9(X4503,X4504,X4505,X4506,X4507,X4508,X4509,X4510,X4511)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4509),tc_HOL_Obool))))|(~c_Hoare__Mirabelle_Ohoare__derivs(X4509,X4508,hAPP(c_Set_Oimage(X4511,tc_Hoare__Mirabelle_Otriple(X4509),hAPP(hAPP(c_COMBS(X4511,tc_fun(X4509,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4509)),hAPP(hAPP(c_COMBS(X4511,tc_Com_Ocom,tc_fun(tc_fun(X4509,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4509))),hAPP(hAPP(c_COMBB(tc_fun(X4509,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X4509,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4509))),X4511),c_Hoare__Mirabelle_Otriple_Otriple(X4509)),X4507)),X4506)),X4505)),X4510))|c_Hoare__Mirabelle_Ohoare__derivs(X4509,X4508,hAPP(c_Set_Oimage(X4511,tc_Hoare__Mirabelle_Otriple(X4509),hAPP(hAPP(c_COMBS(X4511,tc_fun(X4509,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4509)),hAPP(hAPP(c_COMBS(X4511,tc_Com_Ocom,tc_fun(tc_fun(X4509,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4509))),hAPP(hAPP(c_COMBB(tc_fun(X4509,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X4509,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4509))),X4511),c_Hoare__Mirabelle_Otriple_Otriple(X4509)),X4504)),X4506)),X4503)),X4510)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4511),X4510)))&(~c_Hoare__Mirabelle_Ohoare__derivs(X4509,X4508,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4509)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4509),hAPP(X4504,esk123_9(X4503,X4504,X4505,X4506,X4507,X4508,X4509,X4510,X4511))),hAPP(X4506,esk123_9(X4503,X4504,X4505,X4506,X4507,X4508,X4509,X4510,X4511))),hAPP(X4503,esk123_9(X4503,X4504,X4505,X4506,X4507,X4508,X4509,X4510,X4511)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4509),tc_HOL_Obool))))|(~c_Hoare__Mirabelle_Ohoare__derivs(X4509,X4508,hAPP(c_Set_Oimage(X4511,tc_Hoare__Mirabelle_Otriple(X4509),hAPP(hAPP(c_COMBS(X4511,tc_fun(X4509,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4509)),hAPP(hAPP(c_COMBS(X4511,tc_Com_Ocom,tc_fun(tc_fun(X4509,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4509))),hAPP(hAPP(c_COMBB(tc_fun(X4509,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X4509,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4509))),X4511),c_Hoare__Mirabelle_Otriple_Otriple(X4509)),X4507)),X4506)),X4505)),X4510))|c_Hoare__Mirabelle_Ohoare__derivs(X4509,X4508,hAPP(c_Set_Oimage(X4511,tc_Hoare__Mirabelle_Otriple(X4509),hAPP(hAPP(c_COMBS(X4511,tc_fun(X4509,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4509)),hAPP(hAPP(c_COMBS(X4511,tc_Com_Ocom,tc_fun(tc_fun(X4509,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4509))),hAPP(hAPP(c_COMBB(tc_fun(X4509,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X4509,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X4509))),X4511),c_Hoare__Mirabelle_Otriple_Otriple(X4509)),X4504)),X4506)),X4503)),X4510)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4511),X4510)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__pointwise])])])])])). 4.46/4.69 cnf(c_0_4843, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))=hAPP(c_Code__Numeral_Oint__of,X1)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), inference(split_conjunct,[status(thm)],[c_0_4503])). 4.46/4.69 cnf(c_0_4844, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_4505])). 4.46/4.69 cnf(c_0_4845, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X2)))|X1!=c_Groups_Ozero__class_Ozero(X2)|X3!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_4506])). 4.46/4.69 cnf(c_0_4846, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1)))), inference(split_conjunct,[status(thm)],[c_0_4507])). 4.46/4.69 cnf(c_0_4847, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_4508])). 4.46/4.69 cnf(c_0_4848, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4509])). 4.46/4.69 cnf(c_0_4849, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X2|c_Groups_Ozero__class_Ozero(X1)!=X3|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4510])). 4.46/4.69 cnf(c_0_4850, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_4509])). 4.46/4.69 cnf(c_0_4851, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4511])). 4.46/4.69 cnf(c_0_4852, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_4507])). 4.46/4.69 fof(c_0_4853, plain, ![X7810, X7811, X7812, X7813]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X7813,X7813)),hAPP(hAPP(c_Product__Type_OPair(X7813,X7813),X7811),X7810)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7813,X7813),tc_HOL_Obool)),X7812),c_Relation_OId(X7813))))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7813,tc_fun(X7813,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X7813,tc_fun(tc_prod(X7813,X7813),tc_HOL_Obool),tc_fun(X7813,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7813,tc_fun(tc_fun(tc_prod(X7813,X7813),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7813,X7813),tc_HOL_Obool),tc_fun(X7813,tc_HOL_Obool)),X7813),c_COMBC(X7813,tc_fun(tc_prod(X7813,X7813),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7813,tc_prod(X7813,X7813)),tc_fun(X7813,tc_fun(tc_fun(tc_prod(X7813,X7813),tc_HOL_Obool),tc_HOL_Obool)),X7813),hAPP(c_COMBB(tc_prod(X7813,X7813),tc_fun(tc_fun(tc_prod(X7813,X7813),tc_HOL_Obool),tc_HOL_Obool),X7813),c_member(tc_prod(X7813,X7813)))),c_Product__Type_OPair(X7813,X7813)))),X7812)),c_fequal),X7811),X7810)))&(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7813,tc_fun(X7813,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X7813,tc_fun(tc_prod(X7813,X7813),tc_HOL_Obool),tc_fun(X7813,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7813,tc_fun(tc_fun(tc_prod(X7813,X7813),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7813,X7813),tc_HOL_Obool),tc_fun(X7813,tc_HOL_Obool)),X7813),c_COMBC(X7813,tc_fun(tc_prod(X7813,X7813),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7813,tc_prod(X7813,X7813)),tc_fun(X7813,tc_fun(tc_fun(tc_prod(X7813,X7813),tc_HOL_Obool),tc_HOL_Obool)),X7813),hAPP(c_COMBB(tc_prod(X7813,X7813),tc_fun(tc_fun(tc_prod(X7813,X7813),tc_HOL_Obool),tc_HOL_Obool),X7813),c_member(tc_prod(X7813,X7813)))),c_Product__Type_OPair(X7813,X7813)))),X7812)),c_fequal),X7811),X7810))|hBOOL(hAPP(hAPP(c_member(tc_prod(X7813,X7813)),hAPP(hAPP(c_Product__Type_OPair(X7813,X7813),X7811),X7810)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7813,X7813),tc_HOL_Obool)),X7812),c_Relation_OId(X7813)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflcl__set__eq])])). 4.46/4.69 fof(c_0_4854, plain, ![X4840, X4841, X4842, X4843, X4844, X4845]:((hBOOL(hAPP(hAPP(c_member(X4843),esk140_6(X4840,X4841,X4842,X4843,X4844,X4845)),X4842))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4845,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X4843,tc_HOL_Obool),tc_Nat_Onat,X4845),c_Finite__Set_Ocard(X4843)),hAPP(hAPP(c_COMBB(tc_fun(X4843,tc_HOL_Obool),tc_fun(X4843,tc_HOL_Obool),X4845),c_Set_OCollect(X4843)),hAPP(hAPP(c_COMBB(tc_fun(X4843,tc_HOL_Obool),tc_fun(X4843,tc_HOL_Obool),X4845),hAPP(c_COMBS(X4843,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4843),c_fconj),hAPP(hAPP(c_COMBC(X4843,tc_fun(X4843,tc_HOL_Obool),tc_HOL_Obool),c_member(X4843)),X4842)))),X4841)))),X4844)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4843,tc_Nat_Onat),X4840),X4842)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4843),X4842))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4845),X4844)))&(hAPP(c_Finite__Set_Ocard(X4845),hAPP(c_Set_OCollect(X4845),hAPP(hAPP(c_COMBS(X4845,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4845),c_fconj),hAPP(hAPP(c_COMBC(X4845,tc_fun(X4845,tc_HOL_Obool),tc_HOL_Obool),c_member(X4845)),X4844))),hAPP(hAPP(c_COMBC(X4845,X4843,tc_HOL_Obool),X4841),esk140_6(X4840,X4841,X4842,X4843,X4844,X4845)))))!=hAPP(X4840,esk140_6(X4840,X4841,X4842,X4843,X4844,X4845))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4845,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X4843,tc_HOL_Obool),tc_Nat_Onat,X4845),c_Finite__Set_Ocard(X4843)),hAPP(hAPP(c_COMBB(tc_fun(X4843,tc_HOL_Obool),tc_fun(X4843,tc_HOL_Obool),X4845),c_Set_OCollect(X4843)),hAPP(hAPP(c_COMBB(tc_fun(X4843,tc_HOL_Obool),tc_fun(X4843,tc_HOL_Obool),X4845),hAPP(c_COMBS(X4843,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4843),c_fconj),hAPP(hAPP(c_COMBC(X4843,tc_fun(X4843,tc_HOL_Obool),tc_HOL_Obool),c_member(X4843)),X4842)))),X4841)))),X4844)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4843,tc_Nat_Onat),X4840),X4842)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4843),X4842))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4845),X4844)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__multicount__gen])])])])])). 4.46/4.69 fof(c_0_4855, plain, ![X1722, X1723, X1724]:(~class_Orderings_Olinorder(X1724)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1724),X1723))|(c_Orderings_Obot__class_Obot(tc_fun(X1724,tc_HOL_Obool))=X1723|c_Big__Operators_Olattice_OSup__fin(X1724,c_Orderings_Oord__class_Omax(X1724),hAPP(c_Set_OCollect(X1724),hAPP(hAPP(c_COMBB(tc_fun(X1724,tc_HOL_Obool),tc_HOL_Obool,X1724),c_HOL_OEx(X1724)),hAPP(hAPP(c_COMBC(X1724,tc_fun(X1724,tc_HOL_Obool),tc_fun(X1724,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1724,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1724,tc_HOL_Obool),tc_fun(X1724,tc_HOL_Obool)),X1724),c_COMBS(X1724,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1724,tc_HOL_Obool),tc_fun(X1724,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1724),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1724),c_fconj)),hAPP(hAPP(c_COMBC(X1724,tc_fun(X1724,X1724),tc_fun(X1724,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1724,tc_HOL_Obool),tc_fun(tc_fun(X1724,X1724),tc_fun(X1724,tc_HOL_Obool)),X1724),c_COMBB(X1724,tc_HOL_Obool,X1724)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X1724),X1722))))),hAPP(hAPP(c_COMBC(X1724,tc_fun(X1724,tc_HOL_Obool),tc_HOL_Obool),c_member(X1724)),X1723)))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1724),X1722),c_Big__Operators_Olattice_OSup__fin(X1724,c_Orderings_Oord__class_Omax(X1724),X1723))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__Sup1__distrib])])])). 4.46/4.69 fof(c_0_4856, plain, ![X12261, X12262, X12263]:(~class_Orderings_Olinorder(X12263)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12263),X12262))|(X12262=c_Orderings_Obot__class_Obot(tc_fun(X12263,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X12263),X12261),c_Big__Operators_Olattice_OInf__fin(X12263,c_Orderings_Oord__class_Omin(X12263),X12262))=c_Big__Operators_Olattice_OInf__fin(X12263,c_Orderings_Oord__class_Omin(X12263),hAPP(c_Set_OCollect(X12263),hAPP(hAPP(c_COMBB(tc_fun(X12263,tc_HOL_Obool),tc_HOL_Obool,X12263),c_HOL_OEx(X12263)),hAPP(hAPP(c_COMBC(X12263,tc_fun(X12263,tc_HOL_Obool),tc_fun(X12263,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12263,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X12263,tc_HOL_Obool),tc_fun(X12263,tc_HOL_Obool)),X12263),c_COMBS(X12263,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12263,tc_HOL_Obool),tc_fun(X12263,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X12263),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12263),c_fconj)),hAPP(hAPP(c_COMBC(X12263,tc_fun(X12263,X12263),tc_fun(X12263,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12263,tc_HOL_Obool),tc_fun(tc_fun(X12263,X12263),tc_fun(X12263,tc_HOL_Obool)),X12263),c_COMBB(X12263,tc_HOL_Obool,X12263)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X12263),X12261))))),hAPP(hAPP(c_COMBC(X12263,tc_fun(X12263,tc_HOL_Obool),tc_HOL_Obool),c_member(X12263)),X12262)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__Inf1__distrib])])])). 4.46/4.69 fof(c_0_4857, plain, ![X14179, X14180]:(~class_Lazy__Sequence_Osmall__lazy(X14180)|c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X14180),X14179)=c_Lazy__Sequence_Oappend(tc_List_Olist(X14180),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(X14180)),c_List_Olist_ONil(X14180)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X14180))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14179)),hAPP(c_Lazy__Sequence_Obind(tc_prod(X14180,tc_List_Olist(X14180)),tc_List_Olist(X14180),c_Lazy__Sequence_Oproduct(X14180,tc_List_Olist(X14180),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X14180,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X14179),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X14180),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X14179),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(X14180,tc_List_Olist(X14180),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X14180))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X14180),tc_List_Olist(X14180)),tc_fun(tc_List_Olist(X14180),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X14180))),X14180),hAPP(c_COMBB(tc_List_Olist(X14180),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X14180)),tc_List_Olist(X14180)),c_Lazy__Sequence_Osingle(tc_List_Olist(X14180)))),c_List_Olist_OCons(X14180))))),c_Lazy__Sequence_Oempty(tc_List_Olist(X14180))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_small__lazy__list_Osimps])])])). 4.46/4.69 fof(c_0_4858, plain, ![X9767, X9768, X9769, X9770, X9771, X9772]:((hBOOL(hAPP(hAPP(c_member(X9770),esk280_6(X9767,X9768,X9769,X9770,X9771,X9772)),X9769))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9772,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X9770,tc_HOL_Obool),tc_Nat_Onat,X9772),c_Finite__Set_Ocard(X9770)),hAPP(hAPP(c_COMBB(tc_fun(X9770,tc_HOL_Obool),tc_fun(X9770,tc_HOL_Obool),X9772),c_Set_OCollect(X9770)),hAPP(hAPP(c_COMBB(tc_fun(X9770,tc_HOL_Obool),tc_fun(X9770,tc_HOL_Obool),X9772),hAPP(c_COMBS(X9770,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X9770),c_fconj),hAPP(hAPP(c_COMBC(X9770,tc_fun(X9770,tc_HOL_Obool),tc_HOL_Obool),c_member(X9770)),X9769)))),X9768)))),X9771)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9767),hAPP(c_Finite__Set_Ocard(X9770),X9769))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9770),X9769))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9772),X9771)))&(X9767!=hAPP(c_Finite__Set_Ocard(X9772),hAPP(c_Set_OCollect(X9772),hAPP(hAPP(c_COMBS(X9772,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X9772),c_fconj),hAPP(hAPP(c_COMBC(X9772,tc_fun(X9772,tc_HOL_Obool),tc_HOL_Obool),c_member(X9772)),X9771))),hAPP(hAPP(c_COMBC(X9772,X9770,tc_HOL_Obool),X9768),esk280_6(X9767,X9768,X9769,X9770,X9771,X9772)))))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9772,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X9770,tc_HOL_Obool),tc_Nat_Onat,X9772),c_Finite__Set_Ocard(X9770)),hAPP(hAPP(c_COMBB(tc_fun(X9770,tc_HOL_Obool),tc_fun(X9770,tc_HOL_Obool),X9772),c_Set_OCollect(X9770)),hAPP(hAPP(c_COMBB(tc_fun(X9770,tc_HOL_Obool),tc_fun(X9770,tc_HOL_Obool),X9772),hAPP(c_COMBS(X9770,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X9770),c_fconj),hAPP(hAPP(c_COMBC(X9770,tc_fun(X9770,tc_HOL_Obool),tc_HOL_Obool),c_member(X9770)),X9769)))),X9768)))),X9771)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9767),hAPP(c_Finite__Set_Ocard(X9770),X9769))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9770),X9769))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9772),X9771)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__multicount])])])])])). 4.46/4.69 fof(c_0_4859, plain, ![X9913, X9914, X9915]:(~class_Lattices_Odistrib__lattice(X9915)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9915),X9914))|(c_Orderings_Obot__class_Obot(tc_fun(X9915,tc_HOL_Obool))=X9914|c_Big__Operators_Olattice__class_OInf__fin(X9915,hAPP(c_Set_OCollect(X9915),hAPP(hAPP(c_COMBB(tc_fun(X9915,tc_HOL_Obool),tc_HOL_Obool,X9915),c_HOL_OEx(X9915)),hAPP(hAPP(c_COMBC(X9915,tc_fun(X9915,tc_HOL_Obool),tc_fun(X9915,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9915,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X9915,tc_HOL_Obool),tc_fun(X9915,tc_HOL_Obool)),X9915),c_COMBS(X9915,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9915,tc_HOL_Obool),tc_fun(X9915,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X9915),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X9915),c_fconj)),hAPP(hAPP(c_COMBC(X9915,tc_fun(X9915,X9915),tc_fun(X9915,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9915,tc_HOL_Obool),tc_fun(tc_fun(X9915,X9915),tc_fun(X9915,tc_HOL_Obool)),X9915),c_COMBB(X9915,tc_HOL_Obool,X9915)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9915),X9913))))),hAPP(hAPP(c_COMBC(X9915,tc_fun(X9915,tc_HOL_Obool),tc_HOL_Obool),c_member(X9915)),X9914)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9915),X9913),c_Big__Operators_Olattice__class_OInf__fin(X9915,X9914))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf1__distrib])])). 4.46/4.69 fof(c_0_4860, plain, ![X15736, X15737, X15738]:(~class_Groups_Olinordered__ab__semigroup__add(X15738)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15738),X15737))|(c_Orderings_Obot__class_Obot(tc_fun(X15738,tc_HOL_Obool))=X15737|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15738),X15736),c_Big__Operators_Olinorder__class_OMin(X15738,X15737))=c_Big__Operators_Olinorder__class_OMin(X15738,hAPP(c_Set_OCollect(X15738),hAPP(hAPP(c_COMBB(tc_fun(X15738,tc_HOL_Obool),tc_HOL_Obool,X15738),c_HOL_OEx(X15738)),hAPP(hAPP(c_COMBC(X15738,tc_fun(X15738,tc_HOL_Obool),tc_fun(X15738,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15738,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X15738,tc_HOL_Obool),tc_fun(X15738,tc_HOL_Obool)),X15738),c_COMBS(X15738,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15738,tc_HOL_Obool),tc_fun(X15738,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X15738),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X15738),c_fconj)),hAPP(hAPP(c_COMBC(X15738,tc_fun(X15738,X15738),tc_fun(X15738,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15738,tc_HOL_Obool),tc_fun(tc_fun(X15738,X15738),tc_fun(X15738,tc_HOL_Obool)),X15738),c_COMBB(X15738,tc_HOL_Obool,X15738)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X15738),X15736))))),hAPP(hAPP(c_COMBC(X15738,tc_fun(X15738,tc_HOL_Obool),tc_HOL_Obool),c_member(X15738)),X15737)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__Min__commute])])). 4.46/4.69 fof(c_0_4861, plain, ![X5720, X5721, X5722]:(~class_Lattices_Odistrib__lattice(X5722)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5722),X5721))|(c_Orderings_Obot__class_Obot(tc_fun(X5722,tc_HOL_Obool))=X5721|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5722),X5720),c_Big__Operators_Olattice__class_OSup__fin(X5722,X5721))=c_Big__Operators_Olattice__class_OSup__fin(X5722,hAPP(c_Set_OCollect(X5722),hAPP(hAPP(c_COMBB(tc_fun(X5722,tc_HOL_Obool),tc_HOL_Obool,X5722),c_HOL_OEx(X5722)),hAPP(hAPP(c_COMBC(X5722,tc_fun(X5722,tc_HOL_Obool),tc_fun(X5722,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5722,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5722,tc_HOL_Obool),tc_fun(X5722,tc_HOL_Obool)),X5722),c_COMBS(X5722,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5722,tc_HOL_Obool),tc_fun(X5722,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5722),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5722),c_fconj)),hAPP(hAPP(c_COMBC(X5722,tc_fun(X5722,X5722),tc_fun(X5722,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5722,tc_HOL_Obool),tc_fun(tc_fun(X5722,X5722),tc_fun(X5722,tc_HOL_Obool)),X5722),c_COMBB(X5722,tc_HOL_Obool,X5722)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5722),X5720))))),hAPP(hAPP(c_COMBC(X5722,tc_fun(X5722,tc_HOL_Obool),tc_HOL_Obool),c_member(X5722)),X5721)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup1__distrib])])). 4.46/4.69 cnf(c_0_4862, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_4512])). 4.46/4.69 cnf(c_0_4863, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk409_3(X1,X2,X3)),esk410_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk410_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X1,esk409_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),esk410_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_4513])). 4.46/4.69 cnf(c_0_4864, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4514])). 4.46/4.69 fof(c_0_4865, plain, ![X12923, X12924, X12925]:(~class_Groups_Olinordered__ab__semigroup__add(X12925)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12925),X12924))|(X12924=c_Orderings_Obot__class_Obot(tc_fun(X12925,tc_HOL_Obool))|c_Big__Operators_Olinorder__class_OMax(X12925,hAPP(c_Set_OCollect(X12925),hAPP(hAPP(c_COMBB(tc_fun(X12925,tc_HOL_Obool),tc_HOL_Obool,X12925),c_HOL_OEx(X12925)),hAPP(hAPP(c_COMBC(X12925,tc_fun(X12925,tc_HOL_Obool),tc_fun(X12925,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12925,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X12925,tc_HOL_Obool),tc_fun(X12925,tc_HOL_Obool)),X12925),c_COMBS(X12925,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12925,tc_HOL_Obool),tc_fun(X12925,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X12925),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12925),c_fconj)),hAPP(hAPP(c_COMBC(X12925,tc_fun(X12925,X12925),tc_fun(X12925,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12925,tc_HOL_Obool),tc_fun(tc_fun(X12925,X12925),tc_fun(X12925,tc_HOL_Obool)),X12925),c_COMBB(X12925,tc_HOL_Obool,X12925)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X12925),X12923))))),hAPP(hAPP(c_COMBC(X12925,tc_fun(X12925,tc_HOL_Obool),tc_HOL_Obool),c_member(X12925)),X12924)))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12925),X12923),c_Big__Operators_Olinorder__class_OMax(X12925,X12924))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__Max__commute])])). 4.46/4.69 cnf(c_0_4866, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk474_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))|hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))=c_List_Otranspose(X2,X3)|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_4515])). 4.46/4.69 cnf(c_0_4867, plain, (c_List_Olist_ONil(tc_Nat_Onat)=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_4516, c_0_4517])). 4.46/4.69 cnf(c_0_4868, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_4518]), ['final']). 4.46/4.69 fof(c_0_4869, plain, ![X13015, X13016, X13017]:c_List_Olist_ONil(X13016)=hAPP(hAPP(c_List_Omap(X13017,X13016),X13015),c_List_Olist_ONil(X13017)), inference(variable_rename,[status(thm)],[fact_map_Osimps_I1_J])). 4.46/4.69 cnf(c_0_4870, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk229_3(X1,X2,X3)),esk230_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk230_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X1,esk229_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),esk230_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_4519])). 4.46/4.69 cnf(c_0_4871, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3))|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_4520])). 4.46/4.69 cnf(c_0_4872, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4521])). 4.46/4.69 cnf(c_0_4873, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4522])). 4.46/4.69 cnf(c_0_4874, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4523])). 4.46/4.69 cnf(c_0_4875, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X1)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_Nat_Onat,X1),tc_Nat_Onat),c_List_Onth(X1)),hAPP(c_List_Onth(tc_List_Olist(X1)),X2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))=c_List_Otranspose(X1,X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),esk474_3(X3,X1,X2)))!=X3|X3!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_4515])). 4.46/4.69 fof(c_0_4876, plain, ![X16320, X16321, X16322, X16323]:(~class_Rings_Ocomm__semiring__1(X16323)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16323),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X16323),X16320)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16323),X16322),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16323),X16322),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16323),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X16323),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16320),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X16321))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16323),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16323),c_Groups_Oone__class_Oone(X16323)),c_Groups_Oone__class_Oone(X16323))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X16323),hAPP(hAPP(c_COMBB(X16323,X16323,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X16323),X16322)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X16323,X16323),hAPP(hAPP(c_COMBB(X16323,tc_fun(X16323,X16323),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X16323)),c_Nat_Osemiring__1__class_Oof__nat(X16323))),X16321))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X16320)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_arith__series__general])])])). 4.46/4.69 fof(c_0_4877, plain, ![X2696]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2696)=hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X2696), inference(variable_rename,[status(thm)],[fact_atLeast0LessThan])). 4.46/4.69 fof(c_0_4878, plain, ![X10097, X10098, X10099, X10100, X10101, X10102]:(~class_Groups_Ocomm__monoid__add(X10102)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10101),X10100))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10101,X10102),hAPP(hAPP(c_COMBS(X10101,X10102,X10102),hAPP(hAPP(c_COMBS(X10101,X10102,tc_fun(X10102,X10102)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10102,tc_fun(X10102,X10102)),X10101),c_If(X10102)),X10099)),X10098)),X10097)),X10100)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10102),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10101,X10102),X10098),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10101,tc_HOL_Obool)),X10100),hAPP(c_Set_OCollect(X10101),X10099)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10101,X10102),X10097),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10101,tc_HOL_Obool)),X10100),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10101,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10101),X10099))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__cases])])])). 4.46/4.69 fof(c_0_4879, plain, ![X8537, X8538, X8539]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8539,tc_HOL_Obool)),X8538),X8537)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8539,tc_HOL_Obool)),X8538),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8539,tc_HOL_Obool)),X8537)), inference(variable_rename,[status(thm)],[fact_Diff__eq])). 4.46/4.69 cnf(c_0_4880, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), inference(split_conjunct,[status(thm)],[c_0_4524])). 4.46/4.69 fof(c_0_4881, plain, ![X8796, X8797, X8798, X8799, X8800, X8801]:(~class_Groups_Ocomm__monoid__add(X8801)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8800),X8799))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8797,X8801),hAPP(hAPP(c_COMBB(tc_fun(X8800,tc_HOL_Obool),X8801,X8797),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8800,X8801),X8798)),hAPP(hAPP(c_COMBB(tc_fun(X8800,tc_HOL_Obool),tc_fun(X8800,tc_HOL_Obool),X8797),c_Set_OCollect(X8800)),hAPP(hAPP(c_COMBB(tc_fun(X8800,tc_HOL_Obool),tc_fun(X8800,tc_HOL_Obool),X8797),hAPP(c_COMBS(X8800,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X8800),c_fconj),hAPP(hAPP(c_COMBC(X8800,tc_fun(X8800,tc_HOL_Obool),tc_HOL_Obool),c_member(X8800)),X8799)))),hAPP(c_COMBC(X8800,X8797,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X8797,tc_fun(X8797,tc_HOL_Obool),X8800),c_fequal),X8796)))))),hAPP(c_Set_Oimage(X8800,X8797,X8796),X8799))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8800,X8801),X8798),X8799))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__image__gen])])])). 4.46/4.69 cnf(c_0_4882, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3)))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4525])). 4.46/4.69 fof(c_0_4883, plain, ![X10052, X10053, X10054, X10055]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10055),X10052)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10053),X10054)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X10055),X10054)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X10053),X10052)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X10055),X10054)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X10053),X10052)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10055),X10052)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10053),X10054))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less])])). 4.46/4.69 fof(c_0_4884, plain, ![X12162, X12163, X12164, X12165]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12165),X12162)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12163),X12164)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X12165),X12164)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X12163),X12162)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X12165),X12164)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X12163),X12162)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12165),X12162)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12163),X12164))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le])])). 4.46/4.69 cnf(c_0_4885, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2)))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)))|~class_Rings_Osemiring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_4526])). 4.46/4.69 fof(c_0_4886, plain, ![X12725, X12726, X12727, X12728]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12728),hAPP(c_Set_OCollect(X12728),X12727)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X12726),hAPP(c_Set_OCollect(X12726),hAPP(hAPP(c_COMBB(tc_fun(X12728,tc_HOL_Obool),tc_HOL_Obool,X12726),c_HOL_OEx(X12728)),hAPP(hAPP(c_COMBC(X12726,tc_fun(X12728,tc_HOL_Obool),tc_fun(X12728,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12728,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X12728,tc_HOL_Obool),tc_fun(X12728,tc_HOL_Obool)),X12726),c_COMBS(X12728,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12728,tc_HOL_Obool),tc_fun(X12728,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X12726),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12728),c_fconj)),hAPP(hAPP(c_COMBC(X12726,tc_fun(X12728,X12726),tc_fun(X12728,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12726,tc_HOL_Obool),tc_fun(tc_fun(X12728,X12726),tc_fun(X12728,tc_HOL_Obool)),X12726),c_COMBB(X12726,tc_HOL_Obool,X12728)),c_fequal)),X12725)))),X12727)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__image__set])])])). 4.46/4.69 cnf(c_0_4887, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))|c_Divides_OnegDivAlg(X1,X2)=hAPP(c_Divides_Oadjust(X2),c_Divides_OnegDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_4527])). 4.46/4.69 cnf(c_0_4888, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)))|hAPP(c_Divides_Oadjust(X1),c_Divides_OnegDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1)))=c_Divides_OnegDivAlg(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_4528])). 4.46/4.69 fof(c_0_4889, plain, ![X10323, X10324]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10324))|hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X10324))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X10323)))))=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X10324))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X10323))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__less__Suc2])])])). 4.46/4.69 cnf(c_0_4890, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),X1),c_member(X2)),X3)),X4))=hAPP(c_Set_Ovimage(X1,X2,X3),X4)), inference(split_conjunct,[status(thm)],[c_0_4529])). 4.46/4.69 cnf(c_0_4891, plain, (hAPP(c_Set_Ovimage(X1,X2,X3),X4)=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4530, c_0_4531]), c_0_4531]), ['final']). 4.46/4.69 fof(c_0_4892, plain, ![X17473, X17474, X17475]:(~hBOOL(hAPP(c_List_Odistinct(X17475),hAPP(hAPP(c_List_Omap(tc_prod(X17475,X17474),X17475),c_Product__Type_Ofst(X17475,X17474)),X17473)))|hAPP(c_Set_OCollect(tc_prod(X17475,X17474)),hAPP(c_Product__Type_Oprod_Oprod__case(X17475,X17474,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X17475,tc_fun(X17474,tc_Option_Ooption(X17474)),tc_fun(X17474,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X17474),tc_HOL_Obool),tc_fun(tc_fun(X17474,tc_Option_Ooption(X17474)),tc_fun(X17474,tc_HOL_Obool)),X17475),c_COMBB(tc_Option_Ooption(X17474),tc_HOL_Obool,X17474)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X17474),tc_fun(tc_Option_Ooption(X17474),tc_HOL_Obool),X17475),c_fequal),hAPP(c_Map_Omap__of(X17475,X17474),X17473)))),c_Option_Ooption_OSome(X17474))))=hAPP(c_List_Oset(tc_prod(X17475,X17474)),X17473)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__map__of__compr])])). 4.46/4.69 fof(c_0_4893, plain, ![X7138, X7139]:(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7139))|hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X7139))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X7138)))))=hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X7139))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X7138)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__less__Suc])])])). 4.46/4.69 fof(c_0_4894, plain, ![X15550, X15551, X15552, X15553]:((hBOOL(hAPP(X15553,esk456_4(X15550,X15551,X15552,X15553)))|c_Wellfounded_Owf(X15550,hAPP(c_Set_OCollect(tc_prod(X15550,X15550)),hAPP(c_Product__Type_Oprod_Oprod__case(X15550,X15550,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X15550,tc_HOL_Obool),tc_fun(X15550,tc_HOL_Obool),X15550),hAPP(c_COMBS(X15550,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X15550),c_fconj),X15553))),hAPP(hAPP(c_COMBC(X15550,tc_fun(X15550,X15550),tc_fun(X15550,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15550,tc_HOL_Obool),tc_fun(tc_fun(X15550,X15550),tc_fun(X15550,tc_HOL_Obool)),X15550),c_COMBB(X15550,tc_HOL_Obool,X15550)),c_fequal)),X15551))))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X15552,hAPP(X15551,esk456_4(X15550,X15551,X15552,X15553)))),hAPP(X15552,esk456_4(X15550,X15551,X15552,X15553))))|c_Wellfounded_Owf(X15550,hAPP(c_Set_OCollect(tc_prod(X15550,X15550)),hAPP(c_Product__Type_Oprod_Oprod__case(X15550,X15550,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X15550,tc_HOL_Obool),tc_fun(X15550,tc_HOL_Obool),X15550),hAPP(c_COMBS(X15550,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X15550),c_fconj),X15553))),hAPP(hAPP(c_COMBC(X15550,tc_fun(X15550,X15550),tc_fun(X15550,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15550,tc_HOL_Obool),tc_fun(tc_fun(X15550,X15550),tc_fun(X15550,tc_HOL_Obool)),X15550),c_COMBB(X15550,tc_HOL_Obool,X15550)),c_fequal)),X15551))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__if__measure])])])])). 4.46/4.69 cnf(c_0_4895, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4532])). 4.46/4.69 cnf(c_0_4896, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), inference(split_conjunct,[status(thm)],[c_0_4524])). 4.46/4.69 fof(c_0_4897, plain, ![X14909, X14910, X14911, X14912, X14913, X14914]:(~c_Hoare__Mirabelle_Ohoare__derivs(X14914,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X14914),tc_HOL_Obool)),X14913),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X14914),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X14914,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X14914)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X14914,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X14914))),hAPP(hAPP(c_COMBB(tc_fun(X14914,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X14914,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X14914))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X14914)),X14912)),c_Com_Ocom_OBODY)),X14911)),X14910)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X14914),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X14914,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X14914)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X14914,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X14914))),hAPP(hAPP(c_COMBB(tc_fun(X14914,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X14914,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X14914))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X14914)),X14912)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X14911)),X14910))|(~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X14909),X14910))|c_Hoare__Mirabelle_Ohoare__derivs(X14914,X14913,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X14914)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X14914),hAPP(X14912,X14909)),hAPP(c_Com_Ocom_OBODY,X14909)),hAPP(X14911,X14909))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X14914),tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Body1])])])). 4.46/4.69 fof(c_0_4898, plain, ![X6738, X6739, X6740]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6740),X6739))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X6740)),hAPP(c_Set_OCollect(tc_List_Olist(X6740)),hAPP(hAPP(c_COMBS(tc_List_Olist(X6740),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X6740)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X6740),tc_fun(X6740,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X6740,tc_HOL_Obool),tc_fun(tc_fun(X6740,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X6740)),c_Orderings_Oord__class_Oless__eq(tc_fun(X6740,tc_HOL_Obool))),c_List_Oset(X6740))),X6739))),hAPP(hAPP(c_COMBC(tc_List_Olist(X6740),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X6740)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X6740)))),X6738)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__lists__length__le])])). 4.46/4.69 cnf(c_0_4899, plain, (hAPP(c_Set_OCollect(tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),c_List_Oset(X1))),X2))=c_List_Olists(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4533])). 4.46/4.69 cnf(c_0_4900, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3)))),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_4534])). 4.46/4.69 fof(c_0_4901, plain, ![X11182, X11183, X11184]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11184),X11183))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X11184)),hAPP(c_Set_OCollect(tc_List_Olist(X11184)),hAPP(hAPP(c_COMBS(tc_List_Olist(X11184),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X11184)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X11184),tc_fun(X11184,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X11184,tc_HOL_Obool),tc_fun(tc_fun(X11184,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X11184)),c_Orderings_Oord__class_Oless__eq(tc_fun(X11184,tc_HOL_Obool))),c_List_Oset(X11184))),X11183))),hAPP(hAPP(c_COMBC(tc_List_Olist(X11184),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X11184)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X11184)))),X11182)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__lists__length__eq])])). 4.46/4.69 cnf(c_0_4902, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X2)))|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_4506])). 4.46/4.69 cnf(c_0_4903, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X2)))|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_4506])). 4.46/4.69 cnf(c_0_4904, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Divides_Oadjust(X2),c_Divides_OposDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)))=c_Divides_OposDivAlg(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4535])). 4.46/4.69 cnf(c_0_4905, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|hAPP(c_Divides_Oadjust(X2),c_Divides_OposDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)))=c_Divides_OposDivAlg(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_4536])). 4.46/4.69 cnf(c_0_4906, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))|c_Groups_Ozero__class_Ozero(X1)!=X3|X2!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4509])). 4.46/4.69 cnf(c_0_4907, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_4537])). 4.46/4.69 fof(c_0_4908, plain, ![X9843, X9844, X9845]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X9845,X9845),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X9845,X9845,X9845),X9844),X9843)),X9844))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X9845,tc_HOL_Obool),tc_fun(X9845,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X9845,tc_HOL_Obool),tc_fun(X9845,tc_HOL_Obool),tc_fun(X9845,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X9845,X9844)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X9845,tc_HOL_Obool),tc_fun(X9845,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X9845,X9843)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X9845,tc_HOL_Obool),tc_fun(X9845,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X9845,tc_HOL_Obool),tc_fun(X9845,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X9845,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X9845,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X9845,tc_HOL_Obool),tc_fun(X9845,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X9845,X9844)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__ext__compat])])])). 4.46/4.69 fof(c_0_4909, plain, ![X11029, X11030, X11031]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X11031,X11031),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X11031,X11031,X11031),X11030),X11029)),X11030))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X11031,tc_HOL_Obool),tc_fun(X11031,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X11031,tc_HOL_Obool),tc_fun(X11031,tc_HOL_Obool),tc_fun(X11031,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X11031,X11030)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X11031,tc_HOL_Obool),tc_fun(X11031,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X11031,X11029)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X11031,tc_HOL_Obool),tc_fun(X11031,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X11031,tc_HOL_Obool),tc_fun(X11031,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X11031,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X11031,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X11031,tc_HOL_Obool),tc_fun(X11031,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X11031,X11030)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__compat])])). 4.46/4.69 fof(c_0_4910, plain, ![X6071, X6072, X6073, X6074]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X6074,X6073),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X6072),X6071)))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6074),X6073),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X6071),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6072)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6072)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X6071),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X6073),X6071)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zminus1__lemma])])])). 4.46/4.69 cnf(c_0_4911, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4538])). 4.46/4.69 cnf(c_0_4912, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))), inference(split_conjunct,[status(thm)],[c_0_4539]), ['final']). 4.46/4.69 fof(c_0_4913, plain, ![X7932, X7933, X7934, X7935]:((hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),esk223_4(X7932,X7933,X7934,X7935)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk224_4(X7932,X7933,X7934,X7935)),esk225_4(X7932,X7933,X7934,X7935)))))|hBOOL(hAPP(hAPP(hAPP(X7932,X7935),X7934),X7933))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X7935),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X7934),X7933)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk224_4(X7932,X7933,X7934,X7935)),esk225_4(X7932,X7933,X7934,X7935)))|(hAPP(esk223_4(X7932,X7933,X7934,X7935),esk225_4(X7932,X7933,X7934,X7935))!=c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))|hBOOL(hAPP(hAPP(hAPP(X7932,esk223_4(X7932,X7933,X7934,X7935)),esk224_4(X7932,X7933,X7934,X7935)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk225_4(X7932,X7933,X7934,X7935)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))|hBOOL(hAPP(hAPP(hAPP(X7932,X7935),X7934),X7933))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X7935),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X7934),X7933)))))&(~hBOOL(hAPP(hAPP(hAPP(X7932,esk223_4(X7932,X7933,X7934,X7935)),esk224_4(X7932,X7933,X7934,X7935)),esk225_4(X7932,X7933,X7934,X7935)))|hBOOL(hAPP(hAPP(hAPP(X7932,X7935),X7934),X7933))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X7935),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X7934),X7933))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_small_H_Opinduct])])])])])). 4.46/4.69 cnf(c_0_4914, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_4540])). 4.46/4.69 cnf(c_0_4915, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X3),hAPP(c_List_Orev(X1),c_List_OtakeWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),X2)))=c_List_OdropWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),hAPP(c_List_Orev(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_4541])). 4.46/4.69 cnf(c_0_4916, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)=c_List_OdropWhile(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_4542])). 4.46/4.69 cnf(c_0_4917, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4510])). 4.46/4.69 cnf(c_0_4918, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4543])). 4.46/4.69 cnf(c_0_4919, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Int_Onumber__ring(X1)|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_4544])). 4.46/4.69 cnf(c_0_4920, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4510])). 4.46/4.69 fof(c_0_4921, plain, ![X7630, X7631, X7632, X7633, X7634, X7635, X7636]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X7636,X7635),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X7634),X7633)))|(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X7632,X7635),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X7631),X7630)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7635))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7636),X7632),X7635),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7634),X7631)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7633),X7630)),X7635))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7633),X7630),X7635))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__add1__eq])])). 4.46/4.69 fof(c_0_4922, plain, ![X6749, X6750, X6751, X6752, X6753, X6754, X6755]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X6755,X6754),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X6753),X6752)))|(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X6751,X6754),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X6750),X6749)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X6754|hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6755),X6751),X6754),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6753),X6750)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6752),X6749)),X6754))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6752),X6749),X6754))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zadd1__lemma])])])). 4.46/4.69 cnf(c_0_4923, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3))))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4545])). 4.46/4.69 cnf(c_0_4924, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)))=hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4546])). 4.46/4.69 fof(c_0_4925, plain, ![X10169, X10170, X10171, X10172, X10173, X10174]:((hBOOL(hAPP(hAPP(c_member(X10173),X10171),X10172))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10173,X10174),hAPP(hAPP(c_COMBC(X10173,X10174,X10174),hAPP(hAPP(c_COMBS(X10173,X10174,tc_fun(X10174,X10174)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10174,tc_fun(X10174,X10174)),X10173),c_If(X10174)),hAPP(hAPP(c_COMBC(X10173,X10173,tc_HOL_Obool),c_fequal),X10171))),X10170)),X10169)),X10172)=hAPP(hAPP(c_Power_Opower__class_Opower(X10174),X10169),hAPP(c_Finite__Set_Ocard(X10173),X10172))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10173),X10172))|~class_Groups_Ocomm__monoid__mult(X10174))&(~hBOOL(hAPP(hAPP(c_member(X10173),X10171),X10172))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10174),hAPP(X10170,X10171)),hAPP(hAPP(c_Power_Opower__class_Opower(X10174),X10169),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10173),X10172)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10173,X10174),hAPP(hAPP(c_COMBC(X10173,X10174,X10174),hAPP(hAPP(c_COMBS(X10173,X10174,tc_fun(X10174,X10174)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10174,tc_fun(X10174,X10174)),X10173),c_If(X10174)),hAPP(hAPP(c_COMBC(X10173,X10173,tc_HOL_Obool),c_fequal),X10171))),X10170)),X10169)),X10172)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10173),X10172))|~class_Groups_Ocomm__monoid__mult(X10174))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__gen__delta])])])])). 4.46/4.69 fof(c_0_4926, plain, ![X5557, X5558]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5558),c_Int_OPls))|hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5557),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X5558)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5557)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5558)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5558),c_Int_OPls))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5557)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5558))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5557))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__nat__number__of])])])). 4.46/4.69 cnf(c_0_4927, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X2))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))), inference(split_conjunct,[status(thm)],[c_0_4547])). 4.46/4.69 cnf(c_0_4928, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4548])). 4.46/4.69 cnf(c_0_4929, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_4549])). 4.46/4.69 cnf(c_0_4930, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4457])). 4.46/4.69 fof(c_0_4931, plain, ![X3518, X3519, X3520, X3521]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3520),X3519))|c_Groups_Ozero__class_Ozero(X3521)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3521),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X3521,X3521),hAPP(hAPP(c_COMBB(X3521,tc_fun(X3521,X3521),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X3521)),X3518)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X3521,tc_Nat_Onat),X3518),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3520,X3519))|~class_Groups_Oab__group__add(X3521))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3520),X3519))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3521),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X3521,X3521),hAPP(hAPP(c_COMBB(X3521,tc_fun(X3521,X3521),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X3521)),X3518)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X3521,tc_Nat_Onat),X3518),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3520,X3519))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3521),hAPP(X3518,X3520)),hAPP(X3518,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3519),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~class_Groups_Oab__group__add(X3521))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__natinterval__difff])])])])). 4.46/4.69 cnf(c_0_4932, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X1)))))|hAPP(c_Nat_OSuc,X1)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_4550])). 4.46/4.69 cnf(c_0_4933, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2))),hAPP(c_Set_OCollect(X1),X3))=hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_4551])). 4.46/4.69 cnf(c_0_4934, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_4552]), ['final']). 4.46/4.69 cnf(c_0_4935, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4553])). 4.46/4.69 fof(c_0_4936, plain, ![X13175, X13176]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X13176),X13175)),c_Int_Ointrel))|hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X13176),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))=hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X13175),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))&(hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X13176),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))!=hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X13175),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X13176),X13175)),c_Int_Ointrel)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__intrel__iff])])). 4.46/4.69 fof(c_0_4937, plain, ![X2812, X2813, X2814, X2815, X2816, X2817, X2818, X2819]:(((~hBOOL(hAPP(hAPP(c_member(X2814),X2815),X2813))|hBOOL(hAPP(hAPP(c_member(tc_prod(X2814,X2814)),hAPP(hAPP(c_Product__Type_OPair(X2814,X2814),X2815),X2815)),X2812))|~c_Relation_Orefl__on(X2814,X2813,X2812))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X2814,X2814)),X2816),X2812))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2814,X2814,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2814,tc_fun(X2814,tc_HOL_Obool),tc_fun(X2814,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2814,tc_HOL_Obool),tc_fun(X2814,tc_HOL_Obool)),X2814),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2814)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2814),c_fconj),hAPP(hAPP(c_COMBC(X2814,tc_fun(X2814,tc_HOL_Obool),tc_HOL_Obool),c_member(X2814)),X2813)))),hAPP(hAPP(c_COMBC(X2814,tc_fun(X2814,tc_HOL_Obool),tc_HOL_Obool),c_member(X2814)),X2813))),X2816))|~c_Relation_Orefl__on(X2814,X2813,X2812)))&(((hBOOL(hAPP(hAPP(c_member(tc_prod(X2819,X2819)),esk74_3(X2817,X2818,X2819)),X2817))|hBOOL(hAPP(hAPP(c_member(X2819),esk73_3(X2817,X2818,X2819)),X2818))|c_Relation_Orefl__on(X2819,X2818,X2817))&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2819,X2819,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2819,tc_fun(X2819,tc_HOL_Obool),tc_fun(X2819,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2819,tc_HOL_Obool),tc_fun(X2819,tc_HOL_Obool)),X2819),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2819)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2819),c_fconj),hAPP(hAPP(c_COMBC(X2819,tc_fun(X2819,tc_HOL_Obool),tc_HOL_Obool),c_member(X2819)),X2818)))),hAPP(hAPP(c_COMBC(X2819,tc_fun(X2819,tc_HOL_Obool),tc_HOL_Obool),c_member(X2819)),X2818))),esk74_3(X2817,X2818,X2819)))|hBOOL(hAPP(hAPP(c_member(X2819),esk73_3(X2817,X2818,X2819)),X2818))|c_Relation_Orefl__on(X2819,X2818,X2817)))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X2819,X2819)),esk74_3(X2817,X2818,X2819)),X2817))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2819,X2819)),hAPP(hAPP(c_Product__Type_OPair(X2819,X2819),esk73_3(X2817,X2818,X2819)),esk73_3(X2817,X2818,X2819))),X2817))|c_Relation_Orefl__on(X2819,X2818,X2817))&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2819,X2819,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2819,tc_fun(X2819,tc_HOL_Obool),tc_fun(X2819,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2819,tc_HOL_Obool),tc_fun(X2819,tc_HOL_Obool)),X2819),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2819)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2819),c_fconj),hAPP(hAPP(c_COMBC(X2819,tc_fun(X2819,tc_HOL_Obool),tc_HOL_Obool),c_member(X2819)),X2818)))),hAPP(hAPP(c_COMBC(X2819,tc_fun(X2819,tc_HOL_Obool),tc_HOL_Obool),c_member(X2819)),X2818))),esk74_3(X2817,X2818,X2819)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2819,X2819)),hAPP(hAPP(c_Product__Type_OPair(X2819,X2819),esk73_3(X2817,X2818,X2819)),esk73_3(X2817,X2818,X2819))),X2817))|c_Relation_Orefl__on(X2819,X2818,X2817))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__on__def_H])])])])])])])). 4.46/4.69 fof(c_0_4938, plain, ![X1528, X1529, X1530, X1531, X1532]:(~class_Groups_Ocomm__monoid__add(X1532)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1531),X1530))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1531,X1532),hAPP(hAPP(c_COMBC(X1531,X1532,X1532),hAPP(hAPP(c_COMBS(X1531,X1532,tc_fun(X1532,X1532)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1532,tc_fun(X1532,X1532)),X1531),c_If(X1532)),hAPP(hAPP(c_COMBC(X1531,tc_fun(X1531,tc_HOL_Obool),tc_HOL_Obool),c_member(X1531)),X1528))),X1529)),c_Groups_Ozero__class_Ozero(X1532))),X1530)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1531,X1532),X1529),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1531,tc_HOL_Obool)),X1530),X1528)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__restrict__set])])])). 4.46/4.69 fof(c_0_4939, plain, ![X4007, X4008, X4009, X4010]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4009),X4008))|c_Groups_Ozero__class_Ozero(X4010)=c_Nitpick_Osetsum_H(X4009,X4010,X4007,X4008)|~class_Groups_Ocomm__monoid__add(X4010))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4009),X4008))|hAPP(c_List_Omonoid__add__class_Olistsum(X4010),hAPP(hAPP(c_List_Omap(X4009,X4010),X4007),c_Hilbert__Choice_OEps(tc_List_Olist(X4009),hAPP(hAPP(c_COMBS(tc_List_Olist(X4009),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4009)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X4009),tc_fun(X4009,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4009,tc_HOL_Obool),tc_fun(tc_fun(X4009,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X4009)),c_fequal),c_List_Oset(X4009))),X4008))),c_List_Odistinct(X4009)))))=c_Nitpick_Osetsum_H(X4009,X4010,X4007,X4008)|~class_Groups_Ocomm__monoid__add(X4010))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nitpick_Osetsum_H__def])])])])). 4.46/4.69 fof(c_0_4940, plain, ![X1199, X1200, X1201]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1201,tc_HOL_Obool)),X1199),X1200)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1201,tc_HOL_Obool)),X1200),X1199), inference(variable_rename,[status(thm)],[fact_Int__commute])). 4.46/4.69 cnf(c_0_4941, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4554])). 4.46/4.69 fof(c_0_4942, plain, ![X1685, X1686, X1687]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X1687,esk40_3(X1685,X1686,X1687))),hAPP(X1686,esk40_3(X1685,X1686,X1687))))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1686)),X1687)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1685))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1686),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1685))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1687),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1685)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__diff__distrib])])])). 4.46/4.69 cnf(c_0_4943, plain, (c_Groups_Oone__class_Oone(X2)=hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|X1!=hAPP(c_Groups_Ouminus__class_Ouminus(X2),c_Groups_Oone__class_Oone(X2))|~class_Rings_Oring__1__no__zero__divisors(X2)), inference(split_conjunct,[status(thm)],[c_0_4456])). 4.46/4.69 cnf(c_0_4944, plain, (c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),c_Orderings_Oord__class_Oless__eq(X1)))))=c_Complete__Lattice_OInf__class_OInf(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_4555])). 4.46/4.69 cnf(c_0_4945, plain, (hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)=X2), inference(rw,[status(thm)],[c_0_4556, c_0_4531]), ['final']). 4.46/4.69 cnf(c_0_4946, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),hAPP(c_COMBC(X2,X1,tc_HOL_Obool),X4)))=hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))),X4)))), inference(split_conjunct,[status(thm)],[c_0_4557])). 4.46/4.69 cnf(c_0_4947, plain, (c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1))))))=c_Complete__Lattice_OSup__class_OSup(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_4558])). 4.46/4.69 cnf(c_0_4948, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1)),c_Int_Onat)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))), inference(split_conjunct,[status(thm)],[c_0_4559])). 4.46/4.69 cnf(c_0_4949, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1)),c_Int_Onat)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))), inference(split_conjunct,[status(thm)],[c_0_4560])). 4.46/4.69 fof(c_0_4950, plain, ![X4123]:hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4123))=hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4123), inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw])). 4.46/4.69 cnf(c_0_4951, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4561])). 4.46/4.69 cnf(c_0_4952, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4562])). 4.46/4.69 cnf(c_0_4953, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_4563])). 4.46/4.69 cnf(c_0_4954, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4564])). 4.46/4.69 cnf(c_0_4955, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),X2)|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_4565])). 4.46/4.69 cnf(c_0_4956, plain, (hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4566, c_0_4471]), c_0_4471])). 4.46/4.69 fof(c_0_4957, plain, ![X6662, X6663, X6664, X6665, X6666, X6667]:(((~hBOOL(hAPP(hAPP(c_member(X6667),X6664),X6665))|hAPP(c_Set_Ovimage(X6663,X6667,hAPP(hAPP(c_COMBC(X6663,X6667,X6667),hAPP(hAPP(c_COMBC(X6663,X6667,tc_fun(X6667,X6667)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X6667,tc_fun(X6667,X6667)),X6663),c_If(X6667)),hAPP(hAPP(c_COMBC(X6663,tc_fun(X6663,tc_HOL_Obool),tc_HOL_Obool),c_member(X6663)),X6662))),X6666)),X6664)),X6665)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6663,tc_HOL_Obool)),X6662)|hBOOL(hAPP(hAPP(c_member(X6667),X6666),X6665)))&(hBOOL(hAPP(hAPP(c_member(X6667),X6664),X6665))|c_Orderings_Obot__class_Obot(tc_fun(X6663,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X6663,X6667,hAPP(hAPP(c_COMBC(X6663,X6667,X6667),hAPP(hAPP(c_COMBC(X6663,X6667,tc_fun(X6667,X6667)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X6667,tc_fun(X6667,X6667)),X6663),c_If(X6667)),hAPP(hAPP(c_COMBC(X6663,tc_fun(X6663,tc_HOL_Obool),tc_HOL_Obool),c_member(X6663)),X6662))),X6666)),X6664)),X6665)|hBOOL(hAPP(hAPP(c_member(X6667),X6666),X6665))))&((hBOOL(hAPP(hAPP(c_member(X6667),X6664),X6665))|hAPP(c_Set_Ovimage(X6663,X6667,hAPP(hAPP(c_COMBC(X6663,X6667,X6667),hAPP(hAPP(c_COMBC(X6663,X6667,tc_fun(X6667,X6667)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X6667,tc_fun(X6667,X6667)),X6663),c_If(X6667)),hAPP(hAPP(c_COMBC(X6663,tc_fun(X6663,tc_HOL_Obool),tc_HOL_Obool),c_member(X6663)),X6662))),X6666)),X6664)),X6665)=X6662|~hBOOL(hAPP(hAPP(c_member(X6667),X6666),X6665)))&(~hBOOL(hAPP(hAPP(c_member(X6667),X6664),X6665))|hAPP(c_Set_Ovimage(X6663,X6667,hAPP(hAPP(c_COMBC(X6663,X6667,X6667),hAPP(hAPP(c_COMBC(X6663,X6667,tc_fun(X6667,X6667)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X6667,tc_fun(X6667,X6667)),X6663),c_If(X6667)),hAPP(hAPP(c_COMBC(X6663,tc_fun(X6663,tc_HOL_Obool),tc_HOL_Obool),c_member(X6663)),X6662))),X6666)),X6664)),X6665)=c_Orderings_Otop__class_Otop(tc_fun(X6663,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X6667),X6666),X6665))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_vimage__if])])])])). 4.46/4.69 cnf(c_0_4958, plain, (hAPP(hAPP(c_HOL_OLet(X2,X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(hAPP(c_COMBS(X2,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X2),c_Groups_Otimes__class_Otimes(X2)),hAPP(c_Groups_Otimes__class_Otimes(X2),X3))),c_COMBI(X2)))=hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_4567])). 4.46/4.69 fof(c_0_4959, plain, ![X9930, X9931, X9932]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X9932,X9932),tc_HOL_Obool)),X9931),hAPP(hAPP(c_Product__Type_OSigma(X9932,X9932),X9930),hAPP(c_COMBK(tc_fun(X9932,tc_HOL_Obool),X9932),X9930))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X9932),tc_List_Olist(X9932)),tc_HOL_Obool)),c_List_Olistrel(X9932,X9931)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X9932),tc_List_Olist(X9932)),c_List_Olists(X9932,X9930)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X9932),tc_HOL_Obool),tc_List_Olist(X9932)),c_List_Olists(X9932,X9930)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel__subset])])])). 4.46/4.69 cnf(c_0_4960, plain, (c_Nitpick_Oprod(X1,X2,X3,X4)=hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X4))))), inference(split_conjunct,[status(thm)],[c_0_4568])). 4.46/4.69 cnf(c_0_4961, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X3))),X4))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4569, c_0_4531]), c_0_4531]), c_0_4531]), ['final']). 4.46/4.69 fof(c_0_4962, plain, ![X16909, X16910, X16911]:(((X16910!=X16909|c_List_Oconcat(X16911,X16910)=c_List_Oconcat(X16911,X16909)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X16911))),X16909)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X16911))),X16910)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16911),tc_List_Olist(X16911))),esk502_3(X16909,X16910,X16911)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X16911),tc_List_Olist(X16911))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X16911),tc_List_Olist(X16911)),X16910),X16909)))))&(c_List_Oconcat(X16911,X16910)!=c_List_Oconcat(X16911,X16909)|X16910=X16909|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X16911))),X16909)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X16911))),X16910)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16911),tc_List_Olist(X16911))),esk502_3(X16909,X16910,X16911)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X16911),tc_List_Olist(X16911))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X16911),tc_List_Olist(X16911)),X16910),X16909))))))&((X16910!=X16909|c_List_Oconcat(X16911,X16910)=c_List_Oconcat(X16911,X16909)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X16911))),X16909)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X16911))),X16910)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X16911),tc_List_Olist(X16911),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X16911),tc_fun(tc_List_Olist(X16911),tc_Nat_Onat),tc_fun(tc_List_Olist(X16911),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X16911),tc_Nat_Onat),tc_fun(tc_List_Olist(X16911),tc_HOL_Obool)),tc_List_Olist(X16911)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X16911))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X16911)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X16911))))),c_Nat_Osize__class_Osize(tc_List_Olist(X16911)))),esk502_3(X16909,X16910,X16911))))&(c_List_Oconcat(X16911,X16910)!=c_List_Oconcat(X16911,X16909)|X16910=X16909|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X16911))),X16909)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X16911))),X16910)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X16911),tc_List_Olist(X16911),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X16911),tc_fun(tc_List_Olist(X16911),tc_Nat_Onat),tc_fun(tc_List_Olist(X16911),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X16911),tc_Nat_Onat),tc_fun(tc_List_Olist(X16911),tc_HOL_Obool)),tc_List_Olist(X16911)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X16911))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X16911)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X16911))))),c_Nat_Osize__class_Osize(tc_List_Olist(X16911)))),esk502_3(X16909,X16910,X16911)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_concat__eq__concat__iff])])])])])). 4.46/4.69 fof(c_0_4963, plain, ![X670, X671, X672]:((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X672),tc_List_Olist(X672))),esk18_3(X670,X671,X672)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X672),tc_List_Olist(X672))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X672),tc_List_Olist(X672)),X671),X670))))|X671=X670|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X672))),X670)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X672))),X671)|c_List_Oconcat(X672,X670)!=c_List_Oconcat(X672,X671))&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X672),tc_List_Olist(X672),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X672),tc_fun(tc_List_Olist(X672),tc_Nat_Onat),tc_fun(tc_List_Olist(X672),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X672),tc_Nat_Onat),tc_fun(tc_List_Olist(X672),tc_HOL_Obool)),tc_List_Olist(X672)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X672))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X672)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X672))))),c_Nat_Osize__class_Osize(tc_List_Olist(X672)))),esk18_3(X670,X671,X672)))|X671=X670|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X672))),X670)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X672))),X671)|c_List_Oconcat(X672,X670)!=c_List_Oconcat(X672,X671))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_concat__injective])])])])])). 4.46/4.69 fof(c_0_4964, plain, ![X11894, X11895, X11896, X11897, X11898]:((hBOOL(hAPP(hAPP(c_member(X11897),X11895),X11896))|c_Groups_Oone__class_Oone(X11898)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X11897,X11898),hAPP(hAPP(c_COMBC(X11897,X11898,X11898),hAPP(hAPP(c_COMBS(X11897,X11898,tc_fun(X11898,X11898)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X11898,tc_fun(X11898,X11898)),X11897),c_If(X11898)),hAPP(hAPP(c_COMBC(X11897,X11897,tc_HOL_Obool),c_fequal),X11895))),X11894)),c_Groups_Oone__class_Oone(X11898))),X11896)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11897),X11896))|~class_Groups_Ocomm__monoid__mult(X11898))&(~hBOOL(hAPP(hAPP(c_member(X11897),X11895),X11896))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X11897,X11898),hAPP(hAPP(c_COMBC(X11897,X11898,X11898),hAPP(hAPP(c_COMBS(X11897,X11898,tc_fun(X11898,X11898)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X11898,tc_fun(X11898,X11898)),X11897),c_If(X11898)),hAPP(hAPP(c_COMBC(X11897,X11897,tc_HOL_Obool),c_fequal),X11895))),X11894)),c_Groups_Oone__class_Oone(X11898))),X11896)=hAPP(X11894,X11895)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11897),X11896))|~class_Groups_Ocomm__monoid__mult(X11898))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__delta])])])])). 4.46/4.69 fof(c_0_4965, plain, ![X17284, X17285, X17286, X17287]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X17286),X17285))|c_Groups_Oone__class_Oone(X17287)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17286,X17287),X17284),X17285)|~class_Groups_Ocomm__monoid__mult(X17287))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17286),X17285))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17286,X17287),X17284),X17285)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17287,X17286,c_Groups_Otimes__class_Otimes(X17287)),X17284),c_Groups_Oone__class_Oone(X17287)),X17285)|~class_Groups_Ocomm__monoid__mult(X17287))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod_OF__eq])])])])). 4.46/4.69 fof(c_0_4966, plain, ![X13159, X13160, X13161, X13162, X13163]:((~hBOOL(hAPP(hAPP(c_member(X13162),X13160),X13161))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13162,X13163),hAPP(hAPP(c_COMBC(X13162,X13163,X13163),hAPP(hAPP(c_COMBS(X13162,X13163,tc_fun(X13163,X13163)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13163,tc_fun(X13163,X13163)),X13162),c_If(X13163)),hAPP(hAPP(c_COMBC(X13162,X13162,tc_HOL_Obool),c_fequal),X13160))),X13159)),c_Groups_Ozero__class_Ozero(X13163))),X13161)=hAPP(X13159,X13160)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13162),X13161))|~class_Groups_Ocomm__monoid__add(X13163))&(hBOOL(hAPP(hAPP(c_member(X13162),X13160),X13161))|c_Groups_Ozero__class_Ozero(X13163)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13162,X13163),hAPP(hAPP(c_COMBC(X13162,X13163,X13163),hAPP(hAPP(c_COMBS(X13162,X13163,tc_fun(X13163,X13163)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X13163,tc_fun(X13163,X13163)),X13162),c_If(X13163)),hAPP(hAPP(c_COMBC(X13162,X13162,tc_HOL_Obool),c_fequal),X13160))),X13159)),c_Groups_Ozero__class_Ozero(X13163))),X13161)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13162),X13161))|~class_Groups_Ocomm__monoid__add(X13163))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__delta])])])])). 4.46/4.69 fof(c_0_4967, plain, ![X13867, X13868, X13869, X13870]:(~class_Groups_Ocomm__monoid__add(X13870)|(hBOOL(hAPP(c_Finite__Set_Ofinite(X13869),X13868))|c_Groups_Ozero__class_Ozero(X13870)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13869,X13870),X13867),X13868))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__infinite])])])). 4.46/4.69 fof(c_0_4968, plain, ![X8760, X8761, X8762, X8763, X8764]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X8764,X8764)),hAPP(hAPP(c_Product__Type_OPair(X8764,X8764),X8763),X8762)),c_Transitive__Closure_Otrancl(X8764,X8761)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X8764,X8764)),hAPP(hAPP(c_Product__Type_OPair(X8764,X8764),X8762),X8760)),c_Transitive__Closure_Otrancl(X8764,X8761)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X8764,X8764)),hAPP(hAPP(c_Product__Type_OPair(X8764,X8764),X8763),X8760)),c_Transitive__Closure_Otrancl(X8764,X8761))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__trans])])])). 4.46/4.69 cnf(c_0_4969, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1)))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2))),c_COMBI(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_4570])). 4.46/4.69 cnf(c_0_4970, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X2))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_4547])). 4.46/4.69 fof(c_0_4971, plain, ![X6096, X6097, X6098, X6099, X6100, X6101, X6102, X6103, X6104]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6100),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6099)),X6098)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6099)),X6097))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6099,X6099)),hAPP(hAPP(c_Product__Type_OPair(X6099,X6099),hAPP(hAPP(c_List_Onth(X6099),X6098),X6100)),hAPP(hAPP(c_List_Onth(X6099),X6097),X6100))),X6096))|hAPP(hAPP(c_List_Otake(X6099),X6100),X6098)!=hAPP(hAPP(c_List_Otake(X6099),X6100),X6097)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6099),tc_List_Olist(X6099))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6099),tc_List_Olist(X6099)),X6098),X6097)),c_List_Olexord(X6099,X6096))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6099)),X6098)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6099)),X6097)))|X6098!=hAPP(hAPP(c_List_Otake(X6099),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6099)),X6098)),X6097)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6099),tc_List_Olist(X6099))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6099),tc_List_Olist(X6099)),X6098),X6097)),c_List_Olexord(X6099,X6096)))))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6104)),X6103)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6104)),X6102)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk189_4(X6101,X6102,X6103,X6104)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6104)),X6103)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6104)),X6102))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6104),tc_List_Olist(X6104))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6104),tc_List_Olist(X6104)),X6103),X6102)),c_List_Olexord(X6104,X6101))))&(X6103=hAPP(hAPP(c_List_Otake(X6104),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6104)),X6103)),X6102)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk189_4(X6101,X6102,X6103,X6104)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6104)),X6103)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6104)),X6102))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6104),tc_List_Olist(X6104))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6104),tc_List_Olist(X6104)),X6103),X6102)),c_List_Olexord(X6104,X6101)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6104)),X6103)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6104)),X6102)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X6104,X6104)),hAPP(hAPP(c_Product__Type_OPair(X6104,X6104),hAPP(hAPP(c_List_Onth(X6104),X6103),esk189_4(X6101,X6102,X6103,X6104))),hAPP(hAPP(c_List_Onth(X6104),X6102),esk189_4(X6101,X6102,X6103,X6104)))),X6101))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6104),tc_List_Olist(X6104))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6104),tc_List_Olist(X6104)),X6103),X6102)),c_List_Olexord(X6104,X6101))))&(X6103=hAPP(hAPP(c_List_Otake(X6104),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6104)),X6103)),X6102)|hBOOL(hAPP(hAPP(c_member(tc_prod(X6104,X6104)),hAPP(hAPP(c_Product__Type_OPair(X6104,X6104),hAPP(hAPP(c_List_Onth(X6104),X6103),esk189_4(X6101,X6102,X6103,X6104))),hAPP(hAPP(c_List_Onth(X6104),X6102),esk189_4(X6101,X6102,X6103,X6104)))),X6101))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6104),tc_List_Olist(X6104))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6104),tc_List_Olist(X6104)),X6103),X6102)),c_List_Olexord(X6104,X6101))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6104)),X6103)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6104)),X6102)))|hAPP(hAPP(c_List_Otake(X6104),esk189_4(X6101,X6102,X6103,X6104)),X6103)=hAPP(hAPP(c_List_Otake(X6104),esk189_4(X6101,X6102,X6103,X6104)),X6102)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6104),tc_List_Olist(X6104))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6104),tc_List_Olist(X6104)),X6103),X6102)),c_List_Olexord(X6104,X6101))))&(X6103=hAPP(hAPP(c_List_Otake(X6104),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6104)),X6103)),X6102)|hAPP(hAPP(c_List_Otake(X6104),esk189_4(X6101,X6102,X6103,X6104)),X6103)=hAPP(hAPP(c_List_Otake(X6104),esk189_4(X6101,X6102,X6103,X6104)),X6102)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6104),tc_List_Olist(X6104))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6104),tc_List_Olist(X6104)),X6103),X6102)),c_List_Olexord(X6104,X6101))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__take__index__conv])])])])])])). 4.46/4.69 cnf(c_0_4972, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4571])). 4.46/4.69 cnf(c_0_4973, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_4572])). 4.46/4.69 cnf(c_0_4974, plain, (c_Groups_Oone__class_Oone(X2)=hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|X1!=c_Groups_Oone__class_Oone(X2)|~class_Rings_Oring__1__no__zero__divisors(X2)), inference(split_conjunct,[status(thm)],[c_0_4456])). 4.46/4.69 fof(c_0_4975, plain, ![X12971, X12972, X12973, X12974, X12975, X12976, X12977]:((~hBOOL(hAPP(hAPP(c_member(X12977),X12976),hAPP(c_List_Oset(X12977),hAPP(hAPP(c_List_Otake(X12977),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12975)),X12974)),X12973))))|c_Map_Omap__upds(X12977,X12975,X12972,X12973,X12974)=c_Map_Omap__upds(X12977,X12975,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X12977,tc_Option_Ooption(X12975)),X12972),X12976),hAPP(c_Option_Ooption_OSome(X12975),X12971)),X12973,X12974))&(hBOOL(hAPP(hAPP(c_member(X12977),X12976),hAPP(c_List_Oset(X12977),hAPP(hAPP(c_List_Otake(X12977),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12975)),X12974)),X12973))))|c_Map_Omap__upds(X12977,X12975,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X12977,tc_Option_Ooption(X12975)),X12972),X12976),hAPP(c_Option_Ooption_OSome(X12975),X12971)),X12973,X12974)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X12977,tc_Option_Ooption(X12975)),c_Map_Omap__upds(X12977,X12975,X12972,X12973,X12974)),X12976),hAPP(c_Option_Ooption_OSome(X12975),X12971)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__upd__upds__conv__if])])])). 4.46/4.69 fof(c_0_4976, plain, ![X10140, X10141, X10142, X10143, X10144, X10145, X10146]:c_Map_Omap__upds(X10146,X10145,X10144,hAPP(hAPP(c_List_Olist_OCons(X10146),X10143),X10142),hAPP(hAPP(c_List_Olist_OCons(X10145),X10141),X10140))=c_Map_Omap__upds(X10146,X10145,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10146,tc_Option_Ooption(X10145)),X10144),X10143),hAPP(c_Option_Ooption_OSome(X10145),X10141)),X10142,X10140), inference(variable_rename,[status(thm)],[fact_map__upds__Cons])). 4.46/4.69 cnf(c_0_4977, plain, (c_List_OtakeWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Orev(X1),hAPP(c_List_Otl(X1),c_List_OdropWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_4573])). 4.46/4.69 cnf(c_0_4978, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(c_List_Otl(X1),X3))=hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4574])). 4.46/4.69 cnf(c_0_4979, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X2)),X3)=hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(c_List_Otl(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_4575]), ['final']). 4.46/4.69 cnf(c_0_4980, plain, (hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Otimes__class_Otimes(X1)),c_COMBI(X1)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X3)))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4576])). 4.46/4.69 fof(c_0_4981, plain, ![X11739, X11740]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk345_2(X11739,X11740)))|hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X11740))=hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X11739)))&((~hBOOL(hAPP(X11739,esk345_2(X11739,X11740)))|~hBOOL(hAPP(X11740,esk345_2(X11739,X11740)))|hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X11740))=hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X11739)))&(hBOOL(hAPP(X11739,esk345_2(X11739,X11740)))|hBOOL(hAPP(X11740,esk345_2(X11739,X11740)))|hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X11740))=hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X11739))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__nat__int__set__cong])])])])])). 4.46/4.69 cnf(c_0_4982, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4577])). 4.46/4.69 cnf(c_0_4983, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4578])). 4.46/4.69 fof(c_0_4984, plain, ![X6401, X6402, X6403, X6404, X6405]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6403)),hAPP(hAPP(c_List_Otake(X6403),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6405)),X6404)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6403)),X6402))),X6402))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6405)),hAPP(hAPP(c_List_Otake(X6405),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6405)),X6404)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6403)),X6402))),X6404))|hBOOL(hAPP(X6401,hAPP(hAPP(c_List_Ozip(X6405,X6403),X6404),X6402))))&(~hBOOL(hAPP(X6401,hAPP(hAPP(c_List_Ozip(X6405,X6403),hAPP(hAPP(c_List_Otake(X6405),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6405)),X6404)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6403)),X6402))),X6404)),hAPP(hAPP(c_List_Otake(X6403),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6405)),X6404)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6403)),X6402))),X6402))))|hBOOL(hAPP(X6401,hAPP(hAPP(c_List_Ozip(X6405,X6403),X6404),X6402))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zip__obtain__same__length])])])])). 4.46/4.69 cnf(c_0_4985, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Otake(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_4579])). 4.46/4.69 cnf(c_0_4986, plain, (c_Orderings_Oord__class_Omin(tc_Nat_Onat)=c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_inf__nat__def]), ['final']). 4.46/4.69 fof(c_0_4987, plain, ![X14756, X14757]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,X14757))|hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X14756),X14757)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X14756)),hAPP(c_Int_Onat,X14757)))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,X14757))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X14756)),hAPP(c_Int_Onat,X14757))=hAPP(c_Int_Onat,X14756))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__nat__eq__if])])])). 4.46/4.69 fof(c_0_4988, plain, ![X15788, X15789, X15790, X15791, X15792, X15793, X15794, X15795]:(((~hBOOL(hAPP(hAPP(c_member(tc_prod(X15795,X15795)),hAPP(hAPP(c_Product__Type_OPair(X15795,X15795),X15793),X15791)),X15789))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X15795,X15794),tc_prod(X15795,X15794))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X15795,X15794),tc_prod(X15795,X15794)),hAPP(hAPP(c_Product__Type_OPair(X15795,X15794),X15793),X15792)),hAPP(hAPP(c_Product__Type_OPair(X15795,X15794),X15791),X15790))),c_Wellfounded_Olex__prod(X15795,X15794,X15789,X15788))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X15794,X15794)),hAPP(hAPP(c_Product__Type_OPair(X15794,X15794),X15792),X15790)),X15788))|X15793!=X15791|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X15795,X15794),tc_prod(X15795,X15794))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X15795,X15794),tc_prod(X15795,X15794)),hAPP(hAPP(c_Product__Type_OPair(X15795,X15794),X15793),X15792)),hAPP(hAPP(c_Product__Type_OPair(X15795,X15794),X15791),X15790))),c_Wellfounded_Olex__prod(X15795,X15794,X15789,X15788)))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X15794,X15794)),hAPP(hAPP(c_Product__Type_OPair(X15794,X15794),X15792),X15790)),X15788))|hBOOL(hAPP(hAPP(c_member(tc_prod(X15795,X15795)),hAPP(hAPP(c_Product__Type_OPair(X15795,X15795),X15793),X15791)),X15789))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X15795,X15794),tc_prod(X15795,X15794))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X15795,X15794),tc_prod(X15795,X15794)),hAPP(hAPP(c_Product__Type_OPair(X15795,X15794),X15793),X15792)),hAPP(hAPP(c_Product__Type_OPair(X15795,X15794),X15791),X15790))),c_Wellfounded_Olex__prod(X15795,X15794,X15789,X15788))))&(X15793=X15791|hBOOL(hAPP(hAPP(c_member(tc_prod(X15795,X15795)),hAPP(hAPP(c_Product__Type_OPair(X15795,X15795),X15793),X15791)),X15789))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X15795,X15794),tc_prod(X15795,X15794))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X15795,X15794),tc_prod(X15795,X15794)),hAPP(hAPP(c_Product__Type_OPair(X15795,X15794),X15793),X15792)),hAPP(hAPP(c_Product__Type_OPair(X15795,X15794),X15791),X15790))),c_Wellfounded_Olex__prod(X15795,X15794,X15789,X15788)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])])). 4.46/4.69 fof(c_0_4989, plain, ![X15129, X15130, X15131, X15132, X15133]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X15133,X15133)),hAPP(hAPP(c_Product__Type_OPair(X15133,X15133),X15132),X15131)),c_Transitive__Closure_Ortrancl(X15133,X15130)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X15133,X15133)),hAPP(hAPP(c_Product__Type_OPair(X15133,X15133),X15131),X15129)),c_Transitive__Closure_Otrancl(X15133,X15130)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X15133,X15133)),hAPP(hAPP(c_Product__Type_OPair(X15133,X15133),X15132),X15129)),c_Transitive__Closure_Otrancl(X15133,X15130))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__trancl__trancl])])])). 4.46/4.69 fof(c_0_4990, plain, ![X10849, X10850, X10851, X10852, X10853]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10853,X10853)),hAPP(hAPP(c_Product__Type_OPair(X10853,X10853),X10852),X10851)),c_Transitive__Closure_Otrancl(X10853,X10850)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10853,X10853)),hAPP(hAPP(c_Product__Type_OPair(X10853,X10853),X10851),X10849)),c_Transitive__Closure_Ortrancl(X10853,X10850)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X10853,X10853)),hAPP(hAPP(c_Product__Type_OPair(X10853,X10853),X10852),X10849)),c_Transitive__Closure_Otrancl(X10853,X10850))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__rtrancl__trancl])])])). 4.46/4.69 fof(c_0_4991, plain, ![X10020, X10021, X10022, X10023]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10023,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10023,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk287_4(X10020,X10021,X10022,X10023))),X10022)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10023,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk287_4(X10020,X10021,X10022,X10023)),X10021))),X10020)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10023,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10023,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X10022)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10023,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X10020)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__finite2__subset])])])])). 4.46/4.69 fof(c_0_4992, plain, ![X13035, X13036, X13037, X13038, X13039, X13040]:((hBOOL(hAPP(hAPP(X13035,esk381_6(X13035,X13036,X13037,X13038,X13039,X13040)),esk382_6(X13035,X13036,X13037,X13038,X13039,X13040)))|c_Hoare__Mirabelle_Ohoare__derivs(X13040,X13039,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X13040)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X13040),X13035),X13037),X13036)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X13040),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X13040,X13039,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X13040)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X13040),X13038),X13037),X13036)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X13040),tc_HOL_Obool)))))&(~hBOOL(hAPP(hAPP(X13038,esk381_6(X13035,X13036,X13037,X13038,X13039,X13040)),esk382_6(X13035,X13036,X13037,X13038,X13039,X13040)))|c_Hoare__Mirabelle_Ohoare__derivs(X13040,X13039,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X13040)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X13040),X13035),X13037),X13036)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X13040),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X13040,X13039,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X13040)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X13040),X13038),X13037),X13036)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X13040),tc_HOL_Obool)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_conseq1])])])])])). 4.46/4.69 fof(c_0_4993, plain, ![X888, X889, X890, X891, X892, X893]:((hBOOL(hAPP(hAPP(X889,esk21_6(X888,X889,X890,X891,X892,X893)),esk22_6(X888,X889,X890,X891,X892,X893)))|c_Hoare__Mirabelle_Ohoare__derivs(X893,X892,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X893)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X893),X891),X890),X888)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X893),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X893,X892,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X893)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X893),X891),X890),X889)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X893),tc_HOL_Obool)))))&(~hBOOL(hAPP(hAPP(X888,esk21_6(X888,X889,X890,X891,X892,X893)),esk22_6(X888,X889,X890,X891,X892,X893)))|c_Hoare__Mirabelle_Ohoare__derivs(X893,X892,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X893)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X893),X891),X890),X888)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X893),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X893,X892,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X893)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X893),X891),X890),X889)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X893),tc_HOL_Obool)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_conseq2])])])])])). 4.46/4.69 fof(c_0_4994, plain, ![X8878, X8879, X8880, X8881, X8882]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X8882,X8882)),hAPP(hAPP(c_Product__Type_OPair(X8882,X8882),X8881),X8880)),X8879))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X8882,X8882)),hAPP(hAPP(c_Product__Type_OPair(X8882,X8882),X8880),X8878)),c_Transitive__Closure_Otrancl(X8882,X8879)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X8882,X8882)),hAPP(hAPP(c_Product__Type_OPair(X8882,X8882),X8881),X8878)),c_Transitive__Closure_Otrancl(X8882,X8879))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__into__trancl2])])])). 4.46/4.69 fof(c_0_4995, plain, ![X3596, X3597, X3598, X3599, X3600]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X3600,X3600)),hAPP(hAPP(c_Product__Type_OPair(X3600,X3600),X3599),X3598)),c_Transitive__Closure_Otrancl(X3600,X3597)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X3600,X3600)),hAPP(hAPP(c_Product__Type_OPair(X3600,X3600),X3598),X3596)),X3597))|hBOOL(hAPP(hAPP(c_member(tc_prod(X3600,X3600)),hAPP(hAPP(c_Product__Type_OPair(X3600,X3600),X3599),X3596)),c_Transitive__Closure_Otrancl(X3600,X3597))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Transitive__Closure_Otrancl__into__trancl])])])). 4.46/4.69 fof(c_0_4996, plain, ![X6831, X6832, X6833, X6834, X6835]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X6832),hAPP(c_Set_OCollect(X6832),hAPP(hAPP(c_COMBB(tc_fun(X6834,tc_HOL_Obool),tc_HOL_Obool,X6832),c_HOL_OEx(X6834)),hAPP(hAPP(c_COMBB(tc_fun(X6834,tc_HOL_Obool),tc_fun(X6834,tc_HOL_Obool),X6832),hAPP(c_COMBS(X6834,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6834),c_fconj),X6833))),X6831)))))|(~hBOOL(hAPP(X6833,X6835))|hBOOL(hAPP(c_Finite__Set_Ofinite(X6832),hAPP(c_Set_OCollect(X6832),hAPP(hAPP(c_COMBC(X6832,X6834,tc_HOL_Obool),X6831),X6835)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6834),hAPP(c_Set_OCollect(X6834),X6833))))&((hBOOL(hAPP(X6833,esk201_4(X6831,X6832,X6833,X6834)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X6832),hAPP(c_Set_OCollect(X6832),hAPP(hAPP(c_COMBB(tc_fun(X6834,tc_HOL_Obool),tc_HOL_Obool,X6832),c_HOL_OEx(X6834)),hAPP(hAPP(c_COMBB(tc_fun(X6834,tc_HOL_Obool),tc_fun(X6834,tc_HOL_Obool),X6832),hAPP(c_COMBS(X6834,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6834),c_fconj),X6833))),X6831)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6834),hAPP(c_Set_OCollect(X6834),X6833))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6832),hAPP(c_Set_OCollect(X6832),hAPP(hAPP(c_COMBC(X6832,X6834,tc_HOL_Obool),X6831),esk201_4(X6831,X6832,X6833,X6834)))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X6832),hAPP(c_Set_OCollect(X6832),hAPP(hAPP(c_COMBB(tc_fun(X6834,tc_HOL_Obool),tc_HOL_Obool,X6832),c_HOL_OEx(X6834)),hAPP(hAPP(c_COMBB(tc_fun(X6834,tc_HOL_Obool),tc_fun(X6834,tc_HOL_Obool),X6832),hAPP(c_COMBS(X6834,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6834),c_fconj),X6833))),X6831)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6834),hAPP(c_Set_OCollect(X6834),X6833)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Collect__bounded__ex])])])])])])). 4.46/4.69 fof(c_0_4997, plain, ![X2389, X2390, X2391, X2392, X2393]:((hBOOL(hAPP(hAPP(c_member(X2392),X2390),X2391))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2392,X2393),hAPP(hAPP(c_COMBC(X2392,X2393,X2393),hAPP(hAPP(c_COMBS(X2392,X2393,tc_fun(X2393,X2393)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2393,tc_fun(X2393,X2393)),X2392),c_If(X2393)),hAPP(c_fequal,X2390))),X2389)),c_Groups_Ozero__class_Ozero(X2393))),X2391)=c_Groups_Ozero__class_Ozero(X2393)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2392),X2391))|~class_Groups_Ocomm__monoid__add(X2393))&(~hBOOL(hAPP(hAPP(c_member(X2392),X2390),X2391))|hAPP(X2389,X2390)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2392,X2393),hAPP(hAPP(c_COMBC(X2392,X2393,X2393),hAPP(hAPP(c_COMBS(X2392,X2393,tc_fun(X2393,X2393)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2393,tc_fun(X2393,X2393)),X2392),c_If(X2393)),hAPP(c_fequal,X2390))),X2389)),c_Groups_Ozero__class_Ozero(X2393))),X2391)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2392),X2391))|~class_Groups_Ocomm__monoid__add(X2393))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__delta_H])])])])). 4.46/4.69 fof(c_0_4998, plain, ![X7761, X7762, X7763, X7764, X7765]:(~hBOOL(hAPP(hAPP(c_member(X7765),X7764),hAPP(c_List_Oset(X7765),X7763)))|(hBOOL(hAPP(X7762,X7764))|hAPP(hAPP(c_List_Oappend(X7765),c_List_OdropWhile(X7765,X7762,X7763)),X7761)=c_List_OdropWhile(X7765,X7762,hAPP(hAPP(c_List_Oappend(X7765),X7763),X7761)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dropWhile__append1])])])). 4.46/4.69 fof(c_0_4999, plain, ![X15408, X15409, X15410, X15411, X15412, X15413, X15414, X15415]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X15415,X15415)),hAPP(hAPP(c_Product__Type_OPair(X15415,X15415),X15414),X15413)),X15412))|(X15411!=hAPP(hAPP(c_List_Oappend(X15415),X15410),hAPP(hAPP(c_List_Olist_OCons(X15415),X15414),X15409))|(X15408!=hAPP(hAPP(c_List_Oappend(X15415),X15410),hAPP(hAPP(c_List_Olist_OCons(X15415),X15413),X15409))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X15415),tc_List_Olist(X15415))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X15415),tc_List_Olist(X15415)),X15411),X15408)),c_List_Olistrel1(X15415,X15412)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel1I])])])). 4.46/4.69 fof(c_0_5000, plain, ![X4693, X4694, X4695, X4696, X4697]:((hBOOL(hAPP(hAPP(c_member(X4696),X4694),X4695))|c_Groups_Oone__class_Oone(X4697)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4696,X4697),hAPP(hAPP(c_COMBC(X4696,X4697,X4697),hAPP(hAPP(c_COMBS(X4696,X4697,tc_fun(X4697,X4697)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4697,tc_fun(X4697,X4697)),X4696),c_If(X4697)),hAPP(c_fequal,X4694))),X4693)),c_Groups_Oone__class_Oone(X4697))),X4695)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4696),X4695))|~class_Groups_Ocomm__monoid__mult(X4697))&(~hBOOL(hAPP(hAPP(c_member(X4696),X4694),X4695))|hAPP(X4693,X4694)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4696,X4697),hAPP(hAPP(c_COMBC(X4696,X4697,X4697),hAPP(hAPP(c_COMBS(X4696,X4697,tc_fun(X4697,X4697)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4697,tc_fun(X4697,X4697)),X4696),c_If(X4697)),hAPP(c_fequal,X4694))),X4693)),c_Groups_Oone__class_Oone(X4697))),X4695)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4696),X4695))|~class_Groups_Ocomm__monoid__mult(X4697))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__delta_H])])])])). 4.46/4.69 cnf(c_0_5001, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))), inference(split_conjunct,[status(thm)],[c_0_4580])). 4.46/4.69 cnf(c_0_5002, plain, (c_Nitpick_Oof__frac(X2,X1,X3)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Nitpick_Onum(X2),X3))),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Nitpick_Odenom(X2),X3)))|~class_Rings_Oring__1(X1)|~class_Rings_Oinverse(X1)), inference(split_conjunct,[status(thm)],[c_0_4581])). 4.46/4.69 cnf(c_0_5003, plain, (c_Nitpick_Onum(X1)=hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1))), inference(split_conjunct,[status(thm)],[c_0_4582])). 4.46/4.69 cnf(c_0_5004, plain, (hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1))=c_Nitpick_Odenom(X1)), inference(split_conjunct,[status(thm)],[c_0_4583])). 4.46/4.69 fof(c_0_5005, plain, ![X11615, X11616, X11617, X11618, X11619, X11620]:hAPP(X11617,hAPP(X11616,X11615))=hAPP(hAPP(c_Fun_Ocomp(X11620,X11619,X11618,X11617),X11616),X11615), inference(variable_rename,[status(thm)],[fact_o__apply])). 4.46/4.69 cnf(c_0_5006, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))), inference(split_conjunct,[status(thm)],[c_0_4584])). 4.46/4.69 fof(c_0_5007, plain, ![X332, X333]:(((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X333)),esk2_2(X332,X333)),hAPP(c_List_Oset(tc_List_Olist(X333)),X332)))|hBOOL(hAPP(c_List_Odistinct(X333),c_List_Oconcat(X333,X332)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X333)),esk1_2(X332,X333)),hAPP(c_List_Oset(tc_List_Olist(X333)),X332)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X333)),X332)))&((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X333)),esk3_2(X332,X333)),hAPP(c_List_Oset(tc_List_Olist(X333)),X332)))|hBOOL(hAPP(c_List_Odistinct(X333),c_List_Oconcat(X333,X332)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X333)),esk1_2(X332,X333)),hAPP(c_List_Oset(tc_List_Olist(X333)),X332)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X333)),X332)))&((esk3_2(X332,X333)!=esk2_2(X332,X333)|hBOOL(hAPP(c_List_Odistinct(X333),c_List_Oconcat(X333,X332)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X333)),esk1_2(X332,X333)),hAPP(c_List_Oset(tc_List_Olist(X333)),X332)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X333)),X332)))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X333,tc_HOL_Obool)),hAPP(c_List_Oset(X333),esk2_2(X332,X333))),hAPP(c_List_Oset(X333),esk3_2(X332,X333)))!=c_Orderings_Obot__class_Obot(tc_fun(X333,tc_HOL_Obool))|hBOOL(hAPP(c_List_Odistinct(X333),c_List_Oconcat(X333,X332)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X333)),esk1_2(X332,X333)),hAPP(c_List_Oset(tc_List_Olist(X333)),X332)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X333)),X332))))))&((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X333)),esk2_2(X332,X333)),hAPP(c_List_Oset(tc_List_Olist(X333)),X332)))|hBOOL(hAPP(c_List_Odistinct(X333),c_List_Oconcat(X333,X332)))|~hBOOL(hAPP(c_List_Odistinct(X333),esk1_2(X332,X333)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X333)),X332)))&((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X333)),esk3_2(X332,X333)),hAPP(c_List_Oset(tc_List_Olist(X333)),X332)))|hBOOL(hAPP(c_List_Odistinct(X333),c_List_Oconcat(X333,X332)))|~hBOOL(hAPP(c_List_Odistinct(X333),esk1_2(X332,X333)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X333)),X332)))&((esk3_2(X332,X333)!=esk2_2(X332,X333)|hBOOL(hAPP(c_List_Odistinct(X333),c_List_Oconcat(X333,X332)))|~hBOOL(hAPP(c_List_Odistinct(X333),esk1_2(X332,X333)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X333)),X332)))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X333,tc_HOL_Obool)),hAPP(c_List_Oset(X333),esk2_2(X332,X333))),hAPP(c_List_Oset(X333),esk3_2(X332,X333)))!=c_Orderings_Obot__class_Obot(tc_fun(X333,tc_HOL_Obool))|hBOOL(hAPP(c_List_Odistinct(X333),c_List_Oconcat(X333,X332)))|~hBOOL(hAPP(c_List_Odistinct(X333),esk1_2(X332,X333)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X333)),X332))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__concat])])])])])). 4.46/4.69 cnf(c_0_5008, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3)))))), inference(split_conjunct,[status(thm)],[c_0_4585])). 4.46/4.69 fof(c_0_5009, plain, ![X3707, X3708, X3709, X3710, X3711, X3712, X3713]:(~c_Hoare__Mirabelle_Ohoare__derivs(X3713,X3712,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3713)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3713),c_Hoare__Mirabelle_Opeek__and(X3713,X3711,X3710)),X3709),X3708)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3713),tc_HOL_Obool))))|(~c_Hoare__Mirabelle_Ohoare__derivs(X3713,X3712,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3713)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3713),c_Hoare__Mirabelle_Opeek__and(X3713,X3711,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X3710))),X3707),X3708)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3713),tc_HOL_Obool))))|c_Hoare__Mirabelle_Ohoare__derivs(X3713,X3712,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3713)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3713),X3711),c_Com_Ocom_OCond(X3710,X3709,X3707)),X3708)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3713),tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OIf])])). 4.46/4.69 fof(c_0_5010, plain, ![X5770, X5771]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5770),X5771))|hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5770)=c_Divides_Odivmod__nat(X5770,X5771))&(X5771!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5770)=c_Divides_Odivmod__nat(X5770,X5771)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5770),X5771))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X5771|c_Divides_Odivmod__nat(X5770,X5771)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5770),X5771),X5771)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__if])])])). 4.46/4.69 fof(c_0_5011, plain, ![X4718, X4719]:c_Divides_Odivmod__nat(X4719,X4718)=c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X4719,X4718)), inference(variable_rename,[status(thm)],[fact_divmod__nat__def])). 4.46/4.69 fof(c_0_5012, plain, ![X10548, X10549]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X10549),X10548))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Nitpick_Ocard_H(X10549,X10548))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10549),X10548))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10549)),c_Hilbert__Choice_OEps(tc_List_Olist(X10549),hAPP(hAPP(c_COMBS(tc_List_Olist(X10549),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10549)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X10549),tc_fun(X10549,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10549,tc_HOL_Obool),tc_fun(tc_fun(X10549,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10549)),c_fequal),c_List_Oset(X10549))),X10548))),c_List_Odistinct(X10549))))=c_Nitpick_Ocard_H(X10549,X10548))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nitpick_Ocard_H__def])])])). 4.46/4.69 fof(c_0_5013, plain, ![X7984, X7985, X7986]:(~class_Rings_Oring__1(X7986)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7986),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7986),X7985)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7986),X7984))=hAPP(c_Int_Oring__1__class_Oof__int(X7986),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X7985),X7984)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int])])). 4.46/4.69 fof(c_0_5014, plain, ![X10914, X10915, X10916, X10917, X10918, X10919]:(((~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10919),tc_List_Olist(X10919))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10919),tc_List_Olist(X10919)),X10917),X10915)),c_List_Olexord(X10919,X10914)))|X10918!=X10916|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10919),tc_List_Olist(X10919))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10919),tc_List_Olist(X10919)),hAPP(hAPP(c_List_Olist_OCons(X10919),X10918),X10917)),hAPP(hAPP(c_List_Olist_OCons(X10919),X10916),X10915))),c_List_Olexord(X10919,X10914))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10919,X10919)),hAPP(hAPP(c_Product__Type_OPair(X10919,X10919),X10918),X10916)),X10914))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10919),tc_List_Olist(X10919))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10919),tc_List_Olist(X10919)),hAPP(hAPP(c_List_Olist_OCons(X10919),X10918),X10917)),hAPP(hAPP(c_List_Olist_OCons(X10919),X10916),X10915))),c_List_Olexord(X10919,X10914)))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10919),tc_List_Olist(X10919))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10919),tc_List_Olist(X10919)),X10917),X10915)),c_List_Olexord(X10919,X10914)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X10919,X10919)),hAPP(hAPP(c_Product__Type_OPair(X10919,X10919),X10918),X10916)),X10914))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10919),tc_List_Olist(X10919))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10919),tc_List_Olist(X10919)),hAPP(hAPP(c_List_Olist_OCons(X10919),X10918),X10917)),hAPP(hAPP(c_List_Olist_OCons(X10919),X10916),X10915))),c_List_Olexord(X10919,X10914))))&(X10918=X10916|hBOOL(hAPP(hAPP(c_member(tc_prod(X10919,X10919)),hAPP(hAPP(c_Product__Type_OPair(X10919,X10919),X10918),X10916)),X10914))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10919),tc_List_Olist(X10919))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10919),tc_List_Olist(X10919)),hAPP(hAPP(c_List_Olist_OCons(X10919),X10918),X10917)),hAPP(hAPP(c_List_Olist_OCons(X10919),X10916),X10915))),c_List_Olexord(X10919,X10914)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__cons__cons])])])). 4.46/4.69 fof(c_0_5015, plain, ![X3754, X3755, X3756, X3757, X3758, X3759]:((X3754!=X3755|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3759),tc_List_Olist(X3759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3759),tc_List_Olist(X3759)),X3758),X3757)),c_List_Olistrel1(X3759,X3756)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3759),tc_List_Olist(X3759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3759),tc_List_Olist(X3759)),hAPP(hAPP(c_List_Oappend(X3759),X3758),X3755)),hAPP(hAPP(c_List_Oappend(X3759),X3757),X3754))),c_List_Olistrel1(X3759,X3756))))&(X3757!=X3758|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3759),tc_List_Olist(X3759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3759),tc_List_Olist(X3759)),X3755),X3754)),c_List_Olistrel1(X3759,X3756)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3759),tc_List_Olist(X3759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3759),tc_List_Olist(X3759)),hAPP(hAPP(c_List_Oappend(X3759),X3758),X3755)),hAPP(hAPP(c_List_Oappend(X3759),X3757),X3754))),c_List_Olistrel1(X3759,X3756))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__listrel1I])])])). 4.46/4.69 fof(c_0_5016, plain, ![X6560, X6561, X6562, X6563, X6564, X6565]:(((X6562!=X6564|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6565),tc_List_Olist(X6565))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6565),tc_List_Olist(X6565)),X6563),X6561)),c_List_Olex(X6565,X6560)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6565),tc_List_Olist(X6565))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6565),tc_List_Olist(X6565)),hAPP(hAPP(c_List_Olist_OCons(X6565),X6564),X6563)),hAPP(hAPP(c_List_Olist_OCons(X6565),X6562),X6561))),c_List_Olex(X6565,X6560))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X6565,X6565)),hAPP(hAPP(c_Product__Type_OPair(X6565,X6565),X6564),X6562)),X6560))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6565)),X6563)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6565)),X6561)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6565),tc_List_Olist(X6565))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6565),tc_List_Olist(X6565)),hAPP(hAPP(c_List_Olist_OCons(X6565),X6564),X6563)),hAPP(hAPP(c_List_Olist_OCons(X6565),X6562),X6561))),c_List_Olex(X6565,X6560)))))&(((hBOOL(hAPP(hAPP(c_member(tc_prod(X6565,X6565)),hAPP(hAPP(c_Product__Type_OPair(X6565,X6565),X6564),X6562)),X6560))|X6562=X6564|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6565),tc_List_Olist(X6565))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6565),tc_List_Olist(X6565)),hAPP(hAPP(c_List_Olist_OCons(X6565),X6564),X6563)),hAPP(hAPP(c_List_Olist_OCons(X6565),X6562),X6561))),c_List_Olex(X6565,X6560))))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6565)),X6563)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6565)),X6561)|X6562=X6564|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6565),tc_List_Olist(X6565))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6565),tc_List_Olist(X6565)),hAPP(hAPP(c_List_Olist_OCons(X6565),X6564),X6563)),hAPP(hAPP(c_List_Olist_OCons(X6565),X6562),X6561))),c_List_Olex(X6565,X6560)))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X6565,X6565)),hAPP(hAPP(c_Product__Type_OPair(X6565,X6565),X6564),X6562)),X6560))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6565),tc_List_Olist(X6565))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6565),tc_List_Olist(X6565)),X6563),X6561)),c_List_Olex(X6565,X6560)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6565),tc_List_Olist(X6565))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6565),tc_List_Olist(X6565)),hAPP(hAPP(c_List_Olist_OCons(X6565),X6564),X6563)),hAPP(hAPP(c_List_Olist_OCons(X6565),X6562),X6561))),c_List_Olex(X6565,X6560))))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6565)),X6563)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6565)),X6561)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6565),tc_List_Olist(X6565))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6565),tc_List_Olist(X6565)),X6563),X6561)),c_List_Olex(X6565,X6560)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6565),tc_List_Olist(X6565))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6565),tc_List_Olist(X6565)),hAPP(hAPP(c_List_Olist_OCons(X6565),X6564),X6563)),hAPP(hAPP(c_List_Olist_OCons(X6565),X6562),X6561))),c_List_Olex(X6565,X6560))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lex])])])). 4.46/4.69 fof(c_0_5017, plain, ![X13372, X13373, X13374, X13375, X13376]:(~class_Groups_Ocomm__monoid__add(X13376)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13375),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13374),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13376),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X13376),X13373),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X13375,X13374))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X13376),X13373),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13374),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13374),X13372))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X13376),X13373),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X13375,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13374),X13372))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__ub__add__nat])])). 4.46/4.69 fof(c_0_5018, plain, ![X10834, X10835, X10836, X10837, X10840, X10841, X10842, X10843, X10844, X10845]:((((hBOOL(hAPP(hAPP(c_member(tc_prod(X10837,X10837)),hAPP(hAPP(c_Product__Type_OPair(X10837,X10837),hAPP(hAPP(c_List_Onth(X10837),X10836),esk322_4(X10834,X10835,X10836,X10837))),esk321_4(X10834,X10835,X10836,X10837))),X10834))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10837),tc_List_Olist(X10837))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10837),tc_List_Olist(X10837)),X10836),X10835)),c_List_Olistrel1(X10837,X10834))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk322_4(X10834,X10835,X10836,X10837)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10837)),X10836)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10837),tc_List_Olist(X10837))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10837),tc_List_Olist(X10837)),X10836),X10835)),c_List_Olistrel1(X10837,X10834)))))&(hAPP(hAPP(c_List_Olist__update(X10837,X10836),esk322_4(X10834,X10835,X10836,X10837)),esk321_4(X10834,X10835,X10836,X10837))=X10835|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10837),tc_List_Olist(X10837))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10837),tc_List_Olist(X10837)),X10836),X10835)),c_List_Olistrel1(X10837,X10834)))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10843,X10843)),hAPP(hAPP(c_Product__Type_OPair(X10843,X10843),hAPP(hAPP(c_List_Onth(X10843),X10842),X10845)),X10844)),X10840))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10845),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10843)),X10842)))|hAPP(hAPP(c_List_Olist__update(X10843,X10842),X10845),X10844)!=X10841|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10843),tc_List_Olist(X10843))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10843),tc_List_Olist(X10843)),X10842),X10841)),c_List_Olistrel1(X10843,X10840))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__iff__update])])])])])])). 4.46/4.69 fof(c_0_5019, plain, ![X12351, X12352, X12353, X12354, X12355]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X12355,X12355)),hAPP(hAPP(c_Product__Type_OPair(X12355,X12355),X12354),X12353)),c_Transitive__Closure_Ortrancl(X12355,X12352)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X12355,X12355)),hAPP(hAPP(c_Product__Type_OPair(X12355,X12355),X12353),X12351)),X12352))|hBOOL(hAPP(hAPP(c_member(tc_prod(X12355,X12355)),hAPP(hAPP(c_Product__Type_OPair(X12355,X12355),X12354),X12351)),c_Transitive__Closure_Otrancl(X12355,X12352))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl1])])). 4.46/4.69 fof(c_0_5020, plain, ![X16164, X16165, X16166, X16167, X16168]:((hAPP(hAPP(c_Equiv__Relations_Oquotient(X16168),hAPP(hAPP(c_Set_Oinsert(X16168),X16164),c_Orderings_Obot__class_Obot(tc_fun(X16168,tc_HOL_Obool)))),X16166)!=hAPP(hAPP(c_Equiv__Relations_Oquotient(X16168),hAPP(hAPP(c_Set_Oinsert(X16168),X16165),c_Orderings_Obot__class_Obot(tc_fun(X16168,tc_HOL_Obool)))),X16166)|hBOOL(hAPP(hAPP(c_member(tc_prod(X16168,X16168)),hAPP(hAPP(c_Product__Type_OPair(X16168,X16168),X16165),X16164)),X16166))|~hBOOL(hAPP(hAPP(c_member(X16168),X16164),X16167))|~hBOOL(hAPP(hAPP(c_member(X16168),X16165),X16167))|~c_Equiv__Relations_Oequiv(X16168,X16167,X16166))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16168,X16168)),hAPP(hAPP(c_Product__Type_OPair(X16168,X16168),X16165),X16164)),X16166))|hAPP(hAPP(c_Equiv__Relations_Oquotient(X16168),hAPP(hAPP(c_Set_Oinsert(X16168),X16164),c_Orderings_Obot__class_Obot(tc_fun(X16168,tc_HOL_Obool)))),X16166)=hAPP(hAPP(c_Equiv__Relations_Oquotient(X16168),hAPP(hAPP(c_Set_Oinsert(X16168),X16165),c_Orderings_Obot__class_Obot(tc_fun(X16168,tc_HOL_Obool)))),X16166)|~hBOOL(hAPP(hAPP(c_member(X16168),X16164),X16167))|~hBOOL(hAPP(hAPP(c_member(X16168),X16165),X16167))|~c_Equiv__Relations_Oequiv(X16168,X16167,X16166))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__equiv__class__iff2])])])])). 4.46/4.69 fof(c_0_5021, plain, ![X4915, X4916, X4917, X4918, X4919]:((((hBOOL(hAPP(hAPP(c_member(X4919),X4915),X4918))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4919,X4919)),hAPP(hAPP(c_Product__Type_OPair(X4919,X4919),X4916),X4915)),X4917))|~c_Equiv__Relations_Oequiv(X4919,X4918,X4917))&(hBOOL(hAPP(hAPP(c_member(X4919),X4916),X4918))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4919,X4919)),hAPP(hAPP(c_Product__Type_OPair(X4919,X4919),X4916),X4915)),X4917))|~c_Equiv__Relations_Oequiv(X4919,X4918,X4917)))&(hAPP(c_Relation_OImage(X4919,X4919,X4917),hAPP(hAPP(c_Set_Oinsert(X4919),X4915),c_Orderings_Obot__class_Obot(tc_fun(X4919,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X4919,X4919,X4917),hAPP(hAPP(c_Set_Oinsert(X4919),X4916),c_Orderings_Obot__class_Obot(tc_fun(X4919,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4919,X4919)),hAPP(hAPP(c_Product__Type_OPair(X4919,X4919),X4916),X4915)),X4917))|~c_Equiv__Relations_Oequiv(X4919,X4918,X4917)))&(~hBOOL(hAPP(hAPP(c_member(X4919),X4915),X4918))|~hBOOL(hAPP(hAPP(c_member(X4919),X4916),X4918))|hAPP(c_Relation_OImage(X4919,X4919,X4917),hAPP(hAPP(c_Set_Oinsert(X4919),X4915),c_Orderings_Obot__class_Obot(tc_fun(X4919,tc_HOL_Obool))))!=hAPP(c_Relation_OImage(X4919,X4919,X4917),hAPP(hAPP(c_Set_Oinsert(X4919),X4916),c_Orderings_Obot__class_Obot(tc_fun(X4919,tc_HOL_Obool))))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4919,X4919)),hAPP(hAPP(c_Product__Type_OPair(X4919,X4919),X4916),X4915)),X4917))|~c_Equiv__Relations_Oequiv(X4919,X4918,X4917))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__eq__iff])])])). 4.46/4.69 cnf(c_0_5022, plain, (X2=c_Groups_Oone__class_Oone(X1)|X2=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))|c_Groups_Oone__class_Oone(X1)!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4586, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.69 cnf(c_0_5023, plain, (c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4587, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.69 cnf(c_0_5024, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4588, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.69 cnf(c_0_5025, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),c_Groups_Ozero__class_Ozero(X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4589, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.69 fof(c_0_5026, plain, ![X9799, X9800, X9801, X9802, X9803, X9804, X9805]:((X9802!=X9801|hBOOL(hAPP(hAPP(c_member(tc_prod(X9805,X9805)),hAPP(hAPP(c_Product__Type_OPair(X9805,X9805),X9800),X9799)),X9803))|~hBOOL(hAPP(hAPP(c_member(X9805),X9799),X9801))|~hBOOL(hAPP(hAPP(c_member(X9805),X9800),X9802))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X9805,tc_HOL_Obool)),X9801),hAPP(hAPP(c_Equiv__Relations_Oquotient(X9805),X9804),X9803)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X9805,tc_HOL_Obool)),X9802),hAPP(hAPP(c_Equiv__Relations_Oquotient(X9805),X9804),X9803)))|~c_Equiv__Relations_Oequiv(X9805,X9804,X9803))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9805,X9805)),hAPP(hAPP(c_Product__Type_OPair(X9805,X9805),X9800),X9799)),X9803))|X9802=X9801|~hBOOL(hAPP(hAPP(c_member(X9805),X9799),X9801))|~hBOOL(hAPP(hAPP(c_member(X9805),X9800),X9802))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X9805,tc_HOL_Obool)),X9801),hAPP(hAPP(c_Equiv__Relations_Oquotient(X9805),X9804),X9803)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X9805,tc_HOL_Obool)),X9802),hAPP(hAPP(c_Equiv__Relations_Oquotient(X9805),X9804),X9803)))|~c_Equiv__Relations_Oequiv(X9805,X9804,X9803))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_quotient__eq__iff])])])])). 4.46/4.69 fof(c_0_5027, plain, ![X15309, X15310]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15310))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15310),X15309))|c_Divides_Odivmod__nat(X15309,X15310)=hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15309),X15310)),X15310))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15309),X15310),X15310)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__step])])). 4.46/4.69 fof(c_0_5028, plain, ![X13147, X13148, X13149, X13150, X13151]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13151,X13151)),hAPP(hAPP(c_Product__Type_OPair(X13151,X13151),X13150),X13149)),X13148))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13151,X13151)),hAPP(hAPP(c_Product__Type_OPair(X13151,X13151),X13149),X13147)),X13148))|hBOOL(hAPP(hAPP(c_member(tc_prod(X13151,X13151)),hAPP(hAPP(c_Product__Type_OPair(X13151,X13151),X13150),X13147)),c_Transitive__Closure_Otrancl(X13151,X13148))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl])])). 4.46/4.69 cnf(c_0_5029, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|~class_Int_Onumber__ring(X1)|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_4544])). 4.46/4.69 fof(c_0_5030, plain, ![X15703, X15704, X15705, X15706]:(((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15706)),X15704)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15706)),X15705)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X15706),tc_List_Olist(X15706))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X15706),tc_List_Olist(X15706)),X15705),X15704)),c_List_Olex(X15706,X15703))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X15706),tc_List_Olist(X15706))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X15706),tc_List_Olist(X15706)),X15705),X15704)),c_List_Olexord(X15706,X15703)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X15706),tc_List_Olist(X15706))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X15706),tc_List_Olist(X15706)),X15705),X15704)),c_List_Olex(X15706,X15703)))))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15706)),X15704)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15706)),X15705)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X15706),tc_List_Olist(X15706))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X15706),tc_List_Olist(X15706)),X15705),X15704)),c_List_Olexord(X15706,X15703)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X15706),tc_List_Olist(X15706))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X15706),tc_List_Olist(X15706)),X15705),X15704)),c_List_Olex(X15706,X15703))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__lex])])])). 4.46/4.69 fof(c_0_5031, plain, ![X10871, X10872, X10873]:((((X10872!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X10871)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X10873,X10872),X10871)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10872))|X10872=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X10873,X10872),X10871)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10872),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10872))|X10872=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X10873,X10872),X10871))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10872))|X10872=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X10873,X10872),X10871)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871)),X10872))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10872))|X10872=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X10873,X10872),X10871))))))&(X10873=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X10871)),X10872)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X10873,X10872),X10871))))&(((X10872!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X10872=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X10873!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X10871)),X10872)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X10873,X10872),X10871)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10872))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10872))|X10872=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X10873!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X10871)),X10872)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X10873,X10872),X10871)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871)),X10872))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10872))|X10872=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X10873!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X10871)),X10872)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X10873,X10872),X10871))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10872))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10872),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871))))|X10872=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X10873!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X10871)),X10872)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X10873,X10872),X10871)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871)),X10872))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10872),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871))))|X10872=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X10873!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X10871)),X10872)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X10873,X10872),X10871))))))&((X10872!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X10871)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X10873!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X10871)),X10872)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X10873,X10872),X10871)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10872))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10872))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X10871)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X10873!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X10871)),X10872)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X10873,X10872),X10871)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871)),X10872))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10872))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X10871)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X10873!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X10871)),X10872)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X10873,X10872),X10871))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10872))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10872),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871))))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X10871)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X10873!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X10871)),X10872)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X10873,X10872),X10871)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871)),X10872))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10872),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871))))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X10871)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X10873!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X10871)),X10872)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X10871))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X10873,X10872),X10871)))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__nat__rel__def])])])])). 4.46/4.69 fof(c_0_5032, plain, ![X3262]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3262)), inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J])). 4.46/4.69 fof(c_0_5033, plain, ![X8895, X8896, X8897, X8898, X8899]:((hBOOL(hAPP(hAPP(c_member(X8899),esk254_5(X8895,X8896,X8897,X8898,X8899)),X8898))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8899,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8899,tc_HOL_Obool)),X8898),hAPP(c_Set_OCollect(X8899),X8896))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8899,tc_HOL_Obool)),X8897),hAPP(c_Set_OCollect(X8899),X8895))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8899,tc_HOL_Obool)),X8898),X8897)))&((hBOOL(hAPP(X8896,esk254_5(X8895,X8896,X8897,X8898,X8899)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8899,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8899,tc_HOL_Obool)),X8898),hAPP(c_Set_OCollect(X8899),X8896))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8899,tc_HOL_Obool)),X8897),hAPP(c_Set_OCollect(X8899),X8895))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8899,tc_HOL_Obool)),X8898),X8897)))&(~hBOOL(hAPP(X8895,esk254_5(X8895,X8896,X8897,X8898,X8899)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8899,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8899,tc_HOL_Obool)),X8898),hAPP(c_Set_OCollect(X8899),X8896))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8899,tc_HOL_Obool)),X8897),hAPP(c_Set_OCollect(X8899),X8895))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8899,tc_HOL_Obool)),X8898),X8897))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__Collect__mono])])])])])). 4.46/4.69 cnf(c_0_5034, plain, (hAPP(c_List_OremoveAll(X2,hAPP(X3,X4)),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))=hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_OremoveAll(X1,X4),X5))|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(c_List_Oset(X1),X5)))), inference(split_conjunct,[status(thm)],[c_0_4590])). 4.46/4.69 cnf(c_0_5035, plain, (c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X2)))=c_List_OremoveAll(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4591])). 4.46/4.69 fof(c_0_5036, plain, ![X2949, X2950, X2951]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2951),X2950))|hAPP(hAPP(c_Finite__Set_Ofold(X2951,tc_fun(X2951,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2951,tc_HOL_Obool),tc_fun(tc_fun(X2951,tc_HOL_Obool),tc_fun(X2951,tc_HOL_Obool)),X2951),hAPP(c_COMBC(tc_fun(X2951,tc_HOL_Obool),tc_fun(X2951,tc_HOL_Obool),tc_fun(X2951,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X2951,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X2951,tc_fun(X2951,tc_HOL_Obool),tc_fun(X2951,tc_HOL_Obool)),c_Set_Oinsert(X2951)),c_Orderings_Obot__class_Obot(tc_fun(X2951,tc_HOL_Obool))))),X2949),X2950)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2951,tc_HOL_Obool)),X2949),X2950)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__fold__remove])])])). 4.46/4.69 fof(c_0_5037, plain, ![X14431, X14432, X14433, X14434]:hAPP(c_Finite__Set_Ofold__image(X14434,X14433,X14432),X14431)=c_Finite__Set_Ofold(X14433,X14434,hAPP(hAPP(c_COMBB(X14434,tc_fun(X14434,X14434),X14433),X14432),X14431)), inference(variable_rename,[status(thm)],[fact_fold__image__def])). 4.46/4.69 fof(c_0_5038, plain, ![X3369, X3370, X3371, X3372, X3373]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3372)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3370)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3372)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3370)))|hAPP(hAPP(c_List_Oappend(X3373),X3370),X3369)=hAPP(hAPP(c_List_Oappend(X3373),X3372),X3371))&(X3372!=hAPP(hAPP(c_List_Otake(X3373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3372)),X3370)|X3371!=hAPP(hAPP(c_List_Oappend(X3373),hAPP(hAPP(c_List_Odrop(X3373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3372)),X3370)),X3369)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3372)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3370)))|hAPP(hAPP(c_List_Oappend(X3373),X3370),X3369)=hAPP(hAPP(c_List_Oappend(X3373),X3372),X3371)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3372)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3370)))|(hAPP(hAPP(c_List_Oappend(X3373),hAPP(hAPP(c_List_Odrop(X3373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3370)),X3372)),X3371)!=X3369|hAPP(hAPP(c_List_Otake(X3373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3370)),X3372)!=X3370)|hAPP(hAPP(c_List_Oappend(X3373),X3370),X3369)=hAPP(hAPP(c_List_Oappend(X3373),X3372),X3371))&(X3372!=hAPP(hAPP(c_List_Otake(X3373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3372)),X3370)|X3371!=hAPP(hAPP(c_List_Oappend(X3373),hAPP(hAPP(c_List_Odrop(X3373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3372)),X3370)),X3369)|(hAPP(hAPP(c_List_Oappend(X3373),hAPP(hAPP(c_List_Odrop(X3373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3370)),X3372)),X3371)!=X3369|hAPP(hAPP(c_List_Otake(X3373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3370)),X3372)!=X3370)|hAPP(hAPP(c_List_Oappend(X3373),X3370),X3369)=hAPP(hAPP(c_List_Oappend(X3373),X3372),X3371))))&(((hAPP(hAPP(c_List_Oappend(X3373),hAPP(hAPP(c_List_Odrop(X3373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3370)),X3372)),X3371)=X3369|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3372)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3370)))|hAPP(hAPP(c_List_Oappend(X3373),X3370),X3369)!=hAPP(hAPP(c_List_Oappend(X3373),X3372),X3371))&(hAPP(hAPP(c_List_Otake(X3373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3370)),X3372)=X3370|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3372)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3370)))|hAPP(hAPP(c_List_Oappend(X3373),X3370),X3369)!=hAPP(hAPP(c_List_Oappend(X3373),X3372),X3371)))&((X3372=hAPP(hAPP(c_List_Otake(X3373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3372)),X3370)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3372)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3370)))|hAPP(hAPP(c_List_Oappend(X3373),X3370),X3369)!=hAPP(hAPP(c_List_Oappend(X3373),X3372),X3371))&(X3371=hAPP(hAPP(c_List_Oappend(X3373),hAPP(hAPP(c_List_Odrop(X3373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3372)),X3370)),X3369)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3372)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3373)),X3370)))|hAPP(hAPP(c_List_Oappend(X3373),X3370),X3369)!=hAPP(hAPP(c_List_Oappend(X3373),X3372),X3371))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_append__eq__append__conv__if])])])])). 4.46/4.69 fof(c_0_5039, plain, ![X3964, X3965, X3966, X3967]:(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X3967,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk108_4(X3964,X3965,X3966,X3967))),X3966)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X3967,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk108_4(X3964,X3965,X3966,X3967)),X3965))),X3964)|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X3967,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X3966)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X3967,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X3964)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite2__eq])])])). 4.46/4.69 fof(c_0_5040, plain, ![X3425, X3426, X3427]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3427,X3427),tc_HOL_Obool)),X3426),hAPP(hAPP(c_Product__Type_OSigma(X3427,X3427),X3425),hAPP(c_COMBK(tc_fun(X3427,tc_HOL_Obool),X3427),X3425))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3427,X3427),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X3427,X3426)),hAPP(hAPP(c_Product__Type_OSigma(X3427,X3427),X3425),hAPP(c_COMBK(tc_fun(X3427,tc_HOL_Obool),X3427),X3425))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma])])). 4.46/4.69 cnf(c_0_5041, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4592])). 4.46/4.69 cnf(c_0_5042, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4593])). 4.46/4.69 fof(c_0_5043, plain, ![X12429, X12430, X12431, X12432, X12433, X12434, X12435]:(~c_Fun_Oinj__on(X12435,X12434,X12433,hAPP(c_Set_Oimage(X12432,X12435,X12431),X12430))|(~c_Fun_Oinj__on(X12432,X12435,X12431,X12430)|(~hBOOL(hAPP(hAPP(c_member(X12434),X12429),hAPP(c_Set_Oimage(X12435,X12434,X12433),hAPP(c_Set_Oimage(X12432,X12435,X12431),X12430))))|hAPP(hAPP(c_Fun_Ocomp(X12435,X12432,X12434,c_Fun_Othe__inv__into(X12432,X12435,X12430,X12431)),c_Fun_Othe__inv__into(X12435,X12434,hAPP(c_Set_Oimage(X12432,X12435,X12431),X12430),X12433)),X12429)=hAPP(c_Fun_Othe__inv__into(X12432,X12434,X12430,hAPP(c_Fun_Ocomp(X12435,X12434,X12432,X12433),X12431)),X12429)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_the__inv__into__comp])])])). 4.46/4.69 cnf(c_0_5044, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4594])). 4.46/4.69 fof(c_0_5045, plain, ![X8751, X8752, X8753]:((hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk246_3(X8751,X8752,X8753)),esk247_3(X8751,X8752,X8753))))|hBOOL(hAPP(hAPP(X8751,X8753),X8752))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X8753),X8752))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk246_3(X8751,X8752,X8753)),esk247_3(X8751,X8752,X8753)))|hBOOL(hAPP(hAPP(X8751,esk246_3(X8751,X8752,X8753)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk247_3(X8751,X8752,X8753)),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(hAPP(X8751,X8753),X8752))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X8753),X8752))))&(~hBOOL(hAPP(hAPP(X8751,esk246_3(X8751,X8752,X8753)),esk247_3(X8751,X8752,X8753)))|hBOOL(hAPP(hAPP(X8751,X8753),X8752))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X8753),X8752)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_small__lazy_H_Opinduct])])])])])). 4.46/4.69 fof(c_0_5046, plain, ![X5207, X5208, X5209, X5210]:(~c_Fun_Oinj__on(X5210,X5209,X5208,c_Orderings_Otop__class_Otop(tc_fun(X5210,tc_HOL_Obool)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5210,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5210,X5209,X5208),hAPP(hAPP(c_Set_Oinsert(X5209),X5207),c_Orderings_Obot__class_Obot(tc_fun(X5209,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X5210),c_HOL_OThe(X5210,hAPP(hAPP(c_COMBC(X5210,X5209,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5209,tc_fun(X5209,tc_HOL_Obool),X5210),c_fequal),X5208)),X5207))),c_Orderings_Obot__class_Obot(tc_fun(X5210,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__vimage__singleton])])])). 4.46/4.69 fof(c_0_5047, plain, ![X15126, X15127, X15128]:((~c_Wellfounded_Owf(X15128,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15128,X15128),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15128,X15128),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X15128,X15128,X15128),X15127),X15127)),hAPP(hAPP(c_Relation_Orel__comp(X15128,X15128,X15128),X15126),X15127))),X15126))|c_Wellfounded_Owf(X15128,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15128,X15128),tc_HOL_Obool)),X15127),X15126)))&(~c_Wellfounded_Owf(X15128,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15128,X15128),tc_HOL_Obool)),X15127),X15126))|c_Wellfounded_Owf(X15128,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15128,X15128),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15128,X15128),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X15128,X15128,X15128),X15127),X15127)),hAPP(hAPP(c_Relation_Orel__comp(X15128,X15128,X15128),X15126),X15127))),X15126)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__union__merge])])). 4.46/4.69 fof(c_0_5048, plain, ![X12661, X12662, X12663, X12664]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12664,tc_HOL_Obool)),X12663),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12664,tc_HOL_Obool)),X12662),X12661))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12664,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12664,tc_HOL_Obool)),X12663),X12662)),X12661), inference(variable_rename,[status(thm)],[fact_Un__assoc])). 4.46/4.69 fof(c_0_5049, plain, ![X4073, X4074, X4075]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4075,tc_HOL_Obool)),X4074),X4073)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4075,tc_HOL_Obool)),X4073),X4074), inference(variable_rename,[status(thm)],[fact_Un__commute])). 4.46/4.69 fof(c_0_5050, plain, ![X6327, X6328, X6329, X6330]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6330),X6329))|(~hBOOL(hAPP(hAPP(c_member(X6330),X6328),X6329))|(~hBOOL(hAPP(hAPP(c_member(X6330),X6327),X6329))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X6330),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6330,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6330,tc_HOL_Obool)),X6329),hAPP(hAPP(c_Set_Oinsert(X6330),X6328),c_Orderings_Obot__class_Obot(tc_fun(X6330,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X6330),X6327),c_Orderings_Obot__class_Obot(tc_fun(X6330,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X6330),X6329)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff2__less])])])). 4.46/4.69 fof(c_0_5051, plain, ![X6217, X6218, X6219, X6220]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6220,tc_HOL_Obool)),X6219),hAPP(hAPP(c_Set_Oinsert(X6220),X6218),X6217))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6220,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6220,tc_HOL_Obool)),X6219),hAPP(hAPP(c_Set_Oinsert(X6220),X6218),c_Orderings_Obot__class_Obot(tc_fun(X6220,tc_HOL_Obool))))),X6217), inference(variable_rename,[status(thm)],[fact_Diff__insert2])). 4.46/4.69 cnf(c_0_5052, plain, (hAPP(hAPP(c_List_Onth(X2),c_List_OdropWhile(X2,X3,X4)),X1)=hAPP(hAPP(c_List_Onth(X2),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OdropWhile(X2,X3,X4))))), inference(split_conjunct,[status(thm)],[c_0_4595])). 4.46/4.69 fof(c_0_5053, plain, ![X15768, X15769, X15770]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15770)),hAPP(hAPP(c_List_Odrop(X15770),X15769),X15768))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15770)),X15768)),X15769), inference(variable_rename,[status(thm)],[fact_length__drop])). 4.46/4.69 fof(c_0_5054, plain, ![X15884, X15885, X15886]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15886,X15886),tc_HOL_Obool)),X15885),X15884))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15886,X15886),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X15886,X15886,X15886),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X15886,X15886),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X15886,X15885)),X15884)),X15885)),X15884))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15886,X15886),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X15886,X15885)),X15884)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__Int__subset])])])). 4.46/4.69 cnf(c_0_5055, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1))), inference(split_conjunct,[status(thm)],[c_0_4596])). 4.46/4.69 fof(c_0_5056, plain, ![X10424, X10425, X10426, X10427]:((hBOOL(hAPP(hAPP(c_member(X10427),esk304_4(X10424,X10425,X10426,X10427)),hAPP(c_List_Oset(X10427),X10426)))|c_List_OdropWhile(X10427,X10425,hAPP(hAPP(c_List_Oappend(X10427),X10426),X10424))=c_List_OdropWhile(X10427,X10425,X10424))&(~hBOOL(hAPP(X10425,esk304_4(X10424,X10425,X10426,X10427)))|c_List_OdropWhile(X10427,X10425,hAPP(hAPP(c_List_Oappend(X10427),X10426),X10424))=c_List_OdropWhile(X10427,X10425,X10424))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dropWhile__append2])])])])). 4.46/4.69 cnf(c_0_5057, plain, (hAPP(c_Nat_OSuc,X2)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X2)))))), inference(split_conjunct,[status(thm)],[c_0_4550])). 4.46/4.69 cnf(c_0_5058, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2)),c_Int_Onat)))))), inference(split_conjunct,[status(thm)],[c_0_4559])). 4.46/4.69 cnf(c_0_5059, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2)),c_Int_Onat)))))), inference(split_conjunct,[status(thm)],[c_0_4560])). 4.46/4.69 fof(c_0_5060, plain, ![X10707, X10708, X10709, X10710]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk316_4(X10707,X10708,X10709,X10710)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10709)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10708),X10710))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10708),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10710),X10709))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10708),c_Groups_Oone__class_Oone(tc_Int_Oint))),X10707))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10709)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk317_4(X10707,X10708,X10709,X10710)),X10707))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10708),X10710))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10708),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10710),X10709))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10708),c_Groups_Oone__class_Oone(tc_Int_Oint))),X10707))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10709)))&(X10710=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk317_4(X10707,X10708,X10709,X10710)),esk316_4(X10707,X10708,X10709,X10710))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10708),X10710))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10708),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10710),X10709))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10708),c_Groups_Oone__class_Oone(tc_Int_Oint))),X10707))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10709))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bset_I8_J])])])])])])). 4.46/4.69 fof(c_0_5061, plain, ![X15324, X15325, X15328, X15330]:((((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk445_2(X15324,X15325)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X15325)))|~hBOOL(hAPP(X15324,X15328))|(~hBOOL(hAPP(X15324,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X15324,X15325)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk444_2(X15324,X15325)),X15325))))|~hBOOL(hAPP(X15324,esk443_2(X15324,X15325))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15325)))&(hBOOL(hAPP(X15324,esk445_2(X15324,X15325)))|~hBOOL(hAPP(X15324,X15328))|(~hBOOL(hAPP(X15324,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X15324,X15325)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk444_2(X15324,X15325)),X15325))))|~hBOOL(hAPP(X15324,esk443_2(X15324,X15325))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15325))))&(~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X15330),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X15325)))|~hBOOL(hAPP(X15324,X15330))|hBOOL(hAPP(X15324,esk446_2(X15324,X15325)))|(~hBOOL(hAPP(X15324,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X15324,X15325)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk444_2(X15324,X15325)),X15325))))|~hBOOL(hAPP(X15324,esk443_2(X15324,X15325))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15325))))&(((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk445_2(X15324,X15325)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X15325)))|~hBOOL(hAPP(X15324,X15328))|(hBOOL(hAPP(X15324,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X15324,X15325)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk444_2(X15324,X15325)),X15325))))|hBOOL(hAPP(X15324,esk443_2(X15324,X15325))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15325)))&(hBOOL(hAPP(X15324,esk445_2(X15324,X15325)))|~hBOOL(hAPP(X15324,X15328))|(hBOOL(hAPP(X15324,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X15324,X15325)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk444_2(X15324,X15325)),X15325))))|hBOOL(hAPP(X15324,esk443_2(X15324,X15325))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15325))))&(~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X15330),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X15325)))|~hBOOL(hAPP(X15324,X15330))|hBOOL(hAPP(X15324,esk446_2(X15324,X15325)))|(hBOOL(hAPP(X15324,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X15324,X15325)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk444_2(X15324,X15325)),X15325))))|hBOOL(hAPP(X15324,esk443_2(X15324,X15325))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15325))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_periodic__finite__ex])])])])])])). 4.46/4.69 fof(c_0_5062, plain, ![X7496, X7497]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7497),X7496)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7496),X7497), inference(variable_rename,[status(thm)],[fact_zmult__commute])). 4.46/4.69 cnf(c_0_5063, plain, (hAPP(c_List_OremoveAll(X2,hAPP(X3,X4)),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))=hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_OremoveAll(X1,X4),X5))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_4597])). 4.46/4.69 fof(c_0_5064, plain, ![X12572, X12573, X12574, X12575, X12576, X12577, X12578, X12579]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12578),X12576),esk372_8(X12572,X12573,X12574,X12575,X12576,X12577,X12578,X12579)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12578,X12579),X12573),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X12578,X12577),X12575))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12578,X12579),X12572),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X12578,X12576),X12574))|X12575!=X12574|X12576!=X12577|(~class_Orderings_Oord(X12578)|~class_Groups_Ocomm__monoid__add(X12579)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12578),esk372_8(X12572,X12573,X12574,X12575,X12576,X12577,X12578,X12579)),X12574))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12578,X12579),X12573),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X12578,X12577),X12575))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12578,X12579),X12572),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X12578,X12576),X12574))|X12575!=X12574|X12576!=X12577|(~class_Orderings_Oord(X12578)|~class_Groups_Ocomm__monoid__add(X12579)))&(hAPP(X12573,esk372_8(X12572,X12573,X12574,X12575,X12576,X12577,X12578,X12579))!=hAPP(X12572,esk372_8(X12572,X12573,X12574,X12575,X12576,X12577,X12578,X12579))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12578,X12579),X12573),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X12578,X12577),X12575))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12578,X12579),X12572),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X12578,X12576),X12574))|X12575!=X12574|X12576!=X12577|(~class_Orderings_Oord(X12578)|~class_Groups_Ocomm__monoid__add(X12579))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__ivl__cong])])])])])). 4.46/4.69 fof(c_0_5065, plain, ![X9651, X9652, X9653, X9654]:((hBOOL(hAPP(hAPP(c_member(X9654),esk274_4(X9651,X9652,X9653,X9654)),X9653))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9652),hAPP(c_Set_Oimage(X9654,X9652,X9651),X9653)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X9654),X9653)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9654),hAPP(c_Set_OCollect(X9654),hAPP(hAPP(c_COMBS(X9654,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X9654),c_fconj),hAPP(hAPP(c_COMBC(X9654,tc_fun(X9654,tc_HOL_Obool),tc_HOL_Obool),c_member(X9654)),X9653))),hAPP(hAPP(c_COMBC(X9654,X9652,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X9652,tc_fun(X9652,tc_HOL_Obool),X9654),c_fequal),X9651)),hAPP(X9651,esk274_4(X9651,X9652,X9653,X9654)))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9652),hAPP(c_Set_Oimage(X9654,X9652,X9651),X9653)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X9654),X9653)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pigeonhole__infinite])])])])])). 4.46/4.69 fof(c_0_5066, plain, ![X3086, X3087, X3088, X3089]:(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk79_4(X3086,X3087,X3088,X3089)),X3088))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3086),hAPP(X3087,X3088)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3087,X3089)),X3086))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3089),X3088))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3089),esk78_4(X3086,X3087,X3088,X3089))))&(hAPP(X3087,esk79_4(X3086,X3087,X3088,X3089))=X3086|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3086),hAPP(X3087,X3088)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3087,X3089)),X3086))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3089),X3088))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3089),esk78_4(X3086,X3087,X3088,X3089)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3089),esk79_4(X3086,X3087,X3088,X3089)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3086),hAPP(X3087,X3088)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3087,X3089)),X3086))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3089),X3088))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3089),esk78_4(X3086,X3087,X3088,X3089)))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk79_4(X3086,X3087,X3088,X3089)),X3088))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3086),hAPP(X3087,X3088)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3087,X3089)),X3086))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3089),X3088))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk78_4(X3086,X3087,X3088,X3089)),X3088)))&(hAPP(X3087,esk79_4(X3086,X3087,X3088,X3089))=X3086|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3086),hAPP(X3087,X3088)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3087,X3089)),X3086))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3089),X3088))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk78_4(X3086,X3087,X3088,X3089)),X3088))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3089),esk79_4(X3086,X3087,X3088,X3089)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3086),hAPP(X3087,X3088)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3087,X3089)),X3086))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3089),X3088))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk78_4(X3086,X3087,X3088,X3089)),X3088)))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk79_4(X3086,X3087,X3088,X3089)),X3088))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3086),hAPP(X3087,X3088)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3087,X3089)),X3086))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3089),X3088))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X3087,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk78_4(X3086,X3087,X3088,X3089)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X3087,esk78_4(X3086,X3087,X3088,X3089))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))&(hAPP(X3087,esk79_4(X3086,X3087,X3088,X3089))=X3086|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3086),hAPP(X3087,X3088)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3087,X3089)),X3086))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3089),X3088))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X3087,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk78_4(X3086,X3087,X3088,X3089)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X3087,esk78_4(X3086,X3087,X3088,X3089))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3089),esk79_4(X3086,X3087,X3088,X3089)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3086),hAPP(X3087,X3088)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3087,X3089)),X3086))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3089),X3088))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X3087,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk78_4(X3086,X3087,X3088,X3089)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X3087,esk78_4(X3086,X3087,X3088,X3089))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__intermed__int__val])])])])])). 4.46/4.69 fof(c_0_5067, plain, ![X15094, X15095, X15096, X15097, X15098, X15099]:((hBOOL(hAPP(hAPP(c_member(X15099),X15098),X15097))|c_Map_Orestrict__map(X15099,X15096,X15095,X15097)=c_Map_Orestrict__map(X15099,X15096,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X15099,tc_Option_Ooption(X15096)),X15095),X15098),X15094),X15097))&(~hBOOL(hAPP(hAPP(c_member(X15099),X15098),X15097))|c_Map_Orestrict__map(X15099,X15096,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X15099,tc_Option_Ooption(X15096)),X15095),X15098),X15094),X15097)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X15099,tc_Option_Ooption(X15096)),c_Map_Orestrict__map(X15099,X15096,X15095,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15099,tc_HOL_Obool)),X15097),hAPP(hAPP(c_Set_Oinsert(X15099),X15098),c_Orderings_Obot__class_Obot(tc_fun(X15099,tc_HOL_Obool)))))),X15098),X15094))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_restrict__fun__upd])])])). 4.46/4.69 fof(c_0_5068, plain, ![X3748, X3749, X3750, X3751, X3752, X3753]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3753,tc_Option_Ooption(X3752)),c_Map_Orestrict__map(X3753,X3752,X3751,X3750)),X3749),X3748)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3753,tc_Option_Ooption(X3752)),c_Map_Orestrict__map(X3753,X3752,X3751,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3753,tc_HOL_Obool)),X3750),hAPP(hAPP(c_Set_Oinsert(X3753),X3749),c_Orderings_Obot__class_Obot(tc_fun(X3753,tc_HOL_Obool)))))),X3749),X3748), inference(variable_rename,[status(thm)],[fact_fun__upd__restrict])). 4.46/4.69 fof(c_0_5069, plain, ![X7331, X7332, X7333, X7334]:(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7334)),X7333),c_List_Olists(X7334,X7332)))|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7334)),X7333),c_List_Olists(X7334,X7331)))|hBOOL(hAPP(c_List_Olistsp(X7334,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7334,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X7334,tc_fun(X7334,tc_HOL_Obool),tc_HOL_Obool),c_member(X7334)),X7332)),hAPP(hAPP(c_COMBC(X7334,tc_fun(X7334,tc_HOL_Obool),tc_HOL_Obool),c_member(X7334)),X7331))),X7333)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lists__IntI])])])). 4.46/4.69 fof(c_0_5070, plain, ![X2418, X2419, X2420]:(((hBOOL(hAPP(hAPP(c_member(tc_fun(X2420,tc_HOL_Obool)),esk65_3(X2418,X2419,X2420)),X2419))|hAPP(c_Finite__Set_Ocard(X2420),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2420,tc_HOL_Obool),X2419))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2418),hAPP(c_Finite__Set_Ocard(tc_fun(X2420,tc_HOL_Obool)),X2419))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2420,tc_HOL_Obool)),esk64_3(X2418,X2419,X2420)),X2419))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2420),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2420,tc_HOL_Obool),X2419)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X2420,tc_HOL_Obool)),X2419)))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X2420,tc_HOL_Obool)),esk66_3(X2418,X2419,X2420)),X2419))|hAPP(c_Finite__Set_Ocard(X2420),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2420,tc_HOL_Obool),X2419))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2418),hAPP(c_Finite__Set_Ocard(tc_fun(X2420,tc_HOL_Obool)),X2419))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2420,tc_HOL_Obool)),esk64_3(X2418,X2419,X2420)),X2419))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2420),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2420,tc_HOL_Obool),X2419)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X2420,tc_HOL_Obool)),X2419)))&((esk66_3(X2418,X2419,X2420)!=esk65_3(X2418,X2419,X2420)|hAPP(c_Finite__Set_Ocard(X2420),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2420,tc_HOL_Obool),X2419))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2418),hAPP(c_Finite__Set_Ocard(tc_fun(X2420,tc_HOL_Obool)),X2419))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2420,tc_HOL_Obool)),esk64_3(X2418,X2419,X2420)),X2419))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2420),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2420,tc_HOL_Obool),X2419)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X2420,tc_HOL_Obool)),X2419)))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2420,tc_HOL_Obool)),esk65_3(X2418,X2419,X2420)),esk66_3(X2418,X2419,X2420))!=c_Orderings_Obot__class_Obot(tc_fun(X2420,tc_HOL_Obool))|hAPP(c_Finite__Set_Ocard(X2420),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2420,tc_HOL_Obool),X2419))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2418),hAPP(c_Finite__Set_Ocard(tc_fun(X2420,tc_HOL_Obool)),X2419))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2420,tc_HOL_Obool)),esk64_3(X2418,X2419,X2420)),X2419))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2420),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2420,tc_HOL_Obool),X2419)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X2420,tc_HOL_Obool)),X2419))))))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X2420,tc_HOL_Obool)),esk65_3(X2418,X2419,X2420)),X2419))|hAPP(c_Finite__Set_Ocard(X2420),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2420,tc_HOL_Obool),X2419))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2418),hAPP(c_Finite__Set_Ocard(tc_fun(X2420,tc_HOL_Obool)),X2419))|hAPP(c_Finite__Set_Ocard(X2420),esk64_3(X2418,X2419,X2420))!=X2418|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2420),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2420,tc_HOL_Obool),X2419)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X2420,tc_HOL_Obool)),X2419)))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X2420,tc_HOL_Obool)),esk66_3(X2418,X2419,X2420)),X2419))|hAPP(c_Finite__Set_Ocard(X2420),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2420,tc_HOL_Obool),X2419))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2418),hAPP(c_Finite__Set_Ocard(tc_fun(X2420,tc_HOL_Obool)),X2419))|hAPP(c_Finite__Set_Ocard(X2420),esk64_3(X2418,X2419,X2420))!=X2418|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2420),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2420,tc_HOL_Obool),X2419)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X2420,tc_HOL_Obool)),X2419)))&((esk66_3(X2418,X2419,X2420)!=esk65_3(X2418,X2419,X2420)|hAPP(c_Finite__Set_Ocard(X2420),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2420,tc_HOL_Obool),X2419))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2418),hAPP(c_Finite__Set_Ocard(tc_fun(X2420,tc_HOL_Obool)),X2419))|hAPP(c_Finite__Set_Ocard(X2420),esk64_3(X2418,X2419,X2420))!=X2418|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2420),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2420,tc_HOL_Obool),X2419)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X2420,tc_HOL_Obool)),X2419)))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2420,tc_HOL_Obool)),esk65_3(X2418,X2419,X2420)),esk66_3(X2418,X2419,X2420))!=c_Orderings_Obot__class_Obot(tc_fun(X2420,tc_HOL_Obool))|hAPP(c_Finite__Set_Ocard(X2420),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2420,tc_HOL_Obool),X2419))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2418),hAPP(c_Finite__Set_Ocard(tc_fun(X2420,tc_HOL_Obool)),X2419))|hAPP(c_Finite__Set_Ocard(X2420),esk64_3(X2418,X2419,X2420))!=X2418|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2420),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2420,tc_HOL_Obool),X2419)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X2420,tc_HOL_Obool)),X2419))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__partition])])])])])). 4.46/4.69 fof(c_0_5071, plain, ![X3294, X3295]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3295),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3295,tc_HOL_Obool),X3294)))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3295,tc_HOL_Obool)),X3294))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__UnionD])])])). 4.46/4.69 fof(c_0_5072, plain, ![X17603, X17604, X17605, X17606, X17607, X17610, X17611, X17612, X17613, X17614, X17615, X17616, X17617]:(((((X17603=hAPP(hAPP(c_List_Oappend(X17607),esk528_5(X17603,X17604,X17605,X17606,X17607)),hAPP(hAPP(c_List_Olist_OCons(X17607),X17606),esk529_5(X17603,X17604,X17605,X17606,X17607)))|hAPP(hAPP(c_List_Olist_OCons(X17607),X17606),X17605)!=hAPP(c_List_Ofilter(X17607,X17604),X17603))&(hBOOL(hAPP(X17604,X17606))|hAPP(hAPP(c_List_Olist_OCons(X17607),X17606),X17605)!=hAPP(c_List_Ofilter(X17607,X17604),X17603)))&(X17605=hAPP(c_List_Ofilter(X17607,X17604),esk529_5(X17603,X17604,X17605,X17606,X17607))|hAPP(hAPP(c_List_Olist_OCons(X17607),X17606),X17605)!=hAPP(c_List_Ofilter(X17607,X17604),X17603)))&(~hBOOL(hAPP(hAPP(c_member(X17607),X17610),hAPP(c_List_Oset(X17607),esk528_5(X17603,X17604,X17605,X17606,X17607))))|~hBOOL(hAPP(X17604,X17610))|hAPP(hAPP(c_List_Olist_OCons(X17607),X17606),X17605)!=hAPP(c_List_Ofilter(X17607,X17604),X17603)))&((hBOOL(hAPP(hAPP(c_member(X17615),esk530_6(X17611,X17612,X17613,X17614,X17615,X17616)),hAPP(c_List_Oset(X17615),X17616)))|(X17611!=hAPP(hAPP(c_List_Oappend(X17615),X17616),hAPP(hAPP(c_List_Olist_OCons(X17615),X17614),X17617))|~hBOOL(hAPP(X17612,X17614))|X17613!=hAPP(c_List_Ofilter(X17615,X17612),X17617))|hAPP(hAPP(c_List_Olist_OCons(X17615),X17614),X17613)=hAPP(c_List_Ofilter(X17615,X17612),X17611))&(hBOOL(hAPP(X17612,esk530_6(X17611,X17612,X17613,X17614,X17615,X17616)))|(X17611!=hAPP(hAPP(c_List_Oappend(X17615),X17616),hAPP(hAPP(c_List_Olist_OCons(X17615),X17614),X17617))|~hBOOL(hAPP(X17612,X17614))|X17613!=hAPP(c_List_Ofilter(X17615,X17612),X17617))|hAPP(hAPP(c_List_Olist_OCons(X17615),X17614),X17613)=hAPP(c_List_Ofilter(X17615,X17612),X17611)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Cons__eq__filter__iff])])])])])])])). 4.46/4.69 fof(c_0_5073, plain, ![X3362, X3363, X3364, X3365]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3365),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3364)),X3363)))|hAPP(c_List_Orev(X3364),hAPP(hAPP(c_List_Olist__update(X3364,X3363),X3365),X3362))=hAPP(hAPP(c_List_Olist__update(X3364,hAPP(c_List_Orev(X3364),X3363)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3364)),X3363)),X3365)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3362)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__update])])). 4.46/4.69 fof(c_0_5074, plain, ![X12465, X12466, X12467]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12467),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12466),X12465))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12467),X12466)),X12465), inference(variable_rename,[status(thm)],[fact_diff__diff__left])). 4.46/4.69 fof(c_0_5075, plain, ![X1579, X1580, X1581, X1582, X1583]:((hBOOL(hAPP(hAPP(X1583,esk35_5(X1579,X1580,X1581,X1582,X1583)),esk36_5(X1579,X1580,X1581,X1582,X1583)))|c_Hoare__Mirabelle_Ohoare__derivs(X1582,X1581,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1582)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1582),X1583),X1580),X1579)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1582),tc_HOL_Obool)))))&(~c_Hoare__Mirabelle_Ohoare__derivs(X1582,X1581,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1582)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1582),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X1582),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),esk36_5(X1579,X1580,X1581,X1582,X1583)))),X1580),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X1582),hAPP(X1579,esk35_5(X1579,X1580,X1581,X1582,X1583))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1582),tc_HOL_Obool))))|c_Hoare__Mirabelle_Ohoare__derivs(X1582,X1581,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1582)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1582),X1583),X1580),X1579)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1582),tc_HOL_Obool)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_escape])])])])). 4.46/4.69 fof(c_0_5076, plain, ![X15185, X15186, X15187, X15188, X15189, X15190, X15191]:(~c_Hoare__Mirabelle_Ohoare__derivs(X15191,X15190,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X15191)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X15191),X15189),X15188),X15187)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X15191),tc_HOL_Obool))))|(~c_Hoare__Mirabelle_Ohoare__derivs(X15191,X15190,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X15191)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X15191),X15187),X15186),X15185)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X15191),tc_HOL_Obool))))|c_Hoare__Mirabelle_Ohoare__derivs(X15191,X15190,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X15191)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X15191),X15189),c_Com_Ocom_OSemi(X15188,X15186)),X15185)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X15191),tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Comp])])])). 4.46/4.69 cnf(c_0_5077, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(X2))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4598])). 4.46/4.69 fof(c_0_5078, plain, ![X11414, X11415, X11416, X11417, X11418, X11419, X11420]:(hBOOL(hAPP(hAPP(c_member(X11420),X11419),hAPP(c_List_Oset(X11420),X11418)))|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X11420,tc_Option_Ooption(X11417)),c_Map_Omap__upds(X11420,X11417,X11416,X11418,X11414)),X11419),hAPP(c_Option_Ooption_OSome(X11417),X11415))=c_Map_Omap__upds(X11420,X11417,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X11420,tc_Option_Ooption(X11417)),X11416),X11419),hAPP(c_Option_Ooption_OSome(X11417),X11415)),X11418,X11414)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__upds__twist])])])). 4.46/4.69 fof(c_0_5079, plain, ![X1761, X1762, X1763, X1764]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X1764,X1764)),hAPP(hAPP(c_Product__Type_OPair(X1764,X1764),esk42_4(X1761,X1762,X1763,X1764)),X1762)),c_Transitive__Closure_Ortrancl(X1764,X1761)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1764,X1764)),hAPP(hAPP(c_Product__Type_OPair(X1764,X1764),X1763),X1762)),c_Transitive__Closure_Otrancl(X1764,X1761))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X1764,X1764)),hAPP(hAPP(c_Product__Type_OPair(X1764,X1764),X1763),esk42_4(X1761,X1762,X1763,X1764))),X1761))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1764,X1764)),hAPP(hAPP(c_Product__Type_OPair(X1764,X1764),X1763),X1762)),c_Transitive__Closure_Otrancl(X1764,X1761))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_tranclD])])])])])). 4.46/4.69 cnf(c_0_5080, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4599])). 4.46/4.69 cnf(c_0_5081, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4600])). 4.46/4.69 fof(c_0_5082, plain, ![X14524, X14525, X14526, X14527]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X14527,X14527)),hAPP(hAPP(c_Product__Type_OPair(X14527,X14527),esk427_4(X14524,X14525,X14526,X14527)),X14525)),X14524))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X14527,X14527)),hAPP(hAPP(c_Product__Type_OPair(X14527,X14527),X14526),X14525)),c_Transitive__Closure_Otrancl(X14527,X14524))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X14527,X14527)),hAPP(hAPP(c_Product__Type_OPair(X14527,X14527),X14526),esk427_4(X14524,X14525,X14526,X14527))),c_Transitive__Closure_Ortrancl(X14527,X14524)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X14527,X14527)),hAPP(hAPP(c_Product__Type_OPair(X14527,X14527),X14526),X14525)),c_Transitive__Closure_Otrancl(X14527,X14524))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclD2])])])])). 4.46/4.69 fof(c_0_5083, plain, ![X13890, X13891, X13892, X13893]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13893,X13893)),X13892),c_Transitive__Closure_Otrancl(X13893,X13891)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X13893,X13893),tc_HOL_Obool)),X13891),X13890))|hBOOL(hAPP(hAPP(c_member(tc_prod(X13893,X13893)),X13892),c_Transitive__Closure_Otrancl(X13893,X13890))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__mono])])])). 4.46/4.69 cnf(c_0_5084, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4601])). 4.46/4.69 cnf(c_0_5085, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4602])). 4.46/4.69 fof(c_0_5086, plain, ![X13010, X13011, X13012]:((hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk378_3(X13010,X13011,X13012)),esk379_3(X13010,X13011,X13012))))|hBOOL(hAPP(hAPP(X13010,X13012),X13011))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X13012),X13011))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk378_3(X13010,X13011,X13012)),esk379_3(X13010,X13011,X13012)))|hBOOL(hAPP(hAPP(X13010,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk378_3(X13010,X13011,X13012)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk379_3(X13010,X13011,X13012)))|hBOOL(hAPP(hAPP(X13010,X13012),X13011))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X13012),X13011))))&(~hBOOL(hAPP(hAPP(X13010,esk378_3(X13010,X13011,X13012)),esk379_3(X13010,X13011,X13012)))|hBOOL(hAPP(hAPP(X13010,X13012),X13011))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X13012),X13011)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_upto_Opinduct])])])])])). 4.46/4.69 fof(c_0_5087, plain, ![X12540]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X12540|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12540)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12540))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X12540)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])])). 4.46/4.69 cnf(c_0_5088, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4603])). 4.46/4.69 fof(c_0_5089, plain, ![X17628, X17629, X17630, X17631, X17632, X17633, X17634, X17635, X17636, X17637]:((((X17629!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(X17630,X17628))|~epred1_3(X17630,X17629,X17628))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17629),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17629),X17632))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17632),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17629),X17631)),X17632)!=X17628|hBOOL(hAPP(X17630,X17632)))|~epred1_3(X17630,X17629,X17628)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17629))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17634),X17629))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17629),X17633)),X17634)!=X17628|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17634))|hBOOL(hAPP(X17630,X17634)))|~epred1_3(X17630,X17629,X17628)))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17636))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X17635,X17636,X17637)),X17636))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk533_3(X17635,X17636,X17637))),esk534_3(X17635,X17636,X17637))=X17635|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X17635,X17636,X17637)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635)))&(~hBOOL(hAPP(X17637,esk534_3(X17635,X17636,X17637)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635))))&(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17636))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),esk532_3(X17635,X17636,X17637)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X17635,X17636,X17637)),X17636))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),esk532_3(X17635,X17636,X17637)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk533_3(X17635,X17636,X17637))),esk534_3(X17635,X17636,X17637))=X17635|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),esk532_3(X17635,X17636,X17637)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X17635,X17636,X17637)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),esk532_3(X17635,X17636,X17637)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635)))&(~hBOOL(hAPP(X17637,esk534_3(X17635,X17636,X17637)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),esk532_3(X17635,X17636,X17637)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17636))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X17635,X17636,X17637)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X17635,X17636,X17637)),X17636))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X17635,X17636,X17637)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk533_3(X17635,X17636,X17637))),esk534_3(X17635,X17636,X17637))=X17635|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X17635,X17636,X17637)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X17635,X17636,X17637)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X17635,X17636,X17637)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635)))&(~hBOOL(hAPP(X17637,esk534_3(X17635,X17636,X17637)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X17635,X17636,X17637)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17636))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk531_3(X17635,X17636,X17637))),esk532_3(X17635,X17636,X17637))=X17635|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X17635,X17636,X17637)),X17636))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk531_3(X17635,X17636,X17637))),esk532_3(X17635,X17636,X17637))=X17635|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk533_3(X17635,X17636,X17637))),esk534_3(X17635,X17636,X17637))=X17635|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk531_3(X17635,X17636,X17637))),esk532_3(X17635,X17636,X17637))=X17635|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X17635,X17636,X17637)))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk531_3(X17635,X17636,X17637))),esk532_3(X17635,X17636,X17637))=X17635|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635)))&(~hBOOL(hAPP(X17637,esk534_3(X17635,X17636,X17637)))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk531_3(X17635,X17636,X17637))),esk532_3(X17635,X17636,X17637))=X17635|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17636))|(~hBOOL(hAPP(X17637,esk532_3(X17635,X17636,X17637)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X17635,X17636,X17637)),X17636))|(~hBOOL(hAPP(X17637,esk532_3(X17635,X17636,X17637)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk533_3(X17635,X17636,X17637))),esk534_3(X17635,X17636,X17637))=X17635|(~hBOOL(hAPP(X17637,esk532_3(X17635,X17636,X17637)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X17635,X17636,X17637)))|(~hBOOL(hAPP(X17637,esk532_3(X17635,X17636,X17637)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635)))&(~hBOOL(hAPP(X17637,esk534_3(X17635,X17636,X17637)))|(~hBOOL(hAPP(X17637,esk532_3(X17635,X17636,X17637)))|X17636=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|epred1_3(X17637,X17636,X17635))))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17636))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X17635,X17636,X17637)),X17636))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk533_3(X17635,X17636,X17637))),esk534_3(X17635,X17636,X17637))=X17635|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X17635,X17636,X17637)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635)))&(~hBOOL(hAPP(X17637,esk534_3(X17635,X17636,X17637)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635))))&(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17636))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),esk532_3(X17635,X17636,X17637)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X17635,X17636,X17637)),X17636))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),esk532_3(X17635,X17636,X17637)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk533_3(X17635,X17636,X17637))),esk534_3(X17635,X17636,X17637))=X17635|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),esk532_3(X17635,X17636,X17637)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X17635,X17636,X17637)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),esk532_3(X17635,X17636,X17637)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635)))&(~hBOOL(hAPP(X17637,esk534_3(X17635,X17636,X17637)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17636),esk532_3(X17635,X17636,X17637)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17636))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X17635,X17636,X17637)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X17635,X17636,X17637)),X17636))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X17635,X17636,X17637)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk533_3(X17635,X17636,X17637))),esk534_3(X17635,X17636,X17637))=X17635|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X17635,X17636,X17637)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X17635,X17636,X17637)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X17635,X17636,X17637)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635)))&(~hBOOL(hAPP(X17637,esk534_3(X17635,X17636,X17637)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X17635,X17636,X17637)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17636))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk531_3(X17635,X17636,X17637))),esk532_3(X17635,X17636,X17637))=X17635|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X17635,X17636,X17637)),X17636))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk531_3(X17635,X17636,X17637))),esk532_3(X17635,X17636,X17637))=X17635|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk533_3(X17635,X17636,X17637))),esk534_3(X17635,X17636,X17637))=X17635|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk531_3(X17635,X17636,X17637))),esk532_3(X17635,X17636,X17637))=X17635|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X17635,X17636,X17637)))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk531_3(X17635,X17636,X17637))),esk532_3(X17635,X17636,X17637))=X17635|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635)))&(~hBOOL(hAPP(X17637,esk534_3(X17635,X17636,X17637)))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk531_3(X17635,X17636,X17637))),esk532_3(X17635,X17636,X17637))=X17635|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17636))|(~hBOOL(hAPP(X17637,esk532_3(X17635,X17636,X17637)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X17635,X17636,X17637)),X17636))|(~hBOOL(hAPP(X17637,esk532_3(X17635,X17636,X17637)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17636),esk533_3(X17635,X17636,X17637))),esk534_3(X17635,X17636,X17637))=X17635|(~hBOOL(hAPP(X17637,esk532_3(X17635,X17636,X17637)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X17635,X17636,X17637)))|(~hBOOL(hAPP(X17637,esk532_3(X17635,X17636,X17637)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635)))&(~hBOOL(hAPP(X17637,esk534_3(X17635,X17636,X17637)))|(~hBOOL(hAPP(X17637,esk532_3(X17635,X17636,X17637)))|~hBOOL(hAPP(X17637,X17635)))|epred1_3(X17637,X17636,X17635)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4604])])])])])])). 4.46/4.69 fof(c_0_5090, plain, ![X5110, X5111, X5112, X5113, X5114, X5117, X5118, X5119, X5120, X5121, X5122, X5123, X5124]:(((((hBOOL(hAPP(X5113,X5111))|hAPP(c_List_Ofilter(X5114,X5113),X5112)!=hAPP(hAPP(c_List_Olist_OCons(X5114),X5111),X5110))&(X5110=hAPP(c_List_Ofilter(X5114,X5113),esk153_5(X5110,X5111,X5112,X5113,X5114))|hAPP(c_List_Ofilter(X5114,X5113),X5112)!=hAPP(hAPP(c_List_Olist_OCons(X5114),X5111),X5110)))&(~hBOOL(hAPP(hAPP(c_member(X5114),X5117),hAPP(c_List_Oset(X5114),esk152_5(X5110,X5111,X5112,X5113,X5114))))|~hBOOL(hAPP(X5113,X5117))|hAPP(c_List_Ofilter(X5114,X5113),X5112)!=hAPP(hAPP(c_List_Olist_OCons(X5114),X5111),X5110)))&(X5112=hAPP(hAPP(c_List_Oappend(X5114),esk152_5(X5110,X5111,X5112,X5113,X5114)),hAPP(hAPP(c_List_Olist_OCons(X5114),X5111),esk153_5(X5110,X5111,X5112,X5113,X5114)))|hAPP(c_List_Ofilter(X5114,X5113),X5112)!=hAPP(hAPP(c_List_Olist_OCons(X5114),X5111),X5110)))&((hBOOL(hAPP(hAPP(c_member(X5122),esk154_7(X5118,X5119,X5120,X5121,X5122,X5123,X5124)),hAPP(c_List_Oset(X5122),X5123)))|(~hBOOL(hAPP(X5121,X5119))|X5118!=hAPP(c_List_Ofilter(X5122,X5121),X5124))|X5120!=hAPP(hAPP(c_List_Oappend(X5122),X5123),hAPP(hAPP(c_List_Olist_OCons(X5122),X5119),X5124))|hAPP(c_List_Ofilter(X5122,X5121),X5120)=hAPP(hAPP(c_List_Olist_OCons(X5122),X5119),X5118))&(hBOOL(hAPP(X5121,esk154_7(X5118,X5119,X5120,X5121,X5122,X5123,X5124)))|(~hBOOL(hAPP(X5121,X5119))|X5118!=hAPP(c_List_Ofilter(X5122,X5121),X5124))|X5120!=hAPP(hAPP(c_List_Oappend(X5122),X5123),hAPP(hAPP(c_List_Olist_OCons(X5122),X5119),X5124))|hAPP(c_List_Ofilter(X5122,X5121),X5120)=hAPP(hAPP(c_List_Olist_OCons(X5122),X5119),X5118)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__eq__Cons__iff])])])])])])])). 4.46/4.69 cnf(c_0_5091, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X2))))), inference(split_conjunct,[status(thm)],[c_0_4580])). 4.46/4.69 cnf(c_0_5092, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X2))))), inference(split_conjunct,[status(thm)],[c_0_4584])). 4.46/4.69 fof(c_0_5093, plain, ![X8902, X8903, X8904]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk256_3(X8902,X8903,X8904)),X8904))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8902),hAPP(X8903,X8904)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X8903,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X8902))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk255_3(X8902,X8903,X8904)),X8904)))&(X8902=hAPP(X8903,esk256_3(X8902,X8903,X8904))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8902),hAPP(X8903,X8904)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X8903,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X8902))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk255_3(X8902,X8903,X8904)),X8904))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk256_3(X8902,X8903,X8904)),X8904))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8902),hAPP(X8903,X8904)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X8903,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X8902))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X8903,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk255_3(X8902,X8903,X8904)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X8903,esk255_3(X8902,X8903,X8904))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))&(X8902=hAPP(X8903,esk256_3(X8902,X8903,X8904))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8902),hAPP(X8903,X8904)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X8903,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X8902))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X8903,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk255_3(X8902,X8903,X8904)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X8903,esk255_3(X8902,X8903,X8904))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat0__intermed__int__val])])])])])). 4.46/4.69 fof(c_0_5094, plain, ![X14701, X14702, X14703]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14703),X14702))|c_List_Oupt(X14703,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14702),X14701))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X14703,X14702)),c_List_Oupt(X14702,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14702),X14701)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__add__eq__append])])). 4.46/4.69 fof(c_0_5095, plain, ![X2719, X2720, X2721]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk72_3(X2719,X2720,X2721)),X2721))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2719),hAPP(X2720,X2721)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2720,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2719))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk71_3(X2719,X2720,X2721)),X2721)))&(X2719=hAPP(X2720,esk72_3(X2719,X2720,X2721))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2719),hAPP(X2720,X2721)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2720,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2719))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk71_3(X2719,X2720,X2721)),X2721))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk72_3(X2719,X2720,X2721)),X2721))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2719),hAPP(X2720,X2721)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2720,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2719))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2720,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk71_3(X2719,X2720,X2721)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2720,esk71_3(X2719,X2720,X2721))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))&(X2719=hAPP(X2720,esk72_3(X2719,X2720,X2721))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2719),hAPP(X2720,X2721)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2720,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2719))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2720,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk71_3(X2719,X2720,X2721)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2720,esk71_3(X2719,X2720,X2721))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__val__lemma])])])])])). 4.46/4.69 fof(c_0_5096, plain, ![X17248, X17249, X17250, X17251, X17252]:hAPP(hAPP(c_List_Ozip(X17252,X17251),hAPP(hAPP(c_List_Otake(X17252),X17250),X17249)),hAPP(hAPP(c_List_Otake(X17251),X17250),X17248))=hAPP(hAPP(c_List_Otake(tc_prod(X17252,X17251)),X17250),hAPP(hAPP(c_List_Ozip(X17252,X17251),X17249),X17248)), inference(variable_rename,[status(thm)],[fact_take__zip])). 4.46/4.69 fof(c_0_5097, plain, ![X5048, X5049, X5050, X5051, X5052]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5051),X5050)),X5048)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5052),X5050)),X5049)|X5049=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5051),X5052)),X5050)),X5048)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5052),X5051)))&(X5049!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5051),X5052)),X5050)),X5048)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5051),X5050)),X5048)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5052),X5050)),X5049)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5052),X5051)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__eq__add__iff2])])])])). 4.46/4.69 fof(c_0_5098, plain, ![X13030, X13031, X13032, X13033]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13033),X13031)),X13032)),X13030)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13033),X13032)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13031),X13032)),X13030)), inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib])). 4.46/4.69 cnf(c_0_5099, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X2)=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_4605])). 4.46/4.69 cnf(c_0_5100, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_4606]), ['final']). 4.46/4.69 cnf(c_0_5101, plain, (c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)=c_Orderings_Oord__class_Omax(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_sup__nat__def]), ['final']). 4.46/4.69 fof(c_0_5102, plain, ![X1267, X1268, X1269, X1270]:(((X1269=X1268|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1270,X1270)),hAPP(hAPP(c_Product__Type_OPair(X1270,X1270),X1269),X1268)),c_Transitive__Closure_Otrancl(X1270,X1267)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1270,X1270)),hAPP(hAPP(c_Product__Type_OPair(X1270,X1270),X1269),X1268)),c_Transitive__Closure_Ortrancl(X1270,X1267))))&(X1269!=X1268|hBOOL(hAPP(hAPP(c_member(tc_prod(X1270,X1270)),hAPP(hAPP(c_Product__Type_OPair(X1270,X1270),X1269),X1268)),c_Transitive__Closure_Ortrancl(X1270,X1267)))))&((X1269!=X1268|X1269=X1268|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1270,X1270)),hAPP(hAPP(c_Product__Type_OPair(X1270,X1270),X1269),X1268)),c_Transitive__Closure_Ortrancl(X1270,X1267))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X1270,X1270)),hAPP(hAPP(c_Product__Type_OPair(X1270,X1270),X1269),X1268)),c_Transitive__Closure_Otrancl(X1270,X1267)))|X1269=X1268|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1270,X1270)),hAPP(hAPP(c_Product__Type_OPair(X1270,X1270),X1269),X1268)),c_Transitive__Closure_Ortrancl(X1270,X1267)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__eq__or__trancl])])])). 4.46/4.69 fof(c_0_5103, plain, ![X10576, X10577, X10578, X10579, X10580]:(~c_Hoare__Mirabelle_Ohoare__valids(X10580,X10579,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10580)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10580),c_Hoare__Mirabelle_Opeek__and(X10580,X10578,X10577)),X10576),X10578)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10580),tc_HOL_Obool))))|c_Hoare__Mirabelle_Ohoare__valids(X10580,X10579,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10580)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X10580),X10578),c_Com_Ocom_OWhile(X10577,X10576)),c_Hoare__Mirabelle_Opeek__and(X10580,X10578,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X10577)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10580),tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Loop__sound__lemma])])])). 4.46/4.69 fof(c_0_5104, plain, ![X8054, X8055]:(~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X8055),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X8055))),X8054)))|c_List_Otranspose(X8055,c_List_Otranspose(X8055,X8054))=c_List_OtakeWhile(tc_List_Olist(X8055),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X8055)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X8055),tc_List_Olist(X8055),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X8055))),X8054)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transpose__transpose])])])). 4.46/4.69 fof(c_0_5105, plain, ![X4262, X4263, X4264]:(~hBOOL(hAPP(c_List_Odistinct(X4264),hAPP(hAPP(c_List_Omap(tc_prod(X4264,X4263),X4264),c_Product__Type_Ofst(X4264,X4263)),X4262)))|c_Map_Oran(X4264,X4263,hAPP(c_Map_Omap__of(X4264,X4263),X4262))=hAPP(c_Set_Oimage(tc_prod(X4264,X4263),X4263,c_Product__Type_Osnd(X4264,X4263)),hAPP(c_List_Oset(tc_prod(X4264,X4263)),X4262))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ran__distinct])])). 4.46/4.69 fof(c_0_5106, plain, ![X13734, X13735, X13736]:hAPP(c_Set_Oimage(tc_prod(X13736,X13735),X13735,c_Product__Type_Osnd(X13736,X13735)),X13734)=hAPP(c_Relation_ORange(X13736,X13735),X13734), inference(variable_rename,[status(thm)],[fact_snd__eq__Range])). 4.46/4.69 fof(c_0_5107, plain, ![X12503, X12504, X12505]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12505))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X12504),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X12504),X12503))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X12505))),X12503))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_decr__lemma])])). 4.46/4.69 fof(c_0_5108, plain, ![X7749, X7750, X7751]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7751))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7750),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X7749),X7750))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X7751))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incr__lemma])])). 4.46/4.69 fof(c_0_5109, plain, ![X1114, X1115, X1116, X1117, X1118]:((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X1118|hAPP(c_New__DSequence_Oneg__decr__bind(X1117,X1116,X1115,X1114),X1118)=c_Lazy__Sequence_Ohit__bound(X1116))&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1118|c_Lazy__Sequence_Ohb__bind(X1117,X1116,hAPP(X1115,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1118),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X1117,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1116))),X1114),X1118))=hAPP(c_New__DSequence_Oneg__decr__bind(X1117,X1116,X1115,X1114),X1118))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_New__DSequence_Oneg__decr__bind__def])])])). 4.46/4.69 fof(c_0_5110, plain, ![X6929, X6930, X6931, X6932]:c_Lazy__Sequence_Ohb__flat(X6931,c_Lazy__Sequence_Ohb__map(X6932,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X6931)),X6929,X6930))=c_Lazy__Sequence_Ohb__bind(X6932,X6931,X6930,X6929), inference(variable_rename,[status(thm)],[fact_hb__bind__def])). 4.46/4.69 fof(c_0_5111, plain, ![X1856, X1857, X1858, X1859]:(((X1857=X1858|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1859,X1859)),hAPP(hAPP(c_Product__Type_OPair(X1859,X1859),X1858),X1857)),hAPP(c_List_Oset(tc_prod(X1859,X1859)),hAPP(hAPP(c_List_Ozip(X1859,X1859),X1856),X1856)))))&(hBOOL(hAPP(hAPP(c_member(X1859),X1858),hAPP(c_List_Oset(X1859),X1856)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1859,X1859)),hAPP(hAPP(c_Product__Type_OPair(X1859,X1859),X1858),X1857)),hAPP(c_List_Oset(tc_prod(X1859,X1859)),hAPP(hAPP(c_List_Ozip(X1859,X1859),X1856),X1856))))))&(X1857!=X1858|~hBOOL(hAPP(hAPP(c_member(X1859),X1858),hAPP(c_List_Oset(X1859),X1856)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1859,X1859)),hAPP(hAPP(c_Product__Type_OPair(X1859,X1859),X1858),X1857)),hAPP(c_List_Oset(tc_prod(X1859,X1859)),hAPP(hAPP(c_List_Ozip(X1859,X1859),X1856),X1856)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__same])])])). 4.46/4.69 fof(c_0_5112, plain, ![X3778, X3779, X3780, X3781]:((~hBOOL(hAPP(X3781,X3780))|c_List_OdropWhile(X3779,X3781,hAPP(hAPP(c_List_Olist_OCons(X3779),X3780),X3778))=c_List_OdropWhile(X3779,X3781,X3778))&(hBOOL(hAPP(X3781,X3780))|hAPP(hAPP(c_List_Olist_OCons(X3779),X3780),X3778)=c_List_OdropWhile(X3779,X3781,hAPP(hAPP(c_List_Olist_OCons(X3779),X3780),X3778)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dropWhile_Osimps_I2_J])])])). 4.46/4.69 fof(c_0_5113, plain, ![X17029, X17030, X17031]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X17031,X17031),tc_HOL_Obool)),c_Relation_OId(X17031)),X17030))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X17031,X17031),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X17031,X17031,X17031),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X17031,X17031),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X17031,X17029)),X17030)),X17029)),X17030))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X17031,X17031),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X17031,X17029)),X17030)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__Int__subset])])). 4.46/4.69 fof(c_0_5114, plain, ![X12784, X12785, X12786, X12787, X12788, X12789]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12789),X12788),X12787)),X12786)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12789),X12785),X12787)),X12784)|X12786=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12789),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12789),X12785),X12788)),X12787)),X12784)|~class_Rings_Oring(X12789))&(X12786!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12789),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12789),X12785),X12788)),X12787)),X12784)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12789),X12788),X12787)),X12786)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12789),X12785),X12787)),X12784)|~class_Rings_Oring(X12789))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff2])])])). 4.46/4.69 fof(c_0_5115, plain, ![X14130, X14131, X14132, X14133, X14134]:(~class_Orderings_Olinorder(X14134)|(~c_Fun_Oinj__on(X14133,X14134,X14132,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14133,tc_HOL_Obool)),hAPP(c_List_Oset(X14133),X14131)),hAPP(c_List_Oset(X14133),X14130)))|(~c_List_Olinorder__class_Osorted(X14134,hAPP(hAPP(c_List_Omap(X14133,X14134),X14132),X14131))|(~hBOOL(hAPP(c_List_Odistinct(X14134),hAPP(hAPP(c_List_Omap(X14133,X14134),X14132),X14131)))|(~c_List_Olinorder__class_Osorted(X14134,hAPP(hAPP(c_List_Omap(X14133,X14134),X14132),X14130))|(~hBOOL(hAPP(c_List_Odistinct(X14134),hAPP(hAPP(c_List_Omap(X14133,X14134),X14132),X14130)))|(hAPP(c_List_Oset(X14133),X14131)!=hAPP(c_List_Oset(X14133),X14130)|X14131=X14130))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__sorted__distinct__set__unique])])])). 4.46/4.69 fof(c_0_5116, plain, ![X7033, X7034, X7035]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7035,tc_HOL_Obool)),hAPP(c_List_Oset(X7035),X7034)),hAPP(c_List_Oset(X7035),X7033))=hAPP(c_List_Oset(X7035),hAPP(hAPP(c_List_Oappend(X7035),X7034),X7033)), inference(variable_rename,[status(thm)],[fact_set__append])). 4.46/4.69 fof(c_0_5117, plain, ![X4825, X4826, X4827]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4827))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4825),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4826),X4825),X4827))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4826,X4825))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X4826,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4825),X4827))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zmult2__eq])])). 4.46/4.69 cnf(c_0_5118, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X1))), inference(split_conjunct,[status(thm)],[c_0_4607])). 4.46/4.69 cnf(c_0_5119, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I2_J])). 4.46/4.69 cnf(c_0_5120, plain, (hAPP(c_Int_Onat,X1)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)), inference(rw,[status(thm)],[c_0_4608, c_0_4609]), ['final']). 4.46/4.69 cnf(c_0_5121, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_nat__number__of__Pls])). 4.46/4.69 cnf(c_0_5122, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4610])). 4.46/4.69 cnf(c_0_5123, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4611])). 4.46/4.69 fof(c_0_5124, plain, ![X17642, X17643, X17644, X17645, X17646, X17647, X17648, X17649, X17650, X17651]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17643))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17646))|X17642!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17643),X17645)),X17646)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17646),X17643))|hBOOL(hAPP(X17644,X17645)))|~epred2_3(X17644,X17643,X17642))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17643),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(X17642!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17643),X17647)),X17648)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17648),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17643),X17648))|hBOOL(hAPP(X17644,X17647)))|~epred2_3(X17644,X17643,X17642)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17650),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17650))|epred2_3(X17651,X17650,X17649))&((((X17649=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17650),esk537_3(X17649,X17650,X17651))),esk538_3(X17649,X17650,X17651))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17650))|epred2_3(X17651,X17650,X17649))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk538_3(X17649,X17650,X17651)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17650))|epred2_3(X17651,X17650,X17649)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17650),esk538_3(X17649,X17650,X17651)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17650))|epred2_3(X17651,X17650,X17649)))&(~hBOOL(hAPP(X17651,esk537_3(X17649,X17650,X17651)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17650))|epred2_3(X17651,X17650,X17649))))&(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17650),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk536_3(X17649,X17650,X17651)))|epred2_3(X17651,X17650,X17649))&((((X17649=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17650),esk537_3(X17649,X17650,X17651))),esk538_3(X17649,X17650,X17651))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk536_3(X17649,X17650,X17651)))|epred2_3(X17651,X17650,X17649))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk538_3(X17649,X17650,X17651)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk536_3(X17649,X17650,X17651)))|epred2_3(X17651,X17650,X17649)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17650),esk538_3(X17649,X17650,X17651)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk536_3(X17649,X17650,X17651)))|epred2_3(X17651,X17650,X17649)))&(~hBOOL(hAPP(X17651,esk537_3(X17649,X17650,X17651)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk536_3(X17649,X17650,X17651)))|epred2_3(X17651,X17650,X17649))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17650),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X17649=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17650),esk535_3(X17649,X17650,X17651))),esk536_3(X17649,X17650,X17651))|epred2_3(X17651,X17650,X17649))&((((X17649=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17650),esk537_3(X17649,X17650,X17651))),esk538_3(X17649,X17650,X17651))|X17649=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17650),esk535_3(X17649,X17650,X17651))),esk536_3(X17649,X17650,X17651))|epred2_3(X17651,X17650,X17649))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk538_3(X17649,X17650,X17651)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X17649=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17650),esk535_3(X17649,X17650,X17651))),esk536_3(X17649,X17650,X17651))|epred2_3(X17651,X17650,X17649)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17650),esk538_3(X17649,X17650,X17651)))|X17649=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17650),esk535_3(X17649,X17650,X17651))),esk536_3(X17649,X17650,X17651))|epred2_3(X17651,X17650,X17649)))&(~hBOOL(hAPP(X17651,esk537_3(X17649,X17650,X17651)))|X17649=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17650),esk535_3(X17649,X17650,X17651))),esk536_3(X17649,X17650,X17651))|epred2_3(X17651,X17650,X17649)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17650),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk536_3(X17649,X17650,X17651)),X17650))|epred2_3(X17651,X17650,X17649))&((((X17649=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17650),esk537_3(X17649,X17650,X17651))),esk538_3(X17649,X17650,X17651))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk536_3(X17649,X17650,X17651)),X17650))|epred2_3(X17651,X17650,X17649))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk538_3(X17649,X17650,X17651)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk536_3(X17649,X17650,X17651)),X17650))|epred2_3(X17651,X17650,X17649)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17650),esk538_3(X17649,X17650,X17651)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk536_3(X17649,X17650,X17651)),X17650))|epred2_3(X17651,X17650,X17649)))&(~hBOOL(hAPP(X17651,esk537_3(X17649,X17650,X17651)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk536_3(X17649,X17650,X17651)),X17650))|epred2_3(X17651,X17650,X17649)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17650),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X17651,esk535_3(X17649,X17650,X17651)))|epred2_3(X17651,X17650,X17649))&((((X17649=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17650),esk537_3(X17649,X17650,X17651))),esk538_3(X17649,X17650,X17651))|~hBOOL(hAPP(X17651,esk535_3(X17649,X17650,X17651)))|epred2_3(X17651,X17650,X17649))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk538_3(X17649,X17650,X17651)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X17651,esk535_3(X17649,X17650,X17651)))|epred2_3(X17651,X17650,X17649)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17650),esk538_3(X17649,X17650,X17651)))|~hBOOL(hAPP(X17651,esk535_3(X17649,X17650,X17651)))|epred2_3(X17651,X17650,X17649)))&(~hBOOL(hAPP(X17651,esk537_3(X17649,X17650,X17651)))|~hBOOL(hAPP(X17651,esk535_3(X17649,X17650,X17651)))|epred2_3(X17651,X17650,X17649))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4612])])])])])])). 4.46/4.69 fof(c_0_5125, plain, ![X8873, X8874, X8875, X8876, X8877]:(~c_Hoare__Mirabelle_Ohoare__derivs(X8877,X8876,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X8877)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X8877),c_Hoare__Mirabelle_Opeek__and(X8877,X8875,X8874)),X8873),X8875)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X8877),tc_HOL_Obool))))|c_Hoare__Mirabelle_Ohoare__derivs(X8877,X8876,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X8877)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X8877),X8875),c_Com_Ocom_OWhile(X8874,X8873)),c_Hoare__Mirabelle_Opeek__and(X8877,X8875,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X8874)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X8877),tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Loop])])). 4.46/4.69 fof(c_0_5126, plain, ![X1143, X1144, X1145, X1148, X1149]:(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk28_3(X1143,X1144,X1145)))|hBOOL(hAPP(hAPP(X1144,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1143),X1145)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1143,X1145)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1145)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk28_3(X1143,X1144,X1145)),X1145))|hBOOL(hAPP(hAPP(X1144,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1143),X1145)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1143,X1145)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1145))))&(X1143=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1145),esk27_3(X1143,X1144,X1145))),esk28_3(X1143,X1144,X1145))|hBOOL(hAPP(hAPP(X1144,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1143),X1145)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1143,X1145)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1145))))&(~hBOOL(hAPP(hAPP(X1144,esk27_3(X1143,X1144,X1145)),esk28_3(X1143,X1144,X1145)))|hBOOL(hAPP(hAPP(X1144,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1143),X1145)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1143,X1145)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1145))))&(~hBOOL(hAPP(hAPP(X1144,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1143),X1145)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1143,X1145)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1149))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1149),X1145))|X1143!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1145),X1148)),X1149)|hBOOL(hAPP(hAPP(X1144,X1148),X1149)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1145)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__pos__lemma])])])])])). 4.46/4.69 fof(c_0_5127, plain, ![X13317, X13318, X13319, X13320, X13321]:((X13319!=hAPP(hAPP(c_List_Oappend(X13321),c_List_OtakeWhile(X13321,X13320,X13319)),hAPP(hAPP(c_List_Olist_OCons(X13321),X13318),X13317))|hBOOL(hAPP(X13320,X13318))|hAPP(hAPP(c_List_Olist_OCons(X13321),X13318),X13317)=c_List_OdropWhile(X13321,X13320,X13319))&((X13319=hAPP(hAPP(c_List_Oappend(X13321),c_List_OtakeWhile(X13321,X13320,X13319)),hAPP(hAPP(c_List_Olist_OCons(X13321),X13318),X13317))|hAPP(hAPP(c_List_Olist_OCons(X13321),X13318),X13317)!=c_List_OdropWhile(X13321,X13320,X13319))&(~hBOOL(hAPP(X13320,X13318))|hAPP(hAPP(c_List_Olist_OCons(X13321),X13318),X13317)!=c_List_OdropWhile(X13321,X13320,X13319)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dropWhile__eq__Cons__conv])])])])). 4.46/4.69 fof(c_0_5128, plain, ![X5176, X5177, X5178, X5181, X5182]:(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5178),esk156_3(X5176,X5177,X5178)))|hBOOL(hAPP(hAPP(X5177,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X5176),X5178)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5176,X5178)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5178),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&(X5176=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5178),esk155_3(X5176,X5177,X5178))),esk156_3(X5176,X5177,X5178))|hBOOL(hAPP(hAPP(X5177,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X5176),X5178)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5176,X5178)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5178),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk156_3(X5176,X5177,X5178)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X5177,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X5176),X5178)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5176,X5178)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5178),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))&(~hBOOL(hAPP(hAPP(X5177,esk155_3(X5176,X5177,X5178)),esk156_3(X5176,X5177,X5178)))|hBOOL(hAPP(hAPP(X5177,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X5176),X5178)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5176,X5178)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5178),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))&(~hBOOL(hAPP(hAPP(X5177,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X5176),X5178)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5176,X5178)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5178),X5182))|X5176!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5178),X5181)),X5182)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5182),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X5177,X5181),X5182)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5178),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__neg__lemma])])])])])). 4.46/4.69 fof(c_0_5129, plain, ![X9090, X9091, X9092, X9094, X9095, X9096, X9097]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk263_3(X9090,X9091,X9092)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X9092,X9092)),X9091),c_Transitive__Closure_Otrancl(X9092,X9090))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X9092,X9092)),X9091),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X9092,X9092),tc_HOL_Obool),esk263_3(X9090,X9091,X9092)),X9090)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X9092,X9092)),X9091),c_Transitive__Closure_Otrancl(X9092,X9090)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9097))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X9096,X9096)),X9095),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X9096,X9096),tc_HOL_Obool),X9097),X9094)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X9096,X9096)),X9095),c_Transitive__Closure_Otrancl(X9096,X9094))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__power])])])])])])). 4.46/4.69 fof(c_0_5130, plain, ![X6708, X6709, X6710, X6711]:(~class_Int_Onumber__ring(X6711)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6711),hAPP(c_Int_Onumber__class_Onumber__of(X6711),X6710)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X6711),X6709),hAPP(c_Int_Onumber__class_Onumber__of(X6711),X6708)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6711),hAPP(c_Int_Onumber__class_Onumber__of(X6711),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6710),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6708)))),X6709)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__number__of__diff2])])])). 4.46/4.69 cnf(c_0_5131, plain, (X1=X2|hAPP(c_List_OremoveAll(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))=hAPP(hAPP(c_List_Olist_OCons(X3),X2),hAPP(c_List_OremoveAll(X3,X1),X4))), inference(split_conjunct,[status(thm)],[c_0_4613])). 4.46/4.69 fof(c_0_5132, plain, ![X8295]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8295)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8295)))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8295))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__pos__neg__1__number__of])])])). 4.46/4.69 cnf(c_0_5133, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))=c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X1)), inference(split_conjunct,[status(thm)],[c_0_4614])). 4.46/4.69 cnf(c_0_5134, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(rw,[status(thm)],[c_0_4615, c_0_4443]), ['final']). 4.46/4.69 fof(c_0_5135, plain, ![X5478, X5479]:hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5479),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X5478))=hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5479),X5478)), inference(variable_rename,[status(thm)],[fact_negateSnd__eq])). 4.46/4.69 cnf(c_0_5136, plain, (X4=X1|X1!=hAPP(c_Product__Type_Ofst(X2,X3),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_4616])). 4.46/4.69 fof(c_0_5137, plain, ![X9608, X9609, X9610, X9611]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9610),X9609))|c_Groups_Ozero__class_Ozero(X9611)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X9611),X9608),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X9609),hAPP(c_Nat_OSuc,X9610)))|~class_Groups_Ocomm__monoid__add(X9611))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9610),X9609))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9611),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X9611),X9608),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X9609),X9610))),hAPP(X9608,X9610))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X9611),X9608),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X9609),hAPP(c_Nat_OSuc,X9610)))|~class_Groups_Ocomm__monoid__add(X9611))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__op__ivl__Suc])])])])). 4.46/4.69 fof(c_0_5138, plain, ![X7354]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X7354)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X7354))=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X7354)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__pos__neg__1__number__of])])])). 4.46/4.69 cnf(c_0_5139, plain, (X1=X5|X1!=hAPP(c_Product__Type_Osnd(X2,X3),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_4617])). 4.46/4.69 fof(c_0_5140, plain, ![X1449, X1450, X1451]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1451)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1451)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1450)),X1449))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1450)),X1449))&((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1450)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1451)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1450)),X1449))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1451),X1450))),X1449)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1451))))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1450)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1451)),X1449)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1451)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1450)),X1449))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1451)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__number__of__add__left])])])])). 4.46/4.69 fof(c_0_5141, plain, ![X11153, X11154, X11156, X11157, X11158]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X11154,X11154)),hAPP(hAPP(c_Product__Type_OPair(X11154,X11154),esk331_2(X11153,X11154)),esk331_2(X11153,X11154))),c_Transitive__Closure_Otrancl(X11154,X11153)))|c_Wellfounded_Oacyclic(X11154,X11153))&(~c_Wellfounded_Oacyclic(X11157,X11156)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X11157,X11157)),hAPP(hAPP(c_Product__Type_OPair(X11157,X11157),X11158),X11158)),c_Transitive__Closure_Otrancl(X11157,X11156))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acyclic__def])])])])])])). 4.46/4.69 fof(c_0_5142, plain, ![X4035, X4036]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4036,X4036)),hAPP(hAPP(c_Product__Type_OPair(X4036,X4036),esk110_2(X4035,X4036)),esk110_2(X4035,X4036))),c_Transitive__Closure_Otrancl(X4036,X4035)))|c_Wellfounded_Oacyclic(X4036,X4035)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acyclicI])])])])). 4.46/4.69 fof(c_0_5143, plain, ![X4380, X4381, X4382]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4382,tc_HOL_Obool)),X4381),hAPP(hAPP(c_Set_Oinsert(X4382),X4380),c_Orderings_Obot__class_Obot(tc_fun(X4382,tc_HOL_Obool)))))|c_Partial__Function_Oflat__lub(X4382,X4380,X4381)=c_HOL_OThe(X4382,hAPP(hAPP(c_COMBC(X4382,tc_fun(X4382,tc_HOL_Obool),tc_HOL_Obool),c_member(X4382)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4382,tc_HOL_Obool)),X4381),hAPP(hAPP(c_Set_Oinsert(X4382),X4380),c_Orderings_Obot__class_Obot(tc_fun(X4382,tc_HOL_Obool)))))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4382,tc_HOL_Obool)),X4381),hAPP(hAPP(c_Set_Oinsert(X4382),X4380),c_Orderings_Obot__class_Obot(tc_fun(X4382,tc_HOL_Obool)))))|c_Partial__Function_Oflat__lub(X4382,X4380,X4381)=X4380)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_flat__lub__def])])])). 4.46/4.69 fof(c_0_5144, plain, ![X15073, X15074, X15075, X15077]:((hBOOL(hAPP(X15074,esk442_3(X15073,X15074,X15075)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15073))|(~hBOOL(hAPP(X15074,X15077))|hBOOL(hAPP(X15074,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15073),X15075))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15075)))&(~hBOOL(hAPP(X15074,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk442_3(X15073,X15074,X15075)),X15075)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15073))|(~hBOOL(hAPP(X15074,X15077))|hBOOL(hAPP(X15074,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15073),X15075))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15075)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_incr__mult__lemma])])])])])])). 4.46/4.69 fof(c_0_5145, plain, ![X9641, X9642, X9643, X9644]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9643))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9643))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X9644,X9643),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X9642),X9641)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9643),X9642)),X9641)!=X9644)&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9641),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9643),X9641))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9643))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X9644,X9643),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X9642),X9641)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9643),X9642)),X9641)!=X9644))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9643))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9641))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9641),X9643)))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X9644,X9643),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X9642),X9641)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9643),X9642)),X9641)!=X9644)&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9641),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9643),X9641))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9641))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9641),X9643)))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X9644,X9643),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X9642),X9641)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9643),X9642)),X9641)!=X9644))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__relI])])])])). 4.46/4.69 fof(c_0_5146, plain, ![X10241, X10242, X10243]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10243),X10242))|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10241),X10243)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10242),X10243))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X10243)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X10241),X10242)))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10241),X10242))|hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X10243)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X10241),X10242))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10243),X10242)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10241),X10242))|hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X10243)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X10241),X10242))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10243),X10242))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__minus__const__atLeastLessThan__nat])])])])). 4.46/4.69 cnf(c_0_5147, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4618])). 4.46/4.69 cnf(c_0_5148, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4619])). 4.46/4.69 cnf(c_0_5149, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4620])). 4.46/4.69 fof(c_0_5150, plain, ![X3581, X3582, X3583]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3583),X3582)),X3581))|c_List_Oupt(X3583,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3583),X3582))=hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X3582),c_List_Oupt(X3583,X3581))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__upt])])). 4.46/4.69 cnf(c_0_5151, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~c_Nitpick_Oless__frac(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_4621])). 4.46/4.69 cnf(c_0_5152, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~c_Nitpick_Oless__eq__frac(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_4622])). 4.46/4.69 fof(c_0_5153, plain, ![X14818, X14819, X14820, X14821]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14820))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14820))|(X14820=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14821),X14820)=X14819)|X14821!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14820),X14819)),X14818))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14818),X14820))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14818))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14820))|(X14820=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14821),X14820)=X14819)|X14821!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14820),X14819)),X14818)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14820))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14820),X14818))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14818),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|(X14820=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14821),X14820)=X14819)|X14821!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14820),X14819)),X14818))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14818),X14820))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14818))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14820),X14818))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14818),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|(X14820=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14821),X14820)=X14819)|X14821!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14820),X14819)),X14818)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__div__eq])])])])). 4.46/4.69 fof(c_0_5154, plain, ![X14173, X14174, X14175]:((hBOOL(hAPP(hAPP(c_member(X14175),esk413_3(X14173,X14174,X14175)),hAPP(c_List_Oset(X14175),c_List_OdropWhile(X14175,X14174,X14173))))|hAPP(c_List_Ofilter(X14175,X14174),X14173)=c_List_OtakeWhile(X14175,X14174,X14173))&(hBOOL(hAPP(X14174,esk413_3(X14173,X14174,X14175)))|hAPP(c_List_Ofilter(X14175,X14174),X14173)=c_List_OtakeWhile(X14175,X14174,X14173))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile__eq__filter])])])])])). 4.46/4.69 fof(c_0_5155, plain, ![X3209, X3210, X3211]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3211),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3210)),X3209)))|hAPP(hAPP(c_List_Onth(X3210),X3209),X3211)=hAPP(c_Random_Opick(X3210,hAPP(hAPP(c_List_Omap(X3210,tc_prod(tc_Code__Numeral_Ocode__numeral,X3210)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X3210),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X3209)),hAPP(c_Code__Numeral_Oof__nat,X3211))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pick__same])])). 4.46/4.69 fof(c_0_5156, plain, ![X567, X568, X569]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk13_3(X567,X568,X569)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X569)))|X568=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X568),X569)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X568),c_Groups_Oone__class_Oone(tc_Int_Oint))),X567))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X569)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk14_3(X567,X568,X569)),X567))|X568=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X568),X569)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X568),c_Groups_Oone__class_Oone(tc_Int_Oint))),X567))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X569)))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk14_3(X567,X568,X569)),esk13_3(X567,X568,X569))=X568|X568=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X568),X569)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X568),c_Groups_Oone__class_Oone(tc_Int_Oint))),X567))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X569))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bset_I3_J])])])])])). 4.46/4.69 fof(c_0_5157, plain, ![X12401, X12402, X12403, X12404, X12405, X12406, X12407, X12408]:((hBOOL(hAPP(hAPP(c_member(X12407),esk365_8(X12401,X12402,X12403,X12404,X12405,X12406,X12407,X12408)),X12404))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12407,X12408),X12402),X12404)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12406,X12408),X12401),X12403)|X12403!=hAPP(c_Set_Oimage(X12407,X12406,X12405),X12404)|~c_Fun_Oinj__on(X12407,X12406,X12405,X12404)|~class_Groups_Ocomm__monoid__mult(X12408))&(hAPP(X12402,esk365_8(X12401,X12402,X12403,X12404,X12405,X12406,X12407,X12408))!=hAPP(hAPP(c_Fun_Ocomp(X12406,X12408,X12407,X12401),X12405),esk365_8(X12401,X12402,X12403,X12404,X12405,X12406,X12407,X12408))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12407,X12408),X12402),X12404)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12406,X12408),X12401),X12403)|X12403!=hAPP(c_Set_Oimage(X12407,X12406,X12405),X12404)|~c_Fun_Oinj__on(X12407,X12406,X12405,X12404)|~class_Groups_Ocomm__monoid__mult(X12408))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_strong__setprod__reindex__cong])])])])])). 4.46/4.69 fof(c_0_5158, plain, ![X9377, X9378, X9379, X9380, X9381, X9382, X9383, X9384]:((hBOOL(hAPP(hAPP(c_member(X9383),esk270_8(X9377,X9378,X9379,X9380,X9381,X9382,X9383,X9384)),X9380))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9383,X9384),X9378),X9380)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9382,X9384),X9377),X9379)|X9379!=hAPP(c_Set_Oimage(X9383,X9382,X9381),X9380)|~c_Fun_Oinj__on(X9383,X9382,X9381,X9380)|~class_Groups_Ocomm__monoid__add(X9384))&(hAPP(X9377,hAPP(X9381,esk270_8(X9377,X9378,X9379,X9380,X9381,X9382,X9383,X9384)))!=hAPP(X9378,esk270_8(X9377,X9378,X9379,X9380,X9381,X9382,X9383,X9384))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9383,X9384),X9378),X9380)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9382,X9384),X9377),X9379)|X9379!=hAPP(c_Set_Oimage(X9383,X9382,X9381),X9380)|~c_Fun_Oinj__on(X9383,X9382,X9381,X9380)|~class_Groups_Ocomm__monoid__add(X9384))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__reindex__cong])])])])])). 4.46/4.69 cnf(c_0_5159, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X2))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4623])). 4.46/4.69 cnf(c_0_5160, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OBit1(c_Int_OPls)))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4624])). 4.46/4.69 fof(c_0_5161, plain, ![X4234, X4235, X4236]:(c_List_Olist_ONil(X4235)=X4236|hAPP(hAPP(c_List_Onth(X4235),X4236),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4234,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4235)),X4236)))=hAPP(c_List_Ohd(X4235),hAPP(c_List_Orotate(X4235,X4234),X4236))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__rotate__conv__nth])])])). 4.46/4.69 fof(c_0_5162, plain, ![X5988, X5989, X5990]:((X5989!=c_List_Olist_ONil(X5990)|X5988=c_List_Ofoldr(X5990,X5990,c_Orderings_Oord__class_Omax(X5990),X5989,X5988)|~c_List_Olinorder__class_Osorted(X5990,hAPP(c_List_Orev(X5990),X5989))|~class_Orderings_Olinorder(X5990))&(X5989=c_List_Olist_ONil(X5990)|c_List_Ofoldr(X5990,X5990,c_Orderings_Oord__class_Omax(X5990),X5989,X5988)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X5990),hAPP(hAPP(c_List_Onth(X5990),X5989),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X5988)|~c_List_Olinorder__class_Osorted(X5990,hAPP(c_List_Orev(X5990),X5989))|~class_Orderings_Olinorder(X5990))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldr__max__sorted])])])). 4.46/4.69 cnf(c_0_5163, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1)))=c_Groups_Oone__class_Oone(X2)|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_4567])). 4.46/4.69 fof(c_0_5164, plain, ![X14126, X14127, X14128, X14129]:(hAPP(c_Map_Omap__of(X14129,X14128),X14126)!=hAPP(c_Map_Omap__of(X14129,X14128),X14127)|hAPP(c_Set_Oimage(tc_prod(X14129,X14128),X14129,c_Product__Type_Ofst(X14129,X14128)),hAPP(c_List_Oset(tc_prod(X14129,X14128)),X14126))=hAPP(c_Set_Oimage(tc_prod(X14129,X14128),X14129,c_Product__Type_Ofst(X14129,X14128)),hAPP(c_List_Oset(tc_prod(X14129,X14128)),X14127))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__eq__dom])])). 4.46/4.69 fof(c_0_5165, plain, ![X3687, X3688, X3689]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3689),c_Int_OPls))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3689)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3688)),X3687))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3689),c_Int_OPls))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3689)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3688)),X3687))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3689),X3688))),X3687))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__number__of__mult__left])])])). 4.46/4.69 cnf(c_0_5166, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)))), inference(split_conjunct,[status(thm)],[c_0_4592])). 4.46/4.69 fof(c_0_5167, plain, ![X13737, X13738, X13739]:(~class_Groups_Omonoid__add(X13739)|hAPP(c_List_Ofoldl(X13739,X13739,c_Groups_Oplus__class_Oplus(X13739),X13738),X13737)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13739),X13738),c_List_Ofoldr(X13739,X13739,c_Groups_Oplus__class_Oplus(X13739),X13737,c_Groups_Ozero__class_Ozero(X13739)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__foldr1__lemma])])). 4.46/4.69 cnf(c_0_5168, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)))), inference(split_conjunct,[status(thm)],[c_0_4593])). 4.46/4.69 cnf(c_0_5169, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)))), inference(split_conjunct,[status(thm)],[c_0_4594])). 4.46/4.69 cnf(c_0_5170, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4625])). 4.46/4.69 fof(c_0_5171, plain, ![X15799, X15800]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15800))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15799))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X15799),X15800)),X15799)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X15799),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15800),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__power__div__base])])])). 4.46/4.69 fof(c_0_5172, plain, ![X8024, X8025, X8026, X8027, X8028]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8028),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8027),X8026)))|hAPP(X8024,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8026),X8028))=hAPP(hAPP(c_List_Onth(X8025),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X8025),X8024),c_List_Oupt(X8026,X8027))),X8028)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__map__upt])])). 4.46/4.69 fof(c_0_5173, plain, ![X6112, X6113, X6114, X6115, X6116]:(~class_Complete__Lattice_Ocomplete__lattice(X6116)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6115),X6114))|hAPP(hAPP(c_Finite__Set_Ofold(X6115,X6116,hAPP(hAPP(c_COMBB(X6116,tc_fun(X6116,X6116),X6115),c_Lattices_Osemilattice__sup__class_Osup(X6116)),X6112)),X6113),X6114)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6116),X6113),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6115,X6116),X6114),X6112)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__SUPR__fold__sup])])])). 4.46/4.69 fof(c_0_5174, plain, ![X16089, X16090, X16091, X16092, X16093]:(~class_Complete__Lattice_Ocomplete__lattice(X16093)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16092),X16091))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16093),X16090),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16092,X16093),X16091),X16089))=hAPP(hAPP(c_Finite__Set_Ofold(X16092,X16093,hAPP(hAPP(c_COMBB(X16093,tc_fun(X16093,X16093),X16092),c_Lattices_Osemilattice__inf__class_Oinf(X16093)),X16089)),X16090),X16091))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__INFI__fold__inf])])). 4.46/4.69 fof(c_0_5175, plain, ![X8120, X8121, X8122, X8123]:(~class_Groups_Ocomm__monoid__add(X8123)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8122),X8121))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8123),hAPP(X8120,X8122)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X8123),X8120),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X8122,X8121)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X8123),X8120),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X8122,X8121)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__head])])])). 4.46/4.69 fof(c_0_5176, plain, ![X12545, X12546, X12547, X12548]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12547))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12547))|(X12547=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X12545=c_Divides_Odiv__class_Omod(tc_Int_Oint,X12548,X12547))|X12548!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12547),X12546)),X12545))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12547),X12545))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12545),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12547))|(X12547=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X12545=c_Divides_Odiv__class_Omod(tc_Int_Oint,X12548,X12547))|X12548!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12547),X12546)),X12545)))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12547))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12545))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12545),X12547)))|(X12547=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X12545=c_Divides_Odiv__class_Omod(tc_Int_Oint,X12548,X12547))|X12548!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12547),X12546)),X12545))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12547),X12545))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12545),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12545))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12545),X12547)))|(X12547=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X12545=c_Divides_Odiv__class_Omod(tc_Int_Oint,X12548,X12547))|X12548!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12547),X12546)),X12545)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__mod__eq])])])])). 4.46/4.69 cnf(c_0_5177, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4626])). 4.46/4.69 cnf(c_0_5178, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4627])). 4.46/4.69 fof(c_0_5179, plain, ![X8947, X8948, X8949, X8950]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X8950,X8950)),hAPP(hAPP(c_Product__Type_OPair(X8950,X8950),X8949),X8948)),hAPP(c_Wellfounded_Omeasure(X8950),X8947)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X8947,X8949)),hAPP(X8947,X8948))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X8947,X8949)),hAPP(X8947,X8948)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X8950,X8950)),hAPP(hAPP(c_Product__Type_OPair(X8950,X8950),X8949),X8948)),hAPP(c_Wellfounded_Omeasure(X8950),X8947))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])])). 4.46/4.69 fof(c_0_5180, plain, ![X4319]:hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X4319),c_Wellfounded_Oless__than)=c_Wellfounded_Omeasure(X4319), inference(variable_rename,[status(thm)],[fact_measure__def])). 4.46/4.69 fof(c_0_5181, plain, ![X17309, X17310, X17311, X17312, X17313]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk518_5(X17309,X17310,X17311,X17312,X17313)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X17313),X17310),X17312)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X17313),X17309),X17311)|~c_Nat__Transfer_Onat__set(X17311)|X17312!=X17311|(~class_Groups_Ocomm__monoid__add(X17313)|~class_Groups_Ocomm__monoid__mult(X17313)))&(hAPP(X17310,esk518_5(X17309,X17310,X17311,X17312,X17313))!=hAPP(X17309,esk518_5(X17309,X17310,X17311,X17312,X17313))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X17313),X17310),X17312)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X17313),X17309),X17311)|~c_Nat__Transfer_Onat__set(X17311)|X17312!=X17311|(~class_Groups_Ocomm__monoid__add(X17313)|~class_Groups_Ocomm__monoid__mult(X17313)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I2_J])])])])])). 4.46/4.69 fof(c_0_5182, plain, ![X484, X485, X486, X487, X488]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk9_5(X484,X485,X486,X487,X488)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X488),X485),X487)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X488),X484),X486)|~c_Nat__Transfer_Onat__set(X486)|X486!=X487|(~class_Groups_Ocomm__monoid__mult(X488)|~class_Groups_Ocomm__monoid__add(X488)))&(hAPP(X485,esk9_5(X484,X485,X486,X487,X488))!=hAPP(X484,esk9_5(X484,X485,X486,X487,X488))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X488),X485),X487)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X488),X484),X486)|~c_Nat__Transfer_Onat__set(X486)|X486!=X487|(~class_Groups_Ocomm__monoid__mult(X488)|~class_Groups_Ocomm__monoid__add(X488)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I1_J])])])])])). 4.46/4.69 cnf(c_0_5183, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4628])). 4.46/4.69 cnf(c_0_5184, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4629])). 4.46/4.69 cnf(c_0_5185, plain, (hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X1,X2)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),c_List_Olist_ONil(tc_Nat_Onat)))=c_List_Oupt(X1,hAPP(c_Nat_OSuc,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4630])). 4.46/4.69 cnf(c_0_5186, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OBit1(c_Int_OPls)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4631])). 4.46/4.69 cnf(c_0_5187, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Int_OBit1(c_Int_OPls)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4632])). 4.46/4.69 fof(c_0_5188, plain, ![X605, X606, X607, X608, X609, X610]:((hBOOL(hAPP(hAPP(c_member(X609),esk15_6(X605,X606,X607,X608,X609,X610)),X608))|(X606!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X609,X610),X607),X608)|(~hBOOL(hAPP(hAPP(c_member(X609),X605),X608))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X610),hAPP(X607,X605)),X606))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X609),X608))|~class_Groups_Oordered__ab__group__add(X610))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X610),c_Groups_Ozero__class_Ozero(X610)),hAPP(X607,esk15_6(X605,X606,X607,X608,X609,X610))))|(X606!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X609,X610),X607),X608)|(~hBOOL(hAPP(hAPP(c_member(X609),X605),X608))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X610),hAPP(X607,X605)),X606))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X609),X608))|~class_Groups_Oordered__ab__group__add(X610))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__nonneg__leq__bound])])])])])). 4.46/4.69 fof(c_0_5189, plain, ![X14503, X14504, X14505, X14506, X14507, X14508]:((hAPP(c_Product__Type_Oapsnd(X14508,X14507,X14506,X14505),X14504)!=hAPP(c_Product__Type_Oapsnd(X14508,X14507,X14506,X14503),X14504)|hAPP(X14503,hAPP(c_Product__Type_Osnd(X14506,X14508),X14504))=hAPP(X14505,hAPP(c_Product__Type_Osnd(X14506,X14508),X14504)))&(hAPP(X14503,hAPP(c_Product__Type_Osnd(X14506,X14508),X14504))!=hAPP(X14505,hAPP(c_Product__Type_Osnd(X14506,X14508),X14504))|hAPP(c_Product__Type_Oapsnd(X14508,X14507,X14506,X14505),X14504)=hAPP(c_Product__Type_Oapsnd(X14508,X14507,X14506,X14503),X14504))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_apsnd__eq__conv])])). 4.46/4.69 fof(c_0_5190, plain, ![X3241, X3242, X3243, X3244, X3245, X3246]:((hAPP(c_Product__Type_Oapfst(X3246,X3245,X3244,X3243),X3242)!=hAPP(c_Product__Type_Oapfst(X3246,X3245,X3244,X3241),X3242)|hAPP(X3241,hAPP(c_Product__Type_Ofst(X3246,X3244),X3242))=hAPP(X3243,hAPP(c_Product__Type_Ofst(X3246,X3244),X3242)))&(hAPP(X3241,hAPP(c_Product__Type_Ofst(X3246,X3244),X3242))!=hAPP(X3243,hAPP(c_Product__Type_Ofst(X3246,X3244),X3242))|hAPP(c_Product__Type_Oapfst(X3246,X3245,X3244,X3243),X3242)=hAPP(c_Product__Type_Oapfst(X3246,X3245,X3244,X3241),X3242))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_apfst__eq__conv])])). 4.46/4.69 fof(c_0_5191, plain, ![X3228, X3229, X3230, X3231]:c_Product__Type_Oapfst(X3231,X3230,X3229,X3228)=c_Product__Type_Omap__pair(X3231,X3230,X3229,X3229,X3228,c_Fun_Oid(X3229)), inference(variable_rename,[status(thm)],[fact_apfst__def])). 4.46/4.69 fof(c_0_5192, plain, ![X15595, X15596, X15597, X15598]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15597,X15598)),X15596),X15595))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X15597),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X15597),c_fNot),hAPP(hAPP(c_COMBS(X15597,X15598,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X15598,tc_fun(X15598,tc_HOL_Obool),X15597),c_fequal),X15596)),X15595))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X15597,X15598)),X15596),X15595))|(~class_Enum_Oenum(X15597)|~class_Orderings_Oorder(X15598)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15597,X15598)),X15596),X15595))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X15597,X15598)),X15596),X15595))|(~class_Enum_Oenum(X15597)|~class_Orderings_Oorder(X15598)))&(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X15597),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X15597),c_fNot),hAPP(hAPP(c_COMBS(X15597,X15598,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X15598,tc_fun(X15598,tc_HOL_Obool),X15597),c_fequal),X15596)),X15595))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X15597,X15598)),X15596),X15595))|(~class_Enum_Oenum(X15597)|~class_Orderings_Oorder(X15598))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__fun_I2_J])])])])). 4.46/4.69 fof(c_0_5193, plain, ![X4882, X4883, X4884, X4885]:(~class_Groups_Ocomm__monoid__add(X4885)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4885),X4884),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X4883)),hAPP(c_Nat_OSuc,X4882)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4885),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4885,tc_Nat_Onat),X4884),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X4883),X4882))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__Suc__ivl])])). 4.46/4.69 cnf(c_0_5194, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),X2),c_List_Oupt(X3,X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X3,X4)))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_4633])). 4.46/4.69 cnf(c_0_5195, plain, (hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X1,X2))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_4634])). 4.46/4.69 fof(c_0_5196, plain, ![X2152, X2153, X2154]:(((X2153=c_Groups_Ozero__class_Ozero(X2154)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2154),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2154),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2154),X2153),X2153)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2154),X2152),X2152))),c_Groups_Ozero__class_Ozero(X2154)))|~class_Rings_Olinordered__ring__strict(X2154))&(c_Groups_Ozero__class_Ozero(X2154)=X2152|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2154),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2154),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2154),X2153),X2153)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2154),X2152),X2152))),c_Groups_Ozero__class_Ozero(X2154)))|~class_Rings_Olinordered__ring__strict(X2154)))&(X2153!=c_Groups_Ozero__class_Ozero(X2154)|c_Groups_Ozero__class_Ozero(X2154)!=X2152|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2154),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2154),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2154),X2153),X2153)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2154),X2152),X2152))),c_Groups_Ozero__class_Ozero(X2154)))|~class_Rings_Olinordered__ring__strict(X2154))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff])])])). 4.46/4.69 cnf(c_0_5197, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(X2)))|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)|~class_Int_Oring__char__0(X1)), inference(split_conjunct,[status(thm)],[c_0_4635])). 4.46/4.69 fof(c_0_5198, plain, ![X14852, X14853, X14854, X14855]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk435_4(X14852,X14853,X14854,X14855)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X14854)))|(X14853=X14855|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X14855),X14854)!=X14853)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X14853),X14852))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14854)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk436_4(X14852,X14853,X14854,X14855)),X14852))|(X14853=X14855|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X14855),X14854)!=X14853)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X14853),X14852))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14854)))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk436_4(X14852,X14853,X14854,X14855)),esk435_4(X14852,X14853,X14854,X14855))=X14855|(X14853=X14855|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X14855),X14854)!=X14853)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X14853),X14852))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14854))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bset_I4_J])])])])])])). 4.46/4.69 fof(c_0_5199, plain, ![X6579, X6580]:(~c_Nat__Transfer_Onat__set(X6580)|(~c_Nat__Transfer_Onat__set(X6579)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X6580),X6579)=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X6580)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X6579))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J])])])). 4.46/4.69 fof(c_0_5200, plain, ![X11240, X11241, X11242, X11243, X11244]:hAPP(c_Set_Oimage(X11244,X11243,X11242),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11244,tc_HOL_Obool)),X11241),X11240))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11243,tc_HOL_Obool)),hAPP(c_Set_Oimage(X11244,X11243,X11242),X11241)),hAPP(c_Set_Oimage(X11244,X11243,X11242),X11240)), inference(variable_rename,[status(thm)],[fact_image__Un])). 4.46/4.69 fof(c_0_5201, plain, ![X12581, X12582, X12583, X12584, X12585, X12586]:hAPP(c_Set_Oimage(X12583,X12585,hAPP(hAPP(c_COMBB(X12586,X12585,X12583),X12584),X12582)),X12581)=hAPP(c_Set_Oimage(X12586,X12585,X12584),hAPP(c_Set_Oimage(X12583,X12586,X12582),X12581)), inference(variable_rename,[status(thm)],[fact_image__image])). 4.46/4.69 fof(c_0_5202, plain, ![X12196, X12197, X12198, X12199, X12200]:((c_List_Oconcat(X12197,X12196)!=c_List_Olist_ONil(X12197)|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X12197)),X12198),hAPP(c_List_Oset(tc_List_Olist(X12197)),X12196)))|X12198=c_List_Olist_ONil(X12197)))&((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X12200)),esk357_2(X12199,X12200)),hAPP(c_List_Oset(tc_List_Olist(X12200)),X12199)))|c_List_Oconcat(X12200,X12199)=c_List_Olist_ONil(X12200))&(esk357_2(X12199,X12200)!=c_List_Olist_ONil(X12200)|c_List_Oconcat(X12200,X12199)=c_List_Olist_ONil(X12200)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nil__eq__concat__conv])])])])])])])). 4.46/4.69 fof(c_0_5203, plain, ![X8909, X8910, X8911, X8912]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk257_4(X8909,X8910,X8911,X8912)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X8911)))|(X8912=X8910|X8910!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8912),X8911))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X8910),X8909))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8911)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk258_4(X8909,X8910,X8911,X8912)),X8909))|(X8912=X8910|X8910!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8912),X8911))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X8910),X8909))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8911)))&(X8912=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk258_4(X8909,X8910,X8911,X8912)),esk257_4(X8909,X8910,X8911,X8912))|(X8912=X8910|X8910!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8912),X8911))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X8910),X8909))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8911))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_aset_I4_J])])])])])])). 4.46/4.69 fof(c_0_5204, plain, ![X6623, X6624, X6626, X6627, X6628]:(((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6624)),esk195_2(X6623,X6624)),hAPP(c_List_Oset(tc_List_Olist(X6624)),X6623)))|c_List_Oconcat(X6624,X6623)=c_List_Olist_ONil(X6624))&(esk195_2(X6623,X6624)!=c_List_Olist_ONil(X6624)|c_List_Oconcat(X6624,X6623)=c_List_Olist_ONil(X6624)))&(c_List_Oconcat(X6627,X6626)!=c_List_Olist_ONil(X6627)|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6627)),X6628),hAPP(c_List_Oset(tc_List_Olist(X6627)),X6626)))|X6628=c_List_Olist_ONil(X6627)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_concat__eq__Nil__conv])])])])])])])). 4.46/4.69 cnf(c_0_5205, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1)))=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_4570])). 4.46/4.69 fof(c_0_5206, plain, ![X6461, X6462, X6463, X6464, X6465]:((X6463=X6464|X6462=X6461|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6465),X6464),X6461)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6465),X6463),X6462))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6465),X6464),X6462)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6465),X6463),X6461))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6465))&((X6463!=X6464|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6465),X6464),X6461)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6465),X6463),X6462))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6465),X6464),X6462)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6465),X6463),X6461))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6465))&(X6462!=X6461|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6465),X6464),X6461)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6465),X6463),X6462))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6465),X6464),X6462)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6465),X6463),X6461))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6465)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_crossproduct__noteq])])])])). 4.46/4.69 fof(c_0_5207, plain, ![X7939, X7940, X7941, X7942, X7943]:(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7943),X7940),X7942))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7943),X7942),X7941))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7943,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7943,X7942,X7941)),c_SetInterval_Oord__class_OatLeastAtMost(X7943,X7940,X7939)))|~class_Orderings_Oorder(X7943))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7943),X7941),X7939))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7943),X7942),X7941))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7943,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7943,X7942,X7941)),c_SetInterval_Oord__class_OatLeastAtMost(X7943,X7940,X7939)))|~class_Orderings_Oorder(X7943)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7943),X7941),X7939))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7943),X7940),X7942))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7943),X7942),X7941))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7943,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7943,X7942,X7941)),c_SetInterval_Oord__class_OatLeastAtMost(X7943,X7940,X7939)))|~class_Orderings_Oorder(X7943)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7943),X7940),X7939))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7943,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7943,X7942,X7941)),c_SetInterval_Oord__class_OatLeastAtMost(X7943,X7940,X7939)))|~class_Orderings_Oorder(X7943)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7943),X7942),X7941))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7943),X7940),X7939))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7943,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7943,X7942,X7941)),c_SetInterval_Oord__class_OatLeastAtMost(X7943,X7940,X7939)))|~class_Orderings_Oorder(X7943))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7943),X7941),X7939))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7943),X7940),X7942))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7943),X7941),X7939)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7943),X7940),X7939))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7943,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7943,X7942,X7941)),c_SetInterval_Oord__class_OatLeastAtMost(X7943,X7940,X7939)))|~class_Orderings_Oorder(X7943))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7943),X7940),X7942))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7943),X7940),X7942))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7943),X7941),X7939)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7943),X7940),X7939))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7943,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7943,X7942,X7941)),c_SetInterval_Oord__class_OatLeastAtMost(X7943,X7940,X7939)))|~class_Orderings_Oorder(X7943))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastatMost__psubset__iff])])])])). 4.46/4.69 fof(c_0_5208, plain, ![X13632, X13633, X13634]:(((X13633!=X13632|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13634),X13633),X13632))|~class_Orderings_Oorder(X13634))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13634),X13633),X13632))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13634),X13633),X13632))|~class_Orderings_Oorder(X13634)))&(X13633=X13632|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13634),X13633),X13632))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13634),X13633),X13632))|~class_Orderings_Oorder(X13634))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])])). 4.46/4.69 fof(c_0_5209, plain, ![X6075, X6076, X6077, X6078, X6079, X6080, X6081, X6082]:(((X6075=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6079),X6075))|(X6076!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6075),X6078)),X6079)|hBOOL(hAPP(X6077,X6078))))|~hBOOL(hAPP(X6077,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X6076),X6075))))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X6075|hBOOL(hAPP(X6077,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X6077,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X6076),X6075)))))&(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X6080|X6080!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X6082,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X6081),X6080))))&(~hBOOL(hAPP(X6082,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|X6080!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X6082,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X6081),X6080)))))&(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X6080|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk188_3(X6080,X6081,X6082)),X6080))|hBOOL(hAPP(X6082,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X6081),X6080))))&(~hBOOL(hAPP(X6082,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk188_3(X6080,X6081,X6082)),X6080))|hBOOL(hAPP(X6082,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X6081),X6080)))))&(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X6080|X6081=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6080),esk187_3(X6080,X6081,X6082))),esk188_3(X6080,X6081,X6082))|hBOOL(hAPP(X6082,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X6081),X6080))))&(~hBOOL(hAPP(X6082,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|X6081=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6080),esk187_3(X6080,X6081,X6082))),esk188_3(X6080,X6081,X6082))|hBOOL(hAPP(X6082,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X6081),X6080)))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X6080|~hBOOL(hAPP(X6082,esk187_3(X6080,X6081,X6082)))|hBOOL(hAPP(X6082,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X6081),X6080))))&(~hBOOL(hAPP(X6082,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X6082,esk187_3(X6080,X6081,X6082)))|hBOOL(hAPP(X6082,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X6081),X6080))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_split__div])])])])])])])). 4.46/4.69 fof(c_0_5210, plain, ![X10334, X10335, X10336, X10337]:(~class_Complete__Lattice_Ocomplete__lattice(X10337)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10336),X10335))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10336,X10337),X10335),X10334)=hAPP(hAPP(c_Finite__Set_Ofold(X10336,X10337,hAPP(hAPP(c_COMBB(X10337,tc_fun(X10337,X10337),X10336),c_Lattices_Osemilattice__inf__class_Oinf(X10337)),X10334)),c_Orderings_Otop__class_Otop(X10337)),X10335))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__fold__inf])])). 4.46/4.69 fof(c_0_5211, plain, ![X13988, X13989, X13990, X13991, X13992]:(~c_Hoare__Mirabelle_Ohoare__derivs(X13992,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X13992)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X13992),X13991),hAPP(c_Com_Ocom_OBODY,X13990)),X13989)),X13988),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X13992)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X13992),X13991),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X13990))),X13989)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X13992),tc_HOL_Obool))))|c_Hoare__Mirabelle_Ohoare__derivs(X13992,X13988,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X13992)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X13992),X13991),hAPP(c_Com_Ocom_OBODY,X13990)),X13989)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X13992),tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_BodyN])])). 4.46/4.69 fof(c_0_5212, plain, ![X10528, X10529, X10530]:(~class_Groups_Ocomm__monoid__add(X10530)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10530),X10529),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X10528)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10530),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10530),X10529),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X10528))),hAPP(X10529,X10528))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__lessThan__Suc])])). 4.46/4.69 cnf(c_0_5213, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X1))),X2)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_4636])). 4.46/4.69 fof(c_0_5214, plain, ![X2712, X2713, X2714, X2715]:((hAPP(hAPP(c_Map_Omap__of(X2715,X2714),X2713),X2712)!=c_Option_Ooption_ONone(X2714)|~hBOOL(hAPP(hAPP(c_member(X2715),X2712),hAPP(c_Set_Oimage(tc_prod(X2715,X2714),X2715,c_Product__Type_Ofst(X2715,X2714)),hAPP(c_List_Oset(tc_prod(X2715,X2714)),X2713)))))&(hBOOL(hAPP(hAPP(c_member(X2715),X2712),hAPP(c_Set_Oimage(tc_prod(X2715,X2714),X2715,c_Product__Type_Ofst(X2715,X2714)),hAPP(c_List_Oset(tc_prod(X2715,X2714)),X2713))))|hAPP(hAPP(c_Map_Omap__of(X2715,X2714),X2713),X2712)=c_Option_Ooption_ONone(X2714))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__eq__None__iff])])])). 4.46/4.69 fof(c_0_5215, plain, ![X7014, X7015, X7016]:(~class_Groups_Ocomm__monoid__add(X7016)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7016),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7016),X7015),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X7014))),hAPP(X7015,hAPP(c_Nat_OSuc,X7014)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7016),X7015),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X7014)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__atMost__Suc])])). 4.46/4.69 fof(c_0_5216, plain, ![X2077]:hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X2077)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2077), inference(variable_rename,[status(thm)],[fact_atLeast0AtMost])). 4.46/4.69 fof(c_0_5217, plain, ![X7216, X7217, X7218, X7219, X7220, X7221, X7222, X7223]:(~class_Groups_Ocomm__monoid__mult(X7223)|(~c_Fun_Oinj__on(X7222,X7221,X7220,X7219)|(hAPP(c_Set_Oimage(X7222,X7221,X7220),X7219)!=X7218|(hAPP(c_Fun_Ocomp(X7221,X7223,X7222,X7216),X7220)!=X7217|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7222,X7223),X7217),X7219)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7221,X7223),X7216),X7218))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__reindex__cong])])])). 4.46/4.69 fof(c_0_5218, plain, ![X7214, X7215]:(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7215))|hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X7215))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X7214)))))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__less])])). 4.46/4.69 fof(c_0_5219, plain, ![X1128, X1129, X1130, X1131]:(~class_Groups_Oab__group__add(X1131)|hAPP(c_Groups_Ouminus__class_Ouminus(X1131),hAPP(c_List_Omonoid__add__class_Olistsum(X1131),hAPP(hAPP(c_List_Omap(X1130,X1131),X1129),X1128)))=hAPP(c_List_Omonoid__add__class_Olistsum(X1131),hAPP(hAPP(c_List_Omap(X1130,X1131),hAPP(c_Fun_Ocomp(X1131,X1131,X1130,c_Groups_Ouminus__class_Ouminus(X1131)),X1129)),X1128))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_uminus__listsum__map])])])). 4.46/4.69 fof(c_0_5220, plain, ![X7603, X7604, X7605, X7606, X7607, X7608]:hAPP(hAPP(c_List_Omap(X7608,X7607),X7606),hAPP(hAPP(c_List_Omap(X7605,X7608),X7604),X7603))=hAPP(hAPP(c_List_Omap(X7605,X7607),hAPP(c_Fun_Ocomp(X7608,X7607,X7605,X7606),X7604)),X7603), inference(variable_rename,[status(thm)],[fact_map__map])). 4.46/4.69 cnf(c_0_5221, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)))), inference(split_conjunct,[status(thm)],[c_0_4599])). 4.46/4.69 fof(c_0_5222, plain, ![X3524, X3525, X3526, X3528, X3529]:((((hBOOL(hAPP(hAPP(c_member(X3526),esk92_3(X3524,X3525,X3526)),X3525))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3526,tc_Nat_Onat),X3524),X3525)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3526),X3525)))&(~hBOOL(hAPP(hAPP(c_member(X3526),X3528),X3525))|(X3528=esk92_3(X3524,X3525,X3526)|hAPP(X3524,X3528)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3526,tc_Nat_Onat),X3524),X3525)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3526),X3525))))&(hAPP(X3524,esk92_3(X3524,X3525,X3526))=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3526,tc_Nat_Onat),X3524),X3525)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3526),X3525))))&((hBOOL(hAPP(hAPP(c_member(X3526),esk93_4(X3524,X3525,X3526,X3529)),X3525))|~hBOOL(hAPP(hAPP(c_member(X3526),X3529),X3525))|hAPP(X3524,X3529)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3526,tc_Nat_Onat),X3524),X3525)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3526),X3525)))&((esk93_4(X3524,X3525,X3526,X3529)!=X3529|~hBOOL(hAPP(hAPP(c_member(X3526),X3529),X3525))|hAPP(X3524,X3529)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3526,tc_Nat_Onat),X3524),X3525)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3526),X3525)))&(hAPP(X3524,esk93_4(X3524,X3525,X3526,X3529))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X3526),X3529),X3525))|hAPP(X3524,X3529)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3526,tc_Nat_Onat),X3524),X3525)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3526),X3525)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__eq__Suc0__iff])])])])])])). 4.46/4.69 cnf(c_0_5223, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)))), inference(split_conjunct,[status(thm)],[c_0_4600])). 4.46/4.69 cnf(c_0_5224, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2)))), inference(split_conjunct,[status(thm)],[c_0_4601])). 4.46/4.69 cnf(c_0_5225, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2)))), inference(split_conjunct,[status(thm)],[c_0_4602])). 4.46/4.69 fof(c_0_5226, plain, ![X2441, X2442, X2443, X2444]:(~class_Complete__Lattice_Ocomplete__lattice(X2444)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2443),X2442))|hAPP(hAPP(c_Finite__Set_Ofold(X2443,X2444,hAPP(hAPP(c_COMBB(X2444,tc_fun(X2444,X2444),X2443),c_Lattices_Osemilattice__sup__class_Osup(X2444)),X2441)),c_Orderings_Obot__class_Obot(X2444)),X2442)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2443,X2444),X2442),X2441))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUPR__fold__sup])])])). 4.46/4.69 fof(c_0_5227, plain, ![X16936, X16937, X16938]:(~hBOOL(hAPP(c_List_Odistinct(X16938),X16937))|hAPP(c_List_Ofilter(X16938,hAPP(hAPP(c_COMBC(X16938,tc_fun(X16938,tc_HOL_Obool),tc_HOL_Obool),c_member(X16938)),hAPP(c_List_Oset(X16938),c_List_Osublist(X16938,X16937,X16936)))),X16937)=c_List_Osublist(X16938,X16937,X16936)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__in__sublist])])])). 4.46/4.69 fof(c_0_5228, plain, ![X17471, X17472]:(X17472=c_List_Olist_ONil(X17471)|(~hBOOL(hAPP(c_List_Odistinct(X17471),X17472))|c_List_Obutlast(X17471,X17472)=c_List_OtakeWhile(X17471,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X17471),c_fNot),hAPP(hAPP(c_COMBC(X17471,X17471,tc_HOL_Obool),c_fequal),c_List_Olast(X17471,X17472))),X17472))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile__not__last])])])). 4.46/4.69 fof(c_0_5229, plain, ![X10330, X10331, X10332, X10333]:(((hBOOL(hAPP(X10332,X10331))|c_List_Olist__ex1(X10333,X10332,X10330)|~c_List_Olist__ex1(X10333,X10332,hAPP(hAPP(c_List_Olist_OCons(X10333),X10331),X10330)))&(~hBOOL(hAPP(X10332,X10331))|c_List_Olist__all(X10333,hAPP(hAPP(c_COMBS(X10333,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10333),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10333),c_fNot),X10332))),hAPP(c_fequal,X10331)),X10330)|~c_List_Olist__ex1(X10333,X10332,hAPP(hAPP(c_List_Olist_OCons(X10333),X10331),X10330))))&(((hBOOL(hAPP(X10332,X10331))|~hBOOL(hAPP(X10332,X10331))|c_List_Olist__ex1(X10333,X10332,hAPP(hAPP(c_List_Olist_OCons(X10333),X10331),X10330)))&(~c_List_Olist__all(X10333,hAPP(hAPP(c_COMBS(X10333,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10333),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10333),c_fNot),X10332))),hAPP(c_fequal,X10331)),X10330)|~hBOOL(hAPP(X10332,X10331))|c_List_Olist__ex1(X10333,X10332,hAPP(hAPP(c_List_Olist_OCons(X10333),X10331),X10330))))&((hBOOL(hAPP(X10332,X10331))|~c_List_Olist__ex1(X10333,X10332,X10330)|c_List_Olist__ex1(X10333,X10332,hAPP(hAPP(c_List_Olist_OCons(X10333),X10331),X10330)))&(~c_List_Olist__all(X10333,hAPP(hAPP(c_COMBS(X10333,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10333),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10333),c_fNot),X10332))),hAPP(c_fequal,X10331)),X10330)|~c_List_Olist__ex1(X10333,X10332,X10330)|c_List_Olist__ex1(X10333,X10332,hAPP(hAPP(c_List_Olist_OCons(X10333),X10331),X10330)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__ex1__simps_I2_J])])])])). 4.46/4.69 cnf(c_0_5230, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2)),hAPP(c_Set_OCollect(X1),X3))=hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_4637])). 4.46/4.69 cnf(c_0_5231, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_4628])). 4.46/4.69 fof(c_0_5232, plain, ![X12587, X12588]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X12588))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X12587))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12588),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12588),X12587))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_n__less__n__mult__m])])])). 4.46/4.69 fof(c_0_5233, plain, ![X1564, X1565]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1565))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1564))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1565),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1564),X1565))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_n__less__m__mult__n])])])). 4.46/4.69 cnf(c_0_5234, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_4629])). 4.46/4.69 cnf(c_0_5235, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OBit1(c_Int_OPls)))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_4631])). 4.46/4.69 cnf(c_0_5236, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OBit1(c_Int_OPls)))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_4632])). 4.46/4.69 cnf(c_0_5237, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4638])). 4.46/4.69 cnf(c_0_5238, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_4639])). 4.46/4.69 cnf(c_0_5239, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4640])). 4.46/4.69 cnf(c_0_5240, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_4641])). 4.46/4.69 cnf(c_0_5241, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4642])). 4.46/4.69 fof(c_0_5242, plain, ![X12514, X12515, X12516, X12519, X12520, X12521, X12522, X12523]:((((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X12514|X12514=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X12516,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12515,X12514))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk370_3(X12514,X12515,X12516)),X12514))|X12514=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X12516,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12515,X12514))))&((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12514),esk369_3(X12514,X12515,X12516))),esk370_3(X12514,X12515,X12516))=X12515|X12514=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X12516,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12515,X12514))))&(~hBOOL(hAPP(X12516,esk370_3(X12514,X12515,X12516)))|X12514=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X12516,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12515,X12514)))))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X12514|~hBOOL(hAPP(X12516,X12515))|hBOOL(hAPP(X12516,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12515,X12514))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk370_3(X12514,X12515,X12516)),X12514))|~hBOOL(hAPP(X12516,X12515))|hBOOL(hAPP(X12516,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12515,X12514))))&((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12514),esk369_3(X12514,X12515,X12516))),esk370_3(X12514,X12515,X12516))=X12515|~hBOOL(hAPP(X12516,X12515))|hBOOL(hAPP(X12516,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12515,X12514))))&(~hBOOL(hAPP(X12516,esk370_3(X12514,X12515,X12516)))|~hBOOL(hAPP(X12516,X12515))|hBOOL(hAPP(X12516,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12515,X12514))))))))&((X12519!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X12521,X12520))|~hBOOL(hAPP(X12521,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12520,X12519))))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X12519|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12523),X12519))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12519),X12522)),X12523)!=X12520|hBOOL(hAPP(X12521,X12523))))|~hBOOL(hAPP(X12521,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12520,X12519)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_split__mod])])])])])])])). 4.46/4.69 cnf(c_0_5243, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_4643])). 4.46/4.69 cnf(c_0_5244, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X1))), inference(split_conjunct,[status(thm)],[c_0_4644])). 4.46/4.69 cnf(c_0_5245, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))), inference(split_conjunct,[status(thm)],[c_0_4645])). 4.46/4.69 cnf(c_0_5246, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))), inference(split_conjunct,[status(thm)],[c_0_4646])). 4.46/4.69 cnf(c_0_5247, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))), inference(split_conjunct,[status(thm)],[c_0_4647])). 4.46/4.69 cnf(c_0_5248, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))), inference(split_conjunct,[status(thm)],[c_0_4648])). 4.46/4.69 fof(c_0_5249, plain, ![X5984, X5985, X5986, X5987]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X5987,X5987)),hAPP(hAPP(c_Product__Type_OPair(X5987,X5987),X5986),X5985)),c_Transitive__Closure_Otrancl(X5987,X5984)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X5987,X5987)),hAPP(hAPP(c_Product__Type_OPair(X5987,X5987),X5986),X5985)),c_Transitive__Closure_Ortrancl(X5987,X5984)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__into__rtrancl])])])). 4.46/4.69 fof(c_0_5250, plain, ![X886, X887]:((c_Divides_Odiv__class_Omod(tc_Int_Oint,X886,X887)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X886),X887))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X886),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X887))|X887=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X886,X887)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X886),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X887))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X886),X887))),c_Groups_Oone__class_Oone(tc_Int_Oint))|X887=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zminus2__eq__if])])])). 4.46/4.69 cnf(c_0_5251, plain, (X1=c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3)|c_List_Oupt(X2,X3)!=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X4),X1)), inference(split_conjunct,[status(thm)],[c_0_4649])). 4.46/4.69 fof(c_0_5252, plain, ![X6501, X6502, X6503, X6504, X6505]:(~c_Fun_Oinj__on(X6505,X6504,X6503,c_Orderings_Otop__class_Otop(tc_fun(X6505,tc_HOL_Obool)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6504,tc_HOL_Obool)),X6502),hAPP(c_Set_Oimage(X6505,X6504,X6503),X6501)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6505,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X6505,X6504,X6503),X6502)),X6501)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_vimage__subsetI])])])). 4.46/4.69 fof(c_0_5253, plain, ![X16997, X16998, X16999, X17000, X17001]:(c_Orderings_Otop__class_Otop(tc_fun(X17000,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X17001,X17000,X16999),c_Orderings_Otop__class_Otop(tc_fun(X17001,tc_HOL_Obool)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17001,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X17001,X17000,X16999),X16998)),X16997))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17000,tc_HOL_Obool)),X16998),hAPP(c_Set_Oimage(X17001,X17000,X16999),X16997))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_vimage__subsetD])])])). 4.46/4.69 fof(c_0_5254, plain, ![X14353, X14354, X14355, X14356, X14357]:(hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14357),tc_List_Olist(X14357)),X14354),X14353)!=c_List_Opartition(X14357,X14356,X14355)|hAPP(c_List_Oset(X14357),X14355)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14357,tc_HOL_Obool)),hAPP(c_List_Oset(X14357),X14354)),hAPP(c_List_Oset(X14357),X14353))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_partition__set])])). 4.46/4.69 fof(c_0_5255, plain, ![X4952, X4953, X4954]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4954),X4953))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4954),X4952))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4953),X4954)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4952),X4954))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4953),X4952))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq])])). 4.46/4.69 fof(c_0_5256, plain, ![X3274, X3275, X3276, X3277, X3278, X3279, X3280, X3282, X3283, X3284, X3285, X3286, X3287, X3288, X3289]:(((hAPP(X3276,X3275)=hAPP(c_Option_Ooption_OSome(X3280),esk87_7(X3274,X3275,X3276,X3277,X3278,X3279,X3280))|c_Map_Omap__comp(X3280,X3279,X3278,X3277,X3276,X3275)!=hAPP(c_Option_Ooption_OSome(X3279),X3274))&(hAPP(X3277,esk87_7(X3274,X3275,X3276,X3277,X3278,X3279,X3280))=hAPP(c_Option_Ooption_OSome(X3279),X3274)|c_Map_Omap__comp(X3280,X3279,X3278,X3277,X3276,X3275)!=hAPP(c_Option_Ooption_OSome(X3279),X3274)))&(hAPP(X3284,X3283)!=hAPP(c_Option_Ooption_OSome(X3288),X3289)|hAPP(X3285,X3289)!=hAPP(c_Option_Ooption_OSome(X3287),X3282)|c_Map_Omap__comp(X3288,X3287,X3286,X3285,X3284,X3283)=hAPP(c_Option_Ooption_OSome(X3287),X3282))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__comp__Some__iff])])])])])])). 4.46/4.69 fof(c_0_5257, plain, ![X7242, X7243, X7244, X7245, X7246, X7247]:hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X7246),X7247,c_Option_Ooption_ONone(X7246),X7244),hAPP(X7243,X7242))=c_Map_Omap__comp(X7247,X7246,X7245,X7244,X7243,X7242), inference(variable_rename,[status(thm)],[fact_map__comp__def])). 4.46/4.69 fof(c_0_5258, plain, ![X15771, X15772]:(~class_Groups_Omonoid__add(X15772)|hAPP(c_List_Ofoldl(X15772,X15772,c_Groups_Oplus__class_Oplus(X15772),c_Groups_Ozero__class_Ozero(X15772)),X15771)=c_List_Ofoldr(X15772,X15772,c_Groups_Oplus__class_Oplus(X15772),X15771,c_Groups_Ozero__class_Ozero(X15772))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__foldr1])])). 4.46/4.69 fof(c_0_5259, plain, ![X5612, X5613, X5614, X5615, X5616, X5618]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5613,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5614,X5613,esk170_4(X5612,X5613,X5614,X5615)),X5615)),X5612))|X5615!=hAPP(c_Set_Oimage(X5613,X5614,X5616),X5612)|c_Orderings_Obot__class_Obot(tc_fun(X5614,tc_HOL_Obool))=X5615)&(c_Fun_Oinj__on(X5614,X5613,esk170_4(X5612,X5613,X5614,X5615),X5615)|X5615!=hAPP(c_Set_Oimage(X5613,X5614,X5616),X5612)|c_Orderings_Obot__class_Obot(tc_fun(X5614,tc_HOL_Obool))=X5615))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5613,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5614,X5613,X5618),X5615)),X5612))|~c_Fun_Oinj__on(X5614,X5613,X5618,X5615)|X5615=hAPP(c_Set_Oimage(X5613,X5614,esk171_4(X5612,X5613,X5614,X5615)),X5612)|c_Orderings_Obot__class_Obot(tc_fun(X5614,tc_HOL_Obool))=X5615)), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__surj])])])])])). 4.46/4.69 fof(c_0_5260, plain, ![X7381, X7382]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk214_2(X7381,X7382)),hAPP(X7382,esk214_2(X7381,X7382))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X7382)),X7381))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__less__ub])])])). 4.46/4.69 fof(c_0_5261, plain, ![X3913, X3914, X3917, X3918, X3919, X3920]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X3914),X3913))|X3913=hAPP(c_Set_Oimage(tc_Nat_Onat,X3914,esk103_2(X3913,X3914)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),esk102_2(X3913,X3914)))))&(X3917!=hAPP(c_Set_Oimage(tc_Nat_Onat,X3918,X3920),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X3919)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X3918),X3917)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__conv__nat__seg__image])])])])])). 4.46/4.69 cnf(c_0_5262, plain, (hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4650])). 4.46/4.69 cnf(c_0_5263, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4651]), ['final']). 4.46/4.69 fof(c_0_5264, plain, ![X14388, X14389]:(((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X14388)))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14389),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14388))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14389)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X14389))))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X14388)))|hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X14389),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X14388)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14389),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14388))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X14389)))))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X14389)))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14389),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14388))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__nat__number__of])])])])). 4.46/4.69 cnf(c_0_5265, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X1,X1),X2)),c_Transitive__Closure_Ortrancl(X1,X2))!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),c_Transitive__Closure_Otrancl(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_4652])). 4.46/4.69 cnf(c_0_5266, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))=c_Transitive__Closure_Otrancl(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4653])). 4.46/4.69 fof(c_0_5267, plain, ![X900, X901, X902]:((~hBOOL(hAPP(X902,X901))|hAPP(hAPP(c_Set_Oinsert(X900),X901),c_Orderings_Obot__class_Obot(tc_fun(X900,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X900),hAPP(hAPP(c_COMBS(X900,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X900),c_fconj),hAPP(hAPP(c_COMBC(X900,X900,tc_HOL_Obool),c_fequal),X901))),X902)))&(hBOOL(hAPP(X902,X901))|c_Orderings_Obot__class_Obot(tc_fun(X900,tc_HOL_Obool))=hAPP(c_Set_OCollect(X900),hAPP(hAPP(c_COMBS(X900,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X900),c_fconj),hAPP(hAPP(c_COMBC(X900,X900,tc_HOL_Obool),c_fequal),X901))),X902)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Collect__conv__if])])])). 4.46/4.69 fof(c_0_5268, plain, ![X3934, X3935, X3936, X3937]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3937,tc_HOL_Obool)),X3936),X3935))|(~hBOOL(hAPP(hAPP(c_member(X3937),X3934),X3936))|hBOOL(hAPP(hAPP(c_member(X3937),X3934),X3935)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__mp])])])). 4.46/4.69 fof(c_0_5269, plain, ![X17463, X17464, X17465, X17466]:((c_Orderings_Obot__class_Obot(tc_fun(X17465,tc_HOL_Obool))=X17466|hAPP(c_Set_Oimage(tc_prod(X17465,X17464),X17464,c_Product__Type_Osnd(X17465,X17464)),hAPP(hAPP(c_Product__Type_OSigma(X17465,X17464),X17466),hAPP(c_COMBK(tc_fun(X17464,tc_HOL_Obool),X17465),X17463)))=X17463)&(c_Orderings_Obot__class_Obot(tc_fun(X17465,tc_HOL_Obool))!=X17466|hAPP(c_Set_Oimage(tc_prod(X17465,X17464),X17464,c_Product__Type_Osnd(X17465,X17464)),hAPP(hAPP(c_Product__Type_OSigma(X17465,X17464),X17466),hAPP(c_COMBK(tc_fun(X17464,tc_HOL_Obool),X17465),X17463)))=c_Orderings_Obot__class_Obot(tc_fun(X17464,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_snd__image__times])])])). 4.46/4.69 fof(c_0_5270, plain, ![X15759, X15760, X15761, X15762]:((X15762=c_Orderings_Obot__class_Obot(tc_fun(X15761,tc_HOL_Obool))|hAPP(c_Set_Oimage(tc_prod(X15760,X15761),X15760,c_Product__Type_Ofst(X15760,X15761)),hAPP(hAPP(c_Product__Type_OSigma(X15760,X15761),X15759),hAPP(c_COMBK(tc_fun(X15761,tc_HOL_Obool),X15760),X15762)))=X15759)&(c_Orderings_Obot__class_Obot(tc_fun(X15761,tc_HOL_Obool))!=X15762|hAPP(c_Set_Oimage(tc_prod(X15760,X15761),X15760,c_Product__Type_Ofst(X15760,X15761)),hAPP(hAPP(c_Product__Type_OSigma(X15760,X15761),X15759),hAPP(c_COMBK(tc_fun(X15761,tc_HOL_Obool),X15760),X15762)))=c_Orderings_Obot__class_Obot(tc_fun(X15760,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fst__image__times])])])). 4.46/4.69 fof(c_0_5271, plain, ![X5452, X5453]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X5453))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X5452))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5452),X5453))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__mult])])). 4.46/4.69 fof(c_0_5272, plain, ![X790, X791]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X790))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X791))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X791),X790))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X790))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X791),X790))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X791))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X791),X790)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff])])])). 4.46/4.69 fof(c_0_5273, plain, ![X3235, X3236, X3237, X3238]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3238)),X3237)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3236)),X3235)|(~hBOOL(hAPP(c_List_Odistinct(X3238),X3237))|c_Map_Odom(X3238,X3236,hAPP(c_Map_Omap__of(X3238,X3236),hAPP(hAPP(c_List_Ozip(X3238,X3236),X3237),X3235)))=hAPP(c_List_Oset(X3238),X3237))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__map__of__zip])])). 4.46/4.69 cnf(c_0_5274, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))=c_Map_Odom(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4654])). 4.46/4.69 cnf(c_0_5275, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),X3)=hAPP(c_Relation_ODomain(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_4655]), ['final']). 4.46/4.69 fof(c_0_5276, plain, ![X2174, X2175]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2175),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2175))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2174)))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2175),X2174))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib__neg])])). 4.46/4.69 fof(c_0_5277, plain, ![X12301]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12301),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_mult__0__right])). 4.46/4.69 fof(c_0_5278, plain, ![X11738]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11738),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X11738, inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right])). 4.46/4.69 fof(c_0_5279, plain, ![X714, X715]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X715)))|hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X715)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X714)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X715)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X714)))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X715)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X715)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X714)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__nat__number__of])])])). 4.46/4.69 cnf(c_0_5280, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)))), inference(split_conjunct,[status(thm)],[c_0_4618])). 4.46/4.69 cnf(c_0_5281, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)))), inference(split_conjunct,[status(thm)],[c_0_4619])). 4.46/4.69 cnf(c_0_5282, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)))), inference(split_conjunct,[status(thm)],[c_0_4620])). 4.46/4.69 cnf(c_0_5283, plain, (X2=X1|c_Int_OBit0(X1)!=c_Int_OBit0(X2)), inference(split_conjunct,[status(thm)],[c_0_4656])). 4.46/4.69 fof(c_0_5284, plain, ![X6426, X6427, X6428, X6429, X6430, X6431, X6432]:((c_List_Olist_ONil(X6428)!=c_List_OdropWhile(X6428,X6427,X6426)|(~hBOOL(hAPP(hAPP(c_member(X6428),X6429),hAPP(c_List_Oset(X6428),X6426)))|hBOOL(hAPP(X6427,X6429))))&((hBOOL(hAPP(hAPP(c_member(X6432),esk193_3(X6430,X6431,X6432)),hAPP(c_List_Oset(X6432),X6430)))|c_List_Olist_ONil(X6432)=c_List_OdropWhile(X6432,X6431,X6430))&(~hBOOL(hAPP(X6431,esk193_3(X6430,X6431,X6432)))|c_List_Olist_ONil(X6432)=c_List_OdropWhile(X6432,X6431,X6430)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dropWhile__eq__Nil__conv])])])])])])). 4.46/4.69 fof(c_0_5285, plain, ![X14238, X14239, X14240]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X14240,X14240)),X14239),X14238))|hBOOL(hAPP(hAPP(c_member(tc_prod(X14240,X14240)),X14239),c_Transitive__Closure_Otrancl(X14240,X14238)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__trancl_H])])). 4.46/4.69 fof(c_0_5286, plain, ![X17326, X17327, X17328, X17329, X17330, X17331, X17333, X17334, X17335, X17336, X17337, X17338, X17339]:(((hAPP(c_Option_Ooption_OSome(X17331),esk519_6(X17326,X17327,X17328,X17329,X17330,X17331))=hAPP(X17327,X17326)|c_Option_Ooption_ONone(X17331)=hAPP(X17327,X17326)|c_Option_Ooption_ONone(X17330)!=c_Map_Omap__comp(X17331,X17330,X17329,X17328,X17327,X17326))&(c_Option_Ooption_ONone(X17330)=hAPP(X17328,esk519_6(X17326,X17327,X17328,X17329,X17330,X17331))|c_Option_Ooption_ONone(X17331)=hAPP(X17327,X17326)|c_Option_Ooption_ONone(X17330)!=c_Map_Omap__comp(X17331,X17330,X17329,X17328,X17327,X17326)))&((c_Option_Ooption_ONone(X17338)!=hAPP(X17334,X17333)|c_Option_Ooption_ONone(X17337)=c_Map_Omap__comp(X17338,X17337,X17336,X17335,X17334,X17333))&(hAPP(c_Option_Ooption_OSome(X17338),X17339)!=hAPP(X17334,X17333)|c_Option_Ooption_ONone(X17337)!=hAPP(X17335,X17339)|c_Option_Ooption_ONone(X17337)=c_Map_Omap__comp(X17338,X17337,X17336,X17335,X17334,X17333)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__comp__None__iff])])])])])])). 4.46/4.69 fof(c_0_5287, plain, ![X14596, X14597, X14598]:(~class_Groups_Oab__semigroup__add(X14598)|c_List_Ofoldr(X14598,X14598,c_Groups_Oplus__class_Oplus(X14598),X14597,X14596)=hAPP(c_List_Ofoldl(X14598,X14598,c_Groups_Oplus__class_Oplus(X14598),X14596),X14597)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_foldr__conv__foldl])])])). 4.46/4.69 cnf(c_0_5288, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X1)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))), inference(split_conjunct,[status(thm)],[c_0_4657])). 4.46/4.69 fof(c_0_5289, plain, ![X9559, X9560]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9560),X9559))|c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X9560,X9559))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9560),X9559))|c_List_Oupt(X9560,X9559)=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X9560),c_List_Oupt(hAPP(c_Nat_OSuc,X9560),X9559)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_upt__rec])])])). 4.46/4.69 fof(c_0_5290, plain, ![X5289]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5289)))|c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5289))=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5289)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__1__number__of])])). 4.46/4.69 fof(c_0_5291, plain, ![X10619, X10620, X10621]:(~class_Groups_Ocomm__monoid__add(X10621)|(c_Groups_Ozero__class_Ozero(X10621)!=hAPP(X10620,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10621),X10620),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10619))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10621),X10620),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X10619)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__shift__lb__Suc0__0__upt])])])). 4.46/4.69 fof(c_0_5292, plain, ![X12329]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X12329)))|hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X12329)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X12329))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos__1__number__of])])). 4.46/4.69 fof(c_0_5293, plain, ![X15903, X15904]:((~c_Wellfounded_Oacyclic(X15904,hAPP(c_Set_OCollect(tc_prod(X15904,X15904)),hAPP(c_Product__Type_Oprod_Oprod__case(X15904,X15904,tc_HOL_Obool),X15903)))|c_Wellfounded_Oacyclic(X15904,hAPP(c_Set_OCollect(tc_prod(X15904,X15904)),hAPP(c_Product__Type_Oprod_Oprod__case(X15904,X15904,tc_HOL_Obool),c_Predicate_Oconversep(X15904,X15904,X15903)))))&(~c_Wellfounded_Oacyclic(X15904,hAPP(c_Set_OCollect(tc_prod(X15904,X15904)),hAPP(c_Product__Type_Oprod_Oprod__case(X15904,X15904,tc_HOL_Obool),c_Predicate_Oconversep(X15904,X15904,X15903))))|c_Wellfounded_Oacyclic(X15904,hAPP(c_Set_OCollect(tc_prod(X15904,X15904)),hAPP(c_Product__Type_Oprod_Oprod__case(X15904,X15904,tc_HOL_Obool),X15903))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclicP__converse])])). 4.46/4.69 fof(c_0_5294, plain, ![X2082, X2083, X2084, X2085]:(X2084!=X2085|(~hBOOL(hAPP(hAPP(c_member(X2083),X2085),X2082))|hBOOL(hAPP(hAPP(c_member(tc_prod(X2083,X2083)),hAPP(hAPP(c_Product__Type_OPair(X2083,X2083),X2085),X2084)),c_Relation_OId__on(X2083,X2082))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Id__on__eqI])])])). 4.46/4.69 fof(c_0_5295, plain, ![X6256, X6257]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(X6257,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X6257),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6256))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X6257),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6256))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0])])). 4.46/4.69 fof(c_0_5296, plain, ![X14328, X14329]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X14329,X14329)),X14328),c_Relation_OId(X14329)))|hAPP(hAPP(c_Product__Type_OPair(X14329,X14329),esk422_2(X14328,X14329)),esk422_2(X14328,X14329))=X14328), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_IdE])])])])). 4.46/4.69 fof(c_0_5297, plain, ![X4079, X4080]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4079),c_Int_OPls))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4080)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4080)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4079))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4080),c_Int_OPls)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4079),c_Int_OPls))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4080),X4079))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4080)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4079))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4080),c_Int_OPls))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4080),c_Int_OPls))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4080)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4079))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4079))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__nat__number__of])])])])). 4.46/4.69 cnf(c_0_5298, plain, (X2=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls)))|~class_Int_Onumber__ring(X1)|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_4658])). 4.46/4.69 fof(c_0_5299, plain, ![X7923, X7924, X7925, X7926, X7927]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7927,tc_HOL_Obool)),X7926),X7925))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7924,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X7924,X7927,X7923),X7926)),hAPP(c_Set_Ovimage(X7924,X7927,X7923),X7925)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__mono])])). 4.46/4.69 fof(c_0_5300, plain, ![X1666, X1667, X1668]:(~class_Orderings_Olinorder(X1668)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1668),X1667),X1666))|c_SetInterval_Oord__class_OatLeastAtMost(X1668,X1667,X1666)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1668,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1668,X1667),X1666)),hAPP(hAPP(c_Set_Oinsert(X1668),X1666),c_Orderings_Obot__class_Obot(tc_fun(X1668,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I6_J])])])). 4.46/4.69 fof(c_0_5301, plain, ![X8943, X8944, X8945, X8946]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8946,tc_HOL_Obool)),X8945),hAPP(hAPP(c_Set_Oinsert(X8946),X8944),X8943))=hAPP(hAPP(c_Set_Oinsert(X8946),X8944),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8946,tc_HOL_Obool)),X8945),X8943)), inference(variable_rename,[status(thm)],[fact_Un__insert__right])). 4.46/4.69 fof(c_0_5302, plain, ![X4531, X4532]:X4531=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4532,tc_HOL_Obool)),X4531),c_Orderings_Obot__class_Obot(tc_fun(X4532,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Un__empty__right])). 4.46/4.69 fof(c_0_5303, plain, ![X8413, X8414]:(((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8414)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8413)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8413)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8414))&((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8413)))|X8413=X8414|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8414)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8413)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8414))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8413)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8414)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8414)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8413)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8414))))&(((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8414)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8414)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8413)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8414))&(((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8413)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8413)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8414)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8413)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8414))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8414)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8413)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8414)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8413)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8414)))&((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8413)))|X8413!=X8414|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8414)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8413)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8414))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8414)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X8413!=X8414|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8414)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8413)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8414)))))&((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8414)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8413)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8413)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8414))&(((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8413)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8413)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8413)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8413)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8414))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8414)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8413)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8413)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8413)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8414)))&((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8413)))|X8413!=X8414|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8413)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8413)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8414))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8414)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X8413!=X8414|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8413)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8413)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8414))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__nat__number__of])])])])). 4.46/4.69 fof(c_0_5304, plain, ![X2914, X2915, X2916, X2917, X2918]:((X2915!=hAPP(hAPP(c_List_Omap(tc_prod(X2918,X2916),X2916),c_Product__Type_Osnd(X2918,X2916)),X2914)|X2917!=hAPP(hAPP(c_List_Omap(tc_prod(X2918,X2916),X2918),c_Product__Type_Ofst(X2918,X2916)),X2914)|X2914=hAPP(hAPP(c_List_Ozip(X2918,X2916),X2917),X2915)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2916)),X2915)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2918)),X2917))&((X2915=hAPP(hAPP(c_List_Omap(tc_prod(X2918,X2916),X2916),c_Product__Type_Osnd(X2918,X2916)),X2914)|X2914!=hAPP(hAPP(c_List_Ozip(X2918,X2916),X2917),X2915)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2916)),X2915)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2918)),X2917))&(X2917=hAPP(hAPP(c_List_Omap(tc_prod(X2918,X2916),X2918),c_Product__Type_Ofst(X2918,X2916)),X2914)|X2914!=hAPP(hAPP(c_List_Ozip(X2918,X2916),X2917),X2915)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2916)),X2915)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2918)),X2917)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__eq__conv])])])). 4.46/4.69 fof(c_0_5305, plain, ![X12500, X12501, X12502]:(~class_Orderings_Olinorder(X12502)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12502),X12501),X12500))|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X12502,X12501),X12500)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12502,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X12502),X12501),c_Orderings_Obot__class_Obot(tc_fun(X12502,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X12502,X12501,X12500)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I3_J])])). 4.46/4.69 fof(c_0_5306, plain, ![X15304, X15305, X15306, X15307]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15307,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X15307),X15306),X15305)),X15304)=hAPP(hAPP(c_Set_Oinsert(X15307),X15306),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15307,tc_HOL_Obool)),X15305),X15304)), inference(variable_rename,[status(thm)],[fact_Un__insert__left])). 4.46/4.69 fof(c_0_5307, plain, ![X14794, X14795]:X14794=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14795,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X14795,tc_HOL_Obool))),X14794), inference(variable_rename,[status(thm)],[fact_Un__empty__left])). 4.46/4.69 fof(c_0_5308, plain, ![X10000, X10001, X10002]:(~class_Orderings_Olinorder(X10002)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10002),X10001),X10000))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10002,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10002),X10001),c_Orderings_Obot__class_Obot(tc_fun(X10002,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X10002,X10001,X10000))=c_SetInterval_Oord__class_OatLeastAtMost(X10002,X10001,X10000))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I5_J])])])). 4.46/4.69 fof(c_0_5309, plain, ![X3618, X3619, X3620, X3621]:(~c_Fun_Oinj__on(X3621,X3620,X3619,c_Complete__Lattice_OSup__class_OSup(tc_fun(X3621,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X3621),tc_fun(X3621,tc_HOL_Obool),c_List_Oset(X3621)),X3618)))|c_Fun_Oinj__on(tc_List_Olist(X3621),tc_List_Olist(X3620),hAPP(c_List_Omap(X3621,X3620),X3619),X3618)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__mapI])])])). 4.46/4.69 fof(c_0_5310, plain, ![X6449, X6450, X6451, X6452]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6451,tc_fun(X6452,tc_HOL_Obool)),X6449),X6450)=c_Complete__Lattice_OSup__class_OSup(tc_fun(X6452,tc_HOL_Obool),hAPP(c_Set_Oimage(X6451,tc_fun(X6452,tc_HOL_Obool),X6450),X6449)), inference(variable_rename,[status(thm)],[fact_Union__image__eq])). 4.46/4.69 fof(c_0_5311, plain, ![X17437, X17438, X17439]:(~class_Orderings_Olinorder(X17439)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17439),X17438),X17437))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17439,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X17439,X17438,X17437)),hAPP(hAPP(c_Set_Oinsert(X17439),X17437),c_Orderings_Obot__class_Obot(tc_fun(X17439,tc_HOL_Obool))))=c_SetInterval_Oord__class_OgreaterThanAtMost(X17439,X17438,X17437))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I4_J])])])). 4.46/4.69 fof(c_0_5312, plain, ![X9703]:(~c_Nat__Transfer_Onat__set(X9703)|X9703=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X9703))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__nat__int__set__return__embed])])])). 4.46/4.69 fof(c_0_5313, plain, ![X10597, X10598]:(~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),X10598),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),X10597)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X10597))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),X10597))|c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X10598,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),X10597)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_MGT__Body])])). 4.46/4.69 fof(c_0_5314, plain, ![X2454, X2455, X2456, X2457, X2461]:((((hBOOL(hAPP(hAPP(c_member(X2455),esk67_4(X2454,X2455,X2456,X2457)),hAPP(c_List_Oset(X2455),X2456)))|~c_List_Olinorder__class_Osorted(X2455,X2456)|hAPP(hAPP(c_List_Olist_OCons(X2455),X2457),X2456)!=X2454|c_List_Olinorder__class_Osorted(X2455,X2454)|~class_Orderings_Olinorder(X2455))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2455),X2457),esk67_4(X2454,X2455,X2456,X2457)))|~c_List_Olinorder__class_Osorted(X2455,X2456)|hAPP(hAPP(c_List_Olist_OCons(X2455),X2457),X2456)!=X2454|c_List_Olinorder__class_Osorted(X2455,X2454)|~class_Orderings_Olinorder(X2455)))&(X2454!=c_List_Olist_ONil(X2455)|c_List_Olinorder__class_Osorted(X2455,X2454)|~class_Orderings_Olinorder(X2455)))&(((c_List_Olinorder__class_Osorted(X2455,esk68_2(X2454,X2455))|X2454=c_List_Olist_ONil(X2455)|~c_List_Olinorder__class_Osorted(X2455,X2454)|~class_Orderings_Olinorder(X2455))&(~hBOOL(hAPP(hAPP(c_member(X2455),X2461),hAPP(c_List_Oset(X2455),esk68_2(X2454,X2455))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2455),esk69_2(X2454,X2455)),X2461))|X2454=c_List_Olist_ONil(X2455)|~c_List_Olinorder__class_Osorted(X2455,X2454)|~class_Orderings_Olinorder(X2455)))&(hAPP(hAPP(c_List_Olist_OCons(X2455),esk69_2(X2454,X2455)),esk68_2(X2454,X2455))=X2454|X2454=c_List_Olist_ONil(X2455)|~c_List_Olinorder__class_Osorted(X2455,X2454)|~class_Orderings_Olinorder(X2455)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_Osimps])])])])])). 4.46/4.69 fof(c_0_5315, plain, ![X11544, X11545, X11546]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11546),X11545)),X11544))|hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X11546,X11544)),X11545)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11546),X11545)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__upt])])). 4.46/4.69 cnf(c_0_5316, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X2))=c_Code__Numeral_Onat__of__aux(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4659])). 4.46/4.69 cnf(c_0_5317, plain, (c_Code__Numeral_Onat__of__aux(X1,X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_4660])). 4.46/4.69 cnf(c_0_5318, plain, (hBOOL(hAPP(X1,X2))|hAPP(c_List_Ofilter(X3,X1),X4)=hAPP(c_List_OremoveAll(X3,X2),hAPP(c_List_Ofilter(X3,X1),X4))), inference(split_conjunct,[status(thm)],[c_0_4661])). 4.46/4.69 cnf(c_0_5319, plain, (hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2)),X3)),X4)=hAPP(c_List_Ofilter(X1,X3),hAPP(c_List_Ofilter(X1,X2),X4))), inference(split_conjunct,[status(thm)],[c_0_4662])). 4.46/4.69 cnf(c_0_5320, plain, (hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2)),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4663, c_0_4531]), c_0_4531]), c_0_4531]), ['final']). 4.46/4.69 fof(c_0_5321, plain, ![X16784, X16785, X16786, X16787, X16789, X16790]:(((X16784!=hAPP(X16785,X16789)|esk496_4(X16784,X16785,X16786,X16787)=X16789|~hBOOL(hAPP(hAPP(c_member(X16786),X16784),hAPP(c_Set_Oimage(X16787,X16786,X16785),c_Orderings_Otop__class_Otop(tc_fun(X16787,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X16787,X16786,X16785,c_Orderings_Otop__class_Otop(tc_fun(X16787,tc_HOL_Obool))))&(X16784=hAPP(X16785,esk496_4(X16784,X16785,X16786,X16787))|~hBOOL(hAPP(hAPP(c_member(X16786),X16784),hAPP(c_Set_Oimage(X16787,X16786,X16785),c_Orderings_Otop__class_Otop(tc_fun(X16787,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X16787,X16786,X16785,c_Orderings_Otop__class_Otop(tc_fun(X16787,tc_HOL_Obool)))))&((X16784=hAPP(X16785,esk497_5(X16784,X16785,X16786,X16787,X16790))|X16784!=hAPP(X16785,X16790)|hBOOL(hAPP(hAPP(c_member(X16786),X16784),hAPP(c_Set_Oimage(X16787,X16786,X16785),c_Orderings_Otop__class_Otop(tc_fun(X16787,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X16787,X16786,X16785,c_Orderings_Otop__class_Otop(tc_fun(X16787,tc_HOL_Obool))))&(X16790!=esk497_5(X16784,X16785,X16786,X16787,X16790)|X16784!=hAPP(X16785,X16790)|hBOOL(hAPP(hAPP(c_member(X16786),X16784),hAPP(c_Set_Oimage(X16787,X16786,X16785),c_Orderings_Otop__class_Otop(tc_fun(X16787,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X16787,X16786,X16785,c_Orderings_Otop__class_Otop(tc_fun(X16787,tc_HOL_Obool)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_range__ex1__eq])])])])])])). 4.46/4.69 fof(c_0_5322, plain, ![X2604, X2605, X2606, X2607]:hBOOL(hAPP(hAPP(c_member(X2607),hAPP(X2606,X2605)),hAPP(c_Set_Oimage(X2604,X2607,X2606),c_Orderings_Otop__class_Otop(tc_fun(X2604,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_rangeI])). 4.46/4.69 fof(c_0_5323, plain, ![X1777, X1778, X1779]:(c_List_Olist_ONil(X1779)=c_List_OdropWhile(X1779,X1778,X1777)|~hBOOL(hAPP(X1778,hAPP(c_List_Ohd(X1779),c_List_OdropWhile(X1779,X1778,X1777))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__dropWhile])])])). 4.46/4.69 fof(c_0_5324, plain, ![X15872, X15873, X15874]:((~c_Relation_Ototal__on(X15874,X15873,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X15874,X15874),tc_HOL_Obool)),X15872),c_Relation_OId(X15874)))|c_Relation_Ototal__on(X15874,X15873,X15872))&(~c_Relation_Ototal__on(X15874,X15873,X15872)|c_Relation_Ototal__on(X15874,X15873,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X15874,X15874),tc_HOL_Obool)),X15872),c_Relation_OId(X15874))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__diff__Id])])). 4.46/4.69 fof(c_0_5325, plain, ![X2445, X2446, X2447, X2448]:(~class_Groups_Ocomm__monoid__add(X2448)|hAPP(c_List_Omonoid__add__class_Olistsum(X2448),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X2448),X2447),c_List_Oupto(X2446,X2445)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X2448),X2447),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X2446,X2445)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__set__upto__conv__listsum__int])])). 4.46/4.69 fof(c_0_5326, plain, ![X11174, X11175]:hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X11175,X11174))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X11175,X11174), inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upto])). 4.46/4.69 fof(c_0_5327, plain, ![X6963, X6964]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6964))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6963))|hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6964),X6963))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X6964)),hAPP(c_Int_Onat,X6963)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__distrib])])). 4.46/4.70 fof(c_0_5328, plain, ![X9744]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X9744)))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X9744))=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X9744)))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X9744))=hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X9744))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_one__mod__nat__number__of])])])). 4.46/4.70 fof(c_0_5329, plain, ![X3485, X3486, X3487]:((c_Groups_Ozero__class_Ozero(X3487)!=X3485|X3486!=c_Groups_Ozero__class_Ozero(X3487)|c_Groups_Ozero__class_Ozero(X3487)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3487),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3487),X3486),X3486)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3487),X3485),X3485))|~class_Rings_Olinordered__ring__strict(X3487))&((c_Groups_Ozero__class_Ozero(X3487)=X3485|c_Groups_Ozero__class_Ozero(X3487)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3487),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3487),X3486),X3486)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3487),X3485),X3485))|~class_Rings_Olinordered__ring__strict(X3487))&(X3486=c_Groups_Ozero__class_Ozero(X3487)|c_Groups_Ozero__class_Ozero(X3487)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3487),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3487),X3486),X3486)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3487),X3485),X3485))|~class_Rings_Olinordered__ring__strict(X3487)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sum__squares__eq__zero__iff])])])])). 4.46/4.70 cnf(c_0_5330, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_4596])). 4.46/4.70 fof(c_0_5331, plain, ![X14281, X14282, X14283]:(((c_Groups_Ozero__class_Ozero(X14283)=X14281|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14283),X14282),X14281)!=c_Groups_Ozero__class_Ozero(X14283)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14283),c_Groups_Ozero__class_Ozero(X14283)),X14281))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14283),c_Groups_Ozero__class_Ozero(X14283)),X14282))|~class_Groups_Oordered__comm__monoid__add(X14283))&(X14282=c_Groups_Ozero__class_Ozero(X14283)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14283),X14282),X14281)!=c_Groups_Ozero__class_Ozero(X14283)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14283),c_Groups_Ozero__class_Ozero(X14283)),X14281))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14283),c_Groups_Ozero__class_Ozero(X14283)),X14282))|~class_Groups_Oordered__comm__monoid__add(X14283)))&(c_Groups_Ozero__class_Ozero(X14283)!=X14281|X14282!=c_Groups_Ozero__class_Ozero(X14283)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14283),X14282),X14281)=c_Groups_Ozero__class_Ozero(X14283)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14283),c_Groups_Ozero__class_Ozero(X14283)),X14281))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14283),c_Groups_Ozero__class_Ozero(X14283)),X14282))|~class_Groups_Oordered__comm__monoid__add(X14283))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])])). 4.46/4.70 fof(c_0_5332, plain, ![X17134]:(hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X17134|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X17134)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X17134)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral__decr])])). 4.46/4.70 cnf(c_0_5333, plain, (hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[fact_zero__code__numeral__def])). 4.46/4.70 cnf(c_0_5334, plain, (c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral)=c_Code__Numeral_Oof__nat), inference(split_conjunct,[status(thm)],[fact_Code__Numeral_Oof__nat__code]), ['final']). 4.46/4.70 cnf(c_0_5335, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls))),X2)=X2|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4664])). 4.46/4.70 cnf(c_0_5336, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls)))=X2|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4665])). 4.46/4.70 fof(c_0_5337, plain, ![X7755, X7756]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7756))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7756),X7755))|hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X7755),X7756))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X7755)),hAPP(c_Int_Onat,X7756)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__distrib])])). 4.46/4.70 fof(c_0_5338, plain, ![X15448, X15449, X15451, X15452, X15453]:(((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk452_2(X15448,X15449)),hAPP(c_List_Oset(tc_Nat_Onat),X15448)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X15449|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15449),X15448))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=esk452_2(X15448,X15449)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X15449|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15449),X15448)))&((~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X15453),hAPP(c_List_Oset(tc_Nat_Onat),X15451)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X15453|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15452),X15451))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X15452|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15452),X15451)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sum__eq__0__conv])])])])])])])). 4.46/4.70 fof(c_0_5339, plain, ![X4292, X4293, X4294, X4295]:((hAPP(hAPP(c_List_Oappend(X4295),hAPP(c_List_Orev(X4295),X4292)),hAPP(hAPP(c_List_Olist_OCons(X4295),X4293),c_List_Olist_ONil(X4295)))!=X4294|hAPP(hAPP(c_List_Olist_OCons(X4295),X4293),X4292)=hAPP(c_List_Orev(X4295),X4294))&(hAPP(hAPP(c_List_Olist_OCons(X4295),X4293),X4292)!=hAPP(c_List_Orev(X4295),X4294)|hAPP(hAPP(c_List_Oappend(X4295),hAPP(c_List_Orev(X4295),X4292)),hAPP(hAPP(c_List_Olist_OCons(X4295),X4293),c_List_Olist_ONil(X4295)))=X4294)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__eq__Cons__iff])])). 4.46/4.70 fof(c_0_5340, plain, ![X14771, X14772, X14773]:hAPP(c_List_Orev(X14773),hAPP(hAPP(c_List_Olist_OCons(X14773),X14772),X14771))=hAPP(hAPP(c_List_Oappend(X14773),hAPP(c_List_Orev(X14773),X14771)),hAPP(hAPP(c_List_Olist_OCons(X14773),X14772),c_List_Olist_ONil(X14773))), inference(variable_rename,[status(thm)],[fact_rev_Osimps_I2_J])). 4.46/4.70 cnf(c_0_5341, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_4666])). 4.46/4.70 cnf(c_0_5342, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_4667])). 4.46/4.70 cnf(c_0_5343, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4668])). 4.46/4.70 cnf(c_0_5344, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_4669])). 4.46/4.70 cnf(c_0_5345, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4670])). 4.46/4.70 cnf(c_0_5346, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X1))))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_4671])). 4.46/4.70 cnf(c_0_5347, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1))), inference(split_conjunct,[status(thm)],[c_0_4672])). 4.46/4.70 cnf(c_0_5348, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))), inference(split_conjunct,[status(thm)],[c_0_4673])). 4.46/4.70 cnf(c_0_5349, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))), inference(split_conjunct,[status(thm)],[c_0_4674])). 4.46/4.70 cnf(c_0_5350, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1))), inference(split_conjunct,[status(thm)],[c_0_4675])). 4.46/4.70 cnf(c_0_5351, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))), inference(split_conjunct,[status(thm)],[c_0_4676])). 4.46/4.70 fof(c_0_5352, plain, ![X2682, X2683]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2683),c_Int_OPls))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2683)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2682))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2683),c_Int_OPls))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2683)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2682))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2683),X2682)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__nat__number__of])])])). 4.46/4.70 fof(c_0_5353, plain, ![X16584, X16585]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X16585,X16584)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X16585,X16584),tc_HOL_Obool))))|(hAPP(c_Finite__Set_Ocard(X16584),c_Orderings_Otop__class_Otop(tc_fun(X16584,tc_HOL_Obool)))=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hBOOL(hAPP(c_Finite__Set_Ofinite(X16585),c_Orderings_Otop__class_Otop(tc_fun(X16585,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__fun__UNIVD1])])])). 4.46/4.70 cnf(c_0_5354, plain, (hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(c_fequal,X2))),X1))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_4677])). 4.46/4.70 cnf(c_0_5355, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Oone__class_Oone(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4626])). 4.46/4.70 cnf(c_0_5356, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Oone__class_Oone(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4627])). 4.46/4.70 fof(c_0_5357, plain, ![X2348, X2349, X2350, X2351]:(((hBOOL(hAPP(c_List_Olistsp(X2351,X2349),X2348))|~hBOOL(hAPP(c_List_Olistsp(X2351,hAPP(hAPP(c_COMBS(X2351,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2351),c_fconj),X2350)),X2349)),X2348)))&(hBOOL(hAPP(c_List_Olistsp(X2351,X2350),X2348))|~hBOOL(hAPP(c_List_Olistsp(X2351,hAPP(hAPP(c_COMBS(X2351,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2351),c_fconj),X2350)),X2349)),X2348))))&(~hBOOL(hAPP(c_List_Olistsp(X2351,X2349),X2348))|~hBOOL(hAPP(c_List_Olistsp(X2351,X2350),X2348))|hBOOL(hAPP(c_List_Olistsp(X2351,hAPP(hAPP(c_COMBS(X2351,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2351),c_fconj),X2350)),X2349)),X2348)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__conj__eq])])])). 4.46/4.70 cnf(c_0_5358, plain, (hBOOL(hAPP(X1,X2))|c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))=hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(c_fequal,X2))),X1))), inference(split_conjunct,[status(thm)],[c_0_4677])). 4.46/4.70 fof(c_0_5359, plain, ![X1313, X1314, X1315, X1316]:((((c_Groups_Ozero__class_Ozero(X1316)!=X1314|X1314=c_Groups_Ozero__class_Ozero(X1316)|hAPP(c_Int_Onumber__class_Onumber__of(X1316),X1313)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1316),X1315),X1314)|(~class_Fields_Ofield__inverse__zero(X1316)|~class_Int_Onumber(X1316)))&(X1315!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1316),hAPP(c_Int_Onumber__class_Onumber__of(X1316),X1313)),X1314)|X1314=c_Groups_Ozero__class_Ozero(X1316)|hAPP(c_Int_Onumber__class_Onumber__of(X1316),X1313)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1316),X1315),X1314)|(~class_Fields_Ofield__inverse__zero(X1316)|~class_Int_Onumber(X1316))))&((c_Groups_Ozero__class_Ozero(X1316)!=X1314|hAPP(c_Int_Onumber__class_Onumber__of(X1316),X1313)!=c_Groups_Ozero__class_Ozero(X1316)|hAPP(c_Int_Onumber__class_Onumber__of(X1316),X1313)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1316),X1315),X1314)|(~class_Fields_Ofield__inverse__zero(X1316)|~class_Int_Onumber(X1316)))&(X1315!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1316),hAPP(c_Int_Onumber__class_Onumber__of(X1316),X1313)),X1314)|hAPP(c_Int_Onumber__class_Onumber__of(X1316),X1313)!=c_Groups_Ozero__class_Ozero(X1316)|hAPP(c_Int_Onumber__class_Onumber__of(X1316),X1313)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1316),X1315),X1314)|(~class_Fields_Ofield__inverse__zero(X1316)|~class_Int_Onumber(X1316)))))&((X1314!=c_Groups_Ozero__class_Ozero(X1316)|hAPP(c_Int_Onumber__class_Onumber__of(X1316),X1313)=c_Groups_Ozero__class_Ozero(X1316)|hAPP(c_Int_Onumber__class_Onumber__of(X1316),X1313)!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1316),X1315),X1314)|(~class_Fields_Ofield__inverse__zero(X1316)|~class_Int_Onumber(X1316)))&(c_Groups_Ozero__class_Ozero(X1316)=X1314|X1315=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1316),hAPP(c_Int_Onumber__class_Onumber__of(X1316),X1313)),X1314)|hAPP(c_Int_Onumber__class_Onumber__of(X1316),X1313)!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1316),X1315),X1314)|(~class_Fields_Ofield__inverse__zero(X1316)|~class_Int_Onumber(X1316))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of])])])). 4.46/4.70 fof(c_0_5360, plain, ![X2754, X2755]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2755))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2754))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X2755),hAPP(c_Int_Onat,X2754))=hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2755,X2754)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I2_J])])). 4.46/4.70 fof(c_0_5361, plain, ![X15920, X15921]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15921)))|hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15921)),X15920))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15921)),X15920))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15921)))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15921)),X15920)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15920))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__nat__number__of])])])). 4.46/4.70 fof(c_0_5362, plain, ![X9321, X9322, X9323, X9324, X9325]:(~c_Hoare__Mirabelle_Ohoare__derivs(X9325,X9324,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X9325)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X9325),X9323),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X9322))),X9321)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X9325),tc_HOL_Obool))))|c_Hoare__Mirabelle_Ohoare__derivs(X9325,X9324,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X9325)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X9325),X9323),hAPP(c_Com_Ocom_OBODY,X9322)),X9321)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X9325),tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_weak__Body])])])). 4.46/4.70 fof(c_0_5363, plain, ![X10292, X10293, X10294]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10294),X10293)),X10292))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X10292),X10294)!=X10293|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10294)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10292),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10294),hAPP(c_Nat_OSuc,X10293))))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X10292),X10294)!=X10293|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10294))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10294),X10293)),X10292))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10292),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10294),hAPP(c_Nat_OSuc,X10293))))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X10292),X10294)=X10293|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10294)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__div__lemma])])])). 4.46/4.70 fof(c_0_5364, plain, ![X7571, X7572, X7573, X7574]:((X7573=c_Groups_Ozero__class_Ozero(X7574)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X7574),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7574),X7573),X7572)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7574),X7573),X7571))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X7574),X7572),X7571)|~class_Divides_Osemiring__div(X7574))&(X7573!=c_Groups_Ozero__class_Ozero(X7574)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X7574),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7574),X7573),X7572)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7574),X7573),X7571))=c_Groups_Ozero__class_Ozero(X7574)|~class_Divides_Osemiring__div(X7574))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__mult1__if])])])])). 4.46/4.70 fof(c_0_5365, plain, ![X8128]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8128))|hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,X8128)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8128)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__atLeastZeroLessThan__int])])). 4.46/4.70 fof(c_0_5366, plain, ![X12538, X12539]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X12539,X12539)),X12538))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X12539,X12539)),c_Transitive__Closure_Otrancl(X12539,X12538))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X12539,X12539)),c_Transitive__Closure_Otrancl(X12539,X12538)))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X12539,X12539)),X12538)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__trancl])])). 4.46/4.70 fof(c_0_5367, plain, ![X7266, X7267, X7268]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7266),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7267),X7268)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7266),X7268)),X7267))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7268),X7267)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7266),X7268)),X7267))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7266),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7267),X7268)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7268),X7267)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv2])])])). 4.46/4.70 fof(c_0_5368, plain, ![X14256, X14257, X14258]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14258),X14257)),X14256))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14257),X14256))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__leD2])])])). 4.46/4.70 fof(c_0_5369, plain, ![X2579, X2580, X2581, X2582]:((~hBOOL(hAPP(X2579,X2581))|~hBOOL(hAPP(hAPP(c_member(X2582),X2581),X2580))|hBOOL(hAPP(hAPP(c_member(X2582),X2581),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2582,tc_HOL_Obool)),X2580),hAPP(c_Set_OCollect(X2582),X2579)))))&((hBOOL(hAPP(X2579,X2581))|~hBOOL(hAPP(hAPP(c_member(X2582),X2581),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2582,tc_HOL_Obool)),X2580),hAPP(c_Set_OCollect(X2582),X2579)))))&(hBOOL(hAPP(hAPP(c_member(X2582),X2581),X2580))|~hBOOL(hAPP(hAPP(c_member(X2582),X2581),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2582,tc_HOL_Obool)),X2580),hAPP(c_Set_OCollect(X2582),X2579))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__Collect])])])). 4.46/4.70 fof(c_0_5370, plain, ![X15218, X15219]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15219),X15218))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X15219,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X15219,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X15219,tc_HOL_Obool),tc_fun(X15219,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X15219,tc_HOL_Obool))),X15218))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Collect__subsets])])])). 4.46/4.70 fof(c_0_5371, plain, ![X10313]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X10313)=hAPP(c_Nat_OSuc,X10313), inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left])). 4.46/4.70 fof(c_0_5372, plain, ![X1741, X1742, X1743]:((~hBOOL(hAPP(c_List_Olistsp(X1743,hAPP(hAPP(c_COMBC(X1743,tc_fun(X1743,tc_HOL_Obool),tc_HOL_Obool),c_member(X1743)),X1742)),X1741))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1743)),X1741),c_List_Olists(X1743,X1742))))&(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1743)),X1741),c_List_Olists(X1743,X1742)))|hBOOL(hAPP(c_List_Olistsp(X1743,hAPP(hAPP(c_COMBC(X1743,tc_fun(X1743,tc_HOL_Obool),tc_HOL_Obool),c_member(X1743)),X1742)),X1741)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__lists__eq])])). 4.46/4.70 fof(c_0_5373, plain, ![X16099, X16100, X16101, X16102, X16104]:(((hBOOL(hAPP(hAPP(c_member(X16101),esk469_4(X16099,X16100,X16101,X16102)),hAPP(c_List_Oset(X16101),c_Enum_Oenum__class_Oenum(X16101))))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X16101,X16102)),X16100),X16099))|(~class_Enum_Oenum(X16101)|~class_HOL_Oequal(X16102)))&(hAPP(X16100,esk469_4(X16099,X16100,X16101,X16102))!=hAPP(X16099,esk469_4(X16099,X16100,X16101,X16102))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X16101,X16102)),X16100),X16099))|(~class_Enum_Oenum(X16101)|~class_HOL_Oequal(X16102))))&(~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X16101,X16102)),X16100),X16099))|(~hBOOL(hAPP(hAPP(c_member(X16101),X16104),hAPP(c_List_Oset(X16101),c_Enum_Oenum__class_Oenum(X16101))))|hAPP(X16100,X16104)=hAPP(X16099,X16104))|(~class_Enum_Oenum(X16101)|~class_HOL_Oequal(X16102)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equal__fun__def])])])])])])). 4.46/4.70 fof(c_0_5374, plain, ![X14971, X14972]:(~class_Enum_Oenum(X14972)|hBOOL(hAPP(hAPP(c_member(X14972),X14971),hAPP(c_List_Oset(X14972),c_Enum_Oenum__class_Oenum(X14972))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__enum])])). 4.46/4.70 fof(c_0_5375, plain, ![X4705, X4706, X4707]:(~class_Orderings_Olinorder(X4707)|c_Big__Operators_Olattice_OInf__fin(X4707,c_Orderings_Oord__class_Omin(X4707),hAPP(c_List_Oset(X4707),hAPP(hAPP(c_List_Olist_OCons(X4707),X4706),X4705)))=hAPP(c_List_Ofoldl(X4707,X4707,c_Orderings_Oord__class_Omin(X4707),X4706),X4705)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin__set__fold])])). 4.46/4.70 fof(c_0_5376, plain, ![X4872, X4873, X4874]:hAPP(c_List_Oset(X4874),hAPP(hAPP(c_List_Olist_OCons(X4874),X4873),X4872))=hAPP(hAPP(c_Set_Oinsert(X4874),X4873),hAPP(c_List_Oset(X4874),X4872)), inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I2_J])). 4.46/4.70 fof(c_0_5377, plain, ![X11871, X11872, X11873]:(~class_Orderings_Olinorder(X11873)|hAPP(c_List_Ofoldl(X11873,X11873,c_Orderings_Oord__class_Omax(X11873),X11872),X11871)=c_Big__Operators_Olattice_OSup__fin(X11873,c_Orderings_Oord__class_Omax(X11873),hAPP(c_List_Oset(X11873),hAPP(hAPP(c_List_Olist_OCons(X11873),X11872),X11871)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin__set__fold])])). 4.46/4.70 fof(c_0_5378, plain, ![X3772, X3773]:(~c_Nat__Transfer_Ois__nat(X3773)|(~c_Nat__Transfer_Ois__nat(X3772)|hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,X3773),hAPP(c_Int_Onat,X3772)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X3773,X3772))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__functions])])])). 4.46/4.70 cnf(c_0_5379, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X1))), inference(split_conjunct,[status(thm)],[c_0_4678])). 4.46/4.70 fof(c_0_5380, plain, ![X8052, X8053]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8052),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8053),hAPP(c_Int_Onat,X8052))=hAPP(c_Int_Oring__1__class_Oof__int(X8053),X8052)|~class_Rings_Oring__1(X8053))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8052),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Oring__1__class_Oof__int(X8053),X8052)=hAPP(c_Groups_Ouminus__class_Ouminus(X8053),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8053),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X8052))))|~class_Rings_Oring__1(X8053))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__of__nat])])])])). 4.46/4.70 fof(c_0_5381, plain, ![X8417, X8418, X8419]:((~c_Int_Oiszero(X8419,hAPP(c_Int_Onumber__class_Onumber__of(X8419),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8418),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X8417))))|hAPP(c_Int_Onumber__class_Onumber__of(X8419),X8418)=hAPP(c_Int_Onumber__class_Onumber__of(X8419),X8417)|~class_Int_Onumber__ring(X8419))&(hAPP(c_Int_Onumber__class_Onumber__of(X8419),X8418)!=hAPP(c_Int_Onumber__class_Onumber__of(X8419),X8417)|c_Int_Oiszero(X8419,hAPP(c_Int_Onumber__class_Onumber__of(X8419),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8418),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X8417))))|~class_Int_Onumber__ring(X8419))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__eq])])])). 4.46/4.70 fof(c_0_5382, plain, ![X8608, X8609, X8610]:((~hBOOL(hAPP(c_List_Odistinct(X8610),X8608))|hBOOL(hAPP(c_List_Odistinct(X8610),hAPP(c_List_Orotate(X8610,X8609),X8608))))&(~hBOOL(hAPP(c_List_Odistinct(X8610),hAPP(c_List_Orotate(X8610,X8609),X8608)))|hBOOL(hAPP(c_List_Odistinct(X8610),X8608)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__rotate])])). 4.46/4.70 fof(c_0_5383, plain, ![X4065, X4066, X4067, X4069, X4070, X4071, X4072]:(((X4066=hAPP(hAPP(c_List_Onth(X4067),X4065),esk111_3(X4065,X4066,X4067))|~hBOOL(hAPP(hAPP(c_member(X4067),X4066),hAPP(c_List_Oset(X4067),X4065))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk111_3(X4065,X4066,X4067)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4067)),X4065)))|~hBOOL(hAPP(hAPP(c_member(X4067),X4066),hAPP(c_List_Oset(X4067),X4065)))))&(X4070!=hAPP(hAPP(c_List_Onth(X4071),X4069),X4072)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4072),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4071)),X4069)))|hBOOL(hAPP(hAPP(c_member(X4071),X4070),hAPP(c_List_Oset(X4071),X4069))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__conv__nth])])])])])])). 4.46/4.70 cnf(c_0_5384, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4638])). 4.46/4.70 fof(c_0_5385, plain, ![X5718, X5719]:(~class_Int_Onumber__ring(X5719)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5719),hAPP(c_Groups_Ouminus__class_Ouminus(X5719),c_Groups_Oone__class_Oone(X5719))),hAPP(c_Int_Onumber__class_Onumber__of(X5719),X5718))=hAPP(c_Int_Onumber__class_Onumber__of(X5719),c_Int_Opred(X5718))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__pred])])). 4.46/4.70 cnf(c_0_5386, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4640])). 4.46/4.70 cnf(c_0_5387, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_4639])). 4.46/4.70 cnf(c_0_5388, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_4641])). 4.46/4.70 cnf(c_0_5389, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4642])). 4.46/4.70 cnf(c_0_5390, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))))), inference(split_conjunct,[status(thm)],[c_0_4643])). 4.46/4.70 cnf(c_0_5391, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X1))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1)))), inference(split_conjunct,[status(thm)],[c_0_4644])). 4.46/4.70 cnf(c_0_5392, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1)))), inference(split_conjunct,[status(thm)],[c_0_4645])). 4.46/4.70 cnf(c_0_5393, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1)))), inference(split_conjunct,[status(thm)],[c_0_4647])). 4.46/4.70 fof(c_0_5394, plain, ![X17176, X17177, X17178]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17178)),X17177)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|hAPP(c_List_Orotate(X17178,X17176),X17177)=X17177), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__length01])])). 4.46/4.70 fof(c_0_5395, plain, ![X5304, X5305, X5306, X5307, X5308, X5309, X5310]:(hAPP(c_Option_Ooption_OSome(X5308),X5307)!=hAPP(X5310,X5309)|hAPP(X5304,X5307)=c_Map_Omap__comp(X5308,X5306,X5305,X5304,X5310,X5309)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__comp__simps_I2_J])])])). 4.46/4.70 cnf(c_0_5396, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1)))), inference(split_conjunct,[status(thm)],[c_0_4646])). 4.46/4.70 cnf(c_0_5397, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1)))), inference(split_conjunct,[status(thm)],[c_0_4648])). 4.46/4.70 fof(c_0_5398, plain, ![X11236, X11237]:(~c_Wellfounded_Owf(X11237,hAPP(c_Relation_Oconverse(X11237,X11237),X11236))|c_Wellfounded_Owf(X11237,hAPP(c_Relation_Oconverse(X11237,X11237),c_Transitive__Closure_Otrancl(X11237,X11236)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__converse__trancl])])])). 4.46/4.70 fof(c_0_5399, plain, ![X5395, X5396, X5397]:((~hBOOL(hAPP(c_Predicate_OPowp(X5397,hAPP(hAPP(c_COMBC(X5397,tc_fun(X5397,tc_HOL_Obool),tc_HOL_Obool),c_member(X5397)),X5396)),X5395))|hBOOL(hAPP(hAPP(c_member(tc_fun(X5397,tc_HOL_Obool)),X5395),hAPP(c_Set_OPow(X5397),X5396))))&(~hBOOL(hAPP(hAPP(c_member(tc_fun(X5397,tc_HOL_Obool)),X5395),hAPP(c_Set_OPow(X5397),X5396)))|hBOOL(hAPP(c_Predicate_OPowp(X5397,hAPP(hAPP(c_COMBC(X5397,tc_fun(X5397,tc_HOL_Obool),tc_HOL_Obool),c_member(X5397)),X5396)),X5395)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Powp__Pow__eq])])). 4.46/4.70 cnf(c_0_5400, plain, (X1=c_Int_OPls|c_Int_OPls!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4679, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.70 cnf(c_0_5401, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(X2)))|~class_Int_Onumber__ring(X1)|~class_Int_Oring__char__0(X1)), inference(split_conjunct,[status(thm)],[c_0_4635])). 4.46/4.70 fof(c_0_5402, plain, ![X2710, X2711]:((~c_Predicate_Oreflp(X2711,X2710)|c_Relation_Orefl__on(X2711,c_Orderings_Otop__class_Otop(tc_fun(X2711,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X2711,X2711)),hAPP(c_Product__Type_Oprod_Oprod__case(X2711,X2711,tc_HOL_Obool),X2710))))&(~c_Relation_Orefl__on(X2711,c_Orderings_Otop__class_Otop(tc_fun(X2711,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X2711,X2711)),hAPP(c_Product__Type_Oprod_Oprod__case(X2711,X2711,tc_HOL_Obool),X2710)))|c_Predicate_Oreflp(X2711,X2710))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflp__def])])). 4.46/4.70 fof(c_0_5403, plain, ![X10920, X10921]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X10921))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X10921),X10920)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__one__le__power])])])). 4.46/4.70 fof(c_0_5404, plain, ![X15124, X15125]:((~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X15125)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X15124)))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X15125),X15124))|~c_Nat__Transfer_Onat__set(X15124)|~c_Nat__Transfer_Ois__nat(X15125))&(~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X15125),X15124))|hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X15125)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X15124)))|~c_Nat__Transfer_Onat__set(X15124)|~c_Nat__Transfer_Ois__nat(X15125))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I2_J])])])). 4.46/4.70 fof(c_0_5405, plain, ![X2106, X2107]:(~c_Nat__Transfer_Onat__set(X2107)|(~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2106),X2107))|c_Nat__Transfer_Ois__nat(X2106))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J])])])). 4.46/4.70 fof(c_0_5406, plain, ![X7665, X7666]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7666))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7665))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X7666)),hAPP(c_Int_Onat,X7665))=hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X7666,X7665)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J])])])). 4.46/4.70 fof(c_0_5407, plain, ![X5647, X5648, X5649, X5651, X5652, X5653, X5654]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X5647,X5647)),esk172_3(X5647,X5648,X5649)),hAPP(c_List_Oset(tc_prod(X5647,X5647)),hAPP(hAPP(c_List_Ozip(X5647,X5647),X5649),X5648))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5647)),X5648)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5647)),X5649)|X5649=X5648)&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5647,X5647,tc_HOL_Obool),c_fequal),esk172_3(X5647,X5648,X5649)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5647)),X5648)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5647)),X5649)|X5649=X5648))&((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5651)),X5652)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5651)),X5653)|X5653!=X5652)&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X5651,X5651)),X5654),hAPP(c_List_Oset(tc_prod(X5651,X5651)),hAPP(hAPP(c_List_Ozip(X5651,X5651),X5653),X5652))))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5651,X5651,tc_HOL_Obool),c_fequal),X5654))|X5653!=X5652))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__eq__iff__zip__eq])])])])])])). 4.46/4.70 fof(c_0_5408, plain, ![X11869, X11870]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11870),X11869))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(X11870),X11869))=hAPP(c_Finite__Set_Ocard(tc_fun(X11870,tc_HOL_Obool)),hAPP(c_Set_OPow(X11870),X11869))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Pow])])). 4.46/4.70 fof(c_0_5409, plain, ![X10559, X10560, X10562]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk309_2(X10559,X10560)),X10559))|~hBOOL(hAPP(X10560,X10559))|hBOOL(hAPP(X10560,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10562),esk309_2(X10559,X10560)))|~hBOOL(hAPP(X10560,X10562))|~hBOOL(hAPP(X10560,X10559))|hBOOL(hAPP(X10560,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))&(hBOOL(hAPP(X10560,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk309_2(X10559,X10560)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~hBOOL(hAPP(X10560,X10559))|hBOOL(hAPP(X10560,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ex__least__nat__less])])])])])])). 4.46/4.70 cnf(c_0_5410, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X1))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))), inference(split_conjunct,[status(thm)],[c_0_4680])). 4.46/4.70 fof(c_0_5411, plain, ![X1017, X1018, X1019, X1020]:(((hAPP(hAPP(c_List_Otake(X1020),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1020)),X1019)),X1017)=X1019|hAPP(hAPP(c_List_Oappend(X1020),X1019),X1018)!=X1017)&(X1018=hAPP(hAPP(c_List_Odrop(X1020),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1020)),X1019)),X1017)|hAPP(hAPP(c_List_Oappend(X1020),X1019),X1018)!=X1017))&(hAPP(hAPP(c_List_Otake(X1020),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1020)),X1019)),X1017)!=X1019|X1018!=hAPP(hAPP(c_List_Odrop(X1020),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1020)),X1019)),X1017)|hAPP(hAPP(c_List_Oappend(X1020),X1019),X1018)=X1017)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__conv__conj])])])). 4.46/4.70 fof(c_0_5412, plain, ![X15826, X15827, X15828, X15829]:(hAPP(c_Set_Oimage(X15829,X15828,X15827),c_Orderings_Otop__class_Otop(tc_fun(X15829,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X15828,tc_HOL_Obool))|hAPP(c_Set_Oimage(X15829,X15828,X15827),hAPP(c_Set_Ovimage(X15829,X15828,X15827),X15826))=X15826), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__image__vimage__eq])])). 4.46/4.70 fof(c_0_5413, plain, ![X8933, X8934, X8935, X8936]:(~c_Fun_Oinj__on(X8936,X8935,X8934,c_Orderings_Otop__class_Otop(tc_fun(X8936,tc_HOL_Obool)))|hAPP(c_Set_Ovimage(X8936,X8935,X8934),hAPP(c_Set_Oimage(X8936,X8935,X8934),X8933))=X8933), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__vimage__image__eq])])])). 4.46/4.70 fof(c_0_5414, plain, ![X13797, X13798, X13799, X13800]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13800),hAPP(c_Set_Ovimage(X13800,X13799,X13798),X13797)))|(c_Orderings_Otop__class_Otop(tc_fun(X13799,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X13800,X13799,X13798),c_Orderings_Otop__class_Otop(tc_fun(X13800,tc_HOL_Obool)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X13799),X13797)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__vimageD])])])). 4.46/4.70 fof(c_0_5415, plain, ![X1104, X1105, X1106, X1107]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1107),X1106))|(~c_Fun_Oinj__on(X1105,X1107,X1104,c_Orderings_Otop__class_Otop(tc_fun(X1105,tc_HOL_Obool)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1105),hAPP(c_Set_Ovimage(X1105,X1107,X1104),X1106))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimageI])])). 4.46/4.70 fof(c_0_5416, plain, ![X7384, X7385, X7386, X7387, X7388]:(~hBOOL(hAPP(hAPP(c_member(X7388),hAPP(X7387,X7386)),X7385))|hBOOL(hAPP(hAPP(c_member(X7384),X7386),hAPP(c_Set_Ovimage(X7384,X7388,X7387),X7385)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageI2])])). 4.46/4.70 fof(c_0_5417, plain, ![X5216, X5217, X5218, X5219, X5220]:(~hBOOL(hAPP(hAPP(c_member(X5220),X5219),hAPP(c_Set_Ovimage(X5220,X5218,X5217),X5216)))|hBOOL(hAPP(hAPP(c_member(X5218),hAPP(X5217,X5219)),X5216))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_vimageD])])])). 4.46/4.70 fof(c_0_5418, plain, ![X8782, X8783]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8783),X8782))|c_List_Olast(tc_Nat_Onat,c_List_Oupt(X8783,X8782))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8782),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__upt])])). 4.46/4.70 fof(c_0_5419, plain, ![X6904, X6905, X6906, X6907]:((hBOOL(hAPP(hAPP(c_member(X6907),X6906),X6905))|c_Orderings_Obot__class_Obot(tc_fun(X6904,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X6904,X6907,hAPP(c_COMBK(X6907,X6904),X6906)),X6905))&(~hBOOL(hAPP(hAPP(c_member(X6907),X6906),X6905))|c_Orderings_Otop__class_Otop(tc_fun(X6904,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X6904,X6907,hAPP(c_COMBK(X6907,X6904),X6906)),X6905))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_vimage__const])])])). 4.46/4.70 fof(c_0_5420, plain, ![X12691, X12692, X12693, X12694, X12695, X12696]:(~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X12696)|(c_Groups_Ozero__class_Ozero(X12696)=X12695|(X12692=X12691|X12693!=X12694|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12696),X12694),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12696),X12695),X12692))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12696),X12693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12696),X12695),X12691))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__scale__eq__noteq])])])). 4.46/4.70 fof(c_0_5421, plain, ![X4866, X4867]:(~class_Orderings_Olinorder(X4867)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4867,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X4867),X4866)),hAPP(hAPP(c_Set_Oinsert(X4867),X4866),c_Orderings_Obot__class_Obot(tc_fun(X4867,tc_HOL_Obool))))=hAPP(c_SetInterval_Oord__class_OatMost(X4867),X4866)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I2_J])])])). 4.46/4.70 fof(c_0_5422, plain, ![X2619, X2620]:((~c_Int_Oiszero(X2620,hAPP(c_Int_Onumber__class_Onumber__of(X2620),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2619))))|c_Groups_Ozero__class_Ozero(X2620)=hAPP(c_Int_Onumber__class_Onumber__of(X2620),X2619)|~class_Int_Onumber__ring(X2620))&(c_Groups_Ozero__class_Ozero(X2620)!=hAPP(c_Int_Onumber__class_Onumber__of(X2620),X2619)|c_Int_Oiszero(X2620,hAPP(c_Int_Onumber__class_Onumber__of(X2620),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2619))))|~class_Int_Onumber__ring(X2620))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I1_J])])])). 4.46/4.70 cnf(c_0_5423, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X1)), inference(split_conjunct,[status(thm)],[c_0_4681])). 4.46/4.70 cnf(c_0_5424, plain, (c_Nitpick_Oless__eq__frac(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_4622])). 4.46/4.70 cnf(c_0_5425, plain, (c_Nitpick_Oless__frac(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_4621])). 4.46/4.70 fof(c_0_5426, plain, ![X7596, X7597]:((hAPP(c_Int_Onumber__class_Onumber__of(X7597),X7596)!=c_Groups_Ozero__class_Ozero(X7597)|c_Int_Oiszero(X7597,hAPP(c_Int_Onumber__class_Onumber__of(X7597),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7596),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))|~class_Int_Onumber__ring(X7597))&(~c_Int_Oiszero(X7597,hAPP(c_Int_Onumber__class_Onumber__of(X7597),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7596),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))|hAPP(c_Int_Onumber__class_Onumber__of(X7597),X7596)=c_Groups_Ozero__class_Ozero(X7597)|~class_Int_Onumber__ring(X7597))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I3_J])])])). 4.46/4.70 cnf(c_0_5427, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)=c_Int_OPls), inference(split_conjunct,[status(thm)],[fact_minus__Pls])). 4.46/4.70 fof(c_0_5428, plain, ![X17323, X17324, X17325]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17325,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17324)),X17323))|X17323=hAPP(c_List_Orotate(X17324,X17325),X17323)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__id])])). 4.46/4.70 fof(c_0_5429, plain, ![X17428, X17429]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17429),X17428))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17429)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17428))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17429),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17429)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17428)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17429)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17428)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17429),X17428))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17429),c_Int_OPls))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__nat__number__of])])])])). 4.46/4.70 fof(c_0_5430, plain, ![X2253, X2254, X2255, X2256]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2255)),X2256)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2254|c_List_Olast(X2255,X2256)=c_List_Olast(X2255,hAPP(hAPP(c_List_Olist__update(X2255,X2256),X2254),X2253))|X2256=c_List_Olist_ONil(X2255))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2255)),X2256)),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X2254|X2253=c_List_Olast(X2255,hAPP(hAPP(c_List_Olist__update(X2255,X2256),X2254),X2253))|X2256=c_List_Olist_ONil(X2255))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_last__list__update])])])])). 4.46/4.70 cnf(c_0_5431, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|X3=hAPP(c_List_OremoveAll(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_4682])). 4.46/4.70 fof(c_0_5432, plain, ![X13157, X13158]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13158))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13158),X13157)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X13158),X13157)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__pos__neg__trivial])])])). 4.46/4.70 fof(c_0_5433, plain, ![X5254, X5255, X5256]:(~class_Lattices_Olattice(X5256)|c_Big__Operators_Olattice__class_OSup__fin(X5256,hAPP(c_List_Oset(X5256),hAPP(hAPP(c_List_Olist_OCons(X5256),X5255),X5254)))=hAPP(c_List_Ofoldl(X5256,X5256,c_Lattices_Osemilattice__sup__class_Osup(X5256),X5255),X5254)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin__set__fold])])])). 4.46/4.70 fof(c_0_5434, plain, ![X15021, X15022, X15023]:(~class_Orderings_Olinorder(X15023)|c_Big__Operators_Olinorder__class_OMin(X15023,hAPP(c_List_Oset(X15023),hAPP(hAPP(c_List_Olist_OCons(X15023),X15022),X15021)))=hAPP(c_List_Ofoldl(X15023,X15023,c_Orderings_Oord__class_Omin(X15023),X15022),X15021)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__fin__set__fold])])). 4.46/4.70 fof(c_0_5435, plain, ![X10556, X10557, X10558]:(~class_Orderings_Olinorder(X10558)|hAPP(c_List_Ofoldl(X10558,X10558,c_Orderings_Oord__class_Omax(X10558),X10557),X10556)=c_Big__Operators_Olinorder__class_OMax(X10558,hAPP(c_List_Oset(X10558),hAPP(hAPP(c_List_Olist_OCons(X10558),X10557),X10556)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__fin__set__fold])])). 4.46/4.70 fof(c_0_5436, plain, ![X9395, X9396, X9397]:(~class_Lattices_Olattice(X9397)|hAPP(c_List_Ofoldl(X9397,X9397,c_Lattices_Osemilattice__inf__class_Oinf(X9397),X9396),X9395)=c_Big__Operators_Olattice__class_OInf__fin(X9397,hAPP(c_List_Oset(X9397),hAPP(hAPP(c_List_Olist_OCons(X9397),X9396),X9395)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin__set__fold])])])). 4.46/4.70 fof(c_0_5437, plain, ![X7529, X7530, X7531, X7532, X7533]:((hAPP(hAPP(c_List_Omap(X7533,X7532),X7531),X7529)!=hAPP(hAPP(c_List_Omap(X7533,X7532),X7531),X7530)|X7529=X7530|~c_Fun_Oinj__on(X7533,X7532,X7531,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7533,tc_HOL_Obool)),hAPP(c_List_Oset(X7533),X7530)),hAPP(c_List_Oset(X7533),X7529))))&(X7529!=X7530|hAPP(hAPP(c_List_Omap(X7533,X7532),X7531),X7529)=hAPP(hAPP(c_List_Omap(X7533,X7532),X7531),X7530)|~c_Fun_Oinj__on(X7533,X7532,X7531,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7533,tc_HOL_Obool)),hAPP(c_List_Oset(X7533),X7530)),hAPP(c_List_Oset(X7533),X7529))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__map__eq__map])])])])). 4.46/4.70 fof(c_0_5438, plain, ![X1554, X1555, X1556, X1557, X1558, X1559, X1560, X1561]:(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1554|hAPP(c_Finite__Set_Ocard(X1556),X1558)!=X1554|hBOOL(hAPP(hAPP(c_member(X1556),X1557),X1558))|hAPP(hAPP(c_Set_Oinsert(X1556),X1557),X1558)!=X1555|hAPP(c_Nat_OSuc,X1554)=hAPP(c_Finite__Set_Ocard(X1556),X1555))&(c_Orderings_Obot__class_Obot(tc_fun(X1556,tc_HOL_Obool))!=X1558|hAPP(c_Finite__Set_Ocard(X1556),X1558)!=X1554|hBOOL(hAPP(hAPP(c_member(X1556),X1557),X1558))|hAPP(hAPP(c_Set_Oinsert(X1556),X1557),X1558)!=X1555|hAPP(c_Nat_OSuc,X1554)=hAPP(c_Finite__Set_Ocard(X1556),X1555)))&((((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1559|c_Orderings_Obot__class_Obot(tc_fun(X1561,tc_HOL_Obool))=esk34_3(X1559,X1560,X1561)|hAPP(c_Nat_OSuc,X1559)!=hAPP(c_Finite__Set_Ocard(X1561),X1560))&(hAPP(c_Finite__Set_Ocard(X1561),esk34_3(X1559,X1560,X1561))=X1559|hAPP(c_Nat_OSuc,X1559)!=hAPP(c_Finite__Set_Ocard(X1561),X1560)))&(~hBOOL(hAPP(hAPP(c_member(X1561),esk33_3(X1559,X1560,X1561)),esk34_3(X1559,X1560,X1561)))|hAPP(c_Nat_OSuc,X1559)!=hAPP(c_Finite__Set_Ocard(X1561),X1560)))&(hAPP(hAPP(c_Set_Oinsert(X1561),esk33_3(X1559,X1560,X1561)),esk34_3(X1559,X1560,X1561))=X1560|hAPP(c_Nat_OSuc,X1559)!=hAPP(c_Finite__Set_Ocard(X1561),X1560)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Suc__eq])])])])])])])). 4.46/4.70 fof(c_0_5439, plain, ![X5384, X5385]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5384),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5385),hAPP(c_Int_Onumber__class_Onumber__of(X5385),X5384)),c_Groups_Ozero__class_Ozero(X5385)))|(~class_Rings_Olinordered__idom(X5385)|~class_Int_Onumber__ring(X5385)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5385),hAPP(c_Int_Onumber__class_Onumber__of(X5385),X5384)),c_Groups_Ozero__class_Ozero(X5385)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5384),c_Int_OPls))|(~class_Rings_Olinordered__idom(X5385)|~class_Int_Onumber__ring(X5385)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__special_I3_J])])])])). 4.46/4.70 fof(c_0_5440, plain, ![X16371, X16372]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16372),hAPP(c_Int_Onumber__class_Onumber__of(X16372),X16371)),c_Groups_Ozero__class_Ozero(X16372)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16371),c_Int_OPls))|(~class_Int_Onumber__ring(X16372)|~class_Rings_Olinordered__idom(X16372)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16371),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16372),hAPP(c_Int_Onumber__class_Onumber__of(X16372),X16371)),c_Groups_Ozero__class_Ozero(X16372)))|(~class_Int_Onumber__ring(X16372)|~class_Rings_Olinordered__idom(X16372)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__special_I3_J])])])])). 4.46/4.70 fof(c_0_5441, plain, ![X3129, X3130]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X3129))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3130),c_Groups_Ozero__class_Ozero(X3130)),hAPP(c_Int_Onumber__class_Onumber__of(X3130),X3129)))|(~class_Rings_Olinordered__idom(X3130)|~class_Int_Onumber__ring(X3130)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3130),c_Groups_Ozero__class_Ozero(X3130)),hAPP(c_Int_Onumber__class_Onumber__of(X3130),X3129)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X3129))|(~class_Rings_Olinordered__idom(X3130)|~class_Int_Onumber__ring(X3130)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__special_I1_J])])])])). 4.46/4.70 fof(c_0_5442, plain, ![X4729, X4730]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4730))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X4730)),hAPP(c_Int_Onat,X4729))=hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4730),X4729))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__div__distrib])])])). 4.46/4.70 fof(c_0_5443, plain, ![X15701, X15702]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15702))|hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15702),X15701))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X15702)),hAPP(c_Int_Onat,X15701))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__mult__distrib])])])). 4.46/4.70 fof(c_0_5444, plain, ![X3163, X3164]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X3163))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3164),c_Groups_Ozero__class_Ozero(X3164)),hAPP(c_Int_Onumber__class_Onumber__of(X3164),X3163)))|(~class_Int_Onumber__ring(X3164)|~class_Rings_Olinordered__idom(X3164)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3164),c_Groups_Ozero__class_Ozero(X3164)),hAPP(c_Int_Onumber__class_Onumber__of(X3164),X3163)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X3163))|(~class_Int_Onumber__ring(X3164)|~class_Rings_Olinordered__idom(X3164)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I1_J])])])). 4.46/4.70 fof(c_0_5445, plain, ![X3679, X3680]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3680),X3679))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X3680)),hAPP(c_Int_Onat,X3679))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3679))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X3680)),hAPP(c_Int_Onat,X3679)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3680),X3679))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3679))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X3680)),hAPP(c_Int_Onat,X3679))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__nat__conj])])])). 4.46/4.70 cnf(c_0_5446, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4683])). 4.46/4.70 fof(c_0_5447, plain, ![X4964, X4965]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X4965)),hAPP(c_Int_Onat,X4964)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4965),X4964))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4965)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4965),X4964))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X4965)),hAPP(c_Int_Onat,X4964)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4965)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__eq__zless])])])). 4.46/4.70 fof(c_0_5448, plain, ![X11233, X11234, X11235]:(~class_Orderings_Olinorder(X11235)|c_List_Olinorder__class_Osorted(X11235,hAPP(c_List_Ofilter(X11235,hAPP(hAPP(c_COMBC(X11235,X11235,tc_HOL_Obool),c_fequal),hAPP(X11234,X11233))),X11233))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__same])])). 4.46/4.70 fof(c_0_5449, plain, ![X2525, X2526]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X2526)),X2525))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2526),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2525)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2526)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2526),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2525)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X2526)),X2525))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2526)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__less__iff])])])])). 4.46/4.70 fof(c_0_5450, plain, ![X2749, X2750, X2751, X2752]:((X2751!=X2749|X2750=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X2752),X2751),hAPP(c_List_Oset(X2752),c_List_Oreplicate(X2752,X2750,X2749)))))&((X2751=X2749|~hBOOL(hAPP(hAPP(c_member(X2752),X2751),hAPP(c_List_Oset(X2752),c_List_Oreplicate(X2752,X2750,X2749)))))&(X2750!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X2752),X2751),hAPP(c_List_Oset(X2752),c_List_Oreplicate(X2752,X2750,X2749))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__replicate])])])). 4.46/4.70 fof(c_0_5451, plain, ![X6305]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6305))|c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X6305)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X6305),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__minus1])])). 4.46/4.70 fof(c_0_5452, plain, ![X8485, X8486]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8485)))|hAPP(c_Int_Onumber__class_Onumber__of(X8486),X8485)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8486),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8485))|~class_Int_Onumber__ring(X8486))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8485)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8486),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8485))=c_Groups_Ozero__class_Ozero(X8486)|~class_Int_Onumber__ring(X8486))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__number__of__lemma])])])])). 4.46/4.70 cnf(c_0_5453, plain, (hAPP(c_List_OremoveAll(X1,X3),X2)=c_List_Oremove1(X1,X3,X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4684])). 4.46/4.70 fof(c_0_5454, plain, ![X15740, X15741]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15741),X15740))|c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X15741),hAPP(c_Nat_OSuc,X15740)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15741),X15740))|hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X15740),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X15741),X15740))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X15741),hAPP(c_Nat_OSuc,X15740)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastLessThanSuc])])])). 4.46/4.70 cnf(c_0_5455, plain, (X1=X2|c_Int_OBit1(X1)!=c_Int_OBit1(X2)), inference(split_conjunct,[status(thm)],[c_0_4685])). 4.46/4.70 fof(c_0_5456, plain, ![X3095, X3096, X3097]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3097),c_Groups_Ozero__class_Ozero(X3097)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3097),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3097),X3096),X3096)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3097),X3095),X3095))))|(X3095!=c_Groups_Ozero__class_Ozero(X3097)|c_Groups_Ozero__class_Ozero(X3097)!=X3096)|~class_Rings_Olinordered__ring__strict(X3097))&((X3095=c_Groups_Ozero__class_Ozero(X3097)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3097),c_Groups_Ozero__class_Ozero(X3097)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3097),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3097),X3096),X3096)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3097),X3095),X3095))))|~class_Rings_Olinordered__ring__strict(X3097))&(c_Groups_Ozero__class_Ozero(X3097)=X3096|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3097),c_Groups_Ozero__class_Ozero(X3097)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3097),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3097),X3096),X3096)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3097),X3095),X3095))))|~class_Rings_Olinordered__ring__strict(X3097)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sum__squares__gt__zero__iff])])])])). 4.46/4.70 fof(c_0_5457, plain, ![X911, X912]:(~class_Orderings_Olinorder(X912)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X912,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X912),X911),c_Orderings_Obot__class_Obot(tc_fun(X912,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X912),X911))=hAPP(c_SetInterval_Oord__class_OatLeast(X912),X911)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I1_J])])). 4.46/4.70 cnf(c_0_5458, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_4666])). 4.46/4.70 cnf(c_0_5459, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_4667])). 4.46/4.70 cnf(c_0_5460, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4668])). 4.46/4.70 cnf(c_0_5461, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4670])). 4.46/4.70 cnf(c_0_5462, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_4669])). 4.46/4.70 cnf(c_0_5463, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X1))))), inference(split_conjunct,[status(thm)],[c_0_4671])). 4.46/4.70 cnf(c_0_5464, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1)))), inference(split_conjunct,[status(thm)],[c_0_4672])). 4.46/4.70 cnf(c_0_5465, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1)))), inference(split_conjunct,[status(thm)],[c_0_4673])). 4.46/4.70 cnf(c_0_5466, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1)))), inference(split_conjunct,[status(thm)],[c_0_4675])). 4.46/4.70 cnf(c_0_5467, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1)))), inference(split_conjunct,[status(thm)],[c_0_4674])). 4.46/4.70 cnf(c_0_5468, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1)))), inference(split_conjunct,[status(thm)],[c_0_4676])). 4.46/4.70 fof(c_0_5469, plain, ![X8869, X8870, X8871, X8872]:((X8869=c_List_Olist_ONil(X8872)|X8871!=c_List_Obutlast(X8872,X8869)|c_List_Olast(X8872,X8869)!=X8870|hAPP(hAPP(c_List_Oappend(X8872),X8871),hAPP(hAPP(c_List_Olist_OCons(X8872),X8870),c_List_Olist_ONil(X8872)))=X8869)&(((X8869!=c_List_Olist_ONil(X8872)|hAPP(hAPP(c_List_Oappend(X8872),X8871),hAPP(hAPP(c_List_Olist_OCons(X8872),X8870),c_List_Olist_ONil(X8872)))!=X8869)&(X8871=c_List_Obutlast(X8872,X8869)|hAPP(hAPP(c_List_Oappend(X8872),X8871),hAPP(hAPP(c_List_Olist_OCons(X8872),X8870),c_List_Olist_ONil(X8872)))!=X8869))&(c_List_Olast(X8872,X8869)=X8870|hAPP(hAPP(c_List_Oappend(X8872),X8871),hAPP(hAPP(c_List_Olist_OCons(X8872),X8870),c_List_Olist_ONil(X8872)))!=X8869))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__eq__iff__butlast])])])). 4.46/4.70 fof(c_0_5470, plain, ![X15401, X15402]:((hBOOL(hAPP(hAPP(c_member(X15402),esk449_2(X15401,X15402)),X15401))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X15402),X15401)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15402),X15401)))&(c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X15402),X15401)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15402),X15401)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card_Oneutral])])])])])). 4.46/4.70 fof(c_0_5471, plain, ![X16560, X16561]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X16561),X16560))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X16561),X16560))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16561),X16560))|hAPP(c_Finite__Set_Ocard(X16561),X16560)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X16561,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X16561),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16560))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__def])])])). 4.46/4.70 fof(c_0_5472, plain, ![X7058, X7059, X7061, X7062, X7063]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7058),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk206_2(X7058,X7059))=X7058|hBOOL(hAPP(X7059,hAPP(c_Int_Onat,X7058))))&(~hBOOL(hAPP(X7059,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk206_2(X7058,X7059))=X7058|hBOOL(hAPP(X7059,hAPP(c_Int_Onat,X7058)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7058),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X7059,esk206_2(X7058,X7059)))|hBOOL(hAPP(X7059,hAPP(c_Int_Onat,X7058))))&(~hBOOL(hAPP(X7059,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X7059,esk206_2(X7058,X7059)))|hBOOL(hAPP(X7059,hAPP(c_Int_Onat,X7058))))))&((hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7063)!=X7061|hBOOL(hAPP(X7062,X7063))|~hBOOL(hAPP(X7062,hAPP(c_Int_Onat,X7061))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7061),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X7062,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X7062,hAPP(c_Int_Onat,X7061)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__nat])])])])])])). 4.46/4.70 fof(c_0_5473, plain, ![X5638, X5639]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5639),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X5638),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5639),X5638)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5639),X5638))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5639),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X5638),c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__diff1__eq])])). 4.46/4.70 fof(c_0_5474, plain, ![X2965]:(~class_Orderings_Owellorder(X2965)|c_Wellfounded_Owf(X2965,hAPP(c_Set_OCollect(tc_prod(X2965,X2965)),hAPP(c_Product__Type_Oprod_Oprod__case(X2965,X2965,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X2965))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf])])). 4.46/4.70 cnf(c_0_5475, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_Osucc(X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4686])). 4.46/4.70 fof(c_0_5476, plain, ![X2688]:(~c_List_Onat__list(X2688)|X2688=c_List_Oembed__list(c_List_Oreturn__list(X2688))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__list__return__embed])])). 4.46/4.70 fof(c_0_5477, plain, ![X17201, X17202]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17202),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X17201),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X17202))=c_Nitpick_Onorm__frac(X17201,X17202))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X17202|X17201=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Nitpick_Onorm__frac(X17201,X17202)=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X17201),X17202)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X17201))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X17202)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17202),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X17202|c_Nitpick_Onorm__frac(X17201,X17202)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17202),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&(X17201!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Nitpick_Onorm__frac(X17201,X17202)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17202),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_norm__frac_Osimps])])])])). 4.46/4.70 fof(c_0_5478, plain, ![X1029, X1030]:(~class_Int_Onumber__ring(X1030)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1029))|hBOOL(hAPP(hAPP(c_member(X1030),hAPP(c_Int_Onumber__class_Onumber__of(X1030),X1029)),c_Nat_Osemiring__1__class_ONats(X1030))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nats__number__of])])])). 4.46/4.70 fof(c_0_5479, plain, ![X13529, X13530]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13530))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X13530)),X13529)=hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X13530),X13529))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__eq])])). 4.46/4.70 fof(c_0_5480, plain, ![X14969, X14970]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X14969)))|hAPP(c_Int_Onumber__class_Onumber__of(X14970),X14969)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X14970),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14969))|~class_Int_Onumber__ring(X14970))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X14969)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X14970),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14969))=c_Groups_Ozero__class_Ozero(X14970)|~class_Int_Onumber__ring(X14970))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__number__of__eq])])])])). 4.46/4.70 fof(c_0_5481, plain, ![X755, X756]:(~c_Wellfounded_OwfP(X756,X755)|c_Wellfounded_Oacyclic(X756,hAPP(c_Set_OCollect(tc_prod(X756,X756)),hAPP(c_Product__Type_Oprod_Oprod__case(X756,X756,tc_HOL_Obool),X755)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wfP__acyclicP])])])). 4.46/4.70 fof(c_0_5482, plain, ![X11001, X11002]:((~c_Wellfounded_OwfP(X11002,X11001)|c_Wellfounded_Owf(X11002,hAPP(c_Set_OCollect(tc_prod(X11002,X11002)),hAPP(c_Product__Type_Oprod_Oprod__case(X11002,X11002,tc_HOL_Obool),X11001))))&(~c_Wellfounded_Owf(X11002,hAPP(c_Set_OCollect(tc_prod(X11002,X11002)),hAPP(c_Product__Type_Oprod_Oprod__case(X11002,X11002,tc_HOL_Obool),X11001)))|c_Wellfounded_OwfP(X11002,X11001))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__def])])). 4.46/4.70 fof(c_0_5483, plain, ![X10078, X10079]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X10079)),hAPP(c_Int_Onat,X10078)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10079),X10078))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10078)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10079),X10078))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X10079)),hAPP(c_Int_Onat,X10078)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10078))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X10079)),hAPP(c_Int_Onat,X10078)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10079),X10078))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10079)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10079),X10078))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X10079)),hAPP(c_Int_Onat,X10078)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10079))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__le__eq__zle])])])])). 4.46/4.70 fof(c_0_5484, plain, ![X15441]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X15441))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,X15441))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,X15441)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X15441)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__nat__eq])])). 4.46/4.70 fof(c_0_5485, plain, ![X1919]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1919))|hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X1919))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1919))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__nat__eq__nat__zadd1])])). 4.46/4.70 fof(c_0_5486, plain, ![X1989, X1990]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1990),X1989))|hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X1990,X1989))=X1990), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__upt])])])). 4.46/4.70 fof(c_0_5487, plain, ![X7286, X7287, X7288, X7289, X7290, X7291, X7292, X7293]:((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7288,tc_HOL_Obool)),X7287),X7286)!=c_Orderings_Obot__class_Obot(tc_fun(X7288,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_member(X7288),X7289),X7287))|(~hBOOL(hAPP(hAPP(c_member(X7288),X7290),X7286))|X7289!=X7290)))&((hBOOL(hAPP(hAPP(c_member(X7293),esk210_3(X7291,X7292,X7293)),X7292))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7293,tc_HOL_Obool)),X7292),X7291)=c_Orderings_Obot__class_Obot(tc_fun(X7293,tc_HOL_Obool)))&((hBOOL(hAPP(hAPP(c_member(X7293),esk211_3(X7291,X7292,X7293)),X7291))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7293,tc_HOL_Obool)),X7292),X7291)=c_Orderings_Obot__class_Obot(tc_fun(X7293,tc_HOL_Obool)))&(esk210_3(X7291,X7292,X7293)=esk211_3(X7291,X7292,X7293)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7293,tc_HOL_Obool)),X7292),X7291)=c_Orderings_Obot__class_Obot(tc_fun(X7293,tc_HOL_Obool)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_disjoint__iff__not__equal])])])])])])])). 4.46/4.70 fof(c_0_5488, plain, ![X5313]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5313))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X5313)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__eq__minus1])])). 4.46/4.70 cnf(c_0_5489, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X1))=hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))), inference(split_conjunct,[status(thm)],[c_0_4687])). 4.46/4.70 cnf(c_0_5490, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|c_List_Oupt(X1,hAPP(c_Nat_OSuc,X2))=c_List_Olist_ONil(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_4630])). 4.46/4.70 fof(c_0_5491, plain, ![X1768, X1769]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1769),hAPP(c_Groups_Oabs__class_Oabs(X1769),X1768)),c_Groups_Ozero__class_Ozero(X1769)))|c_Groups_Ozero__class_Ozero(X1769)=X1768|~class_Groups_Oordered__ab__group__add__abs(X1769))&(c_Groups_Ozero__class_Ozero(X1769)!=X1768|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1769),hAPP(c_Groups_Oabs__class_Oabs(X1769),X1768)),c_Groups_Ozero__class_Ozero(X1769)))|~class_Groups_Oordered__ab__group__add__abs(X1769))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff])])])). 4.46/4.70 fof(c_0_5492, plain, ![X13487, X13488]:((X13487!=c_Groups_Ozero__class_Ozero(X13488)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13488),X13487),X13487)=c_Groups_Ozero__class_Ozero(X13488)|~hBOOL(hAPP(hAPP(c_member(X13488),X13487),c_Int_Oring__1__class_OInts(X13488)))|~class_Int_Oring__char__0(X13488))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13488),X13487),X13487)!=c_Groups_Ozero__class_Ozero(X13488)|X13487=c_Groups_Ozero__class_Ozero(X13488)|~hBOOL(hAPP(hAPP(c_member(X13488),X13487),c_Int_Oring__1__class_OInts(X13488)))|~class_Int_Oring__char__0(X13488))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__double__eq__0__iff])])])])). 4.46/4.70 fof(c_0_5493, plain, ![X10222, X10223, X10224, X10225]:(~c_Hoare__Mirabelle_Ohoare__derivs(X10225,X10224,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10225)),X10223),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X10225),tc_HOL_Obool))))|(~c_Hoare__Mirabelle_Ohoare__derivs(X10225,X10224,X10222)|c_Hoare__Mirabelle_Ohoare__derivs(X10225,X10224,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X10225)),X10223),X10222)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hoare__derivs_Oinsert])])])). 4.46/4.70 fof(c_0_5494, plain, ![X14474, X14475, X14476, X14477]:((((c_Groups_Ozero__class_Ozero(X14477)!=X14474|X14474=c_Groups_Ozero__class_Ozero(X14477)|X14476=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14477),X14475),X14474)|~class_Fields_Ofield__inverse__zero(X14477))&(X14475!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14477),X14476),X14474)|X14474=c_Groups_Ozero__class_Ozero(X14477)|X14476=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14477),X14475),X14474)|~class_Fields_Ofield__inverse__zero(X14477)))&((c_Groups_Ozero__class_Ozero(X14477)!=X14474|X14476!=c_Groups_Ozero__class_Ozero(X14477)|X14476=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14477),X14475),X14474)|~class_Fields_Ofield__inverse__zero(X14477))&(X14475!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14477),X14476),X14474)|X14476!=c_Groups_Ozero__class_Ozero(X14477)|X14476=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14477),X14475),X14474)|~class_Fields_Ofield__inverse__zero(X14477))))&((X14474!=c_Groups_Ozero__class_Ozero(X14477)|X14476=c_Groups_Ozero__class_Ozero(X14477)|X14476!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14477),X14475),X14474)|~class_Fields_Ofield__inverse__zero(X14477))&(c_Groups_Ozero__class_Ozero(X14477)=X14474|X14475=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14477),X14476),X14474)|X14476!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14477),X14475),X14474)|~class_Fields_Ofield__inverse__zero(X14477)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__divide__eq])])])])). 4.46/4.70 fof(c_0_5495, plain, ![X15140, X15141]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15141),X15140))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X15141)),X15140)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X15141)),X15140))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15141),X15140)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__pred__less])])). 4.46/4.70 fof(c_0_5496, plain, ![X4473, X4474, X4475, X4476]:((((X4474=c_Groups_Ozero__class_Ozero(X4476)|X4474!=c_Groups_Ozero__class_Ozero(X4476)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4476),X4475),X4474)=X4473|~class_Fields_Ofield__inverse__zero(X4476))&(c_Groups_Ozero__class_Ozero(X4476)!=X4473|X4474!=c_Groups_Ozero__class_Ozero(X4476)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4476),X4475),X4474)=X4473|~class_Fields_Ofield__inverse__zero(X4476)))&((X4474=c_Groups_Ozero__class_Ozero(X4476)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4476),X4473),X4474)!=X4475|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4476),X4475),X4474)=X4473|~class_Fields_Ofield__inverse__zero(X4476))&(c_Groups_Ozero__class_Ozero(X4476)!=X4473|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4476),X4473),X4474)!=X4475|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4476),X4475),X4474)=X4473|~class_Fields_Ofield__inverse__zero(X4476))))&((X4474=c_Groups_Ozero__class_Ozero(X4476)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4476),X4473),X4474)=X4475|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4476),X4475),X4474)!=X4473|~class_Fields_Ofield__inverse__zero(X4476))&(X4474!=c_Groups_Ozero__class_Ozero(X4476)|c_Groups_Ozero__class_Ozero(X4476)=X4473|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4476),X4475),X4474)!=X4473|~class_Fields_Ofield__inverse__zero(X4476)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__eq__eq])])])])). 4.46/4.70 fof(c_0_5497, plain, ![X913, X914, X915]:(hAPP(hAPP(c_Relation_Orel__comp(X915,X915,X915),hAPP(c_Relation_Oconverse(X915,X915),X914)),X914)!=X914|(X913!=hAPP(c_Relation_ODomain(X915,X915),X914)|c_Equiv__Relations_Oequiv(X915,X913,X914))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comp__equivI])])])). 4.46/4.70 fof(c_0_5498, plain, ![X12881, X12882]:(((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X12882|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X12882)),X12881))))&(X12881!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X12882)),X12881)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X12882)),X12881)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X12882|X12881=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff])])])). 4.46/4.70 fof(c_0_5499, plain, ![X12541, X12542, X12543, X12544]:(hBOOL(hAPP(X12544,X12543))|hAPP(c_List_Ofilter(X12542,X12544),X12541)=c_List_Oremove1(X12542,X12543,hAPP(c_List_Ofilter(X12542,X12544),X12541))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_remove1__filter__not])])])). 4.46/4.70 fof(c_0_5500, plain, ![X6346, X6347, X6348, X6349]:hAPP(c_List_Ofilter(X6349,X6348),c_List_Oremove1(X6349,X6347,X6346))=c_List_Oremove1(X6349,X6347,hAPP(c_List_Ofilter(X6349,X6348),X6346)), inference(variable_rename,[status(thm)],[fact_filter__remove1])). 4.46/4.70 fof(c_0_5501, plain, ![X15070, X15071, X15072]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X15072,X15072)),hAPP(hAPP(c_Product__Type_OPair(X15072,X15072),X15071),X15070)),c_Relation_OId(X15072)))|X15071=X15070)&(X15071!=X15070|hBOOL(hAPP(hAPP(c_member(tc_prod(X15072,X15072)),hAPP(hAPP(c_Product__Type_OPair(X15072,X15072),X15071),X15070)),c_Relation_OId(X15072))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__in__Id__conv])])). 4.46/4.70 fof(c_0_5502, plain, ![X6123, X6124, X6125, X6127, X6128, X6129, X6130]:(((hBOOL(hAPP(hAPP(c_member(tc_fun(X6125,tc_HOL_Obool)),esk190_3(X6123,X6124,X6125)),X6124))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6125,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X6125,tc_HOL_Obool),X6124)),X6123)=c_Orderings_Obot__class_Obot(tc_fun(X6125,tc_HOL_Obool)))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6125,tc_HOL_Obool)),esk190_3(X6123,X6124,X6125)),X6123)!=c_Orderings_Obot__class_Obot(tc_fun(X6125,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6125,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X6125,tc_HOL_Obool),X6124)),X6123)=c_Orderings_Obot__class_Obot(tc_fun(X6125,tc_HOL_Obool))))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6129,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X6129,tc_HOL_Obool),X6128)),X6127)!=c_Orderings_Obot__class_Obot(tc_fun(X6129,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_member(tc_fun(X6129,tc_HOL_Obool)),X6130),X6128))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6129,tc_HOL_Obool)),X6130),X6127)=c_Orderings_Obot__class_Obot(tc_fun(X6129,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__disjoint])])])])])])). 4.46/4.70 fof(c_0_5503, plain, ![X4214, X4215, X4216, X4217]:((X4214!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4217),X4215),X4216)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4217),X4214),X4216)=X4215|X4216=c_Groups_Ozero__class_Ozero(X4217)|~class_Rings_Odivision__ring(X4217))&(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4217),X4214),X4216)!=X4215|X4214=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4217),X4215),X4216)|X4216=c_Groups_Ozero__class_Ozero(X4217)|~class_Rings_Odivision__ring(X4217))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nonzero__eq__divide__eq])])])])). 4.46/4.70 cnf(c_0_5504, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_4688])). 4.46/4.70 fof(c_0_5505, plain, ![X17397, X17398]:(~c_Wellfounded_Owf(X17398,X17397)|c_Wellfounded_Owf(X17398,c_Transitive__Closure_Otrancl(X17398,X17397))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__trancl])])). 4.46/4.70 fof(c_0_5506, plain, ![X13935, X13936, X13938]:((((hAPP(c_List_Oset(X13936),esk407_2(X13935,X13936))=X13935|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13936),X13935))|~class_Orderings_Olinorder(X13936))&(hAPP(c_List_Oset(X13936),X13938)!=X13935|~hBOOL(hAPP(c_List_Odistinct(X13936),X13938))|~c_List_Olinorder__class_Osorted(X13936,X13938)|esk407_2(X13935,X13936)=X13938|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13936),X13935))|~class_Orderings_Olinorder(X13936)))&(hBOOL(hAPP(c_List_Odistinct(X13936),esk407_2(X13935,X13936)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13936),X13935))|~class_Orderings_Olinorder(X13936)))&(c_List_Olinorder__class_Osorted(X13936,esk407_2(X13935,X13936))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13936),X13935))|~class_Orderings_Olinorder(X13936))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__sorted__distinct__unique])])])])])])). 4.46/4.70 fof(c_0_5507, plain, ![X540, X541]:hBOOL(hAPP(c_Finite__Set_Ofinite(X541),hAPP(c_List_Oset(X541),X540))), inference(variable_rename,[status(thm)],[fact_finite__set])). 4.46/4.70 fof(c_0_5508, plain, ![X8303]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X8303)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8303)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8303))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X8303))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__nat__eq])])). 4.46/4.70 fof(c_0_5509, plain, ![X1848, X1849, X1850]:(~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X1850)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))|(~c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X1849),X1850),X1848)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))|c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X1849),X1850),X1848)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_MGF__complete])])). 4.46/4.70 fof(c_0_5510, plain, ![X13795, X13796]:((c_List_Olist_ONil(tc_Nat_Onat)!=c_List_Oupt(X13796,X13795)|(X13795=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13795),X13796))))&((X13795!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X13796,X13795))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13795),X13796))|c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X13796,X13795)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__eq__Nil__conv])])])). 4.46/4.70 fof(c_0_5511, plain, ![X11048, X11049]:((~hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11049),X11048))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X11049)),X11048)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X11049)),X11048))|hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11049),X11048)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J])])). 4.46/4.70 fof(c_0_5512, plain, ![X4249]:((~c_Com_OWT__bodies|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),X4249),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),X4249))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),esk117_0),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))|c_Com_OWT__bodies)&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),esk117_0))|c_Com_OWT__bodies))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT__bodies__def])])])])])). 4.46/4.70 fof(c_0_5513, plain, ![X9840, X9841]:((hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),esk283_2(X9840,X9841)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))|(~hBOOL(hAPP(c_Com_OWT,X9840))|c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X9841,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X9840)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))))|~c_Hoare__Mirabelle_Ostate__not__singleton)&(~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X9841,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,esk283_2(X9840,X9841)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))|(~hBOOL(hAPP(c_Com_OWT,X9840))|c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X9841,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X9840)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))))|~c_Hoare__Mirabelle_Ostate__not__singleton)), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_MGF__lemma1])])])])])])])). 4.46/4.70 fof(c_0_5514, plain, ![X13611, X13612, X13613]:(((X13611!=X13612|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13613),X13612),X13612)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13613),X13611),X13611)|~class_Rings_Oidom(X13613))&(hAPP(c_Groups_Ouminus__class_Ouminus(X13613),X13611)!=X13612|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13613),X13612),X13612)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13613),X13611),X13611)|~class_Rings_Oidom(X13613)))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13613),X13612),X13612)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13613),X13611),X13611)|(X13611=X13612|hAPP(c_Groups_Ouminus__class_Ouminus(X13613),X13611)=X13612)|~class_Rings_Oidom(X13613))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__iff])])])). 4.46/4.70 fof(c_0_5515, plain, ![X15666]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15666))|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Osgn__class_Osgn(tc_Int_Oint,X15666)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X15666)&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15666))|c_Groups_Oone__class_Oone(tc_Int_Oint)=c_Groups_Osgn__class_Osgn(tc_Int_Oint,X15666)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X15666))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X15666|c_Groups_Osgn__class_Osgn(tc_Int_Oint,X15666)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zsgn__def])])])])). 4.46/4.70 fof(c_0_5516, plain, ![X13439, X13441, X13442, X13444]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk393_1(X13439)))|hBOOL(hAPP(X13439,X13441)))&(~hBOOL(hAPP(X13439,hAPP(c_Int_Onat,esk393_1(X13439))))|hBOOL(hAPP(X13439,X13441))))&(~hBOOL(hAPP(X13442,esk394_1(X13442)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13444))|hBOOL(hAPP(X13442,hAPP(c_Int_Onat,X13444)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_all__nat])])])])])])). 4.46/4.70 fof(c_0_5517, plain, ![X8411, X8412]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X8411)),X8412))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8412),X8411)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8412),X8411))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X8411)),X8412)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq])])])). 4.46/4.70 fof(c_0_5518, plain, ![X10438, X10439]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X10439)),hAPP(c_Code__Numeral_Oof__nat,X10438)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10439),X10438)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10439),X10438))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X10439)),hAPP(c_Code__Numeral_Oof__nat,X10438))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__code__numeral__code])])). 4.46/4.70 fof(c_0_5519, plain, ![X9553, X9554, X9555]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X9555,X9554),X9553))|X9553=c_Divides_Odivmod__nat(X9555,X9554)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__eq])])). 4.46/4.70 fof(c_0_5520, plain, ![X10419, X10420]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X10420)),hAPP(c_Code__Numeral_Oof__nat,X10419)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10420),X10419)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10420),X10419))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X10420)),hAPP(c_Code__Numeral_Oof__nat,X10419))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__code])])). 4.46/4.70 fof(c_0_5521, plain, ![X591, X592]:((((X591=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X591|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X592),X591)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(X592=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X591|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X592),X591)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&((X591=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X592=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X592),X591)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(X592=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X592=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X592),X591)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))&((hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X591|X592!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X592),X591)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(X591!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X592!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X592),X591)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__1])])])). 4.46/4.70 fof(c_0_5522, plain, ![X4321, X4322]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4322),X4321))|c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X4321,X4322)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_upt__conv__Nil])])])). 4.46/4.70 fof(c_0_5523, plain, ![X5053, X5054]:(~class_Rings_Oring__1(X5054)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5053))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5054),hAPP(c_Int_Onat,X5053))=hAPP(c_Int_Oring__1__class_Oof__int(X5054),X5053))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__nat])])). 4.46/4.70 fof(c_0_5524, plain, ![X4016, X4017, X4018, X4019]:((c_Hoare__Mirabelle_Ohoare__derivs(X4019,X4018,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4019)),X4017),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4019),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X4019,X4018,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4019)),X4017),X4016)))&(c_Hoare__Mirabelle_Ohoare__derivs(X4019,X4018,X4016)|~c_Hoare__Mirabelle_Ohoare__derivs(X4019,X4018,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4019)),X4017),X4016)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_derivs__insertD])])])])). 4.46/4.70 fof(c_0_5525, plain, ![X17361, X17362]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17362)),X17361))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17362),hAPP(c_Int_Onat,X17361))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17362),hAPP(c_Int_Onat,X17361)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17362)),X17361)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__nat__eq__int__zless])])). 4.46/4.70 fof(c_0_5526, plain, ![X2130]:((X2130=hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X2130)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X2130))|X2130!=hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral__not__eq__zero])])). 4.46/4.70 fof(c_0_5527, plain, ![X7005, X7006, X7008, X7009]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk204_1(X7005)))|~hBOOL(hAPP(X7005,X7006)))&(hBOOL(hAPP(X7005,hAPP(c_Int_Onat,esk204_1(X7005))))|~hBOOL(hAPP(X7005,X7006))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7009))|~hBOOL(hAPP(X7008,hAPP(c_Int_Onat,X7009)))|hBOOL(hAPP(X7008,esk205_1(X7008))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__nat])])])])])])). 4.46/4.70 fof(c_0_5528, plain, ![X4471, X4472]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4472),X4471),X4471)!=c_Groups_Oone__class_Oone(X4472)|(hAPP(c_Groups_Ouminus__class_Ouminus(X4472),c_Groups_Oone__class_Oone(X4472))=X4471|c_Groups_Oone__class_Oone(X4472)=X4471)|~class_Rings_Oring__1__no__zero__divisors(X4472))&((hAPP(c_Groups_Ouminus__class_Ouminus(X4472),c_Groups_Oone__class_Oone(X4472))!=X4471|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4472),X4471),X4471)=c_Groups_Oone__class_Oone(X4472)|~class_Rings_Oring__1__no__zero__divisors(X4472))&(c_Groups_Oone__class_Oone(X4472)!=X4471|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4472),X4471),X4471)=c_Groups_Oone__class_Oone(X4472)|~class_Rings_Oring__1__no__zero__divisors(X4472)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_square__eq__1__iff])])])])). 4.46/4.70 fof(c_0_5529, plain, ![X1673]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1673))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1673))=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1673))|X1673=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1673)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__nat__eq])])])). 4.46/4.70 fof(c_0_5530, plain, ![X16014, X16015]:(~class_Int_Onumber__ring(X16015)|~class_Fields_Ofield__inverse__zero(X16015)|c_Groups_Ozero__class_Ozero(X16015)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16015),X16014),hAPP(c_Int_Onumber__class_Onumber__of(X16015),c_Int_OPls))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral0])])). 4.46/4.70 fof(c_0_5531, plain, ![X1571, X1572]:((X1571!=X1572|hAPP(c_Int_Onat,X1571)=hAPP(c_Int_Onat,X1572)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1571))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1572)))&(hAPP(c_Int_Onat,X1571)!=hAPP(c_Int_Onat,X1572)|X1571=X1572|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1571))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1572)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__nat__nat__iff])])])). 4.46/4.70 fof(c_0_5532, plain, ![X9960, X9961, X9962, X9963]:((((c_Groups_Ozero__class_Ozero(X9963)!=hAPP(c_Int_Onumber__class_Onumber__of(X9963),X9961)|hAPP(c_Int_Onumber__class_Onumber__of(X9963),X9961)=c_Groups_Ozero__class_Ozero(X9963)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9963),X9962),hAPP(c_Int_Onumber__class_Onumber__of(X9963),X9961))=X9960|(~class_Int_Onumber(X9963)|~class_Fields_Ofield__inverse__zero(X9963)))&(X9962!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9963),X9960),hAPP(c_Int_Onumber__class_Onumber__of(X9963),X9961))|hAPP(c_Int_Onumber__class_Onumber__of(X9963),X9961)=c_Groups_Ozero__class_Ozero(X9963)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9963),X9962),hAPP(c_Int_Onumber__class_Onumber__of(X9963),X9961))=X9960|(~class_Int_Onumber(X9963)|~class_Fields_Ofield__inverse__zero(X9963))))&((c_Groups_Ozero__class_Ozero(X9963)!=hAPP(c_Int_Onumber__class_Onumber__of(X9963),X9961)|X9960!=c_Groups_Ozero__class_Ozero(X9963)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9963),X9962),hAPP(c_Int_Onumber__class_Onumber__of(X9963),X9961))=X9960|(~class_Int_Onumber(X9963)|~class_Fields_Ofield__inverse__zero(X9963)))&(X9962!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9963),X9960),hAPP(c_Int_Onumber__class_Onumber__of(X9963),X9961))|X9960!=c_Groups_Ozero__class_Ozero(X9963)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9963),X9962),hAPP(c_Int_Onumber__class_Onumber__of(X9963),X9961))=X9960|(~class_Int_Onumber(X9963)|~class_Fields_Ofield__inverse__zero(X9963)))))&((hAPP(c_Int_Onumber__class_Onumber__of(X9963),X9961)!=c_Groups_Ozero__class_Ozero(X9963)|X9960=c_Groups_Ozero__class_Ozero(X9963)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9963),X9962),hAPP(c_Int_Onumber__class_Onumber__of(X9963),X9961))!=X9960|(~class_Int_Onumber(X9963)|~class_Fields_Ofield__inverse__zero(X9963)))&(c_Groups_Ozero__class_Ozero(X9963)=hAPP(c_Int_Onumber__class_Onumber__of(X9963),X9961)|X9962=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9963),X9960),hAPP(c_Int_Onumber__class_Onumber__of(X9963),X9961))|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9963),X9962),hAPP(c_Int_Onumber__class_Onumber__of(X9963),X9961))!=X9960|(~class_Int_Onumber(X9963)|~class_Fields_Ofield__inverse__zero(X9963))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__eq__eq__number__of1])])])])). 4.46/4.70 fof(c_0_5533, plain, ![X14739, X14740, X14741]:(((c_Groups_Ozero__class_Ozero(X14741)=X14740|c_Groups_Ozero__class_Ozero(X14741)!=hAPP(hAPP(c_Power_Opower__class_Opower(X14741),X14740),X14739)|(~class_Rings_Ono__zero__divisors(X14741)|~class_Rings_Ozero__neq__one(X14741)|~class_Rings_Omult__zero(X14741)|~class_Power_Opower(X14741)))&(X14739!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(X14741)!=hAPP(hAPP(c_Power_Opower__class_Opower(X14741),X14740),X14739)|(~class_Rings_Ono__zero__divisors(X14741)|~class_Rings_Ozero__neq__one(X14741)|~class_Rings_Omult__zero(X14741)|~class_Power_Opower(X14741))))&(c_Groups_Ozero__class_Ozero(X14741)!=X14740|X14739=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(X14741)=hAPP(hAPP(c_Power_Opower__class_Opower(X14741),X14740),X14739)|(~class_Rings_Ono__zero__divisors(X14741)|~class_Rings_Ozero__neq__one(X14741)|~class_Rings_Omult__zero(X14741)|~class_Power_Opower(X14741)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff])])])). 4.46/4.70 fof(c_0_5534, plain, ![X1894, X1895]:((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1895),X1894)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|(X1895=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1894))&((X1895!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1895),X1894)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1894|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1895),X1894)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__eq__Suc__0__iff])])])). 4.46/4.70 fof(c_0_5535, plain, ![X9832, X9833]:(((X9832!=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oone__class_Oone(tc_Int_Oint)!=X9833|c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9833),X9832))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)!=X9833|X9832!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)|c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9833),X9832)))&(((hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X9833|X9832=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9833),X9832))&(X9832=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)|X9832=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9833),X9832)))&((hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X9833|c_Groups_Oone__class_Oone(tc_Int_Oint)=X9833|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9833),X9832))&(X9832=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)|c_Groups_Oone__class_Oone(tc_Int_Oint)=X9833|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9833),X9832))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__eq__1__iff])])])). 4.46/4.70 cnf(c_0_5536, plain, (~class_Int_Oring__char__0(X1)|~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(X2)))), inference(split_conjunct,[status(thm)],[c_0_4689])). 4.46/4.70 fof(c_0_5537, axiom, ![X45, X14, X28]:((epred2_3(X28,X45,X14)&(hBOOL(hAPP(X28,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=X45=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>hBOOL(hAPP(X28,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14),X45)))), inference(apply_def,[status(thm)],[fact_split__zdiv, c_0_4612])). 4.46/4.70 fof(c_0_5538, plain, ![X4045, X4046, X4047]:((X4046!=hAPP(c_Groups_Ouminus__class_Ouminus(X4047),X4045)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4047),X4046),X4045)=c_Groups_Ozero__class_Ozero(X4047)|~class_Groups_Ogroup__add(X4047))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4047),X4046),X4045)!=c_Groups_Ozero__class_Ozero(X4047)|X4046=hAPP(c_Groups_Ouminus__class_Ouminus(X4047),X4045)|~class_Groups_Ogroup__add(X4047))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0])])])). 4.46/4.70 cnf(c_0_5539, plain, (~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls)))), inference(split_conjunct,[status(thm)],[c_0_4690])). 4.46/4.70 cnf(c_0_5540, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))))), inference(split_conjunct,[status(thm)],[c_0_4688])). 4.46/4.70 fof(c_0_5541, plain, ![X1639, X1640]:((c_List_Oremdups(X1640,X1639)!=X1639|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1640)),c_List_Oremdups(X1640,X1639))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1640)),X1639))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1640)),c_List_Oremdups(X1640,X1639))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1640)),X1639)|c_List_Oremdups(X1640,X1639)=X1639)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__remdups__eq])])). 4.46/4.70 fof(c_0_5542, plain, ![X1351, X1352]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1352)),c_List_Oremdups(X1352,X1351))=hAPP(c_Finite__Set_Ocard(X1352),hAPP(c_List_Oset(X1352),X1351)), inference(variable_rename,[status(thm)],[fact_length__remdups__card__conv])). 4.46/4.70 fof(c_0_5543, plain, ![X1788, X1789]:(~class_Int_Onumber__ring(X1789)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1789),hAPP(c_Int_Onumber__class_Onumber__of(X1789),c_Int_OPls)),X1788)=X1788), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0])])). 4.46/4.70 fof(c_0_5544, plain, ![X9200, X9201]:(~class_Int_Onumber__ring(X9201)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9201),X9200),hAPP(c_Int_Onumber__class_Onumber__of(X9201),c_Int_OPls))=X9200), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__numeral__0__right])])])). 4.46/4.70 cnf(c_0_5545, plain, (X1=c_Int_OMin|c_Int_OBit1(X1)!=c_Int_OMin), inference(split_conjunct,[status(thm)],[c_0_4691])). 4.46/4.70 fof(c_0_5546, plain, ![X16670, X16671]:((((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16670))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16670))|X16671=hAPP(c_Int_Onat,X16670))&(X16671!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16670))|X16671=hAPP(c_Int_Onat,X16670)))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16670))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16671)!=X16670|X16671=hAPP(c_Int_Onat,X16670))&(X16671!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16671)!=X16670|X16671=hAPP(c_Int_Onat,X16670))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16670))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16671)=X16670|X16671!=hAPP(c_Int_Onat,X16670))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16670))|X16671=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X16671!=hAPP(c_Int_Onat,X16670)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__eq__iff2])])])])). 4.46/4.70 fof(c_0_5547, plain, ![X12869, X12871, X12872, X12873, X12874]:((hBOOL(hAPP(X12869,esk376_1(X12869)))|c_Orderings_Obot__class_Obot(tc_fun(X12871,tc_HOL_Obool))=hAPP(c_Set_OCollect(X12871),X12869))&(c_Orderings_Obot__class_Obot(tc_fun(X12873,tc_HOL_Obool))!=hAPP(c_Set_OCollect(X12873),X12872)|~hBOOL(hAPP(X12872,X12874)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_empty__Collect__eq])])])])])])). 4.46/4.70 fof(c_0_5548, plain, ![X3974, X3976, X3977, X3978, X3979]:((hBOOL(hAPP(X3974,esk109_1(X3974)))|c_Orderings_Obot__class_Obot(tc_fun(X3976,tc_HOL_Obool))=hAPP(c_Set_OCollect(X3976),X3974))&(c_Orderings_Obot__class_Obot(tc_fun(X3978,tc_HOL_Obool))!=hAPP(c_Set_OCollect(X3978),X3977)|~hBOOL(hAPP(X3977,X3979)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq])])])])])])). 4.46/4.70 fof(c_0_5549, plain, ![X2101, X2102, X2103, X2104, X2105]:((X2101!=X2102|X2103=X2104|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2105),X2104),X2103)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2105),X2102),X2101)|~class_Groups_Oab__group__add(X2105))&(X2103!=X2104|X2101=X2102|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2105),X2104),X2103)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2105),X2102),X2101)|~class_Groups_Oab__group__add(X2105))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__eq__diff__eq])])])])). 4.46/4.70 fof(c_0_5550, plain, ![X3955, X3956, X3957]:(((X3956!=c_Groups_Ozero__class_Ozero(X3957)|c_Groups_Ozero__class_Ozero(X3957)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3957),X3956),X3955)|~class_Rings_Oring__no__zero__divisors(X3957))&(c_Groups_Ozero__class_Ozero(X3957)!=X3955|c_Groups_Ozero__class_Ozero(X3957)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3957),X3956),X3955)|~class_Rings_Oring__no__zero__divisors(X3957)))&(c_Groups_Ozero__class_Ozero(X3957)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3957),X3956),X3955)|(X3956=c_Groups_Ozero__class_Ozero(X3957)|c_Groups_Ozero__class_Ozero(X3957)=X3955)|~class_Rings_Oring__no__zero__divisors(X3957))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])])). 4.46/4.70 fof(c_0_5551, plain, ![X2684]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2684)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2684))=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2684)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2684)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2684)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__nat__number__of])])])). 4.46/4.70 fof(c_0_5552, plain, ![X8142, X8143]:(~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X8143))),X8142),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X8143)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))|c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X8142,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X8143))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_MGT__BodyN])])])). 4.46/4.70 cnf(c_0_5553, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ostate__not__singleton|~c_Com_OWT__bodies|~hBOOL(hAPP(c_Com_OWT,X1))), inference(split_conjunct,[status(thm)],[c_0_4692])). 4.46/4.70 cnf(c_0_5554, hypothesis, (c_Com_OWT__bodies), inference(split_conjunct,[status(thm)],[conj_1]), ['final']). 4.46/4.70 cnf(c_0_5555, hypothesis, (c_Hoare__Mirabelle_Ostate__not__singleton), inference(split_conjunct,[status(thm)],[conj_0]), ['final']). 4.46/4.70 fof(c_0_5556, plain, ![X11321, X11322]:((c_Groups_Ozero__class_Ozero(X11322)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11322),X11321),X11321)|c_Groups_Ozero__class_Ozero(X11322)=X11321|~class_Groups_Olinordered__ab__group__add(X11322))&(c_Groups_Ozero__class_Ozero(X11322)!=X11321|c_Groups_Ozero__class_Ozero(X11322)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11322),X11321),X11321)|~class_Groups_Olinordered__ab__group__add(X11322))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])])). 4.46/4.70 fof(c_0_5557, plain, ![X14748, X14749, X14750]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14750),X14749),X14748))|(X14748=X14749|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14750),X14749),X14748)))|~class_Orderings_Oorder(X14750))&((X14748!=X14749|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14750),X14749),X14748))|~class_Orderings_Oorder(X14750))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14750),X14749),X14748))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14750),X14749),X14748))|~class_Orderings_Oorder(X14750)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])])). 4.46/4.70 fof(c_0_5558, plain, ![X14385, X14386, X14387]:((X14385!=c_Groups_Ozero__class_Ozero(X14387)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14387),X14386),X14385)=X14386|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X14387))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14387),X14386),X14385)!=X14386|X14385=c_Groups_Ozero__class_Ozero(X14387)|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X14387))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__0__iff])])])])). 4.46/4.70 fof(c_0_5559, plain, ![X14592, X14593, X14594]:((c_Groups_Ozero__class_Ozero(X14594)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X14594),X14593),X14592)|X14593=X14592|~class_Groups_Oab__group__add(X14594))&(X14593!=X14592|c_Groups_Ozero__class_Ozero(X14594)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X14594),X14593),X14592)|~class_Groups_Oab__group__add(X14594))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0])])])). 4.46/4.70 fof(c_0_5560, plain, ![X8002, X8003, X8004]:((hAPP(c_Groups_Ouminus__class_Ouminus(X8004),X8003)!=X8002|X8003=hAPP(c_Groups_Ouminus__class_Ouminus(X8004),X8002)|~class_Groups_Ogroup__add(X8004))&(X8003!=hAPP(c_Groups_Ouminus__class_Ouminus(X8004),X8002)|hAPP(c_Groups_Ouminus__class_Ouminus(X8004),X8003)=X8002|~class_Groups_Ogroup__add(X8004))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equation__minus__iff])])])). 4.46/4.70 cnf(c_0_5561, plain, (X1=X2|c_Code__Numeral_OSuc__code__numeral(X1)!=c_Code__Numeral_OSuc__code__numeral(X2)), inference(split_conjunct,[status(thm)],[c_0_4693])). 4.46/4.70 cnf(c_0_5562, plain, (hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))=c_Code__Numeral_OSuc__code__numeral(X1)), inference(split_conjunct,[status(thm)],[c_0_4694])). 4.46/4.70 fof(c_0_5563, plain, ![X7017]:(hBOOL(hAPP(c_Nat__Numeral_Oneg,X7017))|X7017=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X7017))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__neg__nat])])])). 4.46/4.70 fof(c_0_5564, plain, ![X9024, X9025]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9025),c_Groups_Ozero__class_Ozero(X9025)),hAPP(c_Groups_Oabs__class_Oabs(X9025),X9024)))|c_Groups_Ozero__class_Ozero(X9025)!=X9024|~class_Groups_Oordered__ab__group__add__abs(X9025))&(c_Groups_Ozero__class_Ozero(X9025)=X9024|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9025),c_Groups_Ozero__class_Ozero(X9025)),hAPP(c_Groups_Oabs__class_Oabs(X9025),X9024)))|~class_Groups_Oordered__ab__group__add__abs(X9025))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff])])])). 4.46/4.70 fof(c_0_5565, plain, ![X469]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X469),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|X469=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(X469!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X469),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc0])])). 4.46/4.70 fof(c_0_5566, plain, ![X12231]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12231)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12231),c_Int_OPls)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12231),c_Int_OPls))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12231))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__0__number__of])])). 4.46/4.70 fof(c_0_5567, plain, ![X4343]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Int_Onat,X4343)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4343),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4343),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,X4343))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__iff])])). 4.46/4.70 fof(c_0_5568, plain, ![X10608]:(~hBOOL(hAPP(c_Nat__Numeral_Oneg,X10608))|hAPP(c_Int_Onat,X10608)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__nat])])). 4.46/4.70 fof(c_0_5569, axiom, ![X45, X14, X28]:(hBOOL(hAPP(X28,c_Divides_Odiv__class_Omod(tc_Int_Oint,X14,X45)))<=>epred1_3(X28,X45,X14)), inference(apply_def,[status(thm)],[fact_split__zmod, c_0_4604])). 4.46/4.70 fof(c_0_5570, plain, ![X8986]:(~class_Int_Onumber__ring(X8986)|c_Int_Oiszero(X8986,hAPP(c_Int_Onumber__class_Onumber__of(X8986),c_Int_OPls))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__Numeral0])])). 4.46/4.70 fof(c_0_5571, plain, ![X15932, X15933]:((X15932!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(c_Int_Oring__1__class_Oof__int(X15933),X15932)=c_Groups_Ozero__class_Ozero(X15933)|~class_Int_Oring__char__0(X15933))&(hAPP(c_Int_Oring__1__class_Oof__int(X15933),X15932)!=c_Groups_Ozero__class_Ozero(X15933)|X15932=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~class_Int_Oring__char__0(X15933))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__eq__0__iff])])])). 4.46/4.70 fof(c_0_5572, plain, ![X357, X358]:((X357!=hAPP(c_Groups_Ouminus__class_Ouminus(X358),X357)|X357=c_Groups_Ozero__class_Ozero(X358)|~class_Groups_Olinordered__ab__group__add(X358))&(X357!=c_Groups_Ozero__class_Ozero(X358)|X357=hAPP(c_Groups_Ouminus__class_Ouminus(X358),X357)|~class_Groups_Olinordered__ab__group__add(X358))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__neg__zero])])])). 4.46/4.70 fof(c_0_5573, plain, ![X6841, X6842]:((X6841!=c_Groups_Ozero__class_Ozero(X6842)|c_Groups_Osgn__class_Osgn(X6842,X6841)=c_Groups_Ozero__class_Ozero(X6842)|~class_Rings_Olinordered__idom(X6842))&(c_Groups_Osgn__class_Osgn(X6842,X6841)!=c_Groups_Ozero__class_Ozero(X6842)|X6841=c_Groups_Ozero__class_Ozero(X6842)|~class_Rings_Olinordered__idom(X6842))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__0__0])])])). 4.46/4.70 fof(c_0_5574, plain, ![X5392, X5393, X5394]:(~class_Orderings_Oorder(X5394)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5394),X5393),X5392))|X5393!=X5392)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__eq])])])). 4.46/4.70 fof(c_0_5575, plain, ![X3980, X3981, X3982]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3982),X3980),X3981))|X3981!=X3980|~class_Orderings_Olinorder(X3982))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3982),X3981),X3980))|X3981!=X3980|~class_Orderings_Olinorder(X3982)))&(X3981=X3980|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3982),X3980),X3981))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3982),X3981),X3980)))|~class_Orderings_Olinorder(X3982))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__neq__iff])])])])). 4.46/4.70 fof(c_0_5576, plain, ![X6794, X6795]:(~c_Com_OWT__bodies|(hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X6794)!=hAPP(c_Com_Obody,X6795)|hBOOL(hAPP(c_Com_OWT,X6794)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_WT__bodiesD])])])). 4.46/4.70 fof(c_0_5577, plain, ![X1736]:(~class_Int_Onumber__ring(X1736)|hAPP(c_Int_Onumber__class_Onumber__of(X1736),c_Int_OPls)=c_Groups_Ozero__class_Ozero(X1736)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Pls])])). 4.46/4.70 fof(c_0_5578, plain, ![X14921, X14922]:((X14921!=X14922|hAPP(c_Code__Numeral_Oof__nat,X14922)=hAPP(c_Code__Numeral_Oof__nat,X14921))&(hAPP(c_Code__Numeral_Oof__nat,X14922)!=hAPP(c_Code__Numeral_Oof__nat,X14921)|X14921=X14922)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Oof__nat__inject])])). 4.46/4.70 cnf(c_0_5579, negated_conjecture, (~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,v_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_4695])). 4.46/4.70 cnf(c_0_5580, plain, (hAPP(c_fequal,X1)=hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))), inference(rw,[status(thm)],[c_0_4696, c_0_4531]), ['final']). 4.46/4.70 cnf(c_0_5581, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)))), inference(split_conjunct,[status(thm)],[c_0_4697])). 4.46/4.70 cnf(c_0_5582, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2)))), inference(split_conjunct,[status(thm)],[c_0_4698])). 4.46/4.70 cnf(c_0_5583, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4699, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.70 cnf(c_0_5584, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4700, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.70 cnf(c_0_5585, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))!=c_Int_OMin), inference(rw,[status(thm)],[c_0_4701, c_0_4500])). 4.46/4.70 cnf(c_0_5586, plain, (c_Int_OBit1(X1)!=c_Int_OBit0(X2)), inference(split_conjunct,[status(thm)],[c_0_4702])). 4.46/4.70 fof(c_0_5587, plain, ![X8436, X8437, X8438, X8439, X8440, X8442, X8443, X8444, X8445, X8447]:(((((hBOOL(hAPP(c_Finite__Set_Ofinite(X8439),X8437))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X8439,tc_HOL_Obool),tc_fun(X8439,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X8439,tc_HOL_Obool),tc_fun(X8439,tc_HOL_Obool)),X8438),X8437)),c_Wellfounded_Omax__ext(X8439,X8436))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X8439,X8439)),hAPP(hAPP(c_Product__Type_OPair(X8439,X8439),X8440),esk237_5(X8436,X8437,X8438,X8439,X8440))),X8436))|~hBOOL(hAPP(hAPP(c_member(X8439),X8440),X8438))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X8439,tc_HOL_Obool),tc_fun(X8439,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X8439,tc_HOL_Obool),tc_fun(X8439,tc_HOL_Obool)),X8438),X8437)),c_Wellfounded_Omax__ext(X8439,X8436))))&(hBOOL(hAPP(hAPP(c_member(X8439),esk237_5(X8436,X8437,X8438,X8439,X8440)),X8437))|~hBOOL(hAPP(hAPP(c_member(X8439),X8440),X8438))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X8439,tc_HOL_Obool),tc_fun(X8439,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X8439,tc_HOL_Obool),tc_fun(X8439,tc_HOL_Obool)),X8438),X8437)),c_Wellfounded_Omax__ext(X8439,X8436))))))&(X8437!=c_Orderings_Obot__class_Obot(tc_fun(X8439,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X8439,tc_HOL_Obool),tc_fun(X8439,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X8439,tc_HOL_Obool),tc_fun(X8439,tc_HOL_Obool)),X8438),X8437)),c_Wellfounded_Omax__ext(X8439,X8436)))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X8439),X8438))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X8439,tc_HOL_Obool),tc_fun(X8439,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X8439,tc_HOL_Obool),tc_fun(X8439,tc_HOL_Obool)),X8438),X8437)),c_Wellfounded_Omax__ext(X8439,X8436)))))&((hBOOL(hAPP(hAPP(c_member(X8445),esk238_4(X8442,X8443,X8444,X8445)),X8444))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8445),X8443))|X8443=c_Orderings_Obot__class_Obot(tc_fun(X8445,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8445),X8444))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X8445,tc_HOL_Obool),tc_fun(X8445,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X8445,tc_HOL_Obool),tc_fun(X8445,tc_HOL_Obool)),X8444),X8443)),c_Wellfounded_Omax__ext(X8445,X8442))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X8445,X8445)),hAPP(hAPP(c_Product__Type_OPair(X8445,X8445),esk238_4(X8442,X8443,X8444,X8445)),X8447)),X8442))|~hBOOL(hAPP(hAPP(c_member(X8445),X8447),X8443))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8445),X8443))|X8443=c_Orderings_Obot__class_Obot(tc_fun(X8445,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8445),X8444))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X8445,tc_HOL_Obool),tc_fun(X8445,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X8445,tc_HOL_Obool),tc_fun(X8445,tc_HOL_Obool)),X8444),X8443)),c_Wellfounded_Omax__ext(X8445,X8442)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_max__ext_Osimps])])])])])])])). 4.46/4.70 fof(c_0_5588, plain, ![X5642, X5643, X5644]:((X5642=X5643|hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5644,X5644,hAPP(hAPP(c_COMBB(tc_fun(X5644,tc_HOL_Obool),tc_fun(X5644,tc_HOL_Obool),X5644),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5644),c_fNot)),c_fequal)),X5643),X5642)))&(~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5644,X5644,hAPP(hAPP(c_COMBB(tc_fun(X5644,tc_HOL_Obool),tc_fun(X5644,tc_HOL_Obool),X5644),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5644),c_fNot)),c_fequal)),X5643),X5642))|X5642!=X5643)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__noteq])])). 4.46/4.70 cnf(c_0_5589, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4703])). 4.46/4.70 cnf(c_0_5590, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1)))), inference(split_conjunct,[status(thm)],[c_0_4704])). 4.46/4.70 cnf(c_0_5591, plain, (c_Int_OPls!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)), inference(rw,[status(thm)],[c_0_4705, c_0_4471])). 4.46/4.70 fof(c_0_5592, plain, ![X9349, X9350, X9351]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9351,tc_HOL_Obool)),X9350),X9349))|X9350=X9349|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9351,tc_HOL_Obool)),X9350),X9349)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9351,tc_HOL_Obool)),X9350),X9349))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9351,tc_HOL_Obool)),X9350),X9349)))&(X9350!=X9349|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9351,tc_HOL_Obool)),X9350),X9349))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])])). 4.46/4.70 fof(c_0_5593, plain, ![X15574, X15575]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15575),X15574))|X15575=X15574|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15575),X15574)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15575),X15574))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15575),X15574)))&(X15575!=X15574|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15575),X15574))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])])). 4.46/4.70 cnf(c_0_5594, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=c_Code__Numeral_OSuc__code__numeral(X1)), inference(split_conjunct,[status(thm)],[c_0_4706])). 4.46/4.70 fof(c_0_5595, plain, ![X16630, X16631, X16632, X16633, X16634, X16636, X16637, X16638, X16639, X16641]:(((((hBOOL(hAPP(c_Finite__Set_Ofinite(X16633),X16630))|~c_Wellfounded_Omax__extp(X16633,X16632,X16631,X16630))&(X16630!=c_Orderings_Obot__class_Obot(tc_fun(X16633,tc_HOL_Obool))|~c_Wellfounded_Omax__extp(X16633,X16632,X16631,X16630)))&((hBOOL(hAPP(hAPP(c_member(X16633),esk488_5(X16630,X16631,X16632,X16633,X16634)),X16630))|~hBOOL(hAPP(hAPP(c_member(X16633),X16634),X16631))|~c_Wellfounded_Omax__extp(X16633,X16632,X16631,X16630))&(hBOOL(hAPP(hAPP(X16632,X16634),esk488_5(X16630,X16631,X16632,X16633,X16634)))|~hBOOL(hAPP(hAPP(c_member(X16633),X16634),X16631))|~c_Wellfounded_Omax__extp(X16633,X16632,X16631,X16630))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X16633),X16631))|~c_Wellfounded_Omax__extp(X16633,X16632,X16631,X16630)))&((hBOOL(hAPP(hAPP(c_member(X16639),esk489_4(X16636,X16637,X16638,X16639)),X16637))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16639),X16636))|X16636=c_Orderings_Obot__class_Obot(tc_fun(X16639,tc_HOL_Obool)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16639),X16637))|c_Wellfounded_Omax__extp(X16639,X16638,X16637,X16636))&(~hBOOL(hAPP(hAPP(c_member(X16639),X16641),X16636))|~hBOOL(hAPP(hAPP(X16638,esk489_4(X16636,X16637,X16638,X16639)),X16641))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16639),X16636))|X16636=c_Orderings_Obot__class_Obot(tc_fun(X16639,tc_HOL_Obool)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16639),X16637))|c_Wellfounded_Omax__extp(X16639,X16638,X16637,X16636)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_max__extp_Oequations])])])])])])])). 4.46/4.70 fof(c_0_5596, plain, ~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)), inference(fof_simplification,[status(thm)],[fact_eq__int__code_I5_J])). 4.46/4.70 fof(c_0_5597, plain, ~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)), inference(fof_simplification,[status(thm)],[fact_eq__int__code_I2_J])). 4.46/4.70 fof(c_0_5598, plain, ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)), inference(fof_simplification,[status(thm)],[fact_rel__simps_I3_J])). 4.46/4.70 fof(c_0_5599, plain, ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)), inference(fof_simplification,[status(thm)],[fact_rel__simps_I20_J])). 4.46/4.70 cnf(c_0_5600, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1,X2)),hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1))),hAPP(hAPP(c_COMBC(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),X3))),c_Transitive__Closure_Ortrancl(X1,X2))))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1))),hAPP(c_Product__Type_OPair(X1,X1),X4))),c_Transitive__Closure_Ortrancl(X1,X2))))))=c_Transitive__Closure_Otrancl(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))), inference(split_conjunct,[status(thm)],[c_0_4707])). 4.46/4.70 cnf(c_0_5601, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X1,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X2)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Oupt(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))))=hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X1,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(X1,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X4))),X2)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))))), inference(split_conjunct,[status(thm)],[c_0_4708])). 4.46/4.70 cnf(c_0_5602, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2))))), inference(split_conjunct,[status(thm)],[c_0_4709])). 4.46/4.70 cnf(c_0_5603, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X2)))), inference(split_conjunct,[status(thm)],[c_0_4710])). 4.46/4.70 fof(c_0_5604, plain, ![X12780, X12781, X12782, X12783]:hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12783),X12781)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12782),X12780))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12783),X12780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12782),X12781)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X12783),X12782)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X12781),X12780)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[fact_mult])). 4.46/4.70 fof(c_0_5605, plain, ![X5043, X5044, X5045, X5046, X5047]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5047,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5047,tc_HOL_Obool)),c_Map_Odom(X5047,X5046,X5044)),hAPP(c_Set_OCollect(X5047),X5045))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5047,tc_HOL_Obool)),c_Map_Odom(X5047,X5046,X5043)),hAPP(c_Set_OCollect(X5047),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5047),c_fNot),X5045))))=c_Map_Odom(X5047,X5046,hAPP(hAPP(c_COMBS(X5047,tc_Option_Ooption(X5046),tc_Option_Ooption(X5046)),hAPP(hAPP(c_COMBS(X5047,tc_Option_Ooption(X5046),tc_fun(tc_Option_Ooption(X5046),tc_Option_Ooption(X5046))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X5046),tc_fun(tc_Option_Ooption(X5046),tc_Option_Ooption(X5046))),X5047),c_If(tc_Option_Ooption(X5046))),X5045)),X5044)),X5043)), inference(variable_rename,[status(thm)],[fact_dom__if])). 4.46/4.70 fof(c_0_5606, plain, ![X12738, X12739, X12740, X12741, X12742, X12743]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12742,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12743,X12742,X12740),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12743,tc_HOL_Obool)),X12738),hAPP(c_Set_OCollect(X12743),X12741)))),hAPP(c_Set_Oimage(X12743,X12742,X12739),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12743,tc_HOL_Obool)),X12738),hAPP(c_Set_OCollect(X12743),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12743),c_fNot),X12741)))))=hAPP(c_Set_Oimage(X12743,X12742,hAPP(hAPP(c_COMBS(X12743,X12742,X12742),hAPP(hAPP(c_COMBS(X12743,X12742,tc_fun(X12742,X12742)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X12742,tc_fun(X12742,X12742)),X12743),c_If(X12742)),X12741)),X12740)),X12739)),X12738), inference(variable_rename,[status(thm)],[fact_if__image__distrib])). 4.46/4.70 fof(c_0_5607, plain, ![X15253, X15254, X15255]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15253),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15255),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15253),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X15254))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15255)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X15254))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X15253))), inference(variable_rename,[status(thm)],[fact_arith__series__nat])). 4.46/4.70 cnf(c_0_5608, plain, (c_List_Ofoldr(tc_List_Olist(X1),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X1)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),c_List_Otranspose(X1,X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1)))),X2))), inference(split_conjunct,[status(thm)],[c_0_4711])). 4.46/4.70 cnf(c_0_5609, plain, (hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X1),hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X1)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X1)),X2))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X2))), inference(rw,[status(thm)],[c_0_4712, c_0_4713])). 4.46/4.70 cnf(c_0_5610, plain, (c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_Osucc(X2)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2))), inference(split_conjunct,[status(thm)],[c_0_4714])). 4.46/4.70 cnf(c_0_5611, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)), inference(split_conjunct,[status(thm)],[c_0_4715])). 4.46/4.70 fof(c_0_5612, plain, ![X8364, X8365, X8366, X8367, X8368, X8369, X8370, X8371, X8372, X8373]:(X8369!=hAPP(c_Set_Oimage(X8373,X8372,X8371),X8370)|(hAPP(c_Set_Oimage(X8368,X8367,X8366),X8365)!=X8364|hAPP(hAPP(c_Product__Type_OSigma(X8372,X8367),X8369),hAPP(c_COMBK(tc_fun(X8367,tc_HOL_Obool),X8372),X8364))=hAPP(c_Set_Oimage(tc_prod(X8373,X8368),tc_prod(X8372,X8367),c_Product__Type_Omap__pair(X8373,X8372,X8368,X8367,X8371,X8366)),hAPP(hAPP(c_Product__Type_OSigma(X8373,X8368),X8370),hAPP(c_COMBK(tc_fun(X8368,tc_HOL_Obool),X8373),X8365))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__pair__surj__on])])])). 4.46/4.70 cnf(c_0_5613, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), inference(split_conjunct,[status(thm)],[c_0_4716])). 4.46/4.70 fof(c_0_5614, plain, ![X380, X381, X382, X383, X384]:hAPP(hAPP(c_List_Omap(X382,X384),X381),c_List_OdropWhile(X382,hAPP(c_Fun_Ocomp(X384,tc_HOL_Obool,X382,X383),X381),X380))=c_List_OdropWhile(X384,X383,hAPP(hAPP(c_List_Omap(X382,X384),X381),X380)), inference(variable_rename,[status(thm)],[fact_dropWhile__map])). 4.46/4.70 cnf(c_0_5615, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X2)))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_4717])). 4.46/4.70 fof(c_0_5616, plain, ![X11993, X11994, X11995]:hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11995)),X11994)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X11993))))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11995)),c_List_Osublist(X11995,X11994,X11993)), inference(variable_rename,[status(thm)],[fact_length__sublist])). 4.46/4.70 fof(c_0_5617, plain, ![X13584, X13585, X13586, X13587, X13588, X13589, X13590]:c_List_Ofoldr(X13587,X13589,hAPP(c_Fun_Ocomp(X13590,tc_fun(X13589,X13589),X13587,X13588),X13586),X13585,X13584)=c_List_Ofoldr(X13590,X13589,X13588,hAPP(hAPP(c_List_Omap(X13587,X13590),X13586),X13585),X13584), inference(variable_rename,[status(thm)],[fact_foldr__map])). 4.46/4.70 cnf(c_0_5618, plain, (c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2))), inference(split_conjunct,[status(thm)],[c_0_4718])). 4.46/4.70 cnf(c_0_5619, plain, (c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2))), inference(split_conjunct,[status(thm)],[c_0_4719])). 4.46/4.70 fof(c_0_5620, plain, ![X1076, X1077, X1078, X1079]:hAPP(c_Set_OCollect(X1078),hAPP(hAPP(c_COMBC(X1078,tc_fun(tc_prod(X1079,X1078),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X1079,X1078),tc_fun(tc_fun(tc_prod(X1079,X1078),tc_HOL_Obool),tc_HOL_Obool),X1078),c_member(tc_prod(X1079,X1078))),hAPP(c_Product__Type_OPair(X1079,X1078),X1076))),X1077))=hAPP(c_Relation_OImage(X1079,X1078,X1077),hAPP(hAPP(c_Set_Oinsert(X1079),X1076),c_Orderings_Obot__class_Obot(tc_fun(X1079,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_Image__singleton])). 4.46/4.70 fof(c_0_5621, plain, ![X7165, X7166, X7167, X7168]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7168,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X7165,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7167),X7165))),X7166)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X7168,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X7167)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X7168,tc_HOL_Obool),tc_Nat_Onat),X7166),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X7165))), inference(variable_rename,[status(thm)],[fact_UN__le__add__shift])). 4.46/4.70 cnf(c_0_5622, plain, (c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_List_Olist(X1)),hAPP(c_List_Omap(X2,X1),X3)),X4))=hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Oconcat(X2,X4))), inference(split_conjunct,[status(thm)],[c_0_4720])). 4.46/4.70 fof(c_0_5623, plain, ![X15850, X15851, X15852, X15853, X15854, X15855, X15856]:hAPP(c_Product__Type_Oapfst(X15852,X15854,X15855,X15851),hAPP(c_Product__Type_Oapsnd(X15856,X15855,X15852,X15853),X15850))=hAPP(c_Product__Type_Oapsnd(X15856,X15855,X15854,X15853),hAPP(c_Product__Type_Oapfst(X15852,X15854,X15856,X15851),X15850)), inference(variable_rename,[status(thm)],[fact_apsnd__apfst__commute])). 4.46/4.70 cnf(c_0_5624, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X1)),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),X2)), inference(split_conjunct,[status(thm)],[c_0_4721])). 4.46/4.70 fof(c_0_5625, plain, ![X1900, X1901, X1902]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1902),X1901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1902),X1900))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1902),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1901),X1900)), inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2])). 4.46/4.70 fof(c_0_5626, plain, ![X11088, X11089, X11090, X11091, X11092, X11093, X11094]:hAPP(c_Product__Type_Oapsnd(X11094,X11093,X11092,X11091),hAPP(c_Product__Type_Oapfst(X11090,X11092,X11094,X11089),X11088))=hAPP(hAPP(c_Product__Type_OPair(X11092,X11093),hAPP(X11089,hAPP(c_Product__Type_Ofst(X11090,X11094),X11088))),hAPP(X11091,hAPP(c_Product__Type_Osnd(X11090,X11094),X11088))), inference(variable_rename,[status(thm)],[fact_apsnd__apfst])). 4.46/4.70 fof(c_0_5627, plain, ![X10476, X10477, X10478, X10479, X10480, X10481, X10482]:hAPP(c_Product__Type_Oapfst(X10482,X10481,X10480,X10479),hAPP(c_Product__Type_Oapsnd(X10478,X10480,X10482,X10477),X10476))=hAPP(hAPP(c_Product__Type_OPair(X10481,X10480),hAPP(X10479,hAPP(c_Product__Type_Ofst(X10482,X10478),X10476))),hAPP(X10477,hAPP(c_Product__Type_Osnd(X10482,X10478),X10476))), inference(variable_rename,[status(thm)],[fact_apfst__apsnd])). 4.46/4.70 cnf(c_0_5628, plain, (c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_4722])). 4.46/4.70 fof(c_0_5629, plain, ![X13725, X13726, X13727, X13728, X13729, X13730]:hAPP(hAPP(X13728,X13727),c_List_Ofoldr(X13730,X13729,X13728,X13726,X13725))=c_List_Ofoldr(X13730,X13729,X13728,hAPP(hAPP(c_List_Olist_OCons(X13730),X13727),X13726),X13725), inference(variable_rename,[status(thm)],[fact_foldr_Osimps_I2_J])). 4.46/4.70 fof(c_0_5630, plain, ![X2919, X2920, X2921, X2922, X2923, X2924, X2925]:hAPP(c_Product__Type_Oapsnd(X2925,X2924,X2923,X2922),hAPP(c_Product__Type_Oapsnd(X2921,X2925,X2923,X2920),X2919))=hAPP(c_Product__Type_Oapsnd(X2921,X2924,X2923,hAPP(c_Fun_Ocomp(X2925,X2924,X2921,X2922),X2920)),X2919), inference(variable_rename,[status(thm)],[fact_apsnd__compose])). 4.46/4.70 fof(c_0_5631, plain, ![X9718, X9719, X9720, X9721, X9722, X9723, X9724]:hAPP(c_Product__Type_Oapfst(X9720,X9723,X9722,hAPP(c_Fun_Ocomp(X9724,X9723,X9720,X9721),X9719)),X9718)=hAPP(c_Product__Type_Oapfst(X9724,X9723,X9722,X9721),hAPP(c_Product__Type_Oapfst(X9720,X9724,X9722,X9719),X9718)), inference(variable_rename,[status(thm)],[fact_apfst__compose])). 4.46/4.70 cnf(c_0_5632, plain, (hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X1))), inference(split_conjunct,[status(thm)],[c_0_4723])). 4.46/4.70 cnf(c_0_5633, plain, (c_Int_OBit0(c_Int_Osucc(X1))=c_Int_Osucc(c_Int_OBit1(X1))), inference(split_conjunct,[status(thm)],[c_0_4724])). 4.46/4.70 fof(c_0_5634, plain, ![X4092, X4093, X4094, X4095, X4096]:hAPP(c_List_Orotate(X4096,X4095),hAPP(hAPP(c_List_Omap(X4094,X4096),X4093),X4092))=hAPP(hAPP(c_List_Omap(X4094,X4096),X4093),hAPP(c_List_Orotate(X4094,X4095),X4092)), inference(variable_rename,[status(thm)],[fact_rotate__map])). 4.46/4.70 fof(c_0_5635, plain, ![X689, X690]:hAPP(c_Set_Oimage(X690,tc_List_Olist(X690),hAPP(hAPP(c_COMBC(X690,tc_List_Olist(X690),tc_List_Olist(X690)),c_List_Olist_OCons(X690)),c_List_Olist_ONil(X690))),X689)=c_List_Oset__Cons(X690,X689,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X690)),c_List_Olist_ONil(X690)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X690),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_set__Cons__sing__Nil])). 4.46/4.70 fof(c_0_5636, plain, ![X10338, X10339]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10339)),c_List_Oconcat(X10339,X10338))=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10339),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X10339))),X10338)), inference(variable_rename,[status(thm)],[fact_length__concat])). 4.46/4.70 fof(c_0_5637, plain, ![X16694, X16695, X16696, X16697, X16698]:((c_Option_Ooption_ONone(X16697)=X16698|hAPP(hAPP(c_Set_Oinsert(X16696),X16694),c_Map_Odom(X16696,X16697,X16695))=c_Map_Odom(X16696,X16697,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X16696,tc_Option_Ooption(X16697)),X16695),X16694),X16698)))&(c_Option_Ooption_ONone(X16697)!=X16698|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16696,tc_HOL_Obool)),c_Map_Odom(X16696,X16697,X16695)),hAPP(hAPP(c_Set_Oinsert(X16696),X16694),c_Orderings_Obot__class_Obot(tc_fun(X16696,tc_HOL_Obool))))=c_Map_Odom(X16696,X16697,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X16696,tc_Option_Ooption(X16697)),X16695),X16694),X16698)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dom__fun__upd])])])). 4.46/4.70 fof(c_0_5638, plain, ![X989, X990, X991, X992]:c_List_Olist_Olist__size(X992,X991,hAPP(hAPP(c_List_Olist_OCons(X992),X990),X989))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X991,X990)),c_List_Olist_Olist__size(X992,X991,X989))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_list_Osize_I2_J])). 4.46/4.70 fof(c_0_5639, plain, ![X13450, X13451, X13452, X13453]:hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X13453,X13452),c_Lazy__Sequence_Olazy__sequence_OInsert(X13453,X13451,X13450))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X13452,X13451)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X13453,X13452),X13450))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I2_J])). 4.46/4.70 fof(c_0_5640, plain, ![X7117, X7118, X7119]:hAPP(c_Set_OCollect(X7118),hAPP(hAPP(c_COMBB(tc_fun(X7119,tc_HOL_Obool),tc_HOL_Obool,X7118),c_HOL_OEx(X7119)),hAPP(c_COMBC(X7119,X7118,tc_HOL_Obool),X7117)))=hAPP(c_Relation_ORange(X7119,X7118),hAPP(c_Set_OCollect(tc_prod(X7119,X7118)),hAPP(c_Product__Type_Oprod_Oprod__case(X7119,X7118,tc_HOL_Obool),X7117))), inference(variable_rename,[status(thm)],[fact_Range__Collect__split])). 4.46/4.70 fof(c_0_5641, plain, ![X4554, X4555, X4556]:hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X4556,X4555,X4554))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X4555)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X4554))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_com_Osize_I13_J])). 4.46/4.70 cnf(c_0_5642, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_4725])). 4.46/4.70 cnf(c_0_5643, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_4726]), ['final']). 4.46/4.70 cnf(c_0_5644, plain, (hAPP(c_Nat_OSuc,X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_4727]), ['final']). 4.46/4.70 cnf(c_0_5645, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[c_0_4728, c_0_4729]), ['final']). 4.46/4.70 fof(c_0_5646, plain, ![X14048, X14049, X14050, X14051, X14052, X14053]:hAPP(c_Set_Ovimage(X14053,X14052,hAPP(c_Fun_Ocomp(X14051,X14052,X14053,X14050),X14049)),X14048)=hAPP(c_Set_Ovimage(X14053,X14051,X14049),hAPP(c_Set_Ovimage(X14051,X14052,X14050),X14048)), inference(variable_rename,[status(thm)],[fact_vimage__compose])). 4.46/4.70 fof(c_0_5647, plain, ![X3563, X3564]:c_Divides_Odivmod__nat(X3564,X3563)=hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3564),X3563)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3564,X3563)), inference(variable_rename,[status(thm)],[fact_divmod__nat__div__mod])). 4.46/4.70 fof(c_0_5648, plain, ![X15539, X15540, X15541]:c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X15541,X15540,X15539))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X15540)),c_Com_Ocom_Ocom__size(X15539))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_com_Osize_I5_J])). 4.46/4.70 cnf(c_0_5649, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_4730])). 4.46/4.70 fof(c_0_5650, plain, ![X13659, X13660]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X13660,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X13660,X13660),tc_HOL_Obool),tc_fun(X13660,tc_HOL_Obool),c_Relation_OField(X13660)),X13659))=hAPP(c_Relation_OField(X13660),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X13660,X13660),tc_HOL_Obool),X13659)), inference(variable_rename,[status(thm)],[fact_Field__Union])). 4.46/4.70 fof(c_0_5651, plain, ![X4920, X4921, X4922, X4923]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4923,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4923,X4922,X4921),X4920))=hAPP(c_Set_Ovimage(X4923,X4922,X4921),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4922,tc_HOL_Obool)),X4920)), inference(variable_rename,[status(thm)],[fact_vimage__Compl])). 4.46/4.70 fof(c_0_5652, plain, ![X15667, X15668, X15669, X15670]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15669,tc_HOL_Obool)),X15667),hAPP(c_Set_Oimage(X15670,X15669,X15668),c_Orderings_Otop__class_Otop(tc_fun(X15670,tc_HOL_Obool))))=hAPP(c_Set_Oimage(X15670,X15669,X15668),hAPP(c_Set_Ovimage(X15670,X15669,X15668),X15667)), inference(variable_rename,[status(thm)],[fact_image__vimage__eq])). 4.46/4.70 fof(c_0_5653, plain, ![X4947, X4948, X4949, X4950, X4951]:((X4951!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4949),X4950),c_List_Olist_ONil(X4949)),X4947)=hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X4950,X4949,X4948),X4951),X4947))&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X4951|hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X4949),X4950),tc_prod(X4949,X4950),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4949),X4950),c_List_Olist_ONil(X4949)),X4947),hAPP(c_Product__Type_Oprod_Oprod__case(X4949,X4950,tc_prod(tc_List_Olist(X4949),X4950)),hAPP(hAPP(c_COMBC(X4949,tc_fun(X4950,tc_prod(tc_List_Olist(X4949),X4950)),tc_fun(X4950,tc_prod(tc_List_Olist(X4949),X4950))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X4949),X4950),tc_prod(tc_List_Olist(X4949),X4950)),tc_fun(tc_fun(X4950,tc_prod(tc_List_Olist(X4949),X4950)),tc_fun(X4950,tc_prod(tc_List_Olist(X4949),X4950))),X4949),c_COMBB(tc_prod(tc_List_Olist(X4949),X4950),tc_prod(tc_List_Olist(X4949),X4950),X4950)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4949),tc_fun(X4950,tc_prod(tc_List_Olist(X4949),X4950))),tc_fun(tc_prod(tc_List_Olist(X4949),X4950),tc_prod(tc_List_Olist(X4949),X4950)),X4949),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X4949),X4950,tc_prod(tc_List_Olist(X4949),X4950))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4949),tc_List_Olist(X4949)),tc_fun(tc_List_Olist(X4949),tc_fun(X4950,tc_prod(tc_List_Olist(X4949),X4950))),X4949),hAPP(c_COMBB(tc_List_Olist(X4949),tc_fun(X4950,tc_prod(tc_List_Olist(X4949),X4950)),tc_List_Olist(X4949)),c_Product__Type_OPair(tc_List_Olist(X4949),X4950))),c_List_Olist_OCons(X4949))))),hAPP(c_Lazy__Sequence_Oanamorph(X4950,X4949,X4948),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X4951),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(X4948,X4947))=hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X4950,X4949,X4948),X4951),X4947))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_anamorph_Osimps])])])). 4.46/4.70 fof(c_0_5654, plain, ![X9368, X9369]:c_Relation_OId(X9369)=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X9369,X9369),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9368), inference(variable_rename,[status(thm)],[fact_relpow_Osimps_I1_J])). 4.46/4.70 fof(c_0_5655, plain, ![X11427, X11428]:hAPP(c_Set_OCollect(tc_fun(X11428,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X11428,tc_HOL_Obool),tc_fun(X11428,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X11428,tc_HOL_Obool))),X11427))=hAPP(c_Set_OPow(X11428),X11427), inference(variable_rename,[status(thm)],[fact_Pow__def])). 4.46/4.70 fof(c_0_5656, plain, ![X17084, X17085]:hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X17085),tc_List_Olist(X17085))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X17085),tc_List_Olist(X17085),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X17085),tc_fun(tc_List_Olist(X17085),tc_HOL_Obool),tc_fun(tc_List_Olist(X17085),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X17085),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X17085),tc_HOL_Obool),tc_fun(tc_List_Olist(X17085),tc_HOL_Obool)),tc_List_Olist(X17085)),c_COMBS(tc_List_Olist(X17085),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X17085),tc_HOL_Obool),tc_fun(tc_List_Olist(X17085),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X17085)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X17085)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X17085),tc_fun(tc_List_Olist(X17085),tc_Nat_Onat),tc_fun(tc_List_Olist(X17085),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X17085),tc_Nat_Onat),tc_fun(tc_List_Olist(X17085),tc_HOL_Obool)),tc_List_Olist(X17085)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X17085))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X17085)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X17085))))),c_Nat_Osize__class_Osize(tc_List_Olist(X17085)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X17085),tc_fun(tc_List_Olist(X17085),tc_HOL_Obool),tc_fun(tc_List_Olist(X17085),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X17085),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X17085),tc_HOL_Obool),tc_fun(tc_List_Olist(X17085),tc_HOL_Obool)),tc_List_Olist(X17085)),c_COMBS(tc_List_Olist(X17085),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X17085),tc_HOL_Obool),tc_fun(tc_List_Olist(X17085),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X17085)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X17085)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X17085),tc_fun(tc_List_Olist(X17085),tc_Nat_Onat),tc_fun(tc_List_Olist(X17085),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X17085),tc_Nat_Onat),tc_fun(tc_List_Olist(X17085),tc_HOL_Obool)),tc_List_Olist(X17085)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X17085))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X17085)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X17085))))),c_Nat_Osize__class_Osize(tc_List_Olist(X17085)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X17085),tc_fun(tc_prod(tc_List_Olist(X17085),tc_List_Olist(X17085)),tc_HOL_Obool),tc_fun(tc_List_Olist(X17085),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X17085),tc_fun(tc_fun(tc_prod(tc_List_Olist(X17085),tc_List_Olist(X17085)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X17085),tc_List_Olist(X17085)),tc_HOL_Obool),tc_fun(tc_List_Olist(X17085),tc_HOL_Obool)),tc_List_Olist(X17085)),c_COMBC(tc_List_Olist(X17085),tc_fun(tc_prod(tc_List_Olist(X17085),tc_List_Olist(X17085)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X17085),tc_prod(tc_List_Olist(X17085),tc_List_Olist(X17085))),tc_fun(tc_List_Olist(X17085),tc_fun(tc_fun(tc_prod(tc_List_Olist(X17085),tc_List_Olist(X17085)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X17085)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X17085),tc_List_Olist(X17085)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X17085),tc_List_Olist(X17085)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X17085)),c_member(tc_prod(tc_List_Olist(X17085),tc_List_Olist(X17085))))),c_Product__Type_OPair(tc_List_Olist(X17085),tc_List_Olist(X17085))))),c_List_Olex(X17085,X17084))))))=c_List_Olenlex(X17085,X17084), inference(variable_rename,[status(thm)],[fact_lenlex__conv])). 4.46/4.70 fof(c_0_5657, plain, ![X9270, X9271, X9272]:hAPP(c_Set_OCollect(tc_List_Olist(X9272)),hAPP(hAPP(c_COMBB(tc_fun(X9272,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X9272)),c_HOL_OEx(X9272)),hAPP(hAPP(c_COMBB(tc_fun(X9272,tc_fun(tc_List_Olist(X9272),tc_HOL_Obool)),tc_fun(X9272,tc_HOL_Obool),tc_List_Olist(X9272)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X9272),tc_HOL_Obool),tc_HOL_Obool,X9272),c_HOL_OEx(tc_List_Olist(X9272)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X9272),tc_fun(X9272,tc_fun(tc_List_Olist(X9272),tc_HOL_Obool)),tc_fun(X9272,tc_fun(tc_List_Olist(X9272),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X9272,tc_fun(tc_fun(tc_List_Olist(X9272),tc_HOL_Obool),tc_fun(tc_List_Olist(X9272),tc_HOL_Obool))),tc_fun(tc_fun(X9272,tc_fun(tc_List_Olist(X9272),tc_HOL_Obool)),tc_fun(X9272,tc_fun(tc_List_Olist(X9272),tc_HOL_Obool))),tc_List_Olist(X9272)),c_COMBS(X9272,tc_fun(tc_List_Olist(X9272),tc_HOL_Obool),tc_fun(tc_List_Olist(X9272),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X9272,tc_fun(tc_List_Olist(X9272),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X9272,tc_fun(tc_fun(tc_List_Olist(X9272),tc_HOL_Obool),tc_fun(tc_List_Olist(X9272),tc_HOL_Obool))),tc_List_Olist(X9272)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X9272),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X9272),tc_HOL_Obool),tc_fun(tc_List_Olist(X9272),tc_HOL_Obool)),X9272),c_COMBS(tc_List_Olist(X9272),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X9272,tc_fun(tc_List_Olist(X9272),tc_HOL_Obool)),tc_fun(X9272,tc_fun(tc_List_Olist(X9272),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X9272)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X9272),tc_HOL_Obool),tc_fun(tc_List_Olist(X9272),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X9272),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X9272)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X9272),tc_fun(X9272,tc_fun(tc_List_Olist(X9272),tc_List_Olist(X9272))),tc_fun(X9272,tc_fun(tc_List_Olist(X9272),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X9272),tc_List_Olist(X9272)),tc_fun(tc_List_Olist(X9272),tc_HOL_Obool)),tc_fun(tc_fun(X9272,tc_fun(tc_List_Olist(X9272),tc_List_Olist(X9272))),tc_fun(X9272,tc_fun(tc_List_Olist(X9272),tc_HOL_Obool))),tc_List_Olist(X9272)),c_COMBB(tc_fun(tc_List_Olist(X9272),tc_List_Olist(X9272)),tc_fun(tc_List_Olist(X9272),tc_HOL_Obool),X9272)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X9272),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X9272),tc_List_Olist(X9272)),tc_fun(tc_List_Olist(X9272),tc_HOL_Obool)),tc_List_Olist(X9272)),c_COMBB(tc_List_Olist(X9272),tc_HOL_Obool,tc_List_Olist(X9272))),c_fequal))),c_List_Olist_OCons(X9272)))))),hAPP(hAPP(c_COMBC(X9272,tc_fun(tc_List_Olist(X9272),tc_HOL_Obool),tc_fun(tc_List_Olist(X9272),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X9272),tc_HOL_Obool),tc_fun(tc_List_Olist(X9272),tc_HOL_Obool)),X9272),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X9272))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X9272),c_fconj),hAPP(hAPP(c_COMBC(X9272,tc_fun(X9272,tc_HOL_Obool),tc_HOL_Obool),c_member(X9272)),X9271)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X9272),tc_fun(tc_List_Olist(X9272),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X9272))),X9270))))))=c_List_Oset__Cons(X9272,X9271,X9270), inference(variable_rename,[status(thm)],[fact_set__Cons__def])). 4.46/4.70 cnf(c_0_5658, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))=c_Divides_Oadjust(X1)), inference(split_conjunct,[status(thm)],[c_0_4731])). 4.46/4.70 fof(c_0_5659, plain, ![X10386, X10387, X10388, X10389, X10390]:hAPP(c_Set_OCollect(tc_prod(X10390,X10388)),hAPP(c_Product__Type_Oprod_Oprod__case(X10390,X10388,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10388,tc_fun(X10389,tc_HOL_Obool)),tc_fun(X10388,tc_HOL_Obool),X10390),hAPP(c_COMBB(tc_fun(X10389,tc_HOL_Obool),tc_HOL_Obool,X10388),c_HOL_OEx(X10389))),hAPP(hAPP(c_COMBC(X10390,tc_fun(X10388,tc_fun(X10389,tc_HOL_Obool)),tc_fun(X10388,tc_fun(X10389,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10389,tc_HOL_Obool),tc_fun(X10389,tc_HOL_Obool)),tc_fun(tc_fun(X10388,tc_fun(X10389,tc_HOL_Obool)),tc_fun(X10388,tc_fun(X10389,tc_HOL_Obool))),X10390),c_COMBB(tc_fun(X10389,tc_HOL_Obool),tc_fun(X10389,tc_HOL_Obool),X10388)),hAPP(hAPP(c_COMBB(tc_fun(X10389,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10389,tc_HOL_Obool),tc_fun(X10389,tc_HOL_Obool)),X10390),c_COMBS(X10389,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10389,tc_HOL_Obool),tc_fun(X10389,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10390),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10389),c_fconj)),hAPP(hAPP(c_COMBC(X10390,tc_fun(tc_prod(X10390,X10389),tc_HOL_Obool),tc_fun(X10389,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10389,tc_fun(tc_fun(tc_prod(X10390,X10389),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10390,X10389),tc_HOL_Obool),tc_fun(X10389,tc_HOL_Obool)),X10390),c_COMBC(X10389,tc_fun(tc_prod(X10390,X10389),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10389,tc_prod(X10390,X10389)),tc_fun(X10389,tc_fun(tc_fun(tc_prod(X10390,X10389),tc_HOL_Obool),tc_HOL_Obool)),X10390),hAPP(c_COMBB(tc_prod(X10390,X10389),tc_fun(tc_fun(tc_prod(X10390,X10389),tc_HOL_Obool),tc_HOL_Obool),X10389),c_member(tc_prod(X10390,X10389)))),c_Product__Type_OPair(X10390,X10389)))),X10387))))),hAPP(hAPP(c_COMBC(X10388,tc_fun(tc_prod(X10389,X10388),tc_HOL_Obool),tc_fun(X10389,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10389,tc_fun(tc_fun(tc_prod(X10389,X10388),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10389,X10388),tc_HOL_Obool),tc_fun(X10389,tc_HOL_Obool)),X10388),c_COMBC(X10389,tc_fun(tc_prod(X10389,X10388),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10389,tc_prod(X10389,X10388)),tc_fun(X10389,tc_fun(tc_fun(tc_prod(X10389,X10388),tc_HOL_Obool),tc_HOL_Obool)),X10388),hAPP(c_COMBB(tc_prod(X10389,X10388),tc_fun(tc_fun(tc_prod(X10389,X10388),tc_HOL_Obool),tc_HOL_Obool),X10389),c_member(tc_prod(X10389,X10388)))),hAPP(c_COMBC(X10389,X10388,tc_prod(X10389,X10388)),c_Product__Type_OPair(X10389,X10388))))),X10386)))))=hAPP(hAPP(c_Relation_Orel__comp(X10390,X10389,X10388),X10387),X10386), inference(variable_rename,[status(thm)],[fact_rel__comp__def])). 4.46/4.70 cnf(c_0_5660, plain, (hAPP(c_Divides_Oadjust(X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X1)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_4732])). 4.46/4.70 fof(c_0_5661, plain, ![X346, X347, X348]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X348),tc_List_Olist(X348)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X348,tc_List_Olist(X348)),tc_prod(X348,tc_List_Olist(X348))),tc_prod(tc_List_Olist(X348),tc_List_Olist(X348)),c_Product__Type_Omap__pair(tc_prod(X348,tc_List_Olist(X348)),tc_List_Olist(X348),tc_prod(X348,tc_List_Olist(X348)),tc_List_Olist(X348),hAPP(c_Product__Type_Oprod_Oprod__case(X348,tc_List_Olist(X348),tc_List_Olist(X348)),c_List_Olist_OCons(X348)),hAPP(c_Product__Type_Oprod_Oprod__case(X348,tc_List_Olist(X348),tc_List_Olist(X348)),c_List_Olist_OCons(X348)))),c_Wellfounded_Olex__prod(X348,tc_List_Olist(X348),X347,hAPP(c_List_Olexn(X348,X347),X346)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X348),tc_List_Olist(X348))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X348),tc_List_Olist(X348),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X348),tc_fun(tc_List_Olist(X348),tc_HOL_Obool),tc_fun(tc_List_Olist(X348),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X348),tc_HOL_Obool),tc_fun(tc_List_Olist(X348),tc_HOL_Obool)),tc_List_Olist(X348)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X348))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X348)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X348),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X348)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X348)))),hAPP(c_Nat_OSuc,X346))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X348),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X348)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X348)))),hAPP(c_Nat_OSuc,X346))))))=hAPP(c_List_Olexn(X348,X347),hAPP(c_Nat_OSuc,X346)), inference(variable_rename,[status(thm)],[fact_lexn_Osimps_I2_J])). 4.46/4.70 fof(c_0_5662, plain, ![X737, X738, X739, X740]:hAPP(c_List_Oset(tc_prod(X740,X739)),hAPP(hAPP(c_List_Ozip(X740,X739),X738),X737))=hAPP(c_Set_OCollect(tc_prod(X740,X739)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X740,X739)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X740,X739),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X740,X739)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(X740,X739)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(X740,X739),tc_fun(tc_Nat_Onat,tc_prod(X740,X739)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X740,X739),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X740,X739)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X740,X739)),c_COMBB(tc_prod(X740,X739),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X739,tc_prod(X740,X739)),hAPP(hAPP(c_COMBB(X740,tc_fun(X739,tc_prod(X740,X739)),tc_Nat_Onat),c_Product__Type_OPair(X740,X739)),hAPP(c_List_Onth(X740),X738))),hAPP(c_List_Onth(X739),X737)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X740)),X738)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X739)),X737)))))), inference(variable_rename,[status(thm)],[fact_set__zip])). 4.46/4.70 cnf(c_0_5663, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X1),X2),hAPP(c_Nitpick_Odenom(X1),X3))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X1),tc_Int_Oint),c_Nitpick_Ofrac(X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),X2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X1),X2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),X3))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X1),X3)))))),c_COMBI(tc_Int_Oint)))=c_Nitpick_Oplus__frac(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_4733])). 4.46/4.70 fof(c_0_5664, plain, ![X5333, X5334, X5335, X5336]:c_Map_Omap__add(X5336,X5335,X5334,hAPP(c_Map_Omap__of(X5336,X5335),X5333))=c_List_Ofoldr(tc_prod(X5336,X5335),tc_fun(X5336,tc_Option_Ooption(X5335)),hAPP(c_Product__Type_Oprod_Oprod__case(X5336,X5335,tc_fun(tc_fun(X5336,tc_Option_Ooption(X5335)),tc_fun(X5336,tc_Option_Ooption(X5335)))),hAPP(hAPP(c_COMBC(X5336,tc_fun(X5335,tc_Option_Ooption(X5335)),tc_fun(X5335,tc_fun(tc_fun(X5336,tc_Option_Ooption(X5335)),tc_fun(X5336,tc_Option_Ooption(X5335))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X5335),tc_fun(tc_fun(X5336,tc_Option_Ooption(X5335)),tc_fun(X5336,tc_Option_Ooption(X5335)))),tc_fun(tc_fun(X5335,tc_Option_Ooption(X5335)),tc_fun(X5335,tc_fun(tc_fun(X5336,tc_Option_Ooption(X5335)),tc_fun(X5336,tc_Option_Ooption(X5335))))),X5336),c_COMBB(tc_Option_Ooption(X5335),tc_fun(tc_fun(X5336,tc_Option_Ooption(X5335)),tc_fun(X5336,tc_Option_Ooption(X5335))),X5335)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5336,tc_Option_Ooption(X5335)),tc_fun(tc_Option_Ooption(X5335),tc_fun(X5336,tc_Option_Ooption(X5335)))),tc_fun(tc_Option_Ooption(X5335),tc_fun(tc_fun(X5336,tc_Option_Ooption(X5335)),tc_fun(X5336,tc_Option_Ooption(X5335)))),X5336),c_COMBC(tc_fun(X5336,tc_Option_Ooption(X5335)),tc_Option_Ooption(X5335),tc_fun(X5336,tc_Option_Ooption(X5335)))),hAPP(c_COMBC(tc_fun(X5336,tc_Option_Ooption(X5335)),X5336,tc_fun(tc_Option_Ooption(X5335),tc_fun(X5336,tc_Option_Ooption(X5335)))),c_Fun_Ofun__upd(X5336,tc_Option_Ooption(X5335)))))),c_Option_Ooption_OSome(X5335))),X5333,X5334), inference(variable_rename,[status(thm)],[fact_map__add__map__of__foldr])). 4.46/4.70 fof(c_0_5665, plain, ![X5952, X5953]:hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,X5953))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5952)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5952))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),X5952))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5952)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5952))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))))=c_Divides_Odivmod__int__rel(X5953,X5952), inference(variable_rename,[status(thm)],[fact_divmod__int__rel__def])). 4.46/4.70 fof(c_0_5666, plain, ![X6989, X6990, X6991, X6992]:hAPP(c_Set_OCollect(tc_prod(X6991,X6991)),hAPP(c_Product__Type_Oprod_Oprod__case(X6991,X6991,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X6991,tc_fun(tc_prod(X6992,X6992),tc_HOL_Obool),tc_fun(X6991,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6991,tc_fun(tc_fun(tc_prod(X6992,X6992),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6992,X6992),tc_HOL_Obool),tc_fun(X6991,tc_HOL_Obool)),X6991),c_COMBC(X6991,tc_fun(tc_prod(X6992,X6992),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6991,tc_prod(X6992,X6992)),tc_fun(X6991,tc_fun(tc_fun(tc_prod(X6992,X6992),tc_HOL_Obool),tc_HOL_Obool)),X6991),hAPP(c_COMBB(tc_prod(X6992,X6992),tc_fun(tc_fun(tc_prod(X6992,X6992),tc_HOL_Obool),tc_HOL_Obool),X6991),c_member(tc_prod(X6992,X6992)))),hAPP(hAPP(c_COMBC(X6991,tc_fun(X6991,X6992),tc_fun(X6991,tc_prod(X6992,X6992))),hAPP(hAPP(c_COMBB(tc_fun(X6992,tc_prod(X6992,X6992)),tc_fun(tc_fun(X6991,X6992),tc_fun(X6991,tc_prod(X6992,X6992))),X6991),c_COMBB(X6992,tc_prod(X6992,X6992),X6991)),hAPP(hAPP(c_COMBB(X6992,tc_fun(X6992,tc_prod(X6992,X6992)),X6991),c_Product__Type_OPair(X6992,X6992)),X6989))),X6989)))),X6990)))=hAPP(hAPP(c_Relation_Oinv__image(X6992,X6991),X6990),X6989), inference(variable_rename,[status(thm)],[fact_inv__image__def])). 4.46/4.70 cnf(c_0_5667, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))))),X3)))),c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),X4),c_List_Oconcat(tc_List_Olist(X1),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1)))))),X3)))))=c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),X3))), inference(split_conjunct,[status(thm)],[c_0_4734])). 4.46/4.70 cnf(c_0_5668, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))))),X2))=hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),c_List_Ohd(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1)))),X2))), inference(rw,[status(thm)],[c_0_4735, c_0_4736])). 4.46/4.70 cnf(c_0_5669, plain, (c_List_Omaps(X1,X2,X3,X4)=hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),hAPP(hAPP(c_List_Omap(X1,tc_List_Olist(X2)),X3),X4))), inference(rw,[status(thm)],[c_0_4737, c_0_4736]), ['final']). 4.46/4.70 cnf(c_0_5670, plain, (hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2)=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(rw,[status(thm)],[c_0_4738, c_0_4531]), ['final']). 4.46/4.70 cnf(c_0_5671, plain, (hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4739, c_0_4531]), c_0_4531]), ['final']). 4.46/4.70 cnf(c_0_5672, plain, (hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Otl(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1)))),X2))=hAPP(c_List_Ofoldl(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1)),c_List_Oappend(tc_List_Olist(X1)),c_List_Olist_ONil(tc_List_Olist(X1))),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1)))))),X2))), inference(rw,[status(thm)],[c_0_4740, c_0_4736])). 4.46/4.70 fof(c_0_5673, plain, ![X11210, X11211, X11212]:hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X11212,tc_Lazy__Sequence_Olazy__sequence(X11212)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X11212,tc_Lazy__Sequence_Olazy__sequence(X11212),tc_Nat_Onat),hAPP(hAPP(c_COMBC(X11212,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11212),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11212),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11212),tc_Nat_Onat)),X11212),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X11212),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11212),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11212),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X11212),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X11212)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X11212,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11212),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11212),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11212),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11212),tc_Nat_Onat)),X11212),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X11212))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X11212),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X11211))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X11212,X11211))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(X11212),X11210))=hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X11212,X11211),X11210), inference(variable_rename,[status(thm)],[fact_lazy__sequence__size__code])). 4.46/4.70 fof(c_0_5674, plain, ![X2666, X2667, X2668, X2669, X2670]:c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X2670,X2669,X2668,X2667,X2666)=hAPP(c_Option_Ooption_Ooption__case(X2670,tc_prod(X2669,tc_Lazy__Sequence_Olazy__sequence(X2669)),X2668,hAPP(c_Product__Type_Oprod_Oprod__case(X2669,tc_Lazy__Sequence_Olazy__sequence(X2669),X2670),X2667)),hAPP(c_Lazy__Sequence_Oyield(X2669),X2666)), inference(variable_rename,[status(thm)],[fact_seq__case])). 4.46/4.70 cnf(c_0_5675, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),c_List_Ofoldr(tc_List_Olist(X3),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3))),X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_List_Ofoldr(tc_List_Olist(X3),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X3),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X3)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_List_Olist(X3),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X3)))),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(split_conjunct,[status(thm)],[c_0_4741])). 4.46/4.70 fof(c_0_5676, plain, ![X4062, X4063, X4064]:hAPP(c_Set_OCollect(X4064),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X4064),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X4064,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X4064),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4064),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X4064,tc_fun(tc_Nat_Onat,X4064),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4064,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X4064),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X4064),c_COMBB(X4064,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X4064),X4063))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4064)),X4063)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X4062)))))=hAPP(c_List_Oset(X4064),c_List_Osublist(X4064,X4063,X4062)), inference(variable_rename,[status(thm)],[fact_set__sublist])). 4.46/4.70 cnf(c_0_5677, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X1,X3,X4),X5))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X3,X4)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5)))))=hAPP(c_Nat_Onat_Onat__rec(X1,X3,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X5))), inference(split_conjunct,[status(thm)],[c_0_4742])). 4.46/4.70 fof(c_0_5678, plain, ![X11140, X11141, X11142]:hAPP(c_Set_OCollect(tc_prod(X11141,X11142)),hAPP(c_Product__Type_Oprod_Oprod__case(X11141,X11142,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X11141,tc_fun(tc_prod(X11142,X11141),tc_HOL_Obool),tc_fun(X11142,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11142,tc_fun(tc_fun(tc_prod(X11142,X11141),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X11142,X11141),tc_HOL_Obool),tc_fun(X11142,tc_HOL_Obool)),X11141),c_COMBC(X11142,tc_fun(tc_prod(X11142,X11141),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11142,tc_prod(X11142,X11141)),tc_fun(X11142,tc_fun(tc_fun(tc_prod(X11142,X11141),tc_HOL_Obool),tc_HOL_Obool)),X11141),hAPP(c_COMBB(tc_prod(X11142,X11141),tc_fun(tc_fun(tc_prod(X11142,X11141),tc_HOL_Obool),tc_HOL_Obool),X11142),c_member(tc_prod(X11142,X11141)))),hAPP(c_COMBC(X11142,X11141,tc_prod(X11142,X11141)),c_Product__Type_OPair(X11142,X11141))))),X11140)))=hAPP(c_Relation_Oconverse(X11142,X11141),X11140), inference(variable_rename,[status(thm)],[fact_converse__def])). 4.46/4.70 fof(c_0_5679, plain, ![X13386, X13387]:hAPP(c_Set_OCollect(tc_fun(X13387,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X13387,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X13387,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X13387,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X13387,tc_HOL_Obool),tc_fun(tc_fun(X13387,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X13387,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X13387,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X13387,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X13387,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X13387,tc_HOL_Obool)),c_COMBS(tc_fun(X13387,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X13387,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X13387,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X13387,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X13387,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X13387,tc_HOL_Obool),tc_fun(tc_fun(X13387,tc_HOL_Obool),tc_fun(X13387,tc_HOL_Obool)),tc_fun(tc_fun(X13387,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X13387,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X13387,tc_HOL_Obool),tc_fun(X13387,tc_HOL_Obool)),tc_fun(tc_fun(X13387,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X13387,tc_HOL_Obool)),c_COMBB(tc_fun(X13387,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X13387,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X13387,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X13387,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X13387,tc_HOL_Obool)),hAPP(c_member(tc_fun(X13387,tc_HOL_Obool)),X13386)),c_Set_OPow(X13387)))))=hAPP(c_Set_OPow(X13387),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X13387,tc_HOL_Obool)),X13386)), inference(variable_rename,[status(thm)],[fact_Pow__Compl])). 4.46/4.70 cnf(c_0_5680, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), inference(split_conjunct,[status(thm)],[c_0_4743])). 4.46/4.70 fof(c_0_5681, plain, ![X11486, X11487]:hAPP(c_Set_OCollect(X11487),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X11487),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X11487,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X11487),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X11487),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X11487,tc_fun(tc_Nat_Onat,X11487),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11487,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X11487),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X11487),c_COMBB(X11487,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X11487),X11486))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11487)),X11486)))))=hAPP(c_List_Oset(X11487),X11486), inference(variable_rename,[status(thm)],[fact_set__conv__nth])). 4.46/4.70 cnf(c_0_5682, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X1,X3,X4,X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))))=c_Nat_Onat_Onat__case(X1,X3,X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X5))), inference(split_conjunct,[status(thm)],[c_0_4744])). 4.46/4.70 fof(c_0_5683, plain, ![X6209, X6210, X6211, X6212, X6213, X6214, X6215, X6216]:hAPP(hAPP(c_List_Ozip(X6216,X6215),hAPP(hAPP(c_List_Omap(X6214,X6216),X6213),X6212)),hAPP(hAPP(c_List_Omap(X6211,X6215),X6210),X6209))=hAPP(hAPP(c_List_Omap(tc_prod(X6214,X6211),tc_prod(X6216,X6215)),hAPP(c_Product__Type_Oprod_Oprod__case(X6214,X6211,tc_prod(X6216,X6215)),hAPP(hAPP(c_COMBC(X6214,tc_fun(X6211,X6215),tc_fun(X6211,tc_prod(X6216,X6215))),hAPP(hAPP(c_COMBB(tc_fun(X6215,tc_prod(X6216,X6215)),tc_fun(tc_fun(X6211,X6215),tc_fun(X6211,tc_prod(X6216,X6215))),X6214),c_COMBB(X6215,tc_prod(X6216,X6215),X6211)),hAPP(hAPP(c_COMBB(X6216,tc_fun(X6215,tc_prod(X6216,X6215)),X6214),c_Product__Type_OPair(X6216,X6215)),X6213))),X6210))),hAPP(hAPP(c_List_Ozip(X6214,X6211),X6212),X6209)), inference(variable_rename,[status(thm)],[fact_zip__map__map])). 4.46/4.70 fof(c_0_5684, plain, ![X9105, X9106, X9107, X9108, X9109, X9110]:hAPP(c_Product__Type_Oprod_Oprod__case(X9110,X9108,tc_prod(X9109,X9107)),hAPP(hAPP(c_COMBC(X9110,tc_fun(X9108,X9107),tc_fun(X9108,tc_prod(X9109,X9107))),hAPP(hAPP(c_COMBB(tc_fun(X9107,tc_prod(X9109,X9107)),tc_fun(tc_fun(X9108,X9107),tc_fun(X9108,tc_prod(X9109,X9107))),X9110),c_COMBB(X9107,tc_prod(X9109,X9107),X9108)),hAPP(hAPP(c_COMBB(X9109,tc_fun(X9107,tc_prod(X9109,X9107)),X9110),c_Product__Type_OPair(X9109,X9107)),X9106))),X9105))=c_Product__Type_Omap__pair(X9110,X9109,X9108,X9107,X9106,X9105), inference(variable_rename,[status(thm)],[fact_map__pair__def])). 4.46/4.70 cnf(c_0_5685, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), inference(split_conjunct,[status(thm)],[c_0_4745])). 4.46/4.70 cnf(c_0_5686, plain, (hAPP(hAPP(c_Nitpick_Ofrac(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),X2)),hAPP(c_Nitpick_Onum(X1),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X1),X2)),hAPP(c_Nitpick_Odenom(X1),X3)))=c_Nitpick_Otimes__frac(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_4746])). 4.46/4.70 cnf(c_0_5687, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),X2))))), inference(split_conjunct,[status(thm)],[c_0_4747])). 4.46/4.70 cnf(c_0_5688, plain, (c_Relation_OId(X1)=hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X1,X1)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(tc_prod(X1,X1),tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_HOL_Obool)),tc_prod(X1,X1)),c_COMBB(tc_prod(X1,X1),tc_HOL_Obool,X1)),c_fequal)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1)))))), inference(split_conjunct,[status(thm)],[c_0_4748])). 4.46/4.70 cnf(c_0_5689, plain, (c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))=c_Relation_OId(X1)), inference(split_conjunct,[status(thm)],[c_0_4749])). 4.46/4.70 cnf(c_0_5690, plain, (hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X4))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),X2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X3),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X2,X3)),c_Int_Onat))))), inference(split_conjunct,[status(thm)],[c_0_4750])). 4.46/4.70 fof(c_0_5691, plain, ![X10457]:c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X10457)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))))=hAPP(c_Int_Onat,X10457), inference(variable_rename,[status(thm)],[fact_nat__def])). 4.46/4.70 cnf(c_0_5692, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),X2))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))), inference(split_conjunct,[status(thm)],[c_0_4751])). 4.46/4.70 cnf(c_0_5693, plain, (c_List_Oconcat(tc_List_Olist(X1),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),tc_List_Olist(X1)),c_List_Omap(X1,tc_List_Olist(X1))),hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)))),X2)),c_Enum_On__lists(X1,X3,X2)))=c_Enum_On__lists(X1,hAPP(c_Nat_OSuc,X3),X2)), inference(split_conjunct,[status(thm)],[c_0_4752])). 4.46/4.70 cnf(c_0_5694, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I3_J])). 4.46/4.70 fof(c_0_5695, plain, ![X2161, X2162, X2163, X2164]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2164),X2163)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2162),X2161)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))=hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2164),X2162)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2163),X2161))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_add])). 4.46/4.70 fof(c_0_5696, plain, ![X10609, X10610, X10611]:hAPP(c_List_Oset(tc_List_Olist(X10611)),c_Enum_On__lists(X10611,X10610,X10609))=hAPP(c_Set_OCollect(tc_List_Olist(X10611)),hAPP(hAPP(c_COMBS(tc_List_Olist(X10611),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10611)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X10611),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10611)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X10611)))),X10610))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10611),tc_fun(X10611,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10611,tc_HOL_Obool),tc_fun(tc_fun(X10611,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10611)),c_Orderings_Oord__class_Oless__eq(tc_fun(X10611,tc_HOL_Obool))),c_List_Oset(X10611))),hAPP(c_List_Oset(X10611),X10609)))), inference(variable_rename,[status(thm)],[fact_set__n__lists])). 4.46/4.70 fof(c_0_5697, plain, ![X2284, X2285]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2285,tc_fun(tc_prod(X2285,X2285),tc_HOL_Obool)),X2284),hAPP(hAPP(c_COMBC(X2285,tc_fun(tc_prod(X2285,X2285),tc_HOL_Obool),tc_fun(tc_prod(X2285,X2285),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X2285,X2285),tc_fun(tc_fun(tc_prod(X2285,X2285),tc_HOL_Obool),tc_fun(tc_prod(X2285,X2285),tc_HOL_Obool)),X2285),c_Set_Oinsert(tc_prod(X2285,X2285))),hAPP(hAPP(c_COMBS(X2285,X2285,tc_prod(X2285,X2285)),c_Product__Type_OPair(X2285,X2285)),c_COMBI(X2285)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2285,X2285),tc_HOL_Obool))))=c_Relation_OId__on(X2285,X2284), inference(variable_rename,[status(thm)],[fact_Id__on__def])). 4.46/4.70 fof(c_0_5698, plain, ![X7643, X7644, X7645, X7646]:hAPP(c_Set_Oimage(X7646,X7645,X7644),X7643)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7646,tc_fun(X7645,tc_HOL_Obool)),X7643),hAPP(hAPP(c_COMBC(X7646,tc_fun(X7645,tc_HOL_Obool),tc_fun(X7645,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X7645,tc_fun(tc_fun(X7645,tc_HOL_Obool),tc_fun(X7645,tc_HOL_Obool)),X7646),c_Set_Oinsert(X7645)),X7644)),c_Orderings_Obot__class_Obot(tc_fun(X7645,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_image__eq__UN])). 4.46/4.70 cnf(c_0_5699, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1)),c_Int_Onat))))), inference(split_conjunct,[status(thm)],[c_0_4753])). 4.46/4.70 cnf(c_0_5700, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X2)),c_Int_Onat))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))), inference(split_conjunct,[status(thm)],[c_0_4754])). 4.46/4.70 cnf(c_0_5701, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X1,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X2)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))))=c_List_Osublist(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_4755])). 4.46/4.70 cnf(c_0_5702, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))), inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I4_J])). 4.46/4.70 fof(c_0_5703, plain, ![X6611, X6612, X6613, X6614]:hAPP(c_Set_OCollect(X6613),hAPP(hAPP(c_COMBB(tc_fun(X6614,tc_HOL_Obool),tc_HOL_Obool,X6613),c_HOL_OAll(X6614)),hAPP(hAPP(c_COMBB(tc_fun(X6614,tc_HOL_Obool),tc_fun(X6614,tc_HOL_Obool),X6613),hAPP(c_COMBS(X6614,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6614),c_fimplies),hAPP(hAPP(c_COMBC(X6614,tc_fun(X6614,tc_HOL_Obool),tc_HOL_Obool),c_member(X6614)),X6612)))),hAPP(hAPP(c_COMBC(X6613,tc_fun(X6614,tc_fun(X6613,tc_HOL_Obool)),tc_fun(X6614,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X6613,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X6614,tc_fun(X6613,tc_HOL_Obool)),tc_fun(X6614,tc_HOL_Obool)),X6613),c_COMBB(tc_fun(X6613,tc_HOL_Obool),tc_HOL_Obool,X6614)),c_member(X6613))),X6611))))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6614,tc_fun(X6613,tc_HOL_Obool)),X6612),X6611), inference(variable_rename,[status(thm)],[fact_INTER__def])). 4.46/4.70 fof(c_0_5704, plain, ![X11727, X11728, X11729, X11730, X11731]:c_Map_Odom(X11731,X11730,c_Fun_Ooverride__on(X11731,tc_Option_Ooption(X11730),X11729,X11728,X11727))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11731,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11731,tc_HOL_Obool)),c_Map_Odom(X11731,X11730,X11729)),hAPP(c_Set_OCollect(X11731),hAPP(hAPP(c_COMBC(X11731,tc_fun(X11731,tc_HOL_Obool),tc_HOL_Obool),c_member(X11731)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11731,tc_HOL_Obool)),X11727),c_Map_Odom(X11731,X11730,X11728)))))),hAPP(c_Set_OCollect(X11731),hAPP(hAPP(c_COMBC(X11731,tc_fun(X11731,tc_HOL_Obool),tc_HOL_Obool),c_member(X11731)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11731,tc_HOL_Obool)),X11727),c_Map_Odom(X11731,X11730,X11728))))), inference(variable_rename,[status(thm)],[fact_dom__override__on])). 4.46/4.70 fof(c_0_5705, plain, ![X9280, X9281, X9282, X9283]:hAPP(hAPP(c_List_Oappend(X9283),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X9283)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9280)),hAPP(hAPP(c_List_Olist_OCons(X9283),X9282),c_List_Olist_ONil(X9283))),c_List_Olist_ONil(X9283))),c_List_Osublist(X9283,X9281,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X9280))))=c_List_Osublist(X9283,hAPP(hAPP(c_List_Olist_OCons(X9283),X9282),X9281),X9280), inference(variable_rename,[status(thm)],[fact_sublist__Cons])). 4.46/4.70 fof(c_0_5706, plain, ![X6309, X6310]:c_List_Olenlex(X6310,X6309)=hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X6310)),tc_List_Olist(X6310)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X6310),c_Wellfounded_Oless__than,c_List_Olex(X6310,X6309))),hAPP(hAPP(c_COMBS(tc_List_Olist(X6310),tc_List_Olist(X6310),tc_prod(tc_Nat_Onat,tc_List_Olist(X6310))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X6310),tc_prod(tc_Nat_Onat,tc_List_Olist(X6310))),tc_List_Olist(X6310)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X6310))),c_Nat_Osize__class_Osize(tc_List_Olist(X6310)))),c_COMBI(tc_List_Olist(X6310)))), inference(variable_rename,[status(thm)],[fact_lenlex__def])). 4.46/4.70 fof(c_0_5707, plain, ![X10233, X10234, X10235]:c_Wellfounded_Omlex__prod(X10235,X10234,X10233)=hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X10235),X10235),c_Wellfounded_Olex__prod(tc_Nat_Onat,X10235,c_Wellfounded_Oless__than,X10233)),hAPP(hAPP(c_COMBS(X10235,X10235,tc_prod(tc_Nat_Onat,X10235)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X10235,tc_prod(tc_Nat_Onat,X10235)),X10235),c_Product__Type_OPair(tc_Nat_Onat,X10235)),X10234)),c_COMBI(X10235))), inference(variable_rename,[status(thm)],[fact_mlex__prod__def])). 4.46/4.70 fof(c_0_5708, plain, ![X2495, X2496]:hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X2496)),X2495)=hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X2496,tc_Lazy__Sequence_Olazy__sequence(X2496)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X2496,tc_Lazy__Sequence_Olazy__sequence(X2496),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X2496),tc_Nat_Onat),X2496),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X2496),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X2496)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X2496)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(c_Lazy__Sequence_Oyield(X2496),X2495)), inference(variable_rename,[status(thm)],[fact_size__code])). 4.46/4.70 fof(c_0_5709, plain, ![X11633, X11634, X11635]:c_List_Olistsp(X11635,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11635,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X11635,tc_fun(X11635,tc_HOL_Obool),tc_HOL_Obool),c_member(X11635)),X11634)),hAPP(hAPP(c_COMBC(X11635,tc_fun(X11635,tc_HOL_Obool),tc_HOL_Obool),c_member(X11635)),X11633)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X11635),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X11635),tc_fun(tc_List_Olist(X11635),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X11635))),c_List_Olists(X11635,X11634))),hAPP(hAPP(c_COMBC(tc_List_Olist(X11635),tc_fun(tc_List_Olist(X11635),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X11635))),c_List_Olists(X11635,X11633))), inference(variable_rename,[status(thm)],[fact_lists__Int__eq])). 4.46/4.70 cnf(c_0_5710, plain, (c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2))), inference(split_conjunct,[status(thm)],[c_0_4756])). 4.46/4.70 fof(c_0_5711, plain, ![X15056, X15057]:hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X15057,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15057)),X15056)))),hAPP(hAPP(c_COMBB(X15057,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X15057,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X15057,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X15057,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X15057),X15056)),c_Code__Numeral_Onat__of)))=c_Random_Oselect(X15057,X15056), inference(variable_rename,[status(thm)],[fact_select__def])). 4.46/4.70 cnf(c_0_5712, plain, (c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2))), inference(split_conjunct,[status(thm)],[c_0_4757])). 4.46/4.70 cnf(c_0_5713, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4758, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_5714, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))=X1), inference(rw,[status(thm)],[c_0_4759, c_0_4760]), ['final']). 4.46/4.70 cnf(c_0_5715, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OAll(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X1,tc_HOL_Obool))),X2)))),c_member(X1))))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)), inference(split_conjunct,[status(thm)],[c_0_4761])). 4.46/4.70 cnf(c_0_5716, plain, (c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X4))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X3),c_Int_Onat)))), inference(split_conjunct,[status(thm)],[c_0_4762])). 4.46/4.70 fof(c_0_5717, plain, ![X13837, X13838]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X13838),X13837)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))=hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X13837),X13838)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_minus])). 4.46/4.70 fof(c_0_5718, plain, ![X11186, X11187, X11188, X11189]:c_List_Osublist(X11189,hAPP(hAPP(c_List_Oappend(X11189),X11188),X11187),X11186)=hAPP(hAPP(c_List_Oappend(X11189),c_List_Osublist(X11189,X11188,X11186)),c_List_Osublist(X11189,X11187,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11189)),X11188)))),X11186)))), inference(variable_rename,[status(thm)],[fact_sublist__append])). 4.46/4.70 cnf(c_0_5719, plain, (c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X1)),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2))), inference(split_conjunct,[status(thm)],[c_0_4763])). 4.46/4.70 fof(c_0_5720, plain, ![X8135, X8136, X8137]:hAPP(hAPP(c_Equiv__Relations_Oquotient(X8137),X8136),X8135)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8137,tc_fun(tc_fun(X8137,tc_HOL_Obool),tc_HOL_Obool)),X8136),hAPP(hAPP(c_COMBC(X8137,tc_fun(tc_fun(X8137,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X8137,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8137,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X8137,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X8137,tc_HOL_Obool),tc_HOL_Obool)),X8137),c_Set_Oinsert(tc_fun(X8137,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X8137,tc_HOL_Obool),tc_fun(X8137,tc_HOL_Obool),X8137),c_Relation_OImage(X8137,X8137,X8135)),hAPP(hAPP(c_COMBC(X8137,tc_fun(X8137,tc_HOL_Obool),tc_fun(X8137,tc_HOL_Obool)),c_Set_Oinsert(X8137)),c_Orderings_Obot__class_Obot(tc_fun(X8137,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X8137,tc_HOL_Obool),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_quotient__def])). 4.46/4.70 cnf(c_0_5721, plain, (X1=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), inference(split_conjunct,[status(thm)],[c_0_4764])). 4.46/4.70 fof(c_0_5722, plain, ![X2653, X2654, X2655, X2656, X2657, X2658]:hAPP(c_Set_Ovimage(X2658,tc_prod(X2657,X2656),X2655),hAPP(hAPP(c_Product__Type_OSigma(X2657,X2656),X2654),hAPP(c_COMBK(tc_fun(X2656,tc_HOL_Obool),X2657),X2653)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2658,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X2658,X2657,hAPP(c_Fun_Ocomp(tc_prod(X2657,X2656),X2657,X2658,c_Product__Type_Ofst(X2657,X2656)),X2655)),X2654)),hAPP(c_Set_Ovimage(X2658,X2656,hAPP(c_Fun_Ocomp(tc_prod(X2657,X2656),X2656,X2658,c_Product__Type_Osnd(X2657,X2656)),X2655)),X2653)), inference(variable_rename,[status(thm)],[fact_vimage__Times])). 4.46/4.70 cnf(c_0_5723, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X2)))), inference(split_conjunct,[status(thm)],[c_0_4765])). 4.46/4.70 fof(c_0_5724, plain, ![X15893]:hAPP(c_Set_OCollect(tc_prod(tc_fun(X15893,tc_HOL_Obool),tc_fun(X15893,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X15893,tc_HOL_Obool),tc_fun(X15893,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X15893,tc_HOL_Obool),tc_fun(tc_fun(X15893,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X15893,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X15893,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X15893,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X15893,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X15893,tc_HOL_Obool)),c_COMBS(tc_fun(X15893,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X15893,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X15893,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X15893,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X15893,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X15893,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X15893))))=c_Wellfounded_Ofinite__psubset(X15893), inference(variable_rename,[status(thm)],[fact_finite__psubset__def])). 4.46/4.70 cnf(c_0_5725, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))), inference(split_conjunct,[status(thm)],[c_0_4766])). 4.46/4.70 cnf(c_0_5726, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J])). 4.46/4.70 fof(c_0_5727, plain, ![X17486, X17487, X17488, X17489]:c_List_Omap__filter(X17489,X17488,X17487,X17486)=hAPP(hAPP(c_List_Omap(X17489,X17488),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X17488),X17488,X17489,c_Option_Othe(X17488)),X17487)),hAPP(c_List_Ofilter(X17489,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X17489),c_fNot),hAPP(hAPP(c_COMBC(X17489,tc_Option_Ooption(X17488),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X17488),tc_fun(tc_Option_Ooption(X17488),tc_HOL_Obool),X17489),c_fequal),X17487)),c_Option_Ooption_ONone(X17488)))),X17486)), inference(variable_rename,[status(thm)],[fact_map__filter__def])). 4.46/4.70 cnf(c_0_5728, plain, (c_Map_Odom(X1,X2,X3)=hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3)),c_Option_Ooption_ONone(X2))))), inference(split_conjunct,[status(thm)],[c_0_4767])). 4.46/4.70 cnf(c_0_5729, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)=c_List_Oconcat(X2,hAPP(hAPP(c_List_Omap(X1,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X2),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_List_Olist(X2),tc_List_Olist(X2)),X1),c_List_Olist_OCons(X2)),X3)),c_List_Olist_ONil(X2))),X4))), inference(split_conjunct,[status(thm)],[c_0_4768])). 4.46/4.70 cnf(c_0_5730, plain, (hAPP(c_New__DSequence_Opos__not__seq(X1),X2)=c_Lazy__Sequence_Ohb__not__seq(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),X2)))), inference(split_conjunct,[status(thm)],[c_0_4769])). 4.46/4.70 fof(c_0_5731, plain, ![X11802, X11803, X11804, X11805]:hAPP(c_Relation_OImage(tc_List_Olist(X11805),tc_List_Olist(X11805),c_List_Olistrel(X11805,X11804)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X11805)),hAPP(hAPP(c_List_Olist_OCons(X11805),X11803),X11802)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X11805),tc_HOL_Obool))))=c_List_Oset__Cons(X11805,hAPP(c_Relation_OImage(X11805,X11805,X11804),hAPP(hAPP(c_Set_Oinsert(X11805),X11803),c_Orderings_Obot__class_Obot(tc_fun(X11805,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X11805),tc_List_Olist(X11805),c_List_Olistrel(X11805,X11804)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X11805)),X11802),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X11805),tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_listrel__Cons])). 4.46/4.70 cnf(c_0_5732, plain, (hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1)))),c_Orderings_Oord__class_Oless(tc_Int_Oint))))=c_Int_Oint__ge__less__than(X1)), inference(split_conjunct,[status(thm)],[c_0_4770])). 4.46/4.70 cnf(c_0_5733, plain, (hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X3))),X4)))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_Set_OCollect(X1),X3)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),X4))), inference(split_conjunct,[status(thm)],[c_0_4771])). 4.46/4.70 cnf(c_0_5734, plain, (hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4772, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_5735, plain, ![X465, X466, X467, X468]:c_HOL_OThe(tc_prod(X468,X467),hAPP(c_Product__Type_Oprod_Oprod__case(X468,X467,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X468,tc_fun(X467,tc_HOL_Obool),tc_fun(X467,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X467,tc_HOL_Obool),tc_fun(X467,tc_HOL_Obool)),X468),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X467)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X468),c_fconj),hAPP(c_fequal,X466)))),hAPP(c_fequal,X465))))=hAPP(hAPP(c_Product__Type_OPair(X468,X467),X466),X465), inference(variable_rename,[status(thm)],[fact_The__split__eq])). 4.46/4.70 fof(c_0_5736, plain, ![X14539, X14540, X14541, X14542]:c_Hilbert__Choice_OEps(tc_prod(X14542,X14541),hAPP(c_Product__Type_Oprod_Oprod__case(X14542,X14541,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X14542,tc_fun(X14541,tc_HOL_Obool),tc_fun(X14541,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X14541,tc_HOL_Obool),tc_fun(X14541,tc_HOL_Obool)),X14542),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X14541)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X14542),c_fconj),hAPP(c_fequal,X14540)))),hAPP(c_fequal,X14539))))=hAPP(hAPP(c_Product__Type_OPair(X14542,X14541),X14540),X14539), inference(variable_rename,[status(thm)],[fact_Eps__split__eq])). 4.46/4.70 cnf(c_0_5737, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2))=c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4773])). 4.46/4.70 fof(c_0_5738, plain, ![X17037, X17038, X17039]:hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17039)),X17037)))),hAPP(hAPP(c_COMBB(X17039,tc_HOL_Obool,tc_Nat_Onat),X17038),hAPP(c_List_Onth(X17039),X17037)))))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17039)),hAPP(c_List_Ofilter(X17039,X17038),X17037)), inference(variable_rename,[status(thm)],[fact_length__filter__conv__card])). 4.46/4.70 fof(c_0_5739, plain, ![X5347, X5348]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5348,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(X5348,tc_HOL_Obool)),tc_fun(X5348,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X5348,tc_HOL_Obool)),tc_fun(X5348,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5348,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X5347))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5348,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X5347), inference(variable_rename,[status(thm)],[fact_UN__UN__finite__eq])). 4.46/4.70 fof(c_0_5740, plain, ![X1381, X1382, X1383, X1384, X1385, X1386]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1386,tc_fun(X1385,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1384,tc_fun(X1386,tc_HOL_Obool)),X1383),X1382)),X1381)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1384,tc_fun(X1385,tc_HOL_Obool)),X1383),hAPP(hAPP(c_COMBC(X1384,tc_fun(X1386,tc_fun(X1385,tc_HOL_Obool)),tc_fun(X1385,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1386,tc_HOL_Obool),tc_fun(tc_fun(X1386,tc_fun(X1385,tc_HOL_Obool)),tc_fun(X1385,tc_HOL_Obool)),X1384),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1386,tc_fun(X1385,tc_HOL_Obool))),X1382)),X1381)), inference(variable_rename,[status(thm)],[fact_UN__simps_I9_J])). 4.46/4.70 fof(c_0_5741, plain, ![X14402, X14403, X14404, X14405]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14405,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14405,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14405,tc_HOL_Obool)),X14404),X14403)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14405,tc_HOL_Obool)),X14403),X14402))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14405,tc_HOL_Obool)),X14402),X14404))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14405,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14405,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14405,tc_HOL_Obool)),X14404),X14403)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14405,tc_HOL_Obool)),X14403),X14402))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14405,tc_HOL_Obool)),X14402),X14404)), inference(variable_rename,[status(thm)],[fact_Un__Int__crazy])). 4.46/4.70 fof(c_0_5742, plain, ![X11274, X11275, X11276, X11277]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11277,tc_HOL_Obool)),X11276),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11277,tc_HOL_Obool)),X11275),X11274))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11277,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11277,tc_HOL_Obool)),X11276),X11275)),X11274), inference(variable_rename,[status(thm)],[fact_Int__assoc])). 4.46/4.70 fof(c_0_5743, plain, ![X7186, X7187, X7188]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7188),X7187)),X7186)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X7188),X7186)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X7187),X7186))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X7188,X7186)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X7187,X7186))),X7186)), inference(variable_rename,[status(thm)],[fact_div__add1__eq])). 4.46/4.70 fof(c_0_5744, plain, ![X1748, X1749, X1750]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1750),X1749)),X1748)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1750),X1748)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1749),X1748))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1750,X1748)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1749,X1748))),X1748)), inference(variable_rename,[status(thm)],[fact_zdiv__zadd1__eq])). 4.46/4.70 cnf(c_0_5745, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))), inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J])). 4.46/4.70 cnf(c_0_5746, plain, (c_Nitpick_OAbs__Frac(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),X2))),hAPP(c_Nitpick_Odenom(X1),X2)))=c_Nitpick_Ouminus__frac(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4774])). 4.46/4.70 cnf(c_0_5747, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=c_Transitive__Closure_Otrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1)))), inference(split_conjunct,[status(thm)],[c_0_4775])). 4.46/4.70 cnf(c_0_5748, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1)))), inference(split_conjunct,[status(thm)],[c_0_4776])). 4.46/4.70 cnf(c_0_5749, plain, (c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J])). 4.46/4.70 fof(c_0_5750, plain, ![X1833, X1834, X1835]:hAPP(c_List_Orev(X1835),hAPP(c_List_Orotate(X1835,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1835)),X1833)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1834,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1835)),X1833)))),X1833))=hAPP(c_List_Orotate(X1835,X1834),hAPP(c_List_Orev(X1835),X1833)), inference(variable_rename,[status(thm)],[fact_rotate__rev])). 4.46/4.70 fof(c_0_5751, plain, ![X11916, X11917, X11918, X11919, X11920]:hAPP(c_Fun_Othe__inv__into(X11920,X11919,X11918,X11917),X11916)=c_HOL_OThe(X11920,hAPP(hAPP(c_COMBS(X11920,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X11920),c_fconj),hAPP(hAPP(c_COMBC(X11920,tc_fun(X11920,tc_HOL_Obool),tc_HOL_Obool),c_member(X11920)),X11918))),hAPP(hAPP(c_COMBC(X11920,X11919,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X11919,tc_fun(X11919,tc_HOL_Obool),X11920),c_fequal),X11917)),X11916))), inference(variable_rename,[status(thm)],[fact_the__inv__into__def])). 4.46/4.70 fof(c_0_5752, plain, ![X4109, X4110, X4111]:hAPP(c_Set_OCollect(X4110),hAPP(hAPP(c_COMBB(tc_fun(X4111,tc_HOL_Obool),tc_HOL_Obool,X4110),c_HOL_OEx(X4111)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X4110),tc_fun(X4111,tc_HOL_Obool),X4110),hAPP(c_COMBC(X4111,tc_Option_Ooption(X4110),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X4110),tc_fun(tc_Option_Ooption(X4110),tc_HOL_Obool),X4111),c_fequal),X4109))),c_Option_Ooption_OSome(X4110))))=c_Map_Oran(X4111,X4110,X4109), inference(variable_rename,[status(thm)],[fact_ran__def])). 4.46/4.70 cnf(c_0_5753, plain, (c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1))), inference(split_conjunct,[status(thm)],[c_0_4777])). 4.46/4.70 fof(c_0_5754, plain, ![X11143, X11144, X11145]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11145),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11144),X11143))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11144),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11145),X11143)), inference(variable_rename,[status(thm)],[fact_zadd__left__commute])). 4.46/4.70 fof(c_0_5755, plain, ![X9087, X9088, X9089]:hAPP(c_List_Orotate(X9089,X9088),X9087)=hAPP(hAPP(c_List_Oappend(X9089),hAPP(hAPP(c_List_Odrop(X9089),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X9088,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9089)),X9087))),X9087)),hAPP(hAPP(c_List_Otake(X9089),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X9088,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9089)),X9087))),X9087)), inference(variable_rename,[status(thm)],[fact_rotate__drop__take])). 4.46/4.70 cnf(c_0_5756, plain, (c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))), inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J])). 4.46/4.70 fof(c_0_5757, plain, ![X11952, X11953]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X11953,X11953),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X11953,X11952)),hAPP(hAPP(c_Product__Type_OSigma(X11953,X11953),hAPP(c_Relation_OField(X11953),X11952)),hAPP(c_COMBK(tc_fun(X11953,tc_HOL_Obool),X11953),hAPP(c_Relation_OField(X11953),X11952))))), inference(variable_rename,[status(thm)],[fact_trancl__subset__Field2])). 4.46/4.70 cnf(c_0_5758, plain, (c_Nitpick_Oint__lcm(X1,X2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))))), inference(split_conjunct,[status(thm)],[c_0_4778])). 4.46/4.70 cnf(c_0_5759, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),c_Nitpick_Onat__gcd(X1,X2))=c_Nitpick_Onat__lcm(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4779])). 4.46/4.70 cnf(c_0_5760, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)))=hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_4780])). 4.46/4.70 fof(c_0_5761, plain, ![X2764, X2765, X2766, X2767, X2768]:c_Hoare__Mirabelle_Ohoare__derivs(X2768,X2767,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2768)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2768),hAPP(hAPP(c_COMBC(X2768,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X2768),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X2768),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),X2766))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),X2765))),c_Com_Ocom_OWhile(X2765,X2764)),X2766)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2768),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_LoopF])). 4.46/4.70 cnf(c_0_5762, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1))=c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))), inference(split_conjunct,[status(thm)],[c_0_4781])). 4.46/4.70 cnf(c_0_5763, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4782, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_5764, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4783, c_0_4784]), c_0_4436]), c_0_4760])). 4.46/4.70 cnf(c_0_5765, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4785, c_0_4500]), c_0_4760]), ['final']). 4.46/4.70 cnf(c_0_5766, plain, (c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X1))), inference(split_conjunct,[status(thm)],[c_0_4786])). 4.46/4.70 cnf(c_0_5767, plain, (c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Orev(X1)),hAPP(c_List_Orev(tc_List_Olist(X1)),X2)))=hAPP(c_List_Orev(X1),c_List_Oconcat(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_4787])). 4.46/4.70 fof(c_0_5768, plain, ![X11003, X11004, X11005, X11006]:hAPP(hAPP(c_List_Omap(X11005,X11006),X11004),hAPP(c_List_Orev(X11005),X11003))=hAPP(c_List_Orev(X11006),hAPP(hAPP(c_List_Omap(X11005,X11006),X11004),X11003)), inference(variable_rename,[status(thm)],[fact_rev__map])). 4.46/4.70 cnf(c_0_5769, plain, (c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X1))), inference(split_conjunct,[status(thm)],[c_0_4788])). 4.46/4.70 fof(c_0_5770, plain, ![X7566, X7567]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7567),X7566)=hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X7567),X7566)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[fact_nat])). 4.46/4.70 fof(c_0_5771, plain, ![X3269, X3270, X3271, X3272]:hAPP(c_List_Orotate(X3272,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3271),X3270)),X3269)=hAPP(c_List_Orotate(X3272,X3271),hAPP(c_List_Orotate(X3272,X3270),X3269)), inference(variable_rename,[status(thm)],[fact_rotate__rotate])). 4.46/4.70 fof(c_0_5772, plain, ![X12601, X12602, X12603, X12604, X12605, X12606]:(hAPP(hAPP(c_List_Olist_OCons(X12603),X12605),X12606)!=X12604|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X12603),tc_List_Olist(X12603))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X12603),tc_List_Olist(X12603)),X12602),hAPP(hAPP(c_List_Oappend(X12603),X12602),X12604))),c_List_Olexord(X12603,X12601)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lexord__append__rightI])])])])). 4.46/4.70 cnf(c_0_5773, plain, (c_List_Oconcat(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Ofilter(X1,X2)),X3))=hAPP(c_List_Ofilter(X1,X2),c_List_Oconcat(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_4789])). 4.46/4.70 fof(c_0_5774, plain, ![X7623]:hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X7623),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7623), inference(variable_rename,[status(thm)],[fact_int__def])). 4.46/4.70 cnf(c_0_5775, plain, (c_Transitive__Closure_Otrancl(X1,X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Otrancl(X1,X2)),X2))), inference(split_conjunct,[status(thm)],[c_0_4790])). 4.46/4.70 fof(c_0_5776, plain, ![X16393, X16394, X16395, X16396, X16397, X16398, X16399]:hAPP(hAPP(c_Relation_Orel__comp(X16399,X16396,X16397),X16395),hAPP(hAPP(c_Relation_Orel__comp(X16396,X16398,X16397),X16394),X16393))=hAPP(hAPP(c_Relation_Orel__comp(X16399,X16398,X16397),hAPP(hAPP(c_Relation_Orel__comp(X16399,X16396,X16398),X16395),X16394)),X16393), inference(variable_rename,[status(thm)],[fact_O__assoc])). 4.46/4.70 cnf(c_0_5777, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2)=c_Transitive__Closure_Otrancl(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4791])). 4.46/4.70 fof(c_0_5778, plain, ![X12348]:hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),esk362_1(X12348)),esk363_1(X12348))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))=X12348, inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__Abs__Integ])])])). 4.46/4.70 fof(c_0_5779, plain, ![X4790]:hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4790)))),c_Orderings_Oord__class_Oless(tc_Int_Oint))))=c_Int_Oint__ge__less__than2(X4790), inference(variable_rename,[status(thm)],[fact_int__ge__less__than2__def])). 4.46/4.70 fof(c_0_5780, plain, ![X13758, X13759, X13760]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13760)),hAPP(c_List_Ofilter(X13760,X13759),X13758))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13760)),hAPP(c_List_Ofilter(X13760,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X13760),c_fNot),X13759)),X13758)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13760)),X13758), inference(variable_rename,[status(thm)],[fact_sum__length__filter__compl])). 4.46/4.70 fof(c_0_5781, plain, ![X725, X726, X727]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X727)),hAPP(hAPP(c_List_Oappend(X727),X726),X725))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X727)),X726)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X727)),X725)), inference(variable_rename,[status(thm)],[fact_length__append])). 4.46/4.70 fof(c_0_5782, plain, ![X9704, X9705, X9706, X9707, X9708]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X9706,hAPP(c_Product__Type_Ofst(X9708,X9707),X9704))),hAPP(X9705,hAPP(c_Product__Type_Osnd(X9708,X9707),X9704)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Product__Type_Oprod_Oprod__size(X9708,X9707,X9706,X9705,X9704), inference(variable_rename,[status(thm)],[fact_prod__size__simp])). 4.46/4.70 fof(c_0_5783, plain, ![X14529, X14530, X14531, X14532, X14533, X14534, X14535, X14536]:((hAPP(hAPP(c_List_Olist_OCons(X14531),X14532),X14533)!=X14530|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X14531),tc_List_Olist(X14531))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14531),tc_List_Olist(X14531)),c_List_Olist_ONil(X14531)),X14530)),c_List_Olexord(X14531,X14529))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X14536),tc_List_Olist(X14536))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14536),tc_List_Olist(X14536)),c_List_Olist_ONil(X14536)),X14535)),c_List_Olexord(X14536,X14534)))|hAPP(hAPP(c_List_Olist_OCons(X14536),esk428_3(X14534,X14535,X14536)),esk429_3(X14534,X14535,X14536))=X14535)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__Nil__left])])])])])). 4.46/4.70 fof(c_0_5784, plain, ![X8356]:hAPP(c_Set_OCollect(tc_Nat_Onat),X8356)=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),X8356),c_Int_Onat)))), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J])). 4.46/4.70 fof(c_0_5785, plain, ![X8129, X8130, X8131]:hAPP(c_List_Oset(X8131),hAPP(c_List_Ofilter(X8131,X8130),X8129))=hAPP(c_Set_OCollect(X8131),hAPP(hAPP(c_COMBS(X8131,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X8131),c_fconj),hAPP(hAPP(c_COMBC(X8131,tc_fun(X8131,tc_HOL_Obool),tc_HOL_Obool),c_member(X8131)),hAPP(c_List_Oset(X8131),X8129)))),X8130)), inference(variable_rename,[status(thm)],[fact_set__filter])). 4.46/4.70 cnf(c_0_5786, plain, (c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(X1)),c_List_Oembed__list(X2)))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_4792])). 4.46/4.70 cnf(c_0_5787, plain, (c_List_Oreturn__list(X1)=hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_4793])). 4.46/4.70 cnf(c_0_5788, plain, (c_List_Oembed__list(X1)=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)), inference(split_conjunct,[status(thm)],[c_0_4794])). 4.46/4.70 fof(c_0_5789, plain, ![X13668, X13669, X13670, X13671, X13672]:hAPP(hAPP(c_List_Oappend(X13671),hAPP(hAPP(c_List_Omap(X13672,X13671),X13670),X13669)),hAPP(hAPP(c_List_Omap(X13672,X13671),X13670),X13668))=hAPP(hAPP(c_List_Omap(X13672,X13671),X13670),hAPP(hAPP(c_List_Oappend(X13672),X13669),X13668)), inference(variable_rename,[status(thm)],[fact_map__append])). 4.46/4.70 fof(c_0_5790, plain, ![X4469, X4470]:hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X4470)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X4469))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X4470),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X4469)))=c_Divides_Opdivmod(X4470,X4469), inference(variable_rename,[status(thm)],[fact_pdivmod__def])). 4.46/4.70 fof(c_0_5791, plain, ![X6729, X6730]:c_Divides_Odivmod__int(X6730,X6729)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6730),X6729)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6730,X6729)), inference(variable_rename,[status(thm)],[fact_divmod__int__mod__div])). 4.46/4.70 fof(c_0_5792, plain, ![X17407]:hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X17407))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),X17407),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J])). 4.46/4.70 cnf(c_0_5793, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2)))),X3))=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_Set_OCollect(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_4795])). 4.46/4.70 fof(c_0_5794, plain, ![X7775, X7776, X7777, X7778, X7779]:((X7779=c_Orderings_Obot__class_Obot(tc_fun(X7778,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7778,tc_fun(X7777,tc_HOL_Obool)),X7779),hAPP(hAPP(c_COMBC(X7778,tc_fun(X7777,tc_HOL_Obool),tc_fun(X7777,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7777,tc_HOL_Obool),tc_fun(tc_fun(X7777,tc_HOL_Obool),tc_fun(X7777,tc_HOL_Obool)),X7778),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7777,tc_HOL_Obool))),X7776)),X7775))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7777,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7778,tc_fun(X7777,tc_HOL_Obool)),X7779),X7776)),X7775))&(c_Orderings_Obot__class_Obot(tc_fun(X7778,tc_HOL_Obool))!=X7779|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7778,tc_fun(X7777,tc_HOL_Obool)),X7779),hAPP(hAPP(c_COMBC(X7778,tc_fun(X7777,tc_HOL_Obool),tc_fun(X7777,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7777,tc_HOL_Obool),tc_fun(tc_fun(X7777,tc_HOL_Obool),tc_fun(X7777,tc_HOL_Obool)),X7778),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7777,tc_HOL_Obool))),X7776)),X7775))=c_Orderings_Obot__class_Obot(tc_fun(X7777,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__simps_I2_J])])])). 4.46/4.70 cnf(c_0_5795, plain, (c_List_Ofoldr(X1,X2,hAPP(c_COMBC(X2,X1,X2),X3),hAPP(c_List_Orev(X1),X4),X5)=hAPP(c_List_Ofoldl(X2,X1,X3,X5),X4)), inference(split_conjunct,[status(thm)],[c_0_4796])). 4.46/4.70 fof(c_0_5796, plain, ![X5562, X5563]:X5562=hAPP(c_List_Orev(X5563),hAPP(c_List_Orev(X5563),X5562)), inference(variable_rename,[status(thm)],[fact_rev__rev__ident])). 4.46/4.70 fof(c_0_5797, plain, ![X7746, X7747, X7748]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,X7748,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7747),X7746))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7747),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X7748),X7747),X7746))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X7748,X7747)), inference(variable_rename,[status(thm)],[fact_mod__mult2__eq])). 4.46/4.70 fof(c_0_5798, plain, ![X7740, X7741, X7742, X7743, X7744, X7745]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7742,tc_fun(X7745,tc_HOL_Obool)),X7741),hAPP(hAPP(c_COMBB(tc_fun(X7744,tc_HOL_Obool),tc_fun(X7745,tc_HOL_Obool),X7742),c_Set_Ovimage(X7745,X7744,X7743)),X7740))=hAPP(c_Set_Ovimage(X7745,X7744,X7743),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7742,tc_fun(X7744,tc_HOL_Obool)),X7741),X7740)), inference(variable_rename,[status(thm)],[fact_vimage__INT])). 4.46/4.70 fof(c_0_5799, plain, ![X15486, X15487, X15488, X15489, X15490, X15491]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15488,tc_fun(X15491,tc_HOL_Obool)),X15487),hAPP(hAPP(c_COMBB(tc_fun(X15490,tc_HOL_Obool),tc_fun(X15491,tc_HOL_Obool),X15488),c_Set_Ovimage(X15491,X15490,X15489)),X15486))=hAPP(c_Set_Ovimage(X15491,X15490,X15489),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15488,tc_fun(X15490,tc_HOL_Obool)),X15487),X15486)), inference(variable_rename,[status(thm)],[fact_vimage__UN])). 4.46/4.70 fof(c_0_5800, plain, ![X6085, X6086, X6087]:hAPP(c_List_Orotate(X6087,X6086),X6085)=hAPP(c_List_Orotate(X6087,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X6086,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6087)),X6085))),X6085), inference(variable_rename,[status(thm)],[fact_rotate__conv__mod])). 4.46/4.70 fof(c_0_5801, plain, ![X9425, X9426, X9427, X9428]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9428,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X9428),X9427),hAPP(hAPP(c_Set_Oinsert(X9428),X9426),c_Orderings_Obot__class_Obot(tc_fun(X9428,tc_HOL_Obool))))),hAPP(c_Relation_OField(X9428),X9425))=hAPP(c_Relation_OField(X9428),hAPP(hAPP(c_Set_Oinsert(tc_prod(X9428,X9428)),hAPP(hAPP(c_Product__Type_OPair(X9428,X9428),X9427),X9426)),X9425)), inference(variable_rename,[status(thm)],[fact_Field__insert])). 4.46/4.70 cnf(c_0_5802, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Relation_OId(X1)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2))), inference(split_conjunct,[status(thm)],[c_0_4797])). 4.46/4.70 fof(c_0_5803, plain, ![X6037, X6038]:hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X6038)),c_List_Olist_ONil(X6038)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X6038),tc_HOL_Obool)))=hAPP(c_Relation_OImage(tc_List_Olist(X6038),tc_List_Olist(X6038),c_List_Olistrel(X6038,X6037)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X6038)),c_List_Olist_ONil(X6038)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X6038),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_listrel__Nil])). 4.46/4.70 fof(c_0_5804, plain, ![X2491, X2492]:c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2491),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),X2491)),X2492)=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X2492),hAPP(c_Nat_OSuc,X2491)), inference(variable_rename,[status(thm)],[fact_max__Suc2])). 4.46/4.70 fof(c_0_5805, plain, ![X699, X700, X701, X702]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X702)),hAPP(hAPP(c_List_Omap(X701,X702),X700),X699))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X701)),X699), inference(variable_rename,[status(thm)],[fact_length__map])). 4.46/4.70 fof(c_0_5806, plain, ![X6198, X6199, X6200, X6201, X6202]:c_Lazy__Sequence_Ohb__bind(X6202,X6201,hAPP(X6200,X6198),hAPP(hAPP(c_COMBC(X6202,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X6201))),X6199),X6198))=hAPP(c_New__DSequence_Oneg__bind(X6202,X6201,X6200,X6199),X6198), inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__bind__def])). 4.46/4.70 fof(c_0_5807, plain, ![X7068, X7069]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X7069),hAPP(c_Nat_OSuc,X7068))=c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),X7068)),X7069), inference(variable_rename,[status(thm)],[fact_min__Suc2])). 4.46/4.70 fof(c_0_5808, plain, ![X14845, X14846, X14847]:hAPP(hAPP(c_Relation_Orel__comp(X14847,X14847,X14847),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X14847,X14847),tc_HOL_Obool),X14845),X14846)),X14846)=hAPP(hAPP(c_Relation_Orel__comp(X14847,X14847,X14847),X14846),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X14847,X14847),tc_HOL_Obool),X14845),X14846)), inference(variable_rename,[status(thm)],[fact_rel__pow__commute])). 4.46/4.70 fof(c_0_5809, plain, ![X1924, X1925, X1926]:hAPP(hAPP(c_Relation_Orel__comp(X1926,X1926,X1926),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1926,X1926),tc_HOL_Obool),X1925),X1924)),X1924)=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1926,X1926),tc_HOL_Obool),hAPP(c_Nat_OSuc,X1925)),X1924), inference(variable_rename,[status(thm)],[fact_relpow_Osimps_I2_J])). 4.46/4.70 fof(c_0_5810, plain, ![X8346, X8347, X8348, X8349, X8350]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8350,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X8350,X8349,X8348),X8347)),hAPP(c_Set_Ovimage(X8350,X8349,X8348),X8346))=hAPP(c_Set_Ovimage(X8350,X8349,X8348),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8349,tc_HOL_Obool)),X8347),X8346)), inference(variable_rename,[status(thm)],[fact_vimage__Un])). 4.46/4.70 fof(c_0_5811, plain, ![X14323, X14324, X14325, X14326, X14327]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14327,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X14327,X14326,X14325),X14324)),hAPP(c_Set_Ovimage(X14327,X14326,X14325),X14323))=hAPP(c_Set_Ovimage(X14327,X14326,X14325),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14326,tc_HOL_Obool)),X14324),X14323)), inference(variable_rename,[status(thm)],[fact_vimage__Int])). 4.46/4.70 fof(c_0_5812, plain, ![X9677, X9678, X9679, X9680, X9681]:hAPP(c_Set_Ovimage(X9681,X9680,X9679),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9680,tc_HOL_Obool)),X9678),X9677))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9681,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X9681,X9680,X9679),X9678)),hAPP(c_Set_Ovimage(X9681,X9680,X9679),X9677)), inference(variable_rename,[status(thm)],[fact_vimage__Diff])). 4.46/4.70 fof(c_0_5813, plain, ![X5271, X5272, X5273, X5274]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X5274,X5273))),hAPP(hAPP(c_List_Ozip(X5274,X5273),X5272),X5271))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5274)),X5272)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5273)),X5271)), inference(variable_rename,[status(thm)],[fact_length__zip])). 4.46/4.70 fof(c_0_5814, plain, ![X10737, X10738]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),X10738)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X10737))))), inference(variable_rename,[status(thm)],[fact_finite__M__bounded__by__nat])). 4.46/4.70 fof(c_0_5815, plain, ![X9984, X9985, X9986, X9987, X9988, X9989]:hAPP(hAPP(c_List_Ozip(X9989,X9988),c_List_Oreplicate(X9989,X9987,X9986)),c_List_Oreplicate(X9988,X9985,X9984))=c_List_Oreplicate(tc_prod(X9989,X9988),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X9987),X9985),hAPP(hAPP(c_Product__Type_OPair(X9989,X9988),X9986),X9984)), inference(variable_rename,[status(thm)],[fact_zip__replicate])). 4.46/4.70 fof(c_0_5816, plain, ![X15654, X15655, X15656, X15657, X15658, X15659, X15660, X15661, X15662]:((X15655!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X15657,tc_Option_Ooption(X15656)),hAPP(c_COMBK(tc_Option_Ooption(X15656),X15657),c_Option_Ooption_ONone(X15656))),X15654),hAPP(c_Option_Ooption_OSome(X15656),X15658))|c_Map_Odom(X15657,X15656,X15655)=hAPP(hAPP(c_Set_Oinsert(X15657),X15654),c_Orderings_Obot__class_Obot(tc_fun(X15657,tc_HOL_Obool))))&(c_Map_Odom(X15662,X15661,X15660)!=hAPP(hAPP(c_Set_Oinsert(X15662),X15659),c_Orderings_Obot__class_Obot(tc_fun(X15662,tc_HOL_Obool)))|X15660=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X15662,tc_Option_Ooption(X15661)),hAPP(c_COMBK(tc_Option_Ooption(X15661),X15662),c_Option_Ooption_ONone(X15661))),X15659),hAPP(c_Option_Ooption_OSome(X15661),esk457_4(X15659,X15660,X15661,X15662))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__eq__singleton__conv])])])])])). 4.46/4.70 fof(c_0_5817, plain, ![X13092, X13093]:hAPP(c_List_Oset(X13093),c_List_Oconcat(X13093,X13092))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X13093),tc_fun(X13093,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X13093)),X13092)),c_List_Oset(X13093)), inference(variable_rename,[status(thm)],[fact_set__concat])). 4.46/4.70 cnf(c_0_5818, plain, (hAPP(c_List_OremoveAll(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))=hAPP(c_List_OremoveAll(X3,X1),X4)|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_4613])). 4.46/4.70 fof(c_0_5819, plain, ![X6473, X6474, X6475]:hAPP(c_List_Orotate(X6475,hAPP(c_Nat_OSuc,X6474)),X6473)=hAPP(c_List_Orotate1(X6475),hAPP(c_List_Orotate(X6475,X6474),X6473)), inference(variable_rename,[status(thm)],[fact_rotate__Suc])). 4.46/4.70 fof(c_0_5820, plain, ![X3115, X3116, X3117]:hAPP(c_List_Ofoldl(tc_List_Olist(X3117),tc_List_Olist(X3117),c_List_Oappend(X3117),X3116),X3115)=hAPP(hAPP(c_List_Oappend(X3117),X3116),c_List_Oconcat(X3117,X3115)), inference(variable_rename,[status(thm)],[fact_foldl__conv__concat])). 4.46/4.70 fof(c_0_5821, plain, ![X6350, X6351, X6352, X6353, X6354, X6355]:((X6355=X6354|hAPP(hAPP(c_Map_Omap__of(X6353,X6352),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X6353,X6352)),hAPP(hAPP(c_Product__Type_OPair(X6353,X6352),X6355),X6351)),X6350)),X6354)=hAPP(hAPP(c_Map_Omap__of(X6353,X6352),X6350),X6354))&(X6354!=X6355|hAPP(hAPP(c_Map_Omap__of(X6353,X6352),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X6353,X6352)),hAPP(hAPP(c_Product__Type_OPair(X6353,X6352),X6355),X6351)),X6350)),X6354)=hAPP(c_Option_Ooption_OSome(X6352),X6351))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__Cons__code_I2_J])])])). 4.46/4.70 fof(c_0_5822, plain, ![X8162, X8163, X8164]:hBOOL(hAPP(c_Finite__Set_Ofinite(X8164),c_Map_Odom(X8164,X8163,hAPP(c_Map_Omap__of(X8164,X8163),X8162)))), inference(variable_rename,[status(thm)],[fact_finite__dom__map__of])). 4.46/4.70 fof(c_0_5823, plain, ![X17063, X17064, X17065, X17066]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17066,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17066,tc_HOL_Obool)),X17065),X17064)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17066,tc_HOL_Obool)),X17065),X17063))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17066,tc_HOL_Obool)),X17065),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17066,tc_HOL_Obool)),X17064),X17063)), inference(variable_rename,[status(thm)],[fact_Diff__Un])). 4.46/4.70 cnf(c_0_5824, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3)), inference(split_conjunct,[status(thm)],[c_0_4798])). 4.46/4.70 cnf(c_0_5825, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4799, c_0_4800]), c_0_4800]), ['final']). 4.46/4.70 fof(c_0_5826, plain, ![X4393, X4394, X4395, X4396]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4396,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4396,tc_HOL_Obool)),X4395),X4394)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4396,tc_HOL_Obool)),X4395),X4393))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4396,tc_HOL_Obool)),X4395),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4396,tc_HOL_Obool)),X4394),X4393)), inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib])). 4.46/4.70 fof(c_0_5827, plain, ![X1260, X1261, X1262]:hAPP(c_Set_OCollect(X1262),hAPP(hAPP(c_COMBB(tc_fun(X1261,tc_HOL_Obool),tc_HOL_Obool,X1262),c_HOL_OEx(X1261)),X1260))=hAPP(c_Relation_ODomain(X1262,X1261),hAPP(c_Set_OCollect(tc_prod(X1262,X1261)),hAPP(c_Product__Type_Oprod_Oprod__case(X1262,X1261,tc_HOL_Obool),X1260))), inference(variable_rename,[status(thm)],[fact_Domain__Collect__split])). 4.46/4.70 fof(c_0_5828, plain, ![X10379]:X10379=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X10379)), inference(variable_rename,[status(thm)],[fact_transfer__int__nat__set__return__embed])). 4.46/4.70 fof(c_0_5829, plain, ![X9446, X9447, X9448, X9449]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X9448,tc_HOL_Obool),tc_fun(X9449,tc_HOL_Obool)),X9446),c_Set_Ovimage(X9449,X9448,X9447))=hAPP(c_Set_Ovimage(X9449,X9448,X9447),c_Complete__Lattice_OSup__class_OSup(tc_fun(X9448,tc_HOL_Obool),X9446)), inference(variable_rename,[status(thm)],[fact_vimage__Union])). 4.46/4.70 fof(c_0_5830, plain, ![X3910, X3911, X3912]:X3910=hAPP(hAPP(c_List_Oappend(X3912),c_List_OtakeWhile(X3912,X3911,X3910)),c_List_OdropWhile(X3912,X3911,X3910)), inference(variable_rename,[status(thm)],[fact_takeWhile__dropWhile__id])). 4.46/4.70 fof(c_0_5831, plain, ![X13534, X13535]:hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X13535),hAPP(c_List_Onth(X13535),X13534)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13535)),X13534)))=X13534, inference(variable_rename,[status(thm)],[fact_map__nth])). 4.46/4.70 fof(c_0_5832, plain, ![X7803, X7804, X7805]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7805),X7804)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7803),X7804))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X7805),X7803)),X7804), inference(variable_rename,[status(thm)],[fact_min__diff])). 4.46/4.70 fof(c_0_5833, plain, ![X16880, X16881, X16882, X16883, X16884, X16885]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X16883,X16881)),hAPP(X16882,X16880))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Nitpick_Opair__box_Opair__box__size(X16885,X16884,X16883,X16882,c_Nitpick_Opair__box_OPairBox(X16885,X16884,X16881,X16880)), inference(variable_rename,[status(thm)],[fact_pair__box_Osize_I1_J])). 4.46/4.70 fof(c_0_5834, plain, ![X1469, X1470, X1471, X1472, X1473]:(hAPP(c_Set_Oimage(X1473,X1472,X1471),X1470)!=X1469|hAPP(c_Set_Oimage(tc_fun(X1473,tc_HOL_Obool),tc_fun(X1472,tc_HOL_Obool),c_Set_Oimage(X1473,X1472,X1471)),hAPP(c_Set_OPow(X1473),X1470))=hAPP(c_Set_OPow(X1472),X1469)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Pow__surj])])). 4.46/4.70 fof(c_0_5835, plain, ![X4176, X4177, X4178]:hAPP(hAPP(c_Equiv__Relations_Oquotient(X4178),hAPP(hAPP(c_Set_Oinsert(X4178),X4177),c_Orderings_Obot__class_Obot(tc_fun(X4178,tc_HOL_Obool)))),X4176)=hAPP(hAPP(c_Set_Oinsert(tc_fun(X4178,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4178,X4178,X4176),hAPP(hAPP(c_Set_Oinsert(X4178),X4177),c_Orderings_Obot__class_Obot(tc_fun(X4178,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4178,tc_HOL_Obool),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_singleton__quotient])). 4.46/4.70 fof(c_0_5836, plain, ![X11453, X11454]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X11454)),X11453)=c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X11454),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X11454)),X11453), inference(variable_rename,[status(thm)],[fact_max__Suc1])). 4.46/4.70 fof(c_0_5837, plain, ![X2639, X2640, X2641]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X2641,tc_Nat_Onat),X2640),X2639))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2641)),X2639))=c_List_Olist_Olist__size(X2641,X2640,X2639), inference(variable_rename,[status(thm)],[fact_list__size__conv__listsum])). 4.46/4.70 fof(c_0_5838, plain, ![X7792, X7793, X7794]:hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X7794),hAPP(c_COMBK(X7794,tc_Nat_Onat),X7793)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7792))=c_List_Oreplicate(X7794,X7792,X7793), inference(variable_rename,[status(thm)],[fact_map__replicate__trivial])). 4.46/4.70 fof(c_0_5839, plain, ![X869, X870]:c_Relation_Orefl__on(X870,c_Orderings_Otop__class_Otop(tc_fun(X870,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X870,X870),tc_HOL_Obool)),X869),c_Relation_OId(X870))), inference(variable_rename,[status(thm)],[fact_refl__reflcl])). 4.46/4.70 fof(c_0_5840, plain, ![X14022, X14023, X14024]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14024)),X14022)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14024)),hAPP(hAPP(c_List_Olist_OCons(X14024),X14023),X14022)), inference(variable_rename,[status(thm)],[fact_list_Osize_I4_J])). 4.46/4.70 cnf(c_0_5841, plain, (c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X1)))), inference(split_conjunct,[status(thm)],[c_0_4801])). 4.46/4.70 fof(c_0_5842, plain, ![X16939, X16940]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X16940)),X16939)=c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X16940)),X16939), inference(variable_rename,[status(thm)],[fact_min__Suc1])). 4.46/4.70 fof(c_0_5843, plain, ![X1843, X1844, X1845]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1845)),X1844)),hAPP(c_Nat_OSuc,X1843))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1845),X1844)),X1843), inference(variable_rename,[status(thm)],[fact_Suc__diff__diff])). 4.46/4.70 fof(c_0_5844, plain, ![X2839, X2840, X2841, X2842, X2843]:((c_Orderings_Obot__class_Obot(tc_fun(X2842,tc_HOL_Obool))!=X2843|c_Orderings_Obot__class_Obot(tc_fun(X2841,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2842,tc_fun(X2841,tc_HOL_Obool)),X2843),hAPP(hAPP(c_COMBB(tc_fun(X2841,tc_HOL_Obool),tc_fun(X2841,tc_HOL_Obool),X2842),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2841,tc_HOL_Obool)),X2840)),X2839)))&(X2843=c_Orderings_Obot__class_Obot(tc_fun(X2842,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2841,tc_HOL_Obool)),X2840),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2842,tc_fun(X2841,tc_HOL_Obool)),X2843),X2839))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2842,tc_fun(X2841,tc_HOL_Obool)),X2843),hAPP(hAPP(c_COMBB(tc_fun(X2841,tc_HOL_Obool),tc_fun(X2841,tc_HOL_Obool),X2842),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2841,tc_HOL_Obool)),X2840)),X2839)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__simps_I3_J])])])). 4.46/4.70 cnf(c_0_5845, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X1,X2))=c_List_Oupt(hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))), inference(split_conjunct,[status(thm)],[c_0_4802])). 4.46/4.70 fof(c_0_5846, plain, ![X9418, X9419, X9420]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9420)),c_List_Osplice(X9420,X9419,X9418))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9420)),X9419)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9420)),X9418)), inference(variable_rename,[status(thm)],[fact_length__splice])). 4.46/4.70 fof(c_0_5847, plain, ![X8056, X8057]:c_Transitive__Closure_Ortrancl(X8057,X8056)=c_Transitive__Closure_Ortrancl(X8057,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X8057,X8057),tc_HOL_Obool)),X8056),c_Relation_OId(X8057))), inference(variable_rename,[status(thm)],[fact_rtrancl__r__diff__Id])). 4.46/4.70 fof(c_0_5848, plain, ![X14351, X14352]:c_Transitive__Closure_Ortrancl(X14352,X14351)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X14352,X14352),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X14352,X14351)),c_Relation_OId(X14352)), inference(variable_rename,[status(thm)],[fact_rtrancl__reflcl__absorb])). 4.46/4.70 fof(c_0_5849, plain, ![X16755, X16756, X16757]:hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X16757),c_List_Oupt(X16756,X16755))=c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16756),X16757),X16755), inference(variable_rename,[status(thm)],[fact_drop__upt])). 4.46/4.70 fof(c_0_5850, plain, ![X17253]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X17253),c_Orderings_Obot__class_Obot(tc_fun(X17253,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_card_Oempty])). 4.46/4.70 fof(c_0_5851, plain, ![X3693, X3694]:~hBOOL(hAPP(hAPP(c_member(X3694),X3693),c_Orderings_Obot__class_Obot(tc_fun(X3694,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_empty__iff])])). 4.46/4.70 fof(c_0_5852, plain, ![X17621, X17622, X17623]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17623)),hAPP(c_List_Orotate(X17623,X17622),X17621))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17623)),X17621), inference(variable_rename,[status(thm)],[fact_length__rotate])). 4.46/4.70 fof(c_0_5853, plain, ![X6566, X6567, X6568, X6569, X6570]:c_Option_Ooption_ONone(X6569)=c_Map_Omap__comp(X6570,X6569,X6568,hAPP(c_COMBK(tc_Option_Ooption(X6569),X6570),c_Option_Ooption_ONone(X6569)),X6567,X6566), inference(variable_rename,[status(thm)],[fact_map__comp__empty_I2_J])). 4.46/4.70 fof(c_0_5854, plain, ![X12769, X12770]:c_List_Olist_ONil(X12770)=c_List_Oconcat(X12770,c_List_Oreplicate(tc_List_Olist(X12770),X12769,c_List_Olist_ONil(X12770))), inference(variable_rename,[status(thm)],[fact_concat__replicate__trivial])). 4.46/4.70 fof(c_0_5855, plain, ![X6254, X6255]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6254),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6255),X6254))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6255,X6254))=X6255, inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality])). 4.46/4.70 fof(c_0_5856, plain, ![X7296]:hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X7296)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7296)), inference(variable_rename,[status(thm)],[fact_one__div__nat__number__of])). 4.46/4.70 fof(c_0_5857, plain, ![X9331, X9332, X9333]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9333,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9333,tc_HOL_Obool)),X9332),X9331))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9333,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9333,tc_HOL_Obool)),X9332)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9333,tc_HOL_Obool)),X9331)), inference(variable_rename,[status(thm)],[fact_Compl__Un])). 4.46/4.70 cnf(c_0_5858, plain, (hBOOL(hAPP(hAPP(c_member(X4),X3),hAPP(c_Set_Ovimage(X4,X5,X2),hAPP(hAPP(c_Set_Oinsert(X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))|X1!=hAPP(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_4803])). 4.46/4.70 fof(c_0_5859, plain, ![X5156, X5157, X5158, X5159]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5159,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5158,X5159,X5157),hAPP(c_Set_Ovimage(X5158,X5159,X5157),X5156))),X5156)), inference(variable_rename,[status(thm)],[fact_image__vimage__subset])). 4.46/4.70 fof(c_0_5860, plain, ![X13601, X13602, X13603]:hAPP(c_Set_Ovimage(X13603,X13602,X13601),c_Orderings_Otop__class_Otop(tc_fun(X13602,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X13603,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_vimage__UNIV])). 4.46/4.70 fof(c_0_5861, plain, ![X2165, X2166]:X2165=hAPP(c_Set_Ovimage(X2166,X2166,c_Fun_Oid(X2166)),X2165), inference(variable_rename,[status(thm)],[fact_vimage__id])). 4.46/4.70 fof(c_0_5862, plain, ![X16421, X16422]:X16421=hAPP(c_Set_Ovimage(X16422,X16422,c_COMBI(X16422)),X16421), inference(variable_rename,[status(thm)],[fact_vimage__ident])). 4.46/4.70 fof(c_0_5863, plain, ![X14214, X14215, X14216]:c_Orderings_Obot__class_Obot(tc_fun(X14216,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X14216,X14215,X14214),c_Orderings_Obot__class_Obot(tc_fun(X14215,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_vimage__empty])). 4.46/4.70 fof(c_0_5864, plain, ![X6857, X6858, X6859]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6859,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X6859,tc_HOL_Obool),X6858)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X6859,tc_HOL_Obool),X6857))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X6859,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X6859,tc_HOL_Obool),tc_HOL_Obool)),X6858),X6857)), inference(variable_rename,[status(thm)],[fact_Inter__Un__distrib])). 4.46/4.70 fof(c_0_5865, plain, ![X15524, X15525, X15526]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15526,tc_HOL_Obool)),X15525),c_Complete__Lattice_OInf__class_OInf(tc_fun(X15526,tc_HOL_Obool),X15524))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X15526,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X15526,tc_HOL_Obool)),X15525),X15524)), inference(variable_rename,[status(thm)],[fact_Inter__insert])). 4.46/4.70 fof(c_0_5866, plain, ![X11176, X11177, X11178]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X11178,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X11178,tc_HOL_Obool),tc_HOL_Obool)),X11177),X11176))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11178,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X11178,tc_HOL_Obool),X11177)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X11178,tc_HOL_Obool),X11176)), inference(variable_rename,[status(thm)],[fact_Union__Un__distrib])). 4.46/4.70 fof(c_0_5867, plain, ![X16617, X16618, X16619]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16619,tc_HOL_Obool)),X16618),c_Complete__Lattice_OSup__class_OSup(tc_fun(X16619,tc_HOL_Obool),X16617))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X16619,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X16619,tc_HOL_Obool)),X16618),X16617)), inference(variable_rename,[status(thm)],[fact_Union__insert])). 4.46/4.70 fof(c_0_5868, plain, ![X5204, X5205, X5206]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X5206|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5206),X5205)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5206),X5204)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X5206|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5206),X5205)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5206),X5204))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X5205),X5204))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__mult__div__cancel__disj])])])). 4.46/4.70 fof(c_0_5869, plain, ![X656]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X656), inference(variable_rename,[status(thm)],[fact_mult__0])). 4.46/4.70 fof(c_0_5870, plain, ![X17585, X17586]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X17586)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X17585))))=hAPP(hAPP(c_Nitpick_Oint__gcd,X17586),X17585), inference(variable_rename,[status(thm)],[fact_Nitpick_Oint__gcd__def])). 4.46/4.70 fof(c_0_5871, plain, ![X2807, X2808, X2809, X2810, X2811]:((c_Orderings_Obot__class_Obot(tc_fun(X2810,tc_HOL_Obool))=X2811|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2810,tc_fun(X2809,tc_HOL_Obool)),X2811),hAPP(hAPP(c_COMBB(tc_fun(X2809,tc_HOL_Obool),tc_fun(X2809,tc_HOL_Obool),X2810),hAPP(c_Set_Oinsert(X2809),X2808)),X2807))=hAPP(hAPP(c_Set_Oinsert(X2809),X2808),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2810,tc_fun(X2809,tc_HOL_Obool)),X2811),X2807)))&(X2811!=c_Orderings_Obot__class_Obot(tc_fun(X2810,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X2809,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2810,tc_fun(X2809,tc_HOL_Obool)),X2811),hAPP(hAPP(c_COMBB(tc_fun(X2809,tc_HOL_Obool),tc_fun(X2809,tc_HOL_Obool),X2810),hAPP(c_Set_Oinsert(X2809),X2808)),X2807)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__simps_I1_J])])])). 4.46/4.70 fof(c_0_5872, plain, ![X5496, X5497, X5498, X5499, X5500, X5501, X5502, X5503]:((hAPP(hAPP(c_List_Oappend(X5498),X5499),hAPP(hAPP(c_List_Olist_OCons(X5498),X5497),X5500))!=X5496|hBOOL(hAPP(hAPP(c_member(X5498),X5497),hAPP(c_List_Oset(X5498),X5496))))&(~hBOOL(hAPP(hAPP(c_member(X5503),X5502),hAPP(c_List_Oset(X5503),X5501)))|hAPP(hAPP(c_List_Oappend(X5503),esk165_3(X5501,X5502,X5503)),hAPP(hAPP(c_List_Olist_OCons(X5503),X5502),esk166_3(X5501,X5502,X5503)))=X5501)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__conv__decomp])])])])])). 4.46/4.70 fof(c_0_5873, plain, ![X804]:hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X804))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X804)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X804)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_greaterThan__Suc])). 4.46/4.70 fof(c_0_5874, plain, ![X5607, X5608]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5608)),X5607))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5608))),c_Enum_Osublists(X5608,X5607)), inference(variable_rename,[status(thm)],[fact_length__sublists])). 4.46/4.70 fof(c_0_5875, plain, ![X4886, X4887]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X4887),X4886)),X4886))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4887,X4886), inference(variable_rename,[status(thm)],[fact_Divides_Omod__div__equality_H])). 4.46/4.70 fof(c_0_5876, plain, ![X14461, X14462]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14462),X14461)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14461),X14462), inference(variable_rename,[status(thm)],[fact_nat__mult__commute])). 4.46/4.70 fof(c_0_5877, plain, ![X17572, X17573]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X17573),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X17573),X17572)),X17572))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X17573,X17572), inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality_H])). 4.46/4.70 fof(c_0_5878, plain, ![X7624, X7625]:c_Relation_Oirrefl(X7625,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X7625,X7625),tc_HOL_Obool)),X7624),c_Relation_OId(X7625))), inference(variable_rename,[status(thm)],[fact_irrefl__diff__Id])). 4.46/4.70 fof(c_0_5879, plain, ![X14463, X14464]:hAPP(c_Relation_ORange(X14464,X14464),X14463)=hAPP(c_Relation_ORange(X14464,X14464),c_Transitive__Closure_Otrancl(X14464,X14463)), inference(variable_rename,[status(thm)],[fact_trancl__range])). 4.46/4.70 fof(c_0_5880, plain, ![X12878, X12879]:hAPP(c_Relation_ODomain(X12879,X12879),X12878)=hAPP(c_Relation_ODomain(X12879,X12879),c_Transitive__Closure_Otrancl(X12879,X12878)), inference(variable_rename,[status(thm)],[fact_trancl__domain])). 4.46/4.70 fof(c_0_5881, plain, ![X2433, X2434, X2435]:hAPP(c_List_Oset(X2435),X2433)=hAPP(c_List_Oset(X2435),hAPP(c_List_Orotate(X2435,X2434),X2433)), inference(variable_rename,[status(thm)],[fact_set__rotate])). 4.46/4.70 fof(c_0_5882, plain, ![X7478]:hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X7478)))=hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X7478)), inference(variable_rename,[status(thm)],[fact_lessThan__Suc__eq__insert__0])). 4.46/4.70 cnf(c_0_5883, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4804])). 4.46/4.70 cnf(c_0_5884, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))), inference(split_conjunct,[status(thm)],[c_0_4805]), ['final']). 4.46/4.70 fof(c_0_5885, plain, ![X5197, X5198, X5199, X5200]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5199)),X5198)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X5200|hAPP(hAPP(c_List_Olist__update(X5199,c_List_Obutlast(X5199,X5198)),X5200),X5197)=c_List_Obutlast(X5199,hAPP(hAPP(c_List_Olist__update(X5199,X5198),X5200),X5197)))&(X5200!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5199)),X5198)),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_List_Obutlast(X5199,hAPP(hAPP(c_List_Olist__update(X5199,X5198),X5200),X5197))=c_List_Obutlast(X5199,X5198))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_butlast__list__update])])])). 4.46/4.70 fof(c_0_5886, plain, ![X3744, X3745, X3746, X3747]:hAPP(hAPP(c_List_Otake(X3747),X3746),hAPP(hAPP(c_List_Otake(X3747),X3745),X3744))=hAPP(hAPP(c_List_Otake(X3747),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X3746),X3745)),X3744), inference(variable_rename,[status(thm)],[fact_take__take])). 4.46/4.70 fof(c_0_5887, plain, ![X1903, X1904, X1905]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1905)),X1903)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1905)),c_Lazy__Sequence_Olazy__sequence_OInsert(X1905,X1904,X1903)), inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I4_J])). 4.46/4.70 fof(c_0_5888, plain, ![X464]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X464)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X464),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))=hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X464)), inference(variable_rename,[status(thm)],[fact_atLeast__Suc])). 4.46/4.70 fof(c_0_5889, plain, ![X3273]:hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3273))=hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X3273), inference(variable_rename,[status(thm)],[fact_atLeast__Suc__greaterThan])). 4.46/4.70 cnf(c_0_5890, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X1))), inference(split_conjunct,[status(thm)],[c_0_4806])). 4.46/4.70 fof(c_0_5891, plain, ![X6597]:c_Relation_OId(X6597)=hAPP(c_Relation_Oconverse(X6597,X6597),c_Relation_OId(X6597)), inference(variable_rename,[status(thm)],[fact_converse__Id])). 4.46/4.70 cnf(c_0_5892, plain, (hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))=hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X2,X1))), inference(split_conjunct,[status(thm)],[c_0_4807])). 4.46/4.70 cnf(c_0_5893, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X2)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)), inference(split_conjunct,[status(thm)],[c_0_4808]), ['final']). 4.46/4.70 cnf(c_0_5894, plain, (hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X2,X1))), inference(split_conjunct,[status(thm)],[c_0_4809])). 4.46/4.70 cnf(c_0_5895, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4810])). 4.46/4.70 fof(c_0_5896, plain, ![X1031, X1032, X1033]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X1033,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1033,tc_HOL_Obool)),X1032),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1033,tc_HOL_Obool)),X1031),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1033,tc_HOL_Obool),tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1033,tc_HOL_Obool)),X1032),X1031), inference(variable_rename,[status(thm)],[fact_Un__eq__Union])). 4.46/4.70 fof(c_0_5897, plain, ![X9241, X9242, X9243]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9243,tc_HOL_Obool)),X9242),X9241)=c_Complete__Lattice_OInf__class_OInf(tc_fun(X9243,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X9243,tc_HOL_Obool)),X9242),hAPP(hAPP(c_Set_Oinsert(tc_fun(X9243,tc_HOL_Obool)),X9241),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X9243,tc_HOL_Obool),tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_Int__eq__Inter])). 4.46/4.70 fof(c_0_5898, plain, ![X11538]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X11538)))), inference(variable_rename,[status(thm)],[fact_finite__Collect__less__nat])). 4.46/4.70 fof(c_0_5899, plain, ![X15039]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X15039)))), inference(variable_rename,[status(thm)],[fact_finite__Collect__le__nat])). 4.46/4.70 cnf(c_0_5900, plain, (c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls))), inference(split_conjunct,[status(thm)],[fact_one__code__numeral__code])). 4.46/4.70 cnf(c_0_5901, plain, (hAPP(c_List_Orotate(X1,X3),X2)=c_List_Olist_ONil(X1)|c_List_Olist_ONil(X1)!=X2), inference(split_conjunct,[status(thm)],[c_0_4811])). 4.46/4.70 cnf(c_0_5902, plain, (hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1))=c_List_Orotate(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4812])). 4.46/4.70 fof(c_0_5903, plain, ![X7495]:hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7495)))=hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X7495), inference(variable_rename,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I1_J])). 4.46/4.70 fof(c_0_5904, plain, ![X8958, X8959, X8960]:((hAPP(c_List_Orev(X8960),X8958)!=hAPP(hAPP(c_List_Olist_OCons(X8960),X8959),c_List_Olist_ONil(X8960))|hAPP(hAPP(c_List_Olist_OCons(X8960),X8959),c_List_Olist_ONil(X8960))=X8958)&(hAPP(hAPP(c_List_Olist_OCons(X8960),X8959),c_List_Olist_ONil(X8960))!=X8958|hAPP(c_List_Orev(X8960),X8958)=hAPP(hAPP(c_List_Olist_OCons(X8960),X8959),c_List_Olist_ONil(X8960)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__rev__conv])])). 4.46/4.70 fof(c_0_5905, plain, ![X5302, X5303]:hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X5303,X5302))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X5303),X5302), inference(variable_rename,[status(thm)],[fact_div__nat__def])). 4.46/4.70 fof(c_0_5906, plain, ![X7224, X7225, X7226, X7227, X7228]:((c_Orderings_Obot__class_Obot(tc_fun(X7227,tc_HOL_Obool))=X7228|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7227,tc_fun(X7226,tc_HOL_Obool)),X7228),hAPP(hAPP(c_COMBB(tc_fun(X7226,tc_HOL_Obool),tc_fun(X7226,tc_HOL_Obool),X7227),hAPP(c_Set_Oinsert(X7226),X7225)),X7224))=hAPP(hAPP(c_Set_Oinsert(X7226),X7225),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7227,tc_fun(X7226,tc_HOL_Obool)),X7228),X7224)))&(X7228!=c_Orderings_Obot__class_Obot(tc_fun(X7227,tc_HOL_Obool))|hAPP(hAPP(c_Set_Oinsert(X7226),X7225),c_Orderings_Obot__class_Obot(tc_fun(X7226,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(X7226),X7225),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7227,tc_fun(X7226,tc_HOL_Obool)),X7228),X7224)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__extend__simps_I1_J])])])). 4.46/4.70 fof(c_0_5907, plain, ![X16226, X16227]:hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X16227,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X16226),c_Groups_Oone__class_Oone(tc_Int_Oint))))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X16227),X16226), inference(variable_rename,[status(thm)],[fact_atLeastLessThan__upto])). 4.46/4.70 fof(c_0_5908, plain, ![X12834, X12835, X12836, X12837]:c_List_Oreplicate(X12837,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X12836),X12835),X12834)=hAPP(hAPP(c_List_Otake(X12837),X12836),c_List_Oreplicate(X12837,X12835,X12834)), inference(variable_rename,[status(thm)],[fact_take__replicate])). 4.46/4.70 fof(c_0_5909, plain, ![X6321, X6322]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X6322,X6321))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6321),X6322), inference(variable_rename,[status(thm)],[fact_length__upt])). 4.46/4.70 fof(c_0_5910, plain, ![X11036, X11037, X11038, X11039, X11040]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11037),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X11038)))!=X11036|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11037),X11036)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11040),X11039))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11040),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk329_2(X11039,X11040))))=X11039)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__iff__Suc__zadd])])])])])). 4.46/4.70 fof(c_0_5911, plain, ![X11307, X11308, X11309]:hAPP(hAPP(c_Relation_Orel__comp(X11309,X11309,X11308),c_Relation_OId(X11309)),X11307)=X11307, inference(variable_rename,[status(thm)],[fact_Id__O__R])). 4.46/4.70 fof(c_0_5912, plain, ![X10464]:hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X10464)),c_List_Olist_ONil(X10464)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X10464),tc_HOL_Obool)))=c_List_Olistset(X10464,c_List_Olist_ONil(tc_fun(X10464,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_listset_Osimps_I1_J])). 4.46/4.70 fof(c_0_5913, plain, ![X3795, X3796, X3797]:hAPP(hAPP(c_Relation_Orel__comp(X3797,X3796,X3796),X3795),c_Relation_OId(X3796))=X3795, inference(variable_rename,[status(thm)],[fact_R__O__Id])). 4.46/4.70 cnf(c_0_5914, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)=hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X1,hAPP(c_Nat_OSuc,X2)))), inference(split_conjunct,[status(thm)],[c_0_4813])). 4.46/4.70 fof(c_0_5915, plain, ![X4416, X4417]:hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X4417,X4416))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4417,X4416), inference(variable_rename,[status(thm)],[fact_mod__nat__def])). 4.46/4.70 fof(c_0_5916, plain, ![X8591, X8592]:c_Transitive__Closure_Ortrancl(X8592,c_Transitive__Closure_Otrancl(X8592,X8591))=c_Transitive__Closure_Ortrancl(X8592,X8591), inference(variable_rename,[status(thm)],[fact_trancl__rtrancl__absorb])). 4.46/4.70 fof(c_0_5917, plain, ![X16112, X16113, X16114, X16115]:((c_Orderings_Obot__class_Obot(tc_fun(X16114,tc_HOL_Obool))!=X16115|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16114,tc_fun(X16113,tc_HOL_Obool)),X16115),hAPP(c_COMBK(tc_fun(X16113,tc_HOL_Obool),X16114),X16112))=c_Orderings_Obot__class_Obot(tc_fun(X16113,tc_HOL_Obool)))&(c_Orderings_Obot__class_Obot(tc_fun(X16114,tc_HOL_Obool))=X16115|X16112=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16114,tc_fun(X16113,tc_HOL_Obool)),X16115),hAPP(c_COMBK(tc_fun(X16113,tc_HOL_Obool),X16114),X16112)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__constant])])])). 4.46/4.70 fof(c_0_5918, plain, ![X7918, X7919, X7920, X7921, X7922]:((c_Orderings_Obot__class_Obot(tc_fun(X7921,tc_HOL_Obool))=X7922|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7921,tc_fun(X7920,tc_HOL_Obool)),X7922),hAPP(hAPP(c_COMBC(X7921,tc_fun(X7920,tc_HOL_Obool),tc_fun(X7920,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7920,tc_HOL_Obool),tc_fun(tc_fun(X7920,tc_HOL_Obool),tc_fun(X7920,tc_HOL_Obool)),X7921),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7920,tc_HOL_Obool))),X7919)),X7918))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7920,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7921,tc_fun(X7920,tc_HOL_Obool)),X7922),X7919)),X7918))&(c_Orderings_Obot__class_Obot(tc_fun(X7921,tc_HOL_Obool))!=X7922|X7918=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7920,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7921,tc_fun(X7920,tc_HOL_Obool)),X7922),X7919)),X7918))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__extend__simps_I2_J])])])). 4.46/4.70 fof(c_0_5919, plain, ![X12486, X12487, X12488, X12489, X12490]:((X12490=c_Orderings_Obot__class_Obot(tc_fun(X12489,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12489,tc_fun(X12488,tc_HOL_Obool)),X12490),hAPP(hAPP(c_COMBB(tc_fun(X12488,tc_HOL_Obool),tc_fun(X12488,tc_HOL_Obool),X12489),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12488,tc_HOL_Obool)),X12487)),X12486))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12488,tc_HOL_Obool)),X12487),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12489,tc_fun(X12488,tc_HOL_Obool)),X12490),X12486)))&(c_Orderings_Obot__class_Obot(tc_fun(X12489,tc_HOL_Obool))!=X12490|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12488,tc_HOL_Obool)),X12487),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12489,tc_fun(X12488,tc_HOL_Obool)),X12490),X12486))=X12487)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INT__extend__simps_I4_J])])])). 4.46/4.70 fof(c_0_5920, plain, ![X8509, X8510, X8511, X8512, X8513]:((X8513!=c_Orderings_Obot__class_Obot(tc_fun(X8512,tc_HOL_Obool))|X8510=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8511,tc_HOL_Obool)),X8510),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8512,tc_fun(X8511,tc_HOL_Obool)),X8513),X8509)))&(X8513=c_Orderings_Obot__class_Obot(tc_fun(X8512,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8511,tc_HOL_Obool)),X8510),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8512,tc_fun(X8511,tc_HOL_Obool)),X8513),X8509))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8512,tc_fun(X8511,tc_HOL_Obool)),X8513),hAPP(hAPP(c_COMBB(tc_fun(X8511,tc_HOL_Obool),tc_fun(X8511,tc_HOL_Obool),X8512),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8511,tc_HOL_Obool)),X8510)),X8509)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__extend__simps_I3_J])])])). 4.46/4.70 fof(c_0_5921, plain, ![X415, X416]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X416),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X415),c_Groups_Oone__class_Oone(tc_Int_Oint))))|(X416=X415|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X416),X415))))&((X416!=X415|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X416),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X415),c_Groups_Oone__class_Oone(tc_Int_Oint)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X416),X415))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X416),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X415),c_Groups_Oone__class_Oone(tc_Int_Oint))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__add1__eq])])])). 4.46/4.70 fof(c_0_5922, plain, ![X16760, X16761, X16762, X16763]:((c_Orderings_Obot__class_Obot(tc_fun(X16763,tc_HOL_Obool))!=X16761|X16760!=c_Orderings_Obot__class_Obot(tc_fun(X16762,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X16763,X16762),tc_HOL_Obool))=c_Sum__Type_OPlus(X16763,X16762,X16761,X16760))&((c_Orderings_Obot__class_Obot(tc_fun(X16763,tc_HOL_Obool))=X16761|c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X16763,X16762),tc_HOL_Obool))!=c_Sum__Type_OPlus(X16763,X16762,X16761,X16760))&(X16760=c_Orderings_Obot__class_Obot(tc_fun(X16762,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X16763,X16762),tc_HOL_Obool))!=c_Sum__Type_OPlus(X16763,X16762,X16761,X16760)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Plus__eq__empty__conv])])])). 4.46/4.70 fof(c_0_5923, plain, ![X13503, X13504]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X13504),X13503)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X13504)),hAPP(c_Code__Numeral_Onat__of,X13503))), inference(variable_rename,[status(thm)],[fact_div__code__numeral__def])). 4.46/4.70 fof(c_0_5924, plain, ![X7863]:hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7863)=c_Divides_Odivmod__nat(X7863,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_divmod__nat__zero])). 4.46/4.70 fof(c_0_5925, plain, ![X9020, X9021]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X9021),X9020)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X9021)),hAPP(c_Code__Numeral_Onat__of,X9020))), inference(variable_rename,[status(thm)],[fact_times__code__numeral__def])). 4.46/4.70 fof(c_0_5926, plain, ![X9085, X9086]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X9086),X9085)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X9086)),hAPP(c_Code__Numeral_Onat__of,X9085))), inference(variable_rename,[status(thm)],[fact_plus__code__numeral__def])). 4.46/4.70 fof(c_0_5927, plain, ![X2060, X2061]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X2061),X2060)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X2061)),hAPP(c_Code__Numeral_Onat__of,X2060))), inference(variable_rename,[status(thm)],[fact_minus__code__numeral__def])). 4.46/4.70 fof(c_0_5928, plain, ![X8728, X8729, X8730]:c_Hoare__Mirabelle_Ohoare__derivs(X8730,X8729,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X8730)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X8730),X8728),c_Com_Ocom_OSKIP),X8728)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X8730),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_hoare__derivs_Oequations_I7_J])). 4.46/4.70 fof(c_0_5929, plain, ![X4383, X4384, X4385]:c_Option_Ooption_Ooption__size(X4385,X4384,hAPP(c_Option_Ooption_OSome(X4385),X4383))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X4384,X4383)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_option_Osize_I2_J])). 4.46/4.70 fof(c_0_5930, plain, ![X6700, X6701, X6702, X6703, X6704]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6701),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6702))!=X6700|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6701),X6700)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6704),X6703))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6704),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk196_2(X6703,X6704)))=X6703)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__iff__zadd])])])])])). 4.46/4.70 fof(c_0_5931, plain, ![X5763, X5764, X5765]:hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X5765,X5764,X5763))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X5763)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_com_Osize_I11_J])). 4.46/4.70 fof(c_0_5932, plain, ![X7582, X7583]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X7583)),hAPP(c_Nat_OSuc,X7582))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X7583),X7582)), inference(variable_rename,[status(thm)],[fact_max__Suc__Suc])). 4.46/4.70 fof(c_0_5933, plain, ![X16172, X16173]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X16173)),hAPP(c_Nat_OSuc,X16172))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X16173),X16172)), inference(variable_rename,[status(thm)],[fact_min__Suc__Suc])). 4.46/4.70 fof(c_0_5934, plain, ![X5581, X5582]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X5582)),hAPP(c_Code__Numeral_Oof__nat,X5581))=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5582),X5581)), inference(variable_rename,[status(thm)],[fact_times__code__numeral__code])). 4.46/4.70 fof(c_0_5935, plain, ![X15576, X15577]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X15577)),hAPP(c_Code__Numeral_Oof__nat,X15576))=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15577),X15576)), inference(variable_rename,[status(thm)],[fact_plus__code__numeral__code])). 4.46/4.70 fof(c_0_5936, plain, ![X5762]:hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5762)),c_List_Olist_ONil(X5762)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5762),tc_HOL_Obool)))=c_List_Olists(X5762,c_Orderings_Obot__class_Obot(tc_fun(X5762,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_lists__empty])). 4.46/4.70 cnf(c_0_5937, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X1))), inference(split_conjunct,[status(thm)],[c_0_4814])). 4.46/4.70 fof(c_0_5938, plain, ![X10574, X10575]:c_HOL_OThe(X10575,hAPP(hAPP(c_COMBC(X10575,X10575,tc_HOL_Obool),c_fequal),X10574))=X10574, inference(variable_rename,[status(thm)],[fact_the__eq__trivial])). 4.46/4.70 fof(c_0_5939, plain, ![X10325, X10326]:c_Hilbert__Choice_OEps(X10326,hAPP(hAPP(c_COMBC(X10326,X10326,tc_HOL_Obool),c_fequal),X10325))=X10325, inference(variable_rename,[status(thm)],[fact_some__eq__trivial])). 4.46/4.70 fof(c_0_5940, plain, ![X10779, X10780, X10781, X10782]:((X10780!=X10779|hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10782,X10781,hAPP(hAPP(c_Set_Oinsert(X10782),X10780),c_Orderings_Obot__class_Obot(tc_fun(X10782,tc_HOL_Obool)))),X10779)))&(~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10782,X10781,hAPP(hAPP(c_Set_Oinsert(X10782),X10780),c_Orderings_Obot__class_Obot(tc_fun(X10782,tc_HOL_Obool)))),X10779))|X10780=X10779)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1Set__sing])])). 4.46/4.70 fof(c_0_5941, plain, ![X462, X463]:hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X463,X462),c_Divides_Odivmod__nat(X463,X462))), inference(variable_rename,[status(thm)],[fact_divmod__nat__rel__divmod__nat])). 4.46/4.70 fof(c_0_5942, plain, ![X11197]:((X11197!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X11197)),c_Groups_Oone__class_Oone(tc_Int_Oint))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X11197)),c_Groups_Oone__class_Oone(tc_Int_Oint)))|X11197=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zabs__less__one__iff])])). 4.46/4.70 fof(c_0_5943, plain, ![X11863, X11864]:X11863=hAPP(c_Relation_OImage(X11864,X11864,c_Relation_OId(X11864)),X11863), inference(variable_rename,[status(thm)],[fact_Image__Id])). 4.46/4.70 fof(c_0_5944, plain, ![X11010, X11011, X11013, X11014, X11015]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11011),X11010))|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11011),esk328_2(X11010,X11011)))=X11010)&(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11014),X11015))!=X11013|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11014),X11013)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__Suc__add])])])])])). 4.46/4.70 fof(c_0_5945, plain, ![X9336]:hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X9336)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X9336))=hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X9336)), inference(variable_rename,[status(thm)],[fact_atMost__Suc])). 4.46/4.70 fof(c_0_5946, plain, ![X1126, X1127]:hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1127),X1126))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1126),X1127)), inference(variable_rename,[status(thm)],[fact_card__atLeastLessThan__int])). 4.46/4.70 fof(c_0_5947, plain, ![X515, X516]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X515)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X516,X515)), inference(variable_rename,[status(thm)],[fact_com_Osize_I14_J])). 4.46/4.70 cnf(c_0_5948, plain, (hAPP(X1,X2)=c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X4,X1,c_Code__Numeral_OSuc__code__numeral(X2))), inference(split_conjunct,[status(thm)],[c_0_4815])). 4.46/4.70 cnf(c_0_5949, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X1)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))=X1), inference(split_conjunct,[status(thm)],[c_0_4816])). 4.46/4.70 fof(c_0_5950, plain, ![X12533, X12534]:hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X12534),hAPP(c_Code__Numeral_Onat__of,X12533)))=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X12534,X12533), inference(variable_rename,[status(thm)],[fact_mod__code__numeral__def])). 4.46/4.70 fof(c_0_5951, plain, ![X3989]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X3989)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3989), inference(variable_rename,[status(thm)],[fact_mult__Min])). 4.46/4.70 fof(c_0_5952, plain, ![X4265, X4266]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X4266|hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X4265))=c_Divides_Opdivmod(X4265,X4266))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X4266|c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X4265),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X4266))=c_Divides_Opdivmod(X4265,X4266))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__posDivAlg])])). 4.46/4.70 fof(c_0_5953, plain, ![X2637, X2638]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2638),X2637))=hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X2638)),hAPP(c_Code__Numeral_Oof__nat,X2637)), inference(variable_rename,[status(thm)],[fact_subtract__code__numeral__code])). 4.46/4.70 cnf(c_0_5954, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X2,X1))), inference(split_conjunct,[status(thm)],[c_0_4817])). 4.46/4.70 cnf(c_0_5955, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)=c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4818]), ['final']). 4.46/4.70 fof(c_0_5956, plain, ![X3203, X3204]:hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3204,X3203))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3203)),X3204), inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost])). 4.46/4.70 cnf(c_0_5957, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_4819])). 4.46/4.70 fof(c_0_5958, plain, ![X7448]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X7448)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X7448)), inference(variable_rename,[status(thm)],[fact_nat_Osize_I2_J])). 4.46/4.70 fof(c_0_5959, plain, ![X16842, X16843, X16844, X16845, X16846]:((X16846=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|hAPP(c_Random_Oiterate(X16845,X16844,X16846,X16843),X16842)=hAPP(hAPP(c_Product__Type_Oscomp(X16844,X16845,X16844,tc_prod(X16845,X16844)),hAPP(X16843,X16842)),c_Random_Oiterate(X16845,X16844,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X16846),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X16843)))&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X16846|hAPP(c_Product__Type_OPair(X16845,X16844),X16842)=hAPP(c_Random_Oiterate(X16845,X16844,X16846,X16843),X16842))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_iterate_Osimps])])])). 4.46/4.70 fof(c_0_5960, plain, ![X14123, X14124, X14125]:c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X14125,X14124,X14123))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X14123)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_com_Osize_I3_J])). 4.46/4.70 fof(c_0_5961, plain, ![X4140]:c_Wellfounded_OwfP(X4140,hAPP(c_COMBK(tc_fun(X4140,tc_HOL_Obool),X4140),hAPP(c_COMBK(tc_HOL_Obool,X4140),c_fFalse))), inference(variable_rename,[status(thm)],[fact_wfP__empty])). 4.46/4.70 cnf(c_0_5962, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse))), inference(split_conjunct,[status(thm)],[c_0_4820])). 4.46/4.70 fof(c_0_5963, plain, ![X545, X546]:hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X546,X545))), inference(variable_rename,[status(thm)],[fact_distinct__upt])). 4.46/4.70 fof(c_0_5964, plain, ![X14838, X14839, X14840]:((c_List_Olist_ONil(X14839)=X14840|hAPP(hAPP(c_List_Olist_OCons(X14839),X14838),c_List_Obutlast(X14839,X14840))=c_List_Obutlast(X14839,hAPP(hAPP(c_List_Olist_OCons(X14839),X14838),X14840)))&(X14840!=c_List_Olist_ONil(X14839)|c_List_Olist_ONil(X14839)=c_List_Obutlast(X14839,hAPP(hAPP(c_List_Olist_OCons(X14839),X14838),X14840)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_butlast_Osimps_I2_J])])])). 4.46/4.70 fof(c_0_5965, plain, ![X3317, X3318, X3319, X3320]:((X3320=X3319|c_List_Oremove1(X3318,X3320,hAPP(hAPP(c_List_Olist_OCons(X3318),X3319),X3317))=hAPP(hAPP(c_List_Olist_OCons(X3318),X3319),c_List_Oremove1(X3318,X3320,X3317)))&(X3320!=X3319|X3317=c_List_Oremove1(X3318,X3320,hAPP(hAPP(c_List_Olist_OCons(X3318),X3319),X3317)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1_Osimps_I2_J])])). 4.46/4.70 fof(c_0_5966, plain, ![X13227]:c_Relation_Osingle__valued(X13227,X13227,c_Relation_OId(X13227)), inference(variable_rename,[status(thm)],[fact_single__valued__Id])). 4.46/4.70 fof(c_0_5967, plain, ![X4487]:hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4487))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X4487),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X4487)), inference(variable_rename,[status(thm)],[fact_lessThan__Suc])). 4.46/4.70 fof(c_0_5968, plain, ![X8664, X8665, X8667, X8668, X8669]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X8665,X8664)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8664),esk245_2(X8664,X8665))=X8665)&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8667),X8669)!=X8668|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X8668,X8667))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__eq__0__iff])])])])])). 4.46/4.70 fof(c_0_5969, plain, ![X8351, X8352, X8353]:hAPP(hAPP(c_List_Otake(X8353),X8351),X8352)=c_List_Osublist(X8353,X8352,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X8351)), inference(variable_rename,[status(thm)],[fact_sublist__upt__eq__take])). 4.46/4.70 fof(c_0_5970, plain, ![X2270, X2271, X2273, X2274, X2275]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X2271,X2270)|X2271=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2270),esk54_2(X2270,X2271)))&(X2274!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2273),X2275)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X2274,X2273))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__eq__0__iff])])])])])). 4.46/4.70 fof(c_0_5971, plain, ![X4572]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4572)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4572),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)), inference(variable_rename,[status(thm)],[fact_zdiv__minus1__right])). 4.46/4.70 fof(c_0_5972, plain, ![X1976, X1977, X1978]:((c_List_Olist_ONil(X1977)=X1978|c_List_Olast(X1977,hAPP(hAPP(c_List_Olist_OCons(X1977),X1976),X1978))=c_List_Olast(X1977,X1978))&(X1978!=c_List_Olist_ONil(X1977)|c_List_Olast(X1977,hAPP(hAPP(c_List_Olist_OCons(X1977),X1976),X1978))=X1976)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last_Osimps])])). 4.46/4.70 fof(c_0_5973, plain, ![X411, X412]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X411)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X412,X411)), inference(variable_rename,[status(thm)],[fact_com_Osize_I6_J])). 4.46/4.70 cnf(c_0_5974, plain, (hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_4821])). 4.46/4.70 fof(c_0_5975, plain, ![X6062, X6063, X6064, X6065, X6066]:((X6066!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|c_Lazy__Sequence_Oempty(X6064)=hAPP(c_New__DSequence_Opos__decr__bind(X6065,X6064,X6063,X6062),X6066))&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X6066|hAPP(c_Lazy__Sequence_Obind(X6065,X6064,hAPP(X6063,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X6066),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X6065,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X6064)),X6062),X6066))=hAPP(c_New__DSequence_Opos__decr__bind(X6065,X6064,X6063,X6062),X6066))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_New__DSequence_Opos__decr__bind__def])])])). 4.46/4.70 fof(c_0_5976, plain, ![X10452]:hAPP(c_Set_OPow(X10452),c_Orderings_Obot__class_Obot(tc_fun(X10452,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(tc_fun(X10452,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10452,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10452,tc_HOL_Obool),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Pow__empty])). 4.46/4.70 cnf(c_0_5977, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X1))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_4822])). 4.46/4.70 fof(c_0_5978, plain, ![X15256, X15257]:c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X15257,X15256)), inference(variable_rename,[status(thm)],[fact_sorted__upt])). 4.46/4.70 fof(c_0_5979, plain, ![X12232]:hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X12232)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_nat__zminus__int])). 4.46/4.70 cnf(c_0_5980, plain, (c_Code__Numeral_Onat__of__aux(X1,X2)=X2|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X1), inference(split_conjunct,[status(thm)],[c_0_4659])). 4.46/4.70 fof(c_0_5981, plain, ![X4551, X4552, X4553]:((~hBOOL(hAPP(hAPP(c_member(X4553),X4552),hAPP(c_fequal,X4551)))|X4552=X4551)&(X4552!=X4551|hBOOL(hAPP(hAPP(c_member(X4553),X4552),hAPP(c_fequal,X4551))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])])). 4.46/4.70 fof(c_0_5982, plain, ![X2489, X2490]:c_Wellfounded_Owf(X2490,hAPP(c_Wellfounded_Omeasure(X2490),X2489)), inference(variable_rename,[status(thm)],[fact_wf__measure])). 4.46/4.70 fof(c_0_5983, plain, ![X16169, X16170, X16171]:((c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X16171,X16170),tc_HOL_Obool))!=X16169|hAPP(c_Relation_ORange(X16171,X16170),X16169)=c_Orderings_Obot__class_Obot(tc_fun(X16170,tc_HOL_Obool)))&(hAPP(c_Relation_ORange(X16171,X16170),X16169)!=c_Orderings_Obot__class_Obot(tc_fun(X16170,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X16171,X16170),tc_HOL_Obool))=X16169)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Range__empty__iff])])). 4.46/4.70 fof(c_0_5984, plain, ![X4850, X4851, X4852]:((hAPP(c_Relation_ODomain(X4852,X4851),X4850)!=c_Orderings_Obot__class_Obot(tc_fun(X4852,tc_HOL_Obool))|X4850=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4852,X4851),tc_HOL_Obool)))&(X4850!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4852,X4851),tc_HOL_Obool))|hAPP(c_Relation_ODomain(X4852,X4851),X4850)=c_Orderings_Obot__class_Obot(tc_fun(X4852,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__empty__iff])])). 4.46/4.70 fof(c_0_5985, plain, ![X1917]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1917),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=X1917, inference(variable_rename,[status(thm)],[fact_div__1])). 4.46/4.70 fof(c_0_5986, plain, ![X9735, X9736, X9737, X9738]:((~c_List_Olist__all2(X9738,X9737,X9736,X9735,c_List_Olist_ONil(X9737))|X9735=c_List_Olist_ONil(X9738))&(X9735!=c_List_Olist_ONil(X9738)|c_List_Olist__all2(X9738,X9737,X9736,X9735,c_List_Olist_ONil(X9737)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Nil2])])). 4.46/4.70 fof(c_0_5987, plain, ![X15134]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,X15134,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_mod__1])). 4.46/4.70 fof(c_0_5988, plain, ![X15158]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X15158,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)), inference(variable_rename,[status(thm)],[fact_zmod__minus1__right])). 4.46/4.70 fof(c_0_5989, plain, ![X11101, X11102]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X11102|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11101),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X11101),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11102),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X11101),X11102))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X11102|c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X11101),X11102))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__eq__if])])])). 4.46/4.70 fof(c_0_5990, plain, ![X4026, X4027, X4028, X4029]:(((~hBOOL(hAPP(X4027,X4026))|hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X4029),X4028),X4027),X4026)))&(X4026!=X4028|hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X4029),X4028),X4027),X4026))))&(~hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X4029),X4028),X4027),X4026))|(hBOOL(hAPP(X4027,X4026))|X4026=X4028))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])])). 4.46/4.70 fof(c_0_5991, plain, ![X7734]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7734)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_min__0L])). 4.46/4.70 fof(c_0_5992, plain, ![X785]:X785=hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X785)), inference(variable_rename,[status(thm)],[fact_nat__int])). 4.46/4.70 fof(c_0_5993, plain, ![X13557]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X13557),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_min__0R])). 4.46/4.70 fof(c_0_5994, plain, ![X9825, X9826, X9827]:((~c_List_Olist__all2(X9825,X9825,c_fequal,X9827,X9826)|X9827=X9826)&(X9827!=X9826|c_List_Olist__all2(X9825,X9825,c_fequal,X9827,X9826))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__eq])])). 4.46/4.70 fof(c_0_5995, plain, ![X5059]:X5059=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5059), inference(variable_rename,[status(thm)],[fact_max__0L])). 4.46/4.70 fof(c_0_5996, plain, ![X5211]:X5211=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X5211),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_max__0R])). 4.46/4.70 fof(c_0_5997, plain, ![X17315, X17316]:(X17316!=X17315|hBOOL(hAPP(hAPP(c_fequal,X17316),X17315))), inference(variable_rename,[status(thm)],[help_c__fequal__2])). 4.46/4.70 fof(c_0_5998, plain, ![X1452]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1452),c_Int_OPls)=X1452, inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I1_J])). 4.46/4.70 fof(c_0_5999, plain, ![X3565]:c_Int_OPls=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X3565), inference(variable_rename,[status(thm)],[fact_mult__Pls])). 4.46/4.70 fof(c_0_6000, plain, ![X17140, X17141]:((X17141=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nitpick_Onat__gcd(X17141,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17140,X17141))=c_Nitpick_Onat__gcd(X17140,X17141))&(X17141!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nitpick_Onat__gcd(X17140,X17141)=X17140)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__gcd_Osimps])])])). 4.46/4.70 fof(c_0_6001, plain, ![X3178, X3179]:((X3178=X3179|c_Random_Oinc__shift(X3179,X3178)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X3178),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))&(X3178!=X3179|c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=c_Random_Oinc__shift(X3179,X3178))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inc__shift__def])])])). 4.46/4.70 fof(c_0_6002, plain, ![X10014]:X10014=hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X10014)), inference(variable_rename,[status(thm)],[fact_nat__of__of__nat])). 4.46/4.70 fof(c_0_6003, plain, ![X11100]:X11100=hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X11100)), inference(variable_rename,[status(thm)],[fact_of__nat__nat__of])). 4.46/4.70 cnf(c_0_6004, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_Fun_Oid(X1)),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X3))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),tc_fun(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X1),c_COMBS(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X2,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,X1)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,X1),tc_fun(X3,tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_fun(X3,X1)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X3,X1),tc_fun(X3,tc_HOL_Obool),X2)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X3,X1),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X3)),c_fequal))),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,X1),tc_fun(X3,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,X1),tc_fun(tc_fun(X3,X1),tc_fun(X3,X1)),X2),c_COMBB(X1,X1,X3)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4))),X5)))))),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X6)))),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X7)))))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),X5),X7))|~class_Rings_Osemiring__0(X1)|~c_Fun_Oinj__on(tc_prod(X2,X3),X1,hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,X1),tc_fun(X3,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,X1),tc_fun(tc_fun(X3,X1),tc_fun(X3,X1)),X2),c_COMBB(X1,X1,X3)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4))),X5)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X6),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X7)))), inference(split_conjunct,[status(thm)],[c_0_4823])). 4.46/4.70 cnf(c_0_6005, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hAPP(c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1))))=c_Divides_Odivmod__int(X2,X1)), inference(rw,[status(thm)],[c_0_4824, c_0_4825])). 4.46/4.70 cnf(c_0_6006, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,X2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1))))=c_Divides_Odivmod__int(X2,X1)), inference(rw,[status(thm)],[c_0_4826, c_0_4825])). 4.46/4.70 cnf(c_0_6007, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Orderings_Oord__class_Omax(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_4827])). 4.46/4.70 cnf(c_0_6008, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Orderings_Oord__class_Omin(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_4828])). 4.46/4.70 cnf(c_0_6009, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))=c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))))))|~class_Lattices_Odistrib__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_4829])). 4.46/4.70 cnf(c_0_6010, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))=c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))))))|~class_Lattices_Odistrib__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_4830])). 4.46/4.70 cnf(c_0_6011, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X2,X2)),tc_fun(tc_Int_Oint,X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X2),X2),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X2,X2)),tc_fun(tc_Int_Oint,X2)),tc_Int_Oint),c_COMBB(tc_fun(X2,X2),X2,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,X2),X2),tc_Int_Oint),c_HOL_OLet(X2,X2)),c_Int_Oring__1__class_Oof__int(X2)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X2,X2),tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X2,X2)),tc_fun(tc_fun(X2,X2),tc_fun(X2,X2)),tc_Int_Oint),c_COMBS(X2,X2,X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X2,X2),tc_fun(X2,tc_fun(X2,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X2,X2)),tc_fun(tc_fun(X2,X2),tc_fun(X2,tc_fun(X2,X2))),tc_Int_Oint),c_COMBB(X2,tc_fun(X2,X2),X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),tc_Int_Oint),c_If(X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(X2,X2,X2),c_Groups_Oplus__class_Oplus(X2)),c_COMBI(X2))))),hAPP(hAPP(c_COMBC(X2,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X2),c_Groups_Oplus__class_Oplus(X2)),hAPP(hAPP(c_COMBS(X2,X2,X2),c_Groups_Oplus__class_Oplus(X2)),c_COMBI(X2)))),c_Groups_Oone__class_Oone(X2))))),c_Divides_Odivmod__int(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Oring__1(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4831, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6012, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4832, c_0_4470]), c_0_4470]), c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6013, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4833, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4836]), ['final']). 4.46/4.70 cnf(c_0_6014, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)),X3))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4837, c_0_4470]), c_0_4470]), c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6015, plain, ![X942, X943, X944, X945, X946, X947, X948]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X948,X946)),hAPP(hAPP(c_Product__Type_OPair(X948,X946),X943),X942)),hAPP(hAPP(c_Relation_Orel__comp(X948,X947,X946),X945),X944)))|hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X948,X947,X946,hAPP(hAPP(c_COMBC(X948,tc_fun(tc_prod(X948,X947),tc_HOL_Obool),tc_fun(X947,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X947,tc_fun(tc_fun(tc_prod(X948,X947),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X948,X947),tc_HOL_Obool),tc_fun(X947,tc_HOL_Obool)),X948),c_COMBC(X947,tc_fun(tc_prod(X948,X947),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X947,tc_prod(X948,X947)),tc_fun(X947,tc_fun(tc_fun(tc_prod(X948,X947),tc_HOL_Obool),tc_HOL_Obool)),X948),hAPP(c_COMBB(tc_prod(X948,X947),tc_fun(tc_fun(tc_prod(X948,X947),tc_HOL_Obool),tc_HOL_Obool),X947),c_member(tc_prod(X948,X947)))),c_Product__Type_OPair(X948,X947)))),X945),hAPP(hAPP(c_COMBC(X947,tc_fun(tc_prod(X947,X946),tc_HOL_Obool),tc_fun(X946,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X946,tc_fun(tc_fun(tc_prod(X947,X946),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X947,X946),tc_HOL_Obool),tc_fun(X946,tc_HOL_Obool)),X947),c_COMBC(X946,tc_fun(tc_prod(X947,X946),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X946,tc_prod(X947,X946)),tc_fun(X946,tc_fun(tc_fun(tc_prod(X947,X946),tc_HOL_Obool),tc_HOL_Obool)),X947),hAPP(c_COMBB(tc_prod(X947,X946),tc_fun(tc_fun(tc_prod(X947,X946),tc_HOL_Obool),tc_HOL_Obool),X946),c_member(tc_prod(X947,X946)))),c_Product__Type_OPair(X947,X946)))),X944)),X943),X942)))&(~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X948,X947,X946,hAPP(hAPP(c_COMBC(X948,tc_fun(tc_prod(X948,X947),tc_HOL_Obool),tc_fun(X947,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X947,tc_fun(tc_fun(tc_prod(X948,X947),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X948,X947),tc_HOL_Obool),tc_fun(X947,tc_HOL_Obool)),X948),c_COMBC(X947,tc_fun(tc_prod(X948,X947),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X947,tc_prod(X948,X947)),tc_fun(X947,tc_fun(tc_fun(tc_prod(X948,X947),tc_HOL_Obool),tc_HOL_Obool)),X948),hAPP(c_COMBB(tc_prod(X948,X947),tc_fun(tc_fun(tc_prod(X948,X947),tc_HOL_Obool),tc_HOL_Obool),X947),c_member(tc_prod(X948,X947)))),c_Product__Type_OPair(X948,X947)))),X945),hAPP(hAPP(c_COMBC(X947,tc_fun(tc_prod(X947,X946),tc_HOL_Obool),tc_fun(X946,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X946,tc_fun(tc_fun(tc_prod(X947,X946),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X947,X946),tc_HOL_Obool),tc_fun(X946,tc_HOL_Obool)),X947),c_COMBC(X946,tc_fun(tc_prod(X947,X946),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X946,tc_prod(X947,X946)),tc_fun(X946,tc_fun(tc_fun(tc_prod(X947,X946),tc_HOL_Obool),tc_HOL_Obool)),X947),hAPP(c_COMBB(tc_prod(X947,X946),tc_fun(tc_fun(tc_prod(X947,X946),tc_HOL_Obool),tc_HOL_Obool),X946),c_member(tc_prod(X947,X946)))),c_Product__Type_OPair(X947,X946)))),X944)),X943),X942))|hBOOL(hAPP(hAPP(c_member(tc_prod(X948,X946)),hAPP(hAPP(c_Product__Type_OPair(X948,X946),X943),X942)),hAPP(hAPP(c_Relation_Orel__comp(X948,X947,X946),X945),X944))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__comp__rel__comp__eq])])). 4.46/4.70 fof(c_0_6016, plain, ![X12104, X12105, X12106, X12107, X12108, X12109]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X12109,X12108)),hAPP(hAPP(c_Product__Type_OPair(X12109,X12108),X12105),X12104)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool)),X12107),X12106)))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12109,tc_fun(X12108,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X12109,tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_fun(X12108,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12108,tc_fun(tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_fun(X12108,tc_HOL_Obool)),X12109),c_COMBC(X12108,tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12108,tc_prod(X12109,X12108)),tc_fun(X12108,tc_fun(tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_HOL_Obool)),X12109),hAPP(c_COMBB(tc_prod(X12109,X12108),tc_fun(tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_HOL_Obool),X12108),c_member(tc_prod(X12109,X12108)))),c_Product__Type_OPair(X12109,X12108)))),X12107)),hAPP(hAPP(c_COMBC(X12109,tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_fun(X12108,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12108,tc_fun(tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_fun(X12108,tc_HOL_Obool)),X12109),c_COMBC(X12108,tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12108,tc_prod(X12109,X12108)),tc_fun(X12108,tc_fun(tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_HOL_Obool)),X12109),hAPP(c_COMBB(tc_prod(X12109,X12108),tc_fun(tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_HOL_Obool),X12108),c_member(tc_prod(X12109,X12108)))),c_Product__Type_OPair(X12109,X12108)))),X12106)),X12105),X12104)))&(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12109,tc_fun(X12108,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X12109,tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_fun(X12108,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12108,tc_fun(tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_fun(X12108,tc_HOL_Obool)),X12109),c_COMBC(X12108,tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12108,tc_prod(X12109,X12108)),tc_fun(X12108,tc_fun(tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_HOL_Obool)),X12109),hAPP(c_COMBB(tc_prod(X12109,X12108),tc_fun(tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_HOL_Obool),X12108),c_member(tc_prod(X12109,X12108)))),c_Product__Type_OPair(X12109,X12108)))),X12107)),hAPP(hAPP(c_COMBC(X12109,tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_fun(X12108,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12108,tc_fun(tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_fun(X12108,tc_HOL_Obool)),X12109),c_COMBC(X12108,tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12108,tc_prod(X12109,X12108)),tc_fun(X12108,tc_fun(tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_HOL_Obool)),X12109),hAPP(c_COMBB(tc_prod(X12109,X12108),tc_fun(tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool),tc_HOL_Obool),X12108),c_member(tc_prod(X12109,X12108)))),c_Product__Type_OPair(X12109,X12108)))),X12106)),X12105),X12104))|hBOOL(hAPP(hAPP(c_member(tc_prod(X12109,X12108)),hAPP(hAPP(c_Product__Type_OPair(X12109,X12108),X12105),X12104)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X12109,X12108),tc_HOL_Obool)),X12107),X12106))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Un__eq2])])). 4.46/4.70 fof(c_0_6017, plain, ![X6542, X6543, X6544, X6545, X6546, X6547]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X6547,X6546)),hAPP(hAPP(c_Product__Type_OPair(X6547,X6546),X6543),X6542)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool)),X6545),X6544)))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6547,tc_fun(X6546,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X6547,tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_fun(X6546,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6546,tc_fun(tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_fun(X6546,tc_HOL_Obool)),X6547),c_COMBC(X6546,tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6546,tc_prod(X6547,X6546)),tc_fun(X6546,tc_fun(tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_HOL_Obool)),X6547),hAPP(c_COMBB(tc_prod(X6547,X6546),tc_fun(tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_HOL_Obool),X6546),c_member(tc_prod(X6547,X6546)))),c_Product__Type_OPair(X6547,X6546)))),X6545)),hAPP(hAPP(c_COMBC(X6547,tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_fun(X6546,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6546,tc_fun(tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_fun(X6546,tc_HOL_Obool)),X6547),c_COMBC(X6546,tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6546,tc_prod(X6547,X6546)),tc_fun(X6546,tc_fun(tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_HOL_Obool)),X6547),hAPP(c_COMBB(tc_prod(X6547,X6546),tc_fun(tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_HOL_Obool),X6546),c_member(tc_prod(X6547,X6546)))),c_Product__Type_OPair(X6547,X6546)))),X6544)),X6543),X6542)))&(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6547,tc_fun(X6546,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X6547,tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_fun(X6546,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6546,tc_fun(tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_fun(X6546,tc_HOL_Obool)),X6547),c_COMBC(X6546,tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6546,tc_prod(X6547,X6546)),tc_fun(X6546,tc_fun(tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_HOL_Obool)),X6547),hAPP(c_COMBB(tc_prod(X6547,X6546),tc_fun(tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_HOL_Obool),X6546),c_member(tc_prod(X6547,X6546)))),c_Product__Type_OPair(X6547,X6546)))),X6545)),hAPP(hAPP(c_COMBC(X6547,tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_fun(X6546,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6546,tc_fun(tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_fun(X6546,tc_HOL_Obool)),X6547),c_COMBC(X6546,tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6546,tc_prod(X6547,X6546)),tc_fun(X6546,tc_fun(tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_HOL_Obool)),X6547),hAPP(c_COMBB(tc_prod(X6547,X6546),tc_fun(tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool),tc_HOL_Obool),X6546),c_member(tc_prod(X6547,X6546)))),c_Product__Type_OPair(X6547,X6546)))),X6544)),X6543),X6542))|hBOOL(hAPP(hAPP(c_member(tc_prod(X6547,X6546)),hAPP(hAPP(c_Product__Type_OPair(X6547,X6546),X6543),X6542)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6547,X6546),tc_HOL_Obool)),X6545),X6544))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2])])). 4.46/4.70 fof(c_0_6018, plain, ![X5443, X5444, X5445, X5446]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5446,tc_fun(X5445,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5446,tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_fun(X5445,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5445,tc_fun(tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_fun(X5445,tc_HOL_Obool)),X5446),c_COMBC(X5445,tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5445,tc_prod(X5446,X5445)),tc_fun(X5445,tc_fun(tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_HOL_Obool)),X5446),hAPP(c_COMBB(tc_prod(X5446,X5445),tc_fun(tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_HOL_Obool),X5445),c_member(tc_prod(X5446,X5445)))),c_Product__Type_OPair(X5446,X5445)))),X5444)),hAPP(hAPP(c_COMBC(X5446,tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_fun(X5445,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5445,tc_fun(tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_fun(X5445,tc_HOL_Obool)),X5446),c_COMBC(X5445,tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5445,tc_prod(X5446,X5445)),tc_fun(X5445,tc_fun(tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_HOL_Obool)),X5446),hAPP(c_COMBB(tc_prod(X5446,X5445),tc_fun(tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_HOL_Obool),X5445),c_member(tc_prod(X5446,X5445)))),c_Product__Type_OPair(X5446,X5445)))),X5443)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool)),X5444),X5443)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool)),X5444),X5443))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5446,tc_fun(X5445,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5446,tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_fun(X5445,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5445,tc_fun(tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_fun(X5445,tc_HOL_Obool)),X5446),c_COMBC(X5445,tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5445,tc_prod(X5446,X5445)),tc_fun(X5445,tc_fun(tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_HOL_Obool)),X5446),hAPP(c_COMBB(tc_prod(X5446,X5445),tc_fun(tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_HOL_Obool),X5445),c_member(tc_prod(X5446,X5445)))),c_Product__Type_OPair(X5446,X5445)))),X5444)),hAPP(hAPP(c_COMBC(X5446,tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_fun(X5445,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5445,tc_fun(tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_fun(X5445,tc_HOL_Obool)),X5446),c_COMBC(X5445,tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5445,tc_prod(X5446,X5445)),tc_fun(X5445,tc_fun(tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_HOL_Obool)),X5446),hAPP(c_COMBB(tc_prod(X5446,X5445),tc_fun(tc_fun(tc_prod(X5446,X5445),tc_HOL_Obool),tc_HOL_Obool),X5445),c_member(tc_prod(X5446,X5445)))),c_Product__Type_OPair(X5446,X5445)))),X5443))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])])). 4.46/4.70 cnf(c_0_6019, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4838, c_0_4470]), c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6020, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),hAPP(hAPP(c_COMBS(X4,tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_fun(tc_fun(X2,tc_HOL_Obool),X1),X4),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1)),hAPP(c_COMBC(X2,X4,X1),X6))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4),c_Set_OCollect(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)))),hAPP(c_COMBC(X2,X4,tc_HOL_Obool),X7))))),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBS(X2,tc_fun(X4,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X4,X1),tc_fun(tc_fun(X4,tc_HOL_Obool),X1),X2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1)),X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X2),c_Set_OCollect(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X2),hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X5)))),X7)))),X3)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5))), inference(split_conjunct,[status(thm)],[c_0_4839])). 4.46/4.70 cnf(c_0_6021, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|hAPP(c_Code__Numeral_Oint__of,X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4840, c_0_4470]), c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6022, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X1))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4841, c_0_4470]), c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6023, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(X3,esk123_9(X4,X5,X6,X7,X3,X2,X1,X8,X9))),hAPP(X7,esk123_9(X4,X5,X6,X7,X3,X2,X1,X8,X9))),hAPP(X6,esk123_9(X4,X5,X6,X7,X3,X2,X1,X8,X9)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))|c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_Set_Oimage(X9,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(X9,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(X9,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),X9),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X5)),X7)),X4)),X8))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_Set_Oimage(X9,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(X9,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(X9,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),X9),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),X7)),X6)),X8))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9),X8))), inference(split_conjunct,[status(thm)],[c_0_4842])). 4.46/4.70 cnf(c_0_6024, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))=hAPP(c_Code__Numeral_Oint__of,X1)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4843, c_0_4470]), c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6025, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4844, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6026, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))),c_Groups_Ozero__class_Ozero(X2)))|X3!=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4845, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6027, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4846, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6028, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4847, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6029, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4848, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6030, plain, ![X6117, X6118, X6119, X6120, X6121, X6122]:((~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6122,tc_fun(X6121,tc_fun(X6120,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X6122,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X6121,X6120),tc_HOL_Obool),tc_fun(X6121,tc_fun(X6120,tc_HOL_Obool)),X6122),hAPP(c_COMBC(X6121,tc_fun(tc_prod(X6121,X6120),tc_HOL_Obool),tc_fun(X6120,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6120,tc_fun(tc_fun(tc_prod(X6121,X6120),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6121,X6120),tc_HOL_Obool),tc_fun(X6120,tc_HOL_Obool)),X6121),c_COMBC(X6120,tc_fun(tc_prod(X6121,X6120),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6120,tc_prod(X6121,X6120)),tc_fun(X6120,tc_fun(tc_fun(tc_prod(X6121,X6120),tc_HOL_Obool),tc_HOL_Obool)),X6121),hAPP(c_COMBB(tc_prod(X6121,X6120),tc_fun(tc_fun(tc_prod(X6121,X6120),tc_HOL_Obool),tc_HOL_Obool),X6120),c_member(tc_prod(X6121,X6120)))),c_Product__Type_OPair(X6121,X6120))))),X6119)),X6118),X6117))|hBOOL(hAPP(hAPP(c_member(tc_prod(X6121,X6120)),hAPP(hAPP(c_Product__Type_OPair(X6121,X6120),X6118),X6117)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6122,tc_fun(tc_prod(X6121,X6120),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X6122,tc_HOL_Obool))),X6119))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X6121,X6120)),hAPP(hAPP(c_Product__Type_OPair(X6121,X6120),X6118),X6117)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6122,tc_fun(tc_prod(X6121,X6120),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X6122,tc_HOL_Obool))),X6119)))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6122,tc_fun(X6121,tc_fun(X6120,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X6122,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X6121,X6120),tc_HOL_Obool),tc_fun(X6121,tc_fun(X6120,tc_HOL_Obool)),X6122),hAPP(c_COMBC(X6121,tc_fun(tc_prod(X6121,X6120),tc_HOL_Obool),tc_fun(X6120,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6120,tc_fun(tc_fun(tc_prod(X6121,X6120),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6121,X6120),tc_HOL_Obool),tc_fun(X6120,tc_HOL_Obool)),X6121),c_COMBC(X6120,tc_fun(tc_prod(X6121,X6120),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6120,tc_prod(X6121,X6120)),tc_fun(X6120,tc_fun(tc_fun(tc_prod(X6121,X6120),tc_HOL_Obool),tc_HOL_Obool)),X6121),hAPP(c_COMBB(tc_prod(X6121,X6120),tc_fun(tc_fun(tc_prod(X6121,X6120),tc_HOL_Obool),tc_HOL_Obool),X6120),c_member(tc_prod(X6121,X6120)))),c_Product__Type_OPair(X6121,X6120))))),X6119)),X6118),X6117)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__INT__eq2])])). 4.46/4.70 fof(c_0_6031, plain, ![X5585, X5586, X5587, X5588, X5589, X5590]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X5589,X5588)),hAPP(hAPP(c_Product__Type_OPair(X5589,X5588),X5586),X5585)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5590,tc_fun(tc_prod(X5589,X5588),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5590,tc_HOL_Obool))),X5587)))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5590,tc_fun(X5589,tc_fun(X5588,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5590,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X5589,X5588),tc_HOL_Obool),tc_fun(X5589,tc_fun(X5588,tc_HOL_Obool)),X5590),hAPP(c_COMBC(X5589,tc_fun(tc_prod(X5589,X5588),tc_HOL_Obool),tc_fun(X5588,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5588,tc_fun(tc_fun(tc_prod(X5589,X5588),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5589,X5588),tc_HOL_Obool),tc_fun(X5588,tc_HOL_Obool)),X5589),c_COMBC(X5588,tc_fun(tc_prod(X5589,X5588),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5588,tc_prod(X5589,X5588)),tc_fun(X5588,tc_fun(tc_fun(tc_prod(X5589,X5588),tc_HOL_Obool),tc_HOL_Obool)),X5589),hAPP(c_COMBB(tc_prod(X5589,X5588),tc_fun(tc_fun(tc_prod(X5589,X5588),tc_HOL_Obool),tc_HOL_Obool),X5588),c_member(tc_prod(X5589,X5588)))),c_Product__Type_OPair(X5589,X5588))))),X5587)),X5586),X5585)))&(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5590,tc_fun(X5589,tc_fun(X5588,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5590,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X5589,X5588),tc_HOL_Obool),tc_fun(X5589,tc_fun(X5588,tc_HOL_Obool)),X5590),hAPP(c_COMBC(X5589,tc_fun(tc_prod(X5589,X5588),tc_HOL_Obool),tc_fun(X5588,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5588,tc_fun(tc_fun(tc_prod(X5589,X5588),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5589,X5588),tc_HOL_Obool),tc_fun(X5588,tc_HOL_Obool)),X5589),c_COMBC(X5588,tc_fun(tc_prod(X5589,X5588),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5588,tc_prod(X5589,X5588)),tc_fun(X5588,tc_fun(tc_fun(tc_prod(X5589,X5588),tc_HOL_Obool),tc_HOL_Obool)),X5589),hAPP(c_COMBB(tc_prod(X5589,X5588),tc_fun(tc_fun(tc_prod(X5589,X5588),tc_HOL_Obool),tc_HOL_Obool),X5588),c_member(tc_prod(X5589,X5588)))),c_Product__Type_OPair(X5589,X5588))))),X5587)),X5586),X5585))|hBOOL(hAPP(hAPP(c_member(tc_prod(X5589,X5588)),hAPP(hAPP(c_Product__Type_OPair(X5589,X5588),X5586),X5585)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5590,tc_fun(tc_prod(X5589,X5588),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5590,tc_HOL_Obool))),X5587))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq2])])). 4.46/4.70 cnf(c_0_6032, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X3|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4849, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6033, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))))|~class_Rings_Olinordered__idom(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4850, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6034, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4851, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6035, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4852, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6036, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_Set_Oimage(X9,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(X9,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(X9,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),X9),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),X6)),X4)),X8))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(X3,esk123_9(X4,X3,X5,X6,X7,X2,X1,X8,X9))),hAPP(X6,esk123_9(X4,X3,X5,X6,X7,X2,X1,X8,X9))),hAPP(X4,esk123_9(X4,X3,X5,X6,X7,X2,X1,X8,X9)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_Set_Oimage(X9,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(X9,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(X9,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),X9),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X7)),X6)),X5)),X8))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9),X8))), inference(split_conjunct,[status(thm)],[c_0_4842])). 4.46/4.70 fof(c_0_6037, plain, ![X1872, X1873, X1874, X1875, X1877, X1878, X1879, X1880, X1881]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X1875,X1875)),esk46_4(X1872,X1873,X1874,X1875)),hAPP(c_List_Oset(tc_prod(X1875,X1875)),hAPP(hAPP(c_List_Ozip(X1875,X1875),X1874),X1873))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1875)),X1874)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1875)),X1873)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1875),tc_List_Olist(X1875))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1875),tc_List_Olist(X1875)),X1874),X1873)),c_List_Olistrel(X1875,X1872))))&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1875,X1875,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1875,tc_fun(tc_prod(X1875,X1875),tc_HOL_Obool),tc_fun(X1875,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1875,tc_fun(tc_fun(tc_prod(X1875,X1875),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1875,X1875),tc_HOL_Obool),tc_fun(X1875,tc_HOL_Obool)),X1875),c_COMBC(X1875,tc_fun(tc_prod(X1875,X1875),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1875,tc_prod(X1875,X1875)),tc_fun(X1875,tc_fun(tc_fun(tc_prod(X1875,X1875),tc_HOL_Obool),tc_HOL_Obool)),X1875),hAPP(c_COMBB(tc_prod(X1875,X1875),tc_fun(tc_fun(tc_prod(X1875,X1875),tc_HOL_Obool),tc_HOL_Obool),X1875),c_member(tc_prod(X1875,X1875)))),c_Product__Type_OPair(X1875,X1875)))),X1872)),esk46_4(X1872,X1873,X1874,X1875)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1875)),X1874)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1875)),X1873)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1875),tc_List_Olist(X1875))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1875),tc_List_Olist(X1875)),X1874),X1873)),c_List_Olistrel(X1875,X1872)))))&((~hBOOL(hAPP(hAPP(c_member(tc_prod(X1880,X1880)),X1881),hAPP(c_List_Oset(tc_prod(X1880,X1880)),hAPP(hAPP(c_List_Ozip(X1880,X1880),X1879),X1878))))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1880,X1880,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1880,tc_fun(tc_prod(X1880,X1880),tc_HOL_Obool),tc_fun(X1880,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1880,tc_fun(tc_fun(tc_prod(X1880,X1880),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1880,X1880),tc_HOL_Obool),tc_fun(X1880,tc_HOL_Obool)),X1880),c_COMBC(X1880,tc_fun(tc_prod(X1880,X1880),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1880,tc_prod(X1880,X1880)),tc_fun(X1880,tc_fun(tc_fun(tc_prod(X1880,X1880),tc_HOL_Obool),tc_HOL_Obool)),X1880),hAPP(c_COMBB(tc_prod(X1880,X1880),tc_fun(tc_fun(tc_prod(X1880,X1880),tc_HOL_Obool),tc_HOL_Obool),X1880),c_member(tc_prod(X1880,X1880)))),c_Product__Type_OPair(X1880,X1880)))),X1877)),X1881))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1880),tc_List_Olist(X1880))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1880),tc_List_Olist(X1880)),X1879),X1878)),c_List_Olistrel(X1880,X1877))))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1880)),X1879)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1880)),X1878)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1880),tc_List_Olist(X1880))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1880),tc_List_Olist(X1880)),X1879),X1878)),c_List_Olistrel(X1880,X1877)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__iff__zip])])])])])])). 4.46/4.70 cnf(c_0_6038, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4)),c_fequal),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),c_Relation_OId(X1))))), inference(split_conjunct,[status(thm)],[c_0_4853])). 4.46/4.70 cnf(c_0_6039, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_Nat_Onat,X1),c_Finite__Set_Ocard(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),c_Set_OCollect(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool),c_member(X3)),X6)))),X4)))),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X5),X6)|hAPP(c_Finite__Set_Ocard(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))),hAPP(hAPP(c_COMBC(X1,X3,tc_HOL_Obool),X4),esk140_6(X5,X4,X6,X3,X2,X1)))))!=hAPP(X5,esk140_6(X5,X4,X6,X3,X2,X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X6))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4854])). 4.46/4.70 cnf(c_0_6040, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X1),X3))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4855])). 4.46/4.70 cnf(c_0_6041, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2))=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X1),X3))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4856])). 4.46/4.70 cnf(c_0_6042, plain, (c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X1),X2)=c_Lazy__Sequence_Oappend(tc_List_Olist(X1),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(X1,tc_List_Olist(X1)),tc_List_Olist(X1),c_Lazy__Sequence_Oproduct(X1,tc_List_Olist(X1),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_List_Olist(X1),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1))),X1),hAPP(c_COMBB(tc_List_Olist(X1),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1)),tc_List_Olist(X1)),c_Lazy__Sequence_Osingle(tc_List_Olist(X1)))),c_List_Olist_OCons(X1))))),c_Lazy__Sequence_Oempty(tc_List_Olist(X1))))|~class_Lazy__Sequence_Osmall__lazy(X1)), inference(split_conjunct,[status(thm)],[c_0_4857])). 4.46/4.70 cnf(c_0_6043, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_Nat_Onat,X2),c_Finite__Set_Ocard(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X2),c_Set_OCollect(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X2),hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X6)))),X5)))),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(X4),X6))|X1!=hAPP(c_Finite__Set_Ocard(X2),hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3))),hAPP(hAPP(c_COMBC(X2,X4,tc_HOL_Obool),X5),esk280_6(X1,X5,X6,X4,X3,X2)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4858])). 4.46/4.70 cnf(c_0_6044, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,X2))|~class_Lattices_Odistrib__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4859])). 4.46/4.70 cnf(c_0_6045, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,X2))=c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X1),X3))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))))|~class_Groups_Olinordered__ab__semigroup__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4860])). 4.46/4.70 cnf(c_0_6046, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,X2))=c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))))|~class_Lattices_Odistrib__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4861])). 4.46/4.70 fof(c_0_6047, plain, ![X10459, X10460, X10461, X10462, X10463]:((~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10463,X10462,hAPP(hAPP(c_COMBC(X10463,tc_fun(tc_prod(X10463,X10462),tc_HOL_Obool),tc_fun(X10462,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10462,tc_fun(tc_fun(tc_prod(X10463,X10462),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10463,X10462),tc_HOL_Obool),tc_fun(X10462,tc_HOL_Obool)),X10463),c_COMBC(X10462,tc_fun(tc_prod(X10463,X10462),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10462,tc_prod(X10463,X10462)),tc_fun(X10462,tc_fun(tc_fun(tc_prod(X10463,X10462),tc_HOL_Obool),tc_HOL_Obool)),X10463),hAPP(c_COMBB(tc_prod(X10463,X10462),tc_fun(tc_fun(tc_prod(X10463,X10462),tc_HOL_Obool),tc_HOL_Obool),X10462),c_member(tc_prod(X10463,X10462)))),c_Product__Type_OPair(X10463,X10462)))),X10461)),X10460),X10459))|hBOOL(hAPP(hAPP(c_member(tc_prod(X10462,X10463)),hAPP(hAPP(c_Product__Type_OPair(X10462,X10463),X10460),X10459)),hAPP(c_Relation_Oconverse(X10463,X10462),X10461))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10462,X10463)),hAPP(hAPP(c_Product__Type_OPair(X10462,X10463),X10460),X10459)),hAPP(c_Relation_Oconverse(X10463,X10462),X10461)))|hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10463,X10462,hAPP(hAPP(c_COMBC(X10463,tc_fun(tc_prod(X10463,X10462),tc_HOL_Obool),tc_fun(X10462,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10462,tc_fun(tc_fun(tc_prod(X10463,X10462),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10463,X10462),tc_HOL_Obool),tc_fun(X10462,tc_HOL_Obool)),X10463),c_COMBC(X10462,tc_fun(tc_prod(X10463,X10462),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10462,tc_prod(X10463,X10462)),tc_fun(X10462,tc_fun(tc_fun(tc_prod(X10463,X10462),tc_HOL_Obool),tc_HOL_Obool)),X10463),hAPP(c_COMBB(tc_prod(X10463,X10462),tc_fun(tc_fun(tc_prod(X10463,X10462),tc_HOL_Obool),tc_HOL_Obool),X10462),c_member(tc_prod(X10463,X10462)))),c_Product__Type_OPair(X10463,X10462)))),X10461)),X10460),X10459)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__converse__eq])])). 4.46/4.70 cnf(c_0_6048, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X3)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))|~class_Groups_Omonoid__mult(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4862, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6049, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk410_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk409_3(X1,X2,X3)),esk410_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,esk409_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),esk410_3(X1,X2,X3))))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4863, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6050, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X3))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4864, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6051, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X1),X3))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,X2))|~class_Groups_Olinordered__ab__semigroup__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4865])). 4.46/4.70 fof(c_0_6052, plain, ![X10795, X10796, X10797, X10798]:((~c_Wellfounded_Omax__extp(X10798,hAPP(hAPP(c_COMBC(X10798,tc_fun(tc_prod(X10798,X10798),tc_HOL_Obool),tc_fun(X10798,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10798,tc_fun(tc_fun(tc_prod(X10798,X10798),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10798,X10798),tc_HOL_Obool),tc_fun(X10798,tc_HOL_Obool)),X10798),c_COMBC(X10798,tc_fun(tc_prod(X10798,X10798),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10798,tc_prod(X10798,X10798)),tc_fun(X10798,tc_fun(tc_fun(tc_prod(X10798,X10798),tc_HOL_Obool),tc_HOL_Obool)),X10798),hAPP(c_COMBB(tc_prod(X10798,X10798),tc_fun(tc_fun(tc_prod(X10798,X10798),tc_HOL_Obool),tc_HOL_Obool),X10798),c_member(tc_prod(X10798,X10798)))),c_Product__Type_OPair(X10798,X10798)))),X10797),X10796,X10795)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X10798,tc_HOL_Obool),tc_fun(X10798,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10798,tc_HOL_Obool),tc_fun(X10798,tc_HOL_Obool)),X10796),X10795)),c_Wellfounded_Omax__ext(X10798,X10797))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X10798,tc_HOL_Obool),tc_fun(X10798,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10798,tc_HOL_Obool),tc_fun(X10798,tc_HOL_Obool)),X10796),X10795)),c_Wellfounded_Omax__ext(X10798,X10797)))|c_Wellfounded_Omax__extp(X10798,hAPP(hAPP(c_COMBC(X10798,tc_fun(tc_prod(X10798,X10798),tc_HOL_Obool),tc_fun(X10798,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10798,tc_fun(tc_fun(tc_prod(X10798,X10798),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10798,X10798),tc_HOL_Obool),tc_fun(X10798,tc_HOL_Obool)),X10798),c_COMBC(X10798,tc_fun(tc_prod(X10798,X10798),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10798,tc_prod(X10798,X10798)),tc_fun(X10798,tc_fun(tc_fun(tc_prod(X10798,X10798),tc_HOL_Obool),tc_HOL_Obool)),X10798),hAPP(c_COMBB(tc_prod(X10798,X10798),tc_fun(tc_fun(tc_prod(X10798,X10798),tc_HOL_Obool),tc_HOL_Obool),X10798),c_member(tc_prod(X10798,X10798)))),c_Product__Type_OPair(X10798,X10798)))),X10797),X10796,X10795))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__extp__max__ext__eq])])). 4.46/4.70 cnf(c_0_6053, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))=c_List_Otranspose(X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk474_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4866, c_0_4517]), c_0_4517])). 4.46/4.70 cnf(c_0_6054, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=c_List_Olist_ONil(tc_Nat_Onat)), inference(rw,[status(thm)],[c_0_4867, c_0_4868]), ['final']). 4.46/4.70 cnf(c_0_6055, plain, (c_List_Olist_ONil(X1)=hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Olist_ONil(X2))), inference(split_conjunct,[status(thm)],[c_0_4869]), ['final']). 4.46/4.70 fof(c_0_6056, plain, ![X5938, X5939, X5940, X5941]:((~c_List_Olistrelp(X5941,hAPP(hAPP(c_COMBC(X5941,tc_fun(tc_prod(X5941,X5941),tc_HOL_Obool),tc_fun(X5941,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5941,tc_fun(tc_fun(tc_prod(X5941,X5941),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5941,X5941),tc_HOL_Obool),tc_fun(X5941,tc_HOL_Obool)),X5941),c_COMBC(X5941,tc_fun(tc_prod(X5941,X5941),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5941,tc_prod(X5941,X5941)),tc_fun(X5941,tc_fun(tc_fun(tc_prod(X5941,X5941),tc_HOL_Obool),tc_HOL_Obool)),X5941),hAPP(c_COMBB(tc_prod(X5941,X5941),tc_fun(tc_fun(tc_prod(X5941,X5941),tc_HOL_Obool),tc_HOL_Obool),X5941),c_member(tc_prod(X5941,X5941)))),c_Product__Type_OPair(X5941,X5941)))),X5940),X5939,X5938)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5941),tc_List_Olist(X5941))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5941),tc_List_Olist(X5941)),X5939),X5938)),c_List_Olistrel(X5941,X5940))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5941),tc_List_Olist(X5941))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5941),tc_List_Olist(X5941)),X5939),X5938)),c_List_Olistrel(X5941,X5940)))|c_List_Olistrelp(X5941,hAPP(hAPP(c_COMBC(X5941,tc_fun(tc_prod(X5941,X5941),tc_HOL_Obool),tc_fun(X5941,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5941,tc_fun(tc_fun(tc_prod(X5941,X5941),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5941,X5941),tc_HOL_Obool),tc_fun(X5941,tc_HOL_Obool)),X5941),c_COMBC(X5941,tc_fun(tc_prod(X5941,X5941),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5941,tc_prod(X5941,X5941)),tc_fun(X5941,tc_fun(tc_fun(tc_prod(X5941,X5941),tc_HOL_Obool),tc_HOL_Obool)),X5941),hAPP(c_COMBB(tc_prod(X5941,X5941),tc_fun(tc_fun(tc_prod(X5941,X5941),tc_HOL_Obool),tc_HOL_Obool),X5941),c_member(tc_prod(X5941,X5941)))),c_Product__Type_OPair(X5941,X5941)))),X5940),X5939,X5938))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp__listrel__eq])])). 4.46/4.70 cnf(c_0_6057, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk474_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))|hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))=c_List_Otranspose(X2,X3)|c_List_Olist_ONil(tc_List_Olist(X2))=X3), inference(split_conjunct,[status(thm)],[c_0_4515])). 4.46/4.70 cnf(c_0_6058, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk230_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk229_3(X1,X2,X3)),esk230_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(X1,esk229_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),esk230_3(X1,X2,X3))))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4870, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6059, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X3))|~class_Groups_Omonoid__mult(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4871, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6060, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X1)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_Nat_Onat,X1),tc_Nat_Onat),c_List_Onth(X1)),hAPP(c_List_Onth(tc_List_Olist(X1)),X2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))=c_List_Otranspose(X1,X2)|c_List_Olist_ONil(tc_List_Olist(X1))=X2|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),esk474_3(X3,X1,X2)))!=X3), inference(split_conjunct,[status(thm)],[c_0_4515])). 4.46/4.70 fof(c_0_6061, plain, ![X12509, X12510, X12511, X12512]:((~hBOOL(hAPP(hAPP(c_member(X12511),X12509),hAPP(c_Relation_ORange(X12512,X12511),X12510)))|hBOOL(hAPP(c_Predicate_ORangeP(X12512,X12511,hAPP(hAPP(c_COMBC(X12512,tc_fun(tc_prod(X12512,X12511),tc_HOL_Obool),tc_fun(X12511,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12511,tc_fun(tc_fun(tc_prod(X12512,X12511),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12512,X12511),tc_HOL_Obool),tc_fun(X12511,tc_HOL_Obool)),X12512),c_COMBC(X12511,tc_fun(tc_prod(X12512,X12511),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12511,tc_prod(X12512,X12511)),tc_fun(X12511,tc_fun(tc_fun(tc_prod(X12512,X12511),tc_HOL_Obool),tc_HOL_Obool)),X12512),hAPP(c_COMBB(tc_prod(X12512,X12511),tc_fun(tc_fun(tc_prod(X12512,X12511),tc_HOL_Obool),tc_HOL_Obool),X12511),c_member(tc_prod(X12512,X12511)))),c_Product__Type_OPair(X12512,X12511)))),X12510)),X12509)))&(~hBOOL(hAPP(c_Predicate_ORangeP(X12512,X12511,hAPP(hAPP(c_COMBC(X12512,tc_fun(tc_prod(X12512,X12511),tc_HOL_Obool),tc_fun(X12511,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12511,tc_fun(tc_fun(tc_prod(X12512,X12511),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12512,X12511),tc_HOL_Obool),tc_fun(X12511,tc_HOL_Obool)),X12512),c_COMBC(X12511,tc_fun(tc_prod(X12512,X12511),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12511,tc_prod(X12512,X12511)),tc_fun(X12511,tc_fun(tc_fun(tc_prod(X12512,X12511),tc_HOL_Obool),tc_HOL_Obool)),X12512),hAPP(c_COMBB(tc_prod(X12512,X12511),tc_fun(tc_fun(tc_prod(X12512,X12511),tc_HOL_Obool),tc_HOL_Obool),X12511),c_member(tc_prod(X12512,X12511)))),c_Product__Type_OPair(X12512,X12511)))),X12510)),X12509))|hBOOL(hAPP(hAPP(c_member(X12511),X12509),hAPP(c_Relation_ORange(X12512,X12511),X12510))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq])])). 4.46/4.70 fof(c_0_6062, plain, ![X16644, X16645, X16646, X16647]:((~hBOOL(hAPP(hAPP(c_member(X16647),X16644),hAPP(c_Relation_ODomain(X16647,X16646),X16645)))|hBOOL(hAPP(c_Predicate_ODomainP(X16647,X16646,hAPP(hAPP(c_COMBC(X16647,tc_fun(tc_prod(X16647,X16646),tc_HOL_Obool),tc_fun(X16646,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16646,tc_fun(tc_fun(tc_prod(X16647,X16646),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X16647,X16646),tc_HOL_Obool),tc_fun(X16646,tc_HOL_Obool)),X16647),c_COMBC(X16646,tc_fun(tc_prod(X16647,X16646),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16646,tc_prod(X16647,X16646)),tc_fun(X16646,tc_fun(tc_fun(tc_prod(X16647,X16646),tc_HOL_Obool),tc_HOL_Obool)),X16647),hAPP(c_COMBB(tc_prod(X16647,X16646),tc_fun(tc_fun(tc_prod(X16647,X16646),tc_HOL_Obool),tc_HOL_Obool),X16646),c_member(tc_prod(X16647,X16646)))),c_Product__Type_OPair(X16647,X16646)))),X16645)),X16644)))&(~hBOOL(hAPP(c_Predicate_ODomainP(X16647,X16646,hAPP(hAPP(c_COMBC(X16647,tc_fun(tc_prod(X16647,X16646),tc_HOL_Obool),tc_fun(X16646,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16646,tc_fun(tc_fun(tc_prod(X16647,X16646),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X16647,X16646),tc_HOL_Obool),tc_fun(X16646,tc_HOL_Obool)),X16647),c_COMBC(X16646,tc_fun(tc_prod(X16647,X16646),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16646,tc_prod(X16647,X16646)),tc_fun(X16646,tc_fun(tc_fun(tc_prod(X16647,X16646),tc_HOL_Obool),tc_HOL_Obool)),X16647),hAPP(c_COMBB(tc_prod(X16647,X16646),tc_fun(tc_fun(tc_prod(X16647,X16646),tc_HOL_Obool),tc_HOL_Obool),X16646),c_member(tc_prod(X16647,X16646)))),c_Product__Type_OPair(X16647,X16646)))),X16645)),X16644))|hBOOL(hAPP(hAPP(c_member(X16647),X16644),hAPP(c_Relation_ODomain(X16647,X16646),X16645))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq])])). 4.46/4.70 cnf(c_0_6063, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4872, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6064, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4873, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6065, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4874, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6066, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X1)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_Nat_Onat,X1),tc_Nat_Onat),c_List_Onth(X1)),hAPP(c_List_Onth(tc_List_Olist(X1)),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))=c_List_Otranspose(X1,X2)|X3!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),esk474_3(X3,X1,X2)))!=X3), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4875, c_0_4517]), c_0_4517])). 4.46/4.70 fof(c_0_6067, plain, ![X9888, X9889, X9890]:((~hBOOL(hAPP(c_Wellfounded_Oaccp(X9890,hAPP(hAPP(c_COMBC(X9890,tc_fun(tc_prod(X9890,X9890),tc_HOL_Obool),tc_fun(X9890,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9890,tc_fun(tc_fun(tc_prod(X9890,X9890),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X9890,X9890),tc_HOL_Obool),tc_fun(X9890,tc_HOL_Obool)),X9890),c_COMBC(X9890,tc_fun(tc_prod(X9890,X9890),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9890,tc_prod(X9890,X9890)),tc_fun(X9890,tc_fun(tc_fun(tc_prod(X9890,X9890),tc_HOL_Obool),tc_HOL_Obool)),X9890),hAPP(c_COMBB(tc_prod(X9890,X9890),tc_fun(tc_fun(tc_prod(X9890,X9890),tc_HOL_Obool),tc_HOL_Obool),X9890),c_member(tc_prod(X9890,X9890)))),c_Product__Type_OPair(X9890,X9890)))),X9889)),X9888))|hBOOL(hAPP(hAPP(c_member(X9890),X9888),c_Wellfounded_Oacc(X9890,X9889))))&(~hBOOL(hAPP(hAPP(c_member(X9890),X9888),c_Wellfounded_Oacc(X9890,X9889)))|hBOOL(hAPP(c_Wellfounded_Oaccp(X9890,hAPP(hAPP(c_COMBC(X9890,tc_fun(tc_prod(X9890,X9890),tc_HOL_Obool),tc_fun(X9890,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9890,tc_fun(tc_fun(tc_prod(X9890,X9890),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X9890,X9890),tc_HOL_Obool),tc_fun(X9890,tc_HOL_Obool)),X9890),c_COMBC(X9890,tc_fun(tc_prod(X9890,X9890),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9890,tc_prod(X9890,X9890)),tc_fun(X9890,tc_fun(tc_fun(tc_prod(X9890,X9890),tc_HOL_Obool),tc_HOL_Obool)),X9890),hAPP(c_COMBB(tc_prod(X9890,X9890),tc_fun(tc_fun(tc_prod(X9890,X9890),tc_HOL_Obool),tc_HOL_Obool),X9890),c_member(tc_prod(X9890,X9890)))),c_Product__Type_OPair(X9890,X9890)))),X9889)),X9888)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__acc__eq])])). 4.46/4.70 cnf(c_0_6068, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk280_6(X2,X3,X4,X1,X5,X6)),X4))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_Nat_Onat,X6),c_Finite__Set_Ocard(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X6),c_Set_OCollect(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X6),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)))),X3)))),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X5))), inference(split_conjunct,[status(thm)],[c_0_4858])). 4.46/4.70 fof(c_0_6069, plain, ![X1370, X1371, X1372, X1373]:((hAPP(hAPP(c_COMBC(X1373,tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_fun(X1372,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1372,tc_fun(tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_fun(X1372,tc_HOL_Obool)),X1373),c_COMBC(X1372,tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1372,tc_prod(X1373,X1372)),tc_fun(X1372,tc_fun(tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_HOL_Obool)),X1373),hAPP(c_COMBB(tc_prod(X1373,X1372),tc_fun(tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_HOL_Obool),X1372),c_member(tc_prod(X1373,X1372)))),c_Product__Type_OPair(X1373,X1372)))),X1370)!=hAPP(hAPP(c_COMBC(X1373,tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_fun(X1372,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1372,tc_fun(tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_fun(X1372,tc_HOL_Obool)),X1373),c_COMBC(X1372,tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1372,tc_prod(X1373,X1372)),tc_fun(X1372,tc_fun(tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_HOL_Obool)),X1373),hAPP(c_COMBB(tc_prod(X1373,X1372),tc_fun(tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_HOL_Obool),X1372),c_member(tc_prod(X1373,X1372)))),c_Product__Type_OPair(X1373,X1372)))),X1371)|X1371=X1370)&(X1371!=X1370|hAPP(hAPP(c_COMBC(X1373,tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_fun(X1372,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1372,tc_fun(tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_fun(X1372,tc_HOL_Obool)),X1373),c_COMBC(X1372,tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1372,tc_prod(X1373,X1372)),tc_fun(X1372,tc_fun(tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_HOL_Obool)),X1373),hAPP(c_COMBB(tc_prod(X1373,X1372),tc_fun(tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_HOL_Obool),X1372),c_member(tc_prod(X1373,X1372)))),c_Product__Type_OPair(X1373,X1372)))),X1370)=hAPP(hAPP(c_COMBC(X1373,tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_fun(X1372,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1372,tc_fun(tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_fun(X1372,tc_HOL_Obool)),X1373),c_COMBC(X1372,tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1372,tc_prod(X1373,X1372)),tc_fun(X1372,tc_fun(tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_HOL_Obool)),X1373),hAPP(c_COMBB(tc_prod(X1373,X1372),tc_fun(tc_fun(tc_prod(X1373,X1372),tc_HOL_Obool),tc_HOL_Obool),X1372),c_member(tc_prod(X1373,X1372)))),c_Product__Type_OPair(X1373,X1372)))),X1371))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])])). 4.46/4.70 cnf(c_0_6070, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X4))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(X1,X1,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X1),X3)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X1)),c_Nat_Osemiring__1__class_Oof__nat(X1))),X4))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X2)))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4876])). 4.46/4.70 cnf(c_0_6071, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_4877]), ['final']). 4.46/4.70 fof(c_0_6072, plain, ![X14584, X14585]:((~c_Equiv__Relations_Oequivp(X14585,hAPP(hAPP(c_COMBC(X14585,tc_fun(tc_prod(X14585,X14585),tc_HOL_Obool),tc_fun(X14585,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14585,tc_fun(tc_fun(tc_prod(X14585,X14585),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X14585,X14585),tc_HOL_Obool),tc_fun(X14585,tc_HOL_Obool)),X14585),c_COMBC(X14585,tc_fun(tc_prod(X14585,X14585),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14585,tc_prod(X14585,X14585)),tc_fun(X14585,tc_fun(tc_fun(tc_prod(X14585,X14585),tc_HOL_Obool),tc_HOL_Obool)),X14585),hAPP(c_COMBB(tc_prod(X14585,X14585),tc_fun(tc_fun(tc_prod(X14585,X14585),tc_HOL_Obool),tc_HOL_Obool),X14585),c_member(tc_prod(X14585,X14585)))),c_Product__Type_OPair(X14585,X14585)))),X14584))|c_Equiv__Relations_Oequiv(X14585,c_Orderings_Otop__class_Otop(tc_fun(X14585,tc_HOL_Obool)),X14584))&(~c_Equiv__Relations_Oequiv(X14585,c_Orderings_Otop__class_Otop(tc_fun(X14585,tc_HOL_Obool)),X14584)|c_Equiv__Relations_Oequivp(X14585,hAPP(hAPP(c_COMBC(X14585,tc_fun(tc_prod(X14585,X14585),tc_HOL_Obool),tc_fun(X14585,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14585,tc_fun(tc_fun(tc_prod(X14585,X14585),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X14585,X14585),tc_HOL_Obool),tc_fun(X14585,tc_HOL_Obool)),X14585),c_COMBC(X14585,tc_fun(tc_prod(X14585,X14585),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14585,tc_prod(X14585,X14585)),tc_fun(X14585,tc_fun(tc_fun(tc_prod(X14585,X14585),tc_HOL_Obool),tc_HOL_Obool)),X14585),hAPP(c_COMBB(tc_prod(X14585,X14585),tc_fun(tc_fun(tc_prod(X14585,X14585),tc_HOL_Obool),tc_HOL_Obool),X14585),c_member(tc_prod(X14585,X14585)))),c_Product__Type_OPair(X14585,X14585)))),X14584)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__equiv])])). 4.46/4.70 cnf(c_0_6073, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBS(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X4)),X5)),X6)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X2),X4)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_OCollect(X2),X4)))))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4878])). 4.46/4.70 cnf(c_0_6074, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))), inference(split_conjunct,[status(thm)],[c_0_4879]), ['final']). 4.46/4.70 cnf(c_0_6075, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk140_6(X2,X3,X4,X1,X5,X6)),X4))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_Nat_Onat,X6),c_Finite__Set_Ocard(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X6),c_Set_OCollect(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X6),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)))),X3)))),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X5))), inference(split_conjunct,[status(thm)],[c_0_4854])). 4.46/4.70 fof(c_0_6076, plain, ![X12417, X12418]:((~c_Wellfounded_OwfP(X12418,hAPP(hAPP(c_COMBC(X12418,tc_fun(tc_prod(X12418,X12418),tc_HOL_Obool),tc_fun(X12418,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12418,tc_fun(tc_fun(tc_prod(X12418,X12418),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12418,X12418),tc_HOL_Obool),tc_fun(X12418,tc_HOL_Obool)),X12418),c_COMBC(X12418,tc_fun(tc_prod(X12418,X12418),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12418,tc_prod(X12418,X12418)),tc_fun(X12418,tc_fun(tc_fun(tc_prod(X12418,X12418),tc_HOL_Obool),tc_HOL_Obool)),X12418),hAPP(c_COMBB(tc_prod(X12418,X12418),tc_fun(tc_fun(tc_prod(X12418,X12418),tc_HOL_Obool),tc_HOL_Obool),X12418),c_member(tc_prod(X12418,X12418)))),c_Product__Type_OPair(X12418,X12418)))),X12417))|c_Wellfounded_Owf(X12418,X12417))&(~c_Wellfounded_Owf(X12418,X12417)|c_Wellfounded_OwfP(X12418,hAPP(hAPP(c_COMBC(X12418,tc_fun(tc_prod(X12418,X12418),tc_HOL_Obool),tc_fun(X12418,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12418,tc_fun(tc_fun(tc_prod(X12418,X12418),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X12418,X12418),tc_HOL_Obool),tc_fun(X12418,tc_HOL_Obool)),X12418),c_COMBC(X12418,tc_fun(tc_prod(X12418,X12418),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12418,tc_prod(X12418,X12418)),tc_fun(X12418,tc_fun(tc_fun(tc_prod(X12418,X12418),tc_HOL_Obool),tc_HOL_Obool)),X12418),hAPP(c_COMBB(tc_prod(X12418,X12418),tc_fun(tc_fun(tc_prod(X12418,X12418),tc_HOL_Obool),tc_HOL_Obool),X12418),c_member(tc_prod(X12418,X12418)))),c_Product__Type_OPair(X12418,X12418)))),X12417)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__wf__eq])])). 4.46/4.70 fof(c_0_6077, plain, ![X6598, X6599, X6600, X6601, X6602, X6603]:((hBOOL(hAPP(hAPP(c_member(X6602),esk194_6(X6598,X6599,X6600,X6601,X6602,X6603)),X6601))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6603,X6602,c_Groups_Otimes__class_Otimes(X6603)),hAPP(hAPP(c_COMBS(X6602,tc_fun(X6600,tc_HOL_Obool),X6603),hAPP(hAPP(c_COMBC(X6602,X6603,tc_fun(tc_fun(X6600,tc_HOL_Obool),X6603)),hAPP(hAPP(c_COMBB(tc_fun(X6600,X6603),tc_fun(X6603,tc_fun(tc_fun(X6600,tc_HOL_Obool),X6603)),X6602),c_Finite__Set_Ofold__image(X6603,X6600,c_Groups_Otimes__class_Otimes(X6603))),X6598)),c_Groups_Oone__class_Oone(X6603))),X6599)),c_Groups_Oone__class_Oone(X6603)),X6601)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6603,tc_prod(X6602,X6600),c_Groups_Otimes__class_Otimes(X6603)),hAPP(c_Product__Type_Oprod_Oprod__case(X6602,X6600,X6603),X6598)),c_Groups_Oone__class_Oone(X6603)),hAPP(hAPP(c_Product__Type_OSigma(X6602,X6600),X6601),X6599))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6602),X6601))|~class_Groups_Ocomm__monoid__mult(X6603))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6600),hAPP(X6599,esk194_6(X6598,X6599,X6600,X6601,X6602,X6603))))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6603,X6602,c_Groups_Otimes__class_Otimes(X6603)),hAPP(hAPP(c_COMBS(X6602,tc_fun(X6600,tc_HOL_Obool),X6603),hAPP(hAPP(c_COMBC(X6602,X6603,tc_fun(tc_fun(X6600,tc_HOL_Obool),X6603)),hAPP(hAPP(c_COMBB(tc_fun(X6600,X6603),tc_fun(X6603,tc_fun(tc_fun(X6600,tc_HOL_Obool),X6603)),X6602),c_Finite__Set_Ofold__image(X6603,X6600,c_Groups_Otimes__class_Otimes(X6603))),X6598)),c_Groups_Oone__class_Oone(X6603))),X6599)),c_Groups_Oone__class_Oone(X6603)),X6601)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6603,tc_prod(X6602,X6600),c_Groups_Otimes__class_Otimes(X6603)),hAPP(c_Product__Type_Oprod_Oprod__case(X6602,X6600,X6603),X6598)),c_Groups_Oone__class_Oone(X6603)),hAPP(hAPP(c_Product__Type_OSigma(X6602,X6600),X6601),X6599))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6602),X6601))|~class_Groups_Ocomm__monoid__mult(X6603))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__Sigma])])])])])). 4.46/4.70 cnf(c_0_6078, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4880, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6079, plain, ![X4331, X4332, X4333, X4334, X4335, X4336, X4337]:(~class_Rings_Osemiring__0(X4337)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4336,X4337),hAPP(hAPP(c_COMBC(X4336,tc_fun(X4333,tc_HOL_Obool),X4337),hAPP(hAPP(c_COMBB(tc_fun(X4333,X4337),tc_fun(tc_fun(X4333,tc_HOL_Obool),X4337),X4336),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4333,X4337)),hAPP(hAPP(c_COMBC(X4336,tc_fun(X4333,X4337),tc_fun(X4333,X4337)),hAPP(hAPP(c_COMBB(tc_fun(X4337,X4337),tc_fun(tc_fun(X4333,X4337),tc_fun(X4333,X4337)),X4336),c_COMBB(X4337,X4337,X4333)),hAPP(hAPP(c_COMBB(X4337,tc_fun(X4337,X4337),X4336),c_Groups_Otimes__class_Otimes(X4337)),X4335))),X4332))),X4331)),X4334)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4337),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4336,X4337),X4335),X4334)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4333,X4337),X4332),X4331))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__product])])). 4.46/4.70 cnf(c_0_6080, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),X1,X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4),c_Set_OCollect(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)))),hAPP(c_COMBC(X2,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,tc_HOL_Obool),X2),c_fequal),X6)))))),hAPP(c_Set_Oimage(X2,X4,X6),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4881])). 4.46/4.70 cnf(c_0_6081, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X3)))|~class_Rings_Ocomm__semiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4882, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6082, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_4883])). 4.46/4.70 fof(c_0_6083, plain, ![X7392, X7393, X7394, X7395]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X7395),X7394))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X7393),X7395)),c_FunDef_Opair__leq))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X7392),X7394)),c_FunDef_Omax__weak))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X7393),X7392)),X7394)),c_FunDef_Omax__weak))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wmax__insertI])])])). 4.46/4.70 fof(c_0_6084, plain, ![X16361, X16362, X16363, X16364]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X16364),X16363))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X16362),X16364)),c_FunDef_Opair__less))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X16361),X16363)),c_FunDef_Omax__strict))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X16362),X16361)),X16363)),c_FunDef_Omax__strict))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_smax__insertI])])])). 4.46/4.70 fof(c_0_6085, plain, ![X5681, X5682, X5683, X5684]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X5684),X5683))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X5684),X5682)),c_FunDef_Opair__less))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X5683),X5681)),c_FunDef_Omin__strict))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X5683),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X5682),X5681))),c_FunDef_Omin__strict))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_smin__insertI])])])). 4.46/4.70 cnf(c_0_6086, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_4884])). 4.46/4.70 fof(c_0_6087, plain, ![X2306, X2307, X2308, X2309, X2310, X2311, X2312, X2313, X2314, X2315, X2316]:((hBOOL(hAPP(hAPP(c_member(X2316),esk55_11(X2306,X2307,X2308,X2309,X2310,X2311,X2312,X2313,X2314,X2315,X2316)),X2315))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2310,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2316,tc_fun(X2310,tc_HOL_Obool)),X2308),hAPP(hAPP(c_COMBB(tc_fun(X2313,tc_fun(X2310,tc_HOL_Obool)),tc_fun(X2310,tc_HOL_Obool),X2316),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2313,tc_fun(X2310,tc_HOL_Obool)),X2307)),X2309))),X2306))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2313,tc_HOL_Obool)),X2307),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2313),X2312),X2311)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2316,tc_HOL_Obool)),X2308),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2316),X2315),X2314)))|~c_Equiv__Relations_Ocongruent2(X2316,X2313,tc_fun(X2310,tc_HOL_Obool),X2314,X2311,X2309)|~c_Equiv__Relations_Oequiv(X2313,X2312,X2311)|~c_Equiv__Relations_Oequiv(X2316,X2315,X2314))&((hBOOL(hAPP(hAPP(c_member(X2313),esk56_11(X2306,X2307,X2308,X2309,X2310,X2311,X2312,X2313,X2314,X2315,X2316)),X2312))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2310,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2316,tc_fun(X2310,tc_HOL_Obool)),X2308),hAPP(hAPP(c_COMBB(tc_fun(X2313,tc_fun(X2310,tc_HOL_Obool)),tc_fun(X2310,tc_HOL_Obool),X2316),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2313,tc_fun(X2310,tc_HOL_Obool)),X2307)),X2309))),X2306))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2313,tc_HOL_Obool)),X2307),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2313),X2312),X2311)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2316,tc_HOL_Obool)),X2308),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2316),X2315),X2314)))|~c_Equiv__Relations_Ocongruent2(X2316,X2313,tc_fun(X2310,tc_HOL_Obool),X2314,X2311,X2309)|~c_Equiv__Relations_Oequiv(X2313,X2312,X2311)|~c_Equiv__Relations_Oequiv(X2316,X2315,X2314))&(~hBOOL(hAPP(hAPP(c_member(tc_fun(X2310,tc_HOL_Obool)),hAPP(hAPP(X2309,esk55_11(X2306,X2307,X2308,X2309,X2310,X2311,X2312,X2313,X2314,X2315,X2316)),esk56_11(X2306,X2307,X2308,X2309,X2310,X2311,X2312,X2313,X2314,X2315,X2316))),X2306))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2310,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2316,tc_fun(X2310,tc_HOL_Obool)),X2308),hAPP(hAPP(c_COMBB(tc_fun(X2313,tc_fun(X2310,tc_HOL_Obool)),tc_fun(X2310,tc_HOL_Obool),X2316),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2313,tc_fun(X2310,tc_HOL_Obool)),X2307)),X2309))),X2306))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2313,tc_HOL_Obool)),X2307),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2313),X2312),X2311)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2316,tc_HOL_Obool)),X2308),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2316),X2315),X2314)))|~c_Equiv__Relations_Ocongruent2(X2316,X2313,tc_fun(X2310,tc_HOL_Obool),X2314,X2311,X2309)|~c_Equiv__Relations_Oequiv(X2313,X2312,X2311)|~c_Equiv__Relations_Oequiv(X2316,X2315,X2314)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__equiv__class__type2])])])])])). 4.46/4.70 fof(c_0_6088, plain, ![X12227, X12228, X12229, X12230]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X12230),X12229))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X12230),X12228)),c_FunDef_Opair__leq))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X12229),X12227)),c_FunDef_Omin__weak))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X12229),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X12228),X12227))),c_FunDef_Omin__weak))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wmin__insertI])])])). 4.46/4.70 cnf(c_0_6089, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2)))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)))|~class_Rings_Osemiring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4885, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6090, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X3),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X3,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X3,tc_fun(X1,X3),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X1,X3),tc_fun(X1,tc_HOL_Obool)),X3),c_COMBB(X3,tc_HOL_Obool,X1)),c_fequal)),X4)))),X2)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_4886])). 4.46/4.70 cnf(c_0_6091, plain, (c_Divides_OnegDivAlg(X1,X2)=hAPP(c_Divides_Oadjust(X2),c_Divides_OnegDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4887, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6092, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1))))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),c_fequal),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_4853])). 4.46/4.70 cnf(c_0_6093, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OnegDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X1)))=c_Divides_OnegDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4888, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6094, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X1))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2)))))=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X1))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2))))), inference(split_conjunct,[status(thm)],[c_0_4889])). 4.46/4.70 cnf(c_0_6095, plain, (hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),X1),c_member(X2)),X3)),X4)=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4890, c_0_4531]), c_0_4891]), ['final']). 4.46/4.70 cnf(c_0_6096, plain, (hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_Option_Ooption(X2),tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),hAPP(c_Map_Omap__of(X1,X2),X3)))),c_Option_Ooption_OSome(X2))))=hAPP(c_List_Oset(tc_prod(X1,X2)),X3)|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_4892])). 4.46/4.70 cnf(c_0_6097, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X1))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2)))))=hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X1))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2)))))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_4893])). 4.46/4.70 cnf(c_0_6098, plain, (c_Wellfounded_Owf(X3,hAPP(c_Set_OCollect(tc_prod(X3,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X3),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),X4))),hAPP(hAPP(c_COMBC(X3,tc_fun(X3,X3),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,X3),tc_fun(X3,tc_HOL_Obool)),X3),c_COMBB(X3,tc_HOL_Obool,X3)),c_fequal)),X2)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,hAPP(X2,esk456_4(X3,X2,X1,X4)))),hAPP(X1,esk456_4(X3,X2,X1,X4))))), inference(split_conjunct,[status(thm)],[c_0_4894])). 4.46/4.70 cnf(c_0_6099, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Ocomm__semiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4895, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6100, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4896, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6101, plain, ![X1202, X1203, X1204, X1205]:(~class_Smallcheck_Osmall(X1204)|~class_Smallcheck_Osmall(X1205)|hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(X1204,X1205)),X1203),X1202)=hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(X1204),hAPP(hAPP(c_COMBC(X1204,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(X1205,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X1204),c_Smallcheck_Osmall__class_Osmall(X1205)),hAPP(hAPP(c_COMBB(tc_fun(X1205,tc_prod(X1204,X1205)),tc_fun(X1205,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X1204),hAPP(c_COMBB(tc_prod(X1204,X1205),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),X1205),X1203)),c_Product__Type_OPair(X1204,X1205)))),X1202)),X1202)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_small__prod__def])])). 4.46/4.70 fof(c_0_6102, plain, ![X13839, X13840, X13841, X13842, X13843, X13844, X13845, X13846, X13847, X13848]:(~c_Equiv__Relations_Oequiv(X13848,X13847,X13846)|(~c_Equiv__Relations_Oequiv(X13845,X13844,X13843)|(~c_Equiv__Relations_Ocongruent2(X13848,X13845,tc_fun(X13842,tc_HOL_Obool),X13846,X13843,X13841)|(~hBOOL(hAPP(hAPP(c_member(X13848),X13840),X13847))|(~hBOOL(hAPP(hAPP(c_member(X13845),X13839),X13844))|hAPP(hAPP(X13841,X13840),X13839)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13848,tc_fun(X13842,tc_HOL_Obool)),hAPP(c_Relation_OImage(X13848,X13848,X13846),hAPP(hAPP(c_Set_Oinsert(X13848),X13840),c_Orderings_Obot__class_Obot(tc_fun(X13848,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X13845,tc_fun(X13842,tc_HOL_Obool)),tc_fun(X13842,tc_HOL_Obool),X13848),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13845,tc_fun(X13842,tc_HOL_Obool)),hAPP(c_Relation_OImage(X13845,X13845,X13843),hAPP(hAPP(c_Set_Oinsert(X13845),X13839),c_Orderings_Obot__class_Obot(tc_fun(X13845,tc_HOL_Obool)))))),X13841))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__equiv__class2])])])). 4.46/4.70 cnf(c_0_6103, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(X3,X6)),hAPP(c_Com_Ocom_OBODY,X6)),hAPP(X4,X6))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),c_Com_Ocom_OBODY)),X4)),X5)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X4)),X5))|~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X6),X5))), inference(split_conjunct,[status(thm)],[c_0_4897])). 4.46/4.70 cnf(c_0_6104, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),hAPP(c_Set_OCollect(tc_List_Olist(X1)),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),c_List_Oset(X1))),X2))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X3)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4898])). 4.46/4.70 cnf(c_0_6105, plain, (hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),c_List_Oset(X1))),X2)=c_List_Olists(X1,X2)), inference(rw,[status(thm)],[c_0_4899, c_0_4531]), ['final']). 4.46/4.70 fof(c_0_6106, plain, ![X14587, X14588, X14589, X14590, X14591]:(~c_Hoare__Mirabelle_Ohoare__valids(X14591,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X14591),tc_HOL_Obool)),X14590),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X14591),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X14591,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X14591)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X14591,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X14591))),hAPP(hAPP(c_COMBB(tc_fun(X14591,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X14591,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X14591))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X14591)),X14589)),c_Com_Ocom_OBODY)),X14588)),X14587)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X14591),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X14591,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X14591)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X14591,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X14591))),hAPP(hAPP(c_COMBB(tc_fun(X14591,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X14591,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X14591))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X14591)),X14589)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X14588)),X14587))|c_Hoare__Mirabelle_Ohoare__valids(X14591,X14590,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X14591),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X14591,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X14591)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X14591,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X14591))),hAPP(hAPP(c_COMBB(tc_fun(X14591,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X14591,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X14591))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X14591)),X14589)),c_Com_Ocom_OBODY)),X14588)),X14587))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Body__sound__lemma])])])). 4.46/4.70 fof(c_0_6107, plain, ![X15857, X15858, X15859, X15860, X15861, X15862]:((hBOOL(hAPP(hAPP(c_member(X15861),esk460_6(X15857,X15858,X15859,X15860,X15861,X15862)),X15860))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X15861,X15859),X15862),hAPP(c_Product__Type_Oprod_Oprod__case(X15861,X15859,X15862),X15857)),hAPP(hAPP(c_Product__Type_OSigma(X15861,X15859),X15860),X15858))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15861,X15862),hAPP(hAPP(c_COMBS(X15861,tc_fun(X15859,tc_HOL_Obool),X15862),hAPP(hAPP(c_COMBB(tc_fun(X15859,X15862),tc_fun(tc_fun(X15859,tc_HOL_Obool),X15862),X15861),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15859,X15862)),X15857)),X15858)),X15860)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15861),X15860))|~class_Groups_Ocomm__monoid__add(X15862))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15859),hAPP(X15858,esk460_6(X15857,X15858,X15859,X15860,X15861,X15862))))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X15861,X15859),X15862),hAPP(c_Product__Type_Oprod_Oprod__case(X15861,X15859,X15862),X15857)),hAPP(hAPP(c_Product__Type_OSigma(X15861,X15859),X15860),X15858))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15861,X15862),hAPP(hAPP(c_COMBS(X15861,tc_fun(X15859,tc_HOL_Obool),X15862),hAPP(hAPP(c_COMBB(tc_fun(X15859,X15862),tc_fun(tc_fun(X15859,tc_HOL_Obool),X15862),X15861),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15859,X15862)),X15857)),X15858)),X15860)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15861),X15860))|~class_Groups_Ocomm__monoid__add(X15862))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__Sigma])])])])])). 4.46/4.70 cnf(c_0_6108, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X3)))),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4900, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6109, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),hAPP(c_Set_OCollect(tc_List_Olist(X1)),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),c_List_Oset(X1))),X2))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X3)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4901])). 4.46/4.70 cnf(c_0_6110, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))),c_Groups_Ozero__class_Ozero(X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4902, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6111, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))),c_Groups_Ozero__class_Ozero(X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4903, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6112, plain, (hAPP(c_Divides_Oadjust(X2),c_Divides_OposDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)))=c_Divides_OposDivAlg(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4904, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6113, plain, ![X13640, X13641, X13642, X13643, X13644]:(~c_Hoare__Mirabelle_Ohoare__derivs(X13644,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X13644),tc_HOL_Obool)),X13643),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X13644),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X13644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X13644)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X13644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X13644))),hAPP(hAPP(c_COMBB(tc_fun(X13644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X13644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X13644))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X13644)),X13642)),c_Com_Ocom_OBODY)),X13641)),X13640)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X13644),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X13644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X13644)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X13644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X13644))),hAPP(hAPP(c_COMBB(tc_fun(X13644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X13644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X13644))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X13644)),X13642)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X13641)),X13640))|c_Hoare__Mirabelle_Ohoare__derivs(X13644,X13643,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X13644),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X13644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X13644)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X13644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X13644))),hAPP(hAPP(c_COMBB(tc_fun(X13644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X13644,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X13644))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X13644)),X13642)),c_Com_Ocom_OBODY)),X13641)),X13640))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hoare__derivs_OBody])])])). 4.46/4.70 cnf(c_0_6114, plain, (hAPP(c_Divides_Oadjust(X2),c_Divides_OposDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)))=c_Divides_OposDivAlg(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4905, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6115, plain, (X2!=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X3|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4906, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6116, plain, ![X13345, X13346]:(~class_Enum_Oenum(X13346)|~class_Enum_Oenum(X13345)|hAPP(hAPP(c_List_Omap(tc_List_Olist(X13345),tc_fun(X13346,X13345)),hAPP(hAPP(c_COMBB(tc_fun(X13346,tc_Option_Ooption(X13345)),tc_fun(X13346,X13345),tc_List_Olist(X13345)),c_Fun_Ocomp(tc_Option_Ooption(X13345),X13345,X13346,c_Option_Othe(X13345))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X13346,X13345)),tc_fun(X13346,tc_Option_Ooption(X13345)),tc_List_Olist(X13345)),c_Map_Omap__of(X13346,X13345)),hAPP(c_List_Ozip(X13346,X13345),c_Enum_Oenum__class_Oenum(X13346))))),c_Enum_On__lists(X13345,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13346)),c_Enum_Oenum__class_Oenum(X13346)),c_Enum_Oenum__class_Oenum(X13345)))=c_Enum_Oenum__class_Oenum(tc_fun(X13346,X13345))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_enum__fun__def])])])). 4.46/4.70 fof(c_0_6117, plain, ![X16661, X16662, X16663]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X16662,X16663)),X16661))|c_Enum_Oall__n__lists(X16663,hAPP(hAPP(c_COMBB(tc_fun(X16662,X16663),tc_HOL_Obool,tc_List_Olist(X16663)),X16661),hAPP(hAPP(c_COMBB(tc_fun(X16662,tc_Option_Ooption(X16663)),tc_fun(X16662,X16663),tc_List_Olist(X16663)),c_Fun_Ocomp(tc_Option_Ooption(X16663),X16663,X16662,c_Option_Othe(X16663))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X16662,X16663)),tc_fun(X16662,tc_Option_Ooption(X16663)),tc_List_Olist(X16663)),c_Map_Omap__of(X16662,X16663)),hAPP(c_List_Ozip(X16662,X16663),c_Enum_Oenum__class_Oenum(X16662))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16662)),c_Enum_Oenum__class_Oenum(X16662)))|(~class_Enum_Oenum(X16662)|~class_Enum_Oenum(X16663)))&(~c_Enum_Oall__n__lists(X16663,hAPP(hAPP(c_COMBB(tc_fun(X16662,X16663),tc_HOL_Obool,tc_List_Olist(X16663)),X16661),hAPP(hAPP(c_COMBB(tc_fun(X16662,tc_Option_Ooption(X16663)),tc_fun(X16662,X16663),tc_List_Olist(X16663)),c_Fun_Ocomp(tc_Option_Ooption(X16663),X16663,X16662,c_Option_Othe(X16663))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X16662,X16663)),tc_fun(X16662,tc_Option_Ooption(X16663)),tc_List_Olist(X16663)),c_Map_Omap__of(X16662,X16663)),hAPP(c_List_Ozip(X16662,X16663),c_Enum_Oenum__class_Oenum(X16662))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16662)),c_Enum_Oenum__class_Oenum(X16662)))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X16662,X16663)),X16661))|(~class_Enum_Oenum(X16662)|~class_Enum_Oenum(X16663)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__all__fun__def])])])). 4.46/4.70 fof(c_0_6118, plain, ![X17266, X17267, X17268]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X17267,X17268)),X17266))|c_Enum_Oex__n__lists(X17268,hAPP(hAPP(c_COMBB(tc_fun(X17267,X17268),tc_HOL_Obool,tc_List_Olist(X17268)),X17266),hAPP(hAPP(c_COMBB(tc_fun(X17267,tc_Option_Ooption(X17268)),tc_fun(X17267,X17268),tc_List_Olist(X17268)),c_Fun_Ocomp(tc_Option_Ooption(X17268),X17268,X17267,c_Option_Othe(X17268))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X17267,X17268)),tc_fun(X17267,tc_Option_Ooption(X17268)),tc_List_Olist(X17268)),c_Map_Omap__of(X17267,X17268)),hAPP(c_List_Ozip(X17267,X17268),c_Enum_Oenum__class_Oenum(X17267))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17267)),c_Enum_Oenum__class_Oenum(X17267)))|(~class_Enum_Oenum(X17268)|~class_Enum_Oenum(X17267)))&(~c_Enum_Oex__n__lists(X17268,hAPP(hAPP(c_COMBB(tc_fun(X17267,X17268),tc_HOL_Obool,tc_List_Olist(X17268)),X17266),hAPP(hAPP(c_COMBB(tc_fun(X17267,tc_Option_Ooption(X17268)),tc_fun(X17267,X17268),tc_List_Olist(X17268)),c_Fun_Ocomp(tc_Option_Ooption(X17268),X17268,X17267,c_Option_Othe(X17268))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X17267,X17268)),tc_fun(X17267,tc_Option_Ooption(X17268)),tc_List_Olist(X17268)),c_Map_Omap__of(X17267,X17268)),hAPP(c_List_Ozip(X17267,X17268),c_Enum_Oenum__class_Oenum(X17267))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17267)),c_Enum_Oenum__class_Oenum(X17267)))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X17267,X17268)),X17266))|(~class_Enum_Oenum(X17268)|~class_Enum_Oenum(X17267)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_enum__ex__fun__def])])])])). 4.46/4.70 cnf(c_0_6119, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4907, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6120, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X1,X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X1,X3)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_4908])). 4.46/4.70 cnf(c_0_6121, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X1,X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X1,X3)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_4909])). 4.46/4.70 cnf(c_0_6122, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X4)))))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_4910])). 4.46/4.70 cnf(c_0_6123, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[c_0_4911, c_0_4912]), ['final']). 4.46/4.70 cnf(c_0_6124, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk224_4(X1,X2,X3,X4)),esk225_4(X1,X2,X3,X4)))|hBOOL(hAPP(hAPP(hAPP(X1,esk223_4(X1,X2,X3,X4)),esk224_4(X1,X2,X3,X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk225_4(X1,X2,X3,X4)),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))|hAPP(esk223_4(X1,X2,X3,X4),esk225_4(X1,X2,X3,X4))!=c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))), inference(split_conjunct,[status(thm)],[c_0_4913])). 4.46/4.70 cnf(c_0_6125, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))),c_Groups_Ozero__class_Ozero(X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4914, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6126, plain, ![X11506, X11507, X11508, X11509, X11510]:(~class_Groups_Ocomm__monoid__mult(X11510)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11509),X11508))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11509),X11507))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11510),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X11510,X11509,c_Groups_Otimes__class_Otimes(X11510)),X11506),c_Groups_Oone__class_Oone(X11510)),X11508)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X11510,X11509,c_Groups_Otimes__class_Otimes(X11510)),X11506),c_Groups_Oone__class_Oone(X11510)),X11507))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11510),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X11510,X11509,c_Groups_Otimes__class_Otimes(X11510)),X11506),c_Groups_Oone__class_Oone(X11510)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11509,tc_HOL_Obool)),X11508),X11507))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X11510,X11509,c_Groups_Otimes__class_Otimes(X11510)),X11506),c_Groups_Oone__class_Oone(X11510)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11509,tc_HOL_Obool)),X11508),X11507)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__Un__Int])])). 4.46/4.70 cnf(c_0_6127, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X3),hAPP(c_List_Orev(X1),c_List_OtakeWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),X2)))=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),hAPP(c_List_Orev(X1),X2)))),hAPP(c_List_Orev(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2)))), inference(rw,[status(thm)],[c_0_4915, c_0_4916])). 4.46/4.70 fof(c_0_6128, plain, ![X2352, X2353, X2354, X2355, X2356]:((hBOOL(hAPP(hAPP(c_member(X2355),esk59_5(X2352,X2353,X2354,X2355,X2356)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2355,tc_HOL_Obool)),X2354),X2353)))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2356),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X2356,X2355,c_Groups_Otimes__class_Otimes(X2356)),X2352),c_Groups_Oone__class_Oone(X2356)),X2354)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X2356,X2355,c_Groups_Otimes__class_Otimes(X2356)),X2352),c_Groups_Oone__class_Oone(X2356)),X2353))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X2356,X2355,c_Groups_Otimes__class_Otimes(X2356)),X2352),c_Groups_Oone__class_Oone(X2356)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2355,tc_HOL_Obool)),X2354),X2353))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2355),X2353))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2355),X2354))|~class_Groups_Ocomm__monoid__mult(X2356))&(c_Groups_Oone__class_Oone(X2356)!=hAPP(X2352,esk59_5(X2352,X2353,X2354,X2355,X2356))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2356),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X2356,X2355,c_Groups_Otimes__class_Otimes(X2356)),X2352),c_Groups_Oone__class_Oone(X2356)),X2354)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X2356,X2355,c_Groups_Otimes__class_Otimes(X2356)),X2352),c_Groups_Oone__class_Oone(X2356)),X2353))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X2356,X2355,c_Groups_Otimes__class_Otimes(X2356)),X2352),c_Groups_Oone__class_Oone(X2356)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2355,tc_HOL_Obool)),X2354),X2353))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2355),X2353))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2355),X2354))|~class_Groups_Ocomm__monoid__mult(X2356))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__Un__one])])])])])). 4.46/4.70 cnf(c_0_6129, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4917, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6130, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4918, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6131, plain, (hBOOL(hAPP(X1,esk456_4(X2,X3,X4,X1)))|c_Wellfounded_Owf(X2,hAPP(c_Set_OCollect(tc_prod(X2,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X2),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X1))),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,X2),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,X2),tc_fun(X2,tc_HOL_Obool)),X2),c_COMBB(X2,tc_HOL_Obool,X2)),c_fequal)),X3)))))), inference(split_conjunct,[status(thm)],[c_0_4894])). 4.46/4.70 fof(c_0_6132, plain, ![X3904, X3905, X3906, X3907]:(~c_Fun_Oinj__on(X3907,tc_fun(tc_fun(X3907,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3907,tc_fun(tc_prod(X3907,X3907),tc_HOL_Obool),tc_fun(tc_fun(X3907,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3907,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X3907,X3907),tc_HOL_Obool),tc_fun(tc_fun(X3907,tc_HOL_Obool),tc_HOL_Obool)),X3907),c_Equiv__Relations_Oquotient(X3907)),hAPP(hAPP(c_COMBC(X3907,tc_fun(X3907,tc_HOL_Obool),tc_fun(X3907,tc_HOL_Obool)),c_Set_Oinsert(X3907)),c_Orderings_Obot__class_Obot(tc_fun(X3907,tc_HOL_Obool))))),X3906),X3905)|(~hBOOL(hAPP(hAPP(c_member(X3907),X3904),X3905))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X3907,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3907),X3905),X3906)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3907),hAPP(hAPP(c_Set_Oinsert(X3907),X3904),c_Orderings_Obot__class_Obot(tc_fun(X3907,tc_HOL_Obool)))),X3906))=hAPP(hAPP(c_Equiv__Relations_Oquotient(X3907),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3907,tc_HOL_Obool)),X3905),hAPP(hAPP(c_Set_Oinsert(X3907),X3904),c_Orderings_Obot__class_Obot(tc_fun(X3907,tc_HOL_Obool))))),X3906))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_quotient__diff1])])])). 4.46/4.70 cnf(c_0_6133, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))|~class_Int_Onumber__ring(X1)|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4919, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6134, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4920, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6135, plain, ![X9299, X9300, X9301, X9302, X9303]:((hBOOL(hAPP(hAPP(c_member(X9302),esk267_5(X9299,X9300,X9301,X9302,X9303)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9302,tc_HOL_Obool)),X9301),X9300)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9302,X9303),X9299),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9302,tc_HOL_Obool)),X9301),X9300))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9303),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9302,X9303),X9299),X9301)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9302,X9303),X9299),X9300))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9302,X9303),X9299),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9302,tc_HOL_Obool)),X9301),X9300)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9302),X9300))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9302),X9301))|~class_Fields_Ofield(X9303))&(c_Groups_Ozero__class_Ozero(X9303)=hAPP(X9299,esk267_5(X9299,X9300,X9301,X9302,X9303))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9302,X9303),X9299),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9302,tc_HOL_Obool)),X9301),X9300))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9303),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9302,X9303),X9299),X9301)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9302,X9303),X9299),X9300))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9302,X9303),X9299),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9302,tc_HOL_Obool)),X9301),X9300)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9302),X9300))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9302),X9301))|~class_Fields_Ofield(X9303))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__Un])])])])])). 4.46/4.70 cnf(c_0_6136, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X5),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X6)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X7)),X2))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X7),X2))))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X5,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X7)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))), inference(split_conjunct,[status(thm)],[c_0_4921])). 4.46/4.70 cnf(c_0_6137, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X5),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X6)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X7)),X2))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X7),X2))))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X5,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X6),X7)))), inference(split_conjunct,[status(thm)],[c_0_4922])). 4.46/4.70 cnf(c_0_6138, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X3))))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4923, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6139, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)))=hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4924, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6140, plain, ![X10538, X10539, X10540, X10541, X10542]:(~class_Groups_Ocomm__monoid__mult(X10542)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10541),X10540))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10542),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10542,X10541,c_Groups_Otimes__class_Otimes(X10542)),X10539),c_Groups_Oone__class_Oone(X10542)),X10540)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10542,X10541,c_Groups_Otimes__class_Otimes(X10542)),X10538),c_Groups_Oone__class_Oone(X10542)),X10540))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10542,X10541,c_Groups_Otimes__class_Otimes(X10542)),hAPP(hAPP(c_COMBS(X10541,X10542,X10542),hAPP(hAPP(c_COMBB(X10542,tc_fun(X10542,X10542),X10541),c_Groups_Otimes__class_Otimes(X10542)),X10539)),X10538)),c_Groups_Oone__class_Oone(X10542)),X10540))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__distrib])])])). 4.46/4.70 cnf(c_0_6141, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(X5,X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),X6)),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Ocomm__monoid__mult(X4)), inference(split_conjunct,[status(thm)],[c_0_4925])). 4.46/4.70 cnf(c_0_6142, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))|hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))), inference(split_conjunct,[status(thm)],[c_0_4926])). 4.46/4.70 cnf(c_0_6143, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4927, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6144, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4928, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6145, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4929, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6146, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4930, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6147, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X3,X3),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,X3),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X3)),X4)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X3,tc_Nat_Onat),X4),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),hAPP(X4,X1)),hAPP(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~class_Groups_Oab__group__add(X3)), inference(split_conjunct,[status(thm)],[c_0_4931])). 4.46/4.70 fof(c_0_6148, plain, ![X15962, X15963, X15964, X15965, X15966, X15967]:(~class_Groups_Ocomm__monoid__mult(X15967)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X15966,X15965),X15967),hAPP(c_Product__Type_Oprod_Oprod__case(X15966,X15965,X15967),X15964)),hAPP(hAPP(c_Product__Type_OSigma(X15966,X15965),X15962),hAPP(c_COMBK(tc_fun(X15965,tc_HOL_Obool),X15966),X15963)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X15966,X15967),hAPP(hAPP(c_COMBC(X15966,tc_fun(X15965,tc_HOL_Obool),X15967),hAPP(hAPP(c_COMBB(tc_fun(X15965,X15967),tc_fun(tc_fun(X15965,tc_HOL_Obool),X15967),X15966),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X15965,X15967)),X15964)),X15963)),X15962)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__cartesian__product])])). 4.46/4.70 fof(c_0_6149, plain, ![X9967, X9968, X9969, X9970, X9971, X9972]:(~class_Groups_Ocomm__monoid__add(X9972)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X9971,X9970),X9972),hAPP(c_Product__Type_Oprod_Oprod__case(X9971,X9970,X9972),X9969)),hAPP(hAPP(c_Product__Type_OSigma(X9971,X9970),X9967),hAPP(c_COMBK(tc_fun(X9970,tc_HOL_Obool),X9971),X9968)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9971,X9972),hAPP(hAPP(c_COMBC(X9971,tc_fun(X9970,tc_HOL_Obool),X9972),hAPP(hAPP(c_COMBB(tc_fun(X9970,X9972),tc_fun(tc_fun(X9970,tc_HOL_Obool),X9972),X9971),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9970,X9972)),X9969)),X9968)),X9967)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__cartesian__product])])). 4.46/4.70 cnf(c_0_6150, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X1)))))|hAPP(c_Nat_OSuc,X1)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)), inference(rw,[status(thm)],[c_0_4932, c_0_4443])). 4.46/4.70 cnf(c_0_6151, plain, (hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),X2)),X3)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4933, c_0_4531]), c_0_4531]), c_0_4934]), c_0_4531]), ['final']). 4.46/4.70 cnf(c_0_6152, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4935, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6153, plain, ![X16020, X16021, X16022, X16023, X16024, X16025]:((hBOOL(hAPP(hAPP(c_member(X16024),esk465_6(X16020,X16021,X16022,X16023,X16024,X16025)),X16023))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X16024,X16022),X16025),hAPP(c_Product__Type_Oprod_Oprod__case(X16024,X16022,X16025),X16020)),hAPP(hAPP(c_Product__Type_OSigma(X16024,X16022),X16023),X16021))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16024,X16025),hAPP(hAPP(c_COMBS(X16024,tc_fun(X16022,tc_HOL_Obool),X16025),hAPP(hAPP(c_COMBB(tc_fun(X16022,X16025),tc_fun(tc_fun(X16022,tc_HOL_Obool),X16025),X16024),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16022,X16025)),X16020)),X16021)),X16023)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16024),X16023))|~class_Groups_Ocomm__monoid__mult(X16025))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16022),hAPP(X16021,esk465_6(X16020,X16021,X16022,X16023,X16024,X16025))))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X16024,X16022),X16025),hAPP(c_Product__Type_Oprod_Oprod__case(X16024,X16022,X16025),X16020)),hAPP(hAPP(c_Product__Type_OSigma(X16024,X16022),X16023),X16021))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16024,X16025),hAPP(hAPP(c_COMBS(X16024,tc_fun(X16022,tc_HOL_Obool),X16025),hAPP(hAPP(c_COMBB(tc_fun(X16022,X16025),tc_fun(tc_fun(X16022,tc_HOL_Obool),X16025),X16024),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16022,X16025)),X16020)),X16021)),X16023)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16024),X16023))|~class_Groups_Ocomm__monoid__mult(X16025))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__Sigma])])])])])). 4.46/4.70 fof(c_0_6154, plain, ![X14275, X14276, X14277, X14278, X14279]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X14279),tc_List_Olist(X14279))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14279),tc_List_Olist(X14279)),hAPP(hAPP(c_List_Oappend(X14279),X14278),X14277)),hAPP(hAPP(c_List_Oappend(X14279),X14278),X14276))),c_List_Olexord(X14279,X14275)))|(hBOOL(hAPP(hAPP(c_member(tc_prod(X14279,X14279)),hAPP(hAPP(c_Product__Type_OPair(X14279,X14279),esk419_5(X14275,X14276,X14277,X14278,X14279)),esk419_5(X14275,X14276,X14277,X14278,X14279))),X14275))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X14279),tc_List_Olist(X14279))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14279),tc_List_Olist(X14279)),X14277),X14276)),c_List_Olexord(X14279,X14275))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lexord__append__leftD])])])])). 4.46/4.70 fof(c_0_6155, plain, ![X14390, X14391, X14392, X14393, X14394, X14395, X14396, X14397]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X14397,X14396),tc_HOL_Obool)),X14395),hAPP(hAPP(c_Product__Type_OSigma(X14397,X14396),X14394),hAPP(c_COMBK(tc_fun(X14396,tc_HOL_Obool),X14397),X14393))))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X14396,X14392),tc_HOL_Obool)),X14391),hAPP(hAPP(c_Product__Type_OSigma(X14396,X14392),X14393),hAPP(c_COMBK(tc_fun(X14392,tc_HOL_Obool),X14396),X14390))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X14397,X14392),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X14397,X14396,X14392),X14395),X14391)),hAPP(hAPP(c_Product__Type_OSigma(X14397,X14392),X14394),hAPP(c_COMBK(tc_fun(X14392,tc_HOL_Obool),X14397),X14390)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__comp__subset__Sigma])])])). 4.46/4.70 cnf(c_0_6156, plain, (hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))=hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2)),c_Int_Ointrel))), inference(split_conjunct,[status(thm)],[c_0_4936])). 4.46/4.70 cnf(c_0_6157, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4))),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3))|~c_Relation_Orefl__on(X1,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_4937])). 4.46/4.70 fof(c_0_6158, plain, ![X3004, X3005, X3006, X3007, X3008]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3008,X3007),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3006),X3005)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3007))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3004),X3008),X3007),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3004),X3006)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3004),X3005)),X3007))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3004),X3005),X3007)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__nat__rel__mult1__eq])])])). 4.46/4.70 cnf(c_0_6159, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBS(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X4))),X5)),c_Groups_Ozero__class_Ozero(X1))),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4938])). 4.46/4.70 cnf(c_0_6160, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),X6)),X3)=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X6),hAPP(c_Finite__Set_Ocard(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Ocomm__monoid__mult(X4)), inference(split_conjunct,[status(thm)],[c_0_4925])). 4.46/4.70 fof(c_0_6161, plain, ![X7427, X7428, X7429]:(~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X7429),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X7429))),X7428)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7427),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X7429))),X7428)))|hAPP(hAPP(c_List_Onth(tc_List_Olist(X7429)),X7428),X7427)=hAPP(hAPP(c_List_Omap(tc_List_Olist(X7429),X7429),hAPP(hAPP(c_COMBC(tc_List_Olist(X7429),tc_Nat_Onat,X7429),c_List_Onth(X7429)),X7427)),hAPP(c_List_Ofilter(tc_List_Olist(X7429),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X7429)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7427)),c_Nat_Osize__class_Osize(tc_List_Olist(X7429)))),c_List_Otranspose(X7429,X7428))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transpose__column])])])). 4.46/4.70 fof(c_0_6162, plain, ![X9581, X9582, X9583, X9584, X9585]:(~c_Relation_Osingle__valued(X9585,X9585,X9584)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9585,X9585)),hAPP(hAPP(c_Product__Type_OPair(X9585,X9585),X9583),X9582)),c_Transitive__Closure_Ortrancl(X9585,X9584)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9585,X9585)),hAPP(hAPP(c_Product__Type_OPair(X9585,X9585),X9583),X9581)),c_Transitive__Closure_Ortrancl(X9585,X9584)))|(hBOOL(hAPP(hAPP(c_member(tc_prod(X9585,X9585)),hAPP(hAPP(c_Product__Type_OPair(X9585,X9585),X9581),X9582)),c_Transitive__Closure_Ortrancl(X9585,X9584)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X9585,X9585)),hAPP(hAPP(c_Product__Type_OPair(X9585,X9585),X9582),X9581)),c_Transitive__Closure_Ortrancl(X9585,X9584))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_single__valued__confluent])])])). 4.46/4.70 cnf(c_0_6163, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X3),hAPP(hAPP(c_List_Omap(X1,X3),X4),c_Hilbert__Choice_OEps(tc_List_Olist(X1),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_List_Oset(X1))),X2))),c_List_Odistinct(X1)))))=c_Nitpick_Osetsum_H(X1,X3,X4,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Groups_Ocomm__monoid__add(X3)), inference(split_conjunct,[status(thm)],[c_0_4939])). 4.46/4.70 cnf(c_0_6164, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_4940]), ['final']). 4.46/4.70 cnf(c_0_6165, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4941, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6166, plain, ![X4251, X4252, X4253, X4254, X4255]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4255,X4254),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4253),X4252)))|(X4254=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4251),X4255),X4254),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4251),X4253)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4251),X4252)),X4254))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4251),X4252),X4254)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult1__lemma])])). 4.46/4.70 fof(c_0_6167, plain, ![X10063, X10064, X10065, X10066, X10067, X10068, X10069, X10070]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10068)),X10067)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10070)),X10069)|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10070)),X10066)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10068)),X10067)|(hBOOL(hAPP(hAPP(c_member(X10068),X10065),hAPP(c_List_Oset(X10068),X10067)))|(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10068,tc_Option_Ooption(X10070)),hAPP(c_Map_Omap__of(X10068,X10070),hAPP(hAPP(c_List_Ozip(X10068,X10070),X10067),X10066))),X10065),hAPP(c_Option_Ooption_OSome(X10070),X10063))!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10068,tc_Option_Ooption(X10070)),hAPP(c_Map_Omap__of(X10068,X10070),hAPP(hAPP(c_List_Ozip(X10068,X10070),X10067),X10069))),X10065),hAPP(c_Option_Ooption_OSome(X10070),X10064))|hAPP(c_Map_Omap__of(X10068,X10070),hAPP(hAPP(c_List_Ozip(X10068,X10070),X10067),X10066))=hAPP(c_Map_Omap__of(X10068,X10070),hAPP(hAPP(c_List_Ozip(X10068,X10070),X10067),X10069)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__zip__upd])])])). 4.46/4.70 cnf(c_0_6168, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X3)),X1)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X1,esk40_3(X2,X3,X1))),hAPP(X3,esk40_3(X2,X3,X1))))), inference(split_conjunct,[status(thm)],[c_0_4942])). 4.46/4.70 cnf(c_0_6169, plain, (c_Groups_Oone__class_Oone(X2)=hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|X1!=hAPP(c_Groups_Ouminus__class_Ouminus(X2),c_Groups_Oone__class_Oone(X2))|~class_Rings_Oring__1__no__zero__divisors(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4943, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6170, plain, ![X1039, X1040, X1041, X1042, X1043, X1044, X1045]:(~c_Fun_Oinj__on(X1045,X1044,X1043,c_Orderings_Otop__class_Otop(tc_fun(X1045,tc_HOL_Obool)))|(hAPP(hAPP(c_Map_Omap__of(X1045,X1042),X1041),X1040)!=hAPP(c_Option_Ooption_OSome(X1042),X1039)|hAPP(c_Option_Ooption_OSome(X1042),X1039)=hAPP(hAPP(c_Map_Omap__of(X1044,X1042),hAPP(hAPP(c_List_Omap(tc_prod(X1045,X1042),tc_prod(X1044,X1042)),hAPP(c_Product__Type_Oprod_Oprod__case(X1045,X1042,tc_prod(X1044,X1042)),hAPP(hAPP(c_COMBB(X1044,tc_fun(X1042,tc_prod(X1044,X1042)),X1045),c_Product__Type_OPair(X1044,X1042)),X1043))),X1041)),hAPP(X1043,X1040)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__mapk__SomeI])])])). 4.46/4.70 fof(c_0_6171, plain, ![X2169, X2170, X2171, X2172]:(~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X2172),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X2172))),X2171)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2170),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2172))),c_List_Otranspose(X2172,X2171))))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2169),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2172))),hAPP(c_List_Ofilter(tc_List_Olist(X2172),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X2172)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2170)),c_Nat_Osize__class_Osize(tc_List_Olist(X2172)))),X2171))))|hAPP(hAPP(c_List_Onth(X2172),hAPP(hAPP(c_List_Onth(tc_List_Olist(X2172)),c_List_Otranspose(X2172,X2171)),X2170)),X2169)=hAPP(hAPP(c_List_Onth(X2172),hAPP(hAPP(c_List_Onth(tc_List_Olist(X2172)),X2171),X2169)),X2170)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__nth__transpose__sorted])])])). 4.46/4.70 cnf(c_0_6172, plain, (c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),X2))),c_Orderings_Oord__class_Oless__eq(X1))))=c_Complete__Lattice_OInf__class_OInf(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4944, c_0_4945]), c_0_4531])). 4.46/4.70 cnf(c_0_6173, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),hAPP(c_COMBC(X2,X1,tc_HOL_Obool),X4)))=hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),X3))),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4946, c_0_4945]), c_0_4531]), ['final']). 4.46/4.70 cnf(c_0_6174, plain, (c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),X2))),hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1)))))=c_Complete__Lattice_OSup__class_OSup(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4947, c_0_4945]), c_0_4531])). 4.46/4.70 fof(c_0_6175, plain, ![X6167, X6168, X6169, X6170, X6171, X6172]:(~class_Groups_Ocomm__monoid__add(X6172)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6170,X6172),hAPP(hAPP(c_COMBC(X6170,tc_fun(X6171,tc_HOL_Obool),X6172),hAPP(hAPP(c_COMBB(tc_fun(X6171,X6172),tc_fun(tc_fun(X6171,tc_HOL_Obool),X6172),X6170),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6171,X6172)),hAPP(c_COMBC(X6171,X6170,X6172),X6169))),X6167)),X6168)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6171,X6172),hAPP(hAPP(c_COMBC(X6171,tc_fun(X6170,tc_HOL_Obool),X6172),hAPP(hAPP(c_COMBB(tc_fun(X6170,X6172),tc_fun(tc_fun(X6170,tc_HOL_Obool),X6172),X6171),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6170,X6172)),X6169)),X6168)),X6167)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__commute])])). 4.46/4.70 cnf(c_0_6176, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1)),c_Int_Onat)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))), inference(rw,[status(thm)],[c_0_4948, c_0_4443])). 4.46/4.70 cnf(c_0_6177, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1)),c_Int_Onat)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))), inference(rw,[status(thm)],[c_0_4949, c_0_4443])). 4.46/4.70 cnf(c_0_6178, plain, (hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))=hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_4950]), ['final']). 4.46/4.70 cnf(c_0_6179, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))), inference(split_conjunct,[status(thm)],[c_0_4883])). 4.46/4.70 cnf(c_0_6180, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))), inference(split_conjunct,[status(thm)],[c_0_4884])). 4.46/4.70 cnf(c_0_6181, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4951, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6182, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4952, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6183, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Groups_Omonoid__mult(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4953, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6184, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4954, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6185, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),X2)|~class_Groups_Omonoid__mult(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4955, c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6186, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))=hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4956, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4836]), ['final']). 4.46/4.70 cnf(c_0_6187, plain, (c_Relation_Orefl__on(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))),esk74_3(X3,X2,X1)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk73_3(X3,X2,X1)),esk73_3(X3,X2,X1))),X3))), inference(split_conjunct,[status(thm)],[c_0_4937])). 4.46/4.70 fof(c_0_6188, plain, ![X6713, X6714, X6715, X6716, X6717, X6718]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6718)),X6717)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6716)),X6715)))|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6718,tc_Option_Ooption(X6716)),c_Map_Omap__upds(X6718,X6716,X6714,X6717,X6715)),X6713),hAPP(c_Option_Ooption_OSome(X6716),hAPP(hAPP(c_List_Onth(X6716),X6715),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6718)),X6717))))=c_Map_Omap__upds(X6718,X6716,X6714,hAPP(hAPP(c_List_Oappend(X6718),X6717),hAPP(hAPP(c_List_Olist_OCons(X6718),X6713),c_List_Olist_ONil(X6718))),X6715)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__upds__append1])])])). 4.46/4.70 fof(c_0_6189, plain, ![X10940, X10941, X10942, X10943, X10944, X10945]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10945,X10945)),hAPP(hAPP(c_Product__Type_OPair(X10945,X10945),X10944),X10943)),c_Transitive__Closure_Ortrancl(X10945,X10942)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10945),tc_List_Olist(X10945))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10945),tc_List_Olist(X10945)),X10941),X10940)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10945),c_List_Olistrel1(X10945,X10942))))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10945),tc_List_Olist(X10945))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10945),tc_List_Olist(X10945)),hAPP(hAPP(c_List_Olist_OCons(X10945),X10944),X10941)),hAPP(hAPP(c_List_Olist_OCons(X10945),X10943),X10940))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10945),c_List_Olistrel1(X10945,X10942)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__listrel1__ConsI2])])])). 4.46/4.70 cnf(c_0_6190, plain, (hAPP(c_Set_Ovimage(X4,X1,hAPP(hAPP(c_COMBC(X4,X1,X1),hAPP(hAPP(c_COMBC(X4,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X4),c_If(X1)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X5))),X6)),X2)),X3)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X5)|hBOOL(hAPP(hAPP(c_member(X1),X6),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4957])). 4.46/4.70 fof(c_0_6191, plain, ![X12313, X12314, X12315, X12316, X12317]:(~class_Groups_Ocomm__monoid__add(X12317)|hAPP(c_List_Omonoid__add__class_Olistsum(X12317),hAPP(hAPP(c_List_Omap(X12316,X12317),hAPP(hAPP(c_COMBS(X12316,X12317,X12317),hAPP(hAPP(c_COMBB(X12317,tc_fun(X12317,X12317),X12316),c_Groups_Oplus__class_Oplus(X12317)),X12315)),X12314)),X12313))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12317),hAPP(c_List_Omonoid__add__class_Olistsum(X12317),hAPP(hAPP(c_List_Omap(X12316,X12317),X12315),X12313))),hAPP(c_List_Omonoid__add__class_Olistsum(X12317),hAPP(hAPP(c_List_Omap(X12316,X12317),X12314),X12313)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__addf])])])). 4.46/4.70 fof(c_0_6192, plain, ![X1226, X1227, X1228, X1229, X1230]:((hBOOL(hAPP(hAPP(c_member(X1229),esk31_5(X1226,X1227,X1228,X1229,X1230)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1229,tc_HOL_Obool)),X1228),X1227)))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1230),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1229,X1230),X1226),X1228)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1229,X1230),X1226),X1227))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1229,X1230),X1226),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1229,tc_HOL_Obool)),X1228),X1227))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1229),X1227))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1229),X1228))|~class_Groups_Ocomm__monoid__mult(X1230))&(c_Groups_Oone__class_Oone(X1230)!=hAPP(X1226,esk31_5(X1226,X1227,X1228,X1229,X1230))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1230),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1229,X1230),X1226),X1228)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1229,X1230),X1226),X1227))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1229,X1230),X1226),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1229,tc_HOL_Obool)),X1228),X1227))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1229),X1227))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1229),X1228))|~class_Groups_Ocomm__monoid__mult(X1230))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__Un__one])])])])])). 4.46/4.70 fof(c_0_6193, plain, ![X4296, X4297, X4298, X4299, X4300]:((hBOOL(hAPP(hAPP(c_member(X4299),esk118_5(X4296,X4297,X4298,X4299,X4300)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4299,tc_HOL_Obool)),X4298),X4297)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4300),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4299,X4300),X4296),X4298)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4299,X4300),X4296),X4297))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4299,X4300),X4296),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4299,tc_HOL_Obool)),X4298),X4297))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4299),X4297))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4299),X4298))|~class_Groups_Ocomm__monoid__add(X4300))&(c_Groups_Ozero__class_Ozero(X4300)!=hAPP(X4296,esk118_5(X4296,X4297,X4298,X4299,X4300))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4300),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4299,X4300),X4296),X4298)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4299,X4300),X4296),X4297))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4299,X4300),X4296),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4299,tc_HOL_Obool)),X4298),X4297))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4299),X4297))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4299),X4298))|~class_Groups_Ocomm__monoid__add(X4300))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__Un__zero])])])])])). 4.46/4.70 fof(c_0_6194, plain, ![X4513, X4514, X4515, X4516, X4517]:((hBOOL(hAPP(hAPP(c_member(X4516),esk124_5(X4513,X4514,X4515,X4516,X4517)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4516,tc_HOL_Obool)),X4515),X4514)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4516,X4517),X4513),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4516,tc_HOL_Obool)),X4515),X4514))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4517),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4516,X4517),X4513),X4515)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4516,X4517),X4513),X4514))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4516),X4514))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4516),X4515))|~class_Groups_Ocomm__monoid__mult(X4517))&(hAPP(X4513,esk124_5(X4513,X4514,X4515,X4516,X4517))!=c_Groups_Oone__class_Oone(X4517)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4516,X4517),X4513),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4516,tc_HOL_Obool)),X4515),X4514))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4517),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4516,X4517),X4513),X4515)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4516,X4517),X4513),X4514))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4516),X4514))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4516),X4515))|~class_Groups_Ocomm__monoid__mult(X4517))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod_Ounion__inter__neutral])])])])])). 4.46/4.70 fof(c_0_6195, plain, ![X14515, X14516, X14517, X14518, X14519]:((hBOOL(hAPP(hAPP(c_member(X14518),esk426_5(X14515,X14516,X14517,X14518,X14519)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14518,tc_HOL_Obool)),X14517),X14516)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14518,X14519),X14515),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14518,tc_HOL_Obool)),X14517),X14516))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14519),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14518,X14519),X14515),X14517)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14518,X14519),X14515),X14516))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14518),X14516))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14518),X14517))|~class_Groups_Ocomm__monoid__add(X14519))&(hAPP(X14515,esk426_5(X14515,X14516,X14517,X14518,X14519))!=c_Groups_Ozero__class_Ozero(X14519)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14518,X14519),X14515),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14518,tc_HOL_Obool)),X14517),X14516))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14519),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14518,X14519),X14515),X14517)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14518,X14519),X14515),X14516))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14518),X14516))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14518),X14517))|~class_Groups_Ocomm__monoid__add(X14519))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum_Ounion__inter__neutral])])])])])). 4.46/4.70 fof(c_0_6196, plain, ![X9155, X9156, X9157, X9158, X9159]:(~class_Groups_Oab__group__add(X9159)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9159),hAPP(c_List_Omonoid__add__class_Olistsum(X9159),hAPP(hAPP(c_List_Omap(X9158,X9159),X9157),X9155))),hAPP(c_List_Omonoid__add__class_Olistsum(X9159),hAPP(hAPP(c_List_Omap(X9158,X9159),X9156),X9155)))=hAPP(c_List_Omonoid__add__class_Olistsum(X9159),hAPP(hAPP(c_List_Omap(X9158,X9159),hAPP(hAPP(c_COMBS(X9158,X9159,X9159),hAPP(hAPP(c_COMBB(X9159,tc_fun(X9159,X9159),X9158),c_Groups_Ominus__class_Ominus(X9159)),X9157)),X9156)),X9155))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__subtractf])])])). 4.46/4.70 cnf(c_0_6197, plain, (hAPP(hAPP(c_HOL_OLet(X2,X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(hAPP(c_COMBS(X2,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X2),c_Groups_Otimes__class_Otimes(X2)),hAPP(c_Groups_Otimes__class_Otimes(X2),X3))),c_COMBI(X2)))=hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[c_0_4958, c_0_4471])). 4.46/4.70 cnf(c_0_6198, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X4,X1,hAPP(hAPP(c_COMBC(X4,X1,X1),hAPP(hAPP(c_COMBC(X4,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X4),c_If(X1)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X5))),X6)),X2)),X3)|hBOOL(hAPP(hAPP(c_member(X1),X6),X3))), inference(split_conjunct,[status(thm)],[c_0_4957])). 4.46/4.70 fof(c_0_6199, plain, ![X2694, X2695]:(((c_Wellfounded_Owf(X2695,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool),tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool)),X2694))|~c_FunDef_Oreduction__pair(X2695,X2694))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X2695,X2695,X2695),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool),tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool)),X2694)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool),tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool)),X2694))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool),tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool)),X2694)))|~c_FunDef_Oreduction__pair(X2695,X2694)))&(~c_Wellfounded_Owf(X2695,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool),tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool)),X2694))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X2695,X2695,X2695),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool),tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool)),X2694)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool),tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool)),X2694))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool),tc_fun(tc_prod(X2695,X2695),tc_HOL_Obool)),X2694)))|c_FunDef_Oreduction__pair(X2695,X2694))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pair__def])])])). 4.46/4.70 cnf(c_0_6200, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olists(X1,X3)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_List_Olist(X1)),c_List_Olists(X1,X3)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))), inference(split_conjunct,[status(thm)],[c_0_4959])). 4.46/4.70 cnf(c_0_6201, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))=c_Nitpick_Oprod(X1,X2,X3,X4)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4960, c_0_4945]), c_0_4945]), c_0_4961]), c_0_4531]), ['final']). 4.46/4.70 cnf(c_0_6202, plain, (X2=X3|c_List_Oconcat(X1,X2)!=c_List_Oconcat(X1,X3)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),esk502_3(X3,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4962])). 4.46/4.70 cnf(c_0_6203, plain, (X3=X2|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),esk18_3(X2,X3,X1)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)|c_List_Oconcat(X1,X2)!=c_List_Oconcat(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_4963])). 4.46/4.70 fof(c_0_6204, plain, ![X16586, X16587, X16588, X16589, X16590]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X16590,X16590)),hAPP(hAPP(c_Product__Type_OPair(X16590,X16590),X16589),esk484_5(X16586,X16587,X16588,X16589,X16590))),c_Transitive__Closure_Ortrancl(X16590,X16587)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X16590,X16590)),hAPP(hAPP(c_Product__Type_OPair(X16590,X16590),X16589),X16588)),c_Transitive__Closure_Ortrancl(X16590,X16587)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16590,X16590)),hAPP(hAPP(c_Product__Type_OPair(X16590,X16590),X16589),X16588)),c_Transitive__Closure_Ortrancl(X16590,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X16590,X16590),tc_HOL_Obool)),X16587),X16586)))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X16590,X16590)),hAPP(hAPP(c_Product__Type_OPair(X16590,X16590),esk484_5(X16586,X16587,X16588,X16589,X16590)),esk485_5(X16586,X16587,X16588,X16589,X16590))),X16586))|hBOOL(hAPP(hAPP(c_member(tc_prod(X16590,X16590)),hAPP(hAPP(c_Product__Type_OPair(X16590,X16590),X16589),X16588)),c_Transitive__Closure_Ortrancl(X16590,X16587)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16590,X16590)),hAPP(hAPP(c_Product__Type_OPair(X16590,X16590),X16589),X16588)),c_Transitive__Closure_Ortrancl(X16590,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X16590,X16590),tc_HOL_Obool)),X16587),X16586)))))&(esk485_5(X16586,X16587,X16588,X16589,X16590)!=esk484_5(X16586,X16587,X16588,X16589,X16590)|hBOOL(hAPP(hAPP(c_member(tc_prod(X16590,X16590)),hAPP(hAPP(c_Product__Type_OPair(X16590,X16590),X16589),X16588)),c_Transitive__Closure_Ortrancl(X16590,X16587)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16590,X16590)),hAPP(hAPP(c_Product__Type_OPair(X16590,X16590),X16589),X16588)),c_Transitive__Closure_Ortrancl(X16590,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X16590,X16590),tc_HOL_Obool)),X16587),X16586))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separatorE])])])])). 4.46/4.70 fof(c_0_6205, plain, ![X16423, X16424, X16425, X16426, X16427]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X16427,X16427)),hAPP(hAPP(c_Product__Type_OPair(X16427,X16427),esk478_5(X16423,X16424,X16425,X16426,X16427)),X16425)),c_Transitive__Closure_Ortrancl(X16427,X16424)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X16427,X16427)),hAPP(hAPP(c_Product__Type_OPair(X16427,X16427),X16426),X16425)),c_Transitive__Closure_Ortrancl(X16427,X16424)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16427,X16427)),hAPP(hAPP(c_Product__Type_OPair(X16427,X16427),X16426),X16425)),c_Transitive__Closure_Ortrancl(X16427,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X16427,X16427),tc_HOL_Obool)),X16424),X16423)))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X16427,X16427)),hAPP(hAPP(c_Product__Type_OPair(X16427,X16427),esk479_5(X16423,X16424,X16425,X16426,X16427)),esk478_5(X16423,X16424,X16425,X16426,X16427))),X16423))|hBOOL(hAPP(hAPP(c_member(tc_prod(X16427,X16427)),hAPP(hAPP(c_Product__Type_OPair(X16427,X16427),X16426),X16425)),c_Transitive__Closure_Ortrancl(X16427,X16424)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16427,X16427)),hAPP(hAPP(c_Product__Type_OPair(X16427,X16427),X16426),X16425)),c_Transitive__Closure_Ortrancl(X16427,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X16427,X16427),tc_HOL_Obool)),X16424),X16423)))))&(esk478_5(X16423,X16424,X16425,X16426,X16427)!=esk479_5(X16423,X16424,X16425,X16426,X16427)|hBOOL(hAPP(hAPP(c_member(tc_prod(X16427,X16427)),hAPP(hAPP(c_Product__Type_OPair(X16427,X16427),X16426),X16425)),c_Transitive__Closure_Ortrancl(X16427,X16424)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16427,X16427)),hAPP(hAPP(c_Product__Type_OPair(X16427,X16427),X16426),X16425)),c_Transitive__Closure_Ortrancl(X16427,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X16427,X16427),tc_HOL_Obool)),X16424),X16423))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separator__converseE])])])])). 4.46/4.70 cnf(c_0_6206, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2)),c_Int_Ointrel))|hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))!=hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_4936])). 4.46/4.70 cnf(c_0_6207, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|c_Groups_Oone__class_Oone(X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),c_Groups_Oone__class_Oone(X4))),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Ocomm__monoid__mult(X4)), inference(split_conjunct,[status(thm)],[c_0_4964])). 4.46/4.70 cnf(c_0_6208, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|c_Groups_Oone__class_Oone(X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X3),X4),X2)|~class_Groups_Ocomm__monoid__mult(X3)), inference(split_conjunct,[status(thm)],[c_0_4965]), ['final']). 4.46/4.70 cnf(c_0_6209, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),c_Groups_Ozero__class_Ozero(X4))),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Ocomm__monoid__add(X4)), inference(split_conjunct,[status(thm)],[c_0_4966])). 4.46/4.70 cnf(c_0_6210, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3)|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_4967]), ['final']). 4.46/4.70 cnf(c_0_6211, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Otrancl(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_4968])). 4.46/4.70 cnf(c_0_6212, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2))),c_COMBI(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[c_0_4969, c_0_4471])). 4.46/4.70 fof(c_0_6213, plain, ![X16268, X16269, X16270, X16271, X16272, X16273, X16274, X16275]:((hBOOL(hAPP(hAPP(c_member(X16271),esk473_8(X16268,X16269,X16270,X16271,X16272,X16273,X16274,X16275)),X16270))|(~hBOOL(hAPP(hAPP(c_member(X16271),X16268),X16270))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16271,tc_fun(X16274,tc_HOL_Obool)),X16270),hAPP(hAPP(c_COMBB(tc_fun(X16275,tc_HOL_Obool),tc_fun(X16274,tc_HOL_Obool),X16271),c_Set_Oimage(X16275,X16274,X16273)),X16269))=hAPP(c_Set_Oimage(X16275,X16274,X16273),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16271,tc_fun(X16275,tc_HOL_Obool)),X16270),X16269)))|~c_Fun_Oinj__on(X16275,X16274,X16273,X16272))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16275,tc_HOL_Obool)),hAPP(X16269,esk473_8(X16268,X16269,X16270,X16271,X16272,X16273,X16274,X16275))),X16272))|(~hBOOL(hAPP(hAPP(c_member(X16271),X16268),X16270))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16271,tc_fun(X16274,tc_HOL_Obool)),X16270),hAPP(hAPP(c_COMBB(tc_fun(X16275,tc_HOL_Obool),tc_fun(X16274,tc_HOL_Obool),X16271),c_Set_Oimage(X16275,X16274,X16273)),X16269))=hAPP(c_Set_Oimage(X16275,X16274,X16273),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16271,tc_fun(X16275,tc_HOL_Obool)),X16270),X16269)))|~c_Fun_Oinj__on(X16275,X16274,X16273,X16272))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__INT])])])])])). 4.46/4.70 cnf(c_0_6214, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4970, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6215, plain, ![X11656, X11657, X11658, X11659, X11660, X11661, X11662]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X11662,X11662)),hAPP(hAPP(c_Product__Type_OPair(X11662,X11662),X11661),X11660)),X11659))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X11662),tc_List_Olist(X11662))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X11662),tc_List_Olist(X11662)),hAPP(hAPP(c_List_Oappend(X11662),X11658),hAPP(hAPP(c_List_Olist_OCons(X11662),X11661),X11657))),hAPP(hAPP(c_List_Oappend(X11662),X11658),hAPP(hAPP(c_List_Olist_OCons(X11662),X11660),X11656)))),c_List_Olexord(X11662,X11659)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__left__rightI])])). 4.46/4.70 cnf(c_0_6216, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk189_4(X4,X3,X2,X1)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_4971])). 4.46/4.70 cnf(c_0_6217, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4972, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6218, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4973, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6219, plain, (c_Groups_Oone__class_Oone(X2)=hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|X1!=c_Groups_Oone__class_Oone(X2)|~class_Rings_Oring__1__no__zero__divisors(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4974, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6220, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(c_Set_Ovimage(X4,X1,hAPP(hAPP(c_COMBC(X4,X1,X1),hAPP(hAPP(c_COMBC(X4,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X4),c_If(X1)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X5))),X6)),X2)),X3)=X5|~hBOOL(hAPP(hAPP(c_member(X1),X6),X3))), inference(split_conjunct,[status(thm)],[c_0_4957])). 4.46/4.70 fof(c_0_6221, plain, ![X2724, X2725, X2726, X2727, X2728, X2729]:((((X2727=X2725|hBOOL(hAPP(hAPP(c_member(tc_prod(X2729,X2729)),hAPP(hAPP(c_Product__Type_OPair(X2729,X2729),X2727),X2725)),X2724))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2729),tc_List_Olist(X2729))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2729),tc_List_Olist(X2729)),hAPP(hAPP(c_List_Oappend(X2729),X2728),hAPP(hAPP(c_List_Olist_OCons(X2729),X2727),c_List_Olist_ONil(X2729)))),hAPP(hAPP(c_List_Oappend(X2729),X2726),hAPP(hAPP(c_List_Olist_OCons(X2729),X2725),c_List_Olist_ONil(X2729))))),c_List_Olistrel1(X2729,X2724))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2729),tc_List_Olist(X2729))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2729),tc_List_Olist(X2729)),X2728),X2726)),c_List_Olistrel1(X2729,X2724)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X2729,X2729)),hAPP(hAPP(c_Product__Type_OPair(X2729,X2729),X2727),X2725)),X2724))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2729),tc_List_Olist(X2729))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2729),tc_List_Olist(X2729)),hAPP(hAPP(c_List_Oappend(X2729),X2728),hAPP(hAPP(c_List_Olist_OCons(X2729),X2727),c_List_Olist_ONil(X2729)))),hAPP(hAPP(c_List_Oappend(X2729),X2726),hAPP(hAPP(c_List_Olist_OCons(X2729),X2725),c_List_Olist_ONil(X2729))))),c_List_Olistrel1(X2729,X2724)))))&((X2727=X2725|X2726=X2728|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2729),tc_List_Olist(X2729))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2729),tc_List_Olist(X2729)),hAPP(hAPP(c_List_Oappend(X2729),X2728),hAPP(hAPP(c_List_Olist_OCons(X2729),X2727),c_List_Olist_ONil(X2729)))),hAPP(hAPP(c_List_Oappend(X2729),X2726),hAPP(hAPP(c_List_Olist_OCons(X2729),X2725),c_List_Olist_ONil(X2729))))),c_List_Olistrel1(X2729,X2724))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2729),tc_List_Olist(X2729))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2729),tc_List_Olist(X2729)),X2728),X2726)),c_List_Olistrel1(X2729,X2724)))|X2726=X2728|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2729),tc_List_Olist(X2729))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2729),tc_List_Olist(X2729)),hAPP(hAPP(c_List_Oappend(X2729),X2728),hAPP(hAPP(c_List_Olist_OCons(X2729),X2727),c_List_Olist_ONil(X2729)))),hAPP(hAPP(c_List_Oappend(X2729),X2726),hAPP(hAPP(c_List_Olist_OCons(X2729),X2725),c_List_Olist_ONil(X2729))))),c_List_Olistrel1(X2729,X2724))))))&((~hBOOL(hAPP(hAPP(c_member(tc_prod(X2729,X2729)),hAPP(hAPP(c_Product__Type_OPair(X2729,X2729),X2727),X2725)),X2724))|X2726!=X2728|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2729),tc_List_Olist(X2729))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2729),tc_List_Olist(X2729)),hAPP(hAPP(c_List_Oappend(X2729),X2728),hAPP(hAPP(c_List_Olist_OCons(X2729),X2727),c_List_Olist_ONil(X2729)))),hAPP(hAPP(c_List_Oappend(X2729),X2726),hAPP(hAPP(c_List_Olist_OCons(X2729),X2725),c_List_Olist_ONil(X2729))))),c_List_Olistrel1(X2729,X2724))))&(X2727!=X2725|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2729),tc_List_Olist(X2729))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2729),tc_List_Olist(X2729)),X2728),X2726)),c_List_Olistrel1(X2729,X2724)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2729),tc_List_Olist(X2729))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2729),tc_List_Olist(X2729)),hAPP(hAPP(c_List_Oappend(X2729),X2728),hAPP(hAPP(c_List_Olist_OCons(X2729),X2727),c_List_Olist_ONil(X2729)))),hAPP(hAPP(c_List_Oappend(X2729),X2726),hAPP(hAPP(c_List_Olist_OCons(X2729),X2725),c_List_Olist_ONil(X2729))))),c_List_Olistrel1(X2729,X2724)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__listrel1__snoc__iff])])])). 4.46/4.70 cnf(c_0_6222, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X3),X4)),c_List_Olexord(X2,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(hAPP(c_List_Onth(X2),X4),X1))),X5))|hAPP(hAPP(c_List_Otake(X2),X1),X3)!=hAPP(hAPP(c_List_Otake(X2),X1),X4)), inference(split_conjunct,[status(thm)],[c_0_4971])). 4.46/4.70 cnf(c_0_6223, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),X5))))|c_Map_Omap__upds(X1,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),X6),X2),hAPP(c_Option_Ooption_OSome(X3),X7)),X5,X4)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),c_Map_Omap__upds(X1,X3,X6,X5,X4)),X2),hAPP(c_Option_Ooption_OSome(X3),X7))), inference(split_conjunct,[status(thm)],[c_0_4975])). 4.46/4.70 cnf(c_0_6224, plain, (c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X6),X7))=c_Map_Omap__upds(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X6)),X5,X7)), inference(split_conjunct,[status(thm)],[c_0_4976]), ['final']). 4.46/4.70 fof(c_0_6225, plain, ![X2574, X2575, X2576]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2576),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2575))),c_List_Otranspose(X2575,X2574))))|hAPP(hAPP(c_List_Omap(tc_List_Olist(X2575),X2575),hAPP(hAPP(c_COMBC(tc_List_Olist(X2575),tc_Nat_Onat,X2575),c_List_Onth(X2575)),X2576)),hAPP(c_List_Ofilter(tc_List_Olist(X2575),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X2575)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2576)),c_Nat_Osize__class_Osize(tc_List_Olist(X2575)))),X2574))=hAPP(hAPP(c_List_Onth(tc_List_Olist(X2575)),c_List_Otranspose(X2575,X2574)),X2576)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__transpose])])])). 4.46/4.70 cnf(c_0_6226, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),c_Groups_Oone__class_Oone(X4))),X3)=hAPP(X5,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Ocomm__monoid__mult(X4)), inference(split_conjunct,[status(thm)],[c_0_4964])). 4.46/4.70 cnf(c_0_6227, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),c_Groups_Ozero__class_Ozero(X4))),X3)=hAPP(X5,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Ocomm__monoid__add(X4)), inference(split_conjunct,[status(thm)],[c_0_4966])). 4.46/4.70 cnf(c_0_6228, plain, (c_List_OtakeWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Orev(X1),hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),X2))),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2)))), inference(rw,[status(thm)],[c_0_4977, c_0_4916])). 4.46/4.70 cnf(c_0_6229, plain, (hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3))=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X2)),X3)), inference(rw,[status(thm)],[c_0_4978, c_0_4979]), ['final']). 4.46/4.70 fof(c_0_6230, plain, ![X16941, X16942, X16943, X16944, X16945, X16946, X16947, X16948]:((hBOOL(hAPP(hAPP(c_member(X16947),esk505_7(X16941,X16942,X16943,X16944,X16945,X16946,X16947)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16947,tc_HOL_Obool)),X16942),X16941)))|hAPP(hAPP(X16946,hAPP(X16943,X16942)),hAPP(X16943,X16941))=hAPP(X16943,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16947,tc_HOL_Obool)),X16942),X16941))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16947),X16941))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16947),X16942))|~c_Finite__Set_Ofolding__image__simple(X16948,X16947,X16946,X16945,X16944,X16943))&(X16945!=hAPP(X16944,esk505_7(X16941,X16942,X16943,X16944,X16945,X16946,X16947))|hAPP(hAPP(X16946,hAPP(X16943,X16942)),hAPP(X16943,X16941))=hAPP(X16943,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16947,tc_HOL_Obool)),X16942),X16941))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16947),X16941))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16947),X16942))|~c_Finite__Set_Ofolding__image__simple(X16948,X16947,X16946,X16945,X16944,X16943))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Ounion__inter__neutral])])])])])])])). 4.46/4.70 fof(c_0_6231, plain, ![X7543, X7544, X7545, X7546, X7547, X7548, X7549]:(~hBOOL(hAPP(X7549,X7548))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X7547,X7547)),hAPP(hAPP(c_Product__Type_OPair(X7547,X7547),X7546),X7545)),hAPP(X7544,X7548)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7543,X7547),tc_prod(X7543,X7547))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7543,X7547),tc_prod(X7543,X7547)),hAPP(hAPP(c_Product__Type_OPair(X7543,X7547),X7548),X7546)),hAPP(hAPP(c_Product__Type_OPair(X7543,X7547),X7548),X7545))),c_Recdef_Osame__fst(X7543,X7547,X7549,X7544))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_same__fstI])])])). 4.46/4.70 fof(c_0_6232, plain, ![X4543, X4544, X4545, X4546, X4547, X4548]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4548,X4548)),hAPP(hAPP(c_Product__Type_OPair(X4548,X4548),X4547),X4546)),X4545))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4548,X4548)),hAPP(hAPP(c_Product__Type_OPair(X4548,X4548),X4546),X4544)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4548,X4548),tc_HOL_Obool),X4543),X4545)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4548,X4548)),hAPP(hAPP(c_Product__Type_OPair(X4548,X4548),X4547),X4544)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4548,X4548),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4543)),X4545))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__I2])])])). 4.46/4.70 cnf(c_0_6233, plain, (hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Otimes__class_Otimes(X1)),c_COMBI(X1)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X3)),X3)),c_Int_OMin)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4980, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.70 fof(c_0_6234, plain, ![X15171, X15172, X15173, X15174, X15175]:(~class_Groups_Ocomm__monoid__mult(X15175)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15174),X15173))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15174),X15172))|(c_Orderings_Obot__class_Obot(tc_fun(X15174,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15174,tc_HOL_Obool)),X15173),X15172)|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X15175,X15174,c_Groups_Otimes__class_Otimes(X15175)),X15171),c_Groups_Oone__class_Oone(X15175)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15174,tc_HOL_Obool)),X15173),X15172))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15175),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X15175,X15174,c_Groups_Otimes__class_Otimes(X15175)),X15171),c_Groups_Oone__class_Oone(X15175)),X15173)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X15175,X15174,c_Groups_Otimes__class_Otimes(X15175)),X15171),c_Groups_Oone__class_Oone(X15175)),X15172)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__Un__disjoint])])])). 4.46/4.70 cnf(c_0_6235, plain, (hBOOL(hAPP(X1,esk345_2(X1,X2)))|hBOOL(hAPP(X2,esk345_2(X1,X2)))|hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X2))=hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X1))), inference(split_conjunct,[status(thm)],[c_0_4981])). 4.46/4.70 fof(c_0_6236, plain, ![X1255, X1256, X1257, X1258, X1259]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1259,X1258),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1257),X1256)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1258))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1255))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1259,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1258),X1255)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1257),X1255)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1258),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1257,X1255))),X1256))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__nat__rel__mult2__eq])])])). 4.46/4.70 cnf(c_0_6237, plain, (hAPP(c_Set_Ovimage(X4,X1,hAPP(hAPP(c_COMBC(X4,X1,X1),hAPP(hAPP(c_COMBC(X4,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X4),c_If(X1)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X5))),X6)),X2)),X3)=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X3))), inference(split_conjunct,[status(thm)],[c_0_4957])). 4.46/4.70 fof(c_0_6238, plain, ![X3247, X3248, X3249, X3250]:(((hBOOL(hAPP(hAPP(c_member(tc_fun(X3249,tc_HOL_Obool)),esk83_4(X3247,X3248,X3249,X3250)),X3248))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3249,tc_HOL_Obool),X3248))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3249,tc_HOL_Obool),X3250),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247)),X3248)|hBOOL(hAPP(hAPP(c_member(tc_fun(X3249,tc_HOL_Obool)),esk82_4(X3247,X3248,X3249,X3250)),X3248))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3249,tc_HOL_Obool)),X3248))|~class_Groups_Ocomm__monoid__add(X3250))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X3249,tc_HOL_Obool)),esk84_4(X3247,X3248,X3249,X3250)),X3248))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3249,tc_HOL_Obool),X3248))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3249,tc_HOL_Obool),X3250),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247)),X3248)|hBOOL(hAPP(hAPP(c_member(tc_fun(X3249,tc_HOL_Obool)),esk82_4(X3247,X3248,X3249,X3250)),X3248))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3249,tc_HOL_Obool)),X3248))|~class_Groups_Ocomm__monoid__add(X3250))&((esk83_4(X3247,X3248,X3249,X3250)!=esk84_4(X3247,X3248,X3249,X3250)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3249,tc_HOL_Obool),X3248))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3249,tc_HOL_Obool),X3250),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247)),X3248)|hBOOL(hAPP(hAPP(c_member(tc_fun(X3249,tc_HOL_Obool)),esk82_4(X3247,X3248,X3249,X3250)),X3248))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3249,tc_HOL_Obool)),X3248))|~class_Groups_Ocomm__monoid__add(X3250))&((hBOOL(hAPP(hAPP(c_member(X3249),esk85_4(X3247,X3248,X3249,X3250)),esk83_4(X3247,X3248,X3249,X3250)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3249,tc_HOL_Obool),X3248))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3249,tc_HOL_Obool),X3250),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247)),X3248)|hBOOL(hAPP(hAPP(c_member(tc_fun(X3249,tc_HOL_Obool)),esk82_4(X3247,X3248,X3249,X3250)),X3248))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3249,tc_HOL_Obool)),X3248))|~class_Groups_Ocomm__monoid__add(X3250))&((hBOOL(hAPP(hAPP(c_member(X3249),esk85_4(X3247,X3248,X3249,X3250)),esk84_4(X3247,X3248,X3249,X3250)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3249,tc_HOL_Obool),X3248))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3249,tc_HOL_Obool),X3250),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247)),X3248)|hBOOL(hAPP(hAPP(c_member(tc_fun(X3249,tc_HOL_Obool)),esk82_4(X3247,X3248,X3249,X3250)),X3248))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3249,tc_HOL_Obool)),X3248))|~class_Groups_Ocomm__monoid__add(X3250))&(hAPP(X3247,esk85_4(X3247,X3248,X3249,X3250))!=c_Groups_Ozero__class_Ozero(X3250)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3249,tc_HOL_Obool),X3248))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3249,tc_HOL_Obool),X3250),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247)),X3248)|hBOOL(hAPP(hAPP(c_member(tc_fun(X3249,tc_HOL_Obool)),esk82_4(X3247,X3248,X3249,X3250)),X3248))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3249,tc_HOL_Obool)),X3248))|~class_Groups_Ocomm__monoid__add(X3250)))))))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X3249,tc_HOL_Obool)),esk83_4(X3247,X3248,X3249,X3250)),X3248))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3249,tc_HOL_Obool),X3248))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3249,tc_HOL_Obool),X3250),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247)),X3248)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3249),esk82_4(X3247,X3248,X3249,X3250)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3249,tc_HOL_Obool)),X3248))|~class_Groups_Ocomm__monoid__add(X3250))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X3249,tc_HOL_Obool)),esk84_4(X3247,X3248,X3249,X3250)),X3248))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3249,tc_HOL_Obool),X3248))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3249,tc_HOL_Obool),X3250),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247)),X3248)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3249),esk82_4(X3247,X3248,X3249,X3250)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3249,tc_HOL_Obool)),X3248))|~class_Groups_Ocomm__monoid__add(X3250))&((esk83_4(X3247,X3248,X3249,X3250)!=esk84_4(X3247,X3248,X3249,X3250)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3249,tc_HOL_Obool),X3248))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3249,tc_HOL_Obool),X3250),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247)),X3248)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3249),esk82_4(X3247,X3248,X3249,X3250)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3249,tc_HOL_Obool)),X3248))|~class_Groups_Ocomm__monoid__add(X3250))&((hBOOL(hAPP(hAPP(c_member(X3249),esk85_4(X3247,X3248,X3249,X3250)),esk83_4(X3247,X3248,X3249,X3250)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3249,tc_HOL_Obool),X3248))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3249,tc_HOL_Obool),X3250),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247)),X3248)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3249),esk82_4(X3247,X3248,X3249,X3250)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3249,tc_HOL_Obool)),X3248))|~class_Groups_Ocomm__monoid__add(X3250))&((hBOOL(hAPP(hAPP(c_member(X3249),esk85_4(X3247,X3248,X3249,X3250)),esk84_4(X3247,X3248,X3249,X3250)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3249,tc_HOL_Obool),X3248))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3249,tc_HOL_Obool),X3250),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247)),X3248)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3249),esk82_4(X3247,X3248,X3249,X3250)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3249,tc_HOL_Obool)),X3248))|~class_Groups_Ocomm__monoid__add(X3250))&(hAPP(X3247,esk85_4(X3247,X3248,X3249,X3250))!=c_Groups_Ozero__class_Ozero(X3250)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3249,tc_HOL_Obool),X3248))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3249,tc_HOL_Obool),X3250),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3249,X3250),X3247)),X3248)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3249),esk82_4(X3247,X3248,X3249,X3250)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3249,tc_HOL_Obool)),X3248))|~class_Groups_Ocomm__monoid__add(X3250)))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__UNION__zero])])])])])). 4.46/4.70 cnf(c_0_6239, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Osemiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4982, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6240, plain, ![X10203, X10204, X10205, X10206, X10207, X10208]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10208,X10208)),hAPP(hAPP(c_Product__Type_OPair(X10208,X10208),X10207),X10206)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10208,X10208),tc_HOL_Obool),X10205),X10204)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10208,X10208)),hAPP(hAPP(c_Product__Type_OPair(X10208,X10208),X10206),X10203)),X10204))|hBOOL(hAPP(hAPP(c_member(tc_prod(X10208,X10208)),hAPP(hAPP(c_Product__Type_OPair(X10208,X10208),X10207),X10203)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10208,X10208),tc_HOL_Obool),hAPP(c_Nat_OSuc,X10205)),X10204))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__I])])])). 4.46/4.70 fof(c_0_6241, plain, ![X2970, X2971, X2972, X2973, X2974, X2975]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X2975,X2975)),hAPP(hAPP(c_Product__Type_OPair(X2975,X2975),X2974),X2973)),X2972))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2975),tc_List_Olist(X2975))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2975),tc_List_Olist(X2975)),X2971),X2970)),c_List_Olistrel(X2975,X2972)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2975),tc_List_Olist(X2975))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2975),tc_List_Olist(X2975)),hAPP(hAPP(c_List_Olist_OCons(X2975),X2974),X2971)),hAPP(hAPP(c_List_Olist_OCons(X2975),X2973),X2970))),c_List_Olistrel(X2975,X2972))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel_OCons])])])). 4.46/4.70 fof(c_0_6242, plain, ![X15005, X15006, X15007]:(~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X15007),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X15007))),X15006)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15005),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X15007))),X15006)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15007)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X15007)),X15006),X15005))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X15007))),hAPP(c_List_Ofilter(tc_List_Olist(X15007),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X15007)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15005)),c_Nat_Osize__class_Osize(tc_List_Olist(X15007)))),c_List_Otranspose(X15007,X15006))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transpose__column__length])])])). 4.46/4.70 cnf(c_0_6243, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Osemiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4983, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6244, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4))),X4))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),hAPP(hAPP(c_List_Otake(X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4))),X3))|hBOOL(hAPP(X5,hAPP(hAPP(c_List_Ozip(X2,X1),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_4984])). 4.46/4.70 cnf(c_0_6245, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Otake(X1),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)), inference(rw,[status(thm)],[c_0_4985, c_0_4986]), ['final']). 4.46/4.70 fof(c_0_6246, plain, ![X14241, X14242, X14243, X14244, X14245]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X14245,X14244),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X14243),X14242)))|(X14244=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14241))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X14245,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14244),X14241)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14243),X14241)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14244),c_Divides_Odiv__class_Omod(tc_Int_Oint,X14243,X14241))),X14242))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma])])). 4.46/4.70 cnf(c_0_6247, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),hAPP(c_Int_Onat,X1))), inference(split_conjunct,[status(thm)],[c_0_4987])). 4.46/4.70 cnf(c_0_6248, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X1),tc_prod(X7,X1))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X1),tc_prod(X7,X1)),hAPP(hAPP(c_Product__Type_OPair(X7,X1),X5),X2)),hAPP(hAPP(c_Product__Type_OPair(X7,X1),X6),X3))),c_Wellfounded_Olex__prod(X7,X1,X8,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|X5!=X6), inference(split_conjunct,[status(thm)],[c_0_4988])). 4.46/4.70 cnf(c_0_6249, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Otrancl(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_4989])). 4.46/4.70 cnf(c_0_6250, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_4990])). 4.46/4.70 fof(c_0_6251, plain, ![X17094, X17095, X17096, X17097]:(((~hBOOL(hAPP(hAPP(c_member(tc_prod(X17097,X17097)),hAPP(hAPP(c_Product__Type_OPair(X17097,X17097),esk511_4(X17094,X17095,X17096,X17097)),esk510_4(X17094,X17095,X17096,X17097))),X17096))|(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17097),tc_List_Olist(X17097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17097),tc_List_Olist(X17097)),X17095),X17094)),c_List_Olexord(X17097,X17096)))|X17095=X17094|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17097),tc_List_Olist(X17097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17097),tc_List_Olist(X17097)),X17094),X17095)),c_List_Olexord(X17097,X17096)))))&(esk511_4(X17094,X17095,X17096,X17097)!=esk510_4(X17094,X17095,X17096,X17097)|(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17097),tc_List_Olist(X17097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17097),tc_List_Olist(X17097)),X17095),X17094)),c_List_Olexord(X17097,X17096)))|X17095=X17094|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17097),tc_List_Olist(X17097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17097),tc_List_Olist(X17097)),X17094),X17095)),c_List_Olexord(X17097,X17096))))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X17097,X17097)),hAPP(hAPP(c_Product__Type_OPair(X17097,X17097),esk510_4(X17094,X17095,X17096,X17097)),esk511_4(X17094,X17095,X17096,X17097))),X17096))|(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17097),tc_List_Olist(X17097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17097),tc_List_Olist(X17097)),X17095),X17094)),c_List_Olexord(X17097,X17096)))|X17095=X17094|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17097),tc_List_Olist(X17097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17097),tc_List_Olist(X17097)),X17094),X17095)),c_List_Olexord(X17097,X17096)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__linear])])])])). 4.46/4.70 fof(c_0_6252, plain, ![X9788, X9789, X9790, X9791, X9792, X9793]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X9793,tc_HOL_Obool),tc_fun(X9793,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X9793,tc_HOL_Obool),tc_fun(X9793,tc_HOL_Obool)),X9792),X9791)),c_Wellfounded_Omax__ext(X9793,X9790)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X9793,tc_HOL_Obool),tc_fun(X9793,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X9793,tc_HOL_Obool),tc_fun(X9793,tc_HOL_Obool)),X9789),X9788)),c_Wellfounded_Omax__ext(X9793,X9790)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X9793,tc_HOL_Obool),tc_fun(X9793,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X9793,tc_HOL_Obool),tc_fun(X9793,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9793,tc_HOL_Obool)),X9792),X9789)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9793,tc_HOL_Obool)),X9791),X9788))),c_Wellfounded_Omax__ext(X9793,X9790))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_max__ext__additive])])])). 4.46/4.70 fof(c_0_6253, plain, ![X16865, X16866, X16867, X16868, X16870, X16871, X16872, X16873, X16874]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X16868,X16868)),esk500_4(X16865,X16866,X16867,X16868)),X16866))|c_Equiv__Relations_Ocongruent(X16868,X16867,X16866,X16865))&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X16868,X16868,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X16868,tc_fun(X16868,X16867),tc_fun(X16868,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16867,tc_HOL_Obool),tc_fun(tc_fun(X16868,X16867),tc_fun(X16868,tc_HOL_Obool)),X16868),c_COMBB(X16867,tc_HOL_Obool,X16868)),hAPP(hAPP(c_COMBB(X16867,tc_fun(X16867,tc_HOL_Obool),X16868),c_fequal),X16865))),X16865)),esk500_4(X16865,X16866,X16867,X16868)))|c_Equiv__Relations_Ocongruent(X16868,X16867,X16866,X16865)))&(~c_Equiv__Relations_Ocongruent(X16873,X16872,X16871,X16870)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16873,X16873)),X16874),X16871))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X16873,X16873,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X16873,tc_fun(X16873,X16872),tc_fun(X16873,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16872,tc_HOL_Obool),tc_fun(tc_fun(X16873,X16872),tc_fun(X16873,tc_HOL_Obool)),X16873),c_COMBB(X16872,tc_HOL_Obool,X16873)),hAPP(hAPP(c_COMBB(X16872,tc_fun(X16872,tc_HOL_Obool),X16873),c_fequal),X16870))),X16870)),X16874))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent__def])])])])])])). 4.46/4.70 fof(c_0_6254, plain, ![X17014, X17015, X17016, X17017, X17018, X17019, X17020, X17021]:((hBOOL(hAPP(hAPP(c_member(X17021),esk507_8(X17014,X17015,X17016,X17017,X17018,X17019,X17020,X17021)),hAPP(c_List_Oset(X17021),X17020)))|hAPP(c_List_Ofoldl(X17019,X17021,hAPP(c_COMBC(X17021,X17019,X17019),X17017),hAPP(X17016,X17014)),X17020)=hAPP(X17016,hAPP(c_List_Ofoldl(X17018,X17021,hAPP(c_COMBC(X17021,X17018,X17018),X17015),X17014),X17020)))&(hAPP(c_Fun_Ocomp(X17018,X17019,X17018,X17016),hAPP(X17015,esk507_8(X17014,X17015,X17016,X17017,X17018,X17019,X17020,X17021)))!=hAPP(c_Fun_Ocomp(X17019,X17019,X17018,hAPP(X17017,esk507_8(X17014,X17015,X17016,X17017,X17018,X17019,X17020,X17021))),X17016)|hAPP(c_List_Ofoldl(X17019,X17021,hAPP(c_COMBC(X17021,X17019,X17019),X17017),hAPP(X17016,X17014)),X17020)=hAPP(X17016,hAPP(c_List_Ofoldl(X17018,X17021,hAPP(c_COMBC(X17021,X17018,X17018),X17015),X17014),X17020)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_foldl__apply])])])])])). 4.46/4.70 cnf(c_0_6255, plain, (X1=hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk189_4(X4,X3,X1,X2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X1),X3)),c_List_Olexord(X2,X4)))), inference(split_conjunct,[status(thm)],[c_0_4971])). 4.46/4.70 fof(c_0_6256, plain, ![X2702, X2703, X2704, X2705, X2706]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2706),tc_List_Olist(X2706))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2706),tc_List_Olist(X2706)),X2705),X2704)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2706),c_List_Olistrel1(X2706,X2703))))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2706),tc_List_Olist(X2706))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2706),tc_List_Olist(X2706)),hAPP(hAPP(c_List_Olist_OCons(X2706),X2702),X2705)),hAPP(hAPP(c_List_Olist_OCons(X2706),X2702),X2704))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2706),c_List_Olistrel1(X2706,X2703))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__listrel1__ConsI1])])])). 4.46/4.70 cnf(c_0_6257, plain, (X2=X3|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk502_3(X3,X2,X1)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3))))|c_List_Oconcat(X1,X2)!=c_List_Oconcat(X1,X3)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)), inference(split_conjunct,[status(thm)],[c_0_4962])). 4.46/4.70 fof(c_0_6258, plain, ![X14561, X14562, X14563, X14564, X14565]:(~class_Groups_Ocomm__monoid__add(X14565)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X14565),X14564),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14563),X14562)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14561),X14562)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X14565),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X14565,tc_Nat_Onat),X14564),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X14562))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X14563),X14561))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__nat__ivl])])). 4.46/4.70 cnf(c_0_6259, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk287_4(X2,X3,X4,X1))),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk287_4(X2,X3,X4,X1)),X3))),X2)))), inference(split_conjunct,[status(thm)],[c_0_4991])). 4.46/4.70 fof(c_0_6260, plain, ![X12204, X12205, X12206, X12207, X12208]:((hBOOL(hAPP(hAPP(c_member(X12207),esk358_5(X12204,X12205,X12206,X12207,X12208)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12207,tc_HOL_Obool)),X12206),X12205)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12208),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12207,X12208),X12204),X12205)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12207,X12208),X12204),X12206)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12207,tc_HOL_Obool)),X12205),X12206))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12207),X12206))|(~class_Groups_Oordered__ab__semigroup__add(X12208)|~class_Groups_Ocomm__monoid__add(X12208)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12208),c_Groups_Ozero__class_Ozero(X12208)),hAPP(X12204,esk358_5(X12204,X12205,X12206,X12207,X12208))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12208),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12207,X12208),X12204),X12205)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12207,X12208),X12204),X12206)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12207,tc_HOL_Obool)),X12205),X12206))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12207),X12206))|(~class_Groups_Oordered__ab__semigroup__add(X12208)|~class_Groups_Ocomm__monoid__add(X12208)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__mono3])])])])])). 4.46/4.70 cnf(c_0_6261, plain, (hBOOL(hAPP(hAPP(X1,esk381_6(X1,X2,X3,X4,X5,X6)),esk382_6(X1,X2,X3,X4,X5,X6)))|c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X1),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X4),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_4992])). 4.46/4.70 cnf(c_0_6262, plain, (hBOOL(hAPP(hAPP(X1,esk21_6(X2,X1,X3,X4,X5,X6)),esk22_6(X2,X1,X3,X4,X5,X6)))|c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X4),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X4),X3),X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_4993])). 4.46/4.70 cnf(c_0_6263, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk18_3(X2,X3,X1)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2))))|X3=X2|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)|c_List_Oconcat(X1,X2)!=c_List_Oconcat(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_4963])). 4.46/4.70 cnf(c_0_6264, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Otrancl(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_4994])). 4.46/4.70 cnf(c_0_6265, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4))), inference(split_conjunct,[status(thm)],[c_0_4995])). 4.46/4.70 fof(c_0_6266, plain, ![X14367, X14368, X14369, X14370, X14371]:(~class_Groups_Oab__group__add(X14371)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14370),X14369))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14370),X14368))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X14371),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14371),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14370,X14371),X14367),X14369)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14370,X14371),X14367),X14368))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14370,X14371),X14367),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14370,tc_HOL_Obool)),X14369),X14368)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14370,X14371),X14367),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14370,tc_HOL_Obool)),X14369),X14368))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__Un])])])). 4.46/4.70 fof(c_0_6267, plain, ![X3723, X3724, X3725, X3726, X3727, X3728, X3729, X3730, X3731]:(~c_Equiv__Relations_Oequiv(X3731,X3730,X3729)|(~c_Equiv__Relations_Oequiv(X3728,X3727,X3726)|(~c_Equiv__Relations_Ocongruent2(X3731,X3728,tc_fun(X3725,tc_HOL_Obool),X3729,X3726,X3724)|(~hBOOL(hAPP(hAPP(c_member(X3728),X3723),X3727))|c_Equiv__Relations_Ocongruent(X3731,tc_fun(X3725,tc_HOL_Obool),X3729,hAPP(hAPP(c_COMBB(tc_fun(X3728,tc_fun(X3725,tc_HOL_Obool)),tc_fun(X3725,tc_HOL_Obool),X3731),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3728,tc_fun(X3725,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3728,X3728,X3726),hAPP(hAPP(c_Set_Oinsert(X3728),X3723),c_Orderings_Obot__class_Obot(tc_fun(X3728,tc_HOL_Obool)))))),X3724)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_congruent2__implies__congruent__UN])])])). 4.46/4.70 cnf(c_0_6268, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X4))),X3)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X3),esk201_4(X3,X1,X4,X2)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),hAPP(c_Set_OCollect(X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_4996])). 4.46/4.70 cnf(c_0_6269, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(c_fequal,X2))),X5)),c_Groups_Ozero__class_Ozero(X4))),X3)=c_Groups_Ozero__class_Ozero(X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Ocomm__monoid__add(X4)), inference(split_conjunct,[status(thm)],[c_0_4997])). 4.46/4.70 fof(c_0_6270, plain, ![X1060, X1061, X1062, X1063, X1064]:(((hAPP(c_Nat_OSuc,esk26_5(X1060,X1061,X1062,X1063,X1064))=X1061|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1061|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1064,X1064)),hAPP(hAPP(c_Product__Type_OPair(X1064,X1064),X1063),X1062)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1064,X1064),tc_HOL_Obool),X1061),X1060))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X1064,X1064)),hAPP(hAPP(c_Product__Type_OPair(X1064,X1064),X1063),esk25_5(X1060,X1061,X1062,X1063,X1064))),X1060))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1061|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1064,X1064)),hAPP(hAPP(c_Product__Type_OPair(X1064,X1064),X1063),X1062)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1064,X1064),tc_HOL_Obool),X1061),X1060))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X1064,X1064)),hAPP(hAPP(c_Product__Type_OPair(X1064,X1064),esk25_5(X1060,X1061,X1062,X1063,X1064)),X1062)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1064,X1064),tc_HOL_Obool),esk26_5(X1060,X1061,X1062,X1063,X1064)),X1060)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1061|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1064,X1064)),hAPP(hAPP(c_Product__Type_OPair(X1064,X1064),X1063),X1062)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1064,X1064),tc_HOL_Obool),X1061),X1060))))))&((hAPP(c_Nat_OSuc,esk26_5(X1060,X1061,X1062,X1063,X1064))=X1061|X1062=X1063|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1064,X1064)),hAPP(hAPP(c_Product__Type_OPair(X1064,X1064),X1063),X1062)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1064,X1064),tc_HOL_Obool),X1061),X1060))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X1064,X1064)),hAPP(hAPP(c_Product__Type_OPair(X1064,X1064),X1063),esk25_5(X1060,X1061,X1062,X1063,X1064))),X1060))|X1062=X1063|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1064,X1064)),hAPP(hAPP(c_Product__Type_OPair(X1064,X1064),X1063),X1062)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1064,X1064),tc_HOL_Obool),X1061),X1060))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X1064,X1064)),hAPP(hAPP(c_Product__Type_OPair(X1064,X1064),esk25_5(X1060,X1061,X1062,X1063,X1064)),X1062)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1064,X1064),tc_HOL_Obool),esk26_5(X1060,X1061,X1062,X1063,X1064)),X1060)))|X1062=X1063|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1064,X1064)),hAPP(hAPP(c_Product__Type_OPair(X1064,X1064),X1063),X1062)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1064,X1064),tc_HOL_Obool),X1061),X1060))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__pow__E2])])])])])). 4.46/4.70 fof(c_0_6271, plain, ![X13347, X13348, X13349, X13350, X13351]:(((X13348=hAPP(c_Nat_OSuc,esk391_5(X13347,X13348,X13349,X13350,X13351))|X13348=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X13351,X13351)),hAPP(hAPP(c_Product__Type_OPair(X13351,X13351),X13350),X13349)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X13351,X13351),tc_HOL_Obool),X13348),X13347))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X13351,X13351)),hAPP(hAPP(c_Product__Type_OPair(X13351,X13351),X13350),esk390_5(X13347,X13348,X13349,X13350,X13351))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X13351,X13351),tc_HOL_Obool),esk391_5(X13347,X13348,X13349,X13350,X13351)),X13347)))|X13348=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X13351,X13351)),hAPP(hAPP(c_Product__Type_OPair(X13351,X13351),X13350),X13349)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X13351,X13351),tc_HOL_Obool),X13348),X13347))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X13351,X13351)),hAPP(hAPP(c_Product__Type_OPair(X13351,X13351),esk390_5(X13347,X13348,X13349,X13350,X13351)),X13349)),X13347))|X13348=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X13351,X13351)),hAPP(hAPP(c_Product__Type_OPair(X13351,X13351),X13350),X13349)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X13351,X13351),tc_HOL_Obool),X13348),X13347))))))&((X13348=hAPP(c_Nat_OSuc,esk391_5(X13347,X13348,X13349,X13350,X13351))|X13350=X13349|~hBOOL(hAPP(hAPP(c_member(tc_prod(X13351,X13351)),hAPP(hAPP(c_Product__Type_OPair(X13351,X13351),X13350),X13349)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X13351,X13351),tc_HOL_Obool),X13348),X13347))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X13351,X13351)),hAPP(hAPP(c_Product__Type_OPair(X13351,X13351),X13350),esk390_5(X13347,X13348,X13349,X13350,X13351))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X13351,X13351),tc_HOL_Obool),esk391_5(X13347,X13348,X13349,X13350,X13351)),X13347)))|X13350=X13349|~hBOOL(hAPP(hAPP(c_member(tc_prod(X13351,X13351)),hAPP(hAPP(c_Product__Type_OPair(X13351,X13351),X13350),X13349)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X13351,X13351),tc_HOL_Obool),X13348),X13347))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X13351,X13351)),hAPP(hAPP(c_Product__Type_OPair(X13351,X13351),esk390_5(X13347,X13348,X13349,X13350,X13351)),X13349)),X13347))|X13350=X13349|~hBOOL(hAPP(hAPP(c_member(tc_prod(X13351,X13351)),hAPP(hAPP(c_Product__Type_OPair(X13351,X13351),X13350),X13349)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X13351,X13351),tc_HOL_Obool),X13348),X13347))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__pow__E])])])])])). 4.46/4.70 cnf(c_0_6272, plain, (hBOOL(hAPP(X4,X2))|hAPP(hAPP(c_List_Oappend(X1),c_List_OdropWhile(X1,X4,X3)),X5)=c_List_OdropWhile(X1,X4,hAPP(hAPP(c_List_Oappend(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_4998])). 4.46/4.70 fof(c_0_6273, plain, ![X16918, X16919, X16920, X16921, X16922]:(~class_Groups_Ocomm__monoid__add(X16922)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X16922),X16921),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16920),X16919),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16918),X16919)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X16922),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X16922,tc_Nat_Onat),X16921),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X16919))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X16920,X16918))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__shift__bounds__cl__nat__ivl])])])). 4.46/4.70 cnf(c_0_6274, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X8)),c_List_Olistrel1(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|X5!=hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X7))|X8!=hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X7))), inference(split_conjunct,[status(thm)],[c_0_4999])). 4.46/4.70 cnf(c_0_6275, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|c_Groups_Oone__class_Oone(X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(c_fequal,X2))),X5)),c_Groups_Oone__class_Oone(X4))),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Ocomm__monoid__mult(X4)), inference(split_conjunct,[status(thm)],[c_0_5000])). 4.46/4.70 cnf(c_0_6276, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk345_2(X1,X2)))|hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X2))=hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X1))), inference(split_conjunct,[status(thm)],[c_0_4981])). 4.46/4.70 fof(c_0_6277, plain, ![X6389, X6390, X6391, X6392]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6392),X6391))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6392),X6390))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6392,tc_Nat_Onat),X6389),X6391)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6392,tc_Nat_Onat),X6389),X6390))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6392,tc_Nat_Onat),X6389),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6392,tc_HOL_Obool)),X6391),X6390)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6392,tc_Nat_Onat),X6389),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6392,tc_HOL_Obool)),X6391),X6390)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__Un__nat])])])). 4.46/4.70 cnf(c_0_6278, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))), inference(rw,[status(thm)],[c_0_5001, c_0_4443])). 4.46/4.70 fof(c_0_6279, plain, ![X6980, X6981, X6982, X6983, X6984, X6985]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6982),X6981)),X6980)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6985),X6984)),X6983)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6982),X6981)),X6980)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6983),X6985))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6980))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6982))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6982),X6985))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6981),X6984)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma])])). 4.46/4.70 cnf(c_0_6280, plain, (c_Nitpick_Oof__frac(X2,X1,X3)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X2,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X2)),X3))),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X2,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X2)),X3)))|~class_Rings_Oring__1(X1)|~class_Rings_Oinverse(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5002, c_0_5003]), c_0_5004])). 4.46/4.70 cnf(c_0_6281, plain, (hAPP(X1,hAPP(X2,X3))=hAPP(hAPP(c_Fun_Ocomp(X4,X5,X6,X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_5005]), ['final']). 4.46/4.70 cnf(c_0_6282, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))), inference(rw,[status(thm)],[c_0_5006, c_0_4443])). 4.46/4.70 cnf(c_0_6283, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk3_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(X1,X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk1_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_5007])). 4.46/4.70 cnf(c_0_6284, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X3)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5008, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6285, plain, ![X11387, X11388, X11389, X11390, X11391, X11392, X11393, X11394, X11395, X11396, X11397, X11398, X11399, X11400, X11401, X11402]:(((~c_Nitpick_Ofold__graph_H(X11393,X11392,X11391,X11390,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11393,tc_HOL_Obool)),X11389),hAPP(hAPP(c_Set_Oinsert(X11393),X11394),c_Orderings_Obot__class_Obot(tc_fun(X11393,tc_HOL_Obool)))),X11395)|~hBOOL(hAPP(hAPP(c_member(X11393),X11394),X11389))|hAPP(hAPP(X11391,X11388),X11387)!=hAPP(hAPP(X11391,X11394),X11395)|c_Nitpick_Ofold__graph_H(X11393,X11392,X11391,X11390,X11389,hAPP(hAPP(X11391,X11388),X11387)))&(c_Orderings_Obot__class_Obot(tc_fun(X11393,tc_HOL_Obool))!=X11389|X11390!=hAPP(hAPP(X11391,X11388),X11387)|c_Nitpick_Ofold__graph_H(X11393,X11392,X11391,X11390,X11389,hAPP(hAPP(X11391,X11388),X11387))))&((((c_Orderings_Obot__class_Obot(tc_fun(X11402,tc_HOL_Obool))=X11398|c_Nitpick_Ofold__graph_H(X11402,X11401,X11400,X11399,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11402,tc_HOL_Obool)),X11398),hAPP(hAPP(c_Set_Oinsert(X11402),esk333_7(X11396,X11397,X11398,X11399,X11400,X11401,X11402)),c_Orderings_Obot__class_Obot(tc_fun(X11402,tc_HOL_Obool)))),esk334_7(X11396,X11397,X11398,X11399,X11400,X11401,X11402))|~c_Nitpick_Ofold__graph_H(X11402,X11401,X11400,X11399,X11398,hAPP(hAPP(X11400,X11397),X11396)))&(X11399=hAPP(hAPP(X11400,X11397),X11396)|c_Nitpick_Ofold__graph_H(X11402,X11401,X11400,X11399,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11402,tc_HOL_Obool)),X11398),hAPP(hAPP(c_Set_Oinsert(X11402),esk333_7(X11396,X11397,X11398,X11399,X11400,X11401,X11402)),c_Orderings_Obot__class_Obot(tc_fun(X11402,tc_HOL_Obool)))),esk334_7(X11396,X11397,X11398,X11399,X11400,X11401,X11402))|~c_Nitpick_Ofold__graph_H(X11402,X11401,X11400,X11399,X11398,hAPP(hAPP(X11400,X11397),X11396))))&((c_Orderings_Obot__class_Obot(tc_fun(X11402,tc_HOL_Obool))=X11398|hBOOL(hAPP(hAPP(c_member(X11402),esk333_7(X11396,X11397,X11398,X11399,X11400,X11401,X11402)),X11398))|~c_Nitpick_Ofold__graph_H(X11402,X11401,X11400,X11399,X11398,hAPP(hAPP(X11400,X11397),X11396)))&(X11399=hAPP(hAPP(X11400,X11397),X11396)|hBOOL(hAPP(hAPP(c_member(X11402),esk333_7(X11396,X11397,X11398,X11399,X11400,X11401,X11402)),X11398))|~c_Nitpick_Ofold__graph_H(X11402,X11401,X11400,X11399,X11398,hAPP(hAPP(X11400,X11397),X11396)))))&((c_Orderings_Obot__class_Obot(tc_fun(X11402,tc_HOL_Obool))=X11398|hAPP(hAPP(X11400,X11397),X11396)=hAPP(hAPP(X11400,esk333_7(X11396,X11397,X11398,X11399,X11400,X11401,X11402)),esk334_7(X11396,X11397,X11398,X11399,X11400,X11401,X11402))|~c_Nitpick_Ofold__graph_H(X11402,X11401,X11400,X11399,X11398,hAPP(hAPP(X11400,X11397),X11396)))&(X11399=hAPP(hAPP(X11400,X11397),X11396)|hAPP(hAPP(X11400,X11397),X11396)=hAPP(hAPP(X11400,esk333_7(X11396,X11397,X11398,X11399,X11400,X11401,X11402)),esk334_7(X11396,X11397,X11398,X11399,X11400,X11401,X11402))|~c_Nitpick_Ofold__graph_H(X11402,X11401,X11400,X11399,X11398,hAPP(hAPP(X11400,X11397),X11396)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Oequations_I2_J])])])])])])). 4.46/4.70 cnf(c_0_6286, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk2_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(X1,X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk1_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_5007])). 4.46/4.70 cnf(c_0_6287, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OCond(X4,X5,X7)),X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,X4)),X5),X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X4))),X7),X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5009])). 4.46/4.70 fof(c_0_6288, plain, ![X6806, X6807, X6808, X6809]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6809),X6808))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6807),X6806))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6809),X6807)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6808),X6806))),c_FunDef_Opair__leq)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__leqI2])])). 4.46/4.70 fof(c_0_6289, plain, ![X7231, X7232, X7233, X7234]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7234),X7233))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7232),X7231))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X7234),X7232)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X7233),X7231))),c_FunDef_Opair__less)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__lessI2])])). 4.46/4.70 fof(c_0_6290, plain, ![X16200, X16201, X16202, X16203, X16204]:((hBOOL(hAPP(hAPP(c_member(X16203),esk471_5(X16200,X16201,X16202,X16203,X16204)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16203,tc_HOL_Obool)),X16202),X16201)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16204),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16203,X16204),X16200),X16201)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16203,X16204),X16200),X16202)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16203,tc_HOL_Obool)),X16201),X16202))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16203),X16202))|~class_Groups_Oordered__comm__monoid__add(X16204))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16204),c_Groups_Ozero__class_Ozero(X16204)),hAPP(X16200,esk471_5(X16200,X16201,X16202,X16203,X16204))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16204),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16203,X16204),X16200),X16201)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16203,X16204),X16200),X16202)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16203,tc_HOL_Obool)),X16201),X16202))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16203),X16202))|~class_Groups_Oordered__comm__monoid__add(X16204))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__mono2])])])])])). 4.46/4.70 cnf(c_0_6291, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|c_Divides_Odivmod__nat(X1,X2)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),X2))), inference(split_conjunct,[status(thm)],[c_0_5010])). 4.46/4.70 cnf(c_0_6292, plain, (c_Divides_Odivmod__nat(X1,X2)=c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5011])). 4.46/4.70 cnf(c_0_6293, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Hilbert__Choice_OEps(tc_List_Olist(X1),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_List_Oset(X1))),X2))),c_List_Odistinct(X1))))=c_Nitpick_Ocard_H(X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5012])). 4.46/4.70 fof(c_0_6294, plain, ![X14078, X14079, X14080, X14081, X14082]:(~class_Groups_Ocomm__monoid__mult(X14082)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14081),X14080))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14081),X14079))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14082),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X14081,X14082),X14078),X14080)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X14081,X14082),X14078),X14079))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14082),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X14081,X14082),X14078),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14081,tc_HOL_Obool)),X14080),X14079))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X14081,X14082),X14078),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14081,tc_HOL_Obool)),X14080),X14079)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__Un__Int])])])). 4.46/4.70 fof(c_0_6295, plain, ![X5432, X5433, X5434, X5435, X5436]:(~class_Groups_Ocomm__monoid__add(X5436)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5435),X5434))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5435),X5433))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5436),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5435,X5436),X5432),X5434)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5435,X5436),X5432),X5433))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5436),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5435,X5436),X5432),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5435,tc_HOL_Obool)),X5434),X5433))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5435,X5436),X5432),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5435,tc_HOL_Obool)),X5434),X5433)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__Un__Int])])])). 4.46/4.70 fof(c_0_6296, plain, ![X17023, X17024, X17025, X17026, X17027, X17028]:(((~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17028),tc_List_Olist(X17028))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17028),tc_List_Olist(X17028)),X17026),X17024)),c_List_Olistrel1(X17028,X17023)))|X17025!=X17027|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17028),tc_List_Olist(X17028))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17028),tc_List_Olist(X17028)),hAPP(hAPP(c_List_Olist_OCons(X17028),X17027),X17026)),hAPP(hAPP(c_List_Olist_OCons(X17028),X17025),X17024))),c_List_Olistrel1(X17028,X17023))))&(X17024!=X17026|~hBOOL(hAPP(hAPP(c_member(tc_prod(X17028,X17028)),hAPP(hAPP(c_Product__Type_OPair(X17028,X17028),X17027),X17025)),X17023))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17028),tc_List_Olist(X17028))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17028),tc_List_Olist(X17028)),hAPP(hAPP(c_List_Olist_OCons(X17028),X17027),X17026)),hAPP(hAPP(c_List_Olist_OCons(X17028),X17025),X17024))),c_List_Olistrel1(X17028,X17023)))))&(((X17024=X17026|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17028),tc_List_Olist(X17028))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17028),tc_List_Olist(X17028)),X17026),X17024)),c_List_Olistrel1(X17028,X17023)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17028),tc_List_Olist(X17028))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17028),tc_List_Olist(X17028)),hAPP(hAPP(c_List_Olist_OCons(X17028),X17027),X17026)),hAPP(hAPP(c_List_Olist_OCons(X17028),X17025),X17024))),c_List_Olistrel1(X17028,X17023))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X17028,X17028)),hAPP(hAPP(c_Product__Type_OPair(X17028,X17028),X17027),X17025)),X17023))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17028),tc_List_Olist(X17028))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17028),tc_List_Olist(X17028)),X17026),X17024)),c_List_Olistrel1(X17028,X17023)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17028),tc_List_Olist(X17028))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17028),tc_List_Olist(X17028)),hAPP(hAPP(c_List_Olist_OCons(X17028),X17027),X17026)),hAPP(hAPP(c_List_Olist_OCons(X17028),X17025),X17024))),c_List_Olistrel1(X17028,X17023)))))&((X17024=X17026|X17025=X17027|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17028),tc_List_Olist(X17028))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17028),tc_List_Olist(X17028)),hAPP(hAPP(c_List_Olist_OCons(X17028),X17027),X17026)),hAPP(hAPP(c_List_Olist_OCons(X17028),X17025),X17024))),c_List_Olistrel1(X17028,X17023))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X17028,X17028)),hAPP(hAPP(c_Product__Type_OPair(X17028,X17028),X17027),X17025)),X17023))|X17025=X17027|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17028),tc_List_Olist(X17028))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17028),tc_List_Olist(X17028)),hAPP(hAPP(c_List_Olist_OCons(X17028),X17027),X17026)),hAPP(hAPP(c_List_Olist_OCons(X17028),X17025),X17024))),c_List_Olistrel1(X17028,X17023))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__listrel1__Cons])])])). 4.46/4.70 fof(c_0_6297, plain, ![X16460, X16461, X16462, X16463, X16464, X16465, X16466, X16467, X16468]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16464),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16463)),X16462)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X16463,X16463)),hAPP(hAPP(c_Product__Type_OPair(X16463,X16463),hAPP(hAPP(c_List_Onth(X16463),X16462),X16464)),hAPP(hAPP(c_List_Onth(X16463),X16461),X16464))),X16460))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16463),tc_List_Olist(X16463))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16463),tc_List_Olist(X16463)),X16462),X16461)),c_List_Olistrel(X16463,X16460))))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16463)),X16462)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16463)),X16461)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16463),tc_List_Olist(X16463))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16463),tc_List_Olist(X16463)),X16462),X16461)),c_List_Olistrel(X16463,X16460)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk481_4(X16465,X16466,X16467,X16468)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16468)),X16467)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16468)),X16467)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16468)),X16466)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16468),tc_List_Olist(X16468))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16468),tc_List_Olist(X16468)),X16467),X16466)),c_List_Olistrel(X16468,X16465))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16468,X16468)),hAPP(hAPP(c_Product__Type_OPair(X16468,X16468),hAPP(hAPP(c_List_Onth(X16468),X16467),esk481_4(X16465,X16466,X16467,X16468))),hAPP(hAPP(c_List_Onth(X16468),X16466),esk481_4(X16465,X16466,X16467,X16468)))),X16465))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16468)),X16467)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16468)),X16466)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16468),tc_List_Olist(X16468))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16468),tc_List_Olist(X16468)),X16467),X16466)),c_List_Olistrel(X16468,X16465)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__iff__nth])])])])])])). 4.46/4.70 fof(c_0_6298, plain, ![X10003, X10004, X10005, X10006, X10007, X10008]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X10008),X10007)),X10006)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X10005),X10004)),X10003)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X10005),X10004)),X10003)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10003),X10005))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10006))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10005))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10005),X10008))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10007),X10004)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono2__lemma])])])). 4.46/4.70 cnf(c_0_6299, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_5013])). 4.46/4.70 cnf(c_0_6300, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olexord(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))|X5!=X6), inference(split_conjunct,[status(thm)],[c_0_5014])). 4.46/4.70 fof(c_0_6301, plain, ![X15345, X15346, X15347]:(~class_Orderings_Olinorder(X15347)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15347),X15346))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15347),X15345))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15347,tc_HOL_Obool)),X15346),X15345)=c_Orderings_Obot__class_Obot(tc_fun(X15347,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X15347),c_Big__Operators_Olattice_OInf__fin(X15347,c_Orderings_Oord__class_Omin(X15347),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15347,tc_HOL_Obool)),X15346),X15345))),c_Big__Operators_Olattice_OInf__fin(X15347,c_Orderings_Oord__class_Omin(X15347),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15347,tc_HOL_Obool)),X15346),X15345)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X15347),c_Big__Operators_Olattice_OInf__fin(X15347,c_Orderings_Oord__class_Omin(X15347),X15346)),c_Big__Operators_Olattice_OInf__fin(X15347,c_Orderings_Oord__class_Omin(X15347),X15345)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Ounion__inter])])])). 4.46/4.70 fof(c_0_6302, plain, ![X10363, X10364, X10365, X10366, X10367]:(~class_Fields_Ofield__inverse__zero(X10367)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10366),X10365))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10366,X10367),hAPP(hAPP(c_COMBS(X10366,X10367,X10367),hAPP(hAPP(c_COMBB(X10367,tc_fun(X10367,X10367),X10366),c_Rings_Oinverse__class_Odivide(X10367)),X10364)),X10363)),X10365)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10367),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10366,X10367),X10364),X10365)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10366,X10367),X10363),X10365)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__dividef])])])). 4.46/4.70 fof(c_0_6303, plain, ![X5664, X5665, X5666, X5667, X5669]:((hBOOL(hAPP(hAPP(c_member(X5667),esk173_4(X5664,X5665,X5666,X5667)),X5666))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5667,tc_HOL_Obool),tc_fun(X5667,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5667,tc_HOL_Obool),tc_fun(X5667,tc_HOL_Obool)),X5666),X5665)),c_Wellfounded_Omax__ext(X5667,X5664)))|c_Orderings_Obot__class_Obot(tc_fun(X5667,tc_HOL_Obool))=X5665|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5667),X5665))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5667),X5666)))&(~hBOOL(hAPP(hAPP(c_member(X5667),X5669),X5665))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5667,X5667)),hAPP(hAPP(c_Product__Type_OPair(X5667,X5667),esk173_4(X5664,X5665,X5666,X5667)),X5669)),X5664))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5667,tc_HOL_Obool),tc_fun(X5667,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5667,tc_HOL_Obool),tc_fun(X5667,tc_HOL_Obool)),X5666),X5665)),c_Wellfounded_Omax__ext(X5667,X5664)))|c_Orderings_Obot__class_Obot(tc_fun(X5667,tc_HOL_Obool))=X5665|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5667),X5665))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5667),X5666)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_max__ext_Ointros])])])])])])). 4.46/4.70 cnf(c_0_6304, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Oappend(X3),X2),X4)),hAPP(hAPP(c_List_Oappend(X3),X1),X5))),c_List_Olistrel1(X3,X6)))|X1!=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X4),X5)),c_List_Olistrel1(X3,X6)))), inference(split_conjunct,[status(thm)],[c_0_5015])). 4.46/4.70 fof(c_0_6305, plain, ![X939, X940, X941]:(~class_Orderings_Olinorder(X941)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X941),X940))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X941),X939))|(c_Orderings_Obot__class_Obot(tc_fun(X941,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X941,tc_HOL_Obool)),X940),X939)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X941),c_Big__Operators_Olattice_OSup__fin(X941,c_Orderings_Oord__class_Omax(X941),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X941,tc_HOL_Obool)),X940),X939))),c_Big__Operators_Olattice_OSup__fin(X941,c_Orderings_Oord__class_Omax(X941),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X941,tc_HOL_Obool)),X940),X939)))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X941),c_Big__Operators_Olattice_OSup__fin(X941,c_Orderings_Oord__class_Omax(X941),X940)),c_Big__Operators_Olattice_OSup__fin(X941,c_Orderings_Oord__class_Omax(X941),X939)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Ounion__inter])])])). 4.46/4.70 cnf(c_0_6306, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Oappend(X3),X4),X2)),hAPP(hAPP(c_List_Oappend(X3),X5),X1))),c_List_Olistrel1(X3,X6)))|X1!=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X4),X5)),c_List_Olistrel1(X3,X6)))), inference(split_conjunct,[status(thm)],[c_0_5015])). 4.46/4.70 cnf(c_0_6307, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X5))),c_List_Olex(X3,X6)))|X1!=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X4),X5)),c_List_Olex(X3,X6)))), inference(split_conjunct,[status(thm)],[c_0_5016])). 4.46/4.70 fof(c_0_6308, plain, ![X9693, X9694, X9695, X9696, X9697, X9698, X9699, X9700]:((hAPP(hAPP(c_Product__Type_OPair(X9700,X9699),hAPP(X9695,esk275_8(X9693,X9694,X9695,X9696,X9697,X9698,X9699,X9700))),hAPP(X9694,esk276_8(X9693,X9694,X9695,X9696,X9697,X9698,X9699,X9700)))=X9698|~hBOOL(hAPP(hAPP(c_member(tc_prod(X9700,X9699)),X9698),hAPP(c_Set_Oimage(tc_prod(X9697,X9696),tc_prod(X9700,X9699),c_Product__Type_Omap__pair(X9697,X9700,X9696,X9699,X9695,X9694)),X9693))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X9697,X9696)),hAPP(hAPP(c_Product__Type_OPair(X9697,X9696),esk275_8(X9693,X9694,X9695,X9696,X9697,X9698,X9699,X9700)),esk276_8(X9693,X9694,X9695,X9696,X9697,X9698,X9699,X9700))),X9693))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X9700,X9699)),X9698),hAPP(c_Set_Oimage(tc_prod(X9697,X9696),tc_prod(X9700,X9699),c_Product__Type_Omap__pair(X9697,X9700,X9696,X9699,X9695,X9694)),X9693))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_prod__fun__imageE])])])])])). 4.46/4.70 cnf(c_0_6309, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X5))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X5)))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))))), inference(split_conjunct,[status(thm)],[c_0_5017])). 4.46/4.70 fof(c_0_6310, plain, ![X4442, X4443, X4444, X4445]:((hBOOL(hAPP(hAPP(c_member(X4445),esk122_4(X4442,X4443,X4444,X4445)),hAPP(c_List_Oset(X4445),hAPP(hAPP(c_List_Omap(tc_prod(X4445,X4444),X4445),c_Product__Type_Ofst(X4445,X4444)),X4443))))|hAPP(c_Map_Omap__of(X4445,X4444),X4442)=hAPP(c_Map_Omap__of(X4445,X4444),X4443)|hAPP(c_List_Oset(X4445),hAPP(hAPP(c_List_Omap(tc_prod(X4445,X4444),X4445),c_Product__Type_Ofst(X4445,X4444)),X4442))!=hAPP(c_List_Oset(X4445),hAPP(hAPP(c_List_Omap(tc_prod(X4445,X4444),X4445),c_Product__Type_Ofst(X4445,X4444)),X4443)))&(hAPP(hAPP(c_Map_Omap__of(X4445,X4444),X4443),esk122_4(X4442,X4443,X4444,X4445))!=hAPP(hAPP(c_Map_Omap__of(X4445,X4444),X4442),esk122_4(X4442,X4443,X4444,X4445))|hAPP(c_Map_Omap__of(X4445,X4444),X4442)=hAPP(c_Map_Omap__of(X4445,X4444),X4443)|hAPP(c_List_Oset(X4445),hAPP(hAPP(c_List_Omap(tc_prod(X4445,X4444),X4445),c_Product__Type_Ofst(X4445,X4444)),X4442))!=hAPP(c_List_Oset(X4445),hAPP(hAPP(c_List_Omap(tc_prod(X4445,X4444),X4445),c_Product__Type_Ofst(X4445,X4444)),X4443)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__eqI])])])])])). 4.46/4.70 cnf(c_0_6311, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X6)),c_List_Olistrel1(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),X4)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)!=X6), inference(split_conjunct,[status(thm)],[c_0_5018])). 4.46/4.70 fof(c_0_6312, plain, ![X12665, X12666, X12667, X12668, X12669]:((hBOOL(hAPP(hAPP(c_member(X12668),esk373_5(X12665,X12666,X12667,X12668,X12669)),hAPP(c_List_Oset(X12668),X12667)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12669),hAPP(c_List_Omonoid__add__class_Olistsum(X12669),hAPP(hAPP(c_List_Omap(X12668,X12669),X12666),X12667))),hAPP(c_List_Omonoid__add__class_Olistsum(X12669),hAPP(hAPP(c_List_Omap(X12668,X12669),X12665),X12667))))|(~class_Groups_Oordered__ab__semigroup__add(X12669)|~class_Groups_Omonoid__add(X12669)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12669),hAPP(X12666,esk373_5(X12665,X12666,X12667,X12668,X12669))),hAPP(X12665,esk373_5(X12665,X12666,X12667,X12668,X12669))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12669),hAPP(c_List_Omonoid__add__class_Olistsum(X12669),hAPP(hAPP(c_List_Omap(X12668,X12669),X12666),X12667))),hAPP(c_List_Omonoid__add__class_Olistsum(X12669),hAPP(hAPP(c_List_Omap(X12668,X12669),X12665),X12667))))|(~class_Groups_Oordered__ab__semigroup__add(X12669)|~class_Groups_Omonoid__add(X12669)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__mono])])])])])). 4.46/4.70 fof(c_0_6313, plain, ![X12264, X12265, X12266, X12267, X12268]:(~class_Groups_Oordered__ab__group__add__abs(X12268)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12268),hAPP(c_Groups_Oabs__class_Oabs(X12268),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12268),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12268),X12267),X12266)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12268),X12265),X12264)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12268),hAPP(c_Groups_Oabs__class_Oabs(X12268),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12268),X12267),X12265))),hAPP(c_Groups_Oabs__class_Oabs(X12268),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12268),X12266),X12264)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq])])). 4.46/4.70 cnf(c_0_6314, plain, (hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X2))=hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X1))|~hBOOL(hAPP(X1,esk345_2(X1,X2)))|~hBOOL(hAPP(X2,esk345_2(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_4981])). 4.46/4.70 cnf(c_0_6315, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4))), inference(split_conjunct,[status(thm)],[c_0_5019])). 4.46/4.70 fof(c_0_6316, plain, ![X9415, X9416, X9417]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X9417),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X9417)),X9416))))|hBOOL(hAPP(hAPP(c_member(X9417),hAPP(c_Product__Type_Ofst(X9417,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X9417,X9416),X9415))),hAPP(c_List_Oset(X9417),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X9417),X9417),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X9417)),X9416))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_select__weight__member])])])). 4.46/4.70 fof(c_0_6317, plain, ![X16186, X16187, X16188, X16189, X16190, X16191, X16192, X16193]:(~c_Finite__Set_Ofolding(X16193,X16192,X16191,X16190)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16193),X16189))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16193),X16188))|hAPP(c_Fun_Ocomp(X16192,X16192,X16187,hAPP(X16190,X16188)),hAPP(c_Fun_Ocomp(X16192,X16192,X16187,hAPP(X16190,X16189)),X16186))=hAPP(c_Fun_Ocomp(X16192,X16192,X16187,hAPP(X16190,X16189)),hAPP(c_Fun_Ocomp(X16192,X16192,X16187,hAPP(X16190,X16188)),X16186))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Ocommute__left__comp_H_H])])])). 4.46/4.70 fof(c_0_6318, plain, ![X5672, X5673, X5674, X5675, X5676, X5677, X5678]:((hBOOL(hAPP(hAPP(c_member(X5678),esk174_7(X5672,X5673,X5674,X5675,X5676,X5677,X5678)),X5677))|X5673=X5672|~hBOOL(hAPP(hAPP(c_member(tc_fun(X5678,tc_HOL_Obool)),X5672),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5678),X5677),X5676)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X5678,tc_HOL_Obool)),X5673),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5678),X5677),X5676)))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5678,tc_fun(X5675,tc_HOL_Obool)),X5672),X5674)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5678,tc_fun(X5675,tc_HOL_Obool)),X5673),X5674)|~c_Equiv__Relations_Ocongruent(X5678,tc_fun(X5675,tc_HOL_Obool),X5676,X5674)|~c_Equiv__Relations_Oequiv(X5678,X5677,X5676))&((hBOOL(hAPP(hAPP(c_member(X5678),esk175_7(X5672,X5673,X5674,X5675,X5676,X5677,X5678)),X5677))|X5673=X5672|~hBOOL(hAPP(hAPP(c_member(tc_fun(X5678,tc_HOL_Obool)),X5672),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5678),X5677),X5676)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X5678,tc_HOL_Obool)),X5673),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5678),X5677),X5676)))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5678,tc_fun(X5675,tc_HOL_Obool)),X5672),X5674)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5678,tc_fun(X5675,tc_HOL_Obool)),X5673),X5674)|~c_Equiv__Relations_Ocongruent(X5678,tc_fun(X5675,tc_HOL_Obool),X5676,X5674)|~c_Equiv__Relations_Oequiv(X5678,X5677,X5676))&((hAPP(X5674,esk174_7(X5672,X5673,X5674,X5675,X5676,X5677,X5678))=hAPP(X5674,esk175_7(X5672,X5673,X5674,X5675,X5676,X5677,X5678))|X5673=X5672|~hBOOL(hAPP(hAPP(c_member(tc_fun(X5678,tc_HOL_Obool)),X5672),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5678),X5677),X5676)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X5678,tc_HOL_Obool)),X5673),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5678),X5677),X5676)))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5678,tc_fun(X5675,tc_HOL_Obool)),X5672),X5674)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5678,tc_fun(X5675,tc_HOL_Obool)),X5673),X5674)|~c_Equiv__Relations_Ocongruent(X5678,tc_fun(X5675,tc_HOL_Obool),X5676,X5674)|~c_Equiv__Relations_Oequiv(X5678,X5677,X5676))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X5678,X5678)),hAPP(hAPP(c_Product__Type_OPair(X5678,X5678),esk174_7(X5672,X5673,X5674,X5675,X5676,X5677,X5678)),esk175_7(X5672,X5673,X5674,X5675,X5676,X5677,X5678))),X5676))|X5673=X5672|~hBOOL(hAPP(hAPP(c_member(tc_fun(X5678,tc_HOL_Obool)),X5672),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5678),X5677),X5676)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X5678,tc_HOL_Obool)),X5673),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5678),X5677),X5676)))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5678,tc_fun(X5675,tc_HOL_Obool)),X5672),X5674)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5678,tc_fun(X5675,tc_HOL_Obool)),X5673),X5674)|~c_Equiv__Relations_Ocongruent(X5678,tc_fun(X5675,tc_HOL_Obool),X5676,X5674)|~c_Equiv__Relations_Oequiv(X5678,X5677,X5676))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__equiv__class__inject])])])])])). 4.46/4.70 cnf(c_0_6319, plain, (hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4)=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|~c_Equiv__Relations_Oequiv(X1,X5,X4)), inference(split_conjunct,[status(thm)],[c_0_5020])). 4.46/4.70 cnf(c_0_6320, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X5))|~c_Equiv__Relations_Oequiv(X1,X3,X5)), inference(split_conjunct,[status(thm)],[c_0_5021]), ['final']). 4.46/4.70 cnf(c_0_6321, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),X5))|~c_Equiv__Relations_Oequiv(X1,X3,X5)), inference(split_conjunct,[status(thm)],[c_0_5021]), ['final']). 4.46/4.70 cnf(c_0_6322, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk73_3(X3,X2,X1)),X2))|c_Relation_Orefl__on(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))),esk74_3(X3,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4937])). 4.46/4.70 fof(c_0_6323, plain, ![X9633, X9634, X9635, X9636]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9634),X9635)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9636),X9633)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X9636),X9635)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X9634),X9633))),c_Int_Ointrel)))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X9636),X9635)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X9634),X9633))),c_Int_Ointrel))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9634),X9635)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9636),X9633))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_intrel__iff])])). 4.46/4.70 fof(c_0_6324, plain, ![X4980, X4981, X4982, X4983, X4984]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4984),tc_List_Olist(X4984))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4984),tc_List_Olist(X4984)),X4983),X4982)),c_List_Olexord(X4984,X4981)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4984),tc_List_Olist(X4984))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4984),tc_List_Olist(X4984)),hAPP(hAPP(c_List_Oappend(X4984),X4980),X4983)),hAPP(hAPP(c_List_Oappend(X4984),X4980),X4982))),c_List_Olexord(X4984,X4981)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__leftI])])). 4.46/4.70 fof(c_0_6325, plain, ![X1119, X1120, X1121, X1122, X1123]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1123),tc_List_Olist(X1123))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1123),tc_List_Olist(X1123)),X1122),X1121)),c_List_Olistrel1(X1123,X1120)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1123),tc_List_Olist(X1123))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1123),tc_List_Olist(X1123)),hAPP(hAPP(c_List_Olist_OCons(X1123),X1119),X1122)),hAPP(hAPP(c_List_Olist_OCons(X1123),X1119),X1121))),c_List_Olistrel1(X1123,X1120)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel1I2])])])). 4.46/4.70 fof(c_0_6326, plain, ![X5232, X5233, X5234, X5235, X5236, X5237]:((hBOOL(hAPP(hAPP(c_member(X5236),esk158_6(X5232,X5233,X5234,X5235,X5236,X5237)),X5235))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5232,X5237),X5233),hAPP(c_Set_Oimage(X5236,X5232,X5234),X5235))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5236,X5237),hAPP(c_Fun_Ocomp(X5232,X5237,X5236,X5233),X5234)),X5235)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5236),X5235))|~class_Groups_Ocomm__monoid__add(X5237))&((hBOOL(hAPP(hAPP(c_member(X5236),esk159_6(X5232,X5233,X5234,X5235,X5236,X5237)),X5235))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5232,X5237),X5233),hAPP(c_Set_Oimage(X5236,X5232,X5234),X5235))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5236,X5237),hAPP(c_Fun_Ocomp(X5232,X5237,X5236,X5233),X5234)),X5235)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5236),X5235))|~class_Groups_Ocomm__monoid__add(X5237))&((esk158_6(X5232,X5233,X5234,X5235,X5236,X5237)!=esk159_6(X5232,X5233,X5234,X5235,X5236,X5237)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5232,X5237),X5233),hAPP(c_Set_Oimage(X5236,X5232,X5234),X5235))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5236,X5237),hAPP(c_Fun_Ocomp(X5232,X5237,X5236,X5233),X5234)),X5235)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5236),X5235))|~class_Groups_Ocomm__monoid__add(X5237))&((hAPP(X5234,esk159_6(X5232,X5233,X5234,X5235,X5236,X5237))=hAPP(X5234,esk158_6(X5232,X5233,X5234,X5235,X5236,X5237))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5232,X5237),X5233),hAPP(c_Set_Oimage(X5236,X5232,X5234),X5235))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5236,X5237),hAPP(c_Fun_Ocomp(X5232,X5237,X5236,X5233),X5234)),X5235)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5236),X5235))|~class_Groups_Ocomm__monoid__add(X5237))&(hAPP(X5233,hAPP(X5234,esk158_6(X5232,X5233,X5234,X5235,X5236,X5237)))!=c_Groups_Ozero__class_Ozero(X5237)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5232,X5237),X5233),hAPP(c_Set_Oimage(X5236,X5232,X5234),X5235))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5236,X5237),hAPP(c_Fun_Ocomp(X5232,X5237,X5236,X5233),X5234)),X5235)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5236),X5235))|~class_Groups_Ocomm__monoid__add(X5237)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__reindex__nonzero])])])])])). 4.46/4.70 cnf(c_0_6327, plain, (X1=hAPP(c_Groups_Ouminus__class_Ouminus(X2),c_Groups_Oone__class_Oone(X2))|X1=c_Groups_Oone__class_Oone(X2)|hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))!=c_Groups_Oone__class_Oone(X2)|~class_Rings_Oring__1__no__zero__divisors(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5022, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834])). 4.46/4.70 cnf(c_0_6328, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))), inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5023, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834])])). 4.46/4.70 cnf(c_0_6329, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5024, c_0_4836]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834])). 4.46/4.70 cnf(c_0_6330, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Ozero__class_Ozero(X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5025, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834])). 4.46/4.70 cnf(c_0_6331, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),X6))|X1!=X2|~hBOOL(hAPP(hAPP(c_member(X3),X5),X2))|~hBOOL(hAPP(hAPP(c_member(X3),X4),X1))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6)))|~c_Equiv__Relations_Oequiv(X3,X7,X6)), inference(split_conjunct,[status(thm)],[c_0_5026])). 4.46/4.70 cnf(c_0_6332, plain, (c_Divides_Odivmod__nat(X2,X1)=hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X1))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5027])). 4.46/4.70 cnf(c_0_6333, plain, (hBOOL(hAPP(X1,esk201_4(X2,X3,X1,X4)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X3),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X3),hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),X1))),X2)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Set_OCollect(X4),X1)))), inference(split_conjunct,[status(thm)],[c_0_4996])). 4.46/4.70 cnf(c_0_6334, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4))), inference(split_conjunct,[status(thm)],[c_0_5028])). 4.46/4.70 fof(c_0_6335, plain, ![X7682, X7683, X7684, X7685, X7686, X7687]:((hBOOL(hAPP(hAPP(c_member(X7687),esk218_6(X7682,X7683,X7684,X7685,X7686,X7687)),X7686))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7687,X7684),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X7687,X7684),X7686),X7683)),hAPP(hAPP(c_Product__Type_OSigma(X7687,X7684),X7685),X7682)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7687,tc_HOL_Obool)),X7686),X7685)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7684,tc_HOL_Obool)),hAPP(X7683,esk218_6(X7682,X7683,X7684,X7685,X7686,X7687))),hAPP(X7682,esk218_6(X7682,X7683,X7684,X7685,X7686,X7687))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7687,X7684),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X7687,X7684),X7686),X7683)),hAPP(hAPP(c_Product__Type_OSigma(X7687,X7684),X7685),X7682)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7687,tc_HOL_Obool)),X7686),X7685)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sigma__mono])])])])])). 4.46/4.70 fof(c_0_6336, plain, ![X4652, X4653, X4654, X4657, X4658, X4659, X4660, X4661]:(((hBOOL(hAPP(hAPP(c_member(X4654),esk130_3(X4652,X4653,X4654)),X4653))|c_Relation_Ototal__on(X4654,X4653,X4652))&((hBOOL(hAPP(hAPP(c_member(X4654),esk131_3(X4652,X4653,X4654)),X4653))|c_Relation_Ototal__on(X4654,X4653,X4652))&((esk130_3(X4652,X4653,X4654)!=esk131_3(X4652,X4653,X4654)|c_Relation_Ototal__on(X4654,X4653,X4652))&((~hBOOL(hAPP(hAPP(c_member(tc_prod(X4654,X4654)),hAPP(hAPP(c_Product__Type_OPair(X4654,X4654),esk130_3(X4652,X4653,X4654)),esk131_3(X4652,X4653,X4654))),X4652))|c_Relation_Ototal__on(X4654,X4653,X4652))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4654,X4654)),hAPP(hAPP(c_Product__Type_OPair(X4654,X4654),esk131_3(X4652,X4653,X4654)),esk130_3(X4652,X4653,X4654))),X4652))|c_Relation_Ototal__on(X4654,X4653,X4652))))))&(~c_Relation_Ototal__on(X4659,X4658,X4657)|(~hBOOL(hAPP(hAPP(c_member(X4659),X4660),X4658))|(~hBOOL(hAPP(hAPP(c_member(X4659),X4661),X4658))|(X4660=X4661|(hBOOL(hAPP(hAPP(c_member(tc_prod(X4659,X4659)),hAPP(hAPP(c_Product__Type_OPair(X4659,X4659),X4660),X4661)),X4657))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4659,X4659)),hAPP(hAPP(c_Product__Type_OPair(X4659,X4659),X4661),X4660)),X4657)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_total__on__def])])])])])])])). 4.46/4.70 fof(c_0_6337, plain, ![X16120, X16121, X16122, X16123, X16124, X16125, X16126]:((hBOOL(hAPP(hAPP(c_member(X16126),esk470_7(X16120,X16121,X16122,X16123,X16124,X16125,X16126)),X16125))|hBOOL(hAPP(hAPP(c_member(tc_fun(X16123,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16126,tc_fun(X16123,tc_HOL_Obool)),X16121),X16122)),X16120))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X16126,tc_HOL_Obool)),X16121),hAPP(hAPP(c_Equiv__Relations_Oquotient(X16126),X16125),X16124)))|~c_Equiv__Relations_Ocongruent(X16126,tc_fun(X16123,tc_HOL_Obool),X16124,X16122)|~c_Equiv__Relations_Oequiv(X16126,X16125,X16124))&(~hBOOL(hAPP(hAPP(c_member(tc_fun(X16123,tc_HOL_Obool)),hAPP(X16122,esk470_7(X16120,X16121,X16122,X16123,X16124,X16125,X16126))),X16120))|hBOOL(hAPP(hAPP(c_member(tc_fun(X16123,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16126,tc_fun(X16123,tc_HOL_Obool)),X16121),X16122)),X16120))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X16126,tc_HOL_Obool)),X16121),hAPP(hAPP(c_Equiv__Relations_Oquotient(X16126),X16125),X16124)))|~c_Equiv__Relations_Ocongruent(X16126,tc_fun(X16123,tc_HOL_Obool),X16124,X16122)|~c_Equiv__Relations_Oequiv(X16126,X16125,X16124))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__type])])])])). 4.46/4.70 fof(c_0_6338, plain, ![X15469, X15470, X15471, X15472]:(~c_FunDef_Oreduction__pair(X15472,X15471)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15472,X15472),tc_HOL_Obool)),X15470),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X15472,X15472),tc_HOL_Obool),tc_fun(tc_prod(X15472,X15472),tc_HOL_Obool)),X15471)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15472,X15472),tc_HOL_Obool)),X15469),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X15472,X15472),tc_HOL_Obool),tc_fun(tc_prod(X15472,X15472),tc_HOL_Obool)),X15471)))|(~c_Wellfounded_Owf(X15472,X15469)|c_Wellfounded_Owf(X15472,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15472,X15472),tc_HOL_Obool)),X15470),X15469)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_reduction__pair__lemma])])])). 4.46/4.70 cnf(c_0_6339, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Int_Onumber__ring(X1)|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5029, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6340, plain, ![X2779, X2780, X2781, X2782, X2783, X2784, X2785, X2786, X2787]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X2787,X2786)),hAPP(hAPP(c_Product__Type_OPair(X2787,X2786),X2785),X2784)),X2783))|hBOOL(hAPP(hAPP(c_member(tc_prod(X2782,X2781)),hAPP(hAPP(c_Product__Type_OPair(X2782,X2781),hAPP(X2780,X2785)),hAPP(X2779,X2784))),hAPP(c_Set_Oimage(tc_prod(X2787,X2786),tc_prod(X2782,X2781),c_Product__Type_Omap__pair(X2787,X2782,X2786,X2781,X2780,X2779)),X2783)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__imageI])])). 4.46/4.70 cnf(c_0_6341, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olex(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_5016])). 4.46/4.70 cnf(c_0_6342, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2)),c_List_Olex(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_5030]), ['final']). 4.46/4.70 cnf(c_0_6343, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X3!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1))), inference(split_conjunct,[status(thm)],[c_0_5031])). 4.46/4.70 cnf(c_0_6344, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_5032]), ['final']). 4.46/4.70 cnf(c_0_6345, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X4),X5))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X3))),X4)))))|~hBOOL(hAPP(X3,X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),hAPP(c_Set_OCollect(X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_4996])). 4.46/4.70 cnf(c_0_6346, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk254_5(X2,X3,X4,X5,X1)),X5))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(c_Set_OCollect(X1),X3))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X1),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X4))), inference(split_conjunct,[status(thm)],[c_0_5033])). 4.46/4.70 cnf(c_0_6347, plain, (hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2),c_fNot),hAPP(c_fequal,hAPP(X3,X4)))),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))=hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X4))),X5))|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(c_List_Oset(X1),X5)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5034, c_0_5035]), c_0_5035])). 4.46/4.70 cnf(c_0_6348, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3),X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5036])). 4.46/4.70 cnf(c_0_6349, plain, (hAPP(c_Finite__Set_Ofold__image(X1,X2,X3),X4)=c_Finite__Set_Ofold(X2,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5037]), ['final']). 4.46/4.70 fof(c_0_6350, plain, ![X11748, X11749, X11750, X11751, X11752, X11753, X11754, X11755]:(~c_Finite__Set_Ofolding(X11755,X11754,X11753,X11752)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11755),X11751))|hAPP(c_Fun_Ocomp(X11754,X11754,X11750,hAPP(X11752,X11751)),hAPP(c_Fun_Ocomp(X11754,X11754,X11750,hAPP(X11753,X11749)),X11748))=hAPP(c_Fun_Ocomp(X11754,X11754,X11750,hAPP(X11753,X11749)),hAPP(c_Fun_Ocomp(X11754,X11754,X11750,hAPP(X11752,X11751)),X11748)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Ocommute__left__comp_H])])])). 4.46/4.70 cnf(c_0_6351, plain, (hAPP(hAPP(c_List_Oappend(X2),X3),X5)=hAPP(hAPP(c_List_Oappend(X2),X1),X4)|X1!=hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3)|X4!=hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3)),X5)|hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X1)),X4)!=X5|hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X1)!=X3), inference(split_conjunct,[status(thm)],[c_0_5038])). 4.46/4.70 fof(c_0_6352, plain, ![X4634, X4635, X4636, X4637, X4638, X4639, X4640]:((hAPP(hAPP(X4638,X4634),esk129_7(X4634,X4635,X4636,X4637,X4638,X4639,X4640))=X4635|~hBOOL(hAPP(hAPP(c_member(X4640),X4634),X4636))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4640,X4639,X4638,X4637,X4636),X4635))|~c_Finite__Set_Ofun__left__comm(X4640,X4639,X4638))&(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4640,X4639,X4638,X4637,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4640,tc_HOL_Obool)),X4636),hAPP(hAPP(c_Set_Oinsert(X4640),X4634),c_Orderings_Obot__class_Obot(tc_fun(X4640,tc_HOL_Obool))))),esk129_7(X4634,X4635,X4636,X4637,X4638,X4639,X4640)))|~hBOOL(hAPP(hAPP(c_member(X4640),X4634),X4636))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4640,X4639,X4638,X4637,X4636),X4635))|~c_Finite__Set_Ofun__left__comm(X4640,X4639,X4638))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE__aux])])])])])). 4.46/4.70 cnf(c_0_6353, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2)|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk108_4(X2,X3,X4,X1))),X4)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk108_4(X2,X3,X4,X1)),X3))),X2)), inference(split_conjunct,[status(thm)],[c_0_5039])). 4.46/4.70 cnf(c_0_6354, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))), inference(split_conjunct,[status(thm)],[c_0_5040])). 4.46/4.70 fof(c_0_6355, plain, ![X3857, X3858, X3859, X3860, X3861]:(~class_Groups_Ocomm__monoid__mult(X3861)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3860,X3861),hAPP(hAPP(c_COMBS(X3860,X3861,X3861),hAPP(hAPP(c_COMBB(X3861,tc_fun(X3861,X3861),X3860),c_Groups_Otimes__class_Otimes(X3861)),X3859)),X3858)),X3857)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3861),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3860,X3861),X3859),X3857)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3860,X3861),X3858),X3857))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__timesf])])])). 4.46/4.70 fof(c_0_6356, plain, ![X5074, X5075, X5076, X5077, X5078, X5079, X5080, X5081]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X5081,X5080)),hAPP(hAPP(c_Product__Type_OPair(X5081,X5080),X5079),X5078)),X5077))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X5080,X5076)),hAPP(hAPP(c_Product__Type_OPair(X5080,X5076),X5078),X5075)),X5074))|hBOOL(hAPP(hAPP(c_member(tc_prod(X5081,X5076)),hAPP(hAPP(c_Product__Type_OPair(X5081,X5076),X5079),X5075)),hAPP(hAPP(c_Relation_Orel__comp(X5081,X5080,X5076),X5077),X5074))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__compI])])])). 4.46/4.70 fof(c_0_6357, plain, ![X4910, X4911, X4912, X4913, X4914]:(~class_Groups_Ocomm__monoid__add(X4914)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4913,X4914),hAPP(hAPP(c_COMBS(X4913,X4914,X4914),hAPP(hAPP(c_COMBB(X4914,tc_fun(X4914,X4914),X4913),c_Groups_Oplus__class_Oplus(X4914)),X4912)),X4911)),X4910)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4914),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4913,X4914),X4912),X4910)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4913,X4914),X4911),X4910))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__addf])])])). 4.46/4.70 cnf(c_0_6358, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5041, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6359, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5042, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6360, plain, ![X15558, X15559, X15560, X15561, X15562]:(~class_Groups_Oab__group__add(X15562)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15561,X15562),hAPP(hAPP(c_COMBS(X15561,X15562,X15562),hAPP(hAPP(c_COMBB(X15562,tc_fun(X15562,X15562),X15561),c_Groups_Ominus__class_Ominus(X15562)),X15560)),X15559)),X15558)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15562),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15561,X15562),X15560),X15558)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15561,X15562),X15559),X15558))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__subtractf])])). 4.46/4.70 cnf(c_0_6361, plain, (hAPP(hAPP(c_Fun_Ocomp(X1,X4,X2,c_Fun_Othe__inv__into(X4,X1,X6,X5)),c_Fun_Othe__inv__into(X1,X2,hAPP(c_Set_Oimage(X4,X1,X5),X6),X3)),X7)=hAPP(c_Fun_Othe__inv__into(X4,X2,X6,hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X7)|~c_Fun_Oinj__on(X1,X2,X3,hAPP(c_Set_Oimage(X4,X1,X5),X6))|~c_Fun_Oinj__on(X4,X1,X5,X6)|~hBOOL(hAPP(hAPP(c_member(X2),X7),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X4,X1,X5),X6))))), inference(split_conjunct,[status(thm)],[c_0_5043])). 4.46/4.70 fof(c_0_6362, plain, ![X3714, X3715, X3716, X3717, X3718, X3719]:(~class_Rings_Olinordered__semiring__1__strict(X3719)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3719),X3718),X3717))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3719),X3716),X3717))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3719),c_Groups_Ozero__class_Ozero(X3719)),X3715))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3719),c_Groups_Ozero__class_Ozero(X3719)),X3714))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3719),X3715),X3714)!=c_Groups_Oone__class_Oone(X3719)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3719),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3719),X3715),X3718)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3719),X3714),X3716))),X3717)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_convex__bound__lt])])])). 4.46/4.70 fof(c_0_6363, plain, ![X13537, X13538, X13539, X13540, X13541, X13542]:(~class_Rings_Olinordered__semiring__1(X13542)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13542),X13541),X13540))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13542),X13539),X13540))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13542),c_Groups_Ozero__class_Ozero(X13542)),X13538))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13542),c_Groups_Ozero__class_Ozero(X13542)),X13537))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13542),X13538),X13537)!=c_Groups_Oone__class_Oone(X13542)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13542),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13542),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13542),X13538),X13541)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13542),X13537),X13539))),X13540)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_convex__bound__le])])])). 4.46/4.70 cnf(c_0_6364, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5044, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6365, plain, ![X6986, X6987, X6988]:(~class_Lattices_Olattice(X6988)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6988),X6987))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6988),X6986))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6988,tc_HOL_Obool)),X6987),X6986)=c_Orderings_Obot__class_Obot(tc_fun(X6988,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6988),c_Big__Operators_Olattice__class_OSup__fin(X6988,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6988,tc_HOL_Obool)),X6987),X6986))),c_Big__Operators_Olattice__class_OSup__fin(X6988,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6988,tc_HOL_Obool)),X6987),X6986)))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6988),c_Big__Operators_Olattice__class_OSup__fin(X6988,X6987)),c_Big__Operators_Olattice__class_OSup__fin(X6988,X6986)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Ounion__inter])])])). 4.46/4.70 cnf(c_0_6366, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk246_3(X1,X2,X3)),esk247_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(X1,esk246_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk247_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_5045])). 4.46/4.70 fof(c_0_6367, plain, ![X2659, X2660, X2661]:(~class_Orderings_Olinorder(X2661)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2661),X2660))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2661),X2659))|(c_Orderings_Obot__class_Obot(tc_fun(X2661,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2661,tc_HOL_Obool)),X2660),X2659)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X2661),c_Big__Operators_Olinorder__class_OMin(X2661,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2661,tc_HOL_Obool)),X2660),X2659))),c_Big__Operators_Olinorder__class_OMin(X2661,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2661,tc_HOL_Obool)),X2660),X2659)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X2661),c_Big__Operators_Olinorder__class_OMin(X2661,X2660)),c_Big__Operators_Olinorder__class_OMin(X2661,X2659)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Ounion__inter])])])). 4.46/4.70 fof(c_0_6368, plain, ![X3603, X3604, X3605, X3606, X3607]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3607),X3606))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3606),X3605)),X3604)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3607),X3605)),X3603))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3606),X3607)),X3605)),X3604)),X3603)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__diff__add__eq1])])])). 4.46/4.70 fof(c_0_6369, plain, ![X11050, X11051, X11052, X11053, X11054]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11054),X11053))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11051),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11053),X11054)),X11052)),X11050))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11054),X11052)),X11051)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11053),X11052)),X11050))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2])])). 4.46/4.70 fof(c_0_6370, plain, ![X16535, X16536, X16537, X16538, X16539, X16540]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X16537,X16540),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X16537,X16540),X16536),hAPP(c_COMBK(tc_fun(X16540,tc_HOL_Obool),X16537),X16538))),hAPP(hAPP(c_Product__Type_OSigma(X16537,X16540),X16535),hAPP(c_COMBK(tc_fun(X16540,tc_HOL_Obool),X16537),X16538))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16537,tc_HOL_Obool)),X16536),X16535))|~hBOOL(hAPP(hAPP(c_member(X16540),X16539),X16538)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16537,tc_HOL_Obool)),X16536),X16535))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X16537,X16540),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X16537,X16540),X16536),hAPP(c_COMBK(tc_fun(X16540,tc_HOL_Obool),X16537),X16538))),hAPP(hAPP(c_Product__Type_OSigma(X16537,X16540),X16535),hAPP(c_COMBK(tc_fun(X16540,tc_HOL_Obool),X16537),X16538))))|~hBOOL(hAPP(hAPP(c_member(X16540),X16539),X16538)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Times__subset__cancel2])])])])). 4.46/4.70 cnf(c_0_6371, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X1),c_HOL_OThe(X1,hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X3)),X4))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5046])). 4.46/4.70 fof(c_0_6372, plain, ![X5903, X5904, X5905, X5906, X5907]:((hBOOL(hAPP(hAPP(c_member(X5906),esk183_5(X5903,X5904,X5905,X5906,X5907)),X5905))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5907),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5906,X5907),X5904),X5905)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5906,X5907),X5903),X5905)))|c_Orderings_Obot__class_Obot(tc_fun(X5906,tc_HOL_Obool))=X5905|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5906),X5905))|(~class_Groups_Oordered__cancel__ab__semigroup__add(X5907)|~class_Groups_Ocomm__monoid__add(X5907)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5907),hAPP(X5904,esk183_5(X5903,X5904,X5905,X5906,X5907))),hAPP(X5903,esk183_5(X5903,X5904,X5905,X5906,X5907))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5907),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5906,X5907),X5904),X5905)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5906,X5907),X5903),X5905)))|c_Orderings_Obot__class_Obot(tc_fun(X5906,tc_HOL_Obool))=X5905|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5906),X5905))|(~class_Groups_Oordered__cancel__ab__semigroup__add(X5907)|~class_Groups_Ocomm__monoid__add(X5907)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__strict__mono])])])])])). 4.46/4.70 fof(c_0_6373, plain, ![X14497, X14498, X14499, X14500, X14501]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X14501,X14501)),hAPP(hAPP(c_Product__Type_OPair(X14501,X14501),X14500),esk425_5(X14497,X14498,X14499,X14500,X14501))),X14497))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X14501,X14501)),hAPP(hAPP(c_Product__Type_OPair(X14501,X14501),X14500),X14499)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X14501,X14501),tc_HOL_Obool),hAPP(c_Nat_OSuc,X14498)),X14497))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X14501,X14501)),hAPP(hAPP(c_Product__Type_OPair(X14501,X14501),esk425_5(X14497,X14498,X14499,X14500,X14501)),X14499)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X14501,X14501),tc_HOL_Obool),X14498),X14497)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X14501,X14501)),hAPP(hAPP(c_Product__Type_OPair(X14501,X14501),X14500),X14499)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X14501,X14501),tc_HOL_Obool),hAPP(c_Nat_OSuc,X14498)),X14497))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__E2])])])])])). 4.46/4.70 fof(c_0_6374, plain, ![X4614, X4615, X4616, X4617, X4618]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4618,X4618)),hAPP(hAPP(c_Product__Type_OPair(X4618,X4618),X4617),esk128_5(X4614,X4615,X4616,X4617,X4618))),X4614))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4618,X4618)),hAPP(hAPP(c_Product__Type_OPair(X4618,X4618),X4617),X4616)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4618,X4618),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4615)),X4614))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X4618,X4618)),hAPP(hAPP(c_Product__Type_OPair(X4618,X4618),esk128_5(X4614,X4615,X4616,X4617,X4618)),X4616)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4618,X4618),tc_HOL_Obool),X4615),X4614)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4618,X4618)),hAPP(hAPP(c_Product__Type_OPair(X4618,X4618),X4617),X4616)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4618,X4618),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4615)),X4614))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__D2])])])])). 4.46/4.70 fof(c_0_6375, plain, ![X1436, X1437, X1438, X1439, X1440]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X1440,X1440)),hAPP(hAPP(c_Product__Type_OPair(X1440,X1440),X1439),esk32_5(X1436,X1437,X1438,X1439,X1440))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1440,X1440),tc_HOL_Obool),X1437),X1436)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1440,X1440)),hAPP(hAPP(c_Product__Type_OPair(X1440,X1440),X1439),X1438)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1440,X1440),tc_HOL_Obool),hAPP(c_Nat_OSuc,X1437)),X1436))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X1440,X1440)),hAPP(hAPP(c_Product__Type_OPair(X1440,X1440),esk32_5(X1436,X1437,X1438,X1439,X1440)),X1438)),X1436))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1440,X1440)),hAPP(hAPP(c_Product__Type_OPair(X1440,X1440),X1439),X1438)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1440,X1440),tc_HOL_Obool),hAPP(c_Nat_OSuc,X1437)),X1436))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__E])])])])])). 4.46/4.70 fof(c_0_6376, plain, ![X16001, X16002, X16003, X16004, X16005]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16005,X16005)),hAPP(hAPP(c_Product__Type_OPair(X16005,X16005),X16004),X16003)),X16002))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16005),tc_List_Olist(X16005))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16005),tc_List_Olist(X16005)),hAPP(hAPP(c_List_Olist_OCons(X16005),X16004),X16001)),hAPP(hAPP(c_List_Olist_OCons(X16005),X16003),X16001))),c_List_Olistrel1(X16005,X16002)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I1])])). 4.46/4.70 fof(c_0_6377, plain, ![X15321, X15322, X15323]:(~class_Lattices_Olattice(X15323)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15323),X15322))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15323),X15321))|(c_Orderings_Obot__class_Obot(tc_fun(X15323,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15323,tc_HOL_Obool)),X15322),X15321)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15323),c_Big__Operators_Olattice__class_OInf__fin(X15323,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15323,tc_HOL_Obool)),X15322),X15321))),c_Big__Operators_Olattice__class_OInf__fin(X15323,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15323,tc_HOL_Obool)),X15322),X15321)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15323),c_Big__Operators_Olattice__class_OInf__fin(X15323,X15322)),c_Big__Operators_Olattice__class_OInf__fin(X15323,X15321)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Ounion__inter])])])). 4.46/4.70 fof(c_0_6378, plain, ![X9709, X9710, X9711, X9712, X9713]:(~class_Groups_Oab__semigroup__mult(X9713)|(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X9713,X9713,c_Groups_Otimes__class_Otimes(X9713),X9712,X9711),X9710))|(~hBOOL(hAPP(hAPP(c_member(X9713),X9709),X9711))|(hBOOL(hAPP(hAPP(c_member(X9713),X9712),X9711))|hBOOL(hAPP(c_Finite__Set_Ofold__graph(X9713,X9713,c_Groups_Otimes__class_Otimes(X9713),X9709,hAPP(hAPP(c_Set_Oinsert(X9713),X9712),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9713,tc_HOL_Obool)),X9711),hAPP(hAPP(c_Set_Oinsert(X9713),X9709),c_Orderings_Obot__class_Obot(tc_fun(X9713,tc_HOL_Obool)))))),X9710)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__graph__permute__diff])])])). 4.46/4.70 fof(c_0_6379, plain, ![X9175]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X9175))|(X9175=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X9175)),c_FunDef_Omax__strict)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smax__emptyI])])). 4.46/4.70 cnf(c_0_6380, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),X2))),X3))|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5047])). 4.46/4.70 cnf(c_0_6381, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)), inference(split_conjunct,[status(thm)],[c_0_5048]), ['final']). 4.46/4.70 cnf(c_0_6382, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_5049]), ['final']). 4.46/4.70 cnf(c_0_6383, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X1),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_5050])). 4.46/4.70 cnf(c_0_6384, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)), inference(split_conjunct,[status(thm)],[c_0_5051]), ['final']). 4.46/4.70 cnf(c_0_6385, plain, (hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X4))),X4)),X1)=hAPP(hAPP(c_List_Onth(X2),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X4))),X4))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5052, c_0_4916]), c_0_4916])). 4.46/4.70 cnf(c_0_6386, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Odrop(X1),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)), inference(split_conjunct,[status(thm)],[c_0_5053]), ['final']). 4.46/4.70 fof(c_0_6387, plain, ![X2533, X2534, X2535, X2536, X2537, X2538, X2539]:(~class_Groups_Oab__semigroup__mult(X2539)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2538),X2537))|(~c_Fun_Oinj__on(X2538,X2536,X2535,X2537)|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X2539,X2536,c_Groups_Otimes__class_Otimes(X2539)),X2534),X2533),hAPP(c_Set_Oimage(X2538,X2536,X2535),X2537))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X2539,X2538,c_Groups_Otimes__class_Otimes(X2539)),hAPP(c_Fun_Ocomp(X2536,X2539,X2538,X2534),X2535)),X2533),X2537)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__reindex])])])). 4.46/4.70 fof(c_0_6388, plain, ![X11612, X11613, X11614]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X11614),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X11613),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X11613)),X11612))))|hBOOL(hAPP(hAPP(c_member(X11613),hAPP(c_Random_Opick(X11613,X11612),X11614)),hAPP(c_List_Oset(X11613),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X11613),X11613),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X11613)),X11612))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pick__member])])])). 4.46/4.70 fof(c_0_6389, plain, ![X13769, X13770, X13771, X13772, X13773, X13774]:((hBOOL(hAPP(hAPP(c_member(X13773),esk401_6(X13769,X13770,X13771,X13772,X13773,X13774)),X13772))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13774,X13773,c_Groups_Otimes__class_Otimes(X13774)),X13771),X13769),X13772)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13774,X13773,c_Groups_Otimes__class_Otimes(X13774)),X13770),X13769),X13772)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13773),X13772))|~class_Groups_Oab__semigroup__mult(X13774))&(hAPP(X13770,esk401_6(X13769,X13770,X13771,X13772,X13773,X13774))!=hAPP(X13771,esk401_6(X13769,X13770,X13771,X13772,X13773,X13774))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13774,X13773,c_Groups_Otimes__class_Otimes(X13774)),X13771),X13769),X13772)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13774,X13773,c_Groups_Otimes__class_Otimes(X13774)),X13770),X13769),X13772)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13773),X13772))|~class_Groups_Oab__semigroup__mult(X13774))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__cong])])])])])). 4.46/4.70 fof(c_0_6390, plain, ![X11663, X11664, X11665]:(~class_Orderings_Olinorder(X11665)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11665),X11664))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11665),X11663))|(c_Orderings_Obot__class_Obot(tc_fun(X11665,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11665,tc_HOL_Obool)),X11664),X11663)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X11665),c_Big__Operators_Olinorder__class_OMax(X11665,X11664)),c_Big__Operators_Olinorder__class_OMax(X11665,X11663))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X11665),c_Big__Operators_Olinorder__class_OMax(X11665,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11665,tc_HOL_Obool)),X11664),X11663))),c_Big__Operators_Olinorder__class_OMax(X11665,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11665,tc_HOL_Obool)),X11664),X11663))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Ounion__inter])])])). 4.46/4.70 cnf(c_0_6391, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X2),X4),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(X1,esk381_6(X2,X3,X4,X1,X5,X6)),esk382_6(X2,X3,X4,X1,X5,X6)))|~c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X1),X4),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_4992])). 4.46/4.70 cnf(c_0_6392, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X4),X3),X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(X1,esk21_6(X1,X2,X3,X4,X5,X6)),esk22_6(X1,X2,X3,X4,X5,X6)))|~c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X4),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_4993])). 4.46/4.70 fof(c_0_6393, plain, ![X16894, X16895, X16896, X16897, X16898]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X16898,X16897)),hAPP(X16898,X16896)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16895,X16895)),hAPP(hAPP(c_Product__Type_OPair(X16895,X16895),X16897),X16896)),c_List_Omeasures(X16895,X16894)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X16895,X16895)),hAPP(hAPP(c_Product__Type_OPair(X16895,X16895),X16897),X16896)),c_List_Omeasures(X16895,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X16895,tc_Nat_Onat)),X16898),X16894)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_measures__lesseq])])])). 4.46/4.70 cnf(c_0_6394, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1,X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1,X2)),X3)),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_5054])). 4.46/4.70 cnf(c_0_6395, plain, (hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[c_0_5055, c_0_4471])). 4.46/4.70 cnf(c_0_6396, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk304_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),X4)))|c_List_OdropWhile(X1,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X2))=c_List_OdropWhile(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_5056])). 4.46/4.70 fof(c_0_6397, plain, ![X4597, X4598, X4599, X4600, X4601]:((hAPP(hAPP(c_List_Olist_OCons(X4601),esk126_5(X4597,X4598,X4599,X4600,X4601)),esk127_5(X4597,X4598,X4599,X4600,X4601))=X4600|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4601),tc_List_Olist(X4601))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4601),tc_List_Olist(X4601)),X4600),hAPP(hAPP(c_List_Olist_OCons(X4601),X4599),X4598))),c_List_Olistrel(X4601,X4597))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X4601,X4601)),hAPP(hAPP(c_Product__Type_OPair(X4601,X4601),esk126_5(X4597,X4598,X4599,X4600,X4601)),X4599)),X4597))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4601),tc_List_Olist(X4601))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4601),tc_List_Olist(X4601)),X4600),hAPP(hAPP(c_List_Olist_OCons(X4601),X4599),X4598))),c_List_Olistrel(X4601,X4597))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4601),tc_List_Olist(X4601))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4601),tc_List_Olist(X4601)),esk127_5(X4597,X4598,X4599,X4600,X4601)),X4598)),c_List_Olistrel(X4601,X4597)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4601),tc_List_Olist(X4601))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4601),tc_List_Olist(X4601)),X4600),hAPP(hAPP(c_List_Olist_OCons(X4601),X4599),X4598))),c_List_Olistrel(X4601,X4597)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel__Cons2])])])])])). 4.46/4.70 fof(c_0_6398, plain, ![X10531, X10532, X10533, X10534, X10535]:((hAPP(hAPP(c_List_Olist_OCons(X10535),esk307_5(X10531,X10532,X10533,X10534,X10535)),esk308_5(X10531,X10532,X10533,X10534,X10535))=X10532|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10535),tc_List_Olist(X10535))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10535),tc_List_Olist(X10535)),hAPP(hAPP(c_List_Olist_OCons(X10535),X10534),X10533)),X10532)),c_List_Olistrel(X10535,X10531))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X10535,X10535)),hAPP(hAPP(c_Product__Type_OPair(X10535,X10535),X10534),esk307_5(X10531,X10532,X10533,X10534,X10535))),X10531))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10535),tc_List_Olist(X10535))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10535),tc_List_Olist(X10535)),hAPP(hAPP(c_List_Olist_OCons(X10535),X10534),X10533)),X10532)),c_List_Olistrel(X10535,X10531))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10535),tc_List_Olist(X10535))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10535),tc_List_Olist(X10535)),X10533),esk308_5(X10531,X10532,X10533,X10534,X10535))),c_List_Olistrel(X10535,X10531)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10535),tc_List_Olist(X10535))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10535),tc_List_Olist(X10535)),hAPP(hAPP(c_List_Olist_OCons(X10535),X10534),X10533)),X10532)),c_List_Olistrel(X10535,X10531)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel__Cons1])])])])])). 4.46/4.70 fof(c_0_6399, plain, ![X8298, X8299, X8300, X8301, X8302]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X8299,X8301)),hAPP(X8299,X8300)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X8302,X8302)),hAPP(hAPP(c_Product__Type_OPair(X8302,X8302),X8301),X8300)),c_List_Omeasures(X8302,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X8302,tc_Nat_Onat)),X8299),X8298)))))&(hAPP(X8299,X8301)!=hAPP(X8299,X8300)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X8302,X8302)),hAPP(hAPP(c_Product__Type_OPair(X8302,X8302),X8301),X8300)),c_List_Omeasures(X8302,X8298)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X8302,X8302)),hAPP(hAPP(c_Product__Type_OPair(X8302,X8302),X8301),X8300)),c_List_Omeasures(X8302,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X8302,tc_Nat_Onat)),X8299),X8298))))))&((hAPP(X8299,X8301)=hAPP(X8299,X8300)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X8299,X8301)),hAPP(X8299,X8300)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X8302,X8302)),hAPP(hAPP(c_Product__Type_OPair(X8302,X8302),X8301),X8300)),c_List_Omeasures(X8302,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X8302,tc_Nat_Onat)),X8299),X8298)))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X8302,X8302)),hAPP(hAPP(c_Product__Type_OPair(X8302,X8302),X8301),X8300)),c_List_Omeasures(X8302,X8298)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X8299,X8301)),hAPP(X8299,X8300)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X8302,X8302)),hAPP(hAPP(c_Product__Type_OPair(X8302,X8302),X8301),X8300)),c_List_Omeasures(X8302,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X8302,tc_Nat_Onat)),X8299),X8298))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measures_I2_J])])])). 4.46/4.70 fof(c_0_6400, plain, ![X11636, X11637, X11638, X11639, X11640, X11641]:(~class_Groups_Oab__semigroup__mult(X11641)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11640),X11639))|(hBOOL(hAPP(hAPP(c_member(X11640),X11638),X11639))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11641),hAPP(X11637,X11638)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X11641,X11640,c_Groups_Otimes__class_Otimes(X11641)),X11637),X11636),X11639))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X11641,X11640,c_Groups_Otimes__class_Otimes(X11641)),X11637),X11636),hAPP(hAPP(c_Set_Oinsert(X11640),X11638),X11639))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__insert])])])). 4.46/4.70 cnf(c_0_6401, plain, (hAPP(c_Nat_OSuc,X2)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X2)))))), inference(rw,[status(thm)],[c_0_5057, c_0_4443])). 4.46/4.70 cnf(c_0_6402, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2)),c_Int_Onat)))))), inference(rw,[status(thm)],[c_0_5058, c_0_4443])). 4.46/4.70 cnf(c_0_6403, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2)),c_Int_Onat)))))), inference(rw,[status(thm)],[c_0_5059, c_0_4443])). 4.46/4.70 fof(c_0_6404, plain, ![X928, X929, X930]:((c_Orderings_Obot__class_Obot(tc_fun(X930,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X930,tc_HOL_Obool)),X929),hAPP(hAPP(c_Set_Oinsert(X930),X928),c_Orderings_Obot__class_Obot(tc_fun(X930,tc_HOL_Obool))))|c_Big__Operators_Olattice_OSup__fin(X930,c_Orderings_Oord__class_Omax(X930),X929)=X928|~hBOOL(hAPP(hAPP(c_member(X930),X928),X929))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X930),X929))|~class_Orderings_Olinorder(X930))&(c_Orderings_Obot__class_Obot(tc_fun(X930,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X930,tc_HOL_Obool)),X929),hAPP(hAPP(c_Set_Oinsert(X930),X928),c_Orderings_Obot__class_Obot(tc_fun(X930,tc_HOL_Obool))))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X930),X928),c_Big__Operators_Olattice_OSup__fin(X930,c_Orderings_Oord__class_Omax(X930),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X930,tc_HOL_Obool)),X929),hAPP(hAPP(c_Set_Oinsert(X930),X928),c_Orderings_Obot__class_Obot(tc_fun(X930,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OSup__fin(X930,c_Orderings_Oord__class_Omax(X930),X929)|~hBOOL(hAPP(hAPP(c_member(X930),X928),X929))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X930),X929))|~class_Orderings_Olinorder(X930))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oremove])])])])). 4.46/4.70 fof(c_0_6405, plain, ![X15948, X15949, X15950, X15951]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk462_4(X15948,X15949,X15950,X15951)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X15950)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15951),X15949))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15951),X15950)),X15949)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15949),c_Groups_Oone__class_Oone(tc_Int_Oint))),X15948))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15950)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk463_4(X15948,X15949,X15950,X15951)),X15948))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15951),X15949))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15951),X15950)),X15949)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15949),c_Groups_Oone__class_Oone(tc_Int_Oint))),X15948))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15950)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk463_4(X15948,X15949,X15950,X15951)),esk462_4(X15948,X15949,X15950,X15951))=X15951|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15951),X15949))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15951),X15950)),X15949)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15949),c_Groups_Oone__class_Oone(tc_Int_Oint))),X15948))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15950))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_aset_I6_J])])])])])])). 4.46/4.70 cnf(c_0_6406, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk316_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X4))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5060])). 4.46/4.70 fof(c_0_6407, plain, ![X5454, X5455, X5456, X5457, X5458]:(hAPP(c_Relation_OImage(X5458,X5458,X5457),hAPP(hAPP(c_Set_Oinsert(X5458),X5456),c_Orderings_Obot__class_Obot(tc_fun(X5458,tc_HOL_Obool))))!=hAPP(c_Relation_OImage(X5458,X5458,X5457),hAPP(hAPP(c_Set_Oinsert(X5458),X5455),c_Orderings_Obot__class_Obot(tc_fun(X5458,tc_HOL_Obool))))|(~c_Equiv__Relations_Oequiv(X5458,X5454,X5457)|(~hBOOL(hAPP(hAPP(c_member(X5458),X5455),X5454))|hBOOL(hAPP(hAPP(c_member(tc_prod(X5458,X5458)),hAPP(hAPP(c_Product__Type_OPair(X5458,X5458),X5456),X5455)),X5457))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__equiv__class])])])). 4.46/4.70 fof(c_0_6408, plain, ![X9111, X9112, X9113, X9114]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9114),X9113))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X9114),X9112)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X9113),X9111))),c_FunDef_Opair__leq))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pair__leqI1])])])). 4.46/4.70 cnf(c_0_6409, plain, (hBOOL(hAPP(X3,esk446_2(X3,X2)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X3,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk444_2(X3,X2)),X2))))|hBOOL(hAPP(X3,esk443_2(X3,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(X3,X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5061])). 4.46/4.70 cnf(c_0_6410, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_5062]), ['final']). 4.46/4.70 fof(c_0_6411, plain, ![X12097, X12098, X12099]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12099,tc_HOL_Obool)),X12098),hAPP(hAPP(c_Set_Oinsert(X12099),X12097),c_Orderings_Obot__class_Obot(tc_fun(X12099,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X12099,tc_HOL_Obool))|X12097=c_Big__Operators_Olattice_OInf__fin(X12099,c_Orderings_Oord__class_Omin(X12099),X12098)|~hBOOL(hAPP(hAPP(c_member(X12099),X12097),X12098))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12099),X12098))|~class_Orderings_Olinorder(X12099))&(c_Orderings_Obot__class_Obot(tc_fun(X12099,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12099,tc_HOL_Obool)),X12098),hAPP(hAPP(c_Set_Oinsert(X12099),X12097),c_Orderings_Obot__class_Obot(tc_fun(X12099,tc_HOL_Obool))))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X12099),X12097),c_Big__Operators_Olattice_OInf__fin(X12099,c_Orderings_Oord__class_Omin(X12099),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12099,tc_HOL_Obool)),X12098),hAPP(hAPP(c_Set_Oinsert(X12099),X12097),c_Orderings_Obot__class_Obot(tc_fun(X12099,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OInf__fin(X12099,c_Orderings_Oord__class_Omin(X12099),X12098)|~hBOOL(hAPP(hAPP(c_member(X12099),X12097),X12098))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12099),X12098))|~class_Orderings_Olinorder(X12099))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oremove])])])])). 4.46/4.70 fof(c_0_6412, plain, ![X10080, X10081, X10082, X10083, X10084, X10085]:(~c_Finite__Set_Ofolding(X10085,X10084,X10083,X10082)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10085),X10081))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10085),X10080))|hAPP(c_Fun_Ocomp(X10084,X10084,X10084,hAPP(X10082,X10081)),hAPP(X10082,X10080))=hAPP(c_Fun_Ocomp(X10084,X10084,X10084,hAPP(X10082,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10085,tc_HOL_Obool)),X10081),X10080))),hAPP(X10082,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10085,tc_HOL_Obool)),X10081),X10080)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Ounion__inter])])])). 4.46/4.70 cnf(c_0_6413, plain, (hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2),c_fNot),hAPP(c_fequal,hAPP(X3,X4)))),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))=hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X4))),X5))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5063, c_0_5035]), c_0_5035])). 4.46/4.70 fof(c_0_6414, plain, ![X11084, X11085, X11086, X11087]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11087),X11086))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X11087),X11085)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X11086),X11084))),c_FunDef_Opair__less))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__lessI1])])). 4.46/4.70 cnf(c_0_6415, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk3_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(X1,X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),esk1_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_5007])). 4.46/4.70 cnf(c_0_6416, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X3!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2))), inference(split_conjunct,[status(thm)],[c_0_5031])). 4.46/4.70 fof(c_0_6417, plain, ![X7892, X7893, X7894, X7895, X7896, X7897, X7898, X7899]:(~c_Finite__Set_Ofolding__image(X7899,X7898,X7897,X7896,X7895)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7898),X7894))|hAPP(hAPP(X7897,hAPP(hAPP(X7895,X7893),X7894)),hAPP(hAPP(X7895,X7892),X7894))=hAPP(hAPP(X7895,hAPP(hAPP(c_COMBS(X7898,X7899,X7899),hAPP(hAPP(c_COMBB(X7899,tc_fun(X7899,X7899),X7898),X7897),X7893)),X7892)),X7894))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image_Odistrib])])])). 4.46/4.70 cnf(c_0_6418, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk2_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(X1,X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),esk1_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_5007])). 4.46/4.70 cnf(c_0_6419, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X6),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7,X5),X3))|hAPP(X1,esk372_8(X2,X1,X3,X4,X5,X6,X7,X8))!=hAPP(X2,esk372_8(X2,X1,X3,X4,X5,X6,X7,X8))|X4!=X3|X5!=X6|~class_Orderings_Oord(X7)|~class_Groups_Ocomm__monoid__add(X8)), inference(split_conjunct,[status(thm)],[c_0_5064])). 4.46/4.70 cnf(c_0_6420, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|hAPP(hAPP(c_List_Oappend(X1),X3),X5)=hAPP(hAPP(c_List_Oappend(X1),X2),X4)|hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)),X4)!=X5|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)!=X3), inference(split_conjunct,[status(thm)],[c_0_5038])). 4.46/4.70 fof(c_0_6421, plain, ![X17376, X17377, X17378]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X17377,X17378)),X17376))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X17377),hAPP(hAPP(c_COMBB(tc_fun(X17378,tc_HOL_Obool),tc_HOL_Obool,X17377),c_Enum_Oenum__class_Oenum__all(X17378)),hAPP(hAPP(c_COMBB(tc_fun(X17378,tc_prod(X17377,X17378)),tc_fun(X17378,tc_HOL_Obool),X17377),hAPP(c_COMBB(tc_prod(X17377,X17378),tc_HOL_Obool,X17378),X17376)),c_Product__Type_OPair(X17377,X17378)))))|(~class_Enum_Oenum(X17377)|~class_Enum_Oenum(X17378)))&(~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X17377),hAPP(hAPP(c_COMBB(tc_fun(X17378,tc_HOL_Obool),tc_HOL_Obool,X17377),c_Enum_Oenum__class_Oenum__all(X17378)),hAPP(hAPP(c_COMBB(tc_fun(X17378,tc_prod(X17377,X17378)),tc_fun(X17378,tc_HOL_Obool),X17377),hAPP(c_COMBB(tc_prod(X17377,X17378),tc_HOL_Obool,X17378),X17376)),c_Product__Type_OPair(X17377,X17378)))))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X17377,X17378)),X17376))|(~class_Enum_Oenum(X17377)|~class_Enum_Oenum(X17378)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__all__prod__def])])])). 4.46/4.70 fof(c_0_6422, plain, ![X10383, X10384, X10385]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X10384,X10385)),X10383))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X10384),hAPP(hAPP(c_COMBB(tc_fun(X10385,tc_HOL_Obool),tc_HOL_Obool,X10384),c_Enum_Oenum__class_Oenum__ex(X10385)),hAPP(hAPP(c_COMBB(tc_fun(X10385,tc_prod(X10384,X10385)),tc_fun(X10385,tc_HOL_Obool),X10384),hAPP(c_COMBB(tc_prod(X10384,X10385),tc_HOL_Obool,X10385),X10383)),c_Product__Type_OPair(X10384,X10385)))))|(~class_Enum_Oenum(X10384)|~class_Enum_Oenum(X10385)))&(~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X10384),hAPP(hAPP(c_COMBB(tc_fun(X10385,tc_HOL_Obool),tc_HOL_Obool,X10384),c_Enum_Oenum__class_Oenum__ex(X10385)),hAPP(hAPP(c_COMBB(tc_fun(X10385,tc_prod(X10384,X10385)),tc_fun(X10385,tc_HOL_Obool),X10384),hAPP(c_COMBB(tc_prod(X10384,X10385),tc_HOL_Obool,X10385),X10383)),c_Product__Type_OPair(X10384,X10385)))))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X10384,X10385)),X10383))|(~class_Enum_Oenum(X10384)|~class_Enum_Oenum(X10385)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__ex__prod__def])])])). 4.46/4.70 cnf(c_0_6423, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2))),hAPP(hAPP(c_COMBC(X1,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,tc_HOL_Obool),X1),c_fequal),X4)),hAPP(X4,esk274_4(X4,X3,X2,X1)))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2)))), inference(split_conjunct,[status(thm)],[c_0_5065])). 4.46/4.70 cnf(c_0_6424, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk79_4(X1,X2,X3,X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X4)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk78_4(X1,X2,X3,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk78_4(X1,X2,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5066])). 4.46/4.70 cnf(c_0_6425, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk79_4(X2,X3,X4,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk78_4(X2,X3,X4,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X3,esk78_4(X2,X3,X4,X1))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5066])). 4.46/4.70 fof(c_0_6426, plain, ![X9597, X9598, X9599, X9600, X9601, X9602, X9603, X9604]:(~c_Finite__Set_Ofolding(X9604,X9603,X9602,X9601)|hAPP(c_Fun_Ocomp(X9603,X9603,X9600,hAPP(X9602,X9599)),hAPP(c_Fun_Ocomp(X9603,X9603,X9600,hAPP(X9602,X9598)),X9597))=hAPP(c_Fun_Ocomp(X9603,X9603,X9600,hAPP(X9602,X9598)),hAPP(c_Fun_Ocomp(X9603,X9603,X9600,hAPP(X9602,X9599)),X9597))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Ocommute__left__comp])])])). 4.46/4.70 fof(c_0_6427, plain, ![X1641, X1642, X1643, X1644, X1645]:(~class_Fields_Ofield(X1645)|(X1644=c_Groups_Ozero__class_Ozero(X1645)|(c_Groups_Ozero__class_Ozero(X1645)=X1643|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1645),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1645),X1642),X1643)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1645),X1641),X1644))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1645),X1644),X1643))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1645),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1645),X1642),X1644)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1645),X1641),X1643))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__frac__eq])])). 4.46/4.70 fof(c_0_6428, plain, ![X10825, X10826, X10827, X10828]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10828),X10827))|(~hBOOL(hAPP(hAPP(c_member(X10828),X10826),X10827))|(hBOOL(hAPP(hAPP(c_member(X10828),X10826),X10825))|hAPP(c_Finite__Set_Ocard(X10828),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10828,tc_HOL_Obool)),X10827),hAPP(hAPP(c_Set_Oinsert(X10828),X10826),X10825)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10828),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10828,tc_HOL_Obool)),X10827),X10825))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff__insert])])])). 4.46/4.70 cnf(c_0_6429, plain, (c_Map_Orestrict__map(X1,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),X5),X2),X6),X3)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Orestrict__map(X1,X4,X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),X2),X6)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5067])). 4.46/4.70 cnf(c_0_6430, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X4)),X5),X6)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),X5),X6)), inference(split_conjunct,[status(thm)],[c_0_5068]), ['final']). 4.46/4.70 fof(c_0_6431, plain, ![X1096, X1097, X1098]:((c_Orderings_Obot__class_Obot(tc_fun(X1098,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1098,tc_HOL_Obool)),X1097),hAPP(hAPP(c_Set_Oinsert(X1098),X1096),c_Orderings_Obot__class_Obot(tc_fun(X1098,tc_HOL_Obool))))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1098),X1096),c_Big__Operators_Olattice_OSup__fin(X1098,c_Orderings_Oord__class_Omax(X1098),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1098,tc_HOL_Obool)),X1097),hAPP(hAPP(c_Set_Oinsert(X1098),X1096),c_Orderings_Obot__class_Obot(tc_fun(X1098,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OSup__fin(X1098,c_Orderings_Oord__class_Omax(X1098),hAPP(hAPP(c_Set_Oinsert(X1098),X1096),X1097))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1098),X1097))|~class_Orderings_Olinorder(X1098))&(c_Orderings_Obot__class_Obot(tc_fun(X1098,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1098,tc_HOL_Obool)),X1097),hAPP(hAPP(c_Set_Oinsert(X1098),X1096),c_Orderings_Obot__class_Obot(tc_fun(X1098,tc_HOL_Obool))))|c_Big__Operators_Olattice_OSup__fin(X1098,c_Orderings_Oord__class_Omax(X1098),hAPP(hAPP(c_Set_Oinsert(X1098),X1096),X1097))=X1096|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1098),X1097))|~class_Orderings_Olinorder(X1098))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oinsert__remove])])])])). 4.46/4.70 cnf(c_0_6432, plain, (c_List_OdropWhile(X4,X1,hAPP(hAPP(c_List_Oappend(X4),X3),X2))=c_List_OdropWhile(X4,X1,X2)|~hBOOL(hAPP(X1,esk304_4(X2,X1,X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_5056])). 4.46/4.70 fof(c_0_6433, plain, ![X10393, X10394, X10395, X10396, X10397]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10397,X10397)),hAPP(hAPP(c_Product__Type_OPair(X10397,X10397),X10396),X10395)),c_Transitive__Closure_Ortrancl(X10397,X10394)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10397,X10397)),hAPP(hAPP(c_Product__Type_OPair(X10397,X10397),X10395),X10393)),c_Transitive__Closure_Ortrancl(X10397,X10394)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X10397,X10397)),hAPP(hAPP(c_Product__Type_OPair(X10397,X10397),X10396),X10393)),c_Transitive__Closure_Ortrancl(X10397,X10394))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__trans])])])). 4.46/4.70 fof(c_0_6434, plain, ![X7120, X7121, X7122, X7123]:(hAPP(c_List_Oset(X7123),X7122)!=c_Map_Odom(X7123,X7121,X7120)|hAPP(c_Map_Omap__of(X7123,X7121),hAPP(hAPP(c_List_Omap(X7123,tc_prod(X7123,X7121)),hAPP(hAPP(c_COMBS(X7123,X7121,tc_prod(X7123,X7121)),c_Product__Type_OPair(X7123,X7121)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X7121),X7121,X7123),c_Option_Othe(X7121)),X7120))),X7122))=X7120), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__map__keys])])])). 4.46/4.70 fof(c_0_6435, plain, ![X10700, X10701, X10702, X10703, X10704]:(~class_Fields_Ofield(X10704)|(X10703=c_Groups_Ozero__class_Ozero(X10704)|(c_Groups_Ozero__class_Ozero(X10704)=X10702|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10704),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10704),X10701),X10703)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10704),X10700),X10702))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10704),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10704),X10701),X10702)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10704),X10700),X10703))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10704),X10703),X10702))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__frac__eq])])])). 4.46/4.70 fof(c_0_6436, plain, ![X9234, X9235, X9236]:((c_Orderings_Obot__class_Obot(tc_fun(X9236,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9236,tc_HOL_Obool)),X9235),hAPP(hAPP(c_Set_Oinsert(X9236),X9234),c_Orderings_Obot__class_Obot(tc_fun(X9236,tc_HOL_Obool))))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X9236),X9234),c_Big__Operators_Olattice_OInf__fin(X9236,c_Orderings_Oord__class_Omin(X9236),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9236,tc_HOL_Obool)),X9235),hAPP(hAPP(c_Set_Oinsert(X9236),X9234),c_Orderings_Obot__class_Obot(tc_fun(X9236,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OInf__fin(X9236,c_Orderings_Oord__class_Omin(X9236),hAPP(hAPP(c_Set_Oinsert(X9236),X9234),X9235))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9236),X9235))|~class_Orderings_Olinorder(X9236))&(c_Orderings_Obot__class_Obot(tc_fun(X9236,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9236,tc_HOL_Obool)),X9235),hAPP(hAPP(c_Set_Oinsert(X9236),X9234),c_Orderings_Obot__class_Obot(tc_fun(X9236,tc_HOL_Obool))))|X9234=c_Big__Operators_Olattice_OInf__fin(X9236,c_Orderings_Oord__class_Omin(X9236),hAPP(hAPP(c_Set_Oinsert(X9236),X9234),X9235))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9236),X9235))|~class_Orderings_Olinorder(X9236))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oinsert__remove])])])])). 4.46/4.70 cnf(c_0_6437, plain, (hBOOL(hAPP(X1,esk254_5(X2,X1,X3,X4,X5)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X5),X1))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X5),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_5033])). 4.46/4.70 fof(c_0_6438, plain, ![X365, X366, X367, X368, X369]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X368),X367)),X366)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X369),X367)),X365)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X368),X369)),X367)),X366)),X365))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X369),X368)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X368),X369)),X367)),X366)),X365))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X368),X367)),X366)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X369),X367)),X365)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X369),X368)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__less__add__iff1])])])])). 4.46/4.70 fof(c_0_6439, plain, ![X3009, X3010, X3011, X3012, X3013]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3012),X3013)),X3011)),X3010)),X3009))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3012),X3011)),X3010)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3013),X3011)),X3009)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3013),X3012)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3012),X3011)),X3010)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3013),X3011)),X3009)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3012),X3013)),X3011)),X3010)),X3009))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3013),X3012)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1])])])). 4.46/4.70 cnf(c_0_6440, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk445_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk444_2(X1,X2)),X2))))|hBOOL(hAPP(X1,esk443_2(X1,X2)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5061])). 4.46/4.70 fof(c_0_6441, plain, ![X6415, X6416, X6417, X6418, X6419]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6419),X6417)),X6416)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6418),X6417)),X6415)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6416),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6418),X6419)),X6417)),X6415)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6419),X6418)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6416),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6418),X6419)),X6417)),X6415)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6419),X6417)),X6416)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6418),X6417)),X6415)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6419),X6418)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__less__add__iff2])])])])). 4.46/4.70 fof(c_0_6442, plain, ![X13043, X13044, X13045, X13046, X13047]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13047),X13045)),X13044)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13046),X13045)),X13043)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13044),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13046),X13047)),X13045)),X13043)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13047),X13046)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13044),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13046),X13047)),X13045)),X13043)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13047),X13045)),X13044)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13046),X13045)),X13043)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13047),X13046)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__le__add__iff2])])])])). 4.46/4.70 cnf(c_0_6443, plain, (hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4))),X2))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_5069])). 4.46/4.70 cnf(c_0_6444, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk66_3(X2,X3,X1)),X3))|hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk64_3(X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))), inference(split_conjunct,[status(thm)],[c_0_5070])). 4.46/4.70 cnf(c_0_6445, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))), inference(split_conjunct,[status(thm)],[c_0_5071]), ['final']). 4.46/4.70 cnf(c_0_6446, plain, (hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oconcat(X2,X1)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),esk1_2(X1,X2)),hAPP(c_List_Oset(tc_List_Olist(X2)),X1)))|esk3_2(X1,X2)!=esk2_2(X1,X2)|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1))), inference(split_conjunct,[status(thm)],[c_0_5007])). 4.46/4.70 cnf(c_0_6447, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk530_6(X2,X3,X4,X5,X1,X6)),hAPP(c_List_Oset(X1),X6)))|hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)=hAPP(c_List_Ofilter(X1,X3),X2)|X2!=hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X7))|~hBOOL(hAPP(X3,X5))|X4!=hAPP(c_List_Ofilter(X1,X3),X7)), inference(split_conjunct,[status(thm)],[c_0_5072])). 4.46/4.70 cnf(c_0_6448, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk65_3(X2,X3,X1)),X3))|hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk64_3(X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))), inference(split_conjunct,[status(thm)],[c_0_5070])). 4.46/4.70 fof(c_0_6449, plain, ![X7726, X7727, X7728, X7729, X7730]:(~c_Equiv__Relations_Oequiv(X7730,X7729,X7728)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X7730,X7730)),hAPP(hAPP(c_Product__Type_OPair(X7730,X7730),X7727),X7726)),X7728))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7730,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7730,X7730,X7728),hAPP(hAPP(c_Set_Oinsert(X7730),X7727),c_Orderings_Obot__class_Obot(tc_fun(X7730,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X7730,X7730,X7728),hAPP(hAPP(c_Set_Oinsert(X7730),X7726),c_Orderings_Obot__class_Obot(tc_fun(X7730,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equiv__class__subset])])])). 4.46/4.70 fof(c_0_6450, plain, ![X12855, X12856, X12857]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12857),X12856))|(~c_Fun_Oinj__on(X12857,tc_fun(tc_fun(X12857,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X12857,tc_fun(tc_prod(X12857,X12857),tc_HOL_Obool),tc_fun(tc_fun(X12857,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12857,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X12857,X12857),tc_HOL_Obool),tc_fun(tc_fun(X12857,tc_HOL_Obool),tc_HOL_Obool)),X12857),c_Equiv__Relations_Oquotient(X12857)),hAPP(hAPP(c_COMBC(X12857,tc_fun(X12857,tc_HOL_Obool),tc_fun(X12857,tc_HOL_Obool)),c_Set_Oinsert(X12857)),c_Orderings_Obot__class_Obot(tc_fun(X12857,tc_HOL_Obool))))),X12855),X12856)|hAPP(c_Finite__Set_Ocard(tc_fun(X12857,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X12857),X12856),X12855))=hAPP(c_Finite__Set_Ocard(X12857),X12856))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__quotient__disjoint])])). 4.46/4.70 fof(c_0_6451, plain, ![X9924, X9925, X9926, X9927, X9928]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9928,X9928)),hAPP(hAPP(c_Product__Type_OPair(X9928,X9928),hAPP(X9927,hAPP(c_Nat_OSuc,esk285_5(X9924,X9925,X9926,X9927,X9928)))),hAPP(X9927,esk285_5(X9924,X9925,X9926,X9927,X9928)))),c_Transitive__Closure_Ortrancl(X9928,X9926)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X9928,X9928)),hAPP(hAPP(c_Product__Type_OPair(X9928,X9928),hAPP(X9927,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9925),X9924))),hAPP(X9927,X9925))),c_Transitive__Closure_Ortrancl(X9928,X9926)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sequence__trans])])])). 4.46/4.70 fof(c_0_6452, plain, ![X12958, X12959, X12960, X12961, X12962, X12963]:(~c_Fun_Oinj__on(X12963,X12962,X12961,X12960)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12963,tc_HOL_Obool)),X12959),X12960))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12963,tc_HOL_Obool)),X12958),X12960))|hAPP(c_Set_Oimage(X12963,X12962,X12961),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12963,tc_HOL_Obool)),X12959),X12958))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12962,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12963,X12962,X12961),X12959)),hAPP(c_Set_Oimage(X12963,X12962,X12961),X12958))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__image__set__diff])])])). 4.46/4.70 fof(c_0_6453, plain, ![X2220, X2221, X2222, X2223, X2224, X2225]:(~c_Fun_Oinj__on(X2225,X2224,X2223,X2222)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2225,tc_HOL_Obool)),X2221),X2222))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2225,tc_HOL_Obool)),X2220),X2222))|hAPP(c_Set_Oimage(X2225,X2224,X2223),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2225,tc_HOL_Obool)),X2221),X2220))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2224,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2225,X2224,X2223),X2221)),hAPP(c_Set_Oimage(X2225,X2224,X2223),X2220))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__image__Int])])])). 4.46/4.70 fof(c_0_6454, plain, ![X10996, X10997, X10998, X10999, X11000]:(~c_Equiv__Relations_Oequiv(X11000,X10999,X10998)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11000,tc_HOL_Obool)),hAPP(c_Relation_OImage(X11000,X11000,X10998),hAPP(hAPP(c_Set_Oinsert(X11000),X10997),c_Orderings_Obot__class_Obot(tc_fun(X11000,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X11000,X11000,X10998),hAPP(hAPP(c_Set_Oinsert(X11000),X10996),c_Orderings_Obot__class_Obot(tc_fun(X11000,tc_HOL_Obool))))))|(~hBOOL(hAPP(hAPP(c_member(X11000),X10997),X10999))|hBOOL(hAPP(hAPP(c_member(tc_prod(X11000,X11000)),hAPP(hAPP(c_Product__Type_OPair(X11000,X11000),X10996),X10997)),X10998))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__equiv__class])])])). 4.46/4.70 fof(c_0_6455, plain, ![X6880, X6881, X6882, X6883, X6884, X6885]:(~class_Complete__Lattice_Ocomplete__lattice(X6885)|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6884,X6885),X6883),hAPP(hAPP(c_COMBB(tc_fun(X6882,X6885),X6885,X6884),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6882,X6885),X6881)),X6880))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6882,X6885),X6881),hAPP(hAPP(c_COMBB(tc_fun(X6884,X6885),X6885,X6882),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6884,X6885),X6883)),hAPP(c_COMBC(X6884,X6882,X6885),X6880)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF__commute])])])). 4.46/4.70 cnf(c_0_6456, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk317_4(X2,X3,X4,X1)),esk316_4(X2,X3,X4,X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X1))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))), inference(split_conjunct,[status(thm)],[c_0_5060])). 4.46/4.70 fof(c_0_6457, plain, ![X6283, X6284, X6285, X6286, X6287, X6288]:(~class_Complete__Lattice_Ocomplete__lattice(X6288)|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6287,X6288),X6286),hAPP(hAPP(c_COMBB(tc_fun(X6285,X6288),X6288,X6287),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6285,X6288),X6284)),X6283))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6285,X6288),X6284),hAPP(hAPP(c_COMBB(tc_fun(X6287,X6288),X6288,X6285),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6287,X6288),X6286)),hAPP(c_COMBC(X6287,X6285,X6288),X6283)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUP__commute])])])). 4.46/4.70 fof(c_0_6458, plain, ![X1981, X1982, X1983, X1984, X1985, X1986]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1986),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1986),X1985),X1984)),X1983)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1986),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1986),X1982),X1984)),X1981)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1986),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1986),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1986),X1985),X1982)),X1984)),X1983)),X1981))|~class_Rings_Oordered__ring(X1986))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1986),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1986),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1986),X1985),X1982)),X1984)),X1983)),X1981))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1986),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1986),X1985),X1984)),X1983)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1986),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1986),X1982),X1984)),X1981)))|~class_Rings_Oordered__ring(X1986))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__add__iff1])])])])). 4.46/4.70 fof(c_0_6459, plain, ![X4040, X4041, X4042, X4043, X4044]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4044,X4044)),hAPP(hAPP(c_Product__Type_OPair(X4044,X4044),X4043),X4042)),X4041))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4044,X4044)),hAPP(hAPP(c_Product__Type_OPair(X4044,X4044),X4042),X4040)),c_Transitive__Closure_Ortrancl(X4044,X4041)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4044,X4044)),hAPP(hAPP(c_Product__Type_OPair(X4044,X4044),X4043),X4040)),c_Transitive__Closure_Ortrancl(X4044,X4041))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_converse__rtrancl__into__rtrancl])])])). 4.46/4.70 fof(c_0_6460, plain, ![X6631, X6632, X6633, X6634, X6635]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X6635,X6635)),hAPP(hAPP(c_Product__Type_OPair(X6635,X6635),X6634),X6633)),c_Transitive__Closure_Ortrancl(X6635,X6632)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X6635,X6635)),hAPP(hAPP(c_Product__Type_OPair(X6635,X6635),X6633),X6631)),X6632))|hBOOL(hAPP(hAPP(c_member(tc_prod(X6635,X6635)),hAPP(hAPP(c_Product__Type_OPair(X6635,X6635),X6634),X6631)),c_Transitive__Closure_Ortrancl(X6635,X6632))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl])])])). 4.46/4.70 cnf(c_0_6461, plain, (hAPP(c_List_Orev(X2),hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4))=hAPP(hAPP(c_List_Olist__update(X2,hAPP(c_List_Orev(X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_5073])). 4.46/4.70 cnf(c_0_6462, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_5074]), ['final']). 4.46/4.70 fof(c_0_6463, plain, ![X1191, X1192, X1193, X1194, X1195, X1196]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1196),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1196),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1196),X1195),X1192)),X1194)),X1193)),X1191))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1196),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1196),X1195),X1194)),X1193)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1196),X1192),X1194)),X1191)))|~class_Rings_Oordered__ring(X1196))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1196),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1196),X1195),X1194)),X1193)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1196),X1192),X1194)),X1191)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1196),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1196),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1196),X1195),X1192)),X1194)),X1193)),X1191))|~class_Rings_Oordered__ring(X1196))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff1])])])). 4.46/4.70 fof(c_0_6464, plain, ![X7372, X7373, X7374, X7375, X7376, X7377]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7377),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7377),X7376),X7375)),X7374)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7377),X7373),X7375)),X7372)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7377),X7374),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7377),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7377),X7373),X7376)),X7375)),X7372)))|~class_Rings_Oordered__ring(X7377))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7377),X7374),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7377),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7377),X7373),X7376)),X7375)),X7372)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7377),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7377),X7376),X7375)),X7374)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7377),X7373),X7375)),X7372)))|~class_Rings_Oordered__ring(X7377))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff2])])])). 4.46/4.70 fof(c_0_6465, plain, ![X12926, X12927, X12928, X12929, X12930, X12931]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12931),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12931),X12930),X12929)),X12928)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12931),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12931),X12927),X12929)),X12926)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12931),X12928),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12931),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12931),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12931),X12927),X12930)),X12929)),X12926)))|~class_Rings_Oordered__ring(X12931))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12931),X12928),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12931),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12931),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12931),X12927),X12930)),X12929)),X12926)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12931),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12931),X12930),X12929)),X12928)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12931),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12931),X12927),X12929)),X12926)))|~class_Rings_Oordered__ring(X12931))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__add__iff2])])])])). 4.46/4.70 cnf(c_0_6466, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X5),X4),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),esk36_5(X3,X4,X2,X1,X5)))),X4),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X1),hAPP(X3,esk35_5(X3,X4,X2,X1,X5))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5075])). 4.46/4.70 fof(c_0_6467, plain, ![X10256, X10257, X10258, X10259, X10260]:((hBOOL(hAPP(hAPP(c_member(X10259),esk295_5(X10256,X10257,X10258,X10259,X10260)),hAPP(c_List_Oset(X10259),X10258)))|hAPP(c_List_Omonoid__add__class_Olistsum(X10260),hAPP(hAPP(c_List_Omap(X10259,X10260),X10256),hAPP(c_List_Ofilter(X10259,X10257),X10258)))=hAPP(c_List_Omonoid__add__class_Olistsum(X10260),hAPP(hAPP(c_List_Omap(X10259,X10260),X10256),X10258))|~class_Groups_Omonoid__add(X10260))&((~hBOOL(hAPP(X10257,esk295_5(X10256,X10257,X10258,X10259,X10260)))|hAPP(c_List_Omonoid__add__class_Olistsum(X10260),hAPP(hAPP(c_List_Omap(X10259,X10260),X10256),hAPP(c_List_Ofilter(X10259,X10257),X10258)))=hAPP(c_List_Omonoid__add__class_Olistsum(X10260),hAPP(hAPP(c_List_Omap(X10259,X10260),X10256),X10258))|~class_Groups_Omonoid__add(X10260))&(hAPP(X10256,esk295_5(X10256,X10257,X10258,X10259,X10260))!=c_Groups_Ozero__class_Ozero(X10260)|hAPP(c_List_Omonoid__add__class_Olistsum(X10260),hAPP(hAPP(c_List_Omap(X10259,X10260),X10256),hAPP(c_List_Ofilter(X10259,X10257),X10258)))=hAPP(c_List_Omonoid__add__class_Olistsum(X10260),hAPP(hAPP(c_List_Omap(X10259,X10260),X10256),X10258))|~class_Groups_Omonoid__add(X10260)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__map__filter])])])])])). 4.46/4.70 cnf(c_0_6468, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(X1,X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk1_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),esk2_2(X2,X1))),hAPP(c_List_Oset(X1),esk3_2(X2,X1)))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_5007])). 4.46/4.70 fof(c_0_6469, plain, ![X3264, X3265, X3266, X3267]:((hBOOL(hAPP(hAPP(c_member(X3267),esk86_4(X3264,X3265,X3266,X3267)),X3266))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3267,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X3265,tc_HOL_Obool),tc_Nat_Onat,X3267),c_Finite__Set_Ocard(X3265)),X3264)),X3266)=hAPP(c_Finite__Set_Ocard(tc_prod(X3267,X3265)),hAPP(hAPP(c_Product__Type_OSigma(X3267,X3265),X3266),X3264))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3267),X3266)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3265),hAPP(X3264,esk86_4(X3264,X3265,X3266,X3267))))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3267,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X3265,tc_HOL_Obool),tc_Nat_Onat,X3267),c_Finite__Set_Ocard(X3265)),X3264)),X3266)=hAPP(c_Finite__Set_Ocard(tc_prod(X3267,X3265)),hAPP(hAPP(c_Product__Type_OSigma(X3267,X3265),X3266),X3264))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3267),X3266)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__SigmaI])])])])])). 4.46/4.70 cnf(c_0_6470, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OSemi(X4,X6)),X7)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X5),X6),X7)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5076])). 4.46/4.70 fof(c_0_6471, plain, ![X13024, X13025, X13026, X13027, X13028]:((hBOOL(hAPP(hAPP(c_member(X13027),esk380_5(X13024,X13025,X13026,X13027,X13028)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13027,tc_HOL_Obool)),X13026),X13025)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13027,X13028),X13024),X13025)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13027,X13028),X13024),X13026)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13027,tc_HOL_Obool)),X13025),X13026))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13027),X13026))|~class_Groups_Ocomm__monoid__mult(X13028))&(hAPP(X13024,esk380_5(X13024,X13025,X13026,X13027,X13028))!=c_Groups_Oone__class_Oone(X13028)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13027,X13028),X13024),X13025)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13027,X13028),X13024),X13026)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13027,tc_HOL_Obool)),X13025),X13026))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13027),X13026))|~class_Groups_Ocomm__monoid__mult(X13028))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__mono__one__left])])])])])). 4.46/4.70 fof(c_0_6472, plain, ![X5844, X5845, X5846, X5847, X5848]:((hBOOL(hAPP(hAPP(c_member(X5847),esk181_5(X5844,X5845,X5846,X5847,X5848)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5847,tc_HOL_Obool)),X5846),X5845)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5847,X5848),X5844),X5846)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5847,X5848),X5844),X5845)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5847,tc_HOL_Obool)),X5845),X5846))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5847),X5846))|~class_Groups_Ocomm__monoid__mult(X5848))&(hAPP(X5844,esk181_5(X5844,X5845,X5846,X5847,X5848))!=c_Groups_Oone__class_Oone(X5848)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5847,X5848),X5844),X5846)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5847,X5848),X5844),X5845)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5847,tc_HOL_Obool)),X5845),X5846))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5847),X5846))|~class_Groups_Ocomm__monoid__mult(X5848))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__mono__one__right])])])])])). 4.46/4.70 fof(c_0_6473, plain, ![X15361, X15362, X15363, X15364, X15365]:((hBOOL(hAPP(hAPP(c_member(X15364),esk447_5(X15361,X15362,X15363,X15364,X15365)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15364,tc_HOL_Obool)),X15363),X15362)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15364,X15365),X15361),X15362)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15364,X15365),X15361),X15363)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15364,tc_HOL_Obool)),X15362),X15363))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15364),X15363))|~class_Groups_Ocomm__monoid__add(X15365))&(hAPP(X15361,esk447_5(X15361,X15362,X15363,X15364,X15365))!=c_Groups_Ozero__class_Ozero(X15365)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15364,X15365),X15361),X15362)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15364,X15365),X15361),X15363)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15364,tc_HOL_Obool)),X15362),X15363))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15364),X15363))|~class_Groups_Ocomm__monoid__add(X15365))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__mono__zero__right])])])])])). 4.46/4.70 cnf(c_0_6474, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5077, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.70 fof(c_0_6475, plain, ![X14901, X14902, X14903]:(~class_Lattices_Oab__semigroup__idem__mult(X14903)|(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14903),hAPP(X14902,esk437_3(X14901,X14902,X14903))),hAPP(X14902,esk438_3(X14901,X14902,X14903)))!=hAPP(X14902,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14903),esk437_3(X14901,X14902,X14903)),esk438_3(X14901,X14902,X14903)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14903),X14901))|(c_Orderings_Obot__class_Obot(tc_fun(X14903,tc_HOL_Obool))=X14901|hAPP(c_Finite__Set_Ofold1(X14903,c_Groups_Otimes__class_Otimes(X14903)),hAPP(c_Set_Oimage(X14903,X14903,X14902),X14901))=hAPP(X14902,hAPP(c_Finite__Set_Ofold1(X14903,c_Groups_Otimes__class_Otimes(X14903)),X14901)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hom__fold1__commute])])])])). 4.46/4.70 fof(c_0_6476, plain, ![X553, X554, X555, X556, X558, X559, X560, X561, X562, X563, X566]:((((~hBOOL(hAPP(hAPP(c_member(X556),X558),X554))|hBOOL(hAPP(X553,X558))|hBOOL(hAPP(hAPP(c_member(X556),esk10_4(X553,X554,X555,X556)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X556,tc_HOL_Obool)),X555),X554))))&(~hBOOL(hAPP(hAPP(c_member(X556),X559),X555))|hBOOL(hAPP(X553,X559))|hBOOL(hAPP(hAPP(c_member(X556),esk10_4(X553,X554,X555,X556)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X556,tc_HOL_Obool)),X555),X554)))))&((~hBOOL(hAPP(hAPP(c_member(X556),X558),X554))|hBOOL(hAPP(X553,X558))|~hBOOL(hAPP(X553,esk10_4(X553,X554,X555,X556))))&(~hBOOL(hAPP(hAPP(c_member(X556),X559),X555))|hBOOL(hAPP(X553,X559))|~hBOOL(hAPP(X553,esk10_4(X553,X554,X555,X556))))))&(((hBOOL(hAPP(hAPP(c_member(X563),esk12_4(X560,X561,X562,X563)),X562))|hBOOL(hAPP(hAPP(c_member(X563),esk11_4(X560,X561,X562,X563)),X561))|(~hBOOL(hAPP(hAPP(c_member(X563),X566),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X563,tc_HOL_Obool)),X562),X561)))|hBOOL(hAPP(X560,X566))))&(~hBOOL(hAPP(X560,esk12_4(X560,X561,X562,X563)))|hBOOL(hAPP(hAPP(c_member(X563),esk11_4(X560,X561,X562,X563)),X561))|(~hBOOL(hAPP(hAPP(c_member(X563),X566),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X563,tc_HOL_Obool)),X562),X561)))|hBOOL(hAPP(X560,X566)))))&((hBOOL(hAPP(hAPP(c_member(X563),esk12_4(X560,X561,X562,X563)),X562))|~hBOOL(hAPP(X560,esk11_4(X560,X561,X562,X563)))|(~hBOOL(hAPP(hAPP(c_member(X563),X566),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X563,tc_HOL_Obool)),X562),X561)))|hBOOL(hAPP(X560,X566))))&(~hBOOL(hAPP(X560,esk12_4(X560,X561,X562,X563)))|~hBOOL(hAPP(X560,esk11_4(X560,X561,X562,X563)))|(~hBOOL(hAPP(hAPP(c_member(X563),X566),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X563,tc_HOL_Obool)),X562),X561)))|hBOOL(hAPP(X560,X566))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ball__Un])])])])])])])). 4.46/4.70 fof(c_0_6477, plain, ![X11756, X11757, X11758, X11759, X11760]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11760),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11759)),X11758)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11760),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11757)),X11756)))|hAPP(hAPP(c_Product__Type_OPair(X11759,X11757),hAPP(hAPP(c_List_Onth(X11759),X11758),X11760)),hAPP(hAPP(c_List_Onth(X11757),X11756),X11760))=hAPP(hAPP(c_List_Onth(tc_prod(X11759,X11757)),hAPP(hAPP(c_List_Ozip(X11759,X11757),X11758),X11756)),X11760))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__zip])])])). 4.46/4.70 fof(c_0_6478, plain, ![X4974, X4975, X4976, X4977, X4978]:((hBOOL(hAPP(hAPP(c_member(X4977),esk146_5(X4974,X4975,X4976,X4977,X4978)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4977,tc_HOL_Obool)),X4976),X4975)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4977,X4978),X4974),X4975)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4977,X4978),X4974),X4976)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4977,tc_HOL_Obool)),X4975),X4976))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4977),X4976))|~class_Groups_Ocomm__monoid__add(X4978))&(c_Groups_Ozero__class_Ozero(X4978)!=hAPP(X4974,esk146_5(X4974,X4975,X4976,X4977,X4978))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4977,X4978),X4974),X4975)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4977,X4978),X4974),X4976)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4977,tc_HOL_Obool)),X4975),X4976))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4977),X4976))|~class_Groups_Ocomm__monoid__add(X4978))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__mono__zero__left])])])])])). 4.46/4.70 cnf(c_0_6479, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk64_3(X2,X3,X1)),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk65_3(X2,X3,X1)),esk66_3(X2,X3,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))), inference(split_conjunct,[status(thm)],[c_0_5070])). 4.46/4.70 fof(c_0_6480, plain, ![X8258, X8259, X8260, X8261]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8261))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8260))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8260),X8259))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8259),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8258,X8261))),X8260)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8259),X8261)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult2__lemma__aux4])])])). 4.46/4.70 fof(c_0_6481, plain, ![X7558, X7559, X7560, X7561]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7561))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7560),X7559))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7559),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7560),X7561)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7560),c_Divides_Odiv__class_Omod(tc_Int_Oint,X7558,X7561))),X7559)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult2__lemma__aux1])])])). 4.46/4.70 fof(c_0_6482, plain, ![X8165, X8166, X8167, X8168, X8169]:((hBOOL(hAPP(hAPP(c_member(X8168),esk232_5(X8165,X8166,X8167,X8168,X8169)),X8167))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8169),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8168,X8169),X8166),X8167)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8169),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8169),hAPP(c_Finite__Set_Ocard(X8168),X8167))),X8165)))|(~class_Rings_Osemiring__1(X8169)|~class_Groups_Oordered__ab__semigroup__add(X8169)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8169),hAPP(X8166,esk232_5(X8165,X8166,X8167,X8168,X8169))),X8165))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8169),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8168,X8169),X8166),X8167)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8169),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8169),hAPP(c_Finite__Set_Ocard(X8168),X8167))),X8165)))|(~class_Rings_Osemiring__1(X8169)|~class_Groups_Oordered__ab__semigroup__add(X8169)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__bounded])])])])])). 4.46/4.70 fof(c_0_6483, plain, ![X15371, X15372, X15373, X15374, X15375]:(~c_Equiv__Relations_Oequiv(X15375,X15374,X15373)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X15375,X15375)),hAPP(hAPP(c_Product__Type_OPair(X15375,X15375),X15372),X15371)),X15373))|hAPP(c_Relation_OImage(X15375,X15375,X15373),hAPP(hAPP(c_Set_Oinsert(X15375),X15372),c_Orderings_Obot__class_Obot(tc_fun(X15375,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X15375,X15375,X15373),hAPP(hAPP(c_Set_Oinsert(X15375),X15371),c_Orderings_Obot__class_Obot(tc_fun(X15375,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equiv__class__eq])])])). 4.46/4.70 fof(c_0_6484, plain, ![X1888, X1889, X1890, X1891, X1892, X1893]:(~c_Relation_Osingle__valued(X1893,X1892,hAPP(c_Relation_Oconverse(X1892,X1893),X1891))|(X1890=c_Orderings_Obot__class_Obot(tc_fun(X1889,tc_HOL_Obool))|hAPP(c_Relation_OImage(X1892,X1893,X1891),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1889,tc_fun(X1892,tc_HOL_Obool)),X1890),X1888))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1889,tc_fun(X1893,tc_HOL_Obool)),X1890),hAPP(hAPP(c_COMBB(tc_fun(X1892,tc_HOL_Obool),tc_fun(X1893,tc_HOL_Obool),X1889),c_Relation_OImage(X1892,X1893,X1891)),X1888)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Image__INT__eq])])])). 4.46/4.70 fof(c_0_6485, plain, ![X14996, X14997, X14998, X14999, X15000]:(~c_Finite__Set_Ofolding__one(X15000,X14999,X14998)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15000),X14997))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15000),X14996))|(c_Orderings_Obot__class_Obot(tc_fun(X15000,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15000,tc_HOL_Obool)),X14997),X14996)|hAPP(hAPP(X14999,hAPP(X14998,X14997)),hAPP(X14998,X14996))=hAPP(hAPP(X14999,hAPP(X14998,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15000,tc_HOL_Obool)),X14997),X14996))),hAPP(X14998,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15000,tc_HOL_Obool)),X14997),X14996))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Ounion__inter])])])). 4.46/4.70 fof(c_0_6486, plain, ![X15845, X15846, X15847, X15848, X15849]:((~hBOOL(hAPP(hAPP(c_member(X15849),X15848),X15847))|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X15849,tc_Option_Ooption(X15846)),c_Map_Orestrict__map(X15849,X15846,X15845,X15847)),X15848),c_Option_Ooption_ONone(X15846))=c_Map_Orestrict__map(X15849,X15846,X15845,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15849,tc_HOL_Obool)),X15847),hAPP(hAPP(c_Set_Oinsert(X15849),X15848),c_Orderings_Obot__class_Obot(tc_fun(X15849,tc_HOL_Obool))))))&(hBOOL(hAPP(hAPP(c_member(X15849),X15848),X15847))|c_Map_Orestrict__map(X15849,X15846,X15845,X15847)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X15849,tc_Option_Ooption(X15846)),c_Map_Orestrict__map(X15849,X15846,X15845,X15847)),X15848),c_Option_Ooption_ONone(X15846)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__upd__None__restrict])])])). 4.46/4.70 fof(c_0_6487, plain, ![X10043, X10044, X10045, X10046]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk290_4(X10043,X10044,X10045,X10046)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10045)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10046),X10044))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10046),X10045)),X10044)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X10044),X10043))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10045)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk291_4(X10043,X10044,X10045,X10046)),X10043))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10046),X10044))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10046),X10045)),X10044)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X10044),X10043))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10045)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk291_4(X10043,X10044,X10045,X10046)),esk290_4(X10043,X10044,X10045,X10046))=X10046|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10046),X10044))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10046),X10045)),X10044)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X10044),X10043))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10045))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_aset_I5_J])])])])])])). 4.46/4.70 fof(c_0_6488, plain, ![X11794, X11795, X11796, X11797]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk349_4(X11794,X11795,X11796,X11797)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X11796)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11795),X11797))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11795),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X11797),X11796))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X11795),X11794))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11796)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk350_4(X11794,X11795,X11796,X11797)),X11794))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11795),X11797))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11795),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X11797),X11796))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X11795),X11794))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11796)))&(X11797=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk350_4(X11794,X11795,X11796,X11797)),esk349_4(X11794,X11795,X11796,X11797))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11795),X11797))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11795),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X11797),X11796))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X11795),X11794))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11796))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bset_I7_J])])])])])])). 4.46/4.70 cnf(c_0_6489, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Omap__upds(X1,X4,X5,X3,X6)),X2),hAPP(c_Option_Ooption_OSome(X4),X7))=c_Map_Omap__upds(X1,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),X5),X2),hAPP(c_Option_Ooption_OSome(X4),X7)),X3,X6)), inference(split_conjunct,[status(thm)],[c_0_5078])). 4.46/4.70 cnf(c_0_6490, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk66_3(X2,X3,X1)),X3))|hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X3))|hAPP(c_Finite__Set_Ocard(X1),esk64_3(X2,X3,X1))!=X2|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))), inference(split_conjunct,[status(thm)],[c_0_5070])). 4.46/4.70 cnf(c_0_6491, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk65_3(X2,X3,X1)),X3))|hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X3))|hAPP(c_Finite__Set_Ocard(X1),esk64_3(X2,X3,X1))!=X2|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))), inference(split_conjunct,[status(thm)],[c_0_5070])). 4.46/4.70 fof(c_0_6492, plain, ![X17053, X17054, X17055, X17056]:((hBOOL(hAPP(hAPP(c_member(X17056),esk508_4(X17053,X17054,X17055,X17056)),X17055))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17056),hAPP(hAPP(c_Finite__Set_Ofold(X17056,X17056,c_Lattices_Osemilattice__sup__class_Osup(X17056)),X17053),X17055)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17056),X17054),X17053)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X17056),X17055))|~class_Lattices_Osemilattice__sup(X17056))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17056),esk508_4(X17053,X17054,X17055,X17056)),X17054))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17056),hAPP(hAPP(c_Finite__Set_Ofold(X17056,X17056,c_Lattices_Osemilattice__sup__class_Osup(X17056)),X17053),X17055)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17056),X17054),X17053)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X17056),X17055))|~class_Lattices_Osemilattice__sup(X17056))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__sup__le__sup])])])])])). 4.46/4.70 cnf(c_0_6493, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk42_4(X2,X3,X4,X1)),X3)),c_Transitive__Closure_Ortrancl(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),c_Transitive__Closure_Otrancl(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_5079])). 4.46/4.70 fof(c_0_6494, plain, ![X13268, X13269, X13270, X13271]:((hBOOL(hAPP(hAPP(c_member(X13271),esk388_4(X13268,X13269,X13270,X13271)),X13270))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13271),hAPP(hAPP(c_Finite__Set_Ofold(X13271,X13271,c_Orderings_Oord__class_Omax(X13271)),X13268),X13270)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X13271),X13269),X13268)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13271),X13270))|~class_Orderings_Olinorder(X13271))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13271),esk388_4(X13268,X13269,X13270,X13271)),X13269))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13271),hAPP(hAPP(c_Finite__Set_Ofold(X13271,X13271,c_Orderings_Oord__class_Omax(X13271)),X13268),X13270)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X13271),X13269),X13268)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13271),X13270))|~class_Orderings_Olinorder(X13271))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ofold__sup__le__sup])])])])])). 4.46/4.70 fof(c_0_6495, plain, ![X9359, X9360, X9361, X9362, X9363]:((~hBOOL(hAPP(hAPP(c_member(X9362),X9359),X9361))|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9363),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9362,X9363),X9360),X9361)),hAPP(X9360,X9359))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9362,X9363),X9360),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9362,tc_HOL_Obool)),X9361),hAPP(hAPP(c_Set_Oinsert(X9362),X9359),c_Orderings_Obot__class_Obot(tc_fun(X9362,tc_HOL_Obool)))))|hAPP(X9360,X9359)=c_Groups_Ozero__class_Ozero(X9363)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9362),X9361))|~class_Fields_Ofield(X9363))&(hBOOL(hAPP(hAPP(c_member(X9362),X9359),X9361))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9362,X9363),X9360),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9362,tc_HOL_Obool)),X9361),hAPP(hAPP(c_Set_Oinsert(X9362),X9359),c_Orderings_Obot__class_Obot(tc_fun(X9362,tc_HOL_Obool)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9362,X9363),X9360),X9361)|hAPP(X9360,X9359)=c_Groups_Ozero__class_Ozero(X9363)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9362),X9361))|~class_Fields_Ofield(X9363))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__diff1])])])])). 4.46/4.70 cnf(c_0_6496, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5080, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6497, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5081, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6498, plain, ![X17580, X17581, X17582, X17583]:((hBOOL(hAPP(hAPP(c_member(X17583),esk526_4(X17580,X17581,X17582,X17583)),X17582))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17583),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17583),X17581),X17580)),hAPP(hAPP(c_Finite__Set_Ofold(X17583,X17583,c_Lattices_Osemilattice__inf__class_Oinf(X17583)),X17580),X17582)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X17583),X17582))|~class_Lattices_Osemilattice__inf(X17583))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17583),X17581),esk526_4(X17580,X17581,X17582,X17583)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17583),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17583),X17581),X17580)),hAPP(hAPP(c_Finite__Set_Ofold(X17583,X17583,c_Lattices_Osemilattice__inf__class_Oinf(X17583)),X17580),X17582)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X17583),X17582))|~class_Lattices_Osemilattice__inf(X17583))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__le__fold__inf])])])])])). 4.46/4.70 cnf(c_0_6499, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk427_4(X3,X4,X2,X1))),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Transitive__Closure_Otrancl(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_5082])). 4.46/4.70 cnf(c_0_6500, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5083])). 4.46/4.70 fof(c_0_6501, plain, ![X4731, X4732, X4733, X4734]:(~c_Finite__Set_Ofolding__one(X4734,X4733,X4732)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4734),X4731))|(c_Orderings_Obot__class_Obot(tc_fun(X4734,tc_HOL_Obool))=X4731|(~hBOOL(hAPP(hAPP(c_member(X4734),hAPP(hAPP(X4733,esk136_4(X4731,X4732,X4733,X4734)),esk137_4(X4731,X4732,X4733,X4734))),hAPP(hAPP(c_Set_Oinsert(X4734),esk136_4(X4731,X4732,X4733,X4734)),hAPP(hAPP(c_Set_Oinsert(X4734),esk137_4(X4731,X4732,X4733,X4734)),c_Orderings_Obot__class_Obot(tc_fun(X4734,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(X4734),hAPP(X4732,X4731)),X4731)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Oclosed])])])])). 4.46/4.70 fof(c_0_6502, plain, ![X12436, X12437, X12438, X12439]:((hBOOL(hAPP(hAPP(c_member(X12439),esk366_4(X12436,X12437,X12438,X12439)),X12438))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12439),hAPP(hAPP(c_Orderings_Oord__class_Omin(X12439),X12437),X12436)),hAPP(hAPP(c_Finite__Set_Ofold(X12439,X12439,c_Orderings_Oord__class_Omin(X12439)),X12436),X12438)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12439),X12438))|~class_Orderings_Olinorder(X12439))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12439),X12437),esk366_4(X12436,X12437,X12438,X12439)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12439),hAPP(hAPP(c_Orderings_Oord__class_Omin(X12439),X12437),X12436)),hAPP(hAPP(c_Finite__Set_Ofold(X12439,X12439,c_Orderings_Oord__class_Omin(X12439)),X12436),X12438)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12439),X12438))|~class_Orderings_Olinorder(X12439))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__le__fold__inf])])])])])). 4.46/4.70 fof(c_0_6503, plain, ![X11813, X11814, X11815, X11816, X11817]:((hBOOL(hAPP(hAPP(c_member(X11816),X11814),X11815))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11816,X11817),X11813),X11815)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11816,X11817),X11813),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11816,tc_HOL_Obool)),X11815),hAPP(hAPP(c_Set_Oinsert(X11816),X11814),c_Orderings_Obot__class_Obot(tc_fun(X11816,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11816),X11815))|~class_Groups_Oab__group__add(X11817))&(~hBOOL(hAPP(hAPP(c_member(X11816),X11814),X11815))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11816,X11817),X11813),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11816,tc_HOL_Obool)),X11815),hAPP(hAPP(c_Set_Oinsert(X11816),X11814),c_Orderings_Obot__class_Obot(tc_fun(X11816,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X11817),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11816,X11817),X11813),X11815)),hAPP(X11813,X11814))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11816),X11815))|~class_Groups_Oab__group__add(X11817))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__diff1])])])])). 4.46/4.70 cnf(c_0_6504, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5084, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6505, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5085, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6506, plain, ![X11369, X11370, X11371, X11372, X11373]:(~class_Rings_Osemiring__0(X11373)|hAPP(c_List_Omonoid__add__class_Olistsum(X11373),hAPP(hAPP(c_List_Omap(X11372,X11373),hAPP(hAPP(c_COMBC(X11372,X11373,X11373),hAPP(hAPP(c_COMBB(X11373,tc_fun(X11373,X11373),X11372),c_Groups_Otimes__class_Otimes(X11373)),X11371)),X11370)),X11369))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11373),hAPP(c_List_Omonoid__add__class_Olistsum(X11373),hAPP(hAPP(c_List_Omap(X11372,X11373),X11371),X11369))),X11370)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__mult__const])])])). 4.46/4.70 fof(c_0_6507, plain, ![X15266, X15267, X15268, X15269, X15270, X15271]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15269)),X15268)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15271)),X15270)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15271,tc_HOL_Obool)),hAPP(c_List_Oset(X15271),X15270)),X15267))|c_Map_Omap__upds(X15271,X15269,c_Map_Orestrict__map(X15271,X15269,X15266,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15271,tc_HOL_Obool)),X15267),hAPP(c_List_Oset(X15271),X15270))),X15270,X15268)=c_Map_Orestrict__map(X15271,X15269,c_Map_Omap__upds(X15271,X15269,X15266,X15270,X15268),X15267))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_restrict__map__upds])])). 4.46/4.70 fof(c_0_6508, plain, ![X406, X407, X408, X409, X410]:(~class_Rings_Oring(X410)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X409),X408))|(~hBOOL(hAPP(hAPP(c_member(X409),X407),X408))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X410),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X409,X410),X406),X408)),hAPP(X406,X407))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X409,X410),X406),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X409,tc_HOL_Obool)),X408),hAPP(hAPP(c_Set_Oinsert(X409),X407),c_Orderings_Obot__class_Obot(tc_fun(X409,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__diff1__ring])])])). 4.46/4.70 fof(c_0_6509, plain, ![X2246, X2247, X2248, X2249, X2250]:((c_Orderings_Obot__class_Obot(tc_fun(X2249,tc_HOL_Obool))!=X2250|X2246=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2248,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2249,tc_fun(X2248,tc_HOL_Obool)),X2250),X2247)),X2246))&(X2250=c_Orderings_Obot__class_Obot(tc_fun(X2249,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2249,tc_fun(X2248,tc_HOL_Obool)),X2250),hAPP(hAPP(c_COMBC(X2249,tc_fun(X2248,tc_HOL_Obool),tc_fun(X2248,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2248,tc_HOL_Obool),tc_fun(tc_fun(X2248,tc_HOL_Obool),tc_fun(X2248,tc_HOL_Obool)),X2249),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2248,tc_HOL_Obool))),X2247)),X2246))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2248,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2249,tc_fun(X2248,tc_HOL_Obool)),X2250),X2247)),X2246))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I1_J])])). 4.46/4.70 fof(c_0_6510, plain, ![X4269, X4270, X4271, X4272]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4272),tc_List_Olist(X4272))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4272),tc_List_Olist(X4272)),X4271),X4270)),c_List_Olistrel(X4272,X4269)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4272),tc_List_Olist(X4272))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4272),tc_List_Olist(X4272)),X4271),X4270)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X4272),c_List_Olistrel1(X4272,X4269))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__if__listrel])])). 4.46/4.70 cnf(c_0_6511, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk378_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk379_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk378_3(X1,X2,X3)),esk379_3(X1,X2,X3)))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_5086])). 4.46/4.70 cnf(c_0_6512, plain, (hAPP(X1,esk79_4(X2,X1,X3,X4))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk78_4(X2,X1,X3,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk78_4(X2,X1,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5066])). 4.46/4.70 fof(c_0_6513, plain, ![X15504, X15505, X15506]:(~class_Fields_Ofield(X15506)|(c_Groups_Oone__class_Oone(X15506)=X15505|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15506),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15506),hAPP(hAPP(c_Power_Opower__class_Opower(X15506),X15505),X15504)),c_Groups_Oone__class_Oone(X15506))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15506),X15505),c_Groups_Oone__class_Oone(X15506)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X15506),hAPP(c_Power_Opower__class_Opower(X15506),X15505)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15504)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_geometric__sum])])])). 4.46/4.70 fof(c_0_6514, plain, ![X13003, X13004, X13005, X13006, X13007]:((X13007=c_Orderings_Obot__class_Obot(tc_fun(X13006,tc_HOL_Obool))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13005,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13006,tc_fun(X13005,tc_HOL_Obool)),X13007),X13004)),X13003)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13006,tc_fun(X13005,tc_HOL_Obool)),X13007),hAPP(hAPP(c_COMBC(X13006,tc_fun(X13005,tc_HOL_Obool),tc_fun(X13005,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13005,tc_HOL_Obool),tc_fun(tc_fun(X13005,tc_HOL_Obool),tc_fun(X13005,tc_HOL_Obool)),X13006),c_Groups_Ominus__class_Ominus(tc_fun(X13005,tc_HOL_Obool))),X13004)),X13003)))&(X13007!=c_Orderings_Obot__class_Obot(tc_fun(X13006,tc_HOL_Obool))|c_Orderings_Otop__class_Otop(tc_fun(X13005,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13006,tc_fun(X13005,tc_HOL_Obool)),X13007),hAPP(hAPP(c_COMBC(X13006,tc_fun(X13005,tc_HOL_Obool),tc_fun(X13005,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13005,tc_HOL_Obool),tc_fun(tc_fun(X13005,tc_HOL_Obool),tc_fun(X13005,tc_HOL_Obool)),X13006),c_Groups_Ominus__class_Ominus(tc_fun(X13005,tc_HOL_Obool))),X13004)),X13003)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I3_J])])). 4.46/4.70 fof(c_0_6515, plain, ![X16604, X16605, X16606, X16607, X16608, X16609]:(c_Orderings_Otop__class_Otop(tc_fun(X16608,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X16609,X16608,X16607),c_Orderings_Otop__class_Otop(tc_fun(X16609,tc_HOL_Obool)))|(c_Orderings_Otop__class_Otop(tc_fun(X16605,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X16606,X16605,X16604),c_Orderings_Otop__class_Otop(tc_fun(X16606,tc_HOL_Obool)))|hAPP(c_Set_Oimage(tc_prod(X16609,X16606),tc_prod(X16608,X16605),c_Product__Type_Omap__pair(X16609,X16608,X16606,X16605,X16607,X16604)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X16609,X16606),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X16608,X16605),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__pair__surj])])])). 4.46/4.70 fof(c_0_6516, plain, ![X7814, X7815, X7816, X7817, X7818, X7820, X7821, X7822, X7823, X7824, X7825, X7826, X7829]:(((hBOOL(hAPP(hAPP(c_member(X7818),esk219_5(X7814,X7815,X7816,X7817,X7818)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7817,tc_fun(X7818,tc_HOL_Obool)),X7816),X7815)))|(~hBOOL(hAPP(hAPP(c_member(X7817),X7820),X7816))|(~hBOOL(hAPP(hAPP(c_member(X7818),X7821),hAPP(X7815,X7820)))|hBOOL(hAPP(X7814,X7821)))))&(~hBOOL(hAPP(X7814,esk219_5(X7814,X7815,X7816,X7817,X7818)))|(~hBOOL(hAPP(hAPP(c_member(X7817),X7820),X7816))|(~hBOOL(hAPP(hAPP(c_member(X7818),X7821),hAPP(X7815,X7820)))|hBOOL(hAPP(X7814,X7821))))))&((hBOOL(hAPP(hAPP(c_member(X7825),esk220_5(X7822,X7823,X7824,X7825,X7826)),X7824))|(~hBOOL(hAPP(hAPP(c_member(X7826),X7829),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7825,tc_fun(X7826,tc_HOL_Obool)),X7824),X7823)))|hBOOL(hAPP(X7822,X7829))))&((hBOOL(hAPP(hAPP(c_member(X7826),esk221_5(X7822,X7823,X7824,X7825,X7826)),hAPP(X7823,esk220_5(X7822,X7823,X7824,X7825,X7826))))|(~hBOOL(hAPP(hAPP(c_member(X7826),X7829),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7825,tc_fun(X7826,tc_HOL_Obool)),X7824),X7823)))|hBOOL(hAPP(X7822,X7829))))&(~hBOOL(hAPP(X7822,esk221_5(X7822,X7823,X7824,X7825,X7826)))|(~hBOOL(hAPP(hAPP(c_member(X7826),X7829),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7825,tc_fun(X7826,tc_HOL_Obool)),X7824),X7823)))|hBOOL(hAPP(X7822,X7829))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ball__UN])])])])])])])). 4.46/4.70 fof(c_0_6517, plain, ![X1611, X1612, X1613]:((hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk38_3(X1611,X1612,X1613)),esk39_3(X1611,X1612,X1613))))|hBOOL(hAPP(hAPP(X1611,X1613),X1612))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1613),X1612))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk39_3(X1611,X1612,X1613)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X1611,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk38_3(X1611,X1612,X1613))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk39_3(X1611,X1612,X1613))))|hBOOL(hAPP(hAPP(X1611,X1613),X1612))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1613),X1612))))&(~hBOOL(hAPP(hAPP(X1611,esk38_3(X1611,X1612,X1613)),esk39_3(X1611,X1612,X1613)))|hBOOL(hAPP(hAPP(X1611,X1613),X1612))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1613),X1612)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_norm__frac_Opinduct])])])])])). 4.46/4.70 fof(c_0_6518, plain, ![X10440, X10441, X10442, X10443, X10444]:(~class_Groups_Ocomm__monoid__add(X10444)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10443),X10442))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10442),X10441))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10444),X10440),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X10443),X10441))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10444),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10444),X10440),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X10443),X10442))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10444),X10440),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X10442),X10441)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__add__nat__ivl])])). 4.46/4.70 fof(c_0_6519, plain, ![X5533, X5534, X5535, X5536, X5537]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X5537,X5536)),esk168_5(X5533,X5534,X5535,X5536,X5537)),hAPP(c_List_Oset(tc_prod(X5537,X5536)),hAPP(hAPP(c_List_Ozip(X5537,X5536),X5535),X5534))))|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5536)),X5534)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5537)),X5535)|c_List_Olist__all2(X5537,X5536,X5533,X5535,X5534)))&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5537,X5536,tc_HOL_Obool),X5533),esk168_5(X5533,X5534,X5535,X5536,X5537)))|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5536)),X5534)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5537)),X5535)|c_List_Olist__all2(X5537,X5536,X5533,X5535,X5534)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2I])])])])])). 4.46/4.70 fof(c_0_6520, plain, ![X16710, X16711, X16712, X16713, X16714, X16715, X16716, X16717, X16718, X16719, X16720]:(((~hBOOL(hAPP(hAPP(c_member(tc_prod(X16714,X16713)),X16715),hAPP(c_List_Oset(tc_prod(X16714,X16713)),hAPP(hAPP(c_List_Ozip(X16714,X16713),X16711),X16710))))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X16714,X16713,tc_HOL_Obool),X16712),X16715))|~c_List_Olist__all2(X16714,X16713,X16712,X16711,X16710))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16714)),X16711)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16713)),X16710)|~c_List_Olist__all2(X16714,X16713,X16712,X16711,X16710)))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X16720,X16719)),esk491_5(X16716,X16717,X16718,X16719,X16720)),hAPP(c_List_Oset(tc_prod(X16720,X16719)),hAPP(hAPP(c_List_Ozip(X16720,X16719),X16717),X16716))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16720)),X16717)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16719)),X16716)|c_List_Olist__all2(X16720,X16719,X16718,X16717,X16716))&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X16720,X16719,tc_HOL_Obool),X16718),esk491_5(X16716,X16717,X16718,X16719,X16720)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16720)),X16717)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16719)),X16716)|c_List_Olist__all2(X16720,X16719,X16718,X16717,X16716)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__def])])])])])])). 4.46/4.70 cnf(c_0_6521, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X3!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1))), inference(split_conjunct,[status(thm)],[c_0_5031])). 4.46/4.70 fof(c_0_6522, plain, ![X2900, X2901, X2902, X2903]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2903),X2902))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X2901,tc_HOL_Obool),X2903,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2901,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X2903,tc_fun(X2901,tc_HOL_Obool),tc_fun(X2901,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2901,tc_fun(tc_fun(X2901,tc_HOL_Obool),tc_fun(X2901,tc_HOL_Obool)),X2903),c_Set_Oinsert(X2901)),X2900)),c_Orderings_Obot__class_Obot(tc_fun(X2901,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X2901,tc_HOL_Obool))),X2902)=hAPP(c_Set_Oimage(X2903,X2901,X2900),X2902)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__eq__fold__image])])])). 4.46/4.70 cnf(c_0_6523, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|X3!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1))), inference(split_conjunct,[status(thm)],[c_0_5031])). 4.46/4.70 cnf(c_0_6524, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_5087]), ['final']). 4.46/4.70 cnf(c_0_6525, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5088, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.70 fof(c_0_6526, plain, ![X3622, X3623, X3624, X3625]:(~class_Orderings_Olinorder(X3625)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3625,X3625,c_COMBI(X3625)),X3624),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3625,X3625,c_COMBI(X3625)),X3623),X3622))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3625,X3625,c_COMBI(X3625)),X3623),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3625,X3625,c_COMBI(X3625)),X3624),X3622))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__left__comm])])])). 4.46/4.70 fof(c_0_6527, plain, ![X5341, X5342, X5343, X5344, X5345]:(~class_Groups_Oab__group__add(X5345)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5344),X5343))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5343),X5342))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5345),X5341),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5343),X5342))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5345),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5345),X5341),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5344),X5342))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5345),X5341),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5344),X5343)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat__ivl])])). 4.46/4.70 fof(c_0_6528, plain, ![X4502]:(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))=X4502|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X4502),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_smin__emptyI])])])). 4.46/4.70 cnf(c_0_6529, plain, (hBOOL(hAPP(X1,esk445_2(X1,X2)))|hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk444_2(X1,X2)),X2))))|hBOOL(hAPP(X1,esk443_2(X1,X2)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5061])). 4.46/4.70 fof(c_0_6530, plain, ![X10983]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X10983))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X10983)),c_FunDef_Omax__weak))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wmax__emptyI])])])). 4.46/4.70 cnf(c_0_6531, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk533_3(X2,X1,X3))),esk534_3(X2,X1,X3))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk531_3(X2,X1,X3))),esk532_3(X2,X1,X3))=X2|epred1_3(X3,X1,X2)|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.70 fof(c_0_6532, plain, ![X10665, X10666, X10667, X10668]:((hAPP(c_List_Oset(tc_prod(X10668,X10667)),X10665)!=hAPP(c_List_Oset(tc_prod(X10668,X10667)),X10666)|hAPP(c_Map_Omap__of(X10668,X10667),X10665)=hAPP(c_Map_Omap__of(X10668,X10667),X10666)|~hBOOL(hAPP(c_List_Odistinct(X10668),hAPP(hAPP(c_List_Omap(tc_prod(X10668,X10667),X10668),c_Product__Type_Ofst(X10668,X10667)),X10665)))|~hBOOL(hAPP(c_List_Odistinct(X10668),hAPP(hAPP(c_List_Omap(tc_prod(X10668,X10667),X10668),c_Product__Type_Ofst(X10668,X10667)),X10666))))&(hAPP(c_Map_Omap__of(X10668,X10667),X10665)!=hAPP(c_Map_Omap__of(X10668,X10667),X10666)|hAPP(c_List_Oset(tc_prod(X10668,X10667)),X10665)=hAPP(c_List_Oset(tc_prod(X10668,X10667)),X10666)|~hBOOL(hAPP(c_List_Odistinct(X10668),hAPP(hAPP(c_List_Omap(tc_prod(X10668,X10667),X10668),c_Product__Type_Ofst(X10668,X10667)),X10665)))|~hBOOL(hAPP(c_List_Odistinct(X10668),hAPP(hAPP(c_List_Omap(tc_prod(X10668,X10667),X10668),c_Product__Type_Ofst(X10668,X10667)),X10666))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__inject__set])])])). 4.46/4.70 cnf(c_0_6533, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk154_7(X2,X3,X4,X5,X1,X6,X7)),hAPP(c_List_Oset(X1),X6)))|hAPP(c_List_Ofilter(X1,X5),X4)=hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)|~hBOOL(hAPP(X5,X3))|X2!=hAPP(c_List_Ofilter(X1,X5),X7)|X4!=hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X7))), inference(split_conjunct,[status(thm)],[c_0_5090])). 4.46/4.70 fof(c_0_6534, plain, ![X2795, X2796, X2797, X2798, X2799]:(~class_Groups_Ocomm__monoid__add(X2799)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2798),X2797))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2798),X2796))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2798,tc_HOL_Obool)),X2797),X2796)!=c_Orderings_Obot__class_Obot(tc_fun(X2798,tc_HOL_Obool))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2798,X2799),X2795),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2798,tc_HOL_Obool)),X2797),X2796))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2799),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2798,X2799),X2795),X2797)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2798,X2799),X2795),X2796)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__Un__disjoint])])])). 4.46/4.70 fof(c_0_6535, plain, ![X12168, X12169, X12170, X12171, X12172, X12173, X12174]:((~c_List_Olist__all2(X12174,X12170,hAPP(hAPP(c_COMBC(X12174,tc_fun(X12170,X12173),tc_fun(X12170,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12173,tc_HOL_Obool),tc_fun(tc_fun(X12170,X12173),tc_fun(X12170,tc_HOL_Obool)),X12174),c_COMBB(X12173,tc_HOL_Obool,X12170)),X12172)),X12169),X12171,X12168)|c_List_Olist__all2(X12174,X12173,X12172,X12171,hAPP(hAPP(c_List_Omap(X12170,X12173),X12169),X12168)))&(~c_List_Olist__all2(X12174,X12173,X12172,X12171,hAPP(hAPP(c_List_Omap(X12170,X12173),X12169),X12168))|c_List_Olist__all2(X12174,X12170,hAPP(hAPP(c_COMBC(X12174,tc_fun(X12170,X12173),tc_fun(X12170,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12173,tc_HOL_Obool),tc_fun(tc_fun(X12170,X12173),tc_fun(X12170,tc_HOL_Obool)),X12174),c_COMBB(X12173,tc_HOL_Obool,X12170)),X12172)),X12169),X12171,X12168))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__map2])])). 4.46/4.70 fof(c_0_6536, plain, ![X3811, X3812, X3813, X3814, X3815, X3816]:(~c_Equiv__Relations_Oequiv(X3816,X3815,X3814)|(~hBOOL(hAPP(hAPP(c_member(X3816),X3813),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3816,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3816,X3816,X3814),hAPP(hAPP(c_Set_Oinsert(X3816),X3812),c_Orderings_Obot__class_Obot(tc_fun(X3816,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X3816,X3816,X3814),hAPP(hAPP(c_Set_Oinsert(X3816),X3811),c_Orderings_Obot__class_Obot(tc_fun(X3816,tc_HOL_Obool)))))))|hBOOL(hAPP(hAPP(c_member(tc_prod(X3816,X3816)),hAPP(hAPP(c_Product__Type_OPair(X3816,X3816),X3812),X3811)),X3814)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equiv__class__nondisjoint])])])). 4.46/4.70 cnf(c_0_6537, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk372_8(X2,X3,X4,X5,X6,X7,X1,X8)),X4))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X7),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X6),X4))|X5!=X4|X6!=X7|~class_Orderings_Oord(X1)|~class_Groups_Ocomm__monoid__add(X8)), inference(split_conjunct,[status(thm)],[c_0_5064])). 4.46/4.70 cnf(c_0_6538, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk372_8(X3,X4,X5,X6,X2,X7,X1,X8)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X7),X6))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X5))|X6!=X5|X2!=X7|~class_Orderings_Oord(X1)|~class_Groups_Ocomm__monoid__add(X8)), inference(split_conjunct,[status(thm)],[c_0_5064])). 4.46/4.70 fof(c_0_6539, plain, ![X11162, X11163, X11164, X11165, X11166]:(~class_Groups_Ocomm__monoid__mult(X11166)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11165),X11164))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11165),X11163))|(c_Orderings_Obot__class_Obot(tc_fun(X11165,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11165,tc_HOL_Obool)),X11164),X11163)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X11165,X11166),X11162),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11165,tc_HOL_Obool)),X11164),X11163))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11166),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X11165,X11166),X11162),X11164)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X11165,X11166),X11162),X11163)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__Un__disjoint])])])). 4.46/4.70 cnf(c_0_6540, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X2))))), inference(rw,[status(thm)],[c_0_5091, c_0_4443])). 4.46/4.70 cnf(c_0_6541, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X2))))), inference(rw,[status(thm)],[c_0_5092, c_0_4443])). 4.46/4.70 cnf(c_0_6542, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk256_3(X1,X2,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk255_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk255_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5093])). 4.46/4.70 cnf(c_0_6543, plain, (c_List_Oupt(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X1,X2)),c_List_Oupt(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5094])). 4.46/4.70 cnf(c_0_6544, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk72_3(X1,X2,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk71_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk71_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5095])). 4.46/4.70 fof(c_0_6545, plain, ![X9816, X9817, X9818]:(~class_Orderings_Olinorder(X9818)|(hAPP(hAPP(c_Orderings_Oord__class_Omin(X9818),hAPP(X9817,esk281_3(X9816,X9817,X9818))),hAPP(X9817,esk282_3(X9816,X9817,X9818)))!=hAPP(X9817,hAPP(hAPP(c_Orderings_Oord__class_Omin(X9818),esk281_3(X9816,X9817,X9818)),esk282_3(X9816,X9817,X9818)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9818),X9816))|(c_Orderings_Obot__class_Obot(tc_fun(X9818,tc_HOL_Obool))=X9816|hAPP(X9817,c_Big__Operators_Olattice_OInf__fin(X9818,c_Orderings_Oord__class_Omin(X9818),X9816))=c_Big__Operators_Olattice_OInf__fin(X9818,c_Orderings_Oord__class_Omin(X9818),hAPP(c_Set_Oimage(X9818,X9818,X9817),X9816)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Ohom__commute])])])])). 4.46/4.70 fof(c_0_6546, plain, ![X12110, X12111, X12112]:(~class_Orderings_Olinorder(X12112)|(hAPP(hAPP(c_Orderings_Oord__class_Omax(X12112),hAPP(X12111,esk354_3(X12110,X12111,X12112))),hAPP(X12111,esk355_3(X12110,X12111,X12112)))!=hAPP(X12111,hAPP(hAPP(c_Orderings_Oord__class_Omax(X12112),esk354_3(X12110,X12111,X12112)),esk355_3(X12110,X12111,X12112)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12112),X12110))|(c_Orderings_Obot__class_Obot(tc_fun(X12112,tc_HOL_Obool))=X12110|hAPP(X12111,c_Big__Operators_Olattice_OSup__fin(X12112,c_Orderings_Oord__class_Omax(X12112),X12110))=c_Big__Operators_Olattice_OSup__fin(X12112,c_Orderings_Oord__class_Omax(X12112),hAPP(c_Set_Oimage(X12112,X12112,X12111),X12110)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Ohom__commute])])])])). 4.46/4.70 fof(c_0_6547, plain, ![X4256, X4257, X4258, X4259, X4260, X4261]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4261)),X4260)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4259)),X4258)|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4259)),X4256)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4261)),X4257)|hAPP(hAPP(c_List_Ozip(X4261,X4259),hAPP(hAPP(c_List_Oappend(X4261),X4260),X4257)),hAPP(hAPP(c_List_Oappend(X4259),X4258),X4256))=hAPP(hAPP(c_List_Oappend(tc_prod(X4261,X4259)),hAPP(hAPP(c_List_Ozip(X4261,X4259),X4260),X4258)),hAPP(hAPP(c_List_Ozip(X4261,X4259),X4257),X4256)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zip__append])])])). 4.46/4.70 fof(c_0_6548, plain, ![X13457, X13458, X13459, X13460, X13461, X13462]:(hAPP(hAPP(c_Map_Omap__of(X13462,X13461),X13460),X13459)!=hAPP(c_Option_Ooption_OSome(X13461),X13458)|(~hBOOL(hAPP(hAPP(X13457,X13459),X13458))|hAPP(hAPP(c_Map_Omap__of(X13462,X13461),hAPP(c_List_Ofilter(tc_prod(X13462,X13461),hAPP(c_Product__Type_Oprod_Oprod__case(X13462,X13461,tc_HOL_Obool),X13457)),X13460)),X13459)=hAPP(c_Option_Ooption_OSome(X13461),X13458))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__filter__in])])])). 4.46/4.70 cnf(c_0_6549, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Ozip(X2,X3),X4),X5)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Ozip(X2,X3),hAPP(hAPP(c_List_Otake(X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X5))),X4)),hAPP(hAPP(c_List_Otake(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X5))),X5))))), inference(split_conjunct,[status(thm)],[c_0_4984])). 4.46/4.70 cnf(c_0_6550, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Otake(X1),X3),X4)),hAPP(hAPP(c_List_Otake(X2),X3),X5))=hAPP(hAPP(c_List_Otake(tc_prod(X1,X2)),X3),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.46/4.70 cnf(c_0_6551, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk533_3(X2,X1,X3))),esk534_3(X2,X1,X3))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk531_3(X2,X1,X3))),esk532_3(X2,X1,X3))=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.70 cnf(c_0_6552, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X1)|X1!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)),X4)),X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5097])). 4.46/4.70 cnf(c_0_6553, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_5098]), ['final']). 4.46/4.70 cnf(c_0_6554, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X2),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5099, c_0_5100]), c_0_5101]), ['final']). 4.46/4.70 fof(c_0_6555, plain, ![X1108, X1109, X1110, X1111, X1112, X1113]:(hBOOL(hAPP(hAPP(c_member(X1113),X1112),c_Map_Odom(X1113,X1111,X1110)))|c_Map_Omap__add(X1113,X1111,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1113,tc_Option_Ooption(X1111)),X1109),X1112),hAPP(c_Option_Ooption_OSome(X1111),X1108)),X1110)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1113,tc_Option_Ooption(X1111)),c_Map_Omap__add(X1113,X1111,X1109,X1110)),X1112),hAPP(c_Option_Ooption_OSome(X1111),X1108))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__add__upd__left])])])). 4.46/4.70 fof(c_0_6556, plain, ![X16262, X16263, X16264, X16265]:(~class_Enum_Oenum(X16264)|~class_Enum_Oenum(X16265)|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16265)),c_Enum_Oenum__class_Oenum(X16265))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16264)),X16263)|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16265)),c_Enum_Oenum__class_Oenum(X16265))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16264)),X16262)|(hAPP(c_Fun_Ocomp(tc_Option_Ooption(X16264),X16264,X16265,c_Option_Othe(X16264)),hAPP(c_Map_Omap__of(X16265,X16264),hAPP(hAPP(c_List_Ozip(X16265,X16264),c_Enum_Oenum__class_Oenum(X16265)),X16263)))!=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X16264),X16264,X16265,c_Option_Othe(X16264)),hAPP(c_Map_Omap__of(X16265,X16264),hAPP(hAPP(c_List_Ozip(X16265,X16264),c_Enum_Oenum__class_Oenum(X16265)),X16262)))|X16263=X16262)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__zip__enum__inject])])])). 4.46/4.70 cnf(c_0_6557, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))|X2=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_5102])). 4.46/4.70 fof(c_0_6558, plain, ![X14990, X14991, X14992, X14993, X14994, X14995]:(~class_Orderings_Olinorder(X14995)|(hAPP(X14994,X14992)=hAPP(X14994,X14993)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X14991,X14995,X14994),X14993),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X14991,X14995,X14994),X14992),X14990))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X14991,X14995,X14994),X14992),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X14991,X14995,X14994),X14993),X14990)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__key__left__comm])])])). 4.46/4.70 cnf(c_0_6559, plain, (c_Hoare__Mirabelle_Ohoare__valids(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OWhile(X4,X5)),c_Hoare__Mirabelle_Opeek__and(X1,X3,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X4)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__valids(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,X4)),X5),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5103])). 4.46/4.70 fof(c_0_6560, plain, ![X17340, X17341]:(~class_Groups_Oab__semigroup__mult(X17341)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17341),X17340))|(X17340=c_Orderings_Obot__class_Obot(tc_fun(X17341,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_member(X17341),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17341),esk520_2(X17340,X17341)),esk521_2(X17340,X17341))),hAPP(hAPP(c_Set_Oinsert(X17341),esk520_2(X17340,X17341)),hAPP(hAPP(c_Set_Oinsert(X17341),esk521_2(X17340,X17341)),c_Orderings_Obot__class_Obot(tc_fun(X17341,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(X17341),hAPP(c_Finite__Set_Ofold1(X17341,c_Groups_Otimes__class_Otimes(X17341)),X17340)),X17340)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__in])])])])). 4.46/4.70 cnf(c_0_6561, plain, (c_List_Otranspose(X1,c_List_Otranspose(X1,X2))=c_List_OtakeWhile(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1))),X2)|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)))), inference(split_conjunct,[status(thm)],[c_0_5104])). 4.46/4.70 fof(c_0_6562, plain, ![X13531, X13532, X13533]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13533,tc_HOL_Obool)),X13532),hAPP(hAPP(c_Set_Oinsert(X13533),X13531),c_Orderings_Obot__class_Obot(tc_fun(X13533,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X13533,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13533),X13531),c_Big__Operators_Olattice__class_OSup__fin(X13533,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13533,tc_HOL_Obool)),X13532),hAPP(hAPP(c_Set_Oinsert(X13533),X13531),c_Orderings_Obot__class_Obot(tc_fun(X13533,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OSup__fin(X13533,X13532)|~hBOOL(hAPP(hAPP(c_member(X13533),X13531),X13532))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13533),X13532))|~class_Lattices_Olattice(X13533))&(c_Orderings_Obot__class_Obot(tc_fun(X13533,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13533,tc_HOL_Obool)),X13532),hAPP(hAPP(c_Set_Oinsert(X13533),X13531),c_Orderings_Obot__class_Obot(tc_fun(X13533,tc_HOL_Obool))))|X13531=c_Big__Operators_Olattice__class_OSup__fin(X13533,X13532)|~hBOOL(hAPP(hAPP(c_member(X13533),X13531),X13532))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13533),X13532))|~class_Lattices_Olattice(X13533))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oremove])])])])). 4.46/4.70 fof(c_0_6563, plain, ![X11304, X11305, X11306]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11306,tc_HOL_Obool)),X11305),hAPP(hAPP(c_Set_Oinsert(X11306),X11304),c_Orderings_Obot__class_Obot(tc_fun(X11306,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X11306,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X11306),X11304),c_Big__Operators_Olattice__class_OInf__fin(X11306,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11306,tc_HOL_Obool)),X11305),hAPP(hAPP(c_Set_Oinsert(X11306),X11304),c_Orderings_Obot__class_Obot(tc_fun(X11306,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OInf__fin(X11306,X11305)|~hBOOL(hAPP(hAPP(c_member(X11306),X11304),X11305))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11306),X11305))|~class_Lattices_Olattice(X11306))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11306,tc_HOL_Obool)),X11305),hAPP(hAPP(c_Set_Oinsert(X11306),X11304),c_Orderings_Obot__class_Obot(tc_fun(X11306,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X11306,tc_HOL_Obool))|c_Big__Operators_Olattice__class_OInf__fin(X11306,X11305)=X11304|~hBOOL(hAPP(hAPP(c_member(X11306),X11304),X11305))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11306),X11305))|~class_Lattices_Olattice(X11306))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oremove])])])])). 4.46/4.70 fof(c_0_6564, plain, ![X10357, X10358, X10359]:((c_Orderings_Obot__class_Obot(tc_fun(X10359,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10359,tc_HOL_Obool)),X10358),hAPP(hAPP(c_Set_Oinsert(X10359),X10357),c_Orderings_Obot__class_Obot(tc_fun(X10359,tc_HOL_Obool))))|X10357=c_Big__Operators_Olinorder__class_OMax(X10359,X10358)|~hBOOL(hAPP(hAPP(c_member(X10359),X10357),X10358))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10359),X10358))|~class_Orderings_Olinorder(X10359))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10359,tc_HOL_Obool)),X10358),hAPP(hAPP(c_Set_Oinsert(X10359),X10357),c_Orderings_Obot__class_Obot(tc_fun(X10359,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X10359,tc_HOL_Obool))|c_Big__Operators_Olinorder__class_OMax(X10359,X10358)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X10359),X10357),c_Big__Operators_Olinorder__class_OMax(X10359,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10359,tc_HOL_Obool)),X10358),hAPP(hAPP(c_Set_Oinsert(X10359),X10357),c_Orderings_Obot__class_Obot(tc_fun(X10359,tc_HOL_Obool))))))|~hBOOL(hAPP(hAPP(c_member(X10359),X10357),X10358))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10359),X10358))|~class_Orderings_Olinorder(X10359))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Oremove])])])])). 4.46/4.70 fof(c_0_6565, plain, ![X8976, X8977, X8978]:((c_Orderings_Obot__class_Obot(tc_fun(X8978,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8978,tc_HOL_Obool)),X8977),hAPP(hAPP(c_Set_Oinsert(X8978),X8976),c_Orderings_Obot__class_Obot(tc_fun(X8978,tc_HOL_Obool))))|X8976=c_Big__Operators_Olinorder__class_OMin(X8978,X8977)|~hBOOL(hAPP(hAPP(c_member(X8978),X8976),X8977))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8978),X8977))|~class_Orderings_Olinorder(X8978))&(c_Orderings_Obot__class_Obot(tc_fun(X8978,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8978,tc_HOL_Obool)),X8977),hAPP(hAPP(c_Set_Oinsert(X8978),X8976),c_Orderings_Obot__class_Obot(tc_fun(X8978,tc_HOL_Obool))))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X8978),X8976),c_Big__Operators_Olinorder__class_OMin(X8978,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8978,tc_HOL_Obool)),X8977),hAPP(hAPP(c_Set_Oinsert(X8978),X8976),c_Orderings_Obot__class_Obot(tc_fun(X8978,tc_HOL_Obool))))))=c_Big__Operators_Olinorder__class_OMin(X8978,X8977)|~hBOOL(hAPP(hAPP(c_member(X8978),X8976),X8977))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8978),X8977))|~class_Orderings_Olinorder(X8978))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Oremove])])])])). 4.46/4.70 fof(c_0_6566, plain, ![X13968, X13969, X13970, X13971, X13972, X13973]:(~c_Finite__Set_Ofun__left__comm(X13973,X13972,X13971)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13973),X13970))|(~hBOOL(hAPP(hAPP(c_member(X13973),X13969),X13970))|hAPP(hAPP(X13971,X13969),hAPP(hAPP(c_Finite__Set_Ofold(X13973,X13972,X13971),X13968),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13973,tc_HOL_Obool)),X13970),hAPP(hAPP(c_Set_Oinsert(X13973),X13969),c_Orderings_Obot__class_Obot(tc_fun(X13973,tc_HOL_Obool))))))=hAPP(hAPP(c_Finite__Set_Ofold(X13973,X13972,X13971),X13968),X13970)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__rec])])])). 4.46/4.70 fof(c_0_6567, plain, ![X12282, X12283, X12284, X12285, X12286, X12287, X12288]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X12288,X12287),tc_HOL_Obool)),X12286),X12285))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X12287,X12284),tc_HOL_Obool)),X12283),X12282))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X12288,X12284),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X12288,X12287,X12284),X12286),X12283)),hAPP(hAPP(c_Relation_Orel__comp(X12288,X12287,X12284),X12285),X12282))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__comp__mono])])])). 4.46/4.70 fof(c_0_6568, plain, ![X7316, X7317, X7318]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7318),X7317))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7318),X7316))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7318),X7317)),hAPP(c_Finite__Set_Ocard(X7318),X7316))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7318),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7318,tc_HOL_Obool)),X7317),X7316))),hAPP(c_Finite__Set_Ocard(X7318),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7318,tc_HOL_Obool)),X7317),X7316))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card_Ounion__inter])])])). 4.46/4.70 fof(c_0_6569, plain, ![X16032, X16033, X16034, X16035, X16036]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16036),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16035)),X16034)))|hAPP(hAPP(c_List_Oappend(X16035),X16034),hAPP(hAPP(c_List_Olist__update(X16035,X16033),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16036),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16035)),X16034))),X16032))=hAPP(hAPP(c_List_Olist__update(X16035,hAPP(hAPP(c_List_Oappend(X16035),X16034),X16033)),X16036),X16032))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16036),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16035)),X16034)))|hAPP(hAPP(c_List_Olist__update(X16035,hAPP(hAPP(c_List_Oappend(X16035),X16034),X16033)),X16036),X16032)=hAPP(hAPP(c_List_Oappend(X16035),hAPP(hAPP(c_List_Olist__update(X16035,X16034),X16036),X16032)),X16033))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__update__append])])])). 4.46/4.70 cnf(c_0_6570, plain, (hBOOL(hAPP(hAPP(X1,esk35_5(X2,X3,X4,X5,X1)),esk36_5(X2,X3,X4,X5,X1)))|c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X1),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5075])). 4.46/4.70 fof(c_0_6571, plain, ![X11495, X11496, X11497, X11498, X11499, X11500]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11500),hAPP(X11499,X11498)),hAPP(X11499,X11497)))|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X11496,X11500,X11499),X11498),hAPP(hAPP(c_List_Olist_OCons(X11496),X11497),X11495))=hAPP(hAPP(c_List_Olist_OCons(X11496),X11497),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X11496,X11500,X11499),X11498),X11495))|~class_Orderings_Olinorder(X11500))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11500),hAPP(X11499,X11498)),hAPP(X11499,X11497)))|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X11496,X11500,X11499),X11498),hAPP(hAPP(c_List_Olist_OCons(X11496),X11497),X11495))=hAPP(hAPP(c_List_Olist_OCons(X11496),X11498),hAPP(hAPP(c_List_Olist_OCons(X11496),X11497),X11495))|~class_Orderings_Olinorder(X11500))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__key_Osimps_I2_J])])])])). 4.46/4.70 cnf(c_0_6572, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X5),X2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X5),X1))))|~hBOOL(hAPP(X1,esk254_5(X1,X2,X3,X4,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_5033])). 4.46/4.70 fof(c_0_6573, plain, ![X5808, X5809, X5810, X5811, X5812, X5813, X5815, X5816, X5817, X5818, X5819]:((((hBOOL(hAPP(X5808,esk178_4(X5808,X5809,X5810,X5811)))|(~hBOOL(hAPP(hAPP(c_member(X5811),X5812),X5809))|~hBOOL(hAPP(X5808,X5812))))&(hBOOL(hAPP(hAPP(c_member(X5811),esk178_4(X5808,X5809,X5810,X5811)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5811,tc_HOL_Obool)),X5810),X5809)))|(~hBOOL(hAPP(hAPP(c_member(X5811),X5812),X5809))|~hBOOL(hAPP(X5808,X5812)))))&((hBOOL(hAPP(X5808,esk178_4(X5808,X5809,X5810,X5811)))|(~hBOOL(hAPP(X5808,X5813))|~hBOOL(hAPP(hAPP(c_member(X5811),X5813),X5810))))&(hBOOL(hAPP(hAPP(c_member(X5811),esk178_4(X5808,X5809,X5810,X5811)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5811,tc_HOL_Obool)),X5810),X5809)))|(~hBOOL(hAPP(X5808,X5813))|~hBOOL(hAPP(hAPP(c_member(X5811),X5813),X5810))))))&(((hBOOL(hAPP(X5815,esk180_4(X5815,X5816,X5817,X5818)))|hBOOL(hAPP(hAPP(c_member(X5818),esk179_4(X5815,X5816,X5817,X5818)),X5816))|(~hBOOL(hAPP(X5815,X5819))|~hBOOL(hAPP(hAPP(c_member(X5818),X5819),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5818,tc_HOL_Obool)),X5817),X5816)))))&(hBOOL(hAPP(hAPP(c_member(X5818),esk180_4(X5815,X5816,X5817,X5818)),X5817))|hBOOL(hAPP(hAPP(c_member(X5818),esk179_4(X5815,X5816,X5817,X5818)),X5816))|(~hBOOL(hAPP(X5815,X5819))|~hBOOL(hAPP(hAPP(c_member(X5818),X5819),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5818,tc_HOL_Obool)),X5817),X5816))))))&((hBOOL(hAPP(X5815,esk180_4(X5815,X5816,X5817,X5818)))|hBOOL(hAPP(X5815,esk179_4(X5815,X5816,X5817,X5818)))|(~hBOOL(hAPP(X5815,X5819))|~hBOOL(hAPP(hAPP(c_member(X5818),X5819),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5818,tc_HOL_Obool)),X5817),X5816)))))&(hBOOL(hAPP(hAPP(c_member(X5818),esk180_4(X5815,X5816,X5817,X5818)),X5817))|hBOOL(hAPP(X5815,esk179_4(X5815,X5816,X5817,X5818)))|(~hBOOL(hAPP(X5815,X5819))|~hBOOL(hAPP(hAPP(c_member(X5818),X5819),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5818,tc_HOL_Obool)),X5817),X5816)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bex__Un])])])])])])). 4.46/4.70 fof(c_0_6574, plain, ![X10901, X10902, X10903, X10904, X10905, X10906]:((hAPP(hAPP(c_Product__Type_OPair(X10906,X10905),esk325_6(X10901,X10902,X10903,X10904,X10905,X10906)),esk327_6(X10901,X10902,X10903,X10904,X10905,X10906))=X10904|~hBOOL(hAPP(hAPP(c_member(tc_prod(X10906,X10905)),X10904),hAPP(hAPP(c_Relation_Orel__comp(X10906,X10903,X10905),X10902),X10901))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X10906,X10903)),hAPP(hAPP(c_Product__Type_OPair(X10906,X10903),esk325_6(X10901,X10902,X10903,X10904,X10905,X10906)),esk326_6(X10901,X10902,X10903,X10904,X10905,X10906))),X10902))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X10906,X10905)),X10904),hAPP(hAPP(c_Relation_Orel__comp(X10906,X10903,X10905),X10902),X10901))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X10903,X10905)),hAPP(hAPP(c_Product__Type_OPair(X10903,X10905),esk326_6(X10901,X10902,X10903,X10904,X10905,X10906)),esk327_6(X10901,X10902,X10903,X10904,X10905,X10906))),X10901))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X10906,X10905)),X10904),hAPP(hAPP(c_Relation_Orel__comp(X10906,X10903,X10905),X10902),X10901)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__compE])])])])])). 4.46/4.70 fof(c_0_6575, plain, ![X7487, X7488, X7489, X7490, X7491, X7492, X7493, X7494]:(~c_Finite__Set_Ofolding__image__simple(X7494,X7493,X7492,X7491,X7490,X7489)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7493),X7488))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7493),X7487))|hAPP(hAPP(X7492,hAPP(X7489,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7493,tc_HOL_Obool)),X7488),X7487))),hAPP(X7489,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7493,tc_HOL_Obool)),X7488),X7487)))=hAPP(hAPP(X7492,hAPP(X7489,X7488)),hAPP(X7489,X7487))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__inter])])). 4.46/4.70 fof(c_0_6576, plain, ![X4895, X4896]:(~class_Orderings_Olinorder(X4896)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4896),X4895))|(c_Orderings_Obot__class_Obot(tc_fun(X4896,tc_HOL_Obool))=X4895|(~hBOOL(hAPP(hAPP(c_member(X4896),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4896),esk143_2(X4895,X4896)),esk144_2(X4895,X4896))),hAPP(hAPP(c_Set_Oinsert(X4896),esk143_2(X4895,X4896)),hAPP(hAPP(c_Set_Oinsert(X4896),esk144_2(X4895,X4896)),c_Orderings_Obot__class_Obot(tc_fun(X4896,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(X4896),c_Big__Operators_Olattice_OInf__fin(X4896,c_Orderings_Oord__class_Omin(X4896),X4895)),X4895)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oclosed])])])])). 4.46/4.70 fof(c_0_6577, plain, ![X17420, X17421]:(~class_Orderings_Olinorder(X17421)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17421),X17420))|(c_Orderings_Obot__class_Obot(tc_fun(X17421,tc_HOL_Obool))=X17420|(~hBOOL(hAPP(hAPP(c_member(X17421),hAPP(hAPP(c_Orderings_Oord__class_Omax(X17421),esk522_2(X17420,X17421)),esk523_2(X17420,X17421))),hAPP(hAPP(c_Set_Oinsert(X17421),esk522_2(X17420,X17421)),hAPP(hAPP(c_Set_Oinsert(X17421),esk523_2(X17420,X17421)),c_Orderings_Obot__class_Obot(tc_fun(X17421,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(X17421),c_Big__Operators_Olattice_OSup__fin(X17421,c_Orderings_Oord__class_Omax(X17421),X17420)),X17420)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oclosed])])])])). 4.46/4.70 fof(c_0_6578, plain, ![X16857, X16858, X16859]:((hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),esk498_3(X16857,X16858,X16859)),esk499_3(X16857,X16858,X16859))))|hBOOL(hAPP(hAPP(X16857,X16859),X16858))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X16859),X16858))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=esk499_3(X16857,X16858,X16859)|hBOOL(hAPP(hAPP(X16857,esk499_3(X16857,X16858,X16859)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk498_3(X16857,X16858,X16859),esk499_3(X16857,X16858,X16859))))|hBOOL(hAPP(hAPP(X16857,X16859),X16858))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X16859),X16858))))&(~hBOOL(hAPP(hAPP(X16857,esk498_3(X16857,X16858,X16859)),esk499_3(X16857,X16858,X16859)))|hBOOL(hAPP(hAPP(X16857,X16859),X16858))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X16859),X16858)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__gcd_Opinduct])])])])])). 4.46/4.70 fof(c_0_6579, plain, ![X4434, X4435, X4436]:(~class_Groups_Oab__semigroup__mult(X4436)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4436),X4435))|(c_Orderings_Obot__class_Obot(tc_fun(X4436,tc_HOL_Obool))=X4435|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4436),X4434))|(X4434=c_Orderings_Obot__class_Obot(tc_fun(X4436,tc_HOL_Obool))|(c_Orderings_Obot__class_Obot(tc_fun(X4436,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4436,tc_HOL_Obool)),X4435),X4434)|hAPP(c_Finite__Set_Ofold1(X4436,c_Groups_Otimes__class_Otimes(X4436)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4436,tc_HOL_Obool)),X4435),X4434))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4436),hAPP(c_Finite__Set_Ofold1(X4436,c_Groups_Otimes__class_Otimes(X4436)),X4435)),hAPP(c_Finite__Set_Ofold1(X4436,c_Groups_Otimes__class_Otimes(X4436)),X4434)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__Un])])])). 4.46/4.70 fof(c_0_6580, plain, ![X7575, X7576, X7577]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7577),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7576)),X7575)))|hAPP(hAPP(c_List_Oappend(X7576),hAPP(hAPP(c_List_Otake(X7576),X7577),X7575)),hAPP(hAPP(c_List_Olist_OCons(X7576),hAPP(c_List_Ohd(X7576),hAPP(hAPP(c_List_Odrop(X7576),X7577),X7575))),c_List_Olist_ONil(X7576)))=hAPP(hAPP(c_List_Otake(X7576),hAPP(c_Nat_OSuc,X7577)),X7575)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__hd__drop])])). 4.46/4.70 fof(c_0_6581, plain, ![X14228, X14229, X14230, X14231, X14232]:(~class_Groups_Ocomm__monoid__mult(X14232)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14231),X14230))|(~hBOOL(hAPP(hAPP(c_member(X14231),X14229),X14230))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14232),hAPP(X14228,X14229)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X14231,X14232),X14228),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14231,tc_HOL_Obool)),X14230),hAPP(hAPP(c_Set_Oinsert(X14231),X14229),c_Orderings_Obot__class_Obot(tc_fun(X14231,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X14231,X14232),X14228),X14230)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod_Oremove])])])). 4.46/4.70 fof(c_0_6582, plain, ![X5140, X5141, X5142, X5143, X5144, X5145]:(~c_Finite__Set_Ofun__left__comm(X5145,X5144,X5143)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5145),X5142))|(hBOOL(hAPP(hAPP(c_member(X5145),X5141),X5142))|hAPP(hAPP(X5143,X5141),hAPP(hAPP(c_Finite__Set_Ofold(X5145,X5144,X5143),X5140),X5142))=hAPP(hAPP(c_Finite__Set_Ofold(X5145,X5144,X5143),X5140),hAPP(hAPP(c_Set_Oinsert(X5145),X5141),X5142))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert])])])). 4.46/4.70 fof(c_0_6583, plain, ![X5911, X5912, X5913, X5914, X5915]:(~class_Groups_Ocomm__monoid__add(X5915)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5914),X5913))|(~hBOOL(hAPP(hAPP(c_member(X5914),X5912),X5913))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5914,X5915),X5911),X5913)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5915),hAPP(X5911,X5912)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5914,X5915),X5911),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5914,tc_HOL_Obool)),X5913),hAPP(hAPP(c_Set_Oinsert(X5914),X5912),c_Orderings_Obot__class_Obot(tc_fun(X5914,tc_HOL_Obool))))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum_Oremove])])])). 4.46/4.70 cnf(c_0_6584, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk427_4(X2,X3,X4,X1)),X3)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),c_Transitive__Closure_Otrancl(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_5082])). 4.46/4.70 cnf(c_0_6585, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk42_4(X3,X4,X2,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Transitive__Closure_Otrancl(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_5079])). 4.46/4.70 cnf(c_0_6586, plain, (c_Map_Omap__upds(X1,X3,X6,X5,X4)=c_Map_Omap__upds(X1,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),X6),X2),hAPP(c_Option_Ooption_OSome(X3),X7)),X5,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),X5))))), inference(split_conjunct,[status(thm)],[c_0_4975])). 4.46/4.70 cnf(c_0_6587, plain, (hAPP(c_Finite__Set_Ocard(X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X3,tc_HOL_Obool)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),esk64_3(X1,X2,X3)),X2))|esk66_3(X1,X2,X3)!=esk65_3(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3,tc_HOL_Obool)),X2))), inference(split_conjunct,[status(thm)],[c_0_5070])). 4.46/4.70 fof(c_0_6588, plain, ![X9613, X9614, X9615, X9616, X9617, X9618]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X9618,X9618)),hAPP(hAPP(c_Product__Type_OPair(X9618,X9618),X9617),X9616)),hAPP(hAPP(c_Relation_Oinv__image(X9615,X9618),X9614),X9613)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X9615,X9615)),hAPP(hAPP(c_Product__Type_OPair(X9615,X9615),hAPP(X9613,X9617)),hAPP(X9613,X9616))),X9614)))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9615,X9615)),hAPP(hAPP(c_Product__Type_OPair(X9615,X9615),hAPP(X9613,X9617)),hAPP(X9613,X9616))),X9614))|hBOOL(hAPP(hAPP(c_member(tc_prod(X9618,X9618)),hAPP(hAPP(c_Product__Type_OPair(X9618,X9618),X9617),X9616)),hAPP(hAPP(c_Relation_Oinv__image(X9615,X9618),X9614),X9613))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__inv__image])])). 4.46/4.70 fof(c_0_6589, plain, ![X7180, X7181, X7182, X7183, X7184]:((hBOOL(hAPP(hAPP(c_member(X7184),esk209_5(X7180,X7181,X7182,X7183,X7184)),X7183))|c_Relation_Orefl__on(X7182,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7184,tc_fun(X7182,tc_HOL_Obool)),X7183),X7181),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7184,tc_fun(tc_prod(X7182,X7182),tc_HOL_Obool)),X7183),X7180)))&(~c_Relation_Orefl__on(X7182,hAPP(X7181,esk209_5(X7180,X7181,X7182,X7183,X7184)),hAPP(X7180,esk209_5(X7180,X7181,X7182,X7183,X7184)))|c_Relation_Orefl__on(X7182,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7184,tc_fun(X7182,tc_HOL_Obool)),X7183),X7181),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7184,tc_fun(tc_prod(X7182,X7182),tc_HOL_Obool)),X7183),X7180)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__on__INTER])])])])])). 4.46/4.70 cnf(c_0_6590, plain, (c_Map_Oran(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3))=hAPP(c_Set_Oimage(tc_prod(X1,X2),X2,c_Product__Type_Osnd(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_5105])). 4.46/4.70 cnf(c_0_6591, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),X2,c_Product__Type_Osnd(X1,X2)),X3)=hAPP(c_Relation_ORange(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_5106]), ['final']). 4.46/4.70 fof(c_0_6592, plain, ![X3643, X3644, X3645, X3646]:(~hBOOL(hAPP(c_List_Odistinct(X3646),X3645))|(hBOOL(hAPP(hAPP(c_member(X3646),X3644),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3646,tc_HOL_Obool)),hAPP(c_List_Oset(X3646),X3645)),hAPP(hAPP(c_Set_Oinsert(X3646),hAPP(hAPP(c_List_Onth(X3646),X3645),X3643)),c_Orderings_Obot__class_Obot(tc_fun(X3646,tc_HOL_Obool))))))|hBOOL(hAPP(c_List_Odistinct(X3646),hAPP(hAPP(c_List_Olist__update(X3646,X3645),X3643),X3644))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__list__update])])])). 4.46/4.70 fof(c_0_6593, plain, ![X13614, X13615, X13616, X13617, X13618]:(~class_Groups_Oab__group__add(X13618)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13617),X13616))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13617,tc_HOL_Obool)),X13615),X13616))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13617,X13618),X13614),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13617,tc_HOL_Obool)),X13616),X13615))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13618),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13617,X13618),X13614),X13616)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13617,X13618),X13614),X13615))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__diff])])])). 4.46/4.70 cnf(c_0_6594, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5107])). 4.46/4.70 cnf(c_0_6595, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X2))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5108])). 4.46/4.70 cnf(c_0_6596, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|c_Lazy__Sequence_Ohb__bind(X2,X3,hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X2,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X3))),X5),X1))=hAPP(c_New__DSequence_Oneg__decr__bind(X2,X3,X4,X5),X1)), inference(split_conjunct,[status(thm)],[c_0_5109])). 4.46/4.70 cnf(c_0_6597, plain, (c_Lazy__Sequence_Ohb__flat(X1,c_Lazy__Sequence_Ohb__map(X2,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)),X3,X4))=c_Lazy__Sequence_Ohb__bind(X2,X1,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_5110])). 4.46/4.70 cnf(c_0_6598, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk317_4(X1,X2,X3,X4)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X4))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5060])). 4.46/4.70 fof(c_0_6599, plain, ![X3669, X3670, X3671, X3672]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3671)),X3670))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3672),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3672),X3669),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3670,X3671))),hAPP(X3669,hAPP(c_Nat_OSuc,X3671)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3672),X3669),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3670,hAPP(c_Nat_OSuc,X3671)))|~class_Groups_Ocomm__monoid__add(X3672))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3671)),X3670))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3672),X3669),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3670,hAPP(c_Nat_OSuc,X3671)))=c_Groups_Ozero__class_Ozero(X3672)|~class_Groups_Ocomm__monoid__add(X3672))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__cl__ivl__Suc])])])])). 4.46/4.70 fof(c_0_6600, plain, ![X8893, X8894]:(~class_Rings_Ocomm__semiring__1(X8894)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8894),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8894),X8893)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8894),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8894),X8893)),c_Groups_Oone__class_Oone(X8894)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8894),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8894),c_Groups_Oone__class_Oone(X8894)),c_Groups_Oone__class_Oone(X8894))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X8894),c_Nat_Osemiring__1__class_Oof__nat(X8894)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X8893)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_gauss__sum])])])). 4.46/4.70 cnf(c_0_6601, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),hAPP(c_List_Oset(tc_prod(X3,X3)),hAPP(hAPP(c_List_Ozip(X3,X3),X4),X4))))|X1!=X2|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_5111])). 4.46/4.70 cnf(c_0_6602, plain, (c_List_OdropWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))=c_List_OdropWhile(X3,X1,X4)|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5112])). 4.46/4.70 cnf(c_0_6603, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Relation_OId(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X3)),X2)),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_5113])). 4.46/4.70 cnf(c_0_6604, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X5)),X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X5)),X6)|X1!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X3),X4)),X5)),X6)|~class_Rings_Oring(X2)), inference(split_conjunct,[status(thm)],[c_0_5114])). 4.46/4.70 fof(c_0_6605, plain, ![X5547, X5548, X5549, X5550]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5550),X5549)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5548)),X5547)))|hAPP(hAPP(c_List_Oappend(X5548),hAPP(hAPP(c_List_Otake(X5548),X5550),X5547)),hAPP(hAPP(c_List_Otake(X5548),X5549),hAPP(hAPP(c_List_Odrop(X5548),X5550),X5547)))=hAPP(hAPP(c_List_Otake(X5548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5550),X5549)),X5547)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__add])])). 4.46/4.70 fof(c_0_6606, plain, ![X13433, X13434, X13435]:((hBOOL(hAPP(hAPP(c_member(X13435),esk392_3(X13433,X13434,X13435)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13435,tc_HOL_Obool)),X13434),X13433)))|hAPP(c_Finite__Set_Ocard(X13435),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13435,tc_HOL_Obool)),X13434),X13433))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X13435),X13434)),hAPP(c_Finite__Set_Ocard(X13435),X13433))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13435),X13433))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13435),X13434)))&(c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Finite__Set_Ocard(X13435),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13435,tc_HOL_Obool)),X13434),X13433))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X13435),X13434)),hAPP(c_Finite__Set_Ocard(X13435),X13433))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13435),X13433))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13435),X13434)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card_Ounion__inter__neutral])])])])])). 4.46/4.70 cnf(c_0_6607, plain, (X4=X5|~class_Orderings_Olinorder(X1)|~c_Fun_Oinj__on(X2,X1,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(c_List_Oset(X2),X4)),hAPP(c_List_Oset(X2),X5)))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5)))|hAPP(c_List_Oset(X2),X4)!=hAPP(c_List_Oset(X2),X5)), inference(split_conjunct,[status(thm)],[c_0_5115])). 4.46/4.70 cnf(c_0_6608, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3))=hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5116]), ['final']). 4.46/4.70 fof(c_0_6609, plain, ![X6723, X6724, X6725, X6726]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk197_4(X6723,X6724,X6725,X6726)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X6725)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6726),X6723))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X6726),X6725)),X6723)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6725)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk198_4(X6723,X6724,X6725,X6726)),X6724))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6726),X6723))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X6726),X6725)),X6723)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6725)))&(X6726=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk198_4(X6723,X6724,X6725,X6726)),esk197_4(X6723,X6724,X6725,X6726))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6726),X6723))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X6726),X6725)),X6723)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6725))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bset_I5_J])])])])])])). 4.46/4.70 fof(c_0_6610, plain, ![X3922, X3923, X3924, X3925]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk104_4(X3922,X3923,X3924,X3925)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3924)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3925),X3922))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3925),X3924)),X3922)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3924)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk105_4(X3922,X3923,X3924,X3925)),X3923))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3925),X3922))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3925),X3924)),X3922)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3924)))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk105_4(X3922,X3923,X3924,X3925)),esk104_4(X3922,X3923,X3924,X3925))=X3925|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3925),X3922))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3925),X3924)),X3922)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3924))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bset_I6_J])])])])])])). 4.46/4.70 fof(c_0_6611, plain, ![X3949, X3950, X3951, X3952]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk106_4(X3949,X3950,X3951,X3952)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3951)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3949),X3952))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3949),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3952),X3951))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3951)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk107_4(X3949,X3950,X3951,X3952)),X3950))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3949),X3952))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3949),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3952),X3951))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3951)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk107_4(X3949,X3950,X3951,X3952)),esk106_4(X3949,X3950,X3951,X3952))=X3952|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3949),X3952))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3949),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3952),X3951))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3951))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_aset_I7_J])])])])])])). 4.46/4.70 cnf(c_0_6612, plain, (hAPP(hAPP(c_List_Oappend(X2),X3),X5)=hAPP(hAPP(c_List_Oappend(X2),X1),X4)|X1!=hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3)|X4!=hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3)),X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_5038])). 4.46/4.70 fof(c_0_6613, plain, ![X11644, X11645, X11646, X11647, X11648]:((c_Orderings_Obot__class_Obot(tc_fun(X11648,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11648,tc_HOL_Obool)),X11645),hAPP(hAPP(c_Set_Oinsert(X11648),X11644),c_Orderings_Obot__class_Obot(tc_fun(X11648,tc_HOL_Obool))))|hAPP(hAPP(X11647,X11644),hAPP(X11646,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11648,tc_HOL_Obool)),X11645),hAPP(hAPP(c_Set_Oinsert(X11648),X11644),c_Orderings_Obot__class_Obot(tc_fun(X11648,tc_HOL_Obool))))))=hAPP(X11646,X11645)|~hBOOL(hAPP(hAPP(c_member(X11648),X11644),X11645))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11648),X11645))|~c_Finite__Set_Ofolding__one(X11648,X11647,X11646))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11648,tc_HOL_Obool)),X11645),hAPP(hAPP(c_Set_Oinsert(X11648),X11644),c_Orderings_Obot__class_Obot(tc_fun(X11648,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X11648,tc_HOL_Obool))|X11644=hAPP(X11646,X11645)|~hBOOL(hAPP(hAPP(c_member(X11648),X11644),X11645))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11648),X11645))|~c_Finite__Set_Ofolding__one(X11648,X11647,X11646))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Oremove])])])])). 4.46/4.70 fof(c_0_6614, plain, ![X4847, X4848, X4849]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4849,tc_HOL_Obool)),X4848),hAPP(hAPP(c_Set_Oinsert(X4849),X4847),c_Orderings_Obot__class_Obot(tc_fun(X4849,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X4849,tc_HOL_Obool))|c_Big__Operators_Olinorder__class_OMax(X4849,hAPP(hAPP(c_Set_Oinsert(X4849),X4847),X4848))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4849),X4847),c_Big__Operators_Olinorder__class_OMax(X4849,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4849,tc_HOL_Obool)),X4848),hAPP(hAPP(c_Set_Oinsert(X4849),X4847),c_Orderings_Obot__class_Obot(tc_fun(X4849,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4849),X4848))|~class_Orderings_Olinorder(X4849))&(c_Orderings_Obot__class_Obot(tc_fun(X4849,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4849,tc_HOL_Obool)),X4848),hAPP(hAPP(c_Set_Oinsert(X4849),X4847),c_Orderings_Obot__class_Obot(tc_fun(X4849,tc_HOL_Obool))))|c_Big__Operators_Olinorder__class_OMax(X4849,hAPP(hAPP(c_Set_Oinsert(X4849),X4847),X4848))=X4847|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4849),X4848))|~class_Orderings_Olinorder(X4849))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Oinsert__remove])])])])). 4.46/4.70 fof(c_0_6615, plain, ![X12841, X12842, X12843, X12844, X12845, X12846, X12847]:(X12846=X12847|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X12845,X12844),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X12845,X12844),X12843),X12847),X12842)),X12846),X12841)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X12845,X12844),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X12845,X12844),X12843),X12846),X12841)),X12847),X12842)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__twist])])). 4.46/4.70 fof(c_0_6616, plain, ![X15442, X15443, X15444, X15445]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk450_4(X15442,X15443,X15444,X15445)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X15444)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15442),X15445))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15442),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15445),X15444))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15444)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk451_4(X15442,X15443,X15444,X15445)),X15443))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15442),X15445))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15442),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15445),X15444))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15444)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk451_4(X15442,X15443,X15444,X15445)),esk450_4(X15442,X15443,X15444,X15445))=X15445|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15442),X15445))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15442),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15445),X15444))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15444))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_aset_I8_J])])])])])])). 4.46/4.70 fof(c_0_6617, plain, ![X10657, X10658, X10659, X10660]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X10660,X10660)),hAPP(hAPP(c_Product__Type_OPair(X10660,X10660),esk312_4(X10657,X10658,X10659,X10660)),esk313_4(X10657,X10658,X10659,X10660))),X10657))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10660),tc_List_Olist(X10660))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10660),tc_List_Olist(X10660)),X10659),X10658)),c_List_Olistrel1(X10660,X10657))))&((X10659=hAPP(hAPP(c_List_Oappend(X10660),esk314_4(X10657,X10658,X10659,X10660)),hAPP(hAPP(c_List_Olist_OCons(X10660),esk312_4(X10657,X10658,X10659,X10660)),esk315_4(X10657,X10658,X10659,X10660)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10660),tc_List_Olist(X10660))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10660),tc_List_Olist(X10660)),X10659),X10658)),c_List_Olistrel1(X10660,X10657))))&(X10658=hAPP(hAPP(c_List_Oappend(X10660),esk314_4(X10657,X10658,X10659,X10660)),hAPP(hAPP(c_List_Olist_OCons(X10660),esk313_4(X10657,X10658,X10659,X10660)),esk315_4(X10657,X10658,X10659,X10660)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10660),tc_List_Olist(X10660))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10660),tc_List_Olist(X10660)),X10659),X10658)),c_List_Olistrel1(X10660,X10657)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel1E])])])])])). 4.46/4.70 fof(c_0_6618, plain, ![X6761, X6762, X6763]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6763,tc_HOL_Obool)),X6762),hAPP(hAPP(c_Set_Oinsert(X6763),X6761),c_Orderings_Obot__class_Obot(tc_fun(X6763,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X6763,tc_HOL_Obool))|X6761=c_Big__Operators_Olattice__class_OSup__fin(X6763,hAPP(hAPP(c_Set_Oinsert(X6763),X6761),X6762))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6763),X6762))|~class_Lattices_Olattice(X6763))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6763,tc_HOL_Obool)),X6762),hAPP(hAPP(c_Set_Oinsert(X6763),X6761),c_Orderings_Obot__class_Obot(tc_fun(X6763,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X6763,tc_HOL_Obool))|c_Big__Operators_Olattice__class_OSup__fin(X6763,hAPP(hAPP(c_Set_Oinsert(X6763),X6761),X6762))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6763),X6761),c_Big__Operators_Olattice__class_OSup__fin(X6763,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6763,tc_HOL_Obool)),X6762),hAPP(hAPP(c_Set_Oinsert(X6763),X6761),c_Orderings_Obot__class_Obot(tc_fun(X6763,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6763),X6762))|~class_Lattices_Olattice(X6763))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oinsert__remove])])])])). 4.46/4.70 fof(c_0_6619, plain, ![X8731, X8732, X8733]:((c_Orderings_Obot__class_Obot(tc_fun(X8733,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8733,tc_HOL_Obool)),X8732),hAPP(hAPP(c_Set_Oinsert(X8733),X8731),c_Orderings_Obot__class_Obot(tc_fun(X8733,tc_HOL_Obool))))|X8731=c_Big__Operators_Olattice__class_OInf__fin(X8733,hAPP(hAPP(c_Set_Oinsert(X8733),X8731),X8732))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8733),X8732))|~class_Lattices_Olattice(X8733))&(c_Orderings_Obot__class_Obot(tc_fun(X8733,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8733,tc_HOL_Obool)),X8732),hAPP(hAPP(c_Set_Oinsert(X8733),X8731),c_Orderings_Obot__class_Obot(tc_fun(X8733,tc_HOL_Obool))))|c_Big__Operators_Olattice__class_OInf__fin(X8733,hAPP(hAPP(c_Set_Oinsert(X8733),X8731),X8732))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8733),X8731),c_Big__Operators_Olattice__class_OInf__fin(X8733,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8733,tc_HOL_Obool)),X8732),hAPP(hAPP(c_Set_Oinsert(X8733),X8731),c_Orderings_Obot__class_Obot(tc_fun(X8733,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8733),X8732))|~class_Lattices_Olattice(X8733))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oinsert__remove])])])])). 4.46/4.70 fof(c_0_6620, plain, ![X6512, X6513, X6514]:((c_Orderings_Obot__class_Obot(tc_fun(X6514,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6514,tc_HOL_Obool)),X6513),hAPP(hAPP(c_Set_Oinsert(X6514),X6512),c_Orderings_Obot__class_Obot(tc_fun(X6514,tc_HOL_Obool))))|c_Big__Operators_Olinorder__class_OMin(X6514,hAPP(hAPP(c_Set_Oinsert(X6514),X6512),X6513))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X6514),X6512),c_Big__Operators_Olinorder__class_OMin(X6514,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6514,tc_HOL_Obool)),X6513),hAPP(hAPP(c_Set_Oinsert(X6514),X6512),c_Orderings_Obot__class_Obot(tc_fun(X6514,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6514),X6513))|~class_Orderings_Olinorder(X6514))&(c_Orderings_Obot__class_Obot(tc_fun(X6514,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6514,tc_HOL_Obool)),X6513),hAPP(hAPP(c_Set_Oinsert(X6514),X6512),c_Orderings_Obot__class_Obot(tc_fun(X6514,tc_HOL_Obool))))|c_Big__Operators_Olinorder__class_OMin(X6514,hAPP(hAPP(c_Set_Oinsert(X6514),X6512),X6513))=X6512|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6514),X6513))|~class_Orderings_Olinorder(X6514))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Oinsert__remove])])])])). 4.46/4.70 fof(c_0_6621, plain, ![X14437, X14438, X14439, X14440, X14441, X14442]:(~c_Finite__Set_Ofun__left__comm(X14442,X14441,X14440)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14442),X14439))|hAPP(hAPP(X14440,X14437),hAPP(hAPP(c_Finite__Set_Ofold(X14442,X14441,X14440),X14438),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14442,tc_HOL_Obool)),X14439),hAPP(hAPP(c_Set_Oinsert(X14442),X14437),c_Orderings_Obot__class_Obot(tc_fun(X14442,tc_HOL_Obool))))))=hAPP(hAPP(c_Finite__Set_Ofold(X14442,X14441,X14440),X14438),hAPP(hAPP(c_Set_Oinsert(X14442),X14437),X14439)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert__remove])])])). 4.46/4.70 fof(c_0_6622, plain, ![X16681, X16682, X16683, X16684, X16685]:(~class_Orderings_Olinorder(X16685)|(~hBOOL(hAPP(hAPP(c_member(X16684),X16683),hAPP(c_List_Oset(X16684),X16682)))|(~c_List_Olinorder__class_Osorted(X16685,hAPP(hAPP(c_List_Omap(X16684,X16685),X16681),X16682))|(hAPP(c_List_Ohd(X16684),hAPP(c_List_Ofilter(X16684,hAPP(hAPP(c_COMBB(X16685,tc_HOL_Obool,X16684),hAPP(c_fequal,hAPP(X16681,X16683))),X16681)),X16682))!=X16683|X16682=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16684,X16685,X16681),X16683),c_List_Oremove1(X16684,X16683,X16682)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__key__remove1])])])). 4.46/4.70 cnf(c_0_6623, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X2),X1))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5117])). 4.46/4.70 cnf(c_0_6624, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X1))), inference(rw,[status(thm)],[c_0_5118, c_0_4471])). 4.46/4.70 cnf(c_0_6625, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(rw,[status(thm)],[c_0_5119, c_0_5120]), ['final']). 4.46/4.70 cnf(c_0_6626, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(rw,[status(thm)],[c_0_5121, c_0_4436]), ['final']). 4.46/4.70 fof(c_0_6627, plain, ![X6682, X6683, X6684, X6685, X6686]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X6686)),hAPP(c_Set_Oimage(X6685,tc_Option_Ooption(X6686),X6684),c_Orderings_Otop__class_Otop(tc_fun(X6685,tc_HOL_Obool)))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X6686)),hAPP(c_Set_Oimage(X6685,tc_Option_Ooption(X6686),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6685,tc_Option_Ooption(X6686)),X6684),X6683),hAPP(c_Option_Ooption_OSome(X6686),X6682))),c_Orderings_Otop__class_Otop(tc_fun(X6685,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__updI])])). 4.46/4.70 fof(c_0_6628, plain, ![X17044, X17045, X17046, X17047]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17047))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17046),X17045))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17045),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17046),c_Divides_Odiv__class_Omod(tc_Int_Oint,X17044,X17047))),X17045)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult2__lemma__aux2])])])). 4.46/4.70 fof(c_0_6629, plain, ![X13676, X13677, X13678, X13679]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13679))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13678))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13678),X13677))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13677),c_Divides_Odiv__class_Omod(tc_Int_Oint,X13676,X13679))),X13678)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult2__lemma__aux3])])])). 4.46/4.70 cnf(c_0_6630, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5122, c_0_4471])). 4.46/4.70 cnf(c_0_6631, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Int_OMin), inference(split_conjunct,[status(thm)],[fact_Int_OMin__def]), ['final']). 4.46/4.70 fof(c_0_6632, plain, ![X5693, X5694, X5695, X5696, X5697, X5698]:(~class_Orderings_Olinorder(X5698)|(~c_List_Olinorder__class_Osorted(X5698,hAPP(hAPP(c_List_Omap(X5697,X5698),X5696),X5695))|(~hBOOL(hAPP(X5694,X5693))|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5697,X5698,X5696),X5693),hAPP(c_List_Ofilter(X5697,X5694),X5695))=hAPP(c_List_Ofilter(X5697,X5694),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5697,X5698,X5696),X5693),X5695))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__insort])])). 4.46/4.70 cnf(c_0_6633, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5123, c_0_4471])). 4.46/4.70 fof(c_0_6634, plain, ![X4142, X4143, X4144, X4145, X4146]:(~class_Rings_Osemiring__0(X4146)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4145,X4146),hAPP(hAPP(c_COMBC(X4145,X4146,X4146),hAPP(hAPP(c_COMBB(X4146,tc_fun(X4146,X4146),X4145),c_Groups_Otimes__class_Otimes(X4146)),X4144)),X4142)),X4143)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4146),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4145,X4146),X4144),X4143)),X4142)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__left__distrib])])). 4.46/4.70 cnf(c_0_6635, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3))),esk538_3(X1,X2,X3))|X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3))),esk536_3(X1,X2,X3))|epred2_3(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5124])). 4.46/4.70 cnf(c_0_6636, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OWhile(X4,X5)),c_Hoare__Mirabelle_Opeek__and(X1,X3,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X4)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,X4)),X5),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5125])). 4.46/4.70 cnf(c_0_6637, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk27_3(X1,X3,X2))),esk28_3(X1,X3,X2))|hBOOL(hAPP(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5126])). 4.46/4.70 fof(c_0_6638, plain, ![X10644, X10645, X10646, X10647]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk311_4(X10644,X10645,X10646,X10647)),X10647))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10647),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10645)),X10644)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10647),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10645)),c_List_OtakeWhile(X10645,X10646,X10644))))))&(~hBOOL(hAPP(X10646,hAPP(hAPP(c_List_Onth(X10645),X10644),esk311_4(X10644,X10645,X10646,X10647))))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10647),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10645)),X10644)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10647),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10645)),c_List_OtakeWhile(X10645,X10646,X10644))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_length__takeWhile__less__P__nth])])])])])). 4.46/4.70 cnf(c_0_6639, plain, (hBOOL(hAPP(X3,X4))|hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)=c_List_OdropWhile(X2,X3,X1)|X1!=hAPP(hAPP(c_List_Oappend(X2),c_List_OtakeWhile(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_5127])). 4.46/4.70 cnf(c_0_6640, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk155_3(X1,X3,X2))),esk156_3(X1,X3,X2))|hBOOL(hAPP(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5128])). 4.46/4.70 fof(c_0_6641, plain, ![X4058, X4059, X4060, X4061]:(~class_Int_Onumber(X4061)|~class_Rings_Osemiring(X4061)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4061),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4061),hAPP(c_Int_Onumber__class_Onumber__of(X4061),X4060)),X4059)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4061),hAPP(c_Int_Onumber__class_Onumber__of(X4061),X4060)),X4058))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4061),hAPP(c_Int_Onumber__class_Onumber__of(X4061),X4060)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4061),X4059),X4058))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_right__distrib__number__of])])])). 4.46/4.70 fof(c_0_6642, plain, ![X16700, X16701, X16702, X16703, X16704]:(~class_Rings_Olinordered__idom(X16704)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16704),hAPP(c_Groups_Oabs__class_Oabs(X16704),X16703)),X16702))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16704),hAPP(c_Groups_Oabs__class_Oabs(X16704),X16701)),X16700))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16704),hAPP(c_Groups_Oabs__class_Oabs(X16704),X16703)),hAPP(c_Groups_Oabs__class_Oabs(X16704),X16701))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16704),X16702),X16700)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__mult__less])])])). 4.46/4.70 cnf(c_0_6643, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X3),c_Transitive__Closure_Otrancl(X2,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X3),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),X1),X4)))), inference(split_conjunct,[status(thm)],[c_0_5129])). 4.46/4.70 fof(c_0_6644, plain, ![X6534, X6535, X6536, X6537]:(~class_Rings_Oring(X6537)|~class_Int_Onumber(X6537)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X6537),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6537),hAPP(c_Int_Onumber__class_Onumber__of(X6537),X6536)),X6535)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6537),hAPP(c_Int_Onumber__class_Onumber__of(X6537),X6536)),X6534))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6537),hAPP(c_Int_Onumber__class_Onumber__of(X6537),X6536)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X6537),X6535),X6534))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__diff__distrib__number__of])])). 4.46/4.70 fof(c_0_6645, plain, ![X13401, X13402, X13403, X13404, X13405]:(~class_Groups_Ocomm__monoid__mult(X13405)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13404),X13403))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13405),hAPP(X13402,X13401)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13404,X13405),X13402),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13404,tc_HOL_Obool)),X13403),hAPP(hAPP(c_Set_Oinsert(X13404),X13401),c_Orderings_Obot__class_Obot(tc_fun(X13404,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13404,X13405),X13402),hAPP(hAPP(c_Set_Oinsert(X13404),X13401),X13403)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod_Oinsert__remove])])])). 4.46/4.70 fof(c_0_6646, plain, ![X1353, X1354, X1355, X1356, X1357]:(~class_Groups_Ocomm__monoid__add(X1357)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1356),X1355))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1357),hAPP(X1354,X1353)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1356,X1357),X1354),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1356,tc_HOL_Obool)),X1355),hAPP(hAPP(c_Set_Oinsert(X1356),X1353),c_Orderings_Obot__class_Obot(tc_fun(X1356,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1356,X1357),X1354),hAPP(hAPP(c_Set_Oinsert(X1356),X1353),X1355)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum_Oinsert__remove])])])). 4.46/4.70 fof(c_0_6647, plain, ![X17195, X17196, X17197, X17198, X17199, X17200]:(~c_Finite__Set_Ofolding(X17200,X17199,X17198,X17197)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17200),X17196))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17200),X17195))|(c_Orderings_Obot__class_Obot(tc_fun(X17200,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17200,tc_HOL_Obool)),X17196),X17195)|hAPP(X17197,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17200,tc_HOL_Obool)),X17196),X17195))=hAPP(c_Fun_Ocomp(X17199,X17199,X17199,hAPP(X17197,X17196)),hAPP(X17197,X17195)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Ounion])])])). 4.46/4.70 fof(c_0_6648, plain, ![X12596, X12597, X12598, X12599, X12600]:(~class_Groups_Ocomm__monoid__add(X12600)|(~hBOOL(hAPP(hAPP(c_member(X12599),X12598),hAPP(c_List_Oset(X12599),X12597)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12600),hAPP(X12596,X12598)),hAPP(c_List_Omonoid__add__class_Olistsum(X12600),hAPP(hAPP(c_List_Omap(X12599,X12600),X12596),c_List_Oremove1(X12599,X12598,X12597))))=hAPP(c_List_Omonoid__add__class_Olistsum(X12600),hAPP(hAPP(c_List_Omap(X12599,X12600),X12596),X12597)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__map__remove1])])])). 4.46/4.70 cnf(c_0_6649, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4)))),X3)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5130])). 4.46/4.70 cnf(c_0_6650, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk65_3(X2,X3,X1)),esk66_3(X2,X3,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(c_Finite__Set_Ocard(X1),esk64_3(X2,X3,X1))!=X2|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))), inference(split_conjunct,[status(thm)],[c_0_5070])). 4.46/4.70 cnf(c_0_6651, plain, (X1=X2|hAPP(c_List_Ofilter(X3,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),hAPP(c_fequal,X1))),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))=hAPP(hAPP(c_List_Olist_OCons(X3),X2),hAPP(c_List_Ofilter(X3,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),hAPP(c_fequal,X1))),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5131, c_0_5035]), c_0_5035])). 4.46/4.70 fof(c_0_6652, plain, ![X15045, X15046]:(~class_Lattices_Olattice(X15046)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15046),X15045))|(c_Orderings_Obot__class_Obot(tc_fun(X15046,tc_HOL_Obool))=X15045|(~hBOOL(hAPP(hAPP(c_member(X15046),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15046),esk440_2(X15045,X15046)),esk441_2(X15045,X15046))),hAPP(hAPP(c_Set_Oinsert(X15046),esk440_2(X15045,X15046)),hAPP(hAPP(c_Set_Oinsert(X15046),esk441_2(X15045,X15046)),c_Orderings_Obot__class_Obot(tc_fun(X15046,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(X15046),c_Big__Operators_Olattice__class_OSup__fin(X15046,X15045)),X15045)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oclosed])])])])). 4.46/4.70 fof(c_0_6653, plain, ![X9755, X9756]:(~class_Lattices_Olattice(X9756)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9756),X9755))|(X9755=c_Orderings_Obot__class_Obot(tc_fun(X9756,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_member(X9756),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9756),esk278_2(X9755,X9756)),esk279_2(X9755,X9756))),hAPP(hAPP(c_Set_Oinsert(X9756),esk278_2(X9755,X9756)),hAPP(hAPP(c_Set_Oinsert(X9756),esk279_2(X9755,X9756)),c_Orderings_Obot__class_Obot(tc_fun(X9756,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(X9756),c_Big__Operators_Olattice__class_OInf__fin(X9756,X9755)),X9755)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oclosed])])])])). 4.46/4.70 fof(c_0_6654, plain, ![X8157, X8158, X8159, X8160, X8161]:(~class_Fields_Ofield(X8161)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8160,X8161),hAPP(hAPP(c_COMBC(X8160,X8161,X8161),hAPP(hAPP(c_COMBB(X8161,tc_fun(X8161,X8161),X8160),c_Rings_Oinverse__class_Odivide(X8161)),X8159)),X8157)),X8158)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8161),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8160,X8161),X8159),X8158)),X8157)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__divide__distrib])])])). 4.46/4.70 fof(c_0_6655, plain, ![X11931, X11932, X11933, X11934, X11935, X11936]:(~c_Finite__Set_Ofun__left__comm(X11936,X11935,X11934)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11936),X11933))|(hBOOL(hAPP(hAPP(c_member(X11936),X11932),X11933))|hAPP(hAPP(c_Finite__Set_Ofold(X11936,X11935,X11934),X11931),hAPP(hAPP(c_Set_Oinsert(X11936),X11932),X11933))=hAPP(hAPP(c_Finite__Set_Ofold(X11936,X11935,X11934),hAPP(hAPP(X11934,X11932),X11931)),X11933)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert2])])])). 4.46/4.70 cnf(c_0_6656, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5132])). 4.46/4.70 cnf(c_0_6657, plain, (c_Divides_OnegDivAlg(c_Int_OMin,X1)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5133, c_0_4609]), c_0_4609]), c_0_5134]), ['final']). 4.46/4.70 cnf(c_0_6658, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5135]), ['final']). 4.46/4.70 cnf(c_0_6659, plain, (hAPP(c_Product__Type_Ofst(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4))=X3), inference(er,[status(thm)],[c_0_5136]), ['final']). 4.46/4.70 fof(c_0_6660, plain, ![X16315, X16316, X16317, X16318, X16319]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16319,tc_HOL_Obool)),X16316),hAPP(hAPP(c_Set_Oinsert(X16319),X16315),c_Orderings_Obot__class_Obot(tc_fun(X16319,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X16319,tc_HOL_Obool))|hAPP(hAPP(X16318,X16315),hAPP(X16317,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16319,tc_HOL_Obool)),X16316),hAPP(hAPP(c_Set_Oinsert(X16319),X16315),c_Orderings_Obot__class_Obot(tc_fun(X16319,tc_HOL_Obool))))))=hAPP(X16317,hAPP(hAPP(c_Set_Oinsert(X16319),X16315),X16316))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16319),X16316))|~c_Finite__Set_Ofolding__one(X16319,X16318,X16317))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16319,tc_HOL_Obool)),X16316),hAPP(hAPP(c_Set_Oinsert(X16319),X16315),c_Orderings_Obot__class_Obot(tc_fun(X16319,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X16319,tc_HOL_Obool))|X16315=hAPP(X16317,hAPP(hAPP(c_Set_Oinsert(X16319),X16315),X16316))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16319),X16316))|~c_Finite__Set_Ofolding__one(X16319,X16318,X16317))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Oinsert__remove])])])])). 4.46/4.70 fof(c_0_6661, plain, ![X16016, X16017, X16018, X16019]:((hBOOL(hAPP(hAPP(c_member(X16019),X16018),X16017))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16019,tc_Nat_Onat),X16016),X16017)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16019,tc_Nat_Onat),X16016),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16019,tc_HOL_Obool)),X16017),hAPP(hAPP(c_Set_Oinsert(X16019),X16018),c_Orderings_Obot__class_Obot(tc_fun(X16019,tc_HOL_Obool))))))&(~hBOOL(hAPP(hAPP(c_member(X16019),X16018),X16017))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16019,tc_Nat_Onat),X16016),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16019,tc_HOL_Obool)),X16017),hAPP(hAPP(c_Set_Oinsert(X16019),X16018),c_Orderings_Obot__class_Obot(tc_fun(X16019,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16019,tc_Nat_Onat),X16016),X16017)),hAPP(X16016,X16018)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__diff1__nat])])])). 4.46/4.70 fof(c_0_6662, plain, ![X8242, X8243, X8244, X8245]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8245))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8244),X8243))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8243),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X8242,X8245))),X8244)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8243),X8245))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__lemma])])])). 4.46/4.70 cnf(c_0_6663, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk263_3(X3,X2,X1)),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_5129])). 4.46/4.70 fof(c_0_6664, plain, ![X13996, X13997, X13998, X13999, X14000]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X14000,X14000)),hAPP(hAPP(c_Product__Type_OPair(X14000,X14000),X13999),X13998)),c_Transitive__Closure_Ortrancl(X14000,X13997)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X14000,X14000),tc_HOL_Obool)),X13997),hAPP(hAPP(c_Product__Type_OSigma(X14000,X14000),X13996),hAPP(c_COMBK(tc_fun(X14000,tc_HOL_Obool),X14000),X13996))))|(X13999=X13998|hBOOL(hAPP(hAPP(c_member(X14000),X13999),X13996))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__subset__Sigma__aux])])])). 4.46/4.70 cnf(c_0_6665, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X1))),hAPP(X4,X1))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(c_Nat_OSuc,X1)))|~class_Groups_Ocomm__monoid__add(X3)), inference(split_conjunct,[status(thm)],[c_0_5137])). 4.46/4.70 cnf(c_0_6666, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5138])). 4.46/4.70 cnf(c_0_6667, plain, (hAPP(c_Product__Type_Osnd(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4))=X4), inference(er,[status(thm)],[c_0_5139]), ['final']). 4.46/4.70 cnf(c_0_6668, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk533_3(X2,X1,X3))),esk534_3(X2,X1,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X2,X1,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|epred1_3(X3,X1,X2)|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.70 cnf(c_0_6669, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1))),X3)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))), inference(split_conjunct,[status(thm)],[c_0_5140])). 4.46/4.70 fof(c_0_6670, plain, ![X6316, X6317, X6318, X6319, X6320]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X6320,X6319)),hAPP(X6320,X6318)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X6317,X6317)),hAPP(hAPP(c_Product__Type_OPair(X6317,X6317),X6319),X6318)),c_List_Omeasures(X6317,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X6317,tc_Nat_Onat)),X6320),X6316))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_measures__less])])])). 4.46/4.70 fof(c_0_6671, plain, ![X4099, X4100, X4101, X4102, X4103]:(((~hBOOL(hAPP(hAPP(c_member(X4102),hAPP(X4101,X4100)),hAPP(c_Set_Oimage(X4103,X4102,X4101),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4103,tc_HOL_Obool)),X4099),hAPP(hAPP(c_Set_Oinsert(X4103),X4100),c_Orderings_Obot__class_Obot(tc_fun(X4103,tc_HOL_Obool)))))))|~c_Fun_Oinj__on(X4103,X4102,X4101,hAPP(hAPP(c_Set_Oinsert(X4103),X4100),X4099)))&(c_Fun_Oinj__on(X4103,X4102,X4101,X4099)|~c_Fun_Oinj__on(X4103,X4102,X4101,hAPP(hAPP(c_Set_Oinsert(X4103),X4100),X4099))))&(hBOOL(hAPP(hAPP(c_member(X4102),hAPP(X4101,X4100)),hAPP(c_Set_Oimage(X4103,X4102,X4101),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4103,tc_HOL_Obool)),X4099),hAPP(hAPP(c_Set_Oinsert(X4103),X4100),c_Orderings_Obot__class_Obot(tc_fun(X4103,tc_HOL_Obool)))))))|~c_Fun_Oinj__on(X4103,X4102,X4101,X4099)|c_Fun_Oinj__on(X4103,X4102,X4101,hAPP(hAPP(c_Set_Oinsert(X4103),X4100),X4099)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__insert])])])])). 4.46/4.70 cnf(c_0_6672, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X1,X2,X3)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3))),esk532_3(X1,X2,X3))=X1|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,X1))), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.70 fof(c_0_6673, plain, ![X13993, X13994, X13995]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13995),X13994))|c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))=c_Smallcheck_Osmall_H(X13993,X13995,X13994))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13995),X13994))|hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X13993,X13995,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13994),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X13993,X13994))=c_Smallcheck_Osmall_H(X13993,X13995,X13994))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_small_H_Osimps])])])). 4.46/4.70 fof(c_0_6674, plain, ![X15084, X15085, X15086, X15087, X15088]:(~c_Finite__Set_Ofolding__one(X15088,X15087,X15086)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15088),X15085))|(X15085=c_Orderings_Obot__class_Obot(tc_fun(X15088,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15088),X15084))|(c_Orderings_Obot__class_Obot(tc_fun(X15088,tc_HOL_Obool))=X15084|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15088,tc_HOL_Obool)),X15085),X15084)!=c_Orderings_Obot__class_Obot(tc_fun(X15088,tc_HOL_Obool))|hAPP(X15086,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15088,tc_HOL_Obool)),X15085),X15084))=hAPP(hAPP(X15087,hAPP(X15086,X15085)),hAPP(X15086,X15084)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Ounion__disjoint])])])). 4.46/4.70 fof(c_0_6675, plain, ![X16451, X16452, X16453, X16455]:((hBOOL(hAPP(X16452,esk480_3(X16451,X16452,X16453)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16451))|(~hBOOL(hAPP(X16452,X16455))|hBOOL(hAPP(X16452,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X16455),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16451),X16453))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16453)))&(~hBOOL(hAPP(X16452,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk480_3(X16451,X16452,X16453)),X16453)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16451))|(~hBOOL(hAPP(X16452,X16455))|hBOOL(hAPP(X16452,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X16455),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16451),X16453))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16453)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_decr__mult__lemma])])])])])])). 4.46/4.70 fof(c_0_6676, plain, ![X8530, X8531, X8532, X8533]:((~hBOOL(hAPP(hAPP(c_member(X8532),X8530),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8533,tc_fun(X8532,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8533,tc_HOL_Obool))),X8531)))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8533,tc_fun(X8532,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8533,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X8532,tc_HOL_Obool),tc_fun(X8532,tc_HOL_Obool),X8533),hAPP(c_COMBC(X8532,tc_fun(X8532,tc_HOL_Obool),tc_HOL_Obool),c_member(X8532))),X8531)),X8530)))&(~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8533,tc_fun(X8532,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8533,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X8532,tc_HOL_Obool),tc_fun(X8532,tc_HOL_Obool),X8533),hAPP(c_COMBC(X8532,tc_fun(X8532,tc_HOL_Obool),tc_HOL_Obool),c_member(X8532))),X8531)),X8530))|hBOOL(hAPP(hAPP(c_member(X8532),X8530),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8533,tc_fun(X8532,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8533,tc_HOL_Obool))),X8531))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__INT__eq])])). 4.46/4.70 fof(c_0_6677, plain, ![X873, X874, X875, X876]:((~hBOOL(hAPP(hAPP(c_member(X875),X873),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X876,tc_fun(X875,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X876,tc_HOL_Obool))),X874)))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X876,tc_fun(X875,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X876,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X875,tc_HOL_Obool),tc_fun(X875,tc_HOL_Obool),X876),hAPP(c_COMBC(X875,tc_fun(X875,tc_HOL_Obool),tc_HOL_Obool),c_member(X875))),X874)),X873)))&(~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X876,tc_fun(X875,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X876,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X875,tc_HOL_Obool),tc_fun(X875,tc_HOL_Obool),X876),hAPP(c_COMBC(X875,tc_fun(X875,tc_HOL_Obool),tc_HOL_Obool),c_member(X875))),X874)),X873))|hBOOL(hAPP(hAPP(c_member(X875),X873),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X876,tc_fun(X875,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X876,tc_HOL_Obool))),X874))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq])])). 4.46/4.70 fof(c_0_6678, plain, ![X1494, X1495, X1496, X1497, X1498]:(~c_Relation_Osingle__valued(X1498,X1497,hAPP(c_Relation_Oconverse(X1497,X1498),X1496))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1498,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1497,X1498,X1496),X1495)),hAPP(c_Relation_OImage(X1497,X1498,X1496),X1494))=hAPP(c_Relation_OImage(X1497,X1498,X1496),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1497,tc_HOL_Obool)),X1495),X1494))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__Int__eq])])). 4.46/4.70 fof(c_0_6679, plain, ![X1993, X1994, X1995, X1996, X1997]:(~class_Rings_Olinordered__semiring__strict(X1997)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1997),X1996),X1995))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1997),X1994),X1993))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1997),c_Groups_Ozero__class_Ozero(X1997)),X1995))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1997),c_Groups_Ozero__class_Ozero(X1997)),X1994))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1997),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1997),X1996),X1994)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1997),X1995),X1993)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__mono])])])). 4.46/4.70 fof(c_0_6680, plain, ![X6873, X6874, X6875, X6876, X6877]:(~class_Rings_Olinordered__semiring__strict(X6877)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6877),X6876),X6875))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6877),X6874),X6873))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6877),c_Groups_Ozero__class_Ozero(X6877)),X6876))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6877),c_Groups_Ozero__class_Ozero(X6877)),X6874))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6877),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6877),X6876),X6874)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6877),X6875),X6873)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__mono_H])])])). 4.46/4.70 fof(c_0_6681, plain, ![X13939, X13940, X13941, X13942, X13943]:(~class_Rings_Olinordered__semiring__strict(X13943)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13943),X13942),X13941))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13943),X13940),X13939))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13943),c_Groups_Ozero__class_Ozero(X13943)),X13942))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13943),c_Groups_Ozero__class_Ozero(X13943)),X13940))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13943),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13943),X13942),X13940)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13943),X13941),X13939)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__less__imp__less])])])). 4.46/4.70 fof(c_0_6682, plain, ![X7506, X7507, X7508]:(~class_Orderings_Olinorder(X7508)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7508),X7507))|(X7507=c_Orderings_Obot__class_Obot(tc_fun(X7508,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7508),X7506))|(c_Orderings_Obot__class_Obot(tc_fun(X7508,tc_HOL_Obool))=X7506|hAPP(hAPP(c_Orderings_Oord__class_Omin(X7508),c_Big__Operators_Olattice_OInf__fin(X7508,c_Orderings_Oord__class_Omin(X7508),X7507)),c_Big__Operators_Olattice_OInf__fin(X7508,c_Orderings_Oord__class_Omin(X7508),X7506))=c_Big__Operators_Olattice_OInf__fin(X7508,c_Orderings_Oord__class_Omin(X7508),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7508,tc_HOL_Obool)),X7507),X7506))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Ounion__idem])])])). 4.46/4.70 fof(c_0_6683, plain, ![X16771, X16772, X16773, X16774, X16775, X16776]:((hAPP(hAPP(c_Product__Type_OPair(X16775,X16774),esk494_6(X16771,X16772,X16773,X16774,X16775,X16776)),esk495_6(X16771,X16772,X16773,X16774,X16775,X16776))=X16776|hBOOL(hAPP(hAPP(c_member(X16773),X16772),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X16775,X16774,tc_fun(X16773,tc_HOL_Obool)),X16771),X16776))))&(~hBOOL(hAPP(hAPP(c_member(X16773),X16772),hAPP(hAPP(X16771,esk494_6(X16771,X16772,X16773,X16774,X16775,X16776)),esk495_6(X16771,X16772,X16773,X16774,X16775,X16776))))|hBOOL(hAPP(hAPP(c_member(X16773),X16772),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X16775,X16774,tc_fun(X16773,tc_HOL_Obool)),X16771),X16776))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mem__splitI2])])])])])). 4.46/4.70 fof(c_0_6684, plain, ![X7281, X7282, X7283, X7284, X7285]:(~class_Rings_Olinordered__semiring__strict(X7285)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7285),X7284),X7283))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7285),X7282),X7281))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7285),c_Groups_Ozero__class_Ozero(X7285)),X7284))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7285),c_Groups_Ozero__class_Ozero(X7285)),X7282))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7285),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7285),X7284),X7282)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7285),X7283),X7281)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__le__imp__less])])])). 4.46/4.70 fof(c_0_6685, plain, ![X1453, X1454, X1455, X1456, X1457]:(~class_Fields_Olinordered__field(X1457)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1457),c_Groups_Ozero__class_Ozero(X1457)),X1456))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1457),X1456),X1455))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1457),c_Groups_Ozero__class_Ozero(X1457)),X1454))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1457),X1454),X1453))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1457),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1457),X1456),X1453)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1457),X1455),X1454)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_frac__less2])])])). 4.46/4.70 fof(c_0_6686, plain, ![X2850, X2851, X2852, X2853, X2854]:(~class_Fields_Olinordered__field(X2854)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2854),c_Groups_Ozero__class_Ozero(X2854)),X2853))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2854),X2853),X2852))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2854),c_Groups_Ozero__class_Ozero(X2854)),X2851))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2854),X2851),X2850))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2854),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2854),X2853),X2850)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2854),X2852),X2851)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_frac__less])])])). 4.46/4.70 fof(c_0_6687, plain, ![X15620, X15621, X15622, X15623, X15624]:(~class_Rings_Oordered__semiring(X15624)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15624),X15623),X15622))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15624),X15621),X15620))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15624),c_Groups_Ozero__class_Ozero(X15624)),X15623))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15624),c_Groups_Ozero__class_Ozero(X15624)),X15621))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15624),X15623),X15621)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15624),X15622),X15620)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__mono_H])])])). 4.46/4.70 cnf(c_0_6688, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk331_2(X2,X1)),esk331_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))|c_Wellfounded_Oacyclic(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5141])). 4.46/4.70 fof(c_0_6689, plain, ![X2522, X2523, X2524]:(~class_Orderings_Olinorder(X2524)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2524),X2523))|(X2523=c_Orderings_Obot__class_Obot(tc_fun(X2524,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2524),X2522))|(c_Orderings_Obot__class_Obot(tc_fun(X2524,tc_HOL_Obool))=X2522|c_Big__Operators_Olattice_OSup__fin(X2524,c_Orderings_Oord__class_Omax(X2524),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2524,tc_HOL_Obool)),X2523),X2522))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X2524),c_Big__Operators_Olattice_OSup__fin(X2524,c_Orderings_Oord__class_Omax(X2524),X2523)),c_Big__Operators_Olattice_OSup__fin(X2524,c_Orderings_Oord__class_Omax(X2524),X2522))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Ounion__idem])])])). 4.46/4.70 fof(c_0_6690, plain, ![X2872, X2873, X2874, X2875]:(~hBOOL(hAPP(hAPP(c_member(X2875),X2874),hAPP(c_List_Oset(X2875),X2873)))|(hBOOL(hAPP(X2872,X2874))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2875)),hAPP(c_List_Ofilter(X2875,X2872),X2873))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2875)),X2873))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_length__filter__less])])])). 4.46/4.70 fof(c_0_6691, plain, ![X15148, X15149, X15150, X15151]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15151),X15150))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15151,tc_HOL_Obool)),X15150),X15149))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15151,tc_Nat_Onat),X15148),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15151,tc_HOL_Obool)),X15149),X15150))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15151,tc_Nat_Onat),X15148),X15149)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15151,tc_Nat_Onat),X15148),X15150)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__diff__nat])])])). 4.46/4.70 cnf(c_0_6692, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk110_2(X2,X1)),esk110_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))|c_Wellfounded_Oacyclic(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5142])). 4.46/4.70 fof(c_0_6693, plain, ![X15278, X15279, X15280, X15281, X15282]:(~class_Rings_Oordered__semiring(X15282)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15282),X15281),X15280))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15282),X15279),X15278))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15282),c_Groups_Ozero__class_Ozero(X15282)),X15280))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15282),c_Groups_Ozero__class_Ozero(X15282)),X15279))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15282),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15282),X15281),X15279)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15282),X15280),X15278)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__mono])])])). 4.46/4.70 fof(c_0_6694, plain, ![X17009, X17010, X17011, X17012, X17013]:(~class_Fields_Olinordered__field(X17013)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17013),c_Groups_Ozero__class_Ozero(X17013)),X17012))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17013),X17012),X17011))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17013),c_Groups_Ozero__class_Ozero(X17013)),X17010))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17013),X17010),X17009))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17013),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17013),X17012),X17009)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17013),X17011),X17010)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_frac__le])])])). 4.46/4.70 cnf(c_0_6695, plain, (X1=hAPP(X2,esk256_3(X1,X2,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk255_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk255_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5093])). 4.46/4.70 cnf(c_0_6696, plain, (X1=hAPP(X2,esk72_3(X1,X2,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk71_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk71_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5095])). 4.46/4.70 cnf(c_0_6697, plain, (hBOOL(hAPP(hAPP(X1,X5),X4))|~hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X3))|X2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X5)),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5126])). 4.46/4.70 cnf(c_0_6698, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))|c_Partial__Function_Oflat__lub(X1,X3,X2)=c_HOL_OThe(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_5143])). 4.46/4.70 fof(c_0_6699, plain, ![X6088, X6089, X6090, X6091, X6092, X6093, X6094, X6095]:(~c_Fun_Oinj__on(X6095,X6094,X6093,X6092)|(~c_Fun_Oinj__on(X6091,X6090,X6089,X6088)|c_Fun_Oinj__on(tc_prod(X6095,X6091),tc_prod(X6094,X6090),c_Product__Type_Omap__pair(X6095,X6094,X6091,X6090,X6093,X6089),hAPP(hAPP(c_Product__Type_OSigma(X6095,X6091),X6092),hAPP(c_COMBK(tc_fun(X6091,tc_HOL_Obool),X6095),X6088))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__pair__inj__on])])])). 4.46/4.70 fof(c_0_6700, plain, ![X15381, X15382, X15383, X15384, X15385, X15387]:((~hBOOL(hAPP(hAPP(c_member(X15385),X15381),hAPP(c_List_Oset(X15385),X15384)))|hAPP(c_Option_Ooption_OSome(X15383),esk448_5(X15381,X15382,X15383,X15384,X15385))=hAPP(hAPP(c_Map_Omap__of(X15385,X15383),hAPP(hAPP(c_List_Ozip(X15385,X15383),X15384),X15382)),X15381)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15383)),X15382)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15385)),X15384))&(hAPP(c_Option_Ooption_OSome(X15383),X15387)!=hAPP(hAPP(c_Map_Omap__of(X15385,X15383),hAPP(hAPP(c_List_Ozip(X15385,X15383),X15384),X15382)),X15381)|hBOOL(hAPP(hAPP(c_member(X15385),X15381),hAPP(c_List_Oset(X15385),X15384)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15383)),X15382)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15385)),X15384))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__zip__is__Some])])])])])). 4.46/4.70 fof(c_0_6701, plain, ![X10974, X10975, X10976, X10977, X10978]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X10978,X10977)),hAPP(X10978,X10976)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10975,X10975)),hAPP(hAPP(c_Product__Type_OPair(X10975,X10975),X10977),X10976)),X10974))|hBOOL(hAPP(hAPP(c_member(tc_prod(X10975,X10975)),hAPP(hAPP(c_Product__Type_OPair(X10975,X10975),X10977),X10976)),c_Wellfounded_Omlex__prod(X10975,X10978,X10974))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mlex__leq])])])). 4.46/4.70 fof(c_0_6702, plain, ![X15840, X15841, X15842, X15843, X15844]:(~class_Orderings_Olinorder(X15844)|(~c_List_Olinorder__class_Osorted(X15844,hAPP(c_List_Orev(X15844),hAPP(hAPP(c_List_Omap(X15843,X15844),X15842),X15841)))|hAPP(c_List_Ofilter(X15843,hAPP(hAPP(c_COMBB(X15844,tc_HOL_Obool,X15843),hAPP(c_Orderings_Oord__class_Oless(X15844),X15840)),X15842)),X15841)=c_List_OtakeWhile(X15843,hAPP(hAPP(c_COMBB(X15844,tc_HOL_Obool,X15843),hAPP(c_Orderings_Oord__class_Oless(X15844),X15840)),X15842),X15841))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__equals__takeWhile__sorted__rev])])])). 4.46/4.70 cnf(c_0_6703, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk533_3(X2,X1,X3))),esk534_3(X2,X1,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X2,X1,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.70 cnf(c_0_6704, plain, (hBOOL(hAPP(hAPP(X1,X5),X4))|~hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X4))|X2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X5)),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5128])). 4.46/4.70 fof(c_0_6705, plain, ![X5854, X5855, X5856, X5857]:(~class_Groups_Ocomm__monoid__add(X5857)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5856),X5855))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5857),hAPP(X5854,X5856)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5857),X5854),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X5856)),X5855)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5857),X5854),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5856),X5855)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__head__upt__Suc])])])). 4.46/4.70 fof(c_0_6706, plain, ![X3296, X3297, X3298]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3298),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3297)),X3296)))|X3296=hAPP(hAPP(c_List_Oappend(X3297),hAPP(hAPP(c_List_Otake(X3297),X3298),X3296)),hAPP(hAPP(c_List_Olist_OCons(X3297),hAPP(hAPP(c_List_Onth(X3297),X3296),X3298)),hAPP(hAPP(c_List_Odrop(X3297),hAPP(c_Nat_OSuc,X3298)),X3296)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_id__take__nth__drop])])])). 4.46/4.70 fof(c_0_6707, plain, ![X14181, X14182, X14183, X14184, X14185]:((~c_Fun_Oinj__on(X14185,X14184,X14183,X14181)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14184,tc_HOL_Obool)),hAPP(c_Set_Oimage(X14185,X14184,X14183),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14185,tc_HOL_Obool)),X14182),X14181))),hAPP(c_Set_Oimage(X14185,X14184,X14183),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14185,tc_HOL_Obool)),X14181),X14182)))!=c_Orderings_Obot__class_Obot(tc_fun(X14184,tc_HOL_Obool))|~c_Fun_Oinj__on(X14185,X14184,X14183,X14182)|c_Fun_Oinj__on(X14185,X14184,X14183,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14185,tc_HOL_Obool)),X14182),X14181)))&(((c_Fun_Oinj__on(X14185,X14184,X14183,X14181)|~c_Fun_Oinj__on(X14185,X14184,X14183,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14185,tc_HOL_Obool)),X14182),X14181)))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14184,tc_HOL_Obool)),hAPP(c_Set_Oimage(X14185,X14184,X14183),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14185,tc_HOL_Obool)),X14182),X14181))),hAPP(c_Set_Oimage(X14185,X14184,X14183),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14185,tc_HOL_Obool)),X14181),X14182)))=c_Orderings_Obot__class_Obot(tc_fun(X14184,tc_HOL_Obool))|~c_Fun_Oinj__on(X14185,X14184,X14183,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14185,tc_HOL_Obool)),X14182),X14181))))&(c_Fun_Oinj__on(X14185,X14184,X14183,X14182)|~c_Fun_Oinj__on(X14185,X14184,X14183,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14185,tc_HOL_Obool)),X14182),X14181))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Un])])])). 4.46/4.70 cnf(c_0_6708, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X1,X2,X3)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3))),esk532_3(X1,X2,X3))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.70 cnf(c_0_6709, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk442_3(X2,X1,X3)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5144])). 4.46/4.70 fof(c_0_6710, plain, ![X8227, X8228, X8229, X8230, X8231, X8232]:(~c_Finite__Set_Ofolding(X8232,X8231,X8230,X8229)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8232),X8228))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8232),X8227))|hAPP(c_Fun_Ocomp(X8231,X8231,X8231,hAPP(X8229,X8227)),hAPP(X8229,X8228))=hAPP(c_Fun_Ocomp(X8231,X8231,X8231,hAPP(X8229,X8228)),hAPP(X8229,X8227))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Ocommute__comp_H_H])])])). 4.46/4.70 cnf(c_0_6711, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X3,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X1)!=X3), inference(split_conjunct,[status(thm)],[c_0_5145])). 4.46/4.70 cnf(c_0_6712, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5146])). 4.46/4.70 cnf(c_0_6713, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5147, c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6714, plain, ![X3121, X3122, X3123]:((hBOOL(hAPP(hAPP(c_member(X3123),esk80_3(X3121,X3122,X3123)),X3122))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3123,tc_Int_Oint),X3121),X3122)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3123,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X3123),c_Int_Onat),X3121)),X3122)))&(~c_Nat__Transfer_Ois__nat(hAPP(X3121,esk80_3(X3121,X3122,X3123)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3123,tc_Int_Oint),X3121),X3122)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3123,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X3123),c_Int_Onat),X3121)),X3122)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__int__nat__sum__prod2_I2_J])])])])])). 4.46/4.70 cnf(c_0_6715, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X1,X2,X3)),X2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3))),esk532_3(X1,X2,X3))=X1|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,X1))), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.70 cnf(c_0_6716, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(X3,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X1)!=X3), inference(split_conjunct,[status(thm)],[c_0_5145])). 4.46/4.70 cnf(c_0_6717, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5148, c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6718, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5149, c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6719, plain, ![X5361, X5362, X5363, X5364, X5365]:(~class_Groups_Oab__semigroup__mult(X5365)|(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5365,X5365,c_Groups_Otimes__class_Otimes(X5365),X5364,X5363),X5362))|(hBOOL(hAPP(hAPP(c_member(X5365),X5364),X5363))|hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5365,X5365,c_Groups_Otimes__class_Otimes(X5365),X5361,hAPP(hAPP(c_Set_Oinsert(X5365),X5364),X5363)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5365),X5361),X5362)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__graph__insert__swap])])])). 4.46/4.70 cnf(c_0_6720, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk533_3(X2,X1,X3))),esk534_3(X2,X1,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk532_3(X2,X1,X3)))|epred1_3(X3,X1,X2)|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.70 fof(c_0_6721, plain, ![X9252, X9253, X9254, X9255]:(~class_Int_Onumber(X9255)|~class_Rings_Osemiring(X9255)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9255),X9254),hAPP(c_Int_Onumber__class_Onumber__of(X9255),X9252))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9255),X9253),hAPP(c_Int_Onumber__class_Onumber__of(X9255),X9252)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9255),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9255),X9254),X9253)),hAPP(c_Int_Onumber__class_Onumber__of(X9255),X9252))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_left__distrib__number__of])])])). 4.46/4.70 fof(c_0_6722, plain, ![X3205, X3206, X3207, X3208]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X3208)),hAPP(c_Set_Oimage(X3207,tc_Option_Ooption(X3208),X3206),c_Orderings_Otop__class_Otop(tc_fun(X3207,tc_HOL_Obool)))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X3208)),hAPP(c_Set_Oimage(X3207,tc_Option_Ooption(X3208),c_Map_Omap__add(X3207,X3208,X3206,hAPP(c_Map_Omap__of(X3207,X3208),X3205))),c_Orderings_Otop__class_Otop(tc_fun(X3207,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__range__map__of__map__add])])])). 4.46/4.70 cnf(c_0_6723, plain, (c_List_Oupt(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X2),c_List_Oupt(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_5150])). 4.46/4.70 fof(c_0_6724, plain, ![X16376, X16377, X16378, X16379, X16380]:(~class_Rings_Osemiring(X16380)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16380),X16379),X16378)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16380),X16377),X16378)),X16376))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16380),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16380),X16379),X16377)),X16378)),X16376)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_combine__common__factor])])). 4.46/4.70 cnf(c_0_6725, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~c_Nitpick_Oless__frac(X1,X2,X3)), inference(rw,[status(thm)],[c_0_5151, c_0_5003])). 4.46/4.70 fof(c_0_6726, plain, ![X6370, X6371, X6372, X6373, X6374, X6375, X6376, X6377, X6378, X6379]:(~c_Equiv__Relations_Ocongruent2(X6379,X6378,X6377,X6376,X6375,X6374)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X6379,X6379)),hAPP(hAPP(c_Product__Type_OPair(X6379,X6379),X6373),X6372)),X6376))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X6378,X6378)),hAPP(hAPP(c_Product__Type_OPair(X6378,X6378),X6371),X6370)),X6375))|hAPP(hAPP(X6374,X6372),X6370)=hAPP(hAPP(X6374,X6373),X6371)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_congruent2D])])])). 4.46/4.70 fof(c_0_6727, plain, ![X10718, X10719, X10720, X10721]:(~class_Fields_Olinordered__field(X10721)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10721),X10720),X10719))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10721),c_Groups_Ozero__class_Ozero(X10721)),X10718))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10721),c_Groups_Ozero__class_Ozero(X10721)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10721),X10719),X10720)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10721),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10721),X10718),X10719)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10721),X10718),X10720))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__strict__left__mono])])])). 4.46/4.70 fof(c_0_6728, plain, ![X17272, X17273, X17274, X17275]:(~class_Fields_Olinordered__field(X17275)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17275),X17274),X17273))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17275),c_Groups_Ozero__class_Ozero(X17275)),X17272))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17275),c_Groups_Ozero__class_Ozero(X17275)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17275),X17273),X17274)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17275),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17275),X17272),X17273)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17275),X17272),X17274))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__left__mono])])])). 4.46/4.70 cnf(c_0_6729, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~c_Nitpick_Oless__eq__frac(X1,X2,X3)), inference(rw,[status(thm)],[c_0_5152, c_0_5003])). 4.46/4.70 cnf(c_0_6730, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X2)=X4|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X3!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X1)), inference(split_conjunct,[status(thm)],[c_0_5153])). 4.46/4.70 fof(c_0_6731, plain, ![X9821, X9822, X9823, X9824]:(~class_Orderings_Olinorder(X9824)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9824),hAPP(hAPP(c_Orderings_Oord__class_Omax(X9824),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9824),X9823),X9822)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9824),X9823),X9821))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9824),X9823),hAPP(hAPP(c_Orderings_Oord__class_Omax(X9824),X9822),X9821))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__inf__le])])). 4.46/4.70 fof(c_0_6732, plain, ![X1790, X1791, X1792, X1793]:(~class_Lattices_Olattice(X1793)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1793),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1793),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1793),X1792),X1791)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1793),X1792),X1790))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1793),X1792),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1793),X1791),X1790))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distrib__inf__le])])])). 4.46/4.70 fof(c_0_6733, plain, ![X3169, X3170, X3171, X3172]:(~class_Complete__Lattice_Ocomplete__lattice(X3172)|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3171,X3172),hAPP(c_List_Oset(X3171),X3170)),X3169)=hAPP(c_List_Ofoldl(X3172,X3171,hAPP(c_COMBC(X3171,X3172,X3172),hAPP(hAPP(c_COMBB(X3172,tc_fun(X3172,X3172),X3171),c_Lattices_Osemilattice__inf__class_Oinf(X3172)),X3169)),c_Orderings_Otop__class_Otop(X3172)),X3170)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INFI__set__fold])])])). 4.46/4.70 fof(c_0_6734, plain, ![X5567, X5568, X5569, X5570]:(~class_Fields_Olinordered__field(X5570)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5570),X5569),X5568))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5570),X5567),c_Groups_Ozero__class_Ozero(X5570)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5570),c_Groups_Ozero__class_Ozero(X5570)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5570),X5569),X5568)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5570),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5570),X5567),X5569)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5570),X5567),X5568))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono__neg])])). 4.46/4.70 cnf(c_0_6735, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk413_3(X2,X3,X1)),hAPP(c_List_Oset(X1),c_List_OdropWhile(X1,X3,X2))))|hAPP(c_List_Ofilter(X1,X3),X2)=c_List_OtakeWhile(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_5154])). 4.46/4.70 fof(c_0_6736, plain, ![X963, X964, X965, X966]:(~class_Int_Onumber(X966)|~class_Rings_Oring(X966)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X966),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X966),X965),X964)),hAPP(c_Int_Onumber__class_Onumber__of(X966),X963))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X966),X965),hAPP(c_Int_Onumber__class_Onumber__of(X966),X963))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X966),X964),hAPP(c_Int_Onumber__class_Onumber__of(X966),X963)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_left__diff__distrib__number__of])])])). 4.46/4.70 fof(c_0_6737, plain, ![X4819, X4820, X4821, X4822]:(~class_Orderings_Olinorder(X4822)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4822),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4822),X4821),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4822),X4820),X4819))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4822),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4822),X4821),X4820)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4822),X4821),X4819))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Odistrib__sup__le])])])). 4.46/4.70 fof(c_0_6738, plain, ![X2497, X2498, X2499, X2500]:(~class_Lattices_Olattice(X2500)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2500),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2500),X2499),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2500),X2498),X2497))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2500),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2500),X2499),X2498)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2500),X2499),X2497))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distrib__sup__le])])). 4.46/4.70 fof(c_0_6739, plain, ![X7361, X7362, X7363, X7364, X7365, X7366]:(~c_Finite__Set_Ofolding(X7366,X7365,X7364,X7363)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7366),X7362))|(~hBOOL(hAPP(hAPP(c_member(X7366),X7361),X7362))|hAPP(X7363,X7362)=hAPP(c_Fun_Ocomp(X7365,X7365,X7365,hAPP(X7363,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7366,tc_HOL_Obool)),X7362),hAPP(hAPP(c_Set_Oinsert(X7366),X7361),c_Orderings_Obot__class_Obot(tc_fun(X7366,tc_HOL_Obool)))))),hAPP(X7364,X7361))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oremove])])). 4.46/4.70 fof(c_0_6740, plain, ![X3198, X3199, X3200, X3201, X3202]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3202),X3201)),X3200)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3202),X3199)),X3198)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3200))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3200),X3202))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3198),X3202))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3201),X3199)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_unique__quotient__lemma])])])). 4.46/4.70 fof(c_0_6741, plain, ![X17508, X17509, X17510, X17511, X17512]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17512),X17511)),X17510)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17512),X17509)),X17508)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17508),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17512),X17508))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17512),X17510))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17509),X17511)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_unique__quotient__lemma__neg])])])). 4.46/4.70 fof(c_0_6742, plain, ![X8815, X8816, X8817, X8818]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8818),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8817)),X8816)))|hAPP(hAPP(c_List_Oappend(X8817),hAPP(hAPP(c_List_Otake(X8817),X8818),X8816)),hAPP(hAPP(c_List_Olist_OCons(X8817),X8815),hAPP(hAPP(c_List_Odrop(X8817),hAPP(c_Nat_OSuc,X8818)),X8816)))=hAPP(hAPP(c_List_Olist__update(X8817,X8816),X8818),X8815)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_upd__conv__take__nth__drop])])])). 4.46/4.70 fof(c_0_6743, plain, ![X10895, X10896, X10897, X10898, X10899, X10900]:(~c_Equiv__Relations_Oequiv(X10900,X10899,X10898)|(~c_Equiv__Relations_Ocongruent(X10900,tc_fun(X10897,tc_HOL_Obool),X10898,X10896)|(~hBOOL(hAPP(hAPP(c_member(X10900),X10895),X10899))|hAPP(X10896,X10895)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10900,tc_fun(X10897,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10900,X10900,X10898),hAPP(hAPP(c_Set_Oinsert(X10900),X10895),c_Orderings_Obot__class_Obot(tc_fun(X10900,tc_HOL_Obool))))),X10896)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__equiv__class])])])). 4.46/4.70 fof(c_0_6744, plain, ![X3389, X3390, X3391]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X3391,X3391)),hAPP(hAPP(c_Product__Type_OPair(X3391,X3391),esk89_3(X3389,X3390,X3391)),esk89_3(X3389,X3390,X3391))),X3390))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3391),tc_List_Olist(X3391))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3391),tc_List_Olist(X3391)),X3389),X3389)),c_List_Olexord(X3391,X3390)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lexord__irreflexive])])])])). 4.46/4.70 cnf(c_0_6745, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X1,X2,X3)),X2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3))),esk532_3(X1,X2,X3))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.70 fof(c_0_6746, plain, ![X8461, X8462, X8463]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8463),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8462)),X8461)))|hAPP(hAPP(c_List_Otake(X8462),hAPP(c_Nat_OSuc,X8463)),X8461)=hAPP(hAPP(c_List_Oappend(X8462),hAPP(hAPP(c_List_Otake(X8462),X8463),X8461)),hAPP(hAPP(c_List_Olist_OCons(X8462),hAPP(hAPP(c_List_Onth(X8462),X8461),X8463)),c_List_Olist_ONil(X8462)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_take__Suc__conv__app__nth])])])). 4.46/4.70 cnf(c_0_6747, plain, (hAPP(hAPP(c_List_Onth(X2),X3),X1)=hAPP(c_Random_Opick(X2,hAPP(hAPP(c_List_Omap(X2,tc_prod(tc_Code__Numeral_Ocode__numeral,X2)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X3)),hAPP(c_Code__Numeral_Oof__nat,X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_5155])). 4.46/4.70 cnf(c_0_6748, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk533_3(X2,X1,X3))),esk534_3(X2,X1,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk532_3(X2,X1,X3)))|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.70 fof(c_0_6749, plain, ![X16332, X16333, X16334]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk475_3(X16332,X16333,X16334)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X16334)))|X16333=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16333),X16334)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16333),c_Groups_Oone__class_Oone(tc_Int_Oint))),X16332))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16334)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk476_3(X16332,X16333,X16334)),X16332))|X16333=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16333),X16334)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16333),c_Groups_Oone__class_Oone(tc_Int_Oint))),X16332))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16334)))&(X16333=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk476_3(X16332,X16333,X16334)),esk475_3(X16332,X16333,X16334))|X16333=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16333),X16334)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16333),c_Groups_Oone__class_Oone(tc_Int_Oint))),X16332))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16334))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_aset_I3_J])])])])])). 4.46/4.70 cnf(c_0_6750, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk13_3(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|X2=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5156])). 4.46/4.70 fof(c_0_6751, plain, ![X5368, X5369, X5370, X5371]:(~class_Complete__Lattice_Ocomplete__lattice(X5371)|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5370,X5371),hAPP(c_List_Oset(X5370),X5369)),X5368)=hAPP(c_List_Ofoldl(X5371,X5370,hAPP(c_COMBC(X5370,X5371,X5371),hAPP(hAPP(c_COMBB(X5371,tc_fun(X5371,X5371),X5370),c_Lattices_Osemilattice__sup__class_Osup(X5371)),X5368)),c_Orderings_Obot__class_Obot(X5371)),X5369)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUPR__set__fold])])])). 4.46/4.70 cnf(c_0_6752, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk365_8(X2,X3,X4,X5,X6,X7,X1,X8)),X5))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X8),X3),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X8),X2),X4)|X4!=hAPP(c_Set_Oimage(X1,X7,X6),X5)|~c_Fun_Oinj__on(X1,X7,X6,X5)|~class_Groups_Ocomm__monoid__mult(X8)), inference(split_conjunct,[status(thm)],[c_0_5157])). 4.46/4.70 fof(c_0_6753, plain, ![X8686, X8687, X8688, X8689]:(~class_Groups_Oordered__ab__group__add__abs(X8689)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8689),hAPP(c_Groups_Oabs__class_Oabs(X8689),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8688,X8689),X8687),X8686))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8688,X8689),hAPP(hAPP(c_COMBB(X8689,X8689,X8688),c_Groups_Oabs__class_Oabs(X8689)),X8687)),X8686)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__abs])])])). 4.46/4.70 fof(c_0_6754, plain, ![X16913, X16914, X16915, X16916]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16915),X16913),hAPP(c_Finite__Set_Ofold1(X16915,c_Orderings_Oord__class_Omin(X16915)),X16914)))|(~hBOOL(hAPP(hAPP(c_member(X16915),X16916),X16914))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16915),X16913),X16916)))|c_Orderings_Obot__class_Obot(tc_fun(X16915,tc_HOL_Obool))=X16914|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16915),X16914))|~class_Orderings_Olinorder(X16915))&((hBOOL(hAPP(hAPP(c_member(X16915),esk503_3(X16913,X16914,X16915)),X16914))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16915),X16913),hAPP(c_Finite__Set_Ofold1(X16915,c_Orderings_Oord__class_Omin(X16915)),X16914)))|c_Orderings_Obot__class_Obot(tc_fun(X16915,tc_HOL_Obool))=X16914|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16915),X16914))|~class_Orderings_Olinorder(X16915))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16915),X16913),esk503_3(X16913,X16914,X16915)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16915),X16913),hAPP(c_Finite__Set_Ofold1(X16915,c_Orderings_Oord__class_Omin(X16915)),X16914)))|c_Orderings_Obot__class_Obot(tc_fun(X16915,tc_HOL_Obool))=X16914|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16915),X16914))|~class_Orderings_Olinorder(X16915)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Obelow__fold1__iff])])])])])])). 4.46/4.70 fof(c_0_6755, plain, ![X15473, X15474, X15475, X15476]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15475),X15473),hAPP(c_Finite__Set_Ofold1(X15475,c_Lattices_Osemilattice__inf__class_Oinf(X15475)),X15474)))|(~hBOOL(hAPP(hAPP(c_member(X15475),X15476),X15474))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15475),X15473),X15476)))|c_Orderings_Obot__class_Obot(tc_fun(X15475,tc_HOL_Obool))=X15474|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15475),X15474))|~class_Lattices_Osemilattice__inf(X15475))&((hBOOL(hAPP(hAPP(c_member(X15475),esk454_3(X15473,X15474,X15475)),X15474))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15475),X15473),hAPP(c_Finite__Set_Ofold1(X15475,c_Lattices_Osemilattice__inf__class_Oinf(X15475)),X15474)))|c_Orderings_Obot__class_Obot(tc_fun(X15475,tc_HOL_Obool))=X15474|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15475),X15474))|~class_Lattices_Osemilattice__inf(X15475))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15475),X15473),esk454_3(X15473,X15474,X15475)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15475),X15473),hAPP(c_Finite__Set_Ofold1(X15475,c_Lattices_Osemilattice__inf__class_Oinf(X15475)),X15474)))|c_Orderings_Obot__class_Obot(tc_fun(X15475,tc_HOL_Obool))=X15474|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15475),X15474))|~class_Lattices_Osemilattice__inf(X15475)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_below__fold1__iff])])])])])])). 4.46/4.70 fof(c_0_6756, plain, ![X8081, X8082, X8083, X8084]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8083),X8081),hAPP(c_Finite__Set_Ofold1(X8083,c_Orderings_Oord__class_Omin(X8083)),X8082)))|(~hBOOL(hAPP(hAPP(c_member(X8083),X8084),X8082))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8083),X8081),X8084)))|c_Orderings_Obot__class_Obot(tc_fun(X8083,tc_HOL_Obool))=X8082|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8083),X8082))|~class_Orderings_Olinorder(X8083))&((hBOOL(hAPP(hAPP(c_member(X8083),esk228_3(X8081,X8082,X8083)),X8082))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8083),X8081),hAPP(c_Finite__Set_Ofold1(X8083,c_Orderings_Oord__class_Omin(X8083)),X8082)))|c_Orderings_Obot__class_Obot(tc_fun(X8083,tc_HOL_Obool))=X8082|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8083),X8082))|~class_Orderings_Olinorder(X8083))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8083),X8081),esk228_3(X8081,X8082,X8083)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8083),X8081),hAPP(c_Finite__Set_Ofold1(X8083,c_Orderings_Oord__class_Omin(X8083)),X8082)))|c_Orderings_Obot__class_Obot(tc_fun(X8083,tc_HOL_Obool))=X8082|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8083),X8082))|~class_Orderings_Olinorder(X8083)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_strict__below__fold1__iff])])])])])). 4.46/4.70 cnf(c_0_6757, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk270_8(X2,X3,X4,X5,X6,X7,X1,X8)),X5))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X8),X3),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8),X2),X4)|X4!=hAPP(c_Set_Oimage(X1,X7,X6),X5)|~c_Fun_Oinj__on(X1,X7,X6,X5)|~class_Groups_Ocomm__monoid__add(X8)), inference(split_conjunct,[status(thm)],[c_0_5158])). 4.46/4.70 cnf(c_0_6758, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5159, c_0_4471])). 4.46/4.70 fof(c_0_6759, plain, ![X2118, X2119, X2120, X2121]:(~class_Fields_Olinordered__field__inverse__zero(X2121)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2121),X2120),X2119))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2121),X2118),c_Groups_Ozero__class_Ozero(X2121)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2121),c_Groups_Ozero__class_Ozero(X2121)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2121),X2120),X2119)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2121),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2121),X2118),X2120)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2121),X2118),X2119))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__left__mono__neg])])])). 4.46/4.70 cnf(c_0_6760, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5160, c_0_4471])). 4.46/4.70 cnf(c_0_6761, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_List_Onth(X1),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))=hAPP(c_List_Ohd(X1),hAPP(c_List_Orotate(X1,X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5161])). 4.46/4.70 fof(c_0_6762, plain, ![X2370, X2371, X2372, X2373]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2372)),X2371)))|c_List_OtakeWhile(X2372,X2370,X2371)=hAPP(hAPP(c_List_Otake(X2372),X2373),X2371)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk62_4(X2370,X2371,X2372,X2373)),X2373)))&(hBOOL(hAPP(X2370,hAPP(hAPP(c_List_Onth(X2372),X2371),X2373)))|c_List_OtakeWhile(X2372,X2370,X2371)=hAPP(hAPP(c_List_Otake(X2372),X2373),X2371)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk62_4(X2370,X2371,X2372,X2373)),X2373))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2372)),X2371)))|c_List_OtakeWhile(X2372,X2370,X2371)=hAPP(hAPP(c_List_Otake(X2372),X2373),X2371)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk62_4(X2370,X2371,X2372,X2373)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2372)),X2371))))&(hBOOL(hAPP(X2370,hAPP(hAPP(c_List_Onth(X2372),X2371),X2373)))|c_List_OtakeWhile(X2372,X2370,X2371)=hAPP(hAPP(c_List_Otake(X2372),X2373),X2371)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk62_4(X2370,X2371,X2372,X2373)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2372)),X2371)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2372)),X2371)))|c_List_OtakeWhile(X2372,X2370,X2371)=hAPP(hAPP(c_List_Otake(X2372),X2373),X2371)|~hBOOL(hAPP(X2370,hAPP(hAPP(c_List_Onth(X2372),X2371),esk62_4(X2370,X2371,X2372,X2373)))))&(hBOOL(hAPP(X2370,hAPP(hAPP(c_List_Onth(X2372),X2371),X2373)))|c_List_OtakeWhile(X2372,X2370,X2371)=hAPP(hAPP(c_List_Otake(X2372),X2373),X2371)|~hBOOL(hAPP(X2370,hAPP(hAPP(c_List_Onth(X2372),X2371),esk62_4(X2370,X2371,X2372,X2373)))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile__eq__take__P__nth])])])])])). 4.46/4.70 fof(c_0_6763, plain, ![X16438, X16439, X16440, X16441, X16442, X16443, X16444]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16444,X16443)),hAPP(hAPP(c_Product__Type_OPair(X16444,X16443),X16442),X16441)),X16440))|hBOOL(hAPP(hAPP(c_member(X16439),hAPP(hAPP(X16438,X16442),X16441)),hAPP(c_Set_Oimage(tc_prod(X16444,X16443),X16439,hAPP(c_Product__Type_Oprod_Oprod__case(X16444,X16443,X16439),X16438)),X16440)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__imageI])])). 4.46/4.70 fof(c_0_6764, plain, ![X5013, X5014, X5015, X5016]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X5016,X5016)),hAPP(hAPP(c_Product__Type_OPair(X5016,X5016),X5014),X5015)),c_Transitive__Closure_Ortrancl(X5016,X5013)))|~c_Wellfounded_Oacyclic(X5016,X5013)|c_Wellfounded_Oacyclic(X5016,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5016,X5016)),hAPP(hAPP(c_Product__Type_OPair(X5016,X5016),X5015),X5014)),X5013)))&((~hBOOL(hAPP(hAPP(c_member(tc_prod(X5016,X5016)),hAPP(hAPP(c_Product__Type_OPair(X5016,X5016),X5014),X5015)),c_Transitive__Closure_Ortrancl(X5016,X5013)))|~c_Wellfounded_Oacyclic(X5016,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5016,X5016)),hAPP(hAPP(c_Product__Type_OPair(X5016,X5016),X5015),X5014)),X5013)))&(c_Wellfounded_Oacyclic(X5016,X5013)|~c_Wellfounded_Oacyclic(X5016,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5016,X5016)),hAPP(hAPP(c_Product__Type_OPair(X5016,X5016),X5015),X5014)),X5013))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acyclic__insert])])])])). 4.46/4.70 fof(c_0_6765, plain, ![X2736, X2737, X2738, X2739, X2740, X2741, X2742, X2743]:(~c_Finite__Set_Ofolding__image__simple(X2743,X2742,X2741,X2740,X2739,X2738)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2742),X2737))|(~hBOOL(hAPP(hAPP(c_member(X2742),X2736),X2737))|hAPP(X2738,X2737)=hAPP(hAPP(X2741,hAPP(X2739,X2736)),hAPP(X2738,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2742,tc_HOL_Obool)),X2737),hAPP(hAPP(c_Set_Oinsert(X2742),X2736),c_Orderings_Obot__class_Obot(tc_fun(X2742,tc_HOL_Obool))))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oremove])])])). 4.46/4.70 fof(c_0_6766, plain, ![X13489, X13490, X13491, X13492, X13493, X13494, X13495, X13496]:(~c_Finite__Set_Ofolding__image__simple(X13496,X13495,X13494,X13493,X13492,X13491)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13495),X13490))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13495),X13489))|(c_Orderings_Obot__class_Obot(tc_fun(X13495,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13495,tc_HOL_Obool)),X13490),X13489)|hAPP(X13491,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13495,tc_HOL_Obool)),X13490),X13489))=hAPP(hAPP(X13494,hAPP(X13491,X13490)),hAPP(X13491,X13489)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Ounion__disjoint])])])). 4.46/4.70 fof(c_0_6767, plain, ![X7047, X7048, X7049, X7050, X7051]:(~class_Rings_Osemiring__0(X7051)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7051),X7049),hAPP(c_List_Omonoid__add__class_Olistsum(X7051),hAPP(hAPP(c_List_Omap(X7050,X7051),X7048),X7047)))=hAPP(c_List_Omonoid__add__class_Olistsum(X7051),hAPP(hAPP(c_List_Omap(X7050,X7051),hAPP(hAPP(c_COMBB(X7051,X7051,X7050),hAPP(c_Groups_Otimes__class_Otimes(X7051),X7049)),X7048)),X7047))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__const__mult])])). 4.46/4.70 fof(c_0_6768, plain, ![X9776, X9777, X9778, X9779, X9780]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9780,tc_HOL_Obool)),hAPP(c_Relation_OImage(X9779,X9780,X9778),X9777)),X9776))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9779,tc_HOL_Obool)),X9777),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9779,tc_HOL_Obool)),hAPP(c_Relation_OImage(X9780,X9779,hAPP(c_Relation_Oconverse(X9779,X9780),X9778)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9780,tc_HOL_Obool)),X9776))))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9779,tc_HOL_Obool)),X9777),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9779,tc_HOL_Obool)),hAPP(c_Relation_OImage(X9780,X9779,hAPP(c_Relation_Oconverse(X9779,X9780),X9778)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9780,tc_HOL_Obool)),X9776)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9780,tc_HOL_Obool)),hAPP(c_Relation_OImage(X9779,X9780,X9778),X9777)),X9776)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__subset__eq])])). 4.46/4.70 fof(c_0_6769, plain, ![X5634, X5635, X5636, X5637]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X5637,X5637)),hAPP(hAPP(c_Product__Type_OPair(X5637,X5637),X5635),X5636)),c_Transitive__Closure_Ortrancl(X5637,X5634)))|~c_Wellfounded_Owf(X5637,X5634)|c_Wellfounded_Owf(X5637,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5637,X5637)),hAPP(hAPP(c_Product__Type_OPair(X5637,X5637),X5636),X5635)),X5634)))&((~hBOOL(hAPP(hAPP(c_member(tc_prod(X5637,X5637)),hAPP(hAPP(c_Product__Type_OPair(X5637,X5637),X5635),X5636)),c_Transitive__Closure_Ortrancl(X5637,X5634)))|~c_Wellfounded_Owf(X5637,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5637,X5637)),hAPP(hAPP(c_Product__Type_OPair(X5637,X5637),X5636),X5635)),X5634)))&(c_Wellfounded_Owf(X5637,X5634)|~c_Wellfounded_Owf(X5637,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5637,X5637)),hAPP(hAPP(c_Product__Type_OPair(X5637,X5637),X5636),X5635)),X5634))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__insert])])])])). 4.46/4.70 fof(c_0_6770, plain, ![X1804, X1805, X1806, X1807]:(~class_Orderings_Olinorder(X1807)|(~c_List_Olinorder__class_Osorted(X1807,hAPP(c_List_Orev(X1807),X1806))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1805),X1804))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1804),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1807)),X1806)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1807),hAPP(hAPP(c_List_Onth(X1807),X1806),X1804)),hAPP(hAPP(c_List_Onth(X1807),X1806),X1805))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__rev__nth__mono])])])). 4.46/4.70 fof(c_0_6771, plain, ![X11523, X11524, X11525, X11526, X11527, X11528]:((hBOOL(hAPP(hAPP(c_member(X11527),esk339_6(X11523,X11524,X11525,X11526,X11527,X11528)),X11528))|c_Fun_Oinj__on(X11526,X11525,X11524,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11527,tc_fun(X11526,tc_HOL_Obool)),X11528),X11523))|c_Orderings_Obot__class_Obot(tc_fun(X11527,tc_HOL_Obool))=X11528)&(~c_Fun_Oinj__on(X11526,X11525,X11524,hAPP(X11523,esk339_6(X11523,X11524,X11525,X11526,X11527,X11528)))|c_Fun_Oinj__on(X11526,X11525,X11524,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11527,tc_fun(X11526,tc_HOL_Obool)),X11528),X11523))|c_Orderings_Obot__class_Obot(tc_fun(X11527,tc_HOL_Obool))=X11528)), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__INTER])])])])])). 4.46/4.70 fof(c_0_6772, plain, ![X13199, X13200, X13201]:(~class_Lattices_Oab__semigroup__idem__mult(X13201)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13201),X13200))|(X13200=c_Orderings_Obot__class_Obot(tc_fun(X13201,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13201),X13199))|(c_Orderings_Obot__class_Obot(tc_fun(X13201,tc_HOL_Obool))=X13199|hAPP(c_Finite__Set_Ofold1(X13201,c_Groups_Otimes__class_Otimes(X13201)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13201,tc_HOL_Obool)),X13200),X13199))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13201),hAPP(c_Finite__Set_Ofold1(X13201,c_Groups_Otimes__class_Otimes(X13201)),X13200)),hAPP(c_Finite__Set_Ofold1(X13201,c_Groups_Otimes__class_Otimes(X13201)),X13199))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__Un2])])])). 4.46/4.70 fof(c_0_6773, plain, ![X5389, X5390, X5391]:(~class_Orderings_Olinorder(X5391)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5391),X5390))|c_List_Olinorder__class_Osorted__list__of__set(X5391,hAPP(hAPP(c_Set_Oinsert(X5391),X5389),X5390))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5391,X5391,c_COMBI(X5391)),X5389),c_List_Olinorder__class_Osorted__list__of__set(X5391,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5391,tc_HOL_Obool)),X5390),hAPP(hAPP(c_Set_Oinsert(X5391),X5389),c_Orderings_Obot__class_Obot(tc_fun(X5391,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__list__of__set__insert])])])). 4.46/4.70 fof(c_0_6774, plain, ![X2926, X2927, X2928]:(~c_Wellfounded_Owf(X2928,X2927)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2928,X2928),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X2928,X2928,X2928),X2927),X2926)),X2927))|c_FunDef_Oreduction__pair(X2928,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X2928,X2928),tc_HOL_Obool),tc_fun(tc_prod(X2928,X2928),tc_HOL_Obool)),X2927),X2926)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_reduction__pairI])])])). 4.46/4.70 fof(c_0_6775, plain, ![X4837, X4838]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4838),X4837),c_Groups_Ozero__class_Ozero(X4838)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4838),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4838),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4838),c_Groups_Oone__class_Oone(X4838)),X4837)),X4837)),c_Groups_Ozero__class_Ozero(X4838)))|~hBOOL(hAPP(hAPP(c_member(X4838),X4837),c_Int_Oring__1__class_OInts(X4838)))|~class_Rings_Olinordered__idom(X4838))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4838),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4838),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4838),c_Groups_Oone__class_Oone(X4838)),X4837)),X4837)),c_Groups_Ozero__class_Ozero(X4838)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4838),X4837),c_Groups_Ozero__class_Ozero(X4838)))|~hBOOL(hAPP(hAPP(c_member(X4838),X4837),c_Int_Oring__1__class_OInts(X4838)))|~class_Rings_Olinordered__idom(X4838))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__odd__less__0])])])])). 4.46/4.70 fof(c_0_6776, plain, ![X17590, X17591, X17592, X17593]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk527_4(X17590,X17591,X17592,X17593)),X17593))|hAPP(hAPP(c_List_Otake(X17592),X17593),X17591)=hAPP(hAPP(c_List_Otake(X17592),X17593),X17590)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17593),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17592)),X17590)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17593),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17592)),X17591))))&(hAPP(hAPP(c_List_Onth(X17592),X17590),esk527_4(X17590,X17591,X17592,X17593))!=hAPP(hAPP(c_List_Onth(X17592),X17591),esk527_4(X17590,X17591,X17592,X17593))|hAPP(hAPP(c_List_Otake(X17592),X17593),X17591)=hAPP(hAPP(c_List_Otake(X17592),X17593),X17590)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17593),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17592)),X17590)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17593),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17592)),X17591))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__take__lemma])])])])])). 4.46/4.70 cnf(c_0_6777, plain, (hBOOL(hAPP(X1,esk530_6(X2,X1,X3,X4,X5,X6)))|hAPP(hAPP(c_List_Olist_OCons(X5),X4),X3)=hAPP(c_List_Ofilter(X5,X1),X2)|X2!=hAPP(hAPP(c_List_Oappend(X5),X6),hAPP(hAPP(c_List_Olist_OCons(X5),X4),X7))|~hBOOL(hAPP(X1,X4))|X3!=hAPP(c_List_Ofilter(X5,X1),X7)), inference(split_conjunct,[status(thm)],[c_0_5072])). 4.46/4.70 fof(c_0_6778, plain, ![X15578, X15579, X15580, X15581, X15582, X15583]:(~c_Finite__Set_Ofun__left__comm__idem(X15583,X15582,X15581)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15583),X15580))|hAPP(hAPP(c_Finite__Set_Ofold(X15583,X15582,X15581),X15579),hAPP(hAPP(c_Set_Oinsert(X15583),X15578),X15580))=hAPP(hAPP(X15581,X15578),hAPP(hAPP(c_Finite__Set_Ofold(X15583,X15582,X15581),X15579),X15580)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem])])). 4.46/4.70 fof(c_0_6779, plain, ![X10742, X10743, X10744, X10745, X10746, X10747]:(~c_Finite__Set_Ofun__left__comm__idem(X10747,X10746,X10745)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10747),X10744))|hAPP(hAPP(c_Finite__Set_Ofold(X10747,X10746,X10745),X10743),hAPP(hAPP(c_Set_Oinsert(X10747),X10742),X10744))=hAPP(hAPP(c_Finite__Set_Ofold(X10747,X10746,X10745),hAPP(hAPP(X10745,X10742),X10743)),X10744))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem2])])])). 4.46/4.70 fof(c_0_6780, plain, ![X15114, X15115, X15116, X15117, X15118, X15119]:(~c_Finite__Set_Ofolding(X15119,X15118,X15117,X15116)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15119),X15115))|(hBOOL(hAPP(hAPP(c_member(X15119),X15114),X15115))|hAPP(c_Fun_Ocomp(X15118,X15118,X15118,hAPP(X15116,X15115)),hAPP(X15117,X15114))=hAPP(X15116,hAPP(hAPP(c_Set_Oinsert(X15119),X15114),X15115))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Oinsert])])])). 4.46/4.70 cnf(c_0_6781, plain, (X1=c_List_Olist_ONil(X2)|c_List_Ofoldr(X2,X2,c_Orderings_Oord__class_Omax(X2),X1,X3)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),hAPP(hAPP(c_List_Onth(X2),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3)|~c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Orev(X2),X1))|~class_Orderings_Olinorder(X2)), inference(split_conjunct,[status(thm)],[c_0_5162])). 4.46/4.70 cnf(c_0_6782, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk531_3(X2,X1,X3))),esk532_3(X2,X1,X3))=X2|epred1_3(X3,X1,X2)|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.70 cnf(c_0_6783, plain, (hBOOL(hAPP(X1,esk154_7(X2,X3,X4,X1,X5,X6,X7)))|hAPP(c_List_Ofilter(X5,X1),X4)=hAPP(hAPP(c_List_Olist_OCons(X5),X3),X2)|~hBOOL(hAPP(X1,X3))|X2!=hAPP(c_List_Ofilter(X5,X1),X7)|X4!=hAPP(hAPP(c_List_Oappend(X5),X6),hAPP(hAPP(c_List_Olist_OCons(X5),X3),X7))), inference(split_conjunct,[status(thm)],[c_0_5090])). 4.46/4.70 fof(c_0_6784, plain, ![X13398, X13399, X13400]:(~class_Rings_Olinordered__semidom(X13400)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13400),c_Groups_Ozero__class_Ozero(X13400)),X13399))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13400),X13399),c_Groups_Oone__class_Oone(X13400)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13400),X13399),hAPP(hAPP(c_Power_Opower__class_Opower(X13400),X13399),X13398))),hAPP(hAPP(c_Power_Opower__class_Opower(X13400),X13399),X13398)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__Suc__less])])])). 4.46/4.70 fof(c_0_6785, plain, ![X9099, X9100, X9101, X9102, X9103, X9104]:(~c_Finite__Set_Ofolding(X9104,X9103,X9102,X9101)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9104),X9100))|hAPP(X9101,hAPP(hAPP(c_Set_Oinsert(X9104),X9099),X9100))=hAPP(c_Fun_Ocomp(X9103,X9103,X9103,hAPP(X9101,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9104,tc_HOL_Obool)),X9100),hAPP(hAPP(c_Set_Oinsert(X9104),X9099),c_Orderings_Obot__class_Obot(tc_fun(X9104,tc_HOL_Obool)))))),hAPP(X9102,X9099)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Oinsert__remove])])])). 4.46/4.70 fof(c_0_6786, plain, ![X12984, X12985, X12986]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12986),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X12985)))|hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X12985),X12986),X12984))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X12985)),X12984)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X12985),X12986))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__update__nat])])). 4.46/4.70 cnf(c_0_6787, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk533_3(X2,X1,X3))),esk534_3(X2,X1,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|epred1_3(X3,X1,X2)|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.70 fof(c_0_6788, plain, ![X5790, X5791, X5792, X5793, X5794]:(~class_Orderings_Olinorder(X5794)|(hBOOL(hAPP(hAPP(c_member(X5794),hAPP(X5793,X5792)),hAPP(c_Set_Oimage(X5791,X5794,X5793),hAPP(c_List_Oset(X5791),X5790))))|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5791,X5794,X5793),X5792),X5790)=c_List_Olinorder__class_Oinsort__insert__key(X5791,X5794,X5793,X5792,X5790))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__insert__insort__key])])])). 4.46/4.70 fof(c_0_6789, plain, ![X10025, X10026, X10027, X10028, X10029, X10032, X10033, X10034, X10035, X10036, X10037, X10038]:((((hAPP(hAPP(c_Set_Oinsert(X10029),X10027),X10026)=hAPP(hAPP(c_Set_Oinsert(X10029),esk288_5(X10025,X10026,X10027,X10028,X10029)),esk289_5(X10025,X10026,X10027,X10028,X10029))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10029,X10028,hAPP(hAPP(c_Set_Oinsert(X10029),X10027),X10026)),X10025)))&(~hBOOL(hAPP(hAPP(c_member(X10029),esk288_5(X10025,X10026,X10027,X10028,X10029)),esk289_5(X10025,X10026,X10027,X10028,X10029)))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10029,X10028,hAPP(hAPP(c_Set_Oinsert(X10029),X10027),X10026)),X10025))))&(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10029,X10029,X10028,esk288_5(X10025,X10026,X10027,X10028,X10029),esk289_5(X10025,X10026,X10027,X10028,X10029)),X10025))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10029,X10028,hAPP(hAPP(c_Set_Oinsert(X10029),X10027),X10026)),X10025))))&(hAPP(hAPP(c_Set_Oinsert(X10036),X10034),X10033)!=hAPP(hAPP(c_Set_Oinsert(X10036),X10037),X10038)|hBOOL(hAPP(hAPP(c_member(X10036),X10037),X10038))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10036,X10036,X10035,X10037,X10038),X10032))|hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10036,X10035,hAPP(hAPP(c_Set_Oinsert(X10036),X10034),X10033)),X10032)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1Set_Oequations])])])])])])])). 4.46/4.70 cnf(c_0_6790, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))=c_Groups_Oone__class_Oone(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|~class_Int_Onumber__ring(X2)), inference(rw,[status(thm)],[c_0_5163, c_0_4471])). 4.46/4.70 cnf(c_0_6791, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))=hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X4))|hAPP(c_Map_Omap__of(X1,X2),X3)!=hAPP(c_Map_Omap__of(X1,X2),X4)), inference(split_conjunct,[status(thm)],[c_0_5164])). 4.46/4.70 fof(c_0_6792, plain, ![X9124, X9125, X9126, X9127]:(hAPP(hAPP(c_Relation_Orel__comp(X9127,X9127,X9127),X9126),X9125)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X9127,X9127),tc_HOL_Obool))|(hAPP(hAPP(c_Relation_Orel__comp(X9127,X9127,X9127),X9124),X9125)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X9127,X9127),tc_HOL_Obool))|hAPP(hAPP(c_Relation_Orel__comp(X9127,X9127,X9127),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X9127,X9127),tc_HOL_Obool)),X9126),X9124)),X9125)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X9127,X9127),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_union__comp__emptyL])])])). 4.46/4.70 fof(c_0_6793, plain, ![X17076, X17077, X17078, X17079]:(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X17079,X17079),tc_HOL_Obool))!=hAPP(hAPP(c_Relation_Orel__comp(X17079,X17079,X17079),X17078),X17077)|(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X17079,X17079),tc_HOL_Obool))!=hAPP(hAPP(c_Relation_Orel__comp(X17079,X17079,X17079),X17078),X17076)|hAPP(hAPP(c_Relation_Orel__comp(X17079,X17079,X17079),X17078),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X17079,X17079),tc_HOL_Obool)),X17077),X17076))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X17079,X17079),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_union__comp__emptyR])])])). 4.46/4.70 fof(c_0_6794, plain, ![X13507, X13508, X13509, X13510, X13511, X13512, X13513]:(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X13513,X13512,X13511,X13510,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13513,tc_HOL_Obool)),X13509),hAPP(hAPP(c_Set_Oinsert(X13513),X13508),c_Orderings_Obot__class_Obot(tc_fun(X13513,tc_HOL_Obool))))),X13507))|(~hBOOL(hAPP(hAPP(c_member(X13513),X13508),X13509))|hBOOL(hAPP(c_Finite__Set_Ofold__graph(X13513,X13512,X13511,X13510,X13509),hAPP(hAPP(X13511,X13508),X13507))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff1__fold__graph])])). 4.46/4.70 fof(c_0_6795, plain, ![X8832, X8833, X8834, X8835, X8836, X8837]:((hAPP(hAPP(c_Product__Type_OPair(X8835,X8834),esk249_6(X8832,X8833,X8834,X8835,X8836,X8837)),esk250_6(X8832,X8833,X8834,X8835,X8836,X8837))=X8832|~hBOOL(hAPP(hAPP(c_member(X8837),X8836),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X8835,X8834,tc_fun(X8837,tc_HOL_Obool)),X8833),X8832))))&(hBOOL(hAPP(hAPP(c_member(X8837),X8836),hAPP(hAPP(X8833,esk249_6(X8832,X8833,X8834,X8835,X8836,X8837)),esk250_6(X8832,X8833,X8834,X8835,X8836,X8837))))|~hBOOL(hAPP(hAPP(c_member(X8837),X8836),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X8835,X8834,tc_fun(X8837,tc_HOL_Obool)),X8833),X8832))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mem__splitE])])])])])). 4.46/4.70 cnf(c_0_6796, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),X3)), inference(split_conjunct,[status(thm)],[c_0_5165])). 4.46/4.70 cnf(c_0_6797, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1)=X4|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X3!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2)), inference(split_conjunct,[status(thm)],[c_0_5153])). 4.46/4.70 fof(c_0_6798, plain, ![X15135, X15136, X15137, X15138, X15139]:(~class_Orderings_Olinorder(X15139)|c_List_Olinorder__class_Osorted(X15139,hAPP(hAPP(c_List_Omap(X15138,X15139),X15137),hAPP(c_List_Ofilter(X15138,hAPP(hAPP(c_COMBC(X15138,X15139,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X15139,tc_fun(X15139,tc_HOL_Obool),X15138),c_fequal),X15137)),hAPP(X15136,X15135))),X15135)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__map__same])])])). 4.46/4.70 fof(c_0_6799, plain, ![X12797, X12798, X12799, X12800, X12801, X12802]:((~hBOOL(hAPP(hAPP(c_member(X12802),X12801),X12800))|hAPP(hAPP(c_Set_Oinsert(X12799),X12797),hAPP(c_Set_Oimage(X12802,X12799,X12798),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12802,tc_HOL_Obool)),X12800),hAPP(hAPP(c_Set_Oinsert(X12802),X12801),c_Orderings_Obot__class_Obot(tc_fun(X12802,tc_HOL_Obool))))))=hAPP(c_Set_Oimage(X12802,X12799,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X12802,X12799),X12798),X12801),X12797)),X12800))&(hBOOL(hAPP(hAPP(c_member(X12802),X12801),X12800))|hAPP(c_Set_Oimage(X12802,X12799,X12798),X12800)=hAPP(c_Set_Oimage(X12802,X12799,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X12802,X12799),X12798),X12801),X12797)),X12800))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__upd__image])])])). 4.46/4.70 cnf(c_0_6800, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5166, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6801, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(X1,X1,c_Groups_Oplus__class_Oplus(X1),X3,c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Omonoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5167])). 4.46/4.70 fof(c_0_6802, plain, ![X11568, X11569, X11570, X11571, X11572, X11575, X11576, X11577, X11578, X11579, X11580, X11581]:((((X11571=hAPP(hAPP(c_List_Oappend(X11572),X11569),esk341_5(X11568,X11569,X11570,X11571,X11572))|hAPP(hAPP(c_List_Oappend(X11572),esk340_5(X11568,X11569,X11570,X11571,X11572)),X11568)=X11570|hAPP(hAPP(c_List_Oappend(X11572),X11569),X11568)!=hAPP(hAPP(c_List_Oappend(X11572),X11571),X11570))&(hAPP(hAPP(c_List_Oappend(X11572),esk341_5(X11568,X11569,X11570,X11571,X11572)),X11570)=X11568|hAPP(hAPP(c_List_Oappend(X11572),esk340_5(X11568,X11569,X11570,X11571,X11572)),X11568)=X11570|hAPP(hAPP(c_List_Oappend(X11572),X11569),X11568)!=hAPP(hAPP(c_List_Oappend(X11572),X11571),X11570)))&((X11571=hAPP(hAPP(c_List_Oappend(X11572),X11569),esk341_5(X11568,X11569,X11570,X11571,X11572))|hAPP(hAPP(c_List_Oappend(X11572),X11571),esk340_5(X11568,X11569,X11570,X11571,X11572))=X11569|hAPP(hAPP(c_List_Oappend(X11572),X11569),X11568)!=hAPP(hAPP(c_List_Oappend(X11572),X11571),X11570))&(hAPP(hAPP(c_List_Oappend(X11572),esk341_5(X11568,X11569,X11570,X11571,X11572)),X11570)=X11568|hAPP(hAPP(c_List_Oappend(X11572),X11571),esk340_5(X11568,X11569,X11570,X11571,X11572))=X11569|hAPP(hAPP(c_List_Oappend(X11572),X11569),X11568)!=hAPP(hAPP(c_List_Oappend(X11572),X11571),X11570))))&((hAPP(hAPP(c_List_Oappend(X11579),X11580),X11575)!=X11577|hAPP(hAPP(c_List_Oappend(X11579),X11578),X11580)!=X11576|hAPP(hAPP(c_List_Oappend(X11579),X11576),X11575)=hAPP(hAPP(c_List_Oappend(X11579),X11578),X11577))&(X11578!=hAPP(hAPP(c_List_Oappend(X11579),X11576),X11581)|hAPP(hAPP(c_List_Oappend(X11579),X11581),X11577)!=X11575|hAPP(hAPP(c_List_Oappend(X11579),X11576),X11575)=hAPP(hAPP(c_List_Oappend(X11579),X11578),X11577)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__append__conv2])])])])])])). 4.46/4.70 fof(c_0_6803, plain, ![X3873, X3874, X3875, X3876]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X3876),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X3875),X3874)))|hAPP(c_Random_Opick(X3875,X3873),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X3876),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X3875),X3874)))=hAPP(c_Random_Opick(X3875,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X3875)),X3874),X3873)),X3876))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X3876),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X3875),X3874)))|hAPP(c_Random_Opick(X3875,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X3875)),X3874),X3873)),X3876)=hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X3875),X3874))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pick_Osimps])])])). 4.46/4.70 cnf(c_0_6804, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5168, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 cnf(c_0_6805, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5169, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.70 fof(c_0_6806, plain, ![X3041, X3042, X3043]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3043),X3042))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3041))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3041)),X3043)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3041)),X3042))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2__lemma])])). 4.46/4.70 fof(c_0_6807, plain, ![X17526, X17527, X17528]:(~class_Groups_Oordered__ab__group__add__abs(X17528)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17528),hAPP(c_Groups_Oabs__class_Oabs(X17528),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17528),hAPP(c_Groups_Oabs__class_Oabs(X17528),X17527)),hAPP(c_Groups_Oabs__class_Oabs(X17528),X17526)))),hAPP(c_Groups_Oabs__class_Oabs(X17528),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17528),X17527),X17526))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq3])])). 4.46/4.70 fof(c_0_6808, plain, ![X6837, X6838, X6839, X6840]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),X6838),c_Groups_Ozero__class_Ozero(X6840)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),c_Groups_Ozero__class_Ozero(X6840)),X6837))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),c_Groups_Ozero__class_Ozero(X6840)),X6838))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6840),X6839),X6838)),X6837))|~class_Fields_Olinordered__field__inverse__zero(X6840))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),X6838),c_Groups_Ozero__class_Ozero(X6840)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6840),X6837),X6838)),X6839))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),c_Groups_Ozero__class_Ozero(X6840)),X6838))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6840),X6839),X6838)),X6837))|~class_Fields_Olinordered__field__inverse__zero(X6840)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),c_Groups_Ozero__class_Ozero(X6840)),X6838))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),X6839),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6840),X6837),X6838)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6840),X6839),X6838)),X6837))|~class_Fields_Olinordered__field__inverse__zero(X6840)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),c_Groups_Ozero__class_Ozero(X6840)),X6838))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),c_Groups_Ozero__class_Ozero(X6840)),X6838))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6840),X6839),X6838)),X6837))|~class_Fields_Olinordered__field__inverse__zero(X6840))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),X6839),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6840),X6837),X6838)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),c_Groups_Ozero__class_Ozero(X6840)),X6838))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6840),X6839),X6838)),X6837))|~class_Fields_Olinordered__field__inverse__zero(X6840)))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),c_Groups_Ozero__class_Ozero(X6840)),X6838))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),X6838),c_Groups_Ozero__class_Ozero(X6840)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),X6838),c_Groups_Ozero__class_Ozero(X6840))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6840),X6839),X6838)),X6837))|~class_Fields_Olinordered__field__inverse__zero(X6840))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),X6839),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6840),X6837),X6838)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),X6838),c_Groups_Ozero__class_Ozero(X6840)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),X6838),c_Groups_Ozero__class_Ozero(X6840))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6840),X6839),X6838)),X6837))|~class_Fields_Olinordered__field__inverse__zero(X6840)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),c_Groups_Ozero__class_Ozero(X6840)),X6838))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6840),X6837),X6838)),X6839))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),X6838),c_Groups_Ozero__class_Ozero(X6840))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6840),X6839),X6838)),X6837))|~class_Fields_Olinordered__field__inverse__zero(X6840))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),X6839),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6840),X6837),X6838)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6840),X6837),X6838)),X6839))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),X6838),c_Groups_Ozero__class_Ozero(X6840))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6840),X6839),X6838)),X6837))|~class_Fields_Olinordered__field__inverse__zero(X6840))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),c_Groups_Ozero__class_Ozero(X6840)),X6838))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),X6838),c_Groups_Ozero__class_Ozero(X6840)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),c_Groups_Ozero__class_Ozero(X6840)),X6837)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6840),X6839),X6838)),X6837))|~class_Fields_Olinordered__field__inverse__zero(X6840))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),X6839),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6840),X6837),X6838)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),X6838),c_Groups_Ozero__class_Ozero(X6840)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),c_Groups_Ozero__class_Ozero(X6840)),X6837)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6840),X6839),X6838)),X6837))|~class_Fields_Olinordered__field__inverse__zero(X6840)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),c_Groups_Ozero__class_Ozero(X6840)),X6838))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6840),X6837),X6838)),X6839))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),c_Groups_Ozero__class_Ozero(X6840)),X6837)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6840),X6839),X6838)),X6837))|~class_Fields_Olinordered__field__inverse__zero(X6840))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),X6839),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6840),X6837),X6838)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6840),X6837),X6838)),X6839))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),c_Groups_Ozero__class_Ozero(X6840)),X6837)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6840),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6840),X6839),X6838)),X6837))|~class_Fields_Olinordered__field__inverse__zero(X6840))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__less__eq])])])])). 4.46/4.70 fof(c_0_6809, plain, ![X5971, X5972, X5973]:((hAPP(X5972,esk185_3(X5971,X5972,X5973))!=hAPP(X5972,esk186_3(X5971,X5972,X5973))|c_Wellfounded_OwfP(X5973,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5971,tc_fun(X5973,tc_fun(X5973,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5971,tc_HOL_Obool))),X5972))|~c_Wellfounded_OwfP(X5973,hAPP(X5972,esk184_3(X5971,X5972,X5973))))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5973,tc_HOL_Obool)),c_Predicate_ODomainP(X5973,X5973,hAPP(X5972,esk185_3(X5971,X5972,X5973)))),c_Predicate_ORangeP(X5973,X5973,hAPP(X5972,esk186_3(X5971,X5972,X5973))))!=c_Orderings_Obot__class_Obot(tc_fun(X5973,tc_HOL_Obool))|c_Wellfounded_OwfP(X5973,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5971,tc_fun(X5973,tc_fun(X5973,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5971,tc_HOL_Obool))),X5972))|~c_Wellfounded_OwfP(X5973,hAPP(X5972,esk184_3(X5971,X5972,X5973))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wfP__SUP])])])])])). 4.46/4.70 fof(c_0_6810, plain, ![X3589, X3590, X3591, X3592, X3593]:(~c_Finite__Set_Ofolding__one__idem(X3593,X3592,X3591)|(hAPP(X3590,hAPP(hAPP(X3592,esk94_5(X3589,X3590,X3591,X3592,X3593)),esk95_5(X3589,X3590,X3591,X3592,X3593)))!=hAPP(hAPP(X3592,hAPP(X3590,esk94_5(X3589,X3590,X3591,X3592,X3593))),hAPP(X3590,esk95_5(X3589,X3590,X3591,X3592,X3593)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3593),X3589))|(c_Orderings_Obot__class_Obot(tc_fun(X3593,tc_HOL_Obool))=X3589|hAPP(X3590,hAPP(X3591,X3589))=hAPP(X3591,hAPP(c_Set_Oimage(X3593,X3593,X3590),X3589)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ohom__commute])])])). 4.46/4.70 fof(c_0_6811, plain, ![X13248, X13249, X13250]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13250),X13249))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X13250),X13249)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X13249),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13249),X13248)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X13250),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13249),X13248))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__add__Un])])])). 4.46/4.70 fof(c_0_6812, plain, ![X13310, X13311, X13312, X13313]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),c_Groups_Ozero__class_Ozero(X13313)),X13311))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),c_Groups_Ozero__class_Ozero(X13313)),X13311))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13313),X13312),X13311)),X13310))|~class_Fields_Olinordered__field__inverse__zero(X13313))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),X13312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13313),X13310),X13311)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),c_Groups_Ozero__class_Ozero(X13313)),X13311))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13313),X13312),X13311)),X13310))|~class_Fields_Olinordered__field__inverse__zero(X13313)))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),c_Groups_Ozero__class_Ozero(X13313)),X13311))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),X13311),c_Groups_Ozero__class_Ozero(X13313)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),X13311),c_Groups_Ozero__class_Ozero(X13313))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13313),X13312),X13311)),X13310))|~class_Fields_Olinordered__field__inverse__zero(X13313))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),X13312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13313),X13310),X13311)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),X13311),c_Groups_Ozero__class_Ozero(X13313)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),X13311),c_Groups_Ozero__class_Ozero(X13313))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13313),X13312),X13311)),X13310))|~class_Fields_Olinordered__field__inverse__zero(X13313)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),c_Groups_Ozero__class_Ozero(X13313)),X13311))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),c_Groups_Ozero__class_Ozero(X13313)),X13310))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),X13311),c_Groups_Ozero__class_Ozero(X13313))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13313),X13312),X13311)),X13310))|~class_Fields_Olinordered__field__inverse__zero(X13313))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),X13312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13313),X13310),X13311)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),c_Groups_Ozero__class_Ozero(X13313)),X13310))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),X13311),c_Groups_Ozero__class_Ozero(X13313))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13313),X13312),X13311)),X13310))|~class_Fields_Olinordered__field__inverse__zero(X13313))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),c_Groups_Ozero__class_Ozero(X13313)),X13311))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),X13311),c_Groups_Ozero__class_Ozero(X13313)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13313),X13310),X13311)),X13312)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13313),X13312),X13311)),X13310))|~class_Fields_Olinordered__field__inverse__zero(X13313))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),X13312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13313),X13310),X13311)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),X13311),c_Groups_Ozero__class_Ozero(X13313)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13313),X13310),X13311)),X13312)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13313),X13312),X13311)),X13310))|~class_Fields_Olinordered__field__inverse__zero(X13313)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),c_Groups_Ozero__class_Ozero(X13313)),X13311))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),c_Groups_Ozero__class_Ozero(X13313)),X13310))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13313),X13310),X13311)),X13312)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13313),X13312),X13311)),X13310))|~class_Fields_Olinordered__field__inverse__zero(X13313))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),X13312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13313),X13310),X13311)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),c_Groups_Ozero__class_Ozero(X13313)),X13310))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13313),X13310),X13311)),X13312)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13313),X13312),X13311)),X13310))|~class_Fields_Olinordered__field__inverse__zero(X13313))))))&(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),X13311),c_Groups_Ozero__class_Ozero(X13313)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13313),X13310),X13311)),X13312))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),c_Groups_Ozero__class_Ozero(X13313)),X13311))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13313),X13312),X13311)),X13310))|~class_Fields_Olinordered__field__inverse__zero(X13313))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),X13311),c_Groups_Ozero__class_Ozero(X13313)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),c_Groups_Ozero__class_Ozero(X13313)),X13310))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),c_Groups_Ozero__class_Ozero(X13313)),X13311))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13313),X13312),X13311)),X13310))|~class_Fields_Olinordered__field__inverse__zero(X13313)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13313),c_Groups_Ozero__class_Ozero(X13313)),X13311))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),X13312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13313),X13310),X13311)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13313),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13313),X13312),X13311)),X13310))|~class_Fields_Olinordered__field__inverse__zero(X13313)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__le__eq])])])])). 4.46/4.70 cnf(c_0_6813, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5170, c_0_4471])). 4.46/4.70 cnf(c_0_6814, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk538_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3))),esk536_3(X1,X2,X3))|epred2_3(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5124])). 4.46/4.70 cnf(c_0_6815, plain, (hBOOL(hAPP(X3,esk446_2(X3,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(X3,X1))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X3,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk444_2(X3,X2)),X2))))|~hBOOL(hAPP(X3,esk443_2(X3,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5061])). 4.46/4.70 fof(c_0_6816, plain, ![X456, X457, X458, X459]:((hAPP(hAPP(c_Product__Type_OPair(X459,X458),esk8_4(X456,X457,X458,X459)),esk7_4(X456,X457,X458,X459))=X457|~hBOOL(hAPP(hAPP(c_member(tc_prod(X459,X458)),X457),hAPP(c_Relation_Oconverse(X458,X459),X456))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X458,X459)),hAPP(hAPP(c_Product__Type_OPair(X458,X459),esk7_4(X456,X457,X458,X459)),esk8_4(X456,X457,X458,X459))),X456))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X459,X458)),X457),hAPP(c_Relation_Oconverse(X458,X459),X456))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_converseE])])])])])). 4.46/4.70 fof(c_0_6817, plain, ![X8198, X8199, X8200, X8201]:((hBOOL(hAPP(hAPP(c_member(X8200),esk233_4(X8198,X8199,X8200,X8201)),X8199))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8201,X8200,c_Groups_Otimes__class_Otimes(X8201)),X8198),c_Groups_Oone__class_Oone(X8201)),X8199)=c_Groups_Oone__class_Oone(X8201)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8200),X8199))|~class_Groups_Ocomm__monoid__mult(X8201))&(c_Groups_Oone__class_Oone(X8201)!=hAPP(X8198,esk233_4(X8198,X8199,X8200,X8201))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8201,X8200,c_Groups_Otimes__class_Otimes(X8201)),X8198),c_Groups_Oone__class_Oone(X8201)),X8199)=c_Groups_Oone__class_Oone(X8201)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8200),X8199))|~class_Groups_Ocomm__monoid__mult(X8201))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__1])])])])])). 4.46/4.70 cnf(c_0_6818, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3))),esk538_3(X1,X2,X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk536_3(X1,X2,X3)))|epred2_3(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5124])). 4.46/4.70 cnf(c_0_6819, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X8),X1),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X6,X8),X2),X3)|hAPP(X1,esk365_8(X2,X1,X3,X4,X5,X6,X7,X8))!=hAPP(hAPP(c_Fun_Ocomp(X6,X8,X7,X2),X5),esk365_8(X2,X1,X3,X4,X5,X6,X7,X8))|X3!=hAPP(c_Set_Oimage(X7,X6,X5),X4)|~c_Fun_Oinj__on(X7,X6,X5,X4)|~class_Groups_Ocomm__monoid__mult(X8)), inference(split_conjunct,[status(thm)],[c_0_5157])). 4.46/4.70 fof(c_0_6820, plain, ![X5993, X5994, X5995, X5996, X5997, X5998, X5999, X6000]:(~c_Finite__Set_Ofolding__image__simple(X6000,X5999,X5998,X5997,X5996,X5995)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5999),X5994))|hAPP(X5995,hAPP(hAPP(c_Set_Oinsert(X5999),X5993),X5994))=hAPP(hAPP(X5998,hAPP(X5996,X5993)),hAPP(X5995,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5999,tc_HOL_Obool)),X5994),hAPP(hAPP(c_Set_Oinsert(X5999),X5993),c_Orderings_Obot__class_Obot(tc_fun(X5999,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oinsert__remove])])])). 4.46/4.70 fof(c_0_6821, plain, ![X12937, X12938, X12939, X12940, X12941, X12942]:(~c_Finite__Set_Ofolding__idem(X12942,X12941,X12940,X12939)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12942),X12938))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12942),X12937))|hAPP(c_Fun_Ocomp(X12941,X12941,X12941,hAPP(X12939,X12938)),hAPP(X12939,X12937))=hAPP(X12939,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12942,tc_HOL_Obool)),X12938),X12937))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__idem_Ounion__idem])])])). 4.46/4.70 cnf(c_0_6822, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk531_3(X2,X1,X3))),esk532_3(X2,X1,X3))=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.70 fof(c_0_6823, plain, ![X676, X677, X678, X679, X680, X681]:(~class_Groups_Ocomm__monoid__add(X681)|(~c_Fun_Oinj__on(X680,X679,X678,X677)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X680,X681),hAPP(c_Fun_Ocomp(X679,X681,X680,X676),X678)),X677)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X679,X681),X676),hAPP(c_Set_Oimage(X680,X679,X678),X677)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__reindex])])])). 4.46/4.70 cnf(c_0_6824, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk533_3(X2,X1,X3))),esk534_3(X2,X1,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.70 cnf(c_0_6825, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1)),X2)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5171])). 4.46/4.70 fof(c_0_6826, plain, ![X1596, X1597, X1598, X1599, X1600, X1601]:((~hBOOL(hAPP(hAPP(c_member(X1601),X1599),X1597))|~hBOOL(hAPP(hAPP(c_member(X1600),X1598),hAPP(X1596,X1599)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1601,X1600)),hAPP(hAPP(c_Product__Type_OPair(X1601,X1600),X1599),X1598)),hAPP(hAPP(c_Product__Type_OSigma(X1601,X1600),X1597),X1596))))&((hBOOL(hAPP(hAPP(c_member(X1601),X1599),X1597))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1601,X1600)),hAPP(hAPP(c_Product__Type_OPair(X1601,X1600),X1599),X1598)),hAPP(hAPP(c_Product__Type_OSigma(X1601,X1600),X1597),X1596))))&(hBOOL(hAPP(hAPP(c_member(X1600),X1598),hAPP(X1596,X1599)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1601,X1600)),hAPP(hAPP(c_Product__Type_OPair(X1601,X1600),X1599),X1598)),hAPP(hAPP(c_Product__Type_OSigma(X1601,X1600),X1597),X1596)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__Sigma__iff])])])). 4.46/4.70 cnf(c_0_6827, plain, (hAPP(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1))=hAPP(hAPP(c_List_Onth(X5),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),X4),c_List_Oupt(X3,X2))),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_5172])). 4.46/4.70 cnf(c_0_6828, plain, (hBOOL(hAPP(X1,X2))|hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)=c_List_OdropWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_5112])). 4.46/4.70 cnf(c_0_6829, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__sup__class_Osup(X1)),X4)),X5),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),X4))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5173])). 4.46/4.70 cnf(c_0_6830, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),X5))=hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(X1)),X5)),X4),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5174])). 4.46/4.70 cnf(c_0_6831, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X4,X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X2,X3)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X3))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5175])). 4.46/4.70 fof(c_0_6832, plain, ![X3305, X3306, X3307, X3308, X3309, X3310]:(~c_Fun_Oinj__on(X3310,X3309,X3308,X3307)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3309,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3310,X3309,X3308),X3307)),X3306))|(~c_Fun_Oinj__on(X3309,X3310,X3305,X3306)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3310,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3309,X3310,X3305),X3306)),X3307))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3310),X3307))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3309),X3306))|hAPP(c_Finite__Set_Ocard(X3310),X3307)=hAPP(c_Finite__Set_Ocard(X3309),X3306))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__bij__eq])])])). 4.46/4.70 cnf(c_0_6833, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X2=c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X3!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2)), inference(split_conjunct,[status(thm)],[c_0_5176])). 4.46/4.70 cnf(c_0_6834, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5177, c_0_4471])). 4.46/4.70 cnf(c_0_6835, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5178, c_0_4471])). 4.46/4.70 fof(c_0_6836, plain, ![X2044, X2045, X2046]:(~class_Orderings_Olinorder(X2046)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2046),X2045))|(c_Orderings_Obot__class_Obot(tc_fun(X2046,tc_HOL_Obool))=X2044|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2046,tc_HOL_Obool)),X2044),X2045))|c_Big__Operators_Olattice_OInf__fin(X2046,c_Orderings_Oord__class_Omin(X2046),X2045)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X2046),c_Big__Operators_Olattice_OInf__fin(X2046,c_Orderings_Oord__class_Omin(X2046),X2044)),c_Big__Operators_Olattice_OInf__fin(X2046,c_Orderings_Oord__class_Omin(X2046),X2045)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Osubset__idem])])])). 4.46/4.70 fof(c_0_6837, plain, ![X13951, X13952, X13953]:(~class_Orderings_Olinorder(X13953)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13953),X13952))|(X13951=c_Orderings_Obot__class_Obot(tc_fun(X13953,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13953,tc_HOL_Obool)),X13951),X13952))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X13953),c_Big__Operators_Olattice_OSup__fin(X13953,c_Orderings_Oord__class_Omax(X13953),X13951)),c_Big__Operators_Olattice_OSup__fin(X13953,c_Orderings_Oord__class_Omax(X13953),X13952))=c_Big__Operators_Olattice_OSup__fin(X13953,c_Orderings_Oord__class_Omax(X13953),X13952))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Osubset__idem])])])). 4.46/4.70 fof(c_0_6838, plain, ![X8147, X8148, X8149, X8150]:(~hBOOL(hAPP(hAPP(c_member(X8150),X8149),c_Wellfounded_Oacc(X8150,X8148)))|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8150)),X8147),c_Wellfounded_Oacc(tc_List_Olist(X8150),c_List_Olistrel1(X8150,X8148))))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8150)),hAPP(hAPP(c_List_Olist_OCons(X8150),X8149),X8147)),c_Wellfounded_Oacc(tc_List_Olist(X8150),c_List_Olistrel1(X8150,X8148)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Cons__acc__listrel1I])])])). 4.46/4.70 fof(c_0_6839, plain, ![X1794, X1795, X1796, X1797]:((hBOOL(hAPP(hAPP(c_member(X1797),esk43_4(X1794,X1795,X1796,X1797)),hAPP(c_List_Oset(X1797),X1796)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X1797,X1795,X1796)),c_List_Olist_Olist__size(X1797,X1794,X1796))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1795,esk43_4(X1794,X1795,X1796,X1797))),hAPP(X1794,esk43_4(X1794,X1795,X1796,X1797))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X1797,X1795,X1796)),c_List_Olist_Olist__size(X1797,X1794,X1796))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__size__pointwise])])])])])). 4.46/4.70 fof(c_0_6840, plain, ![X12374, X12375, X12376, X12377]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),c_Groups_Ozero__class_Ozero(X12377)),X12374))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),c_Groups_Ozero__class_Ozero(X12377)),X12374))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12377),X12375),X12374)))|~class_Fields_Olinordered__field__inverse__zero(X12377))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12377),X12376),X12374)),X12375))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),c_Groups_Ozero__class_Ozero(X12377)),X12374))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12377),X12375),X12374)))|~class_Fields_Olinordered__field__inverse__zero(X12377)))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),c_Groups_Ozero__class_Ozero(X12377)),X12374))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),X12374),c_Groups_Ozero__class_Ozero(X12377)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),X12374),c_Groups_Ozero__class_Ozero(X12377))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12377),X12375),X12374)))|~class_Fields_Olinordered__field__inverse__zero(X12377))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12377),X12376),X12374)),X12375))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),X12374),c_Groups_Ozero__class_Ozero(X12377)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),X12374),c_Groups_Ozero__class_Ozero(X12377))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12377),X12375),X12374)))|~class_Fields_Olinordered__field__inverse__zero(X12377)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),c_Groups_Ozero__class_Ozero(X12377)),X12374))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12376),c_Groups_Ozero__class_Ozero(X12377)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),X12374),c_Groups_Ozero__class_Ozero(X12377))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12377),X12375),X12374)))|~class_Fields_Olinordered__field__inverse__zero(X12377))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12377),X12376),X12374)),X12375))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12376),c_Groups_Ozero__class_Ozero(X12377)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),X12374),c_Groups_Ozero__class_Ozero(X12377))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12377),X12375),X12374)))|~class_Fields_Olinordered__field__inverse__zero(X12377))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),c_Groups_Ozero__class_Ozero(X12377)),X12374))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),X12374),c_Groups_Ozero__class_Ozero(X12377)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12377),X12376),X12374))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12377),X12375),X12374)))|~class_Fields_Olinordered__field__inverse__zero(X12377))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12377),X12376),X12374)),X12375))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),X12374),c_Groups_Ozero__class_Ozero(X12377)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12377),X12376),X12374))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12377),X12375),X12374)))|~class_Fields_Olinordered__field__inverse__zero(X12377)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),c_Groups_Ozero__class_Ozero(X12377)),X12374))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12376),c_Groups_Ozero__class_Ozero(X12377)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12377),X12376),X12374))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12377),X12375),X12374)))|~class_Fields_Olinordered__field__inverse__zero(X12377))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12377),X12376),X12374)),X12375))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12376),c_Groups_Ozero__class_Ozero(X12377)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12377),X12376),X12374))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12377),X12375),X12374)))|~class_Fields_Olinordered__field__inverse__zero(X12377))))))&(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),X12374),c_Groups_Ozero__class_Ozero(X12377)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12377),X12376),X12374)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),c_Groups_Ozero__class_Ozero(X12377)),X12374))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12377),X12375),X12374)))|~class_Fields_Olinordered__field__inverse__zero(X12377))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),X12374),c_Groups_Ozero__class_Ozero(X12377)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12376),c_Groups_Ozero__class_Ozero(X12377)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),c_Groups_Ozero__class_Ozero(X12377)),X12374))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12377),X12375),X12374)))|~class_Fields_Olinordered__field__inverse__zero(X12377)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12377),c_Groups_Ozero__class_Ozero(X12377)),X12374))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12377),X12376),X12374)),X12375))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12377),X12376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12377),X12375),X12374)))|~class_Fields_Olinordered__field__inverse__zero(X12377)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__divide__eq])])])])). 4.46/4.70 cnf(c_0_6841, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),hAPP(c_Wellfounded_Omeasure(X4),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_5179])). 4.46/4.70 cnf(c_0_6842, plain, (hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than)=c_Wellfounded_Omeasure(X1)), inference(split_conjunct,[status(thm)],[c_0_5180])). 4.46/4.70 fof(c_0_6843, plain, ![X7129, X7130, X7131]:(~class_Fields_Olinordered__field(X7131)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7131),X7130),X7129))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7131),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7131),X7130),X7129)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7131),c_Groups_Oone__class_Oone(X7131)),c_Groups_Oone__class_Oone(X7131)))),X7129)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_gt__half__sum])])])). 4.46/4.70 cnf(c_0_6844, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk518_5(X1,X2,X3,X4,X5)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X2),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X1),X3)|~c_Nat__Transfer_Onat__set(X3)|X4!=X3|~class_Groups_Ocomm__monoid__add(X5)|~class_Groups_Ocomm__monoid__mult(X5)), inference(split_conjunct,[status(thm)],[c_0_5181])). 4.46/4.70 cnf(c_0_6845, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk9_5(X1,X2,X3,X4,X5)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X2),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X1),X3)|~c_Nat__Transfer_Onat__set(X3)|X3!=X4|~class_Groups_Ocomm__monoid__mult(X5)|~class_Groups_Ocomm__monoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_5182])). 4.46/4.70 fof(c_0_6846, plain, ![X11374, X11375, X11376, X11377]:((((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),c_Groups_Ozero__class_Ozero(X11377)),X11374))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),c_Groups_Ozero__class_Ozero(X11377)),X11374))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11377),X11375),X11374)))|~class_Fields_Olinordered__field__inverse__zero(X11377))&(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11374),c_Groups_Ozero__class_Ozero(X11377)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11374),c_Groups_Ozero__class_Ozero(X11377)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),c_Groups_Ozero__class_Ozero(X11377)),X11374))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11377),X11375),X11374)))|~class_Fields_Olinordered__field__inverse__zero(X11377))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11376),c_Groups_Ozero__class_Ozero(X11377)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11374),c_Groups_Ozero__class_Ozero(X11377)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),c_Groups_Ozero__class_Ozero(X11377)),X11374))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11377),X11375),X11374)))|~class_Fields_Olinordered__field__inverse__zero(X11377)))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11374),c_Groups_Ozero__class_Ozero(X11377)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11377),X11376),X11374)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),c_Groups_Ozero__class_Ozero(X11377)),X11374))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11377),X11375),X11374)))|~class_Fields_Olinordered__field__inverse__zero(X11377))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11376),c_Groups_Ozero__class_Ozero(X11377)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11377),X11376),X11374)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),c_Groups_Ozero__class_Ozero(X11377)),X11374))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11377),X11375),X11374)))|~class_Fields_Olinordered__field__inverse__zero(X11377)))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),c_Groups_Ozero__class_Ozero(X11377)),X11374))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11377),X11376),X11374)),X11375))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11377),X11375),X11374)))|~class_Fields_Olinordered__field__inverse__zero(X11377))&(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11374),c_Groups_Ozero__class_Ozero(X11377)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11374),c_Groups_Ozero__class_Ozero(X11377)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11377),X11376),X11374)),X11375))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11377),X11375),X11374)))|~class_Fields_Olinordered__field__inverse__zero(X11377))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11376),c_Groups_Ozero__class_Ozero(X11377)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11374),c_Groups_Ozero__class_Ozero(X11377)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11377),X11376),X11374)),X11375))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11377),X11375),X11374)))|~class_Fields_Olinordered__field__inverse__zero(X11377)))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11374),c_Groups_Ozero__class_Ozero(X11377)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11377),X11376),X11374)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11377),X11376),X11374)),X11375))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11377),X11375),X11374)))|~class_Fields_Olinordered__field__inverse__zero(X11377))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11376),c_Groups_Ozero__class_Ozero(X11377)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11377),X11376),X11374)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11377),X11376),X11374)),X11375))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11377),X11375),X11374)))|~class_Fields_Olinordered__field__inverse__zero(X11377))))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),c_Groups_Ozero__class_Ozero(X11377)),X11374))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11377),X11376),X11374)),X11375))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11377),X11375),X11374)))|~class_Fields_Olinordered__field__inverse__zero(X11377))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11374),c_Groups_Ozero__class_Ozero(X11377)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11377),X11376),X11374)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),c_Groups_Ozero__class_Ozero(X11377)),X11374))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11377),X11375),X11374)))|~class_Fields_Olinordered__field__inverse__zero(X11377))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11374),c_Groups_Ozero__class_Ozero(X11377)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11376),c_Groups_Ozero__class_Ozero(X11377)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),c_Groups_Ozero__class_Ozero(X11377)),X11374))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11377),X11376),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11377),X11375),X11374)))|~class_Fields_Olinordered__field__inverse__zero(X11377))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__divide__eq])])])])). 4.46/4.70 fof(c_0_6847, plain, ![X11296, X11297, X11298]:(~class_Fields_Olinordered__field(X11298)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11298),X11297),X11296))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11298),X11297),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11298),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11298),X11297),X11296)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11298),c_Groups_Oone__class_Oone(X11298)),c_Groups_Oone__class_Oone(X11298))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__half__sum])])])). 4.46/4.70 cnf(c_0_6848, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),X2))|~class_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))), inference(rw,[status(thm)],[c_0_5183, c_0_4471])). 4.46/4.70 cnf(c_0_6849, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),X2))|~class_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))), inference(rw,[status(thm)],[c_0_5184, c_0_4471])). 4.46/4.70 cnf(c_0_6850, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk445_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk444_2(X1,X2)),X2))))|~hBOOL(hAPP(X1,esk443_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5061])). 4.46/4.70 fof(c_0_6851, plain, ![X16349, X16350, X16351, X16352, X16353, X16354]:(~c_Finite__Set_Ofolding(X16354,X16353,X16352,X16351)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16354),X16350))|hAPP(c_Fun_Ocomp(X16353,X16353,X16353,hAPP(X16351,X16350)),hAPP(X16352,X16349))=hAPP(c_Fun_Ocomp(X16353,X16353,X16353,hAPP(X16352,X16349)),hAPP(X16351,X16350)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Ocommute__comp_H])])])). 4.46/4.70 cnf(c_0_6852, plain, (hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),c_List_Olist_ONil(tc_Nat_Onat)))=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5185, c_0_4517]), c_0_4517])). 4.46/4.71 cnf(c_0_6853, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))|~class_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)))), inference(rw,[status(thm)],[c_0_5186, c_0_4471])). 4.46/4.71 cnf(c_0_6854, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))|~class_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)))), inference(rw,[status(thm)],[c_0_5187, c_0_4471])). 4.46/4.71 fof(c_0_6855, plain, ![X9670, X9671, X9672, X9673]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9673),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9672)),X9671)))|hAPP(hAPP(c_List_Onth(X9672),X9670),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9673),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9672)),X9671)))=hAPP(hAPP(c_List_Onth(X9672),hAPP(hAPP(c_List_Oappend(X9672),X9671),X9670)),X9673))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9673),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9672)),X9671)))|hAPP(hAPP(c_List_Onth(X9672),hAPP(hAPP(c_List_Oappend(X9672),X9671),X9670)),X9673)=hAPP(hAPP(c_List_Onth(X9672),X9671),X9673))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__append])])])). 4.46/4.71 fof(c_0_6856, plain, ![X13337, X13338, X13339, X13340, X13341]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13338,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13340,X13338,X13341),X13339)),X13337))|~c_Fun_Oinj__on(X13340,X13338,X13341,X13339)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X13340),X13339)),hAPP(c_Finite__Set_Ocard(X13338),X13337)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13338),X13337))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13340),X13339)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13338,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13340,X13338,esk389_4(X13337,X13338,X13339,X13340)),X13339)),X13337))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X13340),X13339)),hAPP(c_Finite__Set_Ocard(X13338),X13337)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13338),X13337))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13340),X13339)))&(c_Fun_Oinj__on(X13340,X13338,esk389_4(X13337,X13338,X13339,X13340),X13339)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X13340),X13339)),hAPP(c_Finite__Set_Ocard(X13338),X13337)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13338),X13337))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13340),X13339))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__iff__card__le])])])])])])). 4.46/4.71 cnf(c_0_6857, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk15_6(X2,X3,X4,X5,X1,X6)),X5))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6),hAPP(X4,X2)),X3))|X3!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),X4),X5)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~class_Groups_Oordered__ab__group__add(X6)), inference(split_conjunct,[status(thm)],[c_0_5188])). 4.46/4.71 fof(c_0_6858, plain, ![X11539, X11540, X11541, X11542, X11543]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11543),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11542)),X11541)))|hAPP(hAPP(c_List_Olist__update(X11542,hAPP(hAPP(c_List_Oappend(X11542),X11541),X11540)),X11543),X11539)=hAPP(hAPP(c_List_Oappend(X11542),hAPP(hAPP(c_List_Olist__update(X11542,X11541),X11543),X11539)),X11540)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__append1])])). 4.46/4.71 fof(c_0_6859, plain, ![X349, X350, X351, X352]:(~class_Rings_Olinordered__semidom(X352)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X352),X351),X350))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X352),c_Groups_Ozero__class_Ozero(X352)),X351))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X349))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X352),hAPP(hAPP(c_Power_Opower__class_Opower(X352),X351),X349)),hAPP(hAPP(c_Power_Opower__class_Opower(X352),X350),X349))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__strict__mono])])])). 4.46/4.71 cnf(c_0_6860, plain, (hAPP(c_Product__Type_Oapsnd(X3,X6,X2,X5),X4)=hAPP(c_Product__Type_Oapsnd(X3,X6,X2,X1),X4)|hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4))!=hAPP(X5,hAPP(c_Product__Type_Osnd(X2,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5189])). 4.46/4.71 cnf(c_0_6861, plain, (hAPP(c_Product__Type_Oapfst(X2,X6,X3,X5),X4)=hAPP(c_Product__Type_Oapfst(X2,X6,X3,X1),X4)|hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4))!=hAPP(X5,hAPP(c_Product__Type_Ofst(X2,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5190])). 4.46/4.71 cnf(c_0_6862, plain, (c_Product__Type_Oapfst(X1,X2,X3,X4)=c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3))), inference(split_conjunct,[status(thm)],[c_0_5191])). 4.46/4.71 cnf(c_0_6863, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),X2))),X3))), inference(split_conjunct,[status(thm)],[c_0_5047])). 4.46/4.71 fof(c_0_6864, plain, ![X16626, X16627, X16628, X16629]:(~class_Rings_Olinordered__semidom(X16629)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16628),X16627))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16629),c_Groups_Ozero__class_Ozero(X16629)),X16626))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16629),X16626),c_Groups_Oone__class_Oone(X16629)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16629),hAPP(hAPP(c_Power_Opower__class_Opower(X16629),X16626),X16627)),hAPP(hAPP(c_Power_Opower__class_Opower(X16629),X16626),X16628))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__strict__decreasing])])])). 4.46/4.71 fof(c_0_6865, plain, ![X11582, X11583, X11584, X11585]:(~class_Rings_Olinordered__semidom(X11585)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11584),X11583))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11585),c_Groups_Ozero__class_Ozero(X11585)),X11582))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11585),X11582),c_Groups_Oone__class_Oone(X11585)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11585),hAPP(hAPP(c_Power_Opower__class_Opower(X11585),X11582),X11583)),hAPP(hAPP(c_Power_Opower__class_Opower(X11585),X11582),X11584))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__decreasing])])])). 4.46/4.71 fof(c_0_6866, plain, ![X9503, X9504, X9505, X9507, X9508, X9509, X9510, X9512]:(((hBOOL(hAPP(hAPP(c_member(X9505),esk272_3(X9503,X9504,X9505)),hAPP(c_List_Oset(X9505),X9504)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9507),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9505)),X9504)))|hBOOL(hAPP(X9503,hAPP(hAPP(c_List_Onth(X9505),X9504),X9507)))))&(~hBOOL(hAPP(X9503,esk272_3(X9503,X9504,X9505)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9507),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9505)),X9504)))|hBOOL(hAPP(X9503,hAPP(hAPP(c_List_Onth(X9505),X9504),X9507))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk273_3(X9508,X9509,X9510)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9510)),X9509)))|(~hBOOL(hAPP(hAPP(c_member(X9510),X9512),hAPP(c_List_Oset(X9510),X9509)))|hBOOL(hAPP(X9508,X9512))))&(~hBOOL(hAPP(X9508,hAPP(hAPP(c_List_Onth(X9510),X9509),esk273_3(X9508,X9509,X9510))))|(~hBOOL(hAPP(hAPP(c_member(X9510),X9512),hAPP(c_List_Oset(X9510),X9509)))|hBOOL(hAPP(X9508,X9512)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_all__set__conv__all__nth])])])])])])])). 4.46/4.71 fof(c_0_6867, plain, ![X387, X388, X389, X390]:(~class_Divides_Osemiring__div(X390)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X390),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X390),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X390),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X390),X389),X388)),X388)),c_Divides_Odiv__class_Omod(X390,X389,X388))),X387)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X390),X389),X387)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality])])). 4.46/4.71 fof(c_0_6868, plain, ![X11982, X11983, X11984, X11985]:(~class_Groups_Oordered__ab__group__add__abs(X11985)|hAPP(c_Groups_Oabs__class_Oabs(X11985),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11984,X11985),hAPP(hAPP(c_COMBB(X11985,X11985,X11984),c_Groups_Oabs__class_Oabs(X11985)),X11983)),X11982))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11984,X11985),hAPP(hAPP(c_COMBB(X11985,X11985,X11984),c_Groups_Oabs__class_Oabs(X11985)),X11983)),X11982)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__setsum__abs])])])). 4.46/4.71 fof(c_0_6869, plain, ![X4359, X4360, X4361]:(~class_Orderings_Olinorder(X4361)|(X4360=c_Orderings_Obot__class_Obot(tc_fun(X4361,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4361,tc_HOL_Obool)),X4360),X4359))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4361),X4359))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4361),hAPP(c_Finite__Set_Ofold1(X4361,c_Orderings_Oord__class_Omin(X4361)),X4359)),hAPP(c_Finite__Set_Ofold1(X4361,c_Orderings_Oord__class_Omin(X4361)),X4360))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__antimono])])])). 4.46/4.71 cnf(c_0_6870, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBS(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X3)),X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))|~class_Enum_Oenum(X1)|~class_Orderings_Oorder(X2)), inference(split_conjunct,[status(thm)],[c_0_5192])). 4.46/4.71 fof(c_0_6871, plain, ![X6590, X6591, X6592, X6593]:(~class_Divides_Osemiring__div(X6593)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6593),X6591),X6590)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6593),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6593),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6593),X6592),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X6593),X6591),X6592))),c_Divides_Odiv__class_Omod(X6593,X6591,X6592))),X6590)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality2])])). 4.46/4.71 cnf(c_0_6872, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3)),hAPP(c_Nat_OSuc,X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5193])). 4.46/4.71 fof(c_0_6873, plain, ![X12398, X12399, X12400]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12400),X12399))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X12400),X12398)),hAPP(c_Finite__Set_Ocard(X12400),X12399))),hAPP(c_Finite__Set_Ocard(X12400),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12400,tc_HOL_Obool)),X12398),X12399))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__card__le__card__Diff])])). 4.46/4.71 cnf(c_0_6874, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),X2),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))))|~class_Groups_Ocomm__monoid__add(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5194, c_0_4517]), c_0_4517])). 4.46/4.71 cnf(c_0_6875, plain, (hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)), inference(rw,[status(thm)],[c_0_5195, c_0_4517]), ['final']). 4.46/4.71 cnf(c_0_6876, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3))),c_Groups_Ozero__class_Ozero(X2)))|X1!=c_Groups_Ozero__class_Ozero(X2)|c_Groups_Ozero__class_Ozero(X2)!=X3|~class_Rings_Olinordered__ring__strict(X2)), inference(split_conjunct,[status(thm)],[c_0_5196])). 4.46/4.71 fof(c_0_6877, plain, ![X7018, X7019, X7020, X7021, X7022]:(~c_Equiv__Relations_Oequiv(X7022,X7021,X7020)|(~hBOOL(hAPP(hAPP(c_member(tc_fun(X7022,tc_HOL_Obool)),X7019),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7022),X7021),X7020)))|(~hBOOL(hAPP(hAPP(c_member(tc_fun(X7022,tc_HOL_Obool)),X7018),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7022),X7021),X7020)))|(c_Orderings_Obot__class_Obot(tc_fun(X7022,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7022,tc_HOL_Obool)),X7019),X7018)|X7019=X7018)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_quotient__disj])])])). 4.46/4.71 fof(c_0_6878, plain, ![X4186, X4187, X4188, X4189, X4190, X4191]:(~hBOOL(hAPP(hAPP(c_member(X4191),X4190),X4189))|hAPP(hAPP(c_Set_Oinsert(X4188),X4187),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4191,tc_fun(X4188,tc_HOL_Obool)),X4189),X4186))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4191,tc_fun(X4188,tc_HOL_Obool)),X4189),hAPP(hAPP(c_COMBB(tc_fun(X4188,tc_HOL_Obool),tc_fun(X4188,tc_HOL_Obool),X4191),hAPP(c_Set_Oinsert(X4188),X4187)),X4186))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__insert__distrib])])])). 4.46/4.71 cnf(c_0_6879, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(X3,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2)!=X3), inference(split_conjunct,[status(thm)],[c_0_5145])). 4.46/4.71 fof(c_0_6880, plain, ![X13224, X13225, X13226]:(~class_Groups_Ocomm__monoid__add(X13226)|~class_Groups_Ocomm__monoid__mult(X13226)|(~c_Nat__Transfer_Onat__set(X13225)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X13226),hAPP(hAPP(c_COMBB(tc_Int_Oint,X13226,tc_Nat_Onat),X13224),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X13225))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X13226),X13224),X13225))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__int__nat__sum__prod_I2_J])])])). 4.46/4.71 fof(c_0_6881, plain, ![X3720, X3721, X3722]:(~class_Groups_Ocomm__monoid__add(X3722)|~class_Groups_Ocomm__monoid__mult(X3722)|(~c_Nat__Transfer_Onat__set(X3721)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X3722),X3720),X3721)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3722),hAPP(hAPP(c_COMBB(tc_Int_Oint,X3722,tc_Nat_Onat),X3720),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X3721)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__int__nat__sum__prod_I1_J])])])). 4.46/4.71 cnf(c_0_6882, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))|~class_Int_Onumber__ring(X1)|~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5197, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 cnf(c_0_6883, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3))),esk538_3(X1,X2,X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk536_3(X1,X2,X3)),X2))|epred2_3(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5124])). 4.46/4.71 cnf(c_0_6884, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk14_3(X1,X2,X3)),esk13_3(X1,X2,X3))=X2|X2=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5156])). 4.46/4.71 cnf(c_0_6885, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk538_3(X2,X1,X3)))|X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk535_3(X2,X1,X3))),esk536_3(X2,X1,X3))|epred2_3(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5124])). 4.46/4.71 cnf(c_0_6886, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X2=c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|X3!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2)), inference(split_conjunct,[status(thm)],[c_0_5176])). 4.46/4.71 fof(c_0_6887, plain, ![X12182, X12183, X12184, X12185, X12186, X12187, X12188, X12189]:(~c_Finite__Set_Ofolding__image__simple(X12189,X12188,X12187,X12186,X12185,X12184)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12188),X12183))|(hBOOL(hAPP(hAPP(c_member(X12188),X12182),X12183))|hAPP(hAPP(X12187,hAPP(X12185,X12182)),hAPP(X12184,X12183))=hAPP(X12184,hAPP(hAPP(c_Set_Oinsert(X12188),X12182),X12183))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oinsert])])])). 4.46/4.71 fof(c_0_6888, plain, ![X5400, X5401, X5402, X5403, X5404, X5405, X5406, X5407, X5408, X5409, X5410]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5404,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5403,tc_fun(X5404,tc_HOL_Obool)),X5402),X5401)),X5400))|(~hBOOL(hAPP(hAPP(c_member(X5403),X5405),X5402))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5404,tc_HOL_Obool)),hAPP(X5401,X5405)),X5400))))&((hBOOL(hAPP(hAPP(c_member(X5409),esk164_5(X5406,X5407,X5408,X5409,X5410)),X5408))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5410,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5409,tc_fun(X5410,tc_HOL_Obool)),X5408),X5407)),X5406)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5410,tc_HOL_Obool)),hAPP(X5407,esk164_5(X5406,X5407,X5408,X5409,X5410))),X5406))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5410,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5409,tc_fun(X5410,tc_HOL_Obool)),X5408),X5407)),X5406))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__subset__iff])])])])])])])). 4.46/4.71 fof(c_0_6889, plain, ![X665, X666, X667, X669]:(((hBOOL(hAPP(hAPP(c_member(X667),esk17_3(X665,X666,X667)),X666))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X667),hAPP(c_Finite__Set_Ofold1(X667,c_Orderings_Oord__class_Omin(X667)),X666)),X665))|c_Orderings_Obot__class_Obot(tc_fun(X667,tc_HOL_Obool))=X666|~hBOOL(hAPP(c_Finite__Set_Ofinite(X667),X666))|~class_Orderings_Olinorder(X667))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X667),esk17_3(X665,X666,X667)),X665))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X667),hAPP(c_Finite__Set_Ofold1(X667,c_Orderings_Oord__class_Omin(X667)),X666)),X665))|c_Orderings_Obot__class_Obot(tc_fun(X667,tc_HOL_Obool))=X666|~hBOOL(hAPP(c_Finite__Set_Ofinite(X667),X666))|~class_Orderings_Olinorder(X667)))&(~hBOOL(hAPP(hAPP(c_member(X667),X669),X666))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X667),X669),X665))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X667),hAPP(c_Finite__Set_Ofold1(X667,c_Orderings_Oord__class_Omin(X667)),X666)),X665))|c_Orderings_Obot__class_Obot(tc_fun(X667,tc_HOL_Obool))=X666|~hBOOL(hAPP(c_Finite__Set_Ofinite(X667),X666))|~class_Orderings_Olinorder(X667))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__below__iff])])])])])])). 4.46/4.71 fof(c_0_6890, plain, ![X4759, X4760, X4761, X4762, X4763, X4765, X4766, X4767, X4768, X4769, X4770]:(((hBOOL(hAPP(hAPP(c_member(X4761),esk138_5(X4759,X4760,X4761,X4762,X4763)),X4760))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4763,tc_HOL_Obool)),X4762),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4761,tc_fun(X4763,tc_HOL_Obool)),X4760),X4759))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4763,tc_HOL_Obool)),X4762),hAPP(X4759,esk138_5(X4759,X4760,X4761,X4762,X4763))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4763,tc_HOL_Obool)),X4762),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4761,tc_fun(X4763,tc_HOL_Obool)),X4760),X4759)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4769,tc_HOL_Obool)),X4768),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4767,tc_fun(X4769,tc_HOL_Obool)),X4766),X4765)))|(~hBOOL(hAPP(hAPP(c_member(X4767),X4770),X4766))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4769,tc_HOL_Obool)),X4768),hAPP(X4765,X4770)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INT__subset__iff])])])])])])])). 4.46/4.71 cnf(c_0_6891, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X2)=X4|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|X3!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),X1)), inference(split_conjunct,[status(thm)],[c_0_5153])). 4.46/4.71 fof(c_0_6892, plain, ![X7463, X7464, X7465, X7466, X7467]:((X7467!=c_Orderings_Obot__class_Obot(tc_fun(X7466,tc_HOL_Obool))|c_Orderings_Otop__class_Otop(tc_fun(X7465,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7466,tc_fun(X7465,tc_HOL_Obool)),X7467),hAPP(hAPP(c_COMBB(tc_fun(X7465,tc_HOL_Obool),tc_fun(X7465,tc_HOL_Obool),X7466),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7465,tc_HOL_Obool)),X7464)),X7463)))&(X7467=c_Orderings_Obot__class_Obot(tc_fun(X7466,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7466,tc_fun(X7465,tc_HOL_Obool)),X7467),hAPP(hAPP(c_COMBB(tc_fun(X7465,tc_HOL_Obool),tc_fun(X7465,tc_HOL_Obool),X7466),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7465,tc_HOL_Obool)),X7464)),X7463))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7465,tc_HOL_Obool)),X7464),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7466,tc_fun(X7465,tc_HOL_Obool)),X7467),X7463)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INT__simps_I4_J])])])). 4.46/4.71 fof(c_0_6893, plain, ![X11283, X11284, X11285, X11287]:(((hBOOL(hAPP(hAPP(c_member(X11285),esk332_3(X11283,X11284,X11285)),X11284))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11285),hAPP(c_Finite__Set_Ofold1(X11285,c_Orderings_Oord__class_Omin(X11285)),X11284)),X11283))|X11284=c_Orderings_Obot__class_Obot(tc_fun(X11285,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11285),X11284))|~class_Orderings_Olinorder(X11285))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11285),esk332_3(X11283,X11284,X11285)),X11283))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11285),hAPP(c_Finite__Set_Ofold1(X11285,c_Orderings_Oord__class_Omin(X11285)),X11284)),X11283))|X11284=c_Orderings_Obot__class_Obot(tc_fun(X11285,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11285),X11284))|~class_Orderings_Olinorder(X11285)))&(~hBOOL(hAPP(hAPP(c_member(X11285),X11287),X11284))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11285),X11287),X11283))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11285),hAPP(c_Finite__Set_Ofold1(X11285,c_Orderings_Oord__class_Omin(X11285)),X11284)),X11283))|X11284=c_Orderings_Obot__class_Obot(tc_fun(X11285,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11285),X11284))|~class_Orderings_Olinorder(X11285))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__strict__below__iff])])])])])])). 4.46/4.71 cnf(c_0_6894, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk533_3(X2,X1,X3))),esk534_3(X2,X1,X3))=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X1,X2)|~hBOOL(hAPP(X3,esk532_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.71 cnf(c_0_6895, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk435_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|X2=X4|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)!=X2|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5198])). 4.46/4.71 fof(c_0_6896, plain, ![X10268, X10269, X10270, X10271, X10272]:((X10272=c_Orderings_Obot__class_Obot(tc_fun(X10271,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10270,tc_HOL_Obool)),X10269),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10271,tc_fun(X10270,tc_HOL_Obool)),X10272),X10268))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10271,tc_fun(X10270,tc_HOL_Obool)),X10272),hAPP(hAPP(c_COMBB(tc_fun(X10270,tc_HOL_Obool),tc_fun(X10270,tc_HOL_Obool),X10271),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10270,tc_HOL_Obool)),X10269)),X10268)))&(c_Orderings_Obot__class_Obot(tc_fun(X10271,tc_HOL_Obool))!=X10272|c_Orderings_Otop__class_Otop(tc_fun(X10270,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10271,tc_fun(X10270,tc_HOL_Obool)),X10272),hAPP(hAPP(c_COMBB(tc_fun(X10270,tc_HOL_Obool),tc_fun(X10270,tc_HOL_Obool),X10271),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10270,tc_HOL_Obool)),X10269)),X10268)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INT__simps_I2_J])])])). 4.46/4.71 cnf(c_0_6897, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2)=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))|~c_Nat__Transfer_Onat__set(X1)|~c_Nat__Transfer_Onat__set(X2)), inference(split_conjunct,[status(thm)],[c_0_5199])). 4.46/4.71 cnf(c_0_6898, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5))), inference(split_conjunct,[status(thm)],[c_0_5200]), ['final']). 4.46/4.71 cnf(c_0_6899, plain, (hAPP(c_Set_Oimage(X1,X2,hAPP(hAPP(c_COMBB(X3,X2,X1),X4),X5)),X6)=hAPP(c_Set_Oimage(X3,X2,X4),hAPP(c_Set_Oimage(X1,X3,X5),X6))), inference(split_conjunct,[status(thm)],[c_0_5201]), ['final']). 4.46/4.71 fof(c_0_6900, plain, ![X2577, X2578]:(~c_Nat__Transfer_Onat__set(X2578)|(~c_Nat__Transfer_Onat__set(X2577)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X2578),X2577)=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2578)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2577))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J])])])). 4.46/4.71 cnf(c_0_6901, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk531_3(X2,X3,X1))),esk532_3(X2,X3,X1))=X2|X3=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X1,X3,X2)|~hBOOL(hAPP(X1,esk534_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.71 cnf(c_0_6902, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(X1,X2)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),esk2_2(X2,X1))),hAPP(c_List_Oset(X1),esk3_2(X2,X1)))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(X1),esk1_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_5007])). 4.46/4.71 fof(c_0_6903, plain, ![X13048, X13049, X13050, X13051]:((hBOOL(hAPP(hAPP(c_member(X13051),esk383_4(X13048,X13049,X13050,X13051)),X13050))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X13051,X13049)),hAPP(hAPP(c_Product__Type_OSigma(X13051,X13049),X13050),X13048)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13051),X13050)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13049),hAPP(X13048,esk383_4(X13048,X13049,X13050,X13051))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X13051,X13049)),hAPP(hAPP(c_Product__Type_OSigma(X13051,X13049),X13050),X13048)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13051),X13050)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__SigmaI])])])])])). 4.46/4.71 cnf(c_0_6904, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk357_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|c_List_Oconcat(X1,X2)=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_5202])). 4.46/4.71 cnf(c_0_6905, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk257_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|X4=X2|X2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5203])). 4.46/4.71 fof(c_0_6906, plain, ![X10391, X10392]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10392))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10391),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X10392),X10391)=hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X10392),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X10391)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__neg])])). 4.46/4.71 cnf(c_0_6907, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk195_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|c_List_Oconcat(X1,X2)=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_5204])). 4.46/4.71 fof(c_0_6908, plain, ![X16060, X16061, X16064, X16065]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk466_2(X16060,X16061)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16061)),X16060)))|c_List_Olinorder__class_Osorted(X16061,X16060)|~class_Orderings_Olinorder(X16061))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk467_2(X16060,X16061)),esk466_2(X16060,X16061)))|c_List_Olinorder__class_Osorted(X16061,X16060)|~class_Orderings_Olinorder(X16061))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16061),hAPP(hAPP(c_List_Onth(X16061),X16060),esk467_2(X16060,X16061))),hAPP(hAPP(c_List_Onth(X16061),X16060),esk466_2(X16060,X16061))))|c_List_Olinorder__class_Osorted(X16061,X16060)|~class_Orderings_Olinorder(X16061))))&(~c_List_Olinorder__class_Osorted(X16061,X16060)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16064),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16061)),X16060)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16065),X16064))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16061),hAPP(hAPP(c_List_Onth(X16061),X16060),X16065)),hAPP(hAPP(c_List_Onth(X16061),X16060),X16064)))))|~class_Orderings_Olinorder(X16061))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__equals__nth__mono])])])])])])). 4.46/4.71 fof(c_0_6909, plain, ![X16568, X16569, X16570, X16571]:((hBOOL(hAPP(hAPP(c_member(X16571),esk483_4(X16568,X16569,X16570,X16571)),X16570))|hBOOL(hAPP(c_Finite__Set_Ofinite(X16569),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16571,tc_fun(X16569,tc_HOL_Obool)),X16570),X16568)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16571),X16570)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16569),hAPP(X16568,esk483_4(X16568,X16569,X16570,X16571))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X16569),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16571,tc_fun(X16569,tc_HOL_Obool)),X16570),X16568)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16571),X16570)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UN__I])])])])). 4.46/4.71 fof(c_0_6910, plain, ![X844, X845, X846, X847, X848]:((hBOOL(hAPP(hAPP(c_member(X848),X847),hAPP(c_List_Oset(X848),X846)))|c_Option_Ooption_ONone(X845)=hAPP(hAPP(c_Map_Omap__of(X848,X845),hAPP(hAPP(c_List_Ozip(X848,X845),X846),hAPP(hAPP(c_List_Omap(X848,X845),X844),X846))),X847))&(~hBOOL(hAPP(hAPP(c_member(X848),X847),hAPP(c_List_Oset(X848),X846)))|hAPP(hAPP(c_Map_Omap__of(X848,X845),hAPP(hAPP(c_List_Ozip(X848,X845),X846),hAPP(hAPP(c_List_Omap(X848,X845),X844),X846))),X847)=hAPP(c_Option_Ooption_OSome(X845),hAPP(X844,X847)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__zip__map])])])). 4.46/4.71 fof(c_0_6911, plain, ![X9187, X9188, X9189, X9190, X9191]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X9188),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9190,tc_fun(X9188,tc_HOL_Obool)),X9189),X9187)))|(~hBOOL(hAPP(hAPP(c_member(X9190),X9191),X9189))|hBOOL(hAPP(c_Finite__Set_Ofinite(X9188),hAPP(X9187,X9191))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9190),X9189)))&((hBOOL(hAPP(hAPP(c_member(X9190),esk265_4(X9187,X9188,X9189,X9190)),X9189))|hBOOL(hAPP(c_Finite__Set_Ofinite(X9188),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9190,tc_fun(X9188,tc_HOL_Obool)),X9189),X9187)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9190),X9189)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9188),hAPP(X9187,esk265_4(X9187,X9188,X9189,X9190))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X9188),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9190,tc_fun(X9188,tc_HOL_Obool)),X9189),X9187)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9190),X9189))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UN])])])])])). 4.46/4.71 cnf(c_0_6912, plain, (hAPP(c_Finite__Set_Ocard(X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X3,tc_HOL_Obool)),X2))|esk66_3(X1,X2,X3)!=esk65_3(X1,X2,X3)|hAPP(c_Finite__Set_Ocard(X3),esk64_3(X1,X2,X3))!=X1|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3,tc_HOL_Obool)),X2))), inference(split_conjunct,[status(thm)],[c_0_5070])). 4.46/4.71 cnf(c_0_6913, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))=c_Groups_Oone__class_Oone(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[c_0_5205, c_0_4471])). 4.46/4.71 fof(c_0_6914, plain, ![X16083, X16084, X16085]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16085),X16084))|(~hBOOL(hAPP(hAPP(c_member(X16085),X16083),X16084))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X16085),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16085,tc_HOL_Obool)),X16084),hAPP(hAPP(c_Set_Oinsert(X16085),X16083),c_Orderings_Obot__class_Obot(tc_fun(X16085,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X16085),X16084))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff1__less])])). 4.46/4.71 fof(c_0_6915, plain, ![X3776, X3777]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3777))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3776),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X3777,X3776)=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3777),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3776)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__pos__neg])])])). 4.46/4.71 fof(c_0_6916, plain, ![X1241, X1242]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1242),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1241),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1242,X1241)=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1242),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1241)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__neg])])). 4.46/4.71 fof(c_0_6917, plain, ![X2375, X2376, X2377, X2378, X2379, X2381]:(((hBOOL(hAPP(hAPP(c_member(X2378),esk63_5(X2375,X2376,X2377,X2378,X2379)),X2377))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2379),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2378,X2379),X2377),X2376)),X2375))|~class_Complete__Lattice_Ocomplete__lattice(X2379))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2379),hAPP(X2376,esk63_5(X2375,X2376,X2377,X2378,X2379))),X2375))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2379),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2378,X2379),X2377),X2376)),X2375))|~class_Complete__Lattice_Ocomplete__lattice(X2379)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2379),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2378,X2379),X2377),X2376)),X2375))|(~hBOOL(hAPP(hAPP(c_member(X2378),X2381),X2377))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2379),hAPP(X2376,X2381)),X2375)))|~class_Complete__Lattice_Ocomplete__lattice(X2379))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUP__le__iff])])])])])])). 4.46/4.71 fof(c_0_6918, plain, ![X14233, X14234, X14235, X14236]:((hBOOL(hAPP(hAPP(c_member(X14235),esk416_4(X14233,X14234,X14235,X14236)),X14234))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14236),c_Groups_Ozero__class_Ozero(X14236)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X14235,X14236),X14233),X14234)))|~class_Rings_Olinordered__semidom(X14236))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14236),c_Groups_Ozero__class_Ozero(X14236)),hAPP(X14233,esk416_4(X14233,X14234,X14235,X14236))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14236),c_Groups_Ozero__class_Ozero(X14236)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X14235,X14236),X14233),X14234)))|~class_Rings_Olinordered__semidom(X14236))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__pos])])])])])). 4.46/4.71 cnf(c_0_6919, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X4))|X1!=X2|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)), inference(split_conjunct,[status(thm)],[c_0_5206])). 4.46/4.71 fof(c_0_6920, plain, ![X8341, X8342, X8343, X8344, X8345]:(c_Orderings_Otop__class_Otop(tc_fun(X8344,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X8345,X8344,X8343),c_Orderings_Otop__class_Otop(tc_fun(X8345,tc_HOL_Obool)))|(c_Orderings_Otop__class_Otop(tc_fun(X8342,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X8344,X8342,X8341),c_Orderings_Otop__class_Otop(tc_fun(X8344,tc_HOL_Obool)))|hAPP(c_Set_Oimage(X8345,X8342,hAPP(c_Fun_Ocomp(X8344,X8342,X8345,X8341),X8343)),c_Orderings_Otop__class_Otop(tc_fun(X8345,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X8342,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comp__surj])])])). 4.46/4.71 fof(c_0_6921, plain, ![X14758, X14759, X14760]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X14760,tc_HOL_Obool)),esk432_3(X14758,X14759,X14760)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X14760,tc_HOL_Obool)),X14759),X14758)))|c_Orderings_Obot__class_Obot(tc_fun(X14760,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14760,tc_HOL_Obool)),X14759),c_Complete__Lattice_OSup__class_OSup(tc_fun(X14760,tc_HOL_Obool),X14758))|hBOOL(hAPP(hAPP(c_member(tc_fun(X14760,tc_HOL_Obool)),X14759),X14758)))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X14760,tc_HOL_Obool)),esk433_3(X14758,X14759,X14760)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X14760,tc_HOL_Obool)),X14759),X14758)))|c_Orderings_Obot__class_Obot(tc_fun(X14760,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14760,tc_HOL_Obool)),X14759),c_Complete__Lattice_OSup__class_OSup(tc_fun(X14760,tc_HOL_Obool),X14758))|hBOOL(hAPP(hAPP(c_member(tc_fun(X14760,tc_HOL_Obool)),X14759),X14758)))&((esk433_3(X14758,X14759,X14760)!=esk432_3(X14758,X14759,X14760)|c_Orderings_Obot__class_Obot(tc_fun(X14760,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14760,tc_HOL_Obool)),X14759),c_Complete__Lattice_OSup__class_OSup(tc_fun(X14760,tc_HOL_Obool),X14758))|hBOOL(hAPP(hAPP(c_member(tc_fun(X14760,tc_HOL_Obool)),X14759),X14758)))&(c_Orderings_Obot__class_Obot(tc_fun(X14760,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14760,tc_HOL_Obool)),esk432_3(X14758,X14759,X14760)),esk433_3(X14758,X14759,X14760))|c_Orderings_Obot__class_Obot(tc_fun(X14760,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14760,tc_HOL_Obool)),X14759),c_Complete__Lattice_OSup__class_OSup(tc_fun(X14760,tc_HOL_Obool),X14758))|hBOOL(hAPP(hAPP(c_member(tc_fun(X14760,tc_HOL_Obool)),X14759),X14758)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insert__partition])])])])])). 4.46/4.71 fof(c_0_6922, plain, ![X11682, X11683, X11684, X11685]:((hBOOL(hAPP(hAPP(c_member(X11684),esk344_4(X11682,X11683,X11684,X11685)),X11683))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11685),c_Groups_Ozero__class_Ozero(X11685)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X11684,X11685),X11682),X11683)))|~class_Rings_Olinordered__semidom(X11685))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11685),c_Groups_Ozero__class_Ozero(X11685)),hAPP(X11682,esk344_4(X11682,X11683,X11684,X11685))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11685),c_Groups_Ozero__class_Ozero(X11685)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X11684,X11685),X11682),X11683)))|~class_Rings_Olinordered__semidom(X11685))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__nonneg])])])])])). 4.46/4.71 fof(c_0_6923, plain, ![X8593, X8594, X8595, X8596, X8597, X8599]:(((hBOOL(hAPP(hAPP(c_member(X8595),esk243_5(X8593,X8594,X8595,X8596,X8597)),X8594))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8597),X8596),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8595,X8597),X8594),X8593)))|~class_Complete__Lattice_Ocomplete__lattice(X8597))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8597),X8596),hAPP(X8593,esk243_5(X8593,X8594,X8595,X8596,X8597))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8597),X8596),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8595,X8597),X8594),X8593)))|~class_Complete__Lattice_Ocomplete__lattice(X8597)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8597),X8596),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8595,X8597),X8594),X8593)))|(~hBOOL(hAPP(hAPP(c_member(X8595),X8599),X8594))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8597),X8596),hAPP(X8593,X8599))))|~class_Complete__Lattice_Ocomplete__lattice(X8597))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__INF__iff])])])])])])). 4.46/4.71 cnf(c_0_6924, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X5))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5207])). 4.46/4.71 cnf(c_0_6925, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5208]), ['final']). 4.46/4.71 cnf(c_0_6926, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5207])). 4.46/4.71 fof(c_0_6927, plain, ![X10652, X10653, X10654]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10654))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10653))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10653),X10652))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X10654),X10652)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X10654),X10653)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2])])). 4.46/4.71 fof(c_0_6928, plain, ![X1073, X1074, X1075]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1075),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1074))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1074),X1073))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1075),X1074)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1075),X1073)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono2__neg])])])). 4.46/4.71 fof(c_0_6929, plain, ![X5257, X5258, X5259, X5260, X5261, X5262]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5262,X5261),tc_HOL_Obool)),X5260),hAPP(hAPP(c_Product__Type_OSigma(X5262,X5261),X5259),hAPP(c_COMBK(tc_fun(X5261,tc_HOL_Obool),X5262),X5258))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5261,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5262,X5261,X5260),X5257)),X5258))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Image__subset])])])). 4.46/4.71 fof(c_0_6930, plain, ![X694, X695, X696, X697, X698]:((hAPP(c_Option_Ooption_OSome(X697),X695)!=hAPP(hAPP(c_Map_Omap__of(X698,X697),X696),X694)|hBOOL(hAPP(hAPP(c_member(tc_prod(X698,X697)),hAPP(hAPP(c_Product__Type_OPair(X698,X697),X694),X695)),hAPP(c_List_Oset(tc_prod(X698,X697)),X696)))|~hBOOL(hAPP(c_List_Odistinct(X698),hAPP(hAPP(c_List_Omap(tc_prod(X698,X697),X698),c_Product__Type_Ofst(X698,X697)),X696))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X698,X697)),hAPP(hAPP(c_Product__Type_OPair(X698,X697),X694),X695)),hAPP(c_List_Oset(tc_prod(X698,X697)),X696)))|hAPP(c_Option_Ooption_OSome(X697),X695)=hAPP(hAPP(c_Map_Omap__of(X698,X697),X696),X694)|~hBOOL(hAPP(c_List_Odistinct(X698),hAPP(hAPP(c_List_Omap(tc_prod(X698,X697),X698),c_Product__Type_Ofst(X698,X697)),X696))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Some__eq__map__of__iff])])])). 4.46/4.71 fof(c_0_6931, plain, ![X1725, X1726]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1726),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1725),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1726),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1725))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1726),X1725))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__neg__neg])])])). 4.46/4.71 fof(c_0_6932, plain, ![X5894, X5895, X5896, X5897]:(c_Orderings_Otop__class_Otop(tc_fun(X5896,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X5897,X5896,X5895),c_Orderings_Otop__class_Otop(tc_fun(X5897,tc_HOL_Obool)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5896,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5896,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5897,X5896,X5895),X5894))),hAPP(c_Set_Oimage(X5897,X5896,X5895),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5897,tc_HOL_Obool)),X5894))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_surj__Compl__image__subset])])])). 4.46/4.71 fof(c_0_6933, plain, ![X8492, X8493, X8494]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8494),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8493)),X8492)))|hAPP(hAPP(c_List_Onth(X8493),X8492),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8493)),X8492)),hAPP(c_Nat_OSuc,X8494)))=hAPP(hAPP(c_List_Onth(X8493),hAPP(c_List_Orev(X8493),X8492)),X8494)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__nth])])). 4.46/4.71 fof(c_0_6934, plain, ![X6444, X6445, X6446]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6446),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6446,tc_HOL_Obool)),X6445),X6444)))|hAPP(c_Finite__Set_Ocard(X6446),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6446,tc_HOL_Obool)),X6445),X6444))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X6446),X6445)),hAPP(c_Finite__Set_Ocard(X6446),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6446,tc_HOL_Obool)),X6445),X6444)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff__subset__Int])])])). 4.46/4.71 cnf(c_0_6935, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),esk187_3(X3,X2,X1))),esk188_3(X3,X2,X1))|hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5209])). 4.46/4.71 fof(c_0_6936, plain, ![X7877, X7878, X7879, X7880, X7881, X7882, X7883]:(hBOOL(hAPP(hAPP(c_member(X7883),X7882),X7881))|(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7883,X7880,X7879,X7878,X7881),X7877))|hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7883,X7880,X7879,X7878,hAPP(hAPP(c_Set_Oinsert(X7883),X7882),X7881)),hAPP(hAPP(X7879,X7882),X7877))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__graph_OinsertI])])])). 4.46/4.71 cnf(c_0_6937, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),X4)=hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(X1)),X4)),c_Orderings_Otop__class_Otop(X1)),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5210])). 4.46/4.71 fof(c_0_6938, plain, ![X14622, X14623, X14624, X14625]:(~class_Orderings_Olinorder(X14625)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14625),X14624))|(~hBOOL(hAPP(hAPP(c_member(X14625),X14623),X14624))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14625),hAPP(hAPP(c_Finite__Set_Ofold(X14625,X14625,c_Orderings_Oord__class_Omin(X14625)),X14622),X14624)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X14625),X14623),X14622)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ofold__inf__le__inf])])])). 4.46/4.71 fof(c_0_6939, plain, ![X429, X430, X432, X433, X434, X435]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X430,X430)),hAPP(hAPP(c_Product__Type_OPair(X430,X430),hAPP(esk4_2(X429,X430),hAPP(c_Nat_OSuc,X432))),hAPP(esk4_2(X429,X430),X432))),X429))|c_Wellfounded_Owf(X430,X429))&(~c_Wellfounded_Owf(X434,X433)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X434,X434)),hAPP(hAPP(c_Product__Type_OPair(X434,X434),hAPP(X435,hAPP(c_Nat_OSuc,esk5_3(X433,X434,X435)))),hAPP(X435,esk5_3(X433,X434,X435)))),X433)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__iff__no__infinite__down__chain])])])])])). 4.46/4.71 fof(c_0_6940, plain, ![X8619, X8620, X8621, X8622, X8623]:(~class_Rings_Ocomm__semiring__1(X8623)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8623),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8623),X8622),X8620)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8623),X8621),X8619))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8623),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8623),X8622),X8621)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8623),X8620),X8619))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])])])). 4.46/4.71 fof(c_0_6941, plain, ![X3574, X3575, X3576, X3577]:(~class_Groups_Ocomm__monoid__add(X3577)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3577),X3576),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3575),hAPP(c_Nat_OSuc,X3574)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3577),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X3577,tc_Nat_Onat),X3576),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3575,X3574))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__shift__bounds__cl__Suc__ivl])])])). 4.46/4.71 fof(c_0_6942, plain, ![X4853, X4854, X4855, X4856]:(~class_Lattices_Osemilattice__inf(X4856)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4856),X4855))|(~hBOOL(hAPP(hAPP(c_member(X4856),X4854),X4855))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4856),hAPP(hAPP(c_Finite__Set_Ofold(X4856,X4856,c_Lattices_Osemilattice__inf__class_Oinf(X4856)),X4853),X4855)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4856),X4854),X4853)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__inf__le__inf])])])). 4.46/4.71 fof(c_0_6943, plain, ![X10568, X10569, X10570, X10571]:(~class_Orderings_Olinorder(X10571)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10571),X10570))|(~hBOOL(hAPP(hAPP(c_member(X10571),X10569),X10570))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10571),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10571),X10569),X10568)),hAPP(hAPP(c_Finite__Set_Ofold(X10571,X10571,c_Orderings_Oord__class_Omax(X10571)),X10568),X10570)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__le__fold__sup])])])). 4.46/4.71 fof(c_0_6944, plain, ![X17297, X17298, X17299, X17300]:(~class_Lattices_Osemilattice__sup(X17300)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17300),X17299))|(~hBOOL(hAPP(hAPP(c_member(X17300),X17298),X17299))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17300),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17300),X17298),X17297)),hAPP(hAPP(c_Finite__Set_Ofold(X17300,X17300,c_Lattices_Osemilattice__sup__class_Osup(X17300)),X17297),X17299)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__le__fold__sup])])])). 4.46/4.71 fof(c_0_6945, plain, ![X1799, X1800, X1801, X1802, X1803]:(~class_Rings_Ocomm__semiring__1(X1803)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1803),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1803),X1802),X1800)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1803),X1801),X1799))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1803),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1803),X1802),X1801)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1803),X1800),X1799))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])])])). 4.46/4.71 fof(c_0_6946, plain, ![X1085, X1086, X1087, X1088, X1089, X1090]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1090,X1089),tc_HOL_Obool)),X1088),X1087))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1090,tc_HOL_Obool)),X1086),X1085))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1089,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1090,X1089,X1088),X1086)),hAPP(c_Relation_OImage(X1090,X1089,X1087),X1085))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Image__mono])])])). 4.46/4.71 cnf(c_0_6947, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Com_Ocom_OBODY,X3)),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Com_Ocom_OBODY,X3)),X4)),X5),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X3))),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5211])). 4.46/4.71 fof(c_0_6948, plain, ![X16950, X16951, X16952, X16953, X16954, X16955, X16956]:((X16950=hAPP(hAPP(X16954,X16952),esk506_7(X16950,X16951,X16952,X16953,X16954,X16955,X16956))|hBOOL(hAPP(hAPP(c_member(X16956),X16952),X16951))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X16956,X16955,X16954,X16953,hAPP(hAPP(c_Set_Oinsert(X16956),X16952),X16951)),X16950))|~c_Finite__Set_Ofun__left__comm(X16956,X16955,X16954))&(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X16956,X16955,X16954,X16953,X16951),esk506_7(X16950,X16951,X16952,X16953,X16954,X16955,X16956)))|hBOOL(hAPP(hAPP(c_member(X16956),X16952),X16951))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X16956,X16955,X16954,X16953,hAPP(hAPP(c_Set_Oinsert(X16956),X16952),X16951)),X16950))|~c_Finite__Set_Ofun__left__comm(X16956,X16955,X16954))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE])])])])])). 4.46/4.71 cnf(c_0_6949, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3))),hAPP(X2,X3))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5212])). 4.46/4.71 fof(c_0_6950, plain, ![X15746, X15747, X15748, X15749, X15750, X15751, X15752, X15753]:(~c_Finite__Set_Ofolding__image__simple__idem(X15753,X15752,X15751,X15750,X15749,X15748)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15752),X15747))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15752),X15746))|hAPP(X15748,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15752,tc_HOL_Obool)),X15747),X15746))=hAPP(hAPP(X15751,hAPP(X15748,X15747)),hAPP(X15748,X15746))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Ounion__idem])])). 4.46/4.71 fof(c_0_6951, plain, ![X17490, X17491, X17492, X17493]:(~class_Int_Onumber__ring(X17493)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17493),hAPP(c_Int_Onumber__class_Onumber__of(X17493),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17492),X17491))),X17490)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17493),hAPP(c_Int_Onumber__class_Onumber__of(X17493),X17492)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17493),hAPP(c_Int_Onumber__class_Onumber__of(X17493),X17491)),X17490))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__number__of__left])])])). 4.46/4.71 fof(c_0_6952, plain, ![X3466, X3467, X3468, X3469]:(~class_Int_Onumber__ring(X3469)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3469),hAPP(c_Int_Onumber__class_Onumber__of(X3469),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3468),X3467))),X3466)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3469),hAPP(c_Int_Onumber__class_Onumber__of(X3469),X3468)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3469),hAPP(c_Int_Onumber__class_Onumber__of(X3469),X3467)),X3466))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__left])])). 4.46/4.71 fof(c_0_6953, plain, ![X15958, X15959, X15960, X15961]:(~class_Int_Onumber__ring(X15961)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15961),hAPP(c_Int_Onumber__class_Onumber__of(X15961),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15960),X15959))),X15958)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15961),hAPP(c_Int_Onumber__class_Onumber__of(X15961),X15960)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15961),hAPP(c_Int_Onumber__class_Onumber__of(X15961),X15959)),X15958))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__diff1])])). 4.46/4.71 fof(c_0_6954, plain, ![X8029, X8030, X8031, X8032, X8033, X8034, X8035, X8036]:(~c_List_Olist__all2(X8036,X8035,X8034,X8033,X8032)|(~hBOOL(hAPP(hAPP(X8034,X8031),X8030))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8029),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8035)),X8032)))|c_List_Olist__all2(X8036,X8035,X8034,hAPP(hAPP(c_List_Olist__update(X8036,X8033),X8029),X8031),hAPP(hAPP(c_List_Olist__update(X8035,X8032),X8029),X8030))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2__update__cong2])])])). 4.46/4.71 fof(c_0_6955, plain, ![X8720, X8721, X8722, X8723, X8724, X8725, X8726, X8727]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8727),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8726)),X8725)))|(~c_List_Olist__all2(X8726,X8724,X8723,X8725,X8722)|(~hBOOL(hAPP(hAPP(X8723,X8721),X8720))|c_List_Olist__all2(X8726,X8724,X8723,hAPP(hAPP(c_List_Olist__update(X8726,X8725),X8727),X8721),hAPP(hAPP(c_List_Olist__update(X8724,X8722),X8727),X8720))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__update__cong])])). 4.46/4.71 cnf(c_0_6956, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X8),X3),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X8),X1),X4)|hAPP(X1,hAPP(X2,esk270_8(X1,X3,X4,X5,X2,X6,X7,X8)))!=hAPP(X3,esk270_8(X1,X3,X4,X5,X2,X6,X7,X8))|X4!=hAPP(c_Set_Oimage(X7,X6,X2),X5)|~c_Fun_Oinj__on(X7,X6,X2,X5)|~class_Groups_Ocomm__monoid__add(X8)), inference(split_conjunct,[status(thm)],[c_0_5158])). 4.46/4.71 fof(c_0_6957, plain, ![X10958, X10959, X10960, X10961, X10962]:((hBOOL(hAPP(hAPP(c_member(X10962),X10958),hAPP(c_List_Oset(X10962),X10961)))|c_Option_Ooption_ONone(X10960)=hAPP(hAPP(c_Map_Omap__of(X10962,X10960),hAPP(hAPP(c_List_Ozip(X10962,X10960),X10961),X10959)),X10958)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10962)),X10961)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10960)),X10959))&(c_Option_Ooption_ONone(X10960)!=hAPP(hAPP(c_Map_Omap__of(X10962,X10960),hAPP(hAPP(c_List_Ozip(X10962,X10960),X10961),X10959)),X10958)|~hBOOL(hAPP(hAPP(c_member(X10962),X10958),hAPP(c_List_Oset(X10962),X10961)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10962)),X10961)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10960)),X10959))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__zip__is__None])])])])). 4.46/4.71 fof(c_0_6958, plain, ![X11859, X11860, X11861, X11862]:(~c_Fun_Oinj__on(X11862,X11861,X11860,c_Orderings_Otop__class_Otop(tc_fun(X11862,tc_HOL_Obool)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11861,tc_HOL_Obool)),hAPP(c_Set_Oimage(X11862,X11861,X11860),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11862,tc_HOL_Obool)),X11859))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11861,tc_HOL_Obool)),hAPP(c_Set_Oimage(X11862,X11861,X11860),X11859))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__image__Compl__subset])])])). 4.46/4.71 cnf(c_0_6959, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBS(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X3)),X4))))|~class_Enum_Oenum(X1)|~class_Orderings_Oorder(X2)), inference(split_conjunct,[status(thm)],[c_0_5192])). 4.46/4.71 cnf(c_0_6960, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))),X2)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[c_0_5213, c_0_4431])). 4.46/4.71 cnf(c_0_6961, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),c_List_OtakeWhile(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5))|hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)!=c_List_OdropWhile(X2,X3,X1)), inference(split_conjunct,[status(thm)],[c_0_5127])). 4.46/4.71 cnf(c_0_6962, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Oimage(tc_prod(X1,X3),X1,c_Product__Type_Ofst(X1,X3)),hAPP(c_List_Oset(tc_prod(X1,X3)),X4))))|hAPP(hAPP(c_Map_Omap__of(X1,X3),X4),X2)=c_Option_Ooption_ONone(X3)), inference(split_conjunct,[status(thm)],[c_0_5214])). 4.46/4.71 fof(c_0_6963, plain, ![X10687, X10688]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10688))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10687))|hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X10688),X10687)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X10688,X10687))=c_Divides_OposDivAlg(X10688,X10687))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_posDivAlg__div__mod])])])). 4.46/4.71 cnf(c_0_6964, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X3))),hAPP(X2,hAPP(c_Nat_OSuc,X3)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5215])). 4.46/4.71 cnf(c_0_6965, plain, (hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_5216]), ['final']). 4.46/4.71 fof(c_0_6966, plain, ![X3353, X3354, X3355]:((hBOOL(hAPP(hAPP(c_member(X3355),esk88_3(X3353,X3354,X3355)),X3354))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3355,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X3355),c_Int_Onat),X3353)),X3354))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3355,tc_Int_Oint),X3353),X3354))&(~c_Nat__Transfer_Ois__nat(hAPP(X3353,esk88_3(X3353,X3354,X3355)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3355,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X3355),c_Int_Onat),X3353)),X3354))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3355,tc_Int_Oint),X3353),X3354))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__int__nat__sum__prod2_I1_J])])])])])). 4.46/4.71 fof(c_0_6967, plain, ![X14293, X14294, X14295, X14296, X14297, X14299, X14300, X14301, X14302, X14303, X14304]:(((hBOOL(hAPP(hAPP(c_member(X14295),esk420_5(X14293,X14294,X14295,X14296,X14297)),X14294))|hBOOL(hAPP(hAPP(c_member(X14297),X14296),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14295,tc_fun(X14297,tc_HOL_Obool)),X14294),X14293))))&(~hBOOL(hAPP(hAPP(c_member(X14297),X14296),hAPP(X14293,esk420_5(X14293,X14294,X14295,X14296,X14297))))|hBOOL(hAPP(hAPP(c_member(X14297),X14296),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14295,tc_fun(X14297,tc_HOL_Obool)),X14294),X14293)))))&(~hBOOL(hAPP(hAPP(c_member(X14303),X14302),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14301,tc_fun(X14303,tc_HOL_Obool)),X14300),X14299)))|(~hBOOL(hAPP(hAPP(c_member(X14301),X14304),X14300))|hBOOL(hAPP(hAPP(c_member(X14303),X14302),hAPP(X14299,X14304)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__iff])])])])])])). 4.46/4.71 fof(c_0_6968, plain, ![X8586, X8587, X8588]:(~class_Orderings_Olinorder(X8588)|(hAPP(hAPP(c_Orderings_Oord__class_Omax(X8588),hAPP(X8587,esk241_3(X8586,X8587,X8588))),hAPP(X8587,esk242_3(X8586,X8587,X8588)))!=hAPP(X8587,hAPP(hAPP(c_Orderings_Oord__class_Omax(X8588),esk241_3(X8586,X8587,X8588)),esk242_3(X8586,X8587,X8588)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8588),X8586))|(c_Orderings_Obot__class_Obot(tc_fun(X8588,tc_HOL_Obool))=X8586|hAPP(X8587,c_Big__Operators_Olinorder__class_OMax(X8588,X8586))=c_Big__Operators_Olinorder__class_OMax(X8588,hAPP(c_Set_Oimage(X8588,X8588,X8587),X8586)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Ohom__commute])])])])). 4.46/4.71 fof(c_0_6969, plain, ![X10879, X10880, X10881]:(~class_Lattices_Olattice(X10881)|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10881),hAPP(X10880,esk323_3(X10879,X10880,X10881))),hAPP(X10880,esk324_3(X10879,X10880,X10881)))!=hAPP(X10880,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10881),esk323_3(X10879,X10880,X10881)),esk324_3(X10879,X10880,X10881)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10881),X10879))|(X10879=c_Orderings_Obot__class_Obot(tc_fun(X10881,tc_HOL_Obool))|hAPP(X10880,c_Big__Operators_Olattice__class_OInf__fin(X10881,X10879))=c_Big__Operators_Olattice__class_OInf__fin(X10881,hAPP(c_Set_Oimage(X10881,X10881,X10880),X10879)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Ohom__commute])])])])). 4.46/4.71 fof(c_0_6970, plain, ![X2361, X2362, X2363]:(~class_Lattices_Olattice(X2363)|(hAPP(X2362,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2363),esk60_3(X2361,X2362,X2363)),esk61_3(X2361,X2362,X2363)))!=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2363),hAPP(X2362,esk60_3(X2361,X2362,X2363))),hAPP(X2362,esk61_3(X2361,X2362,X2363)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2363),X2361))|(X2361=c_Orderings_Obot__class_Obot(tc_fun(X2363,tc_HOL_Obool))|hAPP(X2362,c_Big__Operators_Olattice__class_OSup__fin(X2363,X2361))=c_Big__Operators_Olattice__class_OSup__fin(X2363,hAPP(c_Set_Oimage(X2363,X2363,X2362),X2361)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Ohom__commute])])])])). 4.46/4.71 fof(c_0_6971, plain, ![X1948, X1949, X1950]:(~class_Orderings_Olinorder(X1950)|(hAPP(X1949,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1950),esk49_3(X1948,X1949,X1950)),esk50_3(X1948,X1949,X1950)))!=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1950),hAPP(X1949,esk49_3(X1948,X1949,X1950))),hAPP(X1949,esk50_3(X1948,X1949,X1950)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1950),X1948))|(X1948=c_Orderings_Obot__class_Obot(tc_fun(X1950,tc_HOL_Obool))|hAPP(X1949,c_Big__Operators_Olinorder__class_OMin(X1950,X1948))=c_Big__Operators_Olinorder__class_OMin(X1950,hAPP(c_Set_Oimage(X1950,X1950,X1949),X1948)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Ohom__commute])])])])). 4.46/4.71 cnf(c_0_6972, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X8),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X1),X7),X6)|~class_Groups_Ocomm__monoid__mult(X1)|~c_Fun_Oinj__on(X2,X3,X4,X5)|hAPP(c_Set_Oimage(X2,X3,X4),X5)!=X6|hAPP(c_Fun_Ocomp(X3,X1,X2,X7),X4)!=X8), inference(split_conjunct,[status(thm)],[c_0_5217])). 4.46/4.71 cnf(c_0_6973, plain, (~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X1))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2)))))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_5218])). 4.46/4.71 cnf(c_0_6974, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(c_Fun_Ocomp(X1,X1,X2,c_Groups_Ouminus__class_Ouminus(X1)),X3)),X4))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5219])). 4.46/4.71 cnf(c_0_6975, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Omap(X4,X1),X5),X6))=hAPP(hAPP(c_List_Omap(X4,X2),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6)), inference(split_conjunct,[status(thm)],[c_0_5220]), ['final']). 4.46/4.71 fof(c_0_6976, plain, ![X6106, X6107]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6107),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6106))|hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6107),X6106)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6107,X6106))=c_Divides_OnegDivAlg(X6107,X6106))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_negDivAlg__div__mod])])])). 4.46/4.71 fof(c_0_6977, plain, ![X10187, X10188, X10189, X10190]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10190),X10189))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10190,X10190),tc_HOL_Obool)),X10188),hAPP(hAPP(c_Product__Type_OSigma(X10190,X10190),X10189),hAPP(c_COMBK(tc_fun(X10190,tc_HOL_Obool),X10190),X10189))))|(~hBOOL(hAPP(hAPP(c_member(tc_fun(X10190,tc_HOL_Obool)),X10187),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10190),X10189),X10188)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X10190),X10187))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__equiv__class])])])). 4.46/4.71 fof(c_0_6978, plain, ![X4620, X4621, X4622, X4623, X4624]:(~c_Finite__Set_Ofolding__one__idem(X4624,X4623,X4622)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4624),X4621))|(X4621=c_Orderings_Obot__class_Obot(tc_fun(X4624,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4624),X4620))|(c_Orderings_Obot__class_Obot(tc_fun(X4624,tc_HOL_Obool))=X4620|hAPP(hAPP(X4623,hAPP(X4622,X4621)),hAPP(X4622,X4620))=hAPP(X4622,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4624,tc_HOL_Obool)),X4621),X4620))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one__idem_Ounion__idem])])])). 4.46/4.71 fof(c_0_6979, plain, ![X15376, X15377, X15378, X15379, X15380]:(~class_Fields_Ofield__inverse__zero(X15380)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15380),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15380),X15379),X15378)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15380),X15377),X15376))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15380),X15379),X15377)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15380),X15378),X15376))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_times__divide__times__eq])])])). 4.46/4.71 cnf(c_0_6980, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5221, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.71 cnf(c_0_6981, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk533_3(X2,X1,X3))),esk534_3(X2,X1,X3))=X2|epred1_3(X3,X1,X2)|~hBOOL(hAPP(X3,esk532_3(X2,X1,X3)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.71 cnf(c_0_6982, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk531_3(X2,X3,X1))),esk532_3(X2,X3,X1))=X2|epred1_3(X1,X3,X2)|~hBOOL(hAPP(X1,esk534_3(X2,X3,X1)))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.71 cnf(c_0_6983, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk93_4(X2,X3,X1,X4)),X3))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|hAPP(X2,X4)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_5222])). 4.46/4.71 cnf(c_0_6984, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5223, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.71 cnf(c_0_6985, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5224, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.71 cnf(c_0_6986, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X3))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_5140])). 4.46/4.71 cnf(c_0_6987, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5225, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.71 fof(c_0_6988, plain, ![X9277, X9278, X9279]:(~class_Groups_Ocomm__monoid__add(X9279)|~class_Groups_Ocomm__monoid__mult(X9279)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X9279),X9278),X9277)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X9279),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X9279,tc_Int_Oint),X9278),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X9277))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__nat__int__sum__prod_I2_J])])])). 4.46/4.71 fof(c_0_6989, plain, ![X2112, X2113, X2114]:(~class_Groups_Ocomm__monoid__add(X2114)|~class_Groups_Ocomm__monoid__mult(X2114)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X2114),X2113),X2112)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X2114),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X2114,tc_Int_Oint),X2113),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2112))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__nat__int__sum__prod_I1_J])])])). 4.46/4.71 cnf(c_0_6990, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3))),esk538_3(X1,X2,X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|epred2_3(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5124])). 4.46/4.71 cnf(c_0_6991, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk535_3(X2,X1,X3))),esk536_3(X2,X1,X3))|epred2_3(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5124])). 4.46/4.71 fof(c_0_6992, plain, ![X16886, X16887, X16888, X16889, X16890, X16891]:(~class_Divides_Osemiring__div(X16891)|(c_Divides_Odiv__class_Omod(X16891,X16888,X16889)!=c_Divides_Odiv__class_Omod(X16891,X16890,X16889)|(c_Divides_Odiv__class_Omod(X16891,X16887,X16889)!=c_Divides_Odiv__class_Omod(X16891,X16886,X16889)|c_Divides_Odiv__class_Omod(X16891,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16891),X16890),X16887),X16889)=c_Divides_Odiv__class_Omod(X16891,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16891),X16888),X16886),X16889)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__mult__cong])])])). 4.46/4.71 cnf(c_0_6993, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__sup__class_Osup(X1)),X4)),c_Orderings_Obot__class_Obot(X1)),X3)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),X4)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5226])). 4.46/4.71 cnf(c_0_6994, plain, (hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X3)))),X2)=c_List_Osublist(X1,X2,X3)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5227])). 4.46/4.71 fof(c_0_6995, plain, ![X15356, X15357, X15358, X15359, X15360]:(~c_Fun_Oinj__on(X15360,X15359,X15358,X15357)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15359,tc_HOL_Obool)),hAPP(c_Set_Oimage(X15360,X15359,X15358),X15357)),X15356))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15359),X15356))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X15360),X15357)),hAPP(c_Finite__Set_Ocard(X15359),X15356)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__inj__on__le])])])). 4.46/4.71 fof(c_0_6996, plain, ![X4579, X4580, X4581, X4582, X4583]:(~c_Finite__Set_Ofun__left__comm__idem(X4583,X4582,X4581)|hAPP(c_List_Ofoldl(X4582,X4583,hAPP(c_COMBC(X4583,X4582,X4582),X4581),X4580),X4579)=hAPP(hAPP(c_Finite__Set_Ofold(X4583,X4582,X4581),X4580),hAPP(c_List_Oset(X4583),X4579))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__set])])). 4.46/4.71 fof(c_0_6997, plain, ![X5511, X5512, X5513, X5514]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5513,tc_Nat_Onat),X5511),X5512)))|(~hBOOL(hAPP(hAPP(c_member(X5513),X5514),X5512))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X5511,X5514))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5513),X5512)))&((hBOOL(hAPP(hAPP(c_member(X5513),esk167_3(X5511,X5512,X5513)),X5512))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5513,tc_Nat_Onat),X5511),X5512)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5513),X5512)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X5511,esk167_3(X5511,X5512,X5513))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5513,tc_Nat_Onat),X5511),X5512)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5513),X5512))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__pos__nat__iff])])])])])])). 4.46/4.71 cnf(c_0_6998, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk436_4(X1,X2,X3,X4)),esk435_4(X1,X2,X3,X4))=X4|X2=X4|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)!=X2|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5198])). 4.46/4.71 fof(c_0_6999, plain, ![X8425, X8426, X8427, X8428]:(~class_Orderings_Olinorder(X8428)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8428),X8427),X8426))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8428),X8426),X8425))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8428,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X8428,X8427),X8426)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X8428,X8426),X8425))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X8428,X8427),X8425)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I17_J])])])). 4.46/4.71 fof(c_0_7000, plain, ![X13106, X13107, X13108]:(~class_Groups_Oordered__ab__group__add__abs(X13108)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13108),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13108),hAPP(c_Groups_Oabs__class_Oabs(X13108),X13107)),hAPP(c_Groups_Oabs__class_Oabs(X13108),X13106))),hAPP(c_Groups_Oabs__class_Oabs(X13108),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13108),X13107),X13106))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2])])). 4.46/4.71 fof(c_0_7001, plain, ![X683, X684, X685, X686, X687]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X687,X686)),hAPP(hAPP(c_Product__Type_OPair(X687,X686),X685),X684)),hAPP(c_Relation_Oconverse(X686,X687),X683)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X686,X687)),hAPP(hAPP(c_Product__Type_OPair(X686,X687),X684),X685)),X683)))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X686,X687)),hAPP(hAPP(c_Product__Type_OPair(X686,X687),X684),X685)),X683))|hBOOL(hAPP(hAPP(c_member(tc_prod(X687,X686)),hAPP(hAPP(c_Product__Type_OPair(X687,X686),X685),X684)),hAPP(c_Relation_Oconverse(X686,X687),X683))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__iff])])). 4.46/4.71 fof(c_0_7002, plain, ![X16206, X16207, X16208]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X16208,X16208),tc_HOL_Obool)),X16207),X16206))|(~c_Relation_Orefl__on(X16208,c_Orderings_Otop__class_Otop(tc_fun(X16208,tc_HOL_Obool)),X16206)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X16208),tc_List_Olist(X16208)),tc_HOL_Obool)),c_List_Olistrel1(X16208,X16207)),c_List_Olistrel(X16208,X16206))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel1__subset__listrel])])])). 4.46/4.71 cnf(c_0_7003, plain, (X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk258_4(X2,X3,X4,X1)),esk257_4(X2,X3,X4,X1))|X1=X3|X3!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X4)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))), inference(split_conjunct,[status(thm)],[c_0_5203])). 4.46/4.71 fof(c_0_7004, plain, ![X6206, X6207, X6208]:(~class_Groups_Oordered__ab__group__add__abs(X6208)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6208),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X6208),hAPP(c_Groups_Oabs__class_Oabs(X6208),X6207)),hAPP(c_Groups_Oabs__class_Oabs(X6208),X6206))),hAPP(c_Groups_Oabs__class_Oabs(X6208),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X6208),X6206),X6207))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__triangle__ineq2__sym])])])). 4.46/4.71 fof(c_0_7005, plain, ![X15796, X15797, X15798]:(~class_Groups_Oordered__ab__group__add__abs(X15798)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15798),hAPP(c_Groups_Oabs__class_Oabs(X15798),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15798),X15797),X15796))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15798),hAPP(c_Groups_Oabs__class_Oabs(X15798),X15797)),hAPP(c_Groups_Oabs__class_Oabs(X15798),X15796))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq])])). 4.46/4.71 fof(c_0_7006, plain, ![X13076, X13077, X13078]:(~class_Groups_Oordered__ab__group__add__abs(X13078)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13078),hAPP(c_Groups_Oabs__class_Oabs(X13078),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13078),X13077),X13076))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13078),hAPP(c_Groups_Oabs__class_Oabs(X13078),X13077)),hAPP(c_Groups_Oabs__class_Oabs(X13078),X13076))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__triangle__ineq4])])])). 4.46/4.71 fof(c_0_7007, plain, ![X14636, X14637, X14638, X14639]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X14639,X14639)),X14638),c_Transitive__Closure_Ortrancl(X14639,X14637)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X14639,X14639)),X14638),c_Transitive__Closure_Ortrancl(X14639,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X14639,X14639),tc_HOL_Obool)),X14637),X14636)))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X14639,X14639)),X14638),c_Transitive__Closure_Ortrancl(X14639,X14636)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X14639,X14639)),X14638),c_Transitive__Closure_Ortrancl(X14639,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X14639,X14639),tc_HOL_Obool)),X14637),X14636)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__rtrancl__UnI])])])])). 4.46/4.71 fof(c_0_7008, plain, ![X5888, X5889, X5890, X5891, X5892, X5893]:(X5892=X5893|hAPP(hAPP(c_List_Olist__update(X5891,hAPP(hAPP(c_List_Olist__update(X5891,X5890),X5893),X5889)),X5892),X5888)=hAPP(hAPP(c_List_Olist__update(X5891,hAPP(hAPP(c_List_Olist__update(X5891,X5890),X5892),X5888)),X5893),X5889)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__update__swap])])])). 4.46/4.71 fof(c_0_7009, plain, ![X7657, X7658, X7659, X7660, X7661, X7662]:(~class_Divides_Osemiring__div(X7662)|(c_Divides_Odiv__class_Omod(X7662,X7661,X7660)!=c_Divides_Odiv__class_Omod(X7662,X7659,X7660)|(c_Divides_Odiv__class_Omod(X7662,X7657,X7660)!=c_Divides_Odiv__class_Omod(X7662,X7658,X7660)|c_Divides_Odiv__class_Omod(X7662,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7662),X7661),X7658),X7660)=c_Divides_Odiv__class_Omod(X7662,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7662),X7659),X7657),X7660)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__add__cong])])])). 4.46/4.71 fof(c_0_7010, plain, ![X3327, X3328, X3329]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3329),X3328))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3329),X3327))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3329,tc_HOL_Obool)),X3328),X3327)!=c_Orderings_Obot__class_Obot(tc_fun(X3329,tc_HOL_Obool))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X3329),X3328)),hAPP(c_Finite__Set_Ocard(X3329),X3327))=hAPP(c_Finite__Set_Ocard(X3329),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3329,tc_HOL_Obool)),X3328),X3327))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Un__disjoint])])])). 4.46/4.71 fof(c_0_7011, plain, ![X7966, X7967, X7968, X7969]:(~class_Fields_Ofield(X7969)|(X7968=c_Groups_Ozero__class_Ozero(X7969)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7969),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7969),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7969),X7968),X7967)),X7966)),X7968)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7969),X7967),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7969),X7966),X7968)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__eq__iff])])). 4.46/4.71 fof(c_0_7012, plain, ![X2642, X2643, X2644, X2645, X2646]:(hAPP(c_Option_Ooption_OSome(X2645),X2642)!=hAPP(hAPP(c_Map_Omap__of(X2646,X2645),X2644),X2643)|hBOOL(hAPP(hAPP(c_member(tc_prod(X2646,X2645)),hAPP(hAPP(c_Product__Type_OPair(X2646,X2645),X2643),X2642)),hAPP(c_List_Oset(tc_prod(X2646,X2645)),X2644)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__is__SomeD])])). 4.46/4.71 fof(c_0_7013, plain, ![X15636, X15637, X15638]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15638),X15637),c_Groups_Ozero__class_Ozero(X15638)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15638),X15636),c_Groups_Ozero__class_Ozero(X15638)))|hAPP(c_Groups_Oabs__class_Oabs(X15638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15638),X15637),X15636))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15638),hAPP(c_Groups_Oabs__class_Oabs(X15638),X15637)),hAPP(c_Groups_Oabs__class_Oabs(X15638),X15636))|~class_Rings_Oordered__ring__abs(X15638))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15638),c_Groups_Ozero__class_Ozero(X15638)),X15637))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15638),X15636),c_Groups_Ozero__class_Ozero(X15638)))|hAPP(c_Groups_Oabs__class_Oabs(X15638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15638),X15637),X15636))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15638),hAPP(c_Groups_Oabs__class_Oabs(X15638),X15637)),hAPP(c_Groups_Oabs__class_Oabs(X15638),X15636))|~class_Rings_Oordered__ring__abs(X15638)))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15638),X15637),c_Groups_Ozero__class_Ozero(X15638)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15638),c_Groups_Ozero__class_Ozero(X15638)),X15636))|hAPP(c_Groups_Oabs__class_Oabs(X15638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15638),X15637),X15636))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15638),hAPP(c_Groups_Oabs__class_Oabs(X15638),X15637)),hAPP(c_Groups_Oabs__class_Oabs(X15638),X15636))|~class_Rings_Oordered__ring__abs(X15638))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15638),c_Groups_Ozero__class_Ozero(X15638)),X15637))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15638),c_Groups_Ozero__class_Ozero(X15638)),X15636))|hAPP(c_Groups_Oabs__class_Oabs(X15638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15638),X15637),X15636))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15638),hAPP(c_Groups_Oabs__class_Oabs(X15638),X15637)),hAPP(c_Groups_Oabs__class_Oabs(X15638),X15636))|~class_Rings_Oordered__ring__abs(X15638)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__mult])])])). 4.46/4.71 fof(c_0_7014, plain, ![X480, X481, X482, X483]:(~class_Fields_Ofield(X483)|(X482=c_Groups_Ozero__class_Ozero(X483)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X483),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X483),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X483),X482),X481)),X480)),X482)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X483),X481),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X483),X480),X482)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__eq__iff])])). 4.46/4.71 fof(c_0_7015, plain, ![X16562, X16563, X16564, X16565, X16566, X16567]:(~class_Divides_Oring__div(X16567)|(c_Divides_Odiv__class_Omod(X16567,X16564,X16565)!=c_Divides_Odiv__class_Omod(X16567,X16566,X16565)|(c_Divides_Odiv__class_Omod(X16567,X16562,X16565)!=c_Divides_Odiv__class_Omod(X16567,X16563,X16565)|c_Divides_Odiv__class_Omod(X16567,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X16567),X16566),X16563),X16565)=c_Divides_Odiv__class_Omod(X16567,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X16567),X16564),X16562),X16565)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__diff__cong])])])). 4.46/4.71 fof(c_0_7016, plain, ![X4584, X4585, X4586]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4586,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4586,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk125_3(X4584,X4585,X4586))),X4585)),X4584))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4586,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4586,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X4585)),X4584))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite__subset])])])). 4.46/4.71 fof(c_0_7017, plain, ![X8807, X8808, X8809, X8810]:(~class_Fields_Ofield__inverse__zero(X8810)|(c_Groups_Ozero__class_Ozero(X8810)=X8809|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8810),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8810),X8808),X8809)),X8807)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8810),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8810),X8808),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8810),X8807),X8809))),X8809))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__frac__num])])])). 4.46/4.71 fof(c_0_7018, plain, ![X8885, X8886, X8887, X8888]:((hBOOL(hAPP(hAPP(c_member(X8887),esk253_4(X8885,X8886,X8887,X8888)),hAPP(c_List_Oset(X8887),X8886)))|hBOOL(hAPP(X8885,hAPP(hAPP(c_List_Onth(X8887),X8886),X8888)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8888),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8887)),X8886))))&(~hBOOL(hAPP(X8885,esk253_4(X8885,X8886,X8887,X8888)))|hBOOL(hAPP(X8885,hAPP(hAPP(c_List_Onth(X8887),X8886),X8888)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8888),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8887)),X8886))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__ball__nth])])])])])). 4.46/4.71 fof(c_0_7019, plain, ![X14827, X14828, X14829, X14830, X14831, X14832, X14833]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X14829,X14829)),X14828),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X14829,X14829),tc_HOL_Obool),X14830),X14827)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X14829,X14829)),X14828),c_Transitive__Closure_Ortrancl(X14829,X14827))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X14833,X14833)),X14832),c_Transitive__Closure_Ortrancl(X14833,X14831)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X14833,X14833)),X14832),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X14833,X14833),tc_HOL_Obool),esk434_3(X14831,X14832,X14833)),X14831))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__power])])])])])). 4.46/4.71 fof(c_0_7020, plain, ![X3661, X3662, X3663, X3664]:(~class_Fields_Ofield(X3664)|(c_Groups_Ozero__class_Ozero(X3664)=X3663|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3664),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3664),X3662),X3663)),X3661)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3664),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3664),X3662),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3664),X3663),X3661))),X3663))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__diff__eq__iff])])). 4.46/4.71 fof(c_0_7021, plain, ![X12045, X12046, X12047, X12048, X12049]:(~c_Fun_Oinj__on(X12049,X12048,X12047,c_Orderings_Otop__class_Otop(tc_fun(X12049,tc_HOL_Obool)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12048,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12049,X12048,X12047),X12046)),hAPP(c_Set_Oimage(X12049,X12048,X12047),X12045))=hAPP(c_Set_Oimage(X12049,X12048,X12047),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12049,tc_HOL_Obool)),X12046),X12045))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Int])])). 4.46/4.71 fof(c_0_7022, plain, ![X17167, X17168, X17169, X17170, X17171]:(~c_Fun_Oinj__on(X17171,X17170,X17169,c_Orderings_Otop__class_Otop(tc_fun(X17171,tc_HOL_Obool)))|hAPP(c_Set_Oimage(X17171,X17170,X17169),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17171,tc_HOL_Obool)),X17168),X17167))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17170,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17171,X17170,X17169),X17168)),hAPP(c_Set_Oimage(X17171,X17170,X17169),X17167))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__set__diff])])). 4.46/4.71 fof(c_0_7023, plain, ![X3940, X3941, X3942, X3943]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3942,X3943)),X3941),X3940))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X3942),hAPP(hAPP(c_COMBS(X3942,X3943,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X3943,tc_fun(X3943,tc_HOL_Obool),X3942),c_Orderings_Oord__class_Oless__eq(X3943)),X3941)),X3940)))|(~class_Orderings_Oorder(X3943)|~class_Enum_Oenum(X3942)))&(~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X3942),hAPP(hAPP(c_COMBS(X3942,X3943,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X3943,tc_fun(X3943,tc_HOL_Obool),X3942),c_Orderings_Oord__class_Oless__eq(X3943)),X3941)),X3940)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3942,X3943)),X3941),X3940))|(~class_Orderings_Oorder(X3943)|~class_Enum_Oenum(X3942)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__fun_I1_J])])])). 4.46/4.71 fof(c_0_7024, plain, ![X11299, X11300, X11301, X11302, X11303]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11303),hAPP(c_Set_Oimage(X11302,X11303,X11301),c_Orderings_Otop__class_Otop(tc_fun(X11302,tc_HOL_Obool)))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X11300),hAPP(c_Set_Oimage(X11302,X11300,hAPP(hAPP(c_COMBB(X11303,X11300,X11302),X11299),X11301)),c_Orderings_Otop__class_Otop(tc_fun(X11302,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__range__imageI])])])). 4.46/4.71 fof(c_0_7025, plain, ![X10866, X10867, X10868, X10869]:(~class_Fields_Ofield(X10869)|(X10868=c_Groups_Ozero__class_Ozero(X10869)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10869),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10869),X10867),X10868)),X10866)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10869),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10869),X10867),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10869),X10868),X10866))),X10868))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__add__eq__iff])])])). 4.46/4.71 fof(c_0_7026, plain, ![X2291, X2292]:(~class_Orderings_Olinorder(X2292)|c_List_Olinorder__class_Osort__key(X2292,X2292,c_COMBI(X2292),X2291)=hAPP(c_List_Ofoldl(tc_List_Olist(X2292),X2292,hAPP(c_COMBC(X2292,tc_List_Olist(X2292),tc_List_Olist(X2292)),c_List_Olinorder__class_Oinsort__key(X2292,X2292,c_COMBI(X2292))),c_List_Olist_ONil(X2292)),X2291)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sort__foldl__insort])])). 4.46/4.71 fof(c_0_7027, plain, ![X10783, X10784, X10785, X10786]:(~class_Divides_Osemiring__div(X10786)|(c_Groups_Ozero__class_Ozero(X10786)=X10785|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10786),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10786),X10784),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10786),X10785),X10783))),X10785)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10786),X10783),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10786),X10784),X10785)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__self2])])])). 4.46/4.71 fof(c_0_7028, plain, ![X14603, X14604, X14605, X14606]:(~class_Fields_Ofield(X14606)|(X14605=c_Groups_Ozero__class_Ozero(X14606)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14604),X14603))|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14606),hAPP(hAPP(c_Power_Opower__class_Opower(X14606),X14605),X14603)),hAPP(hAPP(c_Power_Opower__class_Opower(X14606),X14605),X14604))=hAPP(hAPP(c_Power_Opower__class_Opower(X14606),X14605),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14603),X14604))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__diff])])])). 4.46/4.71 fof(c_0_7029, plain, ![X14743, X14744, X14745]:(~class_Rings_Olinordered__semidom(X14745)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14745),c_Groups_Oone__class_Oone(X14745)),X14744))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14745),hAPP(hAPP(c_Power_Opower__class_Opower(X14745),X14744),X14743)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14745),X14744),hAPP(hAPP(c_Power_Opower__class_Opower(X14745),X14744),X14743)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__less__power__Suc])])])). 4.46/4.71 fof(c_0_7030, plain, ![X612, X613, X614, X615]:(~class_Divides_Osemiring__div(X615)|(c_Groups_Ozero__class_Ozero(X615)=X614|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X615),X612),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X615),X613),X614))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X615),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X615),X613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X615),X612),X614))),X614))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__self1])])])). 4.46/4.71 fof(c_0_7031, plain, ![X1931, X1932, X1933, X1934]:(~class_Orderings_Olinorder(X1934)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1934),X1933))|hAPP(hAPP(c_Finite__Set_Ofold(X1934,X1934,c_Orderings_Oord__class_Omax(X1934)),X1932),hAPP(hAPP(c_Set_Oinsert(X1934),X1931),X1933))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1934),X1931),hAPP(hAPP(c_Finite__Set_Ofold(X1934,X1934,c_Orderings_Oord__class_Omax(X1934)),X1932),X1933)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ofold__sup__insert])])])). 4.46/4.71 fof(c_0_7032, plain, ![X5780, X5781, X5782, X5783]:(~class_Orderings_Olinorder(X5783)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5783),X5782))|hAPP(hAPP(c_Finite__Set_Ofold(X5783,X5783,c_Orderings_Oord__class_Omin(X5783)),X5781),hAPP(hAPP(c_Set_Oinsert(X5783),X5780),X5782))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5783),X5780),hAPP(hAPP(c_Finite__Set_Ofold(X5783,X5783,c_Orderings_Oord__class_Omin(X5783)),X5781),X5782)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ofold__inf__insert])])])). 4.46/4.71 fof(c_0_7033, plain, ![X11905, X11906, X11907, X11908]:(~class_Fields_Ofield__inverse__zero(X11908)|(X11907=c_Groups_Ozero__class_Ozero(X11908)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11908),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11908),X11905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11908),X11906),X11907))),X11907)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11908),X11906),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11908),X11905),X11907)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__num__frac])])])). 4.46/4.71 fof(c_0_7034, plain, ![X6001, X6002, X6003, X6004]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6004),X6003))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6002,tc_HOL_Obool)),hAPP(c_List_Oset(X6002),hAPP(hAPP(c_List_Odrop(X6002),X6003),X6001))),hAPP(c_List_Oset(X6002),hAPP(hAPP(c_List_Odrop(X6002),X6004),X6001))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__drop__subset__set__drop])])). 4.46/4.71 fof(c_0_7035, plain, ![X490, X491, X492, X493]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X493),X492))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X491,tc_HOL_Obool)),hAPP(c_List_Oset(X491),hAPP(hAPP(c_List_Otake(X491),X493),X490))),hAPP(c_List_Oset(X491),hAPP(hAPP(c_List_Otake(X491),X492),X490))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__take__subset__set__take])])])). 4.46/4.71 cnf(c_0_7036, plain, (X1=c_List_Olist_ONil(X2)|c_List_Obutlast(X2,X1)=c_List_OtakeWhile(X2,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2),c_fNot),hAPP(hAPP(c_COMBC(X2,X2,tc_HOL_Obool),c_fequal),c_List_Olast(X2,X1))),X1)|~hBOOL(hAPP(c_List_Odistinct(X2),X1))), inference(split_conjunct,[status(thm)],[c_0_5228])). 4.46/4.71 fof(c_0_7037, plain, ![X7619, X7620, X7621, X7622]:(~class_Lattices_Osemilattice__sup(X7622)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7622),X7621))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7622),X7619),hAPP(hAPP(c_Finite__Set_Ofold(X7622,X7622,c_Lattices_Osemilattice__sup__class_Osup(X7622)),X7620),X7621))=hAPP(hAPP(c_Finite__Set_Ofold(X7622,X7622,c_Lattices_Osemilattice__sup__class_Osup(X7622)),X7620),hAPP(hAPP(c_Set_Oinsert(X7622),X7619),X7621)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__sup__insert])])). 4.46/4.71 fof(c_0_7038, plain, ![X7091, X7092, X7093, X7094]:(~class_Lattices_Osemilattice__inf(X7094)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7094),X7093))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7094),X7091),hAPP(hAPP(c_Finite__Set_Ofold(X7094,X7094,c_Lattices_Osemilattice__inf__class_Oinf(X7094)),X7092),X7093))=hAPP(hAPP(c_Finite__Set_Ofold(X7094,X7094,c_Lattices_Osemilattice__inf__class_Oinf(X7094)),X7092),hAPP(hAPP(c_Set_Oinsert(X7094),X7091),X7093)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__inf__insert])])])). 4.46/4.71 cnf(c_0_7039, plain, (c_List_Olist__all(X3,hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),X1))),hAPP(c_fequal,X2)),X4)|~hBOOL(hAPP(X1,X2))|~c_List_Olist__ex1(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_5229])). 4.46/4.71 cnf(c_0_7040, plain, (hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),X2)),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5230, c_0_4531]), c_0_4531]), c_0_4531]), ['final']). 4.46/4.71 fof(c_0_7041, plain, ![X7095, X7096, X7097]:(~c_Relation_Orefl__on(X7097,X7096,X7095)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7097,X7097),tc_HOL_Obool)),X7095),hAPP(hAPP(c_Relation_Orel__comp(X7097,X7097,X7097),hAPP(c_Relation_Oconverse(X7097,X7097),X7095)),X7095)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__comp__subset])])). 4.46/4.71 cnf(c_0_7042, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),X1))), inference(rw,[status(thm)],[c_0_5231, c_0_4471])). 4.46/4.71 fof(c_0_7043, plain, ![X9941, X9942, X9943, X9944, X9945]:(~class_Groups_Ocomm__monoid__mult(X9945)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9944),X9943))|(hBOOL(hAPP(hAPP(c_member(X9944),X9942),X9943))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9944,X9945),X9941),hAPP(hAPP(c_Set_Oinsert(X9944),X9942),X9943))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9945),hAPP(X9941,X9942)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9944,X9945),X9941),X9943))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod_Oinsert])])])). 4.46/4.71 cnf(c_0_7044, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))), inference(split_conjunct,[status(thm)],[c_0_5232])). 4.46/4.71 cnf(c_0_7045, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))), inference(split_conjunct,[status(thm)],[c_0_5233])). 4.46/4.71 fof(c_0_7046, plain, ![X2462, X2463, X2464]:(~class_Rings_Oring__1(X2464)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2464),hAPP(hAPP(c_Power_Opower__class_Opower(X2464),hAPP(c_Groups_Ouminus__class_Ouminus(X2464),c_Groups_Oone__class_Oone(X2464))),X2462)),hAPP(hAPP(c_Power_Opower__class_Opower(X2464),X2463),X2462))=hAPP(hAPP(c_Power_Opower__class_Opower(X2464),hAPP(c_Groups_Ouminus__class_Ouminus(X2464),X2463)),X2462)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__minus])])])). 4.46/4.71 cnf(c_0_7047, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),X1))), inference(rw,[status(thm)],[c_0_5234, c_0_4471])). 4.46/4.71 cnf(c_0_7048, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2)))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))), inference(rw,[status(thm)],[c_0_5235, c_0_4471])). 4.46/4.71 cnf(c_0_7049, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2)))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))), inference(rw,[status(thm)],[c_0_5236, c_0_4471])). 4.46/4.71 fof(c_0_7050, plain, ![X6380, X6381, X6382, X6383, X6384]:(~class_Rings_Osemiring__0(X6384)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6382,X6384),hAPP(hAPP(c_COMBB(X6384,X6384,X6382),hAPP(c_Groups_Otimes__class_Otimes(X6384),X6383)),X6381)),X6380)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6384),X6383),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6382,X6384),X6381),X6380))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__right__distrib])])])). 4.46/4.71 fof(c_0_7051, plain, ![X3173, X3174, X3175, X3176, X3177]:(~class_Groups_Ocomm__monoid__add(X3177)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3176),X3175))|(hBOOL(hAPP(hAPP(c_member(X3176),X3174),X3175))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3176,X3177),X3173),hAPP(hAPP(c_Set_Oinsert(X3176),X3174),X3175))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3177),hAPP(X3173,X3174)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3176,X3177),X3173),X3175))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__insert])])])). 4.46/4.71 cnf(c_0_7052, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk187_3(X1,X2,X3))),esk188_3(X1,X2,X3))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_5209])). 4.46/4.71 fof(c_0_7053, plain, ![X3647, X3648, X3649, X3650, X3651, X3652, X3653]:((((X3650=X3648|X3648!=X3650|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3653,tc_Option_Ooption(X3652)),X3651),X3650),hAPP(c_Option_Ooption_OSome(X3652),X3649)),X3648)!=hAPP(c_Option_Ooption_OSome(X3652),X3647))&(X3649=X3647|X3648!=X3650|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3653,tc_Option_Ooption(X3652)),X3651),X3650),hAPP(c_Option_Ooption_OSome(X3652),X3649)),X3648)!=hAPP(c_Option_Ooption_OSome(X3652),X3647)))&((X3650=X3648|hAPP(X3651,X3648)=hAPP(c_Option_Ooption_OSome(X3652),X3647)|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3653,tc_Option_Ooption(X3652)),X3651),X3650),hAPP(c_Option_Ooption_OSome(X3652),X3649)),X3648)!=hAPP(c_Option_Ooption_OSome(X3652),X3647))&(X3649=X3647|hAPP(X3651,X3648)=hAPP(c_Option_Ooption_OSome(X3652),X3647)|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3653,tc_Option_Ooption(X3652)),X3651),X3650),hAPP(c_Option_Ooption_OSome(X3652),X3649)),X3648)!=hAPP(c_Option_Ooption_OSome(X3652),X3647))))&((X3648=X3650|hAPP(X3651,X3648)!=hAPP(c_Option_Ooption_OSome(X3652),X3647)|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3653,tc_Option_Ooption(X3652)),X3651),X3650),hAPP(c_Option_Ooption_OSome(X3652),X3649)),X3648)=hAPP(c_Option_Ooption_OSome(X3652),X3647))&(X3650!=X3648|X3649!=X3647|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3653,tc_Option_Ooption(X3652)),X3651),X3650),hAPP(c_Option_Ooption_OSome(X3652),X3649)),X3648)=hAPP(c_Option_Ooption_OSome(X3652),X3647)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upd__Some__unfold])])])). 4.46/4.71 fof(c_0_7054, plain, ![X2231, X2232, X2233]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2233),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2232)),X2231)))|hAPP(hAPP(c_List_Olist_OCons(X2232),hAPP(hAPP(c_List_Onth(X2232),X2231),X2233)),hAPP(hAPP(c_List_Odrop(X2232),hAPP(c_Nat_OSuc,X2233)),X2231))=hAPP(hAPP(c_List_Odrop(X2232),X2233),X2231)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__drop_H])])])). 4.46/4.71 cnf(c_0_7055, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OPls))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5237, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 fof(c_0_7056, plain, ![X14656, X14657, X14658, X14659, X14660]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X14660,X14659)),hAPP(X14660,X14658)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X14657,X14657)),hAPP(hAPP(c_Product__Type_OPair(X14657,X14657),X14659),X14658)),c_Wellfounded_Omlex__prod(X14657,X14660,X14656)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__less])])). 4.46/4.71 fof(c_0_7057, plain, ![X3505, X3506, X3507, X3509, X3510, X3511, X3512]:(((((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X3505|hBOOL(hAPP(X3507,esk91_3(X3505,X3506,X3507)))|~hBOOL(hAPP(X3507,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3506),X3505))))&(hBOOL(hAPP(X3507,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(X3507,esk91_3(X3505,X3506,X3507)))|~hBOOL(hAPP(X3507,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3506),X3505)))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X3505|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3506),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3505),hAPP(c_Nat_OSuc,esk91_3(X3505,X3506,X3507)))))|~hBOOL(hAPP(X3507,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3506),X3505))))&(hBOOL(hAPP(X3507,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3506),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3505),hAPP(c_Nat_OSuc,esk91_3(X3505,X3506,X3507)))))|~hBOOL(hAPP(X3507,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3506),X3505))))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X3505|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3505),esk91_3(X3505,X3506,X3507))),X3506))|~hBOOL(hAPP(X3507,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3506),X3505))))&(hBOOL(hAPP(X3507,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3505),esk91_3(X3505,X3506,X3507))),X3506))|~hBOOL(hAPP(X3507,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3506),X3505))))))&((~hBOOL(hAPP(X3511,X3512))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3510),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3509),hAPP(c_Nat_OSuc,X3512))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3509),X3512)),X3510))|hBOOL(hAPP(X3511,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3510),X3509))))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X3509|~hBOOL(hAPP(X3511,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(X3511,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3510),X3509)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__div_H])])])])])])). 4.46/4.71 cnf(c_0_7058, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5238, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 cnf(c_0_7059, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5239, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 cnf(c_0_7060, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5240, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 cnf(c_0_7061, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5241, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 cnf(c_0_7062, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk369_3(X1,X2,X3))),esk370_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5242])). 4.46/4.71 fof(c_0_7063, plain, ![X12452, X12453, X12454, X12455, X12456]:(~class_Orderings_Olinorder(X12456)|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X12456,hAPP(hAPP(c_Orderings_Oord__class_Omax(X12456),X12455),X12453)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X12456),X12454),X12452))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12456,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X12456,X12455),X12454)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X12456,X12453),X12452))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__atLeastLessThan])])])). 4.46/4.71 fof(c_0_7064, plain, ![X15014, X15015, X15016, X15017, X15018]:(~c_Finite__Set_Ofolding__one(X15018,X15017,X15016)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15018),X15015))|(hBOOL(hAPP(hAPP(c_member(X15018),X15014),X15015))|hAPP(hAPP(c_Finite__Set_Ofold(X15018,X15018,X15017),X15014),X15015)=hAPP(X15016,hAPP(hAPP(c_Set_Oinsert(X15018),X15014),X15015))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Oeq__fold_H])])])). 4.46/4.71 cnf(c_0_7065, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5243, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 cnf(c_0_7066, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5244, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 cnf(c_0_7067, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5245, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 cnf(c_0_7068, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5246, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 fof(c_0_7069, plain, ![X15677, X15678, X15679, X15680, X15681, X15682, X15683, X15684, X15685, X15686, X15687]:((~hBOOL(hAPP(hAPP(c_member(X15679),X15682),X15677))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X15679,X15681)),hAPP(hAPP(c_Product__Type_OPair(X15679,X15681),X15682),X15680)),X15678))|hBOOL(hAPP(hAPP(c_member(X15681),X15680),hAPP(c_Relation_OImage(X15679,X15681,X15678),X15677))))&((hBOOL(hAPP(hAPP(c_member(X15685),esk458_5(X15683,X15684,X15685,X15686,X15687)),X15683))|~hBOOL(hAPP(hAPP(c_member(X15687),X15686),hAPP(c_Relation_OImage(X15685,X15687,X15684),X15683))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X15685,X15687)),hAPP(hAPP(c_Product__Type_OPair(X15685,X15687),esk458_5(X15683,X15684,X15685,X15686,X15687)),X15686)),X15684))|~hBOOL(hAPP(hAPP(c_member(X15687),X15686),hAPP(c_Relation_OImage(X15685,X15687,X15684),X15683)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__iff])])])])])])). 4.46/4.71 fof(c_0_7070, plain, ![X7523, X7524, X7525, X7526, X7527]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X7525,X7527)),hAPP(hAPP(c_Product__Type_OPair(X7525,X7527),esk216_5(X7523,X7524,X7525,X7526,X7527)),X7526)),X7524))|~hBOOL(hAPP(hAPP(c_member(X7527),X7526),hAPP(c_Relation_OImage(X7525,X7527,X7524),X7523))))&(hBOOL(hAPP(hAPP(c_member(X7525),esk216_5(X7523,X7524,X7525,X7526,X7527)),X7523))|~hBOOL(hAPP(hAPP(c_member(X7527),X7526),hAPP(c_Relation_OImage(X7525,X7527,X7524),X7523))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ImageE])])])])])). 4.46/4.71 fof(c_0_7071, plain, ![X6262, X6263, X6264, X6265, X6266, X6267, X6268]:(~hBOOL(hAPP(hAPP(c_member(X6268),X6267),X6266))|(~c_Nitpick_Ofold__graph_H(X6268,X6265,X6264,X6263,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6268,tc_HOL_Obool)),X6266),hAPP(hAPP(c_Set_Oinsert(X6268),X6267),c_Orderings_Obot__class_Obot(tc_fun(X6268,tc_HOL_Obool)))),X6262)|c_Nitpick_Ofold__graph_H(X6268,X6265,X6264,X6263,X6266,hAPP(hAPP(X6264,X6267),X6262)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__graph_H_Ointros_I2_J])])])). 4.46/4.71 fof(c_0_7072, plain, ![X9674, X9675, X9676]:(~class_Orderings_Olinorder(X9676)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9676),X9675))|(c_Orderings_Obot__class_Obot(tc_fun(X9676,tc_HOL_Obool))=X9675|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9676),X9674))|(c_Orderings_Obot__class_Obot(tc_fun(X9676,tc_HOL_Obool))=X9674|hAPP(hAPP(c_Orderings_Oord__class_Omax(X9676),c_Big__Operators_Olinorder__class_OMax(X9676,X9675)),c_Big__Operators_Olinorder__class_OMax(X9676,X9674))=c_Big__Operators_Olinorder__class_OMax(X9676,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9676,tc_HOL_Obool)),X9675),X9674))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max__Un])])])). 4.46/4.71 cnf(c_0_7073, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5247, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 cnf(c_0_7074, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5248, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 fof(c_0_7075, plain, ![X15258, X15259, X15260, X15261]:(~c_Equiv__Relations_Oequiv(X15261,X15260,X15259)|(~hBOOL(hAPP(hAPP(c_member(X15261),X15258),X15260))|hBOOL(hAPP(hAPP(c_member(X15261),X15258),hAPP(c_Relation_OImage(X15261,X15261,X15259),hAPP(hAPP(c_Set_Oinsert(X15261),X15258),c_Orderings_Obot__class_Obot(tc_fun(X15261,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equiv__class__self])])])). 4.46/4.71 fof(c_0_7076, plain, ![X11603, X11604, X11605, X11606, X11607, X11608]:(~c_Finite__Set_Ofolding(X11608,X11607,X11606,X11605)|hAPP(c_Fun_Ocomp(X11607,X11607,X11607,hAPP(X11606,X11604)),hAPP(X11606,X11603))=hAPP(c_Fun_Ocomp(X11607,X11607,X11607,hAPP(X11606,X11603)),hAPP(X11606,X11604))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Ocommute__comp])])])). 4.46/4.71 fof(c_0_7077, plain, ![X13169, X13170, X13171, X13172, X13173]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk384_5(X13169,X13170,X13171,X13172,X13173)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13173)),X13172)))|c_List_Olist__all2(X13173,X13171,X13169,X13172,X13170)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13173)),X13172)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13171)),X13170))&(~hBOOL(hAPP(hAPP(X13169,hAPP(hAPP(c_List_Onth(X13173),X13172),esk384_5(X13169,X13170,X13171,X13172,X13173))),hAPP(hAPP(c_List_Onth(X13171),X13170),esk384_5(X13169,X13170,X13171,X13172,X13173))))|c_List_Olist__all2(X13173,X13171,X13169,X13172,X13170)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13173)),X13172)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13171)),X13170))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2__all__nthI])])])])])). 4.46/4.71 fof(c_0_7078, plain, ![X10105, X10106, X10107, X10108, X10109, X10110, X10111, X10112, X10113, X10114, X10115]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10110),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10109)),X10106)))|hBOOL(hAPP(hAPP(X10107,hAPP(hAPP(c_List_Onth(X10109),X10106),X10110)),hAPP(hAPP(c_List_Onth(X10108),X10105),X10110)))|~c_List_Olist__all2(X10109,X10108,X10107,X10106,X10105))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10109)),X10106)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10108)),X10105)|~c_List_Olist__all2(X10109,X10108,X10107,X10106,X10105)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk293_5(X10111,X10112,X10113,X10114,X10115)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10115)),X10112)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10115)),X10112)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10114)),X10111)|c_List_Olist__all2(X10115,X10114,X10113,X10112,X10111))&(~hBOOL(hAPP(hAPP(X10113,hAPP(hAPP(c_List_Onth(X10115),X10112),esk293_5(X10111,X10112,X10113,X10114,X10115))),hAPP(hAPP(c_List_Onth(X10114),X10111),esk293_5(X10111,X10112,X10113,X10114,X10115))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10115)),X10112)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10114)),X10111)|c_List_Olist__all2(X10115,X10114,X10113,X10112,X10111)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2__conv__all__nth])])])])])])])). 4.46/4.71 fof(c_0_7079, plain, ![X2177, X2178, X2179]:(~class_Lattices_Olattice(X2179)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2179),X2178))|(c_Orderings_Obot__class_Obot(tc_fun(X2179,tc_HOL_Obool))=X2178|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2179),X2177))|(c_Orderings_Obot__class_Obot(tc_fun(X2179,tc_HOL_Obool))=X2177|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2179),c_Big__Operators_Olattice__class_OInf__fin(X2179,X2178)),c_Big__Operators_Olattice__class_OInf__fin(X2179,X2177))=c_Big__Operators_Olattice__class_OInf__fin(X2179,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2179,tc_HOL_Obool)),X2178),X2177))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Ounion__idem])])])). 4.46/4.71 fof(c_0_7080, plain, ![X7210, X7211, X7212, X7213]:(~class_Rings_Olinordered__semiring__strict(X7213)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7213),X7212),X7211))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7213),c_Groups_Ozero__class_Ozero(X7213)),X7210))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7213),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7213),X7212),X7210)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7213),X7211),X7210)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__right__mono])])])). 4.46/4.71 fof(c_0_7081, plain, ![X15905, X15906, X15907, X15908, X15909, X15910]:(~c_Fun_Oinj__on(X15910,X15909,X15908,X15907)|(~hBOOL(hAPP(hAPP(c_member(X15909),X15906),hAPP(c_Set_Oimage(X15910,X15909,X15908),X15907)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15910,tc_HOL_Obool)),X15907),X15905))|hBOOL(hAPP(hAPP(c_member(X15910),hAPP(c_Fun_Othe__inv__into(X15910,X15909,X15907,X15908),X15906)),X15905))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_the__inv__into__into])])])). 4.46/4.71 fof(c_0_7082, plain, ![X15210, X15211, X15212]:(~c_Wellfounded_Owf(X15212,X15211)|(~c_Wellfounded_Owf(X15212,X15210)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15212,X15212),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X15212,X15212,X15212),X15211),X15210)),X15211))|c_Wellfounded_Owf(X15212,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15212,X15212),tc_HOL_Obool)),X15211),X15210))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__union__compatible])])])). 4.46/4.71 cnf(c_0_7083, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_5249])). 4.46/4.71 fof(c_0_7084, plain, ![X13958, X13959, X13960]:(~class_Orderings_Olinorder(X13960)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13960),X13959))|(X13959=c_Orderings_Obot__class_Obot(tc_fun(X13960,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13960),X13958))|(c_Orderings_Obot__class_Obot(tc_fun(X13960,tc_HOL_Obool))=X13958|c_Big__Operators_Olinorder__class_OMin(X13960,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13960,tc_HOL_Obool)),X13959),X13958))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X13960),c_Big__Operators_Olinorder__class_OMin(X13960,X13959)),c_Big__Operators_Olinorder__class_OMin(X13960,X13958))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min__Un])])])). 4.46/4.71 fof(c_0_7085, plain, ![X11259, X11260, X11261, X11262]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11262),c_Groups_Ozero__class_Ozero(X11262)),X11260))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11262),X11260),c_Groups_Ozero__class_Ozero(X11262)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11262),X11261),X11260)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11262),X11259),X11260)))|~class_Rings_Olinordered__ring__strict(X11262))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11262),X11261),X11259))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11262),X11260),c_Groups_Ozero__class_Ozero(X11262)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11262),X11261),X11260)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11262),X11259),X11260)))|~class_Rings_Olinordered__ring__strict(X11262)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11262),c_Groups_Ozero__class_Ozero(X11262)),X11260))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11262),X11259),X11261))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11262),X11261),X11260)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11262),X11259),X11260)))|~class_Rings_Olinordered__ring__strict(X11262))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11262),X11261),X11259))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11262),X11259),X11261))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11262),X11261),X11260)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11262),X11259),X11260)))|~class_Rings_Olinordered__ring__strict(X11262))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11262),X11260),c_Groups_Ozero__class_Ozero(X11262)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11262),X11259),X11261))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11262),X11261),X11260)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11262),X11259),X11260)))|~class_Rings_Olinordered__ring__strict(X11262))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11262),c_Groups_Ozero__class_Ozero(X11262)),X11260))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11262),X11261),X11259))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11262),X11261),X11260)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11262),X11259),X11260)))|~class_Rings_Olinordered__ring__strict(X11262)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__cancel__right__disj])])])])). 4.46/4.71 fof(c_0_7086, plain, ![X7562, X7563, X7564, X7565]:(~class_Rings_Olinordered__comm__semiring__strict(X7565)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7565),X7564),X7563))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7565),c_Groups_Ozero__class_Ozero(X7565)),X7562))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7565),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7565),X7562),X7564)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7565),X7562),X7563)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__mult__strict__left__mono])])])). 4.46/4.71 fof(c_0_7087, plain, ![X10946, X10947, X10948, X10949]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10949),X10947),X10946))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10949),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10949),X10948),X10947)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10949),X10948),X10946)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10949),c_Groups_Ozero__class_Ozero(X10949)),X10948))|~class_Rings_Olinordered__ring__strict(X10949))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10949),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10949),X10948),X10947)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10949),X10948),X10946)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10949),X10947),X10946))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10949),c_Groups_Ozero__class_Ozero(X10949)),X10948))|~class_Rings_Olinordered__ring__strict(X10949))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__cancel__left__pos])])])])). 4.46/4.71 fof(c_0_7088, plain, ![X11077, X11078, X11079, X11080]:(~class_Fields_Ofield(X11080)|(X11079=c_Groups_Ozero__class_Ozero(X11080)|hAPP(hAPP(c_Power_Opower__class_Opower(X11080),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11080),X11078),X11079)),X11077)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11080),hAPP(hAPP(c_Power_Opower__class_Opower(X11080),X11078),X11077)),hAPP(hAPP(c_Power_Opower__class_Opower(X11080),X11079),X11077)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nonzero__power__divide])])])). 4.46/4.71 cnf(c_0_7089, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X2=c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|X3!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2)), inference(split_conjunct,[status(thm)],[c_0_5176])). 4.46/4.71 fof(c_0_7090, plain, ![X16496, X16497, X16498, X16499]:(~class_Rings_Olinordered__semiring__strict(X16499)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16499),X16498),X16497))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16499),c_Groups_Ozero__class_Ozero(X16499)),X16496))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16499),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16499),X16496),X16498)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16499),X16496),X16497)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__left__mono])])])). 4.46/4.71 fof(c_0_7091, plain, ![X12468, X12469, X12470, X12471]:(~class_Fields_Olinordered__field(X12471)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12471),X12470),X12469))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12471),c_Groups_Ozero__class_Ozero(X12471)),X12468))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12471),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12471),X12470),X12468)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12471),X12469),X12468)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__strict__right__mono])])])). 4.46/4.71 fof(c_0_7092, plain, ![X16820, X16821, X16822, X16823]:(~class_Rings_Oordered__semiring(X16823)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16823),X16822),X16821))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16823),c_Groups_Ozero__class_Ozero(X16823)),X16820))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16823),X16822),X16820)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16823),X16821),X16820)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right__mono])])])). 4.46/4.71 fof(c_0_7093, plain, ![X10507, X10508, X10509, X10510]:(~class_Rings_Oordered__semiring(X10510)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10510),X10509),X10508))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10510),c_Groups_Ozero__class_Ozero(X10510)),X10507))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10510),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10510),X10507),X10509)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10510),X10507),X10508)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left__mono])])])). 4.46/4.71 cnf(c_0_7094, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk14_3(X1,X2,X3)),X1))|X2=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5156])). 4.46/4.71 cnf(c_0_7095, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3))),esk538_3(X1,X2,X3))|epred2_3(X3,X2,X1)|~hBOOL(hAPP(X3,esk535_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_5124])). 4.46/4.71 fof(c_0_7096, plain, ![X12981, X12982, X12983]:(~class_Lattices_Olattice(X12983)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12983),X12982))|(c_Orderings_Obot__class_Obot(tc_fun(X12983,tc_HOL_Obool))=X12982|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12983),X12981))|(X12981=c_Orderings_Obot__class_Obot(tc_fun(X12983,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X12983),c_Big__Operators_Olattice__class_OSup__fin(X12983,X12982)),c_Big__Operators_Olattice__class_OSup__fin(X12983,X12981))=c_Big__Operators_Olattice__class_OSup__fin(X12983,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12983,tc_HOL_Obool)),X12982),X12981))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Ounion__idem])])])). 4.46/4.71 fof(c_0_7097, plain, ![X16990, X16991, X16992, X16993]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16993),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16993),X16992),X16991)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16993),X16992),X16990)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16993),X16991),X16990))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16993),c_Groups_Ozero__class_Ozero(X16993)),X16992))|~class_Rings_Olinordered__ring__strict(X16993))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16993),X16991),X16990))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16993),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16993),X16992),X16991)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16993),X16992),X16990)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16993),c_Groups_Ozero__class_Ozero(X16993)),X16992))|~class_Rings_Olinordered__ring__strict(X16993))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__cancel__left__pos])])])])). 4.46/4.71 fof(c_0_7098, plain, ![X9077, X9078, X9079, X9080]:(~class_Rings_Oordered__comm__semiring(X9080)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9080),X9079),X9078))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9080),c_Groups_Ozero__class_Ozero(X9080)),X9077))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9080),X9077),X9079)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9080),X9077),X9078)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__mult__left__mono])])])). 4.46/4.71 cnf(c_0_7099, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk535_3(X2,X3,X1))),esk536_3(X2,X3,X1))|epred2_3(X1,X3,X2)|~hBOOL(hAPP(X1,esk537_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5124])). 4.46/4.71 fof(c_0_7100, plain, ![X3741, X3742, X3743]:(~class_Groups_Oab__semigroup__mult(X3743)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3743),X3742))|(hBOOL(hAPP(hAPP(c_member(X3743),X3741),X3742))|hAPP(c_Finite__Set_Ofold1(X3743,c_Groups_Otimes__class_Otimes(X3743)),hAPP(hAPP(c_Set_Oinsert(X3743),X3741),X3742))=hAPP(hAPP(c_Finite__Set_Ofold(X3743,X3743,c_Groups_Otimes__class_Otimes(X3743)),X3741),X3742)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__eq__fold])])])). 4.46/4.71 fof(c_0_7101, plain, ![X12639, X12640, X12641, X12642]:(~class_Rings_Olinordered__ring__strict(X12642)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12642),X12641),X12640))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12642),X12639),c_Groups_Ozero__class_Ozero(X12642)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12642),X12639),X12640)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12642),X12639),X12641)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__left__mono__neg])])])). 4.46/4.71 fof(c_0_7102, plain, ![X9259, X9260, X9261, X9262]:(~class_Fields_Olinordered__field(X9262)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9262),X9261),X9260))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9262),X9259),c_Groups_Ozero__class_Ozero(X9262)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9262),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9262),X9260),X9259)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9262),X9261),X9259)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__strict__right__mono__neg])])])). 4.46/4.71 fof(c_0_7103, plain, ![X10297, X10298, X10299, X10300, X10301, X10302]:(hBOOL(hAPP(hAPP(c_member(X10302),X10301),hAPP(c_List_Oset(X10302),X10300)))|hAPP(hAPP(c_List_Omap(X10302,X10299),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10302,X10299),X10298),X10301),X10297)),X10300)=hAPP(hAPP(c_List_Omap(X10302,X10299),X10298),X10300)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__fun__upd])])])). 4.46/4.71 fof(c_0_7104, plain, ![X15639, X15640, X15641, X15642, X15643, X15644]:(~hBOOL(hAPP(hAPP(c_member(X15644),X15643),X15642))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X15644,X15641)),hAPP(hAPP(c_Product__Type_OPair(X15644,X15641),X15643),X15640)),X15639))|hBOOL(hAPP(hAPP(c_member(X15641),X15640),hAPP(c_Relation_OImage(X15644,X15641,X15639),X15642))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rev__ImageI])])])). 4.46/4.71 fof(c_0_7105, plain, ![X3630, X3631, X3632, X3633, X3634]:(~c_Finite__Set_Ofun__left__comm(X3634,X3633,X3632)|hAPP(c_Fun_Ocomp(X3633,X3633,X3633,hAPP(X3632,X3631)),hAPP(X3632,X3630))=hAPP(c_Fun_Ocomp(X3633,X3633,X3633,hAPP(X3632,X3630)),hAPP(X3632,X3631))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofun__comp__comm])])])). 4.46/4.71 cnf(c_0_7106, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))),c_Groups_Oone__class_Oone(tc_Int_Oint))|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_5250])). 4.46/4.71 fof(c_0_7107, plain, ![X8479, X8480, X8481, X8482]:(~class_Rings_Oordered__ring(X8482)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8482),X8481),X8480))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8482),X8479),c_Groups_Ozero__class_Ozero(X8482)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8482),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8482),X8480),X8479)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8482),X8481),X8479)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right__mono__neg])])])). 4.46/4.71 fof(c_0_7108, plain, ![X12589, X12590, X12591, X12592]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12592),X12589),X12590))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12592),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12592),X12591),X12590)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12592),X12591),X12589)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12592),X12591),c_Groups_Ozero__class_Ozero(X12592)))|~class_Rings_Olinordered__ring__strict(X12592))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12592),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12592),X12591),X12590)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12592),X12591),X12589)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12592),X12589),X12590))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12592),X12591),c_Groups_Ozero__class_Ozero(X12592)))|~class_Rings_Olinordered__ring__strict(X12592))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__cancel__left__neg])])])])). 4.46/4.71 fof(c_0_7109, plain, ![X1669, X1670, X1671, X1672]:(~class_Rings_Oordered__ring(X1672)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1672),X1671),X1670))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1672),X1669),c_Groups_Ozero__class_Ozero(X1672)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1672),X1669),X1670)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1672),X1669),X1671)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left__mono__neg])])])). 4.46/4.71 cnf(c_0_7110, plain, (X1=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))|c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))!=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X4),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5251, c_0_4517]), c_0_4517])). 4.46/4.71 fof(c_0_7111, plain, ![X4662, X4663, X4664, X4668, X4669, X4670, X4671, X4672, X4673]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X4664,X4663)),hAPP(hAPP(c_Product__Type_OPair(X4664,X4663),esk132_3(X4662,X4663,X4664)),esk133_3(X4662,X4663,X4664))),X4662))|c_Relation_Osingle__valued(X4664,X4663,X4662))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X4664,X4663)),hAPP(hAPP(c_Product__Type_OPair(X4664,X4663),esk132_3(X4662,X4663,X4664)),esk134_3(X4662,X4663,X4664))),X4662))|c_Relation_Osingle__valued(X4664,X4663,X4662))&(esk134_3(X4662,X4663,X4664)!=esk133_3(X4662,X4663,X4664)|c_Relation_Osingle__valued(X4664,X4663,X4662))))&(~c_Relation_Osingle__valued(X4670,X4669,X4668)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4670,X4669)),hAPP(hAPP(c_Product__Type_OPair(X4670,X4669),X4671),X4672)),X4668))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4670,X4669)),hAPP(hAPP(c_Product__Type_OPair(X4670,X4669),X4671),X4673)),X4668))|X4673=X4672)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_single__valued__def])])])])])])])). 4.46/4.71 fof(c_0_7112, plain, ![X15981, X15982, X15983, X15984]:(~class_Enum_Oenum(X15984)|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15983)),X15982)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15984)),c_Enum_Oenum__class_Oenum(X15984))|hAPP(hAPP(c_Map_Omap__of(X15984,X15983),hAPP(hAPP(c_List_Ozip(X15984,X15983),c_Enum_Oenum__class_Oenum(X15984)),X15982)),X15981)=hAPP(c_Option_Ooption_OSome(X15983),esk464_4(X15981,X15982,X15983,X15984)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__zip__enum__is__Some])])])])). 4.46/4.71 fof(c_0_7113, plain, ![X2329, X2330, X2331, X2332, X2333]:((hBOOL(hAPP(hAPP(c_member(X2333),esk57_5(X2329,X2330,X2331,X2332,X2333)),X2330))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2333,X2332)),X2331),hAPP(hAPP(c_Product__Type_OSigma(X2333,X2332),X2330),X2329))))&((hBOOL(hAPP(hAPP(c_member(X2332),esk58_5(X2329,X2330,X2331,X2332,X2333)),hAPP(X2329,esk57_5(X2329,X2330,X2331,X2332,X2333))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2333,X2332)),X2331),hAPP(hAPP(c_Product__Type_OSigma(X2333,X2332),X2330),X2329))))&(X2331=hAPP(hAPP(c_Product__Type_OPair(X2333,X2332),esk57_5(X2329,X2330,X2331,X2332,X2333)),esk58_5(X2329,X2330,X2331,X2332,X2333))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2333,X2332)),X2331),hAPP(hAPP(c_Product__Type_OSigma(X2333,X2332),X2330),X2329)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SigmaE])])])])])). 4.46/4.71 fof(c_0_7114, plain, ![X12987, X12988, X12989, X12990, X12991, X12993]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12991),hAPP(X12988,esk377_5(X12987,X12988,X12989,X12990,X12991))),X12987))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12991),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12990,X12991),X12989),X12988)),X12987))|(~class_Complete__Lattice_Ocomplete__lattice(X12991)|~class_Orderings_Olinorder(X12991)))&(hBOOL(hAPP(hAPP(c_member(X12990),esk377_5(X12987,X12988,X12989,X12990,X12991)),X12989))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12991),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12990,X12991),X12989),X12988)),X12987))|(~class_Complete__Lattice_Ocomplete__lattice(X12991)|~class_Orderings_Olinorder(X12991))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12991),hAPP(X12988,X12993)),X12987))|~hBOOL(hAPP(hAPP(c_member(X12990),X12993),X12989))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12991),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12990,X12991),X12989),X12988)),X12987))|(~class_Complete__Lattice_Ocomplete__lattice(X12991)|~class_Orderings_Olinorder(X12991)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__less__iff])])])])])). 4.46/4.71 fof(c_0_7115, plain, ![X14949, X14950, X14951]:((~hBOOL(hAPP(hAPP(c_member(X14951),X14949),X14950))|hAPP(c_Finite__Set_Ocard(X14951),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14951,tc_HOL_Obool)),X14950),hAPP(hAPP(c_Set_Oinsert(X14951),X14949),c_Orderings_Obot__class_Obot(tc_fun(X14951,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X14951),X14950)),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14951),X14950)))&(hBOOL(hAPP(hAPP(c_member(X14951),X14949),X14950))|hAPP(c_Finite__Set_Ocard(X14951),X14950)=hAPP(c_Finite__Set_Ocard(X14951),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14951,tc_HOL_Obool)),X14950),hAPP(hAPP(c_Set_Oinsert(X14951),X14949),c_Orderings_Obot__class_Obot(tc_fun(X14951,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14951),X14950)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff__singleton__if])])])])). 4.46/4.71 cnf(c_0_7116, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),X5))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5)))), inference(split_conjunct,[status(thm)],[c_0_5252])). 4.46/4.71 cnf(c_0_7117, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X2,X1,X3),X5)))|c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X2,X1,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X2,X1,X3),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_5253])). 4.46/4.71 cnf(c_0_7118, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk369_3(X1,X2,X3))),esk370_3(X1,X2,X3))=X2|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_5242])). 4.46/4.71 fof(c_0_7119, plain, ![X12491, X12492, X12493, X12494, X12495, X12497]:(((hBOOL(hAPP(hAPP(c_member(X12493),esk368_5(X12491,X12492,X12493,X12494,X12495)),X12492))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12495),X12494),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12493,X12495),X12492),X12491)))|(~class_Complete__Lattice_Ocomplete__lattice(X12495)|~class_Orderings_Olinorder(X12495)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12495),X12494),hAPP(X12491,esk368_5(X12491,X12492,X12493,X12494,X12495))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12495),X12494),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12493,X12495),X12492),X12491)))|(~class_Complete__Lattice_Ocomplete__lattice(X12495)|~class_Orderings_Olinorder(X12495))))&(~hBOOL(hAPP(hAPP(c_member(X12493),X12497),X12492))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12495),X12494),hAPP(X12491,X12497)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12495),X12494),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12493,X12495),X12492),X12491)))|(~class_Complete__Lattice_Ocomplete__lattice(X12495)|~class_Orderings_Olinorder(X12495)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SUP__iff])])])])])). 4.46/4.71 fof(c_0_7120, plain, ![X4339, X4340, X4341, X4342]:(~class_Orderings_Olinorder(X4342)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4342),X4341),X4340))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4342),X4340),X4339))|c_SetInterval_Oord__class_OgreaterThanLessThan(X4342,X4341,X4339)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4342,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4342,X4341,X4340)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4342,X4340),X4339))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I15_J])])])). 4.46/4.71 fof(c_0_7121, plain, ![X6273, X6274, X6275, X6276]:(~class_Orderings_Olinorder(X6276)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6276),X6275),X6274))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6276),X6274),X6273))|c_SetInterval_Oord__class_OatLeastAtMost(X6276,X6275,X6273)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6276,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X6276,X6275),X6274)),c_SetInterval_Oord__class_OatLeastAtMost(X6276,X6274,X6273))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I21_J])])])). 4.46/4.71 fof(c_0_7122, plain, ![X11022, X11023, X11024, X11025, X11026, X11027, X11028]:(~c_Finite__Set_Ofolding__idem(X11028,X11027,X11026,X11025)|hAPP(c_Fun_Ocomp(X11027,X11027,X11024,hAPP(X11026,X11023)),hAPP(c_Fun_Ocomp(X11027,X11027,X11024,hAPP(X11026,X11023)),X11022))=hAPP(c_Fun_Ocomp(X11027,X11027,X11024,hAPP(X11026,X11023)),X11022)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__left__comp])])). 4.46/4.71 cnf(c_0_7123, plain, (hAPP(c_List_Oset(X1),X5)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3))|hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)!=c_List_Opartition(X1,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_5254])). 4.46/4.71 cnf(c_0_7124, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_5255])). 4.46/4.71 cnf(c_0_7125, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X3)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5031])). 4.46/4.71 fof(c_0_7126, plain, ![X10412, X10413, X10414, X10415, X10416]:((hBOOL(hAPP(hAPP(c_member(X10415),esk303_5(X10412,X10413,X10414,X10415,X10416)),hAPP(c_List_Oset(X10415),X10414)))|hAPP(hAPP(c_List_Olist_OCons(X10415),X10412),X10414)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10415,X10416,X10413),X10412),X10414)|~class_Orderings_Olinorder(X10416))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10416),hAPP(X10413,X10412)),hAPP(X10413,esk303_5(X10412,X10413,X10414,X10415,X10416))))|hAPP(hAPP(c_List_Olist_OCons(X10415),X10412),X10414)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10415,X10416,X10413),X10412),X10414)|~class_Orderings_Olinorder(X10416))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__is__Cons])])])])])). 4.46/4.71 fof(c_0_7127, plain, ![X4988, X4989, X4992, X4994, X4995, X4996, X4997, X4999]:(((hBOOL(hAPP(hAPP(c_member(X4989),esk148_2(X4988,X4989)),esk147_2(X4988,X4989)))|c_Wellfounded_Owf(X4989,X4988))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X4989,X4989)),hAPP(hAPP(c_Product__Type_OPair(X4989,X4989),esk149_3(X4988,X4989,X4992)),X4992)),X4988))|~hBOOL(hAPP(hAPP(c_member(X4989),X4992),esk147_2(X4988,X4989)))|c_Wellfounded_Owf(X4989,X4988))&(hBOOL(hAPP(hAPP(c_member(X4989),esk149_3(X4988,X4989,X4992)),esk147_2(X4988,X4989)))|~hBOOL(hAPP(hAPP(c_member(X4989),X4992),esk147_2(X4988,X4989)))|c_Wellfounded_Owf(X4989,X4988))))&((hBOOL(hAPP(hAPP(c_member(X4995),esk150_3(X4994,X4995,X4996)),X4996))|~hBOOL(hAPP(hAPP(c_member(X4995),X4997),X4996))|~c_Wellfounded_Owf(X4995,X4994))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4995,X4995)),hAPP(hAPP(c_Product__Type_OPair(X4995,X4995),X4999),esk150_3(X4994,X4995,X4996))),X4994))|~hBOOL(hAPP(hAPP(c_member(X4995),X4999),X4996))|~hBOOL(hAPP(hAPP(c_member(X4995),X4997),X4996))|~c_Wellfounded_Owf(X4995,X4994)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__eq__minimal])])])])])])])). 4.46/4.71 fof(c_0_7128, plain, ![X1808, X1809, X1810, X1811, X1814]:(((hBOOL(hAPP(hAPP(c_member(X1810),esk44_4(X1808,X1809,X1810,X1811)),X1809))|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(X1808,X1811)|~hBOOL(hAPP(hAPP(c_member(X1810),X1811),X1809))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1810,tc_Nat_Onat),X1808),X1809)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1810),X1809)))&((X1811!=esk44_4(X1808,X1809,X1810,X1811)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(X1808,X1811)|~hBOOL(hAPP(hAPP(c_member(X1810),X1811),X1809))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1810,tc_Nat_Onat),X1808),X1809)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1810),X1809)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(X1808,esk44_4(X1808,X1809,X1810,X1811))|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(X1808,X1811)|~hBOOL(hAPP(hAPP(c_member(X1810),X1811),X1809))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1810,tc_Nat_Onat),X1808),X1809)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1810),X1809)))))&(((~hBOOL(hAPP(hAPP(c_member(X1810),X1814),X1809))|(esk45_3(X1808,X1809,X1810)=X1814|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(X1808,X1814))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1810,tc_Nat_Onat),X1808),X1809)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1810),X1809)))&(c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(X1808,esk45_3(X1808,X1809,X1810))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1810,tc_Nat_Onat),X1808),X1809)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1810),X1809))))&(hBOOL(hAPP(hAPP(c_member(X1810),esk45_3(X1808,X1809,X1810)),X1809))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1810,tc_Nat_Onat),X1808),X1809)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1810),X1809))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__eq__1__iff])])])])])])). 4.46/4.71 fof(c_0_7129, plain, ![X9176, X9177, X9178, X9179, X9180]:((hBOOL(hAPP(hAPP(c_member(X9179),esk264_5(X9176,X9177,X9178,X9179,X9180)),X9178))|(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9179,X9180),X9177),X9178)!=c_Groups_Ozero__class_Ozero(X9180)|(~hBOOL(hAPP(hAPP(c_member(X9179),X9176),X9178))|hAPP(X9177,X9176)=c_Groups_Ozero__class_Ozero(X9180)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9179),X9178))|~class_Groups_Oordered__ab__group__add(X9180))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9180),c_Groups_Ozero__class_Ozero(X9180)),hAPP(X9177,esk264_5(X9176,X9177,X9178,X9179,X9180))))|(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9179,X9180),X9177),X9178)!=c_Groups_Ozero__class_Ozero(X9180)|(~hBOOL(hAPP(hAPP(c_member(X9179),X9176),X9178))|hAPP(X9177,X9176)=c_Groups_Ozero__class_Ozero(X9180)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9179),X9178))|~class_Groups_Oordered__ab__group__add(X9180))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__nonneg__0])])])])])). 4.46/4.71 cnf(c_0_7130, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_5140])). 4.46/4.71 fof(c_0_7131, plain, ![X9452, X9453, X9454, X9455, X9456, X9457]:(~c_Finite__Set_Ofolding__idem(X9457,X9456,X9455,X9454)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9457),X9453))|hAPP(X9454,hAPP(hAPP(c_Set_Oinsert(X9457),X9452),X9453))=hAPP(c_Fun_Ocomp(X9456,X9456,X9456,hAPP(X9454,X9453)),hAPP(X9455,X9452)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oinsert__idem])])). 4.46/4.71 cnf(c_0_7132, plain, (c_Map_Omap__comp(X3,X6,X8,X5,X1,X2)=hAPP(c_Option_Ooption_OSome(X6),X7)|hAPP(X1,X2)!=hAPP(c_Option_Ooption_OSome(X3),X4)|hAPP(X5,X4)!=hAPP(c_Option_Ooption_OSome(X6),X7)), inference(split_conjunct,[status(thm)],[c_0_5256])). 4.46/4.71 cnf(c_0_7133, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X2,c_Option_Ooption_ONone(X1),X3),hAPP(X4,X5))=c_Map_Omap__comp(X2,X1,X6,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_5257])). 4.46/4.71 fof(c_0_7134, plain, ![X15584, X15585, X15586, X15587, X15588]:(c_Option_Ooption_ONone(X15586)!=hAPP(X15588,X15587)|hAPP(hAPP(c_Set_Oinsert(X15586),X15584),c_Map_Oran(X15585,X15586,X15588))=c_Map_Oran(X15585,X15586,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X15585,tc_Option_Ooption(X15586)),X15588),X15587),hAPP(c_Option_Ooption_OSome(X15586),X15584)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ran__map__upd])])])). 4.46/4.71 fof(c_0_7135, plain, ![X9238, X9239, X9240]:(~class_Orderings_Olinorder(X9240)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9240),X9239))|c_List_Oremove1(X9240,X9238,c_List_Olinorder__class_Osorted__list__of__set(X9240,X9239))=c_List_Olinorder__class_Osorted__list__of__set(X9240,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9240,tc_HOL_Obool)),X9239),hAPP(hAPP(c_Set_Oinsert(X9240),X9238),c_Orderings_Obot__class_Obot(tc_fun(X9240,tc_HOL_Obool))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__remove])])). 4.46/4.71 fof(c_0_7136, plain, ![X6676, X6677, X6678, X6679, X6680]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X6680)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6680),X6679),X6678))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6680),X6677),X6676))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6680),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6680),X6679),X6677)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6680),X6678),X6676)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__mono])])])). 4.46/4.71 fof(c_0_7137, plain, ![X13813, X13814, X13815, X13816, X13817]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X13817)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13817),X13816),X13815))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13817),X13814),X13813))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13817),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13817),X13816),X13814)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13817),X13815),X13813)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__less__mono])])])). 4.46/4.71 fof(c_0_7138, plain, ![X13243, X13244, X13245, X13247]:(((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X13245)),esk387_3(X13243,X13244,X13245)),hAPP(c_List_Oset(tc_List_Olist(X13245)),c_Enum_On__lists(X13245,X13243,c_Enum_Oenum__class_Oenum(X13245)))))|c_Enum_Oall__n__lists(X13245,X13244,X13243)|~class_Enum_Oenum(X13245))&(~hBOOL(hAPP(X13244,esk387_3(X13243,X13244,X13245)))|c_Enum_Oall__n__lists(X13245,X13244,X13243)|~class_Enum_Oenum(X13245)))&(~c_Enum_Oall__n__lists(X13245,X13244,X13243)|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X13245)),X13247),hAPP(c_List_Oset(tc_List_Olist(X13245)),c_Enum_On__lists(X13245,X13243,c_Enum_Oenum__class_Oenum(X13245)))))|hBOOL(hAPP(X13244,X13247)))|~class_Enum_Oenum(X13245))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_all__n__lists__def])])])])])])). 4.46/4.71 fof(c_0_7139, plain, ![X10262, X10263, X10264, X10265, X10266]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10266,X10265)),hAPP(hAPP(c_Product__Type_OPair(X10266,X10265),X10264),X10263)),hAPP(c_List_Oset(tc_prod(X10266,X10265)),X10262)))|hAPP(hAPP(c_Map_Omap__of(X10266,X10265),X10262),X10264)=hAPP(c_Option_Ooption_OSome(X10265),esk296_5(X10262,X10263,X10264,X10265,X10266))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_weak__map__of__SomeI])])])). 4.46/4.71 fof(c_0_7140, plain, ![X3455, X3456, X3457, X3458, X3459]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X3459)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3459),X3458),X3457))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3459),X3456),X3455))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3459),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3459),X3458),X3456)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3459),X3457),X3455)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__less__le__mono])])])). 4.46/4.71 fof(c_0_7141, plain, ![X13805, X13806, X13807, X13808, X13809]:(~class_Groups_Oordered__ab__semigroup__add(X13809)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13809),X13808),X13807))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13809),X13806),X13805))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13809),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13809),X13808),X13806)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13809),X13807),X13805)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__mono])])])). 4.46/4.71 fof(c_0_7142, plain, ![X10603, X10604, X10605, X10606, X10607]:(~class_Lattices_Osemilattice__sup(X10607)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10607),X10606),X10605))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10607),X10604),X10603))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10607),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10607),X10606),X10604)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10607),X10605),X10603)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__mono])])])). 4.46/4.71 fof(c_0_7143, plain, ![X6336, X6337, X6338, X6339, X6340]:(~class_Lattices_Osemilattice__inf(X6340)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6340),X6339),X6338))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6340),X6337),X6336))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6340),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6340),X6339),X6337)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6340),X6338),X6336)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__mono])])])). 4.46/4.71 cnf(c_0_7144, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X4,X2)),hAPP(X4,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(c_Wellfounded_Omeasure(X1),X4)))), inference(split_conjunct,[status(thm)],[c_0_5179])). 4.46/4.71 fof(c_0_7145, plain, ![X14973, X14974, X14975, X14976]:(~hBOOL(hAPP(hAPP(c_member(X14976),X14975),hAPP(c_Relation_ORange(X14974,X14976),X14973)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X14974,X14976)),hAPP(hAPP(c_Product__Type_OPair(X14974,X14976),esk439_4(X14973,X14974,X14975,X14976)),X14975)),X14973))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_RangeE])])])])). 4.46/4.71 fof(c_0_7146, plain, ![X14143, X14144, X14145, X14146, X14148, X14149, X14150, X14151, X14152]:((~hBOOL(hAPP(hAPP(c_member(X14146),X14145),hAPP(c_Relation_ORange(X14144,X14146),X14143)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X14144,X14146)),hAPP(hAPP(c_Product__Type_OPair(X14144,X14146),esk411_4(X14143,X14144,X14145,X14146)),X14145)),X14143)))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X14149,X14151)),hAPP(hAPP(c_Product__Type_OPair(X14149,X14151),X14152),X14150)),X14148))|hBOOL(hAPP(hAPP(c_member(X14151),X14150),hAPP(c_Relation_ORange(X14149,X14151),X14148))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Range__iff])])])])])). 4.46/4.71 fof(c_0_7147, plain, ![X13619, X13620, X13621, X13622]:(~hBOOL(hAPP(hAPP(c_member(X13622),X13621),hAPP(c_Relation_ODomain(X13622,X13620),X13619)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X13622,X13620)),hAPP(hAPP(c_Product__Type_OPair(X13622,X13620),X13621),esk398_4(X13619,X13620,X13621,X13622))),X13619))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_DomainE])])])])). 4.46/4.71 fof(c_0_7148, plain, ![X5004, X5005, X5006, X5007]:((X5007=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Olist_OCons(X5006),X5005),hAPP(hAPP(c_List_Otake(X5006),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5007),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X5004))=hAPP(hAPP(c_List_Otake(X5006),X5007),hAPP(hAPP(c_List_Olist_OCons(X5006),X5005),X5004)))&(X5007!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Olist_ONil(X5006)=hAPP(hAPP(c_List_Otake(X5006),X5007),hAPP(hAPP(c_List_Olist_OCons(X5006),X5005),X5004)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_take__Cons_H])])])). 4.46/4.71 fof(c_0_7149, plain, ![X15397, X15398, X15399, X15400]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15400)),X15399)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15398)),X15397)|hAPP(c_List_Orev(tc_prod(X15400,X15398)),hAPP(hAPP(c_List_Ozip(X15400,X15398),X15399),X15397))=hAPP(hAPP(c_List_Ozip(X15400,X15398),hAPP(c_List_Orev(X15400),X15399)),hAPP(c_List_Orev(X15398),X15397))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zip__rev])])])). 4.46/4.71 fof(c_0_7150, plain, ![X3882, X3883, X3884, X3885]:(~class_Fields_Olinordered__field__inverse__zero(X3885)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3885),X3884),X3883))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3885),c_Groups_Ozero__class_Ozero(X3885)),X3882))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3885),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3885),X3884),X3882)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3885),X3883),X3882)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__right__mono])])])). 4.46/4.71 fof(c_0_7151, plain, ![X15976, X15977, X15978, X15979]:(~class_Rings_Olinordered__semidom(X15979)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15979),X15978),X15977))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15979),c_Groups_Ozero__class_Ozero(X15979)),X15978))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15979),hAPP(hAPP(c_Power_Opower__class_Opower(X15979),X15978),X15976)),hAPP(hAPP(c_Power_Opower__class_Opower(X15979),X15977),X15976)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__mono])])])). 4.46/4.71 fof(c_0_7152, plain, ![X1286, X1287, X1288, X1289]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1289),hAPP(hAPP(c_Power_Opower__class_Opower(X1289),X1288),X1287)),hAPP(hAPP(c_Power_Opower__class_Opower(X1289),X1288),X1286)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1287),X1286))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1289),c_Groups_Oone__class_Oone(X1289)),X1288))|~class_Rings_Olinordered__semidom(X1289))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1287),X1286))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1289),hAPP(hAPP(c_Power_Opower__class_Opower(X1289),X1288),X1287)),hAPP(hAPP(c_Power_Opower__class_Opower(X1289),X1288),X1286)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1289),c_Groups_Oone__class_Oone(X1289)),X1288))|~class_Rings_Olinordered__semidom(X1289))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__strict__increasing__iff])])])])). 4.46/4.71 fof(c_0_7153, plain, ![X14186, X14187, X14188, X14189, X14190, X14191, X14192, X14193, X14194, X14195, X14196, X14197, X14198, X14199, X14200]:((~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14192,tc_fun(X14191,tc_fun(X14190,tc_HOL_Obool))),X14189),X14188),X14187),X14186))|(~hBOOL(hAPP(hAPP(c_member(X14192),X14193),X14189))|hBOOL(hAPP(hAPP(hAPP(X14188,X14193),X14187),X14186))))&((hBOOL(hAPP(hAPP(c_member(X14200),esk414_7(X14194,X14195,X14196,X14197,X14198,X14199,X14200)),X14197))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14200,tc_fun(X14199,tc_fun(X14198,tc_HOL_Obool))),X14197),X14196),X14195),X14194)))&(~hBOOL(hAPP(hAPP(hAPP(X14196,esk414_7(X14194,X14195,X14196,X14197,X14198,X14199,X14200)),X14195),X14194))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14200,tc_fun(X14199,tc_fun(X14198,tc_HOL_Obool))),X14197),X14196),X14195),X14194))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF2__iff])])])])])])). 4.46/4.71 fof(c_0_7154, plain, ![X10497, X10498, X10499, X10500, X10501, X10502, X10503, X10504, X10505]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X10500,X10498)),hAPP(hAPP(c_Product__Type_OPair(X10500,X10498),X10499),X10501)),X10497))|hBOOL(hAPP(hAPP(c_member(X10500),X10499),hAPP(c_Relation_ODomain(X10500,X10498),X10497))))&(~hBOOL(hAPP(hAPP(c_member(X10505),X10504),hAPP(c_Relation_ODomain(X10505,X10503),X10502)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X10505,X10503)),hAPP(hAPP(c_Product__Type_OPair(X10505,X10503),X10504),esk306_4(X10502,X10503,X10504,X10505))),X10502)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__iff])])])])])). 4.46/4.71 fof(c_0_7155, plain, ![X1773, X1774, X1775, X1776]:(((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1776)),X1774),c_List_Olists(X1776,X1773)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1776)),hAPP(hAPP(c_List_Oappend(X1776),X1775),X1774)),c_List_Olists(X1776,X1773))))&(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1776)),X1775),c_List_Olists(X1776,X1773)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1776)),hAPP(hAPP(c_List_Oappend(X1776),X1775),X1774)),c_List_Olists(X1776,X1773)))))&(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1776)),X1774),c_List_Olists(X1776,X1773)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1776)),X1775),c_List_Olists(X1776,X1773)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1776)),hAPP(hAPP(c_List_Oappend(X1776),X1775),X1774)),c_List_Olists(X1776,X1773))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__lists__conv])])])). 4.46/4.71 fof(c_0_7156, plain, ![X12711, X12712, X12713, X12714, X12715, X12716, X12717]:((hBOOL(hAPP(hAPP(c_member(X12717),esk375_7(X12711,X12712,X12713,X12714,X12715,X12716,X12717)),X12716))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12717,tc_fun(X12712,tc_fun(X12711,tc_HOL_Obool))),X12716),X12715),X12714),X12713)))&(~hBOOL(hAPP(hAPP(hAPP(X12715,esk375_7(X12711,X12712,X12713,X12714,X12715,X12716,X12717)),X12714),X12713))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12717,tc_fun(X12712,tc_fun(X12711,tc_HOL_Obool))),X12716),X12715),X12714),X12713)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF2__I])])])])])). 4.46/4.71 fof(c_0_7157, plain, ![X6696, X6697, X6698, X6699]:(~class_Rings_Olinordered__semidom(X6699)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6698),X6697))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6699),c_Groups_Oone__class_Oone(X6699)),X6696))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6699),hAPP(hAPP(c_Power_Opower__class_Opower(X6699),X6696),X6698)),hAPP(hAPP(c_Power_Opower__class_Opower(X6699),X6696),X6697)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__increasing])])])). 4.46/4.71 fof(c_0_7158, plain, ![X1836, X1837, X1838, X1839]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1839),hAPP(hAPP(c_Power_Opower__class_Opower(X1839),X1838),X1837)),hAPP(hAPP(c_Power_Opower__class_Opower(X1839),X1838),X1836)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1837),X1836))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1839),c_Groups_Oone__class_Oone(X1839)),X1838))|~class_Rings_Olinordered__semidom(X1839))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1837),X1836))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1839),hAPP(hAPP(c_Power_Opower__class_Opower(X1839),X1838),X1837)),hAPP(hAPP(c_Power_Opower__class_Opower(X1839),X1838),X1836)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1839),c_Groups_Oone__class_Oone(X1839)),X1838))|~class_Rings_Olinordered__semidom(X1839))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__increasing__iff])])])])). 4.46/4.71 fof(c_0_7159, plain, ![X353, X354, X355, X356]:(~class_Fields_Olinordered__field__inverse__zero(X356)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X356),X355),X354))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X356),X353),c_Groups_Ozero__class_Ozero(X356)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X356),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X356),X354),X353)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X356),X355),X353)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__right__mono__neg])])])). 4.46/4.71 fof(c_0_7160, plain, ![X9517, X9518, X9519, X9520]:(~hBOOL(hAPP(hAPP(c_member(X9520),X9519),X9518))|hBOOL(hAPP(hAPP(c_member(tc_fun(X9520,tc_HOL_Obool)),hAPP(c_Relation_OImage(X9520,X9520,X9517),hAPP(hAPP(c_Set_Oinsert(X9520),X9519),c_Orderings_Obot__class_Obot(tc_fun(X9520,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X9520),X9518),X9517)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_quotientI])])])). 4.46/4.71 fof(c_0_7161, plain, ![X10375, X10376, X10377]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X10377,X10377)),hAPP(hAPP(c_Product__Type_OPair(X10377,X10377),esk302_3(X10375,X10376,X10377)),X10376)),X10375))|hBOOL(hAPP(hAPP(c_member(X10377),X10376),c_Wellfounded_Oacc(X10377,X10375))))&(~hBOOL(hAPP(hAPP(c_member(X10377),esk302_3(X10375,X10376,X10377)),c_Wellfounded_Oacc(X10377,X10375)))|hBOOL(hAPP(hAPP(c_member(X10377),X10376),c_Wellfounded_Oacc(X10377,X10375))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acc_OaccI])])])])])). 4.46/4.71 fof(c_0_7162, plain, ![X4431, X4432, X4433]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4433),X4432)),X4431)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4431))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4433))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4432),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_q__neg__lemma])])])). 4.46/4.71 cnf(c_0_7163, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_List_Ofoldr(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Omonoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5258])). 4.46/4.71 fof(c_0_7164, plain, ![X10368, X10369, X10370]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X10370,X10370)),hAPP(hAPP(c_Product__Type_OPair(X10370,X10370),esk300_3(X10368,X10369,X10370)),X10369)),X10368))|hBOOL(hAPP(hAPP(c_member(X10370),X10369),c_Wellfounded_Oacc(X10370,X10368))))&(~hBOOL(hAPP(hAPP(c_member(X10370),esk300_3(X10368,X10369,X10370)),c_Wellfounded_Oacc(X10370,X10368)))|hBOOL(hAPP(hAPP(c_member(X10370),X10369),c_Wellfounded_Oacc(X10370,X10368))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__acc__down])])])])])). 4.46/4.71 cnf(c_0_7165, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk170_4(X3,X1,X2,X4)),X4)),X3))|c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=X4|X4!=hAPP(c_Set_Oimage(X1,X2,X5),X3)), inference(split_conjunct,[status(thm)],[c_0_5259])). 4.46/4.71 cnf(c_0_7166, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X2)),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk214_2(X1,X2)),hAPP(X2,esk214_2(X1,X2))))), inference(split_conjunct,[status(thm)],[c_0_5260])). 4.46/4.71 fof(c_0_7167, plain, ![X3190, X3191, X3192, X3194, X3195, X3196, X3197]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X3192,X3192)),hAPP(hAPP(c_Product__Type_OPair(X3192,X3192),esk81_3(X3190,X3191,X3192)),X3191)),X3190))|hBOOL(hAPP(hAPP(c_member(X3192),X3191),c_Wellfounded_Oacc(X3192,X3190))))&(~hBOOL(hAPP(hAPP(c_member(X3192),esk81_3(X3190,X3191,X3192)),c_Wellfounded_Oacc(X3192,X3190)))|hBOOL(hAPP(hAPP(c_member(X3192),X3191),c_Wellfounded_Oacc(X3192,X3190)))))&(~hBOOL(hAPP(hAPP(c_member(X3196),X3195),c_Wellfounded_Oacc(X3196,X3194)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X3196,X3196)),hAPP(hAPP(c_Product__Type_OPair(X3196,X3196),X3197),X3195)),X3194))|hBOOL(hAPP(hAPP(c_member(X3196),X3197),c_Wellfounded_Oacc(X3196,X3194)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc_Osimps])])])])])])). 4.46/4.71 fof(c_0_7168, plain, ![X13886, X13887, X13888, X13889]:(~class_Orderings_Olinorder(X13889)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13889),X13888),X13887))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13889),X13887),X13886))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13889,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X13889,X13888,X13887)),c_SetInterval_Oord__class_OgreaterThanLessThan(X13889,X13887,X13886))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X13889,X13888),X13886)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I18_J])])])). 4.46/4.71 fof(c_0_7169, plain, ![X13879, X13880, X13881, X13882, X13883]:((hAPP(hAPP(c_Set_Oinsert(X13883),esk405_5(X13879,X13880,X13881,X13882,X13883)),esk406_5(X13879,X13880,X13881,X13882,X13883))=hAPP(hAPP(c_Set_Oinsert(X13883),X13881),X13880)|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X13883,X13882,hAPP(hAPP(c_Set_Oinsert(X13883),X13881),X13880)),X13879)))&((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X13883,X13883,X13882,esk405_5(X13879,X13880,X13881,X13882,X13883),esk406_5(X13879,X13880,X13881,X13882,X13883)),X13879))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X13883,X13882,hAPP(hAPP(c_Set_Oinsert(X13883),X13881),X13880)),X13879)))&(~hBOOL(hAPP(hAPP(c_member(X13883),esk405_5(X13879,X13880,X13881,X13882,X13883)),esk406_5(X13879,X13880,X13881,X13882,X13883)))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X13883,X13882,hAPP(hAPP(c_Set_Oinsert(X13883),X13881),X13880)),X13879))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insert__fold1SetE])])])])])). 4.46/4.71 cnf(c_0_7170, plain, (X2=hAPP(c_Set_Oimage(tc_Nat_Onat,X1,esk103_2(X2,X1)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),esk102_2(X2,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5261])). 4.46/4.71 fof(c_0_7171, plain, ![X16596, X16597, X16599, X16600, X16601, X16603]:(((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk486_2(X16596,X16597)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16597)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16599),X16597))|hBOOL(hAPP(X16596,X16599))))&(~hBOOL(hAPP(X16596,esk486_2(X16596,X16597)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16599),X16597))|hBOOL(hAPP(X16596,X16599)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk487_2(X16600,X16601)),X16601))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X16603),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16601)))|hBOOL(hAPP(X16600,X16603))))&(~hBOOL(hAPP(X16600,esk487_2(X16600,X16601)))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X16603),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16601)))|hBOOL(hAPP(X16600,X16603)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_all__nat__less__eq])])])])])])). 4.46/4.71 fof(c_0_7172, plain, ![X3000, X3001]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3001))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3000),X3001))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3000),X3001)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3000),X3001)),X3001)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__geq])])])). 4.46/4.71 fof(c_0_7173, plain, ![X15527, X15528, X15529, X15530, X15531, X15532, X15533, X15534, X15535, X15536, X15537]:((hAPP(hAPP(c_List_Omap(X15531,X15530),X15529),X15528)!=hAPP(hAPP(c_List_Omap(X15531,X15530),X15527),X15528)|(~hBOOL(hAPP(hAPP(c_member(X15531),X15532),hAPP(c_List_Oset(X15531),X15528)))|hAPP(X15527,X15532)=hAPP(X15529,X15532)))&((hBOOL(hAPP(hAPP(c_member(X15537),esk455_5(X15533,X15534,X15535,X15536,X15537)),hAPP(c_List_Oset(X15537),X15534)))|hAPP(hAPP(c_List_Omap(X15537,X15536),X15535),X15534)=hAPP(hAPP(c_List_Omap(X15537,X15536),X15533),X15534))&(hAPP(X15533,esk455_5(X15533,X15534,X15535,X15536,X15537))!=hAPP(X15535,esk455_5(X15533,X15534,X15535,X15536,X15537))|hAPP(hAPP(c_List_Omap(X15537,X15536),X15535),X15534)=hAPP(hAPP(c_List_Omap(X15537,X15536),X15533),X15534)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__eq__conv])])])])])])). 4.46/4.71 fof(c_0_7174, plain, ![X16303, X16304, X16305, X16306, X16307, X16308, X16309]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16309)),X16308)),X16307))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16307),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16306)),X16305)))|c_Map_Omap__upds(X16309,X16306,X16304,X16308,X16305)=c_Map_Omap__upds(X16309,X16306,X16304,X16308,hAPP(hAPP(c_List_Olist__update(X16306,X16305),X16307),X16303)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__upds__list__update2__drop])])])). 4.46/4.71 fof(c_0_7175, plain, ![X16923, X16924, X16925, X16926]:(~hBOOL(hAPP(hAPP(c_member(X16926),X16925),c_Wellfounded_Oacc(X16926,X16924)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16926,X16926)),hAPP(hAPP(c_Product__Type_OPair(X16926,X16926),X16923),X16925)),c_Transitive__Closure_Ortrancl(X16926,X16924)))|hBOOL(hAPP(hAPP(c_member(X16926),X16923),c_Wellfounded_Oacc(X16926,X16924))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acc__downwards])])])). 4.46/4.71 fof(c_0_7176, plain, ![X13755, X13756, X13757]:(~class_Int_Onumber__ring(X13757)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13757),hAPP(c_Groups_Ouminus__class_Ouminus(X13757),hAPP(c_Int_Onumber__class_Onumber__of(X13757),X13756))),X13755)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13757),hAPP(c_Int_Onumber__class_Onumber__of(X13757),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X13756))),X13755)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__number__of__mult])])])). 4.46/4.71 cnf(c_0_7177, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_4650])). 4.46/4.71 cnf(c_0_7178, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4))), inference(csr,[status(thm)],[c_0_5262, c_0_5263]), ['final']). 4.46/4.71 fof(c_0_7179, plain, ![X6764, X6765, X6766, X6767]:(~c_Fun_Oinj__on(X6767,X6766,X6765,c_Orderings_Otop__class_Otop(tc_fun(X6767,tc_HOL_Obool)))|c_Fun_Oinj__on(X6767,tc_fun(X6764,X6766),hAPP(hAPP(c_COMBB(X6766,tc_fun(X6764,X6766),X6767),c_COMBK(X6766,X6764)),X6765),c_Orderings_Otop__class_Otop(tc_fun(X6767,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__fun])])). 4.46/4.71 fof(c_0_7180, plain, ![X10340, X10341, X10342, X10343]:((hBOOL(hAPP(hAPP(c_member(X10343),esk299_4(X10340,X10341,X10342,X10343)),hAPP(c_List_Oset(X10343),X10342)))|hAPP(hAPP(c_List_Oappend(X10343),X10342),c_List_OtakeWhile(X10343,X10341,X10340))=c_List_OtakeWhile(X10343,X10341,hAPP(hAPP(c_List_Oappend(X10343),X10342),X10340)))&(~hBOOL(hAPP(X10341,esk299_4(X10340,X10341,X10342,X10343)))|hAPP(hAPP(c_List_Oappend(X10343),X10342),c_List_OtakeWhile(X10343,X10341,X10340))=c_List_OtakeWhile(X10343,X10341,hAPP(hAPP(c_List_Oappend(X10343),X10342),X10340)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile__append2])])])])])). 4.46/4.71 cnf(c_0_7181, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))), inference(split_conjunct,[status(thm)],[c_0_5264])). 4.46/4.71 fof(c_0_7182, plain, ![X8704, X8705, X8706]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X8706),X8704))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X8706,tc_HOL_Obool),tc_fun(X8706,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X8706,tc_HOL_Obool),tc_fun(X8706,tc_HOL_Obool)),X8705),X8704)),c_Wellfounded_Ofinite__psubset(X8706))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X8706,tc_HOL_Obool)),X8705),X8704))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X8706,tc_HOL_Obool),tc_fun(X8706,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X8706,tc_HOL_Obool),tc_fun(X8706,tc_HOL_Obool)),X8705),X8704)),c_Wellfounded_Ofinite__psubset(X8706)))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8706),X8704))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X8706,tc_HOL_Obool)),X8705),X8704))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X8706,tc_HOL_Obool),tc_fun(X8706,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X8706,tc_HOL_Obool),tc_fun(X8706,tc_HOL_Obool)),X8705),X8704)),c_Wellfounded_Ofinite__psubset(X8706))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__finite__psubset])])])). 4.46/4.71 fof(c_0_7183, plain, ![X3782, X3783, X3784, X3785]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3785),X3784)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3783)),X3782)))|hAPP(hAPP(c_List_Onth(X3783),X3782),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3785),X3784))=hAPP(hAPP(c_List_Onth(X3783),hAPP(hAPP(c_List_Odrop(X3783),X3785),X3782)),X3784)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__drop])])])). 4.46/4.71 fof(c_0_7184, plain, ![X6956, X6957, X6958, X6961, X6962]:(((hBOOL(hAPP(hAPP(c_member(X6958),esk202_3(X6956,X6957,X6958)),hAPP(c_List_Oset(X6958),X6957)))|~c_List_Olinorder__class_Osorted(X6958,X6956)|~c_List_Olinorder__class_Osorted(X6958,X6957)|c_List_Olinorder__class_Osorted(X6958,hAPP(hAPP(c_List_Oappend(X6958),X6957),X6956))|~class_Orderings_Olinorder(X6958))&((hBOOL(hAPP(hAPP(c_member(X6958),esk203_3(X6956,X6957,X6958)),hAPP(c_List_Oset(X6958),X6956)))|~c_List_Olinorder__class_Osorted(X6958,X6956)|~c_List_Olinorder__class_Osorted(X6958,X6957)|c_List_Olinorder__class_Osorted(X6958,hAPP(hAPP(c_List_Oappend(X6958),X6957),X6956))|~class_Orderings_Olinorder(X6958))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6958),esk202_3(X6956,X6957,X6958)),esk203_3(X6956,X6957,X6958)))|~c_List_Olinorder__class_Osorted(X6958,X6956)|~c_List_Olinorder__class_Osorted(X6958,X6957)|c_List_Olinorder__class_Osorted(X6958,hAPP(hAPP(c_List_Oappend(X6958),X6957),X6956))|~class_Orderings_Olinorder(X6958))))&(((c_List_Olinorder__class_Osorted(X6958,X6956)|~c_List_Olinorder__class_Osorted(X6958,hAPP(hAPP(c_List_Oappend(X6958),X6957),X6956))|~class_Orderings_Olinorder(X6958))&(~hBOOL(hAPP(hAPP(c_member(X6958),X6961),hAPP(c_List_Oset(X6958),X6957)))|(~hBOOL(hAPP(hAPP(c_member(X6958),X6962),hAPP(c_List_Oset(X6958),X6956)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6958),X6961),X6962)))|~c_List_Olinorder__class_Osorted(X6958,hAPP(hAPP(c_List_Oappend(X6958),X6957),X6956))|~class_Orderings_Olinorder(X6958)))&(c_List_Olinorder__class_Osorted(X6958,X6957)|~c_List_Olinorder__class_Osorted(X6958,hAPP(hAPP(c_List_Oappend(X6958),X6957),X6956))|~class_Orderings_Olinorder(X6958)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__append])])])])])])). 4.46/4.71 fof(c_0_7185, plain, ![X13463, X13464, X13465, X13466, X13467]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13467,tc_HOL_Obool)),hAPP(c_List_Oset(X13467),X13466)),X13465))|(~hBOOL(hAPP(hAPP(c_member(X13467),X13464),X13465))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13467,tc_HOL_Obool)),hAPP(c_List_Oset(X13467),hAPP(hAPP(c_List_Olist__update(X13467,X13466),X13463),X13464))),X13465)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__update__subsetI])])])). 4.46/4.71 fof(c_0_7186, plain, ![X13900, X13901, X13902, X13903, X13904, X13905]:(~hBOOL(hAPP(hAPP(c_member(X13905),X13904),X13903))|(~hBOOL(hAPP(hAPP(c_member(X13902),X13901),hAPP(X13900,X13904)))|hBOOL(hAPP(hAPP(c_member(X13902),X13901),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13905,tc_fun(X13902,tc_HOL_Obool)),X13903),X13900))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__I])])])). 4.46/4.71 fof(c_0_7187, plain, ![X17224, X17225, X17227, X17228, X17229, X17231]:(((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk515_2(X17224,X17225)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17225)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17227),X17225))|hBOOL(hAPP(X17224,X17227))))&(~hBOOL(hAPP(X17224,esk515_2(X17224,X17225)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17227),X17225))|hBOOL(hAPP(X17224,X17227)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk516_2(X17228,X17229)),X17229))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X17231),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17229)))|hBOOL(hAPP(X17228,X17231))))&(~hBOOL(hAPP(X17228,esk516_2(X17228,X17229)))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X17231),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17229)))|hBOOL(hAPP(X17228,X17231)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_all__nat__less])])])])])])])). 4.46/4.71 cnf(c_0_7188, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X1,X1),X2)),c_Transitive__Closure_Ortrancl(X1,X2))!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))), inference(rw,[status(thm)],[c_0_5265, c_0_5266])). 4.46/4.71 fof(c_0_7189, plain, ![X12269, X12270, X12271, X12272]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12272),X12271))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12270),X12269))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X12272,X12270)),hAPP(hAPP(c_Product__Type_OSigma(X12272,X12270),X12271),hAPP(c_COMBK(tc_fun(X12270,tc_HOL_Obool),X12272),X12269)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__cartesian__product])])])). 4.46/4.71 fof(c_0_7190, plain, ![X15651, X15652, X15653]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15653),X15652))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X15653),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15653,tc_HOL_Obool)),X15652),hAPP(hAPP(c_Set_Oinsert(X15653),X15651),c_Orderings_Obot__class_Obot(tc_fun(X15653,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X15653),X15652)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff1__le])])])). 4.46/4.71 cnf(c_0_7191, plain, (hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(hAPP(c_COMBC(X3,X3,tc_HOL_Obool),c_fequal),X2))),X1))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5267])). 4.46/4.71 fof(c_0_7192, plain, ![X6524, X6525, X6526, X6527, X6528]:(~class_Orderings_Olinorder(X6528)|c_SetInterval_Oord__class_OgreaterThanLessThan(X6528,hAPP(hAPP(c_Orderings_Oord__class_Omax(X6528),X6527),X6525),hAPP(hAPP(c_Orderings_Oord__class_Omin(X6528),X6526),X6524))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6528,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X6528,X6527,X6526)),c_SetInterval_Oord__class_OgreaterThanLessThan(X6528,X6525,X6524))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__greaterThanLessThan])])])). 4.46/4.71 fof(c_0_7193, plain, ![X10553, X10554, X10555]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X10555),X10554)),X10553)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10553),X10555))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10555))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10554))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_q__pos__lemma])])])). 4.46/4.71 fof(c_0_7194, plain, ![X5877, X5878, X5879, X5880, X5881]:(~class_Orderings_Olinorder(X5881)|c_SetInterval_Oord__class_OgreaterThanAtMost(X5881,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5881),X5880),X5878),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5881),X5879),X5877))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5881,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5881,X5880,X5879)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5881,X5878,X5877))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greaterThanAtMost])])). 4.46/4.71 fof(c_0_7195, plain, ![X7847, X7848, X7849, X7850, X7851]:(~c_Finite__Set_Ofolding__one__idem(X7851,X7850,X7849)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7851),X7848))|(X7847=c_Orderings_Obot__class_Obot(tc_fun(X7851,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7851,tc_HOL_Obool)),X7847),X7848))|hAPP(hAPP(X7850,hAPP(X7849,X7847)),hAPP(X7849,X7848))=hAPP(X7849,X7848))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one__idem_Osubset__idem])])])). 4.46/4.71 fof(c_0_7196, plain, ![X9623, X9624, X9625, X9626, X9627]:(~class_Orderings_Olinorder(X9627)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9627),X9626),X9625))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9627),X9624),X9623))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9627),hAPP(hAPP(c_Orderings_Oord__class_Omax(X9627),X9626),X9624)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X9627),X9625),X9623)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__mono])])])). 4.46/4.71 fof(c_0_7197, plain, ![X8497, X8498, X8499, X8500, X8501]:(~class_Orderings_Olinorder(X8501)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8501),X8500),X8499))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8501),X8498),X8497))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8501),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8501),X8500),X8498)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8501),X8499),X8497)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__mono])])])). 4.46/4.71 fof(c_0_7198, plain, ![X7196, X7197, X7198, X7199, X7200]:(~class_Orderings_Olinorder(X7200)|c_SetInterval_Oord__class_OatLeastAtMost(X7200,hAPP(hAPP(c_Orderings_Oord__class_Omax(X7200),X7199),X7197),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7200),X7198),X7196))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7200,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7200,X7199,X7198)),c_SetInterval_Oord__class_OatLeastAtMost(X7200,X7197,X7196))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__atLeastAtMost])])])). 4.46/4.71 fof(c_0_7199, plain, ![X12907, X12908, X12909, X12910, X12911, X12912]:(~c_Fun_Oinj__on(X12912,X12911,X12910,X12909)|(hBOOL(hAPP(hAPP(c_member(X12911),X12908),hAPP(c_Set_Oimage(X12912,X12911,X12910),X12909)))|c_Fun_Oinj__on(X12912,X12911,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X12912,X12911),X12910),X12907),X12908),X12909))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__fun__updI])])])). 4.46/4.71 fof(c_0_7200, plain, ![X11059, X11060]:((c_List_Olist_ONil(tc_List_Olist(X11060))=X11059|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11060)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X11060)),X11059),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X11060))),c_List_Otranspose(X11060,X11059))|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X11060),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X11060))),X11059))))&(X11059!=c_List_Olist_ONil(tc_List_Olist(X11060))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X11060))),c_List_Otranspose(X11060,X11059))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X11060),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X11060))),X11059))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__transpose__sorted])])])). 4.46/4.71 fof(c_0_7201, plain, ![X15732, X15733, X15734, X15735]:(~class_Orderings_Olinorder(X15735)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15735),X15734),X15733))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15735),X15733),X15732))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15735,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X15735,X15734,X15733)),c_SetInterval_Oord__class_OatLeastAtMost(X15735,X15733,X15732))=c_SetInterval_Oord__class_OgreaterThanAtMost(X15735,X15734,X15732)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I19_J])])])). 4.46/4.71 fof(c_0_7202, plain, ![X3676, X3677, X3678]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3678),hAPP(c_Int_Onumber__class_Onumber__of(X3678),X3677)),hAPP(c_Int_Onumber__class_Onumber__of(X3678),X3676)))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X3678),hAPP(c_Int_Onumber__class_Onumber__of(X3678),X3677)),hAPP(c_Int_Onumber__class_Onumber__of(X3678),X3676))=hAPP(c_Int_Onumber__class_Onumber__of(X3678),X3676)|(~class_Int_Onumber(X3678)|~class_Orderings_Oord(X3678)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3678),hAPP(c_Int_Onumber__class_Onumber__of(X3678),X3677)),hAPP(c_Int_Onumber__class_Onumber__of(X3678),X3676)))|hAPP(c_Int_Onumber__class_Onumber__of(X3678),X3677)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X3678),hAPP(c_Int_Onumber__class_Onumber__of(X3678),X3677)),hAPP(c_Int_Onumber__class_Onumber__of(X3678),X3676))|(~class_Int_Onumber(X3678)|~class_Orderings_Oord(X3678)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_max__number__of])])])])). 4.46/4.71 fof(c_0_7203, plain, ![X12807, X12808, X12809, X12810]:(((hBOOL(hAPP(hAPP(c_member(X12810),X12808),X12809))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12810,tc_HOL_Obool)),X12809),X12807))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12810,tc_HOL_Obool)),X12809),hAPP(hAPP(c_Set_Oinsert(X12810),X12808),X12807))))&(~hBOOL(hAPP(hAPP(c_member(X12810),X12808),X12809))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12810,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12810,tc_HOL_Obool)),X12809),hAPP(hAPP(c_Set_Oinsert(X12810),X12808),c_Orderings_Obot__class_Obot(tc_fun(X12810,tc_HOL_Obool))))),X12807))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12810,tc_HOL_Obool)),X12809),hAPP(hAPP(c_Set_Oinsert(X12810),X12808),X12807)))))&(((hBOOL(hAPP(hAPP(c_member(X12810),X12808),X12809))|~hBOOL(hAPP(hAPP(c_member(X12810),X12808),X12809))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12810,tc_HOL_Obool)),X12809),hAPP(hAPP(c_Set_Oinsert(X12810),X12808),X12807))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12810,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12810,tc_HOL_Obool)),X12809),hAPP(hAPP(c_Set_Oinsert(X12810),X12808),c_Orderings_Obot__class_Obot(tc_fun(X12810,tc_HOL_Obool))))),X12807))|~hBOOL(hAPP(hAPP(c_member(X12810),X12808),X12809))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12810,tc_HOL_Obool)),X12809),hAPP(hAPP(c_Set_Oinsert(X12810),X12808),X12807)))))&((hBOOL(hAPP(hAPP(c_member(X12810),X12808),X12809))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12810,tc_HOL_Obool)),X12809),X12807))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12810,tc_HOL_Obool)),X12809),hAPP(hAPP(c_Set_Oinsert(X12810),X12808),X12807))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12810,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12810,tc_HOL_Obool)),X12809),hAPP(hAPP(c_Set_Oinsert(X12810),X12808),c_Orderings_Obot__class_Obot(tc_fun(X12810,tc_HOL_Obool))))),X12807))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12810,tc_HOL_Obool)),X12809),X12807))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12810,tc_HOL_Obool)),X12809),hAPP(hAPP(c_Set_Oinsert(X12810),X12808),X12807))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__insert__iff])])])])). 4.46/4.71 fof(c_0_7204, plain, ![X10669, X10670, X10671]:(~class_Rings_Olinordered__ring(X10671)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10671),c_Groups_Ozero__class_Ozero(X10671)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10671),X10670),X10670)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10671),X10669),X10669))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sum__squares__ge__zero])])])). 4.46/4.71 cnf(c_0_7205, plain, (hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4650])). 4.46/4.71 cnf(c_0_7206, plain, (hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_5268]), ['final']). 4.46/4.71 cnf(c_0_7207, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(c_Set_Oimage(tc_prod(X1,X3),X3,c_Product__Type_Osnd(X1,X3)),hAPP(hAPP(c_Product__Type_OSigma(X1,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X1),X4)))=X4), inference(split_conjunct,[status(thm)],[c_0_5269])). 4.46/4.71 fof(c_0_7208, plain, ![X16965, X16966, X16967, X16968]:(~class_Orderings_Olinorder(X16968)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16968),X16967),X16966))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16968),X16966),X16965))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16968,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X16968,X16967,X16966)),c_SetInterval_Oord__class_OgreaterThanAtMost(X16968,X16966,X16965))=c_SetInterval_Oord__class_OgreaterThanAtMost(X16968,X16967,X16965)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I20_J])])])). 4.46/4.71 fof(c_0_7209, plain, ![X8068, X8069, X8070, X8071]:(~class_Orderings_Olinorder(X8071)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8071),X8070),X8069))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8071),X8069),X8068))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8071,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X8071,X8070,X8069)),c_SetInterval_Oord__class_OgreaterThanAtMost(X8071,X8069,X8068))=c_SetInterval_Oord__class_OatLeastAtMost(X8071,X8070,X8068)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I22_J])])])). 4.46/4.71 fof(c_0_7210, plain, ![X2882, X2883, X2884, X2885]:(~class_Orderings_Olinorder(X2885)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2885),X2884),X2883))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2885),X2883),X2882))|c_SetInterval_Oord__class_OgreaterThanLessThan(X2885,X2884,X2882)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2885,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X2885,X2884,X2883)),c_SetInterval_Oord__class_OgreaterThanLessThan(X2885,X2883,X2882))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I16_J])])])). 4.46/4.71 fof(c_0_7211, plain, ![X17513, X17514, X17515]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17515))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X17514),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17515),X17513))!=X17515|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17514))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17513),c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_self__quotient__aux2])])])). 4.46/4.71 cnf(c_0_7212, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(c_Set_Oimage(tc_prod(X3,X2),X3,c_Product__Type_Ofst(X3,X2)),hAPP(hAPP(c_Product__Type_OSigma(X3,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X3),X1)))=X4), inference(split_conjunct,[status(thm)],[c_0_5270])). 4.46/4.71 fof(c_0_7213, plain, ![X6687, X6688, X6689]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6689),hAPP(c_Int_Onumber__class_Onumber__of(X6689),X6688)),hAPP(c_Int_Onumber__class_Onumber__of(X6689),X6687)))|hAPP(c_Int_Onumber__class_Onumber__of(X6689),X6687)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X6689),hAPP(c_Int_Onumber__class_Onumber__of(X6689),X6688)),hAPP(c_Int_Onumber__class_Onumber__of(X6689),X6687))|(~class_Orderings_Oord(X6689)|~class_Int_Onumber(X6689)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6689),hAPP(c_Int_Onumber__class_Onumber__of(X6689),X6688)),hAPP(c_Int_Onumber__class_Onumber__of(X6689),X6687)))|hAPP(c_Int_Onumber__class_Onumber__of(X6689),X6688)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X6689),hAPP(c_Int_Onumber__class_Onumber__of(X6689),X6688)),hAPP(c_Int_Onumber__class_Onumber__of(X6689),X6687))|(~class_Orderings_Oord(X6689)|~class_Int_Onumber(X6689)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__number__of])])])])). 4.46/4.71 fof(c_0_7214, plain, ![X4828, X4829, X4830]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4830),X4829))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4829),X4828)),X4830)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4829),X4830)),X4828)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__add__assoc2])])])). 4.46/4.71 fof(c_0_7215, plain, ![X8802, X8803, X8804, X8805, X8806]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8806,tc_HOL_Obool)),X8805),X8804))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8806,tc_HOL_Obool)),X8803),X8802))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8806,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8806,tc_HOL_Obool)),X8805),X8802)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8806,tc_HOL_Obool)),X8804),X8803))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__mono])])). 4.46/4.71 fof(c_0_7216, plain, ![X15222, X15223, X15224, X15225, X15226]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15226,tc_HOL_Obool)),X15225),X15224))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15226,tc_HOL_Obool)),X15223),X15222))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15226,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15226,tc_HOL_Obool)),X15225),X15223)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15226,tc_HOL_Obool)),X15224),X15222))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Un__mono])])])). 4.46/4.71 fof(c_0_7217, plain, ![X2758, X2759, X2760]:(~class_Rings_Olinordered__idom(X2760)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2760),c_Groups_Ozero__class_Ozero(X2760)),X2759))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2760),c_Groups_Ozero__class_Ozero(X2760)),X2758))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2760),X2758),c_Groups_Oone__class_Oone(X2760)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2760),X2759),X2758)),X2759)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right__le__one__le])])])). 4.46/4.71 fof(c_0_7218, plain, ![X836, X837, X838]:(~class_Rings_Olinordered__idom(X838)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X838),c_Groups_Ozero__class_Ozero(X838)),X837))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X838),c_Groups_Ozero__class_Ozero(X838)),X836))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X838),X836),c_Groups_Oone__class_Oone(X838)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X838),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X838),X836),X837)),X837)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left__le__one__le])])])). 4.46/4.71 cnf(c_0_7219, plain, (hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oconcat(X2,X1)))|esk3_2(X1,X2)!=esk2_2(X1,X2)|~hBOOL(hAPP(c_List_Odistinct(X2),esk1_2(X1,X2)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1))), inference(split_conjunct,[status(thm)],[c_0_5007])). 4.46/4.71 fof(c_0_7220, plain, ![X10829, X10830, X10831, X10832]:(~class_Rings_Osemiring__1(X10832)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10832),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10832),hAPP(c_Finite__Set_Ocard(X10831),X10829))),X10830)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10831,X10832),hAPP(c_COMBK(X10832,X10831),X10830)),X10829)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__constant])])])). 4.46/4.71 fof(c_0_7221, plain, ![X1360, X1361, X1362, X1363, X1364]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1364,tc_HOL_Obool)),X1363),X1362))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1364,tc_HOL_Obool)),X1361),X1360))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1364,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1364,tc_HOL_Obool)),X1363),X1361)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1364,tc_HOL_Obool)),X1362),X1360))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__mono])])). 4.46/4.71 cnf(c_0_7222, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))), inference(split_conjunct,[status(thm)],[c_0_5271])). 4.46/4.71 cnf(c_0_7223, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))), inference(split_conjunct,[status(thm)],[c_0_5272])). 4.46/4.71 fof(c_0_7224, plain, ![X16764, X16765]:(~class_Groups_Oordered__ab__group__add__abs(X16765)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16765),hAPP(c_Groups_Oabs__class_Oabs(X16765),hAPP(c_List_Omonoid__add__class_Olistsum(X16765),X16764))),hAPP(c_List_Omonoid__add__class_Olistsum(X16765),hAPP(hAPP(c_List_Omap(X16765,X16765),c_Groups_Oabs__class_Oabs(X16765)),X16764))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__abs])])). 4.46/4.71 fof(c_0_7225, plain, ![X14207, X14208, X14209, X14210]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk415_4(X14207,X14208,X14209,X14210)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14210)),X14209)))|(~hBOOL(hAPP(hAPP(c_member(X14210),X14207),hAPP(c_List_Oset(X14210),X14209)))|hBOOL(hAPP(X14208,X14207))))&(~hBOOL(hAPP(X14208,hAPP(hAPP(c_List_Onth(X14210),X14209),esk415_4(X14207,X14208,X14209,X14210))))|(~hBOOL(hAPP(hAPP(c_member(X14210),X14207),hAPP(c_List_Oset(X14210),X14209)))|hBOOL(hAPP(X14208,X14207))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_all__nth__imp__all__set])])])])])). 4.46/4.71 fof(c_0_7226, plain, ![X1422, X1423, X1424, X1425, X1426]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1424)),X1423)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1426)),X1425)|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1424)),X1423)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1426)),X1422)|(~hBOOL(hAPP(c_List_Odistinct(X1424),X1423))|(hAPP(c_Map_Omap__of(X1424,X1426),hAPP(hAPP(c_List_Ozip(X1424,X1426),X1423),X1422))!=hAPP(c_Map_Omap__of(X1424,X1426),hAPP(hAPP(c_List_Ozip(X1424,X1426),X1423),X1425))|X1422=X1425)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__zip__inject])])])). 4.46/4.71 fof(c_0_7227, plain, ![X2013, X2014, X2015, X2016, X2017, X2018, X2019, X2020]:(~c_Finite__Set_Ofolding__image(X2020,X2019,X2018,X2017,X2016)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2019),X2015))|(~c_Fun_Oinj__on(X2019,X2019,X2014,X2015)|hAPP(hAPP(X2016,X2013),hAPP(c_Set_Oimage(X2019,X2019,X2014),X2015))=hAPP(hAPP(X2016,hAPP(c_Fun_Ocomp(X2019,X2020,X2019,X2013),X2014)),X2015)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image_Oreindex])])])). 4.46/4.71 fof(c_0_7228, plain, ![X5225, X5226]:(~class_Lattices_Oab__semigroup__idem__mult(X5226)|(X5225=c_List_Olist_ONil(X5226)|hAPP(c_List_Ofoldl(X5226,X5226,c_Groups_Otimes__class_Otimes(X5226),hAPP(c_List_Ohd(X5226),X5225)),hAPP(c_List_Otl(X5226),X5225))=hAPP(c_Finite__Set_Ofold1(X5226,c_Groups_Otimes__class_Otimes(X5226)),hAPP(c_List_Oset(X5226),X5225)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__set])])). 4.46/4.71 cnf(c_0_7229, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk15_6(X3,X4,X2,X5,X6,X1))))|X4!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,X1),X2),X5)|~hBOOL(hAPP(hAPP(c_member(X6),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X5))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5188])). 4.46/4.71 fof(c_0_7230, plain, ![X13920, X13921, X13922, X13923, X13924, X13925]:(~c_List_Olist__all2(X13925,X13924,X13923,X13922,X13921)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13920),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13924)),X13921)))|hBOOL(hAPP(hAPP(X13923,hAPP(hAPP(c_List_Onth(X13925),X13922),X13920)),hAPP(hAPP(c_List_Onth(X13924),X13921),X13920))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2__nthD2])])])). 4.46/4.71 cnf(c_0_7231, plain, (c_Map_Odom(X1,X3,hAPP(c_Map_Omap__of(X1,X3),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4)))=hAPP(c_List_Oset(X1),X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5273])). 4.46/4.71 cnf(c_0_7232, plain, (c_Map_Odom(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3))=hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))), inference(rw,[status(thm)],[c_0_5274, c_0_5275]), ['final']). 4.46/4.71 fof(c_0_7233, plain, ![X3449, X3450, X3451, X3452, X3453, X3454]:(~c_Finite__Set_Ofun__left__comm(X3454,X3453,X3452)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3454),X3451))|hAPP(hAPP(X3452,X3450),hAPP(hAPP(c_Finite__Set_Ofold(X3454,X3453,X3452),X3449),X3451))=hAPP(hAPP(c_Finite__Set_Ofold(X3454,X3453,X3452),hAPP(hAPP(X3452,X3450),X3449)),X3451))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__fun__comm])])). 4.46/4.71 fof(c_0_7234, plain, ![X1080, X1081, X1082, X1083, X1084]:((~hBOOL(hAPP(hAPP(c_member(X1084),X1083),hAPP(c_Relation_OImage(X1082,X1084,X1081),hAPP(hAPP(c_Set_Oinsert(X1082),X1080),c_Orderings_Obot__class_Obot(tc_fun(X1082,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1082,X1084)),hAPP(hAPP(c_Product__Type_OPair(X1082,X1084),X1080),X1083)),X1081)))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X1082,X1084)),hAPP(hAPP(c_Product__Type_OPair(X1082,X1084),X1080),X1083)),X1081))|hBOOL(hAPP(hAPP(c_member(X1084),X1083),hAPP(c_Relation_OImage(X1082,X1084,X1081),hAPP(hAPP(c_Set_Oinsert(X1082),X1080),c_Orderings_Obot__class_Obot(tc_fun(X1082,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__singleton__iff])])). 4.46/4.71 fof(c_0_7235, plain, ![X16792, X16793, X16794]:(~class_Rings_Olinordered__semidom(X16794)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16794),c_Groups_Ozero__class_Ozero(X16794)),X16793))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16794),X16793),c_Groups_Oone__class_Oone(X16794)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16794),hAPP(hAPP(c_Power_Opower__class_Opower(X16794),X16793),hAPP(c_Nat_OSuc,X16792))),c_Groups_Oone__class_Oone(X16794)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__Suc__less__one])])])). 4.46/4.71 fof(c_0_7236, plain, ![X7550, X7551, X7552]:(~hBOOL(hAPP(c_List_Odistinct(X7552),X7551))|hAPP(c_List_Oset(X7552),c_List_Oremove1(X7552,X7550,X7551))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7552,tc_HOL_Obool)),hAPP(c_List_Oset(X7552),X7551)),hAPP(hAPP(c_Set_Oinsert(X7552),X7550),c_Orderings_Obot__class_Obot(tc_fun(X7552,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__remove1__eq])])). 4.46/4.71 fof(c_0_7237, plain, ![X7677, X7678, X7679, X7680]:((~hBOOL(hAPP(X7678,X7680))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7679)),X7680),hAPP(c_List_Oset(tc_List_Olist(X7679)),c_Enum_On__lists(X7679,X7677,c_Enum_Oenum__class_Oenum(X7679)))))|c_Enum_Oex__n__lists(X7679,X7678,X7677)|~class_Enum_Oenum(X7679))&((hBOOL(hAPP(X7678,esk217_3(X7677,X7678,X7679)))|~c_Enum_Oex__n__lists(X7679,X7678,X7677)|~class_Enum_Oenum(X7679))&(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X7679)),esk217_3(X7677,X7678,X7679)),hAPP(c_List_Oset(tc_List_Olist(X7679)),c_Enum_On__lists(X7679,X7677,c_Enum_Oenum__class_Oenum(X7679)))))|~c_Enum_Oex__n__lists(X7679,X7678,X7677)|~class_Enum_Oenum(X7679)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__n__lists__def])])])])])). 4.46/4.71 fof(c_0_7238, plain, ![X3377, X3378, X3379, X3380]:((~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3380)),X3378),c_List_Olists(X3380,X3377)))|~hBOOL(hAPP(hAPP(c_member(X3380),X3379),X3377))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3380)),hAPP(hAPP(c_List_Olist_OCons(X3380),X3379),X3378)),c_List_Olists(X3380,X3377))))&((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3380)),X3378),c_List_Olists(X3380,X3377)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3380)),hAPP(hAPP(c_List_Olist_OCons(X3380),X3379),X3378)),c_List_Olists(X3380,X3377))))&(hBOOL(hAPP(hAPP(c_member(X3380),X3379),X3377))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3380)),hAPP(hAPP(c_List_Olist_OCons(X3380),X3379),X3378)),c_List_Olists(X3380,X3377)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lists__iff])])])). 4.46/4.71 fof(c_0_7239, plain, ![X11437, X11438]:(~class_Orderings_Olinorder(X11438)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11438),X11437))|(c_Orderings_Obot__class_Obot(tc_fun(X11438,tc_HOL_Obool))=X11437|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11438),c_Big__Operators_Olattice_OInf__fin(X11438,c_Orderings_Oord__class_Omin(X11438),X11437)),c_Big__Operators_Olattice_OSup__fin(X11438,c_Orderings_Oord__class_Omax(X11438),X11437)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__le__Sup])])). 4.46/4.71 fof(c_0_7240, plain, ![X9525, X9526, X9527]:(~class_Divides_Osemiring__div(X9527)|(c_Groups_Ozero__class_Ozero(X9527)=X9526|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9527),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X9527),X9525),X9526)),c_Groups_Oone__class_Oone(X9527))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X9527),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9527),X9525),X9526)),X9526))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__add__self2])])])). 4.46/4.71 fof(c_0_7241, plain, ![X4720, X4721, X4722, X4723, X4724]:(~class_Complete__Lattice_Ocomplete__lattice(X4724)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4723,tc_HOL_Obool)),X4722),X4721))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4724),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4723,X4724),X4721),X4720)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4723,X4724),X4722),X4720))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__subset])])). 4.46/4.71 fof(c_0_7242, plain, ![X14822, X14823, X14824, X14825, X14826]:(~class_Complete__Lattice_Ocomplete__lattice(X14826)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14825,tc_HOL_Obool)),X14824),X14823))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14826),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14825,X14826),X14824),X14822)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14825,X14826),X14823),X14822))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUP__subset])])])). 4.46/4.71 fof(c_0_7243, plain, ![X12811, X12812, X12813]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12813),X12812))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12813,tc_HOL_Obool)),X12812),X12811))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X12813),X12811)),hAPP(c_Finite__Set_Ocard(X12813),X12812))=hAPP(c_Finite__Set_Ocard(X12813),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12813,tc_HOL_Obool)),X12811),X12812)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff__subset])])])). 4.46/4.71 fof(c_0_7244, plain, ![X8735, X8736, X8737]:(~class_Rings_Ocomm__semiring__1(X8737)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8737),X8736),X8735)),X8735)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8737),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8737),X8736),c_Groups_Oone__class_Oone(X8737))),X8735)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])])). 4.46/4.71 fof(c_0_7245, plain, ![X10273, X10274, X10275, X10277, X10278, X10279]:(((hBOOL(hAPP(X10273,esk297_2(X10273,X10274)))|(~hBOOL(hAPP(X10273,X10275))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10275),X10274))))&(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk297_2(X10273,X10274)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10274)))|(~hBOOL(hAPP(X10273,X10275))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10275),X10274)))))&((hBOOL(hAPP(X10277,esk298_2(X10277,X10278)))|(~hBOOL(hAPP(X10277,X10279))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X10279),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10278)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk298_2(X10277,X10278)),X10278))|(~hBOOL(hAPP(X10277,X10279))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X10279),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10278))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__nat__less__eq])])])])])])). 4.46/4.71 fof(c_0_7246, plain, ![X12913, X12914, X12915, X12916]:(~class_Rings_Oring__1(X12916)|~class_Groups_Ocomm__monoid__mult(X12916)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12915,X12916),hAPP(hAPP(c_COMBB(tc_Int_Oint,X12916,X12915),c_Int_Oring__1__class_Oof__int(X12916)),X12914)),X12913)=hAPP(c_Int_Oring__1__class_Oof__int(X12916),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12915,tc_Int_Oint),X12914),X12913))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__setprod])])])). 4.46/4.71 fof(c_0_7247, plain, ![X16329, X16330, X16331]:(~class_Orderings_Olinorder(X16331)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16331),X16330))|(c_Orderings_Obot__class_Obot(tc_fun(X16331,tc_HOL_Obool))=X16329|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16331,tc_HOL_Obool)),X16329),X16330))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X16331),c_Big__Operators_Olinorder__class_OMin(X16331,X16329)),c_Big__Operators_Olinorder__class_OMin(X16331,X16330))=c_Big__Operators_Olinorder__class_OMin(X16331,X16330))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Osubset__idem])])). 4.46/4.71 fof(c_0_7248, plain, ![X10715, X10716, X10717]:(~class_Lattices_Olattice(X10717)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10717),X10716))|(c_Orderings_Obot__class_Obot(tc_fun(X10717,tc_HOL_Obool))=X10715|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10717,tc_HOL_Obool)),X10715),X10716))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10717),c_Big__Operators_Olattice__class_OInf__fin(X10717,X10715)),c_Big__Operators_Olattice__class_OInf__fin(X10717,X10716))=c_Big__Operators_Olattice__class_OInf__fin(X10717,X10716))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Osubset__idem])])])). 4.46/4.71 fof(c_0_7249, plain, ![X12019, X12020, X12021]:(~class_Lattices_Olattice(X12021)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12021),X12020))|(X12019=c_Orderings_Obot__class_Obot(tc_fun(X12021,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12021,tc_HOL_Obool)),X12019),X12020))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X12021),c_Big__Operators_Olattice__class_OSup__fin(X12021,X12019)),c_Big__Operators_Olattice__class_OSup__fin(X12021,X12020))=c_Big__Operators_Olattice__class_OSup__fin(X12021,X12020))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Osubset__idem])])])). 4.46/4.71 fof(c_0_7250, plain, ![X11411, X11412, X11413]:(~class_Orderings_Olinorder(X11413)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11413),X11412))|(X11411=c_Orderings_Obot__class_Obot(tc_fun(X11413,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11413,tc_HOL_Obool)),X11411),X11412))|c_Big__Operators_Olinorder__class_OMax(X11413,X11412)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X11413),c_Big__Operators_Olinorder__class_OMax(X11413,X11411)),c_Big__Operators_Olinorder__class_OMax(X11413,X11412)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Osubset__idem])])])). 4.46/4.71 fof(c_0_7251, plain, ![X12883, X12884, X12885, X12886]:(~class_Groups_Ocomm__monoid__mult(X12886)|~class_Rings_Osemiring__1(X12886)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X12886),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12885,tc_Nat_Onat),X12884),X12883))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12885,X12886),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X12886,X12885),c_Nat_Osemiring__1__class_Oof__nat(X12886)),X12884)),X12883)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__setprod])])). 4.46/4.71 fof(c_0_7252, plain, ![X11352, X11353, X11354, X11355, X11356]:(((hBOOL(hAPP(c_List_Odistinct(X11355),X11352))|~hBOOL(hAPP(c_List_Odistinct(X11355),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X11355,X11356,X11354),X11353),X11352)))|~class_Orderings_Olinorder(X11356))&(~hBOOL(hAPP(hAPP(c_member(X11355),X11353),hAPP(c_List_Oset(X11355),X11352)))|~hBOOL(hAPP(c_List_Odistinct(X11355),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X11355,X11356,X11354),X11353),X11352)))|~class_Orderings_Olinorder(X11356)))&(~hBOOL(hAPP(c_List_Odistinct(X11355),X11352))|hBOOL(hAPP(hAPP(c_member(X11355),X11353),hAPP(c_List_Oset(X11355),X11352)))|hBOOL(hAPP(c_List_Odistinct(X11355),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X11355,X11356,X11354),X11353),X11352)))|~class_Orderings_Olinorder(X11356))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__insort])])])])). 4.46/4.71 fof(c_0_7253, plain, ![X12671, X12672, X12673, X12674]:((X12673!=X12671|hBOOL(hAPP(hAPP(c_member(tc_prod(X12674,X12674)),hAPP(hAPP(c_Product__Type_OPair(X12674,X12674),X12673),X12671)),c_Transitive__Closure_Ortrancl(X12674,X12672)))|hBOOL(hAPP(hAPP(c_member(X12674),X12673),hAPP(c_Relation_ODomain(X12674,X12674),X12672))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X12674,X12674)),hAPP(hAPP(c_Product__Type_OPair(X12674,X12674),X12673),X12671)),c_Transitive__Closure_Ortrancl(X12674,X12672)))|X12673=X12671|hBOOL(hAPP(hAPP(c_member(X12674),X12673),hAPP(c_Relation_ODomain(X12674,X12674),X12672))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Not__Domain__rtrancl])])])])). 4.46/4.71 cnf(c_0_7254, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5276])). 4.46/4.71 fof(c_0_7255, plain, ![X12891, X12892, X12893, X12894]:(~class_Groups_Oordered__ab__semigroup__add__imp__le(X12894)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X12894),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12894),X12893),X12891)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12894),X12892),X12891))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12894),hAPP(hAPP(c_Orderings_Oord__class_Omax(X12894),X12893),X12892)),X12891)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_max__add__distrib__left])])])). 4.46/4.71 cnf(c_0_7256, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X3!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2))), inference(split_conjunct,[status(thm)],[c_0_5031])). 4.46/4.71 cnf(c_0_7257, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5277]), ['final']). 4.46/4.71 cnf(c_0_7258, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1), inference(split_conjunct,[status(thm)],[c_0_5278]), ['final']). 4.46/4.71 fof(c_0_7259, plain, ![X13711, X13712, X13713, X13716, X13717, X13718, X13719, X13720]:(((hAPP(hAPP(c_List_Oappend(X13713),esk399_3(X13711,X13712,X13713)),hAPP(hAPP(c_List_Olist_OCons(X13713),X13712),esk400_3(X13711,X13712,X13713)))=X13711|~hBOOL(hAPP(hAPP(c_member(X13713),X13712),hAPP(c_List_Oset(X13713),X13711))))&(~hBOOL(hAPP(hAPP(c_member(X13713),X13712),hAPP(c_List_Oset(X13713),esk399_3(X13711,X13712,X13713))))|~hBOOL(hAPP(hAPP(c_member(X13713),X13712),hAPP(c_List_Oset(X13713),X13711)))))&(hAPP(hAPP(c_List_Oappend(X13718),X13719),hAPP(hAPP(c_List_Olist_OCons(X13718),X13717),X13720))!=X13716|hBOOL(hAPP(hAPP(c_member(X13718),X13717),hAPP(c_List_Oset(X13718),X13719)))|hBOOL(hAPP(hAPP(c_member(X13718),X13717),hAPP(c_List_Oset(X13718),X13716))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__set__conv__decomp__first])])])])])])])). 4.46/4.71 fof(c_0_7260, plain, ![X7974, X7975, X7976, X7977, X7978, X7979, X7980, X7981]:((hBOOL(hAPP(hAPP(c_member(X7976),X7975),hAPP(c_List_Oset(X7976),X7978)))|hAPP(hAPP(c_List_Oappend(X7976),X7977),hAPP(hAPP(c_List_Olist_OCons(X7976),X7975),X7978))!=X7974|hBOOL(hAPP(hAPP(c_member(X7976),X7975),hAPP(c_List_Oset(X7976),X7974))))&((~hBOOL(hAPP(hAPP(c_member(X7981),X7980),hAPP(c_List_Oset(X7981),esk227_3(X7979,X7980,X7981))))|~hBOOL(hAPP(hAPP(c_member(X7981),X7980),hAPP(c_List_Oset(X7981),X7979))))&(hAPP(hAPP(c_List_Oappend(X7981),esk226_3(X7979,X7980,X7981)),hAPP(hAPP(c_List_Olist_OCons(X7981),X7980),esk227_3(X7979,X7980,X7981)))=X7979|~hBOOL(hAPP(hAPP(c_member(X7981),X7980),hAPP(c_List_Oset(X7981),X7979)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__set__conv__decomp__last])])])])])])])). 4.46/4.71 fof(c_0_7261, plain, ![X14614, X14615, X14616]:(~class_Divides_Osemiring__div(X14616)|(X14615=c_Groups_Ozero__class_Ozero(X14616)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X14616),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14616),X14615),X14614)),X14615)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14616),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X14616),X14614),X14615)),c_Groups_Oone__class_Oone(X14616)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__add__self1])])])). 4.46/4.71 fof(c_0_7262, plain, ![X8042, X8043, X8044, X8045]:(~class_Groups_Oordered__ab__semigroup__add__imp__le(X8045)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X8045),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8045),X8044),X8042)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8045),X8043),X8042))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8045),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8045),X8044),X8043)),X8042)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__add__distrib__left])])])). 4.46/4.71 fof(c_0_7263, plain, ![X9244, X9245, X9246, X9247]:(~class_Rings_Ocomm__semiring(X9247)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9247),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9247),X9246),X9244)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9247),X9245),X9244))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9247),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9247),X9246),X9245)),X9244)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__class_Odistrib])])])). 4.46/4.71 fof(c_0_7264, plain, ![X7957, X7958, X7959, X7960]:(~class_Rings_Odivision__ring(X7960)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7960),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7960),X7959),X7957)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7960),X7958),X7957))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7960),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7960),X7959),X7958)),X7957)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__divide__distrib])])])). 4.46/4.71 fof(c_0_7265, plain, ![X16727, X16728, X16729, X16730, X16732, X16733, X16734, X16736]:((((hBOOL(hAPP(hAPP(c_member(X16729),esk492_4(X16727,X16728,X16729,X16730)),hAPP(c_List_Oset(X16729),X16727)))|~hBOOL(hAPP(X16728,X16730))|~hBOOL(hAPP(hAPP(c_member(X16729),X16730),hAPP(c_List_Oset(X16729),X16727)))|c_List_Olist__ex1(X16729,X16728,X16727))&(hBOOL(hAPP(X16728,esk492_4(X16727,X16728,X16729,X16730)))|~hBOOL(hAPP(X16728,X16730))|~hBOOL(hAPP(hAPP(c_member(X16729),X16730),hAPP(c_List_Oset(X16729),X16727)))|c_List_Olist__ex1(X16729,X16728,X16727)))&(X16730!=esk492_4(X16727,X16728,X16729,X16730)|~hBOOL(hAPP(X16728,X16730))|~hBOOL(hAPP(hAPP(c_member(X16729),X16730),hAPP(c_List_Oset(X16729),X16727)))|c_List_Olist__ex1(X16729,X16728,X16727)))&(((hBOOL(hAPP(X16733,esk493_3(X16732,X16733,X16734)))|~c_List_Olist__ex1(X16734,X16733,X16732))&(~hBOOL(hAPP(hAPP(c_member(X16734),X16736),hAPP(c_List_Oset(X16734),X16732)))|~hBOOL(hAPP(X16733,X16736))|esk493_3(X16732,X16733,X16734)=X16736|~c_List_Olist__ex1(X16734,X16733,X16732)))&(hBOOL(hAPP(hAPP(c_member(X16734),esk493_3(X16732,X16733,X16734)),hAPP(c_List_Oset(X16734),X16732)))|~c_List_Olist__ex1(X16734,X16733,X16732)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex1__iff__raw])])])])])])). 4.46/4.71 fof(c_0_7266, plain, ![X11626, X11627, X11628, X11629]:(~class_Rings_Osemiring__1(X11629)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11629),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X11629),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11628)),X11626))),X11627)=hAPP(c_List_Omonoid__add__class_Olistsum(X11629),hAPP(hAPP(c_List_Omap(X11628,X11629),hAPP(c_COMBK(X11629,X11628),X11627)),X11626))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__triv])])])). 4.46/4.71 cnf(c_0_7267, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))), inference(split_conjunct,[status(thm)],[c_0_5279])). 4.46/4.71 fof(c_0_7268, plain, ![X3654, X3655, X3656, X3657]:(~class_Lattices_Odistrib__lattice(X3657)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3657),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3657),X3656),X3654)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3657),X3655),X3654))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3657),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3657),X3656),X3655)),X3654)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib2])])). 4.46/4.71 fof(c_0_7269, plain, ![X9528, X9529, X9530, X9531]:(~class_Lattices_Odistrib__lattice(X9531)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9531),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9531),X9530),X9528)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9531),X9529),X9528))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9531),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9531),X9530),X9529)),X9528)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib2])])). 4.46/4.71 fof(c_0_7270, plain, ![X13954, X13955, X13956, X13957]:(~class_Rings_Ocomm__semiring__1(X13957)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13957),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13957),X13956),X13955)),X13954)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13957),X13956),X13954)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13957),X13955),X13954))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])])). 4.46/4.71 fof(c_0_7271, plain, ![X549, X550, X551, X552]:(~class_Rings_Odivision__ring(X552)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X552),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X552),X551),X550)),X549)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X552),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X552),X551),X549)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X552),X550),X549))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__divide__distrib])])])). 4.46/4.71 fof(c_0_7272, plain, ![X5279, X5280, X5281, X5283, X5284, X5285, X5286, X5287]:((((hBOOL(hAPP(hAPP(c_member(X5281),esk162_3(X5279,X5280,X5281)),hAPP(c_List_Oset(X5281),X5279)))|~c_List_Olist__ex1(X5281,X5280,X5279))&(~hBOOL(hAPP(hAPP(c_member(X5281),X5283),hAPP(c_List_Oset(X5281),X5279)))|~hBOOL(hAPP(X5280,X5283))|X5283=esk162_3(X5279,X5280,X5281)|~c_List_Olist__ex1(X5281,X5280,X5279)))&(hBOOL(hAPP(X5280,esk162_3(X5279,X5280,X5281)))|~c_List_Olist__ex1(X5281,X5280,X5279)))&(((hBOOL(hAPP(hAPP(c_member(X5286),esk163_4(X5284,X5285,X5286,X5287)),hAPP(c_List_Oset(X5286),X5284)))|~hBOOL(hAPP(hAPP(c_member(X5286),X5287),hAPP(c_List_Oset(X5286),X5284)))|~hBOOL(hAPP(X5285,X5287))|c_List_Olist__ex1(X5286,X5285,X5284))&(hBOOL(hAPP(X5285,esk163_4(X5284,X5285,X5286,X5287)))|~hBOOL(hAPP(hAPP(c_member(X5286),X5287),hAPP(c_List_Oset(X5286),X5284)))|~hBOOL(hAPP(X5285,X5287))|c_List_Olist__ex1(X5286,X5285,X5284)))&(esk163_4(X5284,X5285,X5286,X5287)!=X5287|~hBOOL(hAPP(hAPP(c_member(X5286),X5287),hAPP(c_List_Oset(X5286),X5284)))|~hBOOL(hAPP(X5285,X5287))|c_List_Olist__ex1(X5286,X5285,X5284)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex1__iff])])])])])])). 4.46/4.71 fof(c_0_7273, plain, ![X9868, X9869, X9870]:(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X9868,X9869)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X9870,X9869)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9868),X9870))|X9870=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9869),esk284_3(X9868,X9869,X9870))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__mod__eq__lemma])])])])). 4.46/4.71 fof(c_0_7274, plain, ![X1864, X1865, X1866, X1867]:(~class_Groups_Oordered__ab__group__add(X1867)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1867),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1867),X1866),X1865)),X1864)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1867),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1867),X1866),X1864)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1867),X1865),X1864))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_max__diff__distrib__left])])])). 4.46/4.71 fof(c_0_7275, plain, ![X10129, X10130, X10131, X10132]:(~class_Groups_Oordered__ab__group__add(X10132)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10132),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10132),X10131),X10130)),X10129)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X10132),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10132),X10131),X10129)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10132),X10130),X10129))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__diff__distrib__left])])). 4.46/4.71 cnf(c_0_7276, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5280, c_0_4471]), c_0_4471])). 4.46/4.71 cnf(c_0_7277, plain, (hBOOL(hAPP(X5,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),X2)!=X4|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~epred1_3(X5,X1,X4)), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.71 cnf(c_0_7278, plain, (hBOOL(hAPP(X5,X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|X3!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|~epred2_3(X5,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_5124])). 4.46/4.71 cnf(c_0_7279, plain, (hBOOL(hAPP(X5,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),X2)!=X4|~epred1_3(X5,X1,X4)), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.71 cnf(c_0_7280, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5281, c_0_4471]), c_0_4471])). 4.46/4.71 cnf(c_0_7281, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5282, c_0_4471]), c_0_4471])). 4.46/4.71 fof(c_0_7282, plain, ![X11836, X11837, X11838]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11838),X11837))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X11838,X11838),tc_HOL_Obool)),X11836),hAPP(hAPP(c_Product__Type_OSigma(X11838,X11838),X11837),hAPP(c_COMBK(tc_fun(X11838,tc_HOL_Obool),X11838),X11837))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X11838,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X11838),X11837),X11836))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__quotient])])])). 4.46/4.71 cnf(c_0_7283, plain, (hBOOL(hAPP(X5,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X4))|~epred2_3(X5,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5124])). 4.46/4.71 fof(c_0_7284, plain, ![X15179, X15180, X15181, X15182, X15183, X15184]:(~c_Finite__Set_Ofolding__idem(X15184,X15183,X15182,X15181)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15184),X15180))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15184,tc_HOL_Obool)),X15179),X15180))|hAPP(c_Fun_Ocomp(X15183,X15183,X15183,hAPP(X15181,X15180)),hAPP(X15181,X15179))=hAPP(X15181,X15180)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__idem_Osubset__comp__idem])])])). 4.46/4.71 fof(c_0_7285, plain, ![X921, X922, X923]:((hBOOL(hAPP(hAPP(c_member(X923),esk23_3(X921,X922,X923)),X922))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X923,tc_Nat_Onat),X921),X922)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X923),X922)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X921,esk23_3(X921,X922,X923))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X923,tc_Nat_Onat),X921),X922)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X923),X922)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__pos__nat])])])])])). 4.46/4.71 fof(c_0_7286, plain, ![X14599, X14600, X14601, X14602]:(~class_Rings_Ocomm__semiring__1(X14602)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14602),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14602),X14601),X14600)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14602),X14601),X14599))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14602),X14601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14602),X14600),X14599))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])])])). 4.46/4.71 fof(c_0_7287, plain, ![X6778, X6779, X6780, X6781, X6782, X6783, X6784, X6785]:(~hBOOL(hAPP(hAPP(c_member(X6785),X6784),X6783))|(~hBOOL(hAPP(hAPP(hAPP(X6782,X6784),X6781),X6780))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6785,tc_fun(X6779,tc_fun(X6778,tc_HOL_Obool))),X6783),X6782),X6781),X6780)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUP2__I])])])). 4.46/4.71 fof(c_0_7288, plain, ![X11253, X11254, X11255]:(~class_Rings_Olinordered__semidom(X11255)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11255),c_Groups_Oone__class_Oone(X11255)),X11254))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11255),c_Groups_Oone__class_Oone(X11255)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11255),X11254),hAPP(hAPP(c_Power_Opower__class_Opower(X11255),X11254),X11253)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma])])). 4.46/4.71 cnf(c_0_7289, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5283, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.71 cnf(c_0_7290, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk193_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|c_List_Olist_ONil(X1)=c_List_OdropWhile(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_5284])). 4.46/4.71 fof(c_0_7291, plain, ![X15728, X15729, X15730]:((hBOOL(hAPP(hAPP(c_member(X15730),esk459_3(X15728,X15729,X15730)),X15728))|c_Relation_Orefl__on(X15730,X15728,X15729)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15730,X15730),tc_HOL_Obool)),X15729),hAPP(hAPP(c_Product__Type_OSigma(X15730,X15730),X15728),hAPP(c_COMBK(tc_fun(X15730,tc_HOL_Obool),X15730),X15728)))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X15730,X15730)),hAPP(hAPP(c_Product__Type_OPair(X15730,X15730),esk459_3(X15728,X15729,X15730)),esk459_3(X15728,X15729,X15730))),X15729))|c_Relation_Orefl__on(X15730,X15728,X15729)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15730,X15730),tc_HOL_Obool)),X15729),hAPP(hAPP(c_Product__Type_OSigma(X15730,X15730),X15728),hAPP(c_COMBK(tc_fun(X15730,tc_HOL_Obool),X15730),X15728)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__onI])])])])])). 4.46/4.71 fof(c_0_7292, plain, ![X1693, X1694, X1695, X1696, X1697, X1698, X1699]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1695,X1695),tc_HOL_Obool)),X1693),hAPP(hAPP(c_Product__Type_OSigma(X1695,X1695),X1694),hAPP(c_COMBK(tc_fun(X1695,tc_HOL_Obool),X1695),X1694))))|~c_Relation_Orefl__on(X1695,X1694,X1693))&(~hBOOL(hAPP(hAPP(c_member(X1695),X1696),X1694))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1695,X1695)),hAPP(hAPP(c_Product__Type_OPair(X1695,X1695),X1696),X1696)),X1693))|~c_Relation_Orefl__on(X1695,X1694,X1693)))&((hBOOL(hAPP(hAPP(c_member(X1699),esk41_3(X1697,X1698,X1699)),X1698))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1699,X1699),tc_HOL_Obool)),X1697),hAPP(hAPP(c_Product__Type_OSigma(X1699,X1699),X1698),hAPP(c_COMBK(tc_fun(X1699,tc_HOL_Obool),X1699),X1698))))|c_Relation_Orefl__on(X1699,X1698,X1697))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X1699,X1699)),hAPP(hAPP(c_Product__Type_OPair(X1699,X1699),esk41_3(X1697,X1698,X1699)),esk41_3(X1697,X1698,X1699))),X1697))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1699,X1699),tc_HOL_Obool)),X1697),hAPP(hAPP(c_Product__Type_OSigma(X1699,X1699),X1698),hAPP(c_COMBK(tc_fun(X1699,tc_HOL_Obool),X1699),X1698))))|c_Relation_Orefl__on(X1699,X1698,X1697)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__def])])])])])])). 4.46/4.71 cnf(c_0_7293, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5285])). 4.46/4.71 fof(c_0_7294, plain, ![X8408, X8409, X8410]:(~class_Groups_Oordered__ab__group__add__abs(X8410)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8410),hAPP(c_Groups_Oabs__class_Oabs(X8410),X8409)),hAPP(c_Groups_Oabs__class_Oabs(X8410),X8408))=hAPP(c_Groups_Oabs__class_Oabs(X8410),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8410),hAPP(c_Groups_Oabs__class_Oabs(X8410),X8409)),hAPP(c_Groups_Oabs__class_Oabs(X8410),X8408)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__add__abs])])])). 4.46/4.71 fof(c_0_7295, plain, ![X13253, X13254, X13255, X13256]:(~class_Lattices_Odistrib__lattice(X13256)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13256),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X13256),X13255),X13254)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X13256),X13255),X13253))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X13256),X13255),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13256),X13254),X13253))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__distrib1])])])). 4.46/4.71 fof(c_0_7296, plain, ![X10637, X10638, X10639]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10638))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10639),X10637))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10639),X10638)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10637),X10638))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10638))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10639),X10638)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10637),X10638))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10639),X10637))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10639),X10638)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10637),X10638)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])])). 4.46/4.71 cnf(c_0_7297, plain, (hAPP(c_Option_Ooption_OSome(X1),esk519_6(X2,X3,X4,X5,X6,X1))=hAPP(X3,X2)|c_Option_Ooption_ONone(X1)=hAPP(X3,X2)|c_Option_Ooption_ONone(X6)!=c_Map_Omap__comp(X1,X6,X5,X4,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_5286])). 4.46/4.71 fof(c_0_7298, plain, ![X2108, X2109, X2110, X2111]:(~class_Lattices_Odistrib__lattice(X2111)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2111),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2111),X2110),X2109)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2111),X2110),X2108))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2111),X2110),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2111),X2109),X2108))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__inf__distrib1])])])). 4.46/4.71 fof(c_0_7299, plain, ![X10993, X10994, X10995]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10995),X10994)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10995),X10993)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10994),X10993))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10995)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10994),X10993))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10995),X10994)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10995),X10993)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10995)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__mult__less__cancel1])])])])). 4.46/4.71 fof(c_0_7300, plain, ![X475, X476, X477]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X477),X476))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X475))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X475),X477)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X475),X476))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult__zless__mono2])])])). 4.46/4.71 fof(c_0_7301, plain, ![X15897, X15898, X15899]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15899))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15899),X15898))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X15897),X15898)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X15897),X15899))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__le__mono2])])])). 4.46/4.71 cnf(c_0_7302, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk263_3(X1,X2,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),X2),c_Transitive__Closure_Otrancl(X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5129])). 4.46/4.71 fof(c_0_7303, plain, ![X11771, X11772, X11773, X11774, X11776, X11777, X11778, X11779, X11781]:(((hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X11773)),esk346_4(X11771,X11772,X11773,X11774)),X11772))|(~hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X11773)),X11776),X11771))|c_Hoare__Mirabelle_Otriple__valid(X11773,X11774,X11776))|~c_Hoare__Mirabelle_Ohoare__valids(X11773,X11772,X11771))&(~c_Hoare__Mirabelle_Otriple__valid(X11773,X11774,esk346_4(X11771,X11772,X11773,X11774))|(~hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X11773)),X11776),X11771))|c_Hoare__Mirabelle_Otriple__valid(X11773,X11774,X11776))|~c_Hoare__Mirabelle_Ohoare__valids(X11773,X11772,X11771)))&((~hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X11779)),X11781),X11778))|c_Hoare__Mirabelle_Otriple__valid(X11779,esk347_3(X11777,X11778,X11779),X11781)|c_Hoare__Mirabelle_Ohoare__valids(X11779,X11778,X11777))&((hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X11779)),esk348_3(X11777,X11778,X11779)),X11777))|c_Hoare__Mirabelle_Ohoare__valids(X11779,X11778,X11777))&(~c_Hoare__Mirabelle_Otriple__valid(X11779,esk347_3(X11777,X11778,X11779),esk348_3(X11777,X11778,X11779))|c_Hoare__Mirabelle_Ohoare__valids(X11779,X11778,X11777))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hoare__valids__def])])])])])])])). 4.46/4.71 fof(c_0_7304, plain, ![X16234, X16235, X16236, X16237]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16237),X16234),X16235))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16237),X16236),c_Groups_Ozero__class_Ozero(X16237)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16237),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16237),X16236),X16235)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16237),X16236),X16234)))|~class_Rings_Olinordered__ring__strict(X16237))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16237),X16235),X16234))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16237),c_Groups_Ozero__class_Ozero(X16237)),X16236))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16237),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16237),X16236),X16235)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16237),X16236),X16234)))|~class_Rings_Olinordered__ring__strict(X16237)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16237),X16235),X16234))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16237),X16234),X16235))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16237),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16237),X16236),X16235)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16237),X16236),X16234)))|~class_Rings_Olinordered__ring__strict(X16237))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16237),c_Groups_Ozero__class_Ozero(X16237)),X16236))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16237),X16234),X16235))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16237),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16237),X16236),X16235)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16237),X16236),X16234)))|~class_Rings_Olinordered__ring__strict(X16237)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16237),X16235),X16234))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16237),X16236),c_Groups_Ozero__class_Ozero(X16237)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16237),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16237),X16236),X16235)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16237),X16236),X16234)))|~class_Rings_Olinordered__ring__strict(X16237))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16237),c_Groups_Ozero__class_Ozero(X16237)),X16236))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16237),X16236),c_Groups_Ozero__class_Ozero(X16237)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16237),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16237),X16236),X16235)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16237),X16236),X16234)))|~class_Rings_Olinordered__ring__strict(X16237))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj])])])). 4.46/4.71 cnf(c_0_7305, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk436_4(X1,X2,X3,X4)),X1))|X2=X4|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)!=X2|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5198])). 4.46/4.71 fof(c_0_7306, plain, ![X8779, X8780, X8781]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8781),X8780))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8779))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8781),X8779)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8780),X8779))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono1])])])). 4.46/4.71 fof(c_0_7307, plain, ![X2685, X2686, X2687]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2687),X2686))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2685),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2686),X2685)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2687),X2685))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono1__neg])])])). 4.46/4.71 fof(c_0_7308, plain, ![X14984, X14985, X14986]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X14986,X14986),tc_HOL_Obool)),X14985),X14984))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X14986),tc_List_Olist(X14986)),tc_HOL_Obool)),c_List_Olistrel1(X14986,X14985)),c_List_Olistrel1(X14986,X14984)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__mono])])). 4.46/4.71 fof(c_0_7309, plain, ![X931, X932, X933]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X933,X933),tc_HOL_Obool)),X932),X931))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X933),tc_List_Olist(X933)),tc_HOL_Obool)),c_List_Olistrel(X933,X932)),c_List_Olistrel(X933,X931)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel__mono])])])). 4.46/4.71 fof(c_0_7310, plain, ![X13476, X13477, X13478, X13479]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X13479),esk396_4(X13476,X13477,X13478,X13479)))|hBOOL(hAPP(X13476,X13478))|~hBOOL(hAPP(X13476,c_Orderings_Obot__class_Obot(tc_fun(X13479,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13479,tc_HOL_Obool)),X13478),X13477))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13479),X13478)))&((hBOOL(hAPP(hAPP(c_member(X13479),esk395_4(X13476,X13477,X13478,X13479)),X13477))|hBOOL(hAPP(X13476,X13478))|~hBOOL(hAPP(X13476,c_Orderings_Obot__class_Obot(tc_fun(X13479,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13479,tc_HOL_Obool)),X13478),X13477))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13479),X13478)))&((~hBOOL(hAPP(hAPP(c_member(X13479),esk395_4(X13476,X13477,X13478,X13479)),esk396_4(X13476,X13477,X13478,X13479)))|hBOOL(hAPP(X13476,X13478))|~hBOOL(hAPP(X13476,c_Orderings_Obot__class_Obot(tc_fun(X13479,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13479,tc_HOL_Obool)),X13478),X13477))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13479),X13478)))&((hBOOL(hAPP(X13476,esk396_4(X13476,X13477,X13478,X13479)))|hBOOL(hAPP(X13476,X13478))|~hBOOL(hAPP(X13476,c_Orderings_Obot__class_Obot(tc_fun(X13479,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13479,tc_HOL_Obool)),X13478),X13477))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13479),X13478)))&(~hBOOL(hAPP(X13476,hAPP(hAPP(c_Set_Oinsert(X13479),esk395_4(X13476,X13477,X13478,X13479)),esk396_4(X13476,X13477,X13478,X13479))))|hBOOL(hAPP(X13476,X13478))|~hBOOL(hAPP(X13476,c_Orderings_Obot__class_Obot(tc_fun(X13479,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13479,tc_HOL_Obool)),X13478),X13477))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13479),X13478))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__subset__induct])])])])])). 4.46/4.71 fof(c_0_7311, plain, ![X4223, X4224, X4225]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4225),esk116_3(X4223,X4224,X4225)))|hBOOL(hAPP(X4223,c_Orderings_Obot__class_Obot(tc_fun(X4225,tc_HOL_Obool))))|~hBOOL(hAPP(X4223,X4224))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4225),X4224)))&((hBOOL(hAPP(hAPP(c_member(X4225),esk115_3(X4223,X4224,X4225)),esk116_3(X4223,X4224,X4225)))|hBOOL(hAPP(X4223,c_Orderings_Obot__class_Obot(tc_fun(X4225,tc_HOL_Obool))))|~hBOOL(hAPP(X4223,X4224))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4225),X4224)))&((hBOOL(hAPP(X4223,esk116_3(X4223,X4224,X4225)))|hBOOL(hAPP(X4223,c_Orderings_Obot__class_Obot(tc_fun(X4225,tc_HOL_Obool))))|~hBOOL(hAPP(X4223,X4224))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4225),X4224)))&(~hBOOL(hAPP(X4223,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4225,tc_HOL_Obool)),esk116_3(X4223,X4224,X4225)),hAPP(hAPP(c_Set_Oinsert(X4225),esk115_3(X4223,X4224,X4225)),c_Orderings_Obot__class_Obot(tc_fun(X4225,tc_HOL_Obool))))))|hBOOL(hAPP(X4223,c_Orderings_Obot__class_Obot(tc_fun(X4225,tc_HOL_Obool))))|~hBOOL(hAPP(X4223,X4224))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4225),X4224)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__empty__induct])])])])])). 4.46/4.71 cnf(c_0_7312, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk258_4(X1,X2,X3,X4)),X1))|X4=X2|X2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5203])). 4.46/4.71 fof(c_0_7313, plain, ![X16231, X16232, X16233]:(~c_Equiv__Relations_Oequiv(X16233,X16232,X16231)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X16233,X16233),tc_HOL_Obool)),X16231),hAPP(hAPP(c_Product__Type_OSigma(X16233,X16233),X16232),hAPP(c_COMBK(tc_fun(X16233,tc_HOL_Obool),X16233),X16232))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__type])])). 4.46/4.71 fof(c_0_7314, plain, ![X3225, X3226, X3227]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3227))|(X3227!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3226),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3227),X3225))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3226),X3227))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X3225))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_self__quotient__aux1])])])). 4.46/4.71 fof(c_0_7315, plain, ![X14454, X14455, X14456, X14457]:((~hBOOL(hAPP(hAPP(c_member(X14457),X14456),hAPP(c_List_Oset(X14457),c_List_Obutlast(X14457,X14455))))|hBOOL(hAPP(hAPP(c_member(X14457),X14456),hAPP(c_List_Oset(X14457),c_List_Obutlast(X14457,hAPP(hAPP(c_List_Oappend(X14457),X14455),X14454))))))&(~hBOOL(hAPP(hAPP(c_member(X14457),X14456),hAPP(c_List_Oset(X14457),c_List_Obutlast(X14457,X14454))))|hBOOL(hAPP(hAPP(c_member(X14457),X14456),hAPP(c_List_Oset(X14457),c_List_Obutlast(X14457,hAPP(hAPP(c_List_Oappend(X14457),X14455),X14454))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__set__butlast__appendI])])])])). 4.46/4.71 fof(c_0_7316, plain, ![X10401, X10402, X10403]:(~class_Groups_Oab__semigroup__mult(X10403)|(c_Orderings_Obot__class_Obot(tc_fun(X10403,tc_HOL_Obool))=X10402|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10403),X10402))|(hBOOL(hAPP(hAPP(c_member(X10403),X10401),X10402))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10403),X10401),hAPP(c_Finite__Set_Ofold1(X10403,c_Groups_Otimes__class_Otimes(X10403)),X10402))=hAPP(c_Finite__Set_Ofold1(X10403,c_Groups_Otimes__class_Otimes(X10403)),hAPP(hAPP(c_Set_Oinsert(X10403),X10401),X10402)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__insert])])])). 4.46/4.71 fof(c_0_7317, plain, ![X1885, X1886, X1887]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1885),X1886))|hBOOL(hAPP(X1887,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1886)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1885))))|~hBOOL(hAPP(X1887,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1886),X1885)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1886),X1885))|hBOOL(hAPP(X1887,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1887,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1886),X1885))))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1886),X1885))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1885),X1886))|hBOOL(hAPP(X1887,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1886),X1885)))))&(~hBOOL(hAPP(X1887,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1885),X1886))|hBOOL(hAPP(X1887,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1886),X1885))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1886),X1885))|~hBOOL(hAPP(X1887,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1886)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1885))))|hBOOL(hAPP(X1887,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1886),X1885)))))&(~hBOOL(hAPP(X1887,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1887,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1886)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1885))))|hBOOL(hAPP(X1887,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1886),X1885)))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiff__int__split])])])])). 4.46/4.71 fof(c_0_7318, plain, ![X5758, X5759, X5760, X5761]:(~class_Groups_Osemigroup__add(X5761)|hAPP(c_List_Ofoldl(X5761,X5761,c_Groups_Oplus__class_Oplus(X5761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5761),X5760),X5759)),X5758)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5761),X5760),hAPP(c_List_Ofoldl(X5761,X5761,c_Groups_Oplus__class_Oplus(X5761),X5759),X5758))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_foldl__assoc])])])). 4.46/4.71 fof(c_0_7319, plain, ![X6393, X6394, X6395, X6396, X6397, X6398]:(~c_Finite__Set_Ofolding__idem(X6398,X6397,X6396,X6395)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6398),X6394))|(~hBOOL(hAPP(hAPP(c_member(X6398),X6393),X6394))|hAPP(c_Fun_Ocomp(X6397,X6397,X6397,hAPP(X6395,X6394)),hAPP(X6396,X6393))=hAPP(X6395,X6394)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__idem_Oin__comp__idem])])])). 4.46/4.71 cnf(c_0_7320, plain, (hBOOL(hAPP(X1,esk445_2(X1,X2)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk444_2(X1,X2)),X2))))|~hBOOL(hAPP(X1,esk443_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5061])). 4.46/4.71 cnf(c_0_7321, plain, (c_List_Ofoldr(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2,X3)=hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X3),X2)|~class_Groups_Oab__semigroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5287])). 4.46/4.71 cnf(c_0_7322, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))), inference(rw,[status(thm)],[c_0_5288, c_0_4443])). 4.46/4.71 fof(c_0_7323, plain, ![X5518, X5519, X5520, X5521]:(~class_Orderings_Olinorder(X5521)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5521),X5520),X5519))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5521,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5521,X5520),X5518)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5521,X5520),X5519))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5521,X5519),X5518))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__diff])])). 4.46/4.71 fof(c_0_7324, plain, ![X1415, X1416, X1417, X1418, X1419]:(~c_Fun_Oinj__on(X1419,X1418,X1417,X1416)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1419,tc_HOL_Obool)),X1415),X1416))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1418,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1419,X1418,X1417),X1415)),hAPP(c_Set_Oimage(X1419,X1418,X1417),X1416))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset])])). 4.46/4.71 cnf(c_0_7325, plain, (c_List_Oupt(X1,X2)=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),c_List_Oupt(hAPP(c_Nat_OSuc,X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5289])). 4.46/4.71 fof(c_0_7326, plain, ![X11986, X11987, X11988, X11989, X11990]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11990),X11987),X11989))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11990),X11989),X11988))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11990,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X11990,X11989,X11988)),c_SetInterval_Oord__class_OatLeastAtMost(X11990,X11987,X11986)))|~class_Orderings_Oorder(X11990))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11990),X11988),X11986))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11990),X11989),X11988))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11990,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X11990,X11989,X11988)),c_SetInterval_Oord__class_OatLeastAtMost(X11990,X11987,X11986)))|~class_Orderings_Oorder(X11990)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11990),X11989),X11988))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11990,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X11990,X11989,X11988)),c_SetInterval_Oord__class_OatLeastAtMost(X11990,X11987,X11986)))|~class_Orderings_Oorder(X11990))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11990),X11987),X11989))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11990),X11988),X11986))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11990,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X11990,X11989,X11988)),c_SetInterval_Oord__class_OatLeastAtMost(X11990,X11987,X11986)))|~class_Orderings_Oorder(X11990)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastatMost__subset__iff])])])])). 4.46/4.71 fof(c_0_7327, plain, ![X6407, X6408, X6409, X6410, X6411]:(((X6410!=X6408|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6411),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6411),X6410),X6407)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6411),X6408),X6409))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6411),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6411),X6410),X6409)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6411),X6408),X6407))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6411))&(X6407!=X6409|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6411),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6411),X6410),X6407)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6411),X6408),X6409))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6411),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6411),X6410),X6409)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6411),X6408),X6407))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6411)))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6411),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6411),X6410),X6407)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6411),X6408),X6409))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6411),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6411),X6410),X6409)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6411),X6408),X6407))|(X6410=X6408|X6407=X6409)|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6411))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_crossproduct__eq])])])])). 4.46/4.71 fof(c_0_7328, plain, ![X6049, X6050, X6051, X6052]:(~class_Groups_Omonoid__mult(X6052)|hAPP(hAPP(c_Power_Opower__class_Opower(X6052),X6051),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6050),X6049))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6052),hAPP(hAPP(c_Power_Opower__class_Opower(X6052),X6051),X6050)),hAPP(hAPP(c_Power_Opower__class_Opower(X6052),X6051),X6049))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__add])])])). 4.46/4.71 fof(c_0_7329, plain, ![X4726, X4727, X4728]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4728),X4727))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4727)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4728),X4726))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4727),X4728))),X4726)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2])])). 4.46/4.71 fof(c_0_7330, plain, ![X4424, X4425, X4426]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4426),X4425))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4424),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4425),X4426)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4424),X4426)),hAPP(c_Nat_OSuc,X4425))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__Suc__diff__eq1])])])). 4.46/4.71 fof(c_0_7331, plain, ![X4402, X4403, X4404, X4405]:(~c_Relation_Orefl__on(X4405,X4404,X4403)|(~hBOOL(hAPP(hAPP(c_member(X4405),X4402),X4404))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4405,X4405)),hAPP(hAPP(c_Product__Type_OPair(X4405,X4405),X4402),X4402)),X4403)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD])])). 4.46/4.71 fof(c_0_7332, plain, ![X9880, X9881, X9882, X9883]:(~class_Groups_Oab__group__add(X9883)|hAPP(c_Groups_Ouminus__class_Ouminus(X9883),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9882,X9883),X9881),X9880))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9882,X9883),hAPP(hAPP(c_COMBB(X9883,X9883,X9882),c_Groups_Ouminus__class_Ouminus(X9883)),X9881)),X9880)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__negf])])). 4.46/4.71 cnf(c_0_7333, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_5290])). 4.46/4.71 fof(c_0_7334, plain, ![X1566, X1567, X1568, X1569, X1570]:(~c_Relation_Orefl__on(X1570,X1569,X1568)|(~c_Relation_Orefl__on(X1570,X1567,X1566)|c_Relation_Orefl__on(X1570,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1570,tc_HOL_Obool)),X1569),X1567),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1570,X1570),tc_HOL_Obool)),X1568),X1566)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__on__Un])])])). 4.46/4.71 fof(c_0_7335, plain, ![X4890, X4891, X4892, X4893, X4894]:(~c_Relation_Orefl__on(X4894,X4893,X4892)|(~c_Relation_Orefl__on(X4894,X4891,X4890)|c_Relation_Orefl__on(X4894,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4894,tc_HOL_Obool)),X4893),X4891),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4894,X4894),tc_HOL_Obool)),X4892),X4890)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__on__Int])])])). 4.46/4.71 cnf(c_0_7336, plain, (hBOOL(hAPP(X1,X2))|c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))=hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(hAPP(c_COMBC(X3,X3,tc_HOL_Obool),c_fequal),X2))),X1))), inference(split_conjunct,[status(thm)],[c_0_5267])). 4.46/4.71 fof(c_0_7337, plain, ![X17561, X17562, X17563, X17564]:(~class_Rings_Osemiring__1(X17564)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17563,X17564),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X17564,X17563),c_Nat_Osemiring__1__class_Oof__nat(X17564)),X17562)),X17561)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X17564),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17563,tc_Nat_Onat),X17562),X17561))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__setsum])])). 4.46/4.71 cnf(c_0_7338, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X5,X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))|X3!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X2)|~hBOOL(hAPP(X5,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))), inference(split_conjunct,[status(thm)],[c_0_5209])). 4.46/4.71 fof(c_0_7339, plain, ![X14095, X14096, X14097, X14098, X14099, X14100, X14101, X14102, X14103, X14104, X14105]:(((hAPP(hAPP(c_List_Olist_OCons(X14099),X14096),X14095)!=X14097|X14098!=c_List_Olist_ONil(X14099)|hAPP(hAPP(c_List_Oappend(X14099),X14098),X14097)=hAPP(hAPP(c_List_Olist_OCons(X14099),X14096),X14095))&(X14098!=hAPP(hAPP(c_List_Olist_OCons(X14099),X14096),X14100)|hAPP(hAPP(c_List_Oappend(X14099),X14100),X14097)!=X14095|hAPP(hAPP(c_List_Oappend(X14099),X14098),X14097)=hAPP(hAPP(c_List_Olist_OCons(X14099),X14096),X14095)))&(((X14104=hAPP(hAPP(c_List_Olist_OCons(X14105),X14102),esk408_5(X14101,X14102,X14103,X14104,X14105))|hAPP(hAPP(c_List_Olist_OCons(X14105),X14102),X14101)=X14103|hAPP(hAPP(c_List_Oappend(X14105),X14104),X14103)!=hAPP(hAPP(c_List_Olist_OCons(X14105),X14102),X14101))&(hAPP(hAPP(c_List_Oappend(X14105),esk408_5(X14101,X14102,X14103,X14104,X14105)),X14103)=X14101|hAPP(hAPP(c_List_Olist_OCons(X14105),X14102),X14101)=X14103|hAPP(hAPP(c_List_Oappend(X14105),X14104),X14103)!=hAPP(hAPP(c_List_Olist_OCons(X14105),X14102),X14101)))&((X14104=hAPP(hAPP(c_List_Olist_OCons(X14105),X14102),esk408_5(X14101,X14102,X14103,X14104,X14105))|X14104=c_List_Olist_ONil(X14105)|hAPP(hAPP(c_List_Oappend(X14105),X14104),X14103)!=hAPP(hAPP(c_List_Olist_OCons(X14105),X14102),X14101))&(hAPP(hAPP(c_List_Oappend(X14105),esk408_5(X14101,X14102,X14103,X14104,X14105)),X14103)=X14101|X14104=c_List_Olist_ONil(X14105)|hAPP(hAPP(c_List_Oappend(X14105),X14104),X14103)!=hAPP(hAPP(c_List_Olist_OCons(X14105),X14102),X14101))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__Cons__conv])])])])])])). 4.46/4.71 fof(c_0_7340, plain, ![X16247, X16248, X16249, X16250, X16251, X16252, X16253, X16254, X16255, X16256, X16257]:(((hAPP(hAPP(c_List_Olist_OCons(X16251),X16250),X16249)!=X16247|c_List_Olist_ONil(X16251)!=X16248|hAPP(hAPP(c_List_Olist_OCons(X16251),X16250),X16249)=hAPP(hAPP(c_List_Oappend(X16251),X16248),X16247))&(X16248!=hAPP(hAPP(c_List_Olist_OCons(X16251),X16250),X16252)|hAPP(hAPP(c_List_Oappend(X16251),X16252),X16247)!=X16249|hAPP(hAPP(c_List_Olist_OCons(X16251),X16250),X16249)=hAPP(hAPP(c_List_Oappend(X16251),X16248),X16247)))&(((X16254=hAPP(hAPP(c_List_Olist_OCons(X16257),X16256),esk472_5(X16253,X16254,X16255,X16256,X16257))|hAPP(hAPP(c_List_Olist_OCons(X16257),X16256),X16255)=X16253|hAPP(hAPP(c_List_Olist_OCons(X16257),X16256),X16255)!=hAPP(hAPP(c_List_Oappend(X16257),X16254),X16253))&(hAPP(hAPP(c_List_Oappend(X16257),esk472_5(X16253,X16254,X16255,X16256,X16257)),X16253)=X16255|hAPP(hAPP(c_List_Olist_OCons(X16257),X16256),X16255)=X16253|hAPP(hAPP(c_List_Olist_OCons(X16257),X16256),X16255)!=hAPP(hAPP(c_List_Oappend(X16257),X16254),X16253)))&((X16254=hAPP(hAPP(c_List_Olist_OCons(X16257),X16256),esk472_5(X16253,X16254,X16255,X16256,X16257))|c_List_Olist_ONil(X16257)=X16254|hAPP(hAPP(c_List_Olist_OCons(X16257),X16256),X16255)!=hAPP(hAPP(c_List_Oappend(X16257),X16254),X16253))&(hAPP(hAPP(c_List_Oappend(X16257),esk472_5(X16253,X16254,X16255,X16256,X16257)),X16253)=X16255|c_List_Olist_ONil(X16257)=X16254|hAPP(hAPP(c_List_Olist_OCons(X16257),X16256),X16255)!=hAPP(hAPP(c_List_Oappend(X16257),X16254),X16253))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__eq__append__conv])])])])])])). 4.46/4.71 cnf(c_0_7341, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3))|~class_Groups_Ocomm__monoid__add(X1)|c_Groups_Ozero__class_Ozero(X1)!=hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5291])). 4.46/4.71 fof(c_0_7342, plain, ![X4124, X4125, X4126]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4126),X4125))|(~hBOOL(hAPP(hAPP(c_member(X4126),X4124),X4125))|hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X4126),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4126,tc_HOL_Obool)),X4125),hAPP(hAPP(c_Set_Oinsert(X4126),X4124),c_Orderings_Obot__class_Obot(tc_fun(X4126,tc_HOL_Obool))))))=hAPP(c_Finite__Set_Ocard(X4126),X4125))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Suc__Diff1])])])). 4.46/4.71 fof(c_0_7343, plain, ![X11229, X11230, X11231, X11232]:(~class_Orderings_Olinorder(X11232)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X11232),hAPP(hAPP(c_Orderings_Oord__class_Omax(X11232),X11231),X11229)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X11232),X11230),X11229))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X11232),hAPP(hAPP(c_Orderings_Oord__class_Omin(X11232),X11231),X11230)),X11229)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib2])])). 4.46/4.71 fof(c_0_7344, plain, ![X1716, X1717, X1718, X1719]:(~c_Wellfounded_Owf(X1719,X1718)|(~c_Fun_Oinj__on(X1719,X1717,X1716,c_Orderings_Otop__class_Otop(tc_fun(X1719,tc_HOL_Obool)))|c_Wellfounded_Owf(X1717,hAPP(c_Set_Oimage(tc_prod(X1719,X1719),tc_prod(X1717,X1717),c_Product__Type_Omap__pair(X1719,X1717,X1719,X1717,X1716,X1716)),X1718)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__map__pair__image])])])). 4.46/4.71 fof(c_0_7345, plain, ![X16610, X16611, X16612, X16613]:(~class_Groups_Oordered__ab__group__add__abs(X16613)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16613),c_Groups_Ozero__class_Ozero(X16613)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16612,X16613),hAPP(hAPP(c_COMBB(X16613,X16613,X16612),c_Groups_Oabs__class_Oabs(X16613)),X16611)),X16610)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__abs__ge__zero])])])). 4.46/4.71 cnf(c_0_7346, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_5292])). 4.46/4.71 fof(c_0_7347, plain, ![X2600, X2601, X2602, X2603]:(~class_Orderings_Olinorder(X2603)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X2603),hAPP(hAPP(c_Orderings_Oord__class_Omax(X2603),X2602),X2601)),X2600)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X2603),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2603),X2602),X2600)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2603),X2601),X2600))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib2])])). 4.46/4.71 fof(c_0_7348, plain, ![X13185, X13186, X13187, X13188]:(~class_Rings_Ocomm__semiring__1(X13188)|hAPP(hAPP(c_Power_Opower__class_Opower(X13188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13188),X13187),X13186)),X13185)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13188),hAPP(hAPP(c_Power_Opower__class_Opower(X13188),X13187),X13185)),hAPP(hAPP(c_Power_Opower__class_Opower(X13188),X13186),X13185))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])])])). 4.46/4.71 fof(c_0_7349, plain, ![X3059, X3060, X3061, X3062]:(~class_Groups_Ocomm__monoid__mult(X3062)|hAPP(hAPP(c_Power_Opower__class_Opower(X3062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3062),X3061),X3060)),X3059)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3062),hAPP(hAPP(c_Power_Opower__class_Opower(X3062),X3061),X3059)),hAPP(hAPP(c_Power_Opower__class_Opower(X3062),X3060),X3059))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__mult__distrib])])])). 4.46/4.71 fof(c_0_7350, plain, ![X9496, X9497, X9498, X9499]:(~class_Fields_Ofield__inverse__zero(X9499)|hAPP(hAPP(c_Power_Opower__class_Opower(X9499),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9499),X9498),X9497)),X9496)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9499),hAPP(hAPP(c_Power_Opower__class_Opower(X9499),X9498),X9496)),hAPP(hAPP(c_Power_Opower__class_Opower(X9499),X9497),X9496))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__divide])])). 4.46/4.71 fof(c_0_7351, plain, ![X8765, X8766, X8767, X8768, X8769, X8770, X8771, X8772, X8773]:(((hBOOL(hAPP(X8765,X8766))|(~hBOOL(hAPP(hAPP(c_member(X8768),X8769),hAPP(c_List_Oset(X8768),c_List_Oreplicate(X8768,X8767,X8766))))|~hBOOL(hAPP(X8765,X8769))))&(X8767!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(~hBOOL(hAPP(hAPP(c_member(X8768),X8769),hAPP(c_List_Oset(X8768),c_List_Oreplicate(X8768,X8767,X8766))))|~hBOOL(hAPP(X8765,X8769)))))&((hBOOL(hAPP(hAPP(c_member(X8773),esk248_4(X8770,X8771,X8772,X8773)),hAPP(c_List_Oset(X8773),c_List_Oreplicate(X8773,X8772,X8771))))|(~hBOOL(hAPP(X8770,X8771))|X8772=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(hBOOL(hAPP(X8770,esk248_4(X8770,X8771,X8772,X8773)))|(~hBOOL(hAPP(X8770,X8771))|X8772=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Bex__set__replicate])])])])])])). 4.46/4.71 cnf(c_0_7352, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_Predicate_Oconversep(X1,X1,X2))))|~c_Wellfounded_Oacyclic(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))), inference(split_conjunct,[status(thm)],[c_0_5293])). 4.46/4.71 fof(c_0_7353, plain, ![X6242, X6243, X6244, X6245, X6246]:(~c_Finite__Set_Ofun__left__comm(X6246,X6245,X6244)|hAPP(c_List_Ofoldl(X6245,X6246,hAPP(c_COMBC(X6246,X6245,X6245),X6244),X6243),c_List_Oremdups(X6246,X6242))=hAPP(hAPP(c_Finite__Set_Ofold(X6246,X6245,X6244),X6243),hAPP(c_List_Oset(X6246),X6242))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__set__remdups])])])). 4.46/4.71 fof(c_0_7354, plain, ![X3014, X3015, X3016, X3017, X3019, X3020, X3021, X3022, X3023]:(((hBOOL(hAPP(hAPP(c_member(X3017),esk77_4(X3014,X3015,X3016,X3017)),hAPP(c_List_Oset(X3017),c_List_Oreplicate(X3017,X3016,X3015))))|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X3016|hBOOL(hAPP(X3014,X3015))))&(~hBOOL(hAPP(X3014,esk77_4(X3014,X3015,X3016,X3017)))|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X3016|hBOOL(hAPP(X3014,X3015)))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X3021|(~hBOOL(hAPP(hAPP(c_member(X3022),X3023),hAPP(c_List_Oset(X3022),c_List_Oreplicate(X3022,X3021,X3020))))|hBOOL(hAPP(X3019,X3023))))&(~hBOOL(hAPP(X3019,X3020))|(~hBOOL(hAPP(hAPP(c_member(X3022),X3023),hAPP(c_List_Oset(X3022),c_List_Oreplicate(X3022,X3021,X3020))))|hBOOL(hAPP(X3019,X3023)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ball__set__replicate])])])])])])). 4.46/4.71 fof(c_0_7355, plain, ![X9402, X9403, X9404, X9405]:(~class_Orderings_Olinorder(X9405)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X9405),hAPP(hAPP(c_Orderings_Oord__class_Omax(X9405),X9404),X9403)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X9405),X9404),X9402))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X9405),X9404),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9405),X9403),X9402))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__inf__distrib1])])])). 4.46/4.71 fof(c_0_7356, plain, ![X1480, X1481, X1482, X1483]:(~class_Orderings_Olinorder(X1483)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1483),X1482),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1483),X1481),X1480))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1483),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1483),X1482),X1481)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1483),X1482),X1480))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__sup__distrib1])])])). 4.46/4.71 fof(c_0_7357, plain, ![X6176, X6177, X6178, X6179]:(~class_Rings_Ocomm__semiring__1(X6179)|hAPP(hAPP(c_Power_Opower__class_Opower(X6179),X6178),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6177),X6176))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6179),hAPP(hAPP(c_Power_Opower__class_Opower(X6179),X6178),X6177)),hAPP(hAPP(c_Power_Opower__class_Opower(X6179),X6178),X6176))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])])). 4.46/4.71 fof(c_0_7358, plain, ![X337, X338, X339, X340]:(~class_Divides_Oring__div(X340)|c_Divides_Odiv__class_Omod(X340,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X340),X339),X338),X337)=c_Divides_Odiv__class_Omod(X340,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X340),c_Divides_Odiv__class_Omod(X340,X339,X337)),c_Divides_Odiv__class_Omod(X340,X338,X337)),X337)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__eq])])). 4.46/4.71 fof(c_0_7359, plain, ![X12943, X12944, X12945, X12946, X12947]:(~hBOOL(hAPP(hAPP(c_member(X12947),X12946),hAPP(c_List_Oset(X12947),X12945)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12944),hAPP(X12943,X12946)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12944),c_List_Olist_Olist__size(X12947,X12943,X12945))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__size__estimation])])])). 4.46/4.71 fof(c_0_7360, plain, ![X10759, X10760, X10761, X10762, X10763]:(~hBOOL(hAPP(hAPP(c_member(X10763),X10762),hAPP(c_List_Oset(X10763),X10761)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10760),hAPP(X10759,X10762)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10760),c_List_Olist_Olist__size(X10763,X10759,X10761))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__size__estimation_H])])])). 4.46/4.71 fof(c_0_7361, plain, ![X3029, X3030, X3031, X3032, X3033]:(~c_Finite__Set_Ofolding__one(X3033,X3032,X3031)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3033),X3030))|(hBOOL(hAPP(hAPP(c_member(X3033),X3029),X3030))|(c_Orderings_Obot__class_Obot(tc_fun(X3033,tc_HOL_Obool))=X3030|hAPP(X3031,hAPP(hAPP(c_Set_Oinsert(X3033),X3029),X3030))=hAPP(hAPP(X3032,X3029),hAPP(X3031,X3030)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Oinsert])])])). 4.46/4.71 fof(c_0_7362, plain, ![X17619, X17620]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17620))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17620),X17619))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X17619),X17620)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17619),X17620)),X17620)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__div__geq])])). 4.46/4.71 fof(c_0_7363, plain, ![X7735, X7736, X7737, X7738, X7739]:(~hBOOL(hAPP(hAPP(c_member(X7739),X7738),hAPP(c_List_Oset(X7739),X7737)))|(hBOOL(hAPP(X7736,X7738))|c_List_OtakeWhile(X7739,X7736,hAPP(hAPP(c_List_Oappend(X7739),X7737),X7735))=c_List_OtakeWhile(X7739,X7736,X7737))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile__append1])])])). 4.46/4.71 fof(c_0_7364, plain, ![X3051, X3052, X3053, X3054, X3055, X3056, X3057, X3058]:(~c_Finite__Set_Ofolding__image__simple__idem(X3058,X3057,X3056,X3055,X3054,X3053)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3057),X3052))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3057,tc_HOL_Obool)),X3051),X3052))|hAPP(hAPP(X3056,hAPP(X3053,X3051)),hAPP(X3053,X3052))=hAPP(X3053,X3052)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem])])])). 4.46/4.71 fof(c_0_7365, plain, ![X2583, X2584]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X2584),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X2583),X2584))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(X2584,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X2583),X2584)))=c_Random_Olog(X2584,X2583))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X2584),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))|c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=c_Random_Olog(X2584,X2583))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X2583),X2584))|c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=c_Random_Olog(X2584,X2583)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_log_Osimps])])])])). 4.46/4.71 fof(c_0_7366, plain, ![X5440, X5441, X5442]:(~class_Rings_Olinordered__semidom(X5442)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5442),c_Groups_Oone__class_Oone(X5442)),X5441))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5440))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5442),c_Groups_Oone__class_Oone(X5442)),hAPP(hAPP(c_Power_Opower__class_Opower(X5442),X5441),X5440)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_one__less__power])])])). 4.46/4.71 cnf(c_0_7367, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),c_Relation_OId__on(X3,X4)))|X1!=X2|~hBOOL(hAPP(hAPP(c_member(X3),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_5294])). 4.46/4.71 cnf(c_0_7368, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5295])). 4.46/4.71 fof(c_0_7369, plain, ![X14978, X14979, X14980, X14981, X14982, X14983]:(~class_Complete__Lattice_Ocomplete__lattice(X14983)|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14982,X14983),X14980),hAPP(hAPP(c_COMBC(X14982,X14981,X14983),X14979),X14978))=hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14982,tc_fun(X14981,X14983)),X14980),X14979),X14978)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__apply])])). 4.46/4.71 fof(c_0_7370, plain, ![X14009, X14010, X14011, X14012, X14013]:(~c_Fun_Oinj__on(X14013,X14012,X14011,c_Orderings_Otop__class_Otop(tc_fun(X14013,tc_HOL_Obool)))|(~c_Fun_Oinj__on(X14010,X14013,X14009,c_Orderings_Otop__class_Otop(tc_fun(X14010,tc_HOL_Obool)))|c_Fun_Oinj__on(X14010,X14012,hAPP(c_Fun_Ocomp(X14013,X14012,X14010,X14011),X14009),c_Orderings_Otop__class_Otop(tc_fun(X14010,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__comp])])])). 4.46/4.71 fof(c_0_7371, plain, ![X3419, X3420, X3421, X3422, X3423, X3424]:(~class_Complete__Lattice_Ocomplete__lattice(X3424)|hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3423,tc_fun(X3422,X3424)),X3421),X3420),X3419)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3423,X3424),X3421),hAPP(hAPP(c_COMBC(X3423,X3422,X3424),X3420),X3419))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__apply])])). 4.46/4.71 cnf(c_0_7372, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X1),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X2),X3)|hAPP(X1,esk518_5(X2,X1,X3,X4,X5))!=hAPP(X2,esk518_5(X2,X1,X3,X4,X5))|~c_Nat__Transfer_Onat__set(X3)|X4!=X3|~class_Groups_Ocomm__monoid__add(X5)|~class_Groups_Ocomm__monoid__mult(X5)), inference(split_conjunct,[status(thm)],[c_0_5181])). 4.46/4.71 cnf(c_0_7373, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X1),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X2),X3)|hAPP(X1,esk9_5(X2,X1,X3,X4,X5))!=hAPP(X2,esk9_5(X2,X1,X3,X4,X5))|~c_Nat__Transfer_Onat__set(X3)|X3!=X4|~class_Groups_Ocomm__monoid__mult(X5)|~class_Groups_Ocomm__monoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_5182])). 4.46/4.71 fof(c_0_7374, plain, ![X6719, X6720, X6721, X6722]:(~class_Rings_Olinordered__semidom(X6722)|(hAPP(hAPP(c_Power_Opower__class_Opower(X6722),X6719),X6720)!=hAPP(hAPP(c_Power_Opower__class_Opower(X6722),X6721),X6720)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6722),c_Groups_Ozero__class_Ozero(X6722)),X6721))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6722),c_Groups_Ozero__class_Ozero(X6722)),X6719))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6720))|X6719=X6721))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__eq__imp__eq__base])])])). 4.46/4.71 fof(c_0_7375, plain, ![X17232, X17233]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17232))|c_Divides_OposDivAlg(X17233,X17232)=c_Divides_Odivmod__int(X17233,X17232)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17233)))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X17233|hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Divides_Odivmod__int(X17233,X17232)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17232))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17233)))&(X17233=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odivmod__int(X17233,X17232)=hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X17233),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X17232)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17232))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17233)))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17232))|c_Divides_Odivmod__int(X17233,X17232)=c_Divides_OnegDivAlg(X17233,X17232)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17233)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17232))|c_Divides_Odivmod__int(X17233,X17232)=hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X17233),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X17232)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17233))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__def])])])])). 4.46/4.71 fof(c_0_7376, plain, ![X12236, X12237, X12238, X12239]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12239),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12239),X12236),X12238)),X12237))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12239),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12239),X12237),X12238)),X12236))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12239),X12238),c_Groups_Ozero__class_Ozero(X12239)))|~class_Fields_Olinordered__field(X12239))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12239),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12239),X12237),X12238)),X12236))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12239),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12239),X12236),X12238)),X12237))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12239),X12238),c_Groups_Ozero__class_Ozero(X12239)))|~class_Fields_Olinordered__field(X12239))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__divide__less__eq])])])])). 4.46/4.71 fof(c_0_7377, plain, ![X968, X969, X970, X971]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X971),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X971),X969),X970)),X968))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X971),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X971),X968),X970)),X969))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X971),X970),c_Groups_Ozero__class_Ozero(X971)))|~class_Fields_Olinordered__field(X971))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X971),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X971),X968),X970)),X969))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X971),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X971),X969),X970)),X968))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X971),X970),c_Groups_Ozero__class_Ozero(X971)))|~class_Fields_Olinordered__field(X971))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__divide__le__eq])])])])). 4.46/4.71 cnf(c_0_7378, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk422_2(X2,X1)),esk422_2(X2,X1))=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Relation_OId(X1)))), inference(split_conjunct,[status(thm)],[c_0_5296])). 4.46/4.71 fof(c_0_7379, plain, ![X11557, X11558, X11559]:(~class_Rings_Ocomm__semiring__1(X11559)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11559),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11559),X11557),c_Groups_Oone__class_Oone(X11559))),X11558)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11559),X11558),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11559),X11557),X11558))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])])). 4.46/4.71 fof(c_0_7380, plain, ![X6478, X6479, X6480, X6481]:(~class_Fields_Olinordered__field(X6481)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6481),c_Groups_Ozero__class_Ozero(X6481)),X6480))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6481),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6481),X6479),X6480)),X6478))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6481),X6479),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6481),X6478),X6480)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__imp__less__div__pos])])])). 4.46/4.71 fof(c_0_7381, plain, ![X2394, X2395, X2396]:(~class_Rings_Olinordered__semiring__strict(X2396)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2396),c_Groups_Ozero__class_Ozero(X2396)),X2395))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2396),X2394),c_Groups_Ozero__class_Ozero(X2396)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2396),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2396),X2395),X2394)),c_Groups_Ozero__class_Ozero(X2396)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__pos__neg])])])). 4.46/4.71 fof(c_0_7382, plain, ![X8635, X8636, X8637]:(~class_Rings_Olinordered__semiring__strict(X8637)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8637),c_Groups_Ozero__class_Ozero(X8637)),X8636))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8637),X8635),c_Groups_Ozero__class_Ozero(X8637)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8637),X8635),X8636)),c_Groups_Ozero__class_Ozero(X8637)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2])])). 4.46/4.71 fof(c_0_7383, plain, ![X16518, X16519, X16520]:(~class_Orderings_Olinorder(X16520)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16520),X16519))|(c_Orderings_Obot__class_Obot(tc_fun(X16520,tc_HOL_Obool))=X16519|c_Big__Operators_Olattice_OInf__fin(X16520,c_Orderings_Oord__class_Omin(X16520),hAPP(hAPP(c_Set_Oinsert(X16520),X16518),X16519))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X16520),X16518),c_Big__Operators_Olattice_OInf__fin(X16520,c_Orderings_Oord__class_Omin(X16520),X16519))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__idem])])). 4.46/4.71 fof(c_0_7384, plain, ![X14331, X14332, X14333, X14334]:(~class_Fields_Olinordered__field(X14334)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14334),c_Groups_Ozero__class_Ozero(X14334)),X14333))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14334),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14334),X14332),X14333)),X14331))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14334),X14332),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14334),X14331),X14333)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__imp__le__div__pos])])])). 4.46/4.71 fof(c_0_7385, plain, ![X17351, X17352, X17353, X17354]:(~class_Fields_Olinordered__field(X17354)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17354),c_Groups_Ozero__class_Ozero(X17354)),X17353))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17354),X17352),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17354),X17351),X17353)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17354),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17354),X17352),X17353)),X17351))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__imp__div__pos__less])])])). 4.46/4.71 fof(c_0_7386, plain, ![X7651, X7652, X7653]:(~class_Fields_Olinordered__field(X7653)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7653),X7652),c_Groups_Ozero__class_Ozero(X7653)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7653),c_Groups_Ozero__class_Ozero(X7653)),X7651))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7653),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7653),X7652),X7651)),c_Groups_Ozero__class_Ozero(X7653)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__neg__pos])])])). 4.46/4.71 fof(c_0_7387, plain, ![X6914, X6915, X6916]:(~class_Fields_Olinordered__field(X6916)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6916),c_Groups_Ozero__class_Ozero(X6916)),X6915))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6916),X6914),c_Groups_Ozero__class_Ozero(X6916)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6916),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6916),X6915),X6914)),c_Groups_Ozero__class_Ozero(X6916)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__pos__neg])])])). 4.46/4.71 fof(c_0_7388, plain, ![X5708, X5709, X5710]:(~class_Orderings_Olinorder(X5710)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5710),X5709))|(c_Orderings_Obot__class_Obot(tc_fun(X5710,tc_HOL_Obool))=X5709|c_Big__Operators_Olattice_OSup__fin(X5710,c_Orderings_Oord__class_Omax(X5710),hAPP(hAPP(c_Set_Oinsert(X5710),X5708),X5709))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X5710),X5708),c_Big__Operators_Olattice_OSup__fin(X5710,c_Orderings_Oord__class_Omax(X5710),X5709))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oinsert__idem])])])). 4.46/4.71 fof(c_0_7389, plain, ![X983, X984, X985, X986]:(~class_Fields_Olinordered__field(X986)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X986),c_Groups_Ozero__class_Ozero(X986)),X985))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X986),X984),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X986),X983),X985)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X986),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X986),X984),X985)),X983))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__imp__div__pos__le])])])). 4.46/4.71 fof(c_0_7390, plain, ![X17072, X17073, X17074, X17075]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17075),X17073),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17075),X17072),X17074)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17075),X17072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17075),X17073),X17074)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17075),X17074),c_Groups_Ozero__class_Ozero(X17075)))|~class_Fields_Olinordered__field(X17075))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17075),X17072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17075),X17073),X17074)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17075),X17073),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17075),X17072),X17074)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17075),X17074),c_Groups_Ozero__class_Ozero(X17075)))|~class_Fields_Olinordered__field(X17075))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__less__divide__eq])])])])). 4.46/4.71 fof(c_0_7391, plain, ![X12968, X12969, X12970]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12970),X12969),c_Groups_Ozero__class_Ozero(X12970)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12970),c_Groups_Ozero__class_Ozero(X12970)),X12968))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12970),X12969),X12968)),c_Groups_Ozero__class_Ozero(X12970)))|~class_Rings_Olinordered__ring__strict(X12970))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12970),X12968),c_Groups_Ozero__class_Ozero(X12970)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12970),c_Groups_Ozero__class_Ozero(X12970)),X12969))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12970),X12969),X12968)),c_Groups_Ozero__class_Ozero(X12970)))|~class_Rings_Olinordered__ring__strict(X12970)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12970),X12968),c_Groups_Ozero__class_Ozero(X12970)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12970),X12969),c_Groups_Ozero__class_Ozero(X12970)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12970),X12969),X12968)),c_Groups_Ozero__class_Ozero(X12970)))|~class_Rings_Olinordered__ring__strict(X12970))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12970),c_Groups_Ozero__class_Ozero(X12970)),X12969))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12970),X12969),c_Groups_Ozero__class_Ozero(X12970)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12970),X12969),X12968)),c_Groups_Ozero__class_Ozero(X12970)))|~class_Rings_Olinordered__ring__strict(X12970)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12970),X12968),c_Groups_Ozero__class_Ozero(X12970)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12970),c_Groups_Ozero__class_Ozero(X12970)),X12968))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12970),X12969),X12968)),c_Groups_Ozero__class_Ozero(X12970)))|~class_Rings_Olinordered__ring__strict(X12970))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12970),c_Groups_Ozero__class_Ozero(X12970)),X12969))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12970),c_Groups_Ozero__class_Ozero(X12970)),X12968))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12970),X12969),X12968)),c_Groups_Ozero__class_Ozero(X12970)))|~class_Rings_Olinordered__ring__strict(X12970))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__0__iff])])])])). 4.46/4.71 fof(c_0_7392, plain, ![X14862, X14863, X14864]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14864),X14863),c_Groups_Ozero__class_Ozero(X14864)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14864),c_Groups_Ozero__class_Ozero(X14864)),X14862))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14864),X14863),X14862)),c_Groups_Ozero__class_Ozero(X14864)))|~class_Rings_Oordered__cancel__semiring(X14864))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14864),X14862),c_Groups_Ozero__class_Ozero(X14864)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14864),c_Groups_Ozero__class_Ozero(X14864)),X14863))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14864),X14863),X14862)),c_Groups_Ozero__class_Ozero(X14864)))|~class_Rings_Oordered__cancel__semiring(X14864))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_split__mult__neg__le])])])])). 4.46/4.71 fof(c_0_7393, plain, ![X8357, X8358, X8359]:(~class_Rings_Oordered__cancel__semiring(X8359)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8359),c_Groups_Ozero__class_Ozero(X8359)),X8358))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8359),X8357),c_Groups_Ozero__class_Ozero(X8359)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8359),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8359),X8357),X8358)),c_Groups_Ozero__class_Ozero(X8359)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__nonneg__nonpos2])])])). 4.46/4.71 cnf(c_0_7394, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_5297])). 4.46/4.71 fof(c_0_7395, plain, ![X1607, X1608, X1609, X1610]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1610),X1608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1610),X1607),X1609)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1610),X1607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1610),X1608),X1609)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1610),X1609),c_Groups_Ozero__class_Ozero(X1610)))|~class_Fields_Olinordered__field(X1610))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1610),X1607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1610),X1608),X1609)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1610),X1608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1610),X1607),X1609)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1610),X1609),c_Groups_Ozero__class_Ozero(X1610)))|~class_Fields_Olinordered__field(X1610))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__le__divide__eq])])])])). 4.46/4.71 fof(c_0_7396, plain, ![X3546, X3547, X3548, X3549, X3550, X3551, X3552, X3553]:(~c_Finite__Set_Ofolding__image__simple__idem(X3553,X3552,X3551,X3550,X3549,X3548)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3552),X3547))|hAPP(X3548,hAPP(hAPP(c_Set_Oinsert(X3552),X3546),X3547))=hAPP(hAPP(X3551,hAPP(X3549,X3546)),hAPP(X3548,X3547)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem])])])). 4.46/4.71 fof(c_0_7397, plain, ![X13177, X13178, X13179]:(~class_Fields_Olinordered__field(X13179)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13179),c_Groups_Ozero__class_Ozero(X13179)),X13178))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13179),X13177),c_Groups_Ozero__class_Ozero(X13179)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13179),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13179),X13178),X13177)),c_Groups_Ozero__class_Ozero(X13179)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__nonneg__neg])])])). 4.46/4.71 fof(c_0_7398, plain, ![X12326, X12327, X12328]:(~class_Fields_Olinordered__field(X12328)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12328),X12327),c_Groups_Ozero__class_Ozero(X12328)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12328),c_Groups_Ozero__class_Ozero(X12328)),X12326))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12328),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12328),X12327),X12326)),c_Groups_Ozero__class_Ozero(X12328)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__nonpos__pos])])])). 4.46/4.71 fof(c_0_7399, plain, ![X5752, X5753, X5754]:(~class_Groups_Oordered__comm__monoid__add(X5754)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5754),X5753),c_Groups_Ozero__class_Ozero(X5754)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5754),X5752),c_Groups_Ozero__class_Ozero(X5754)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5754),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5754),X5753),X5752)),c_Groups_Ozero__class_Ozero(X5754)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__neg__neg])])])). 4.46/4.71 fof(c_0_7400, plain, ![X1263, X1264, X1265, X1266]:(~class_Divides_Osemiring__div(X1266)|(c_Groups_Ozero__class_Ozero(X1266)=X1265|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1266),X1264),X1265)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1266),X1263),X1265))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1266),X1264),X1263))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__mult2])])])). 4.46/4.71 fof(c_0_7401, plain, ![X13128, X13129, X13130, X13131]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13131),X13130))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13129),X13128))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13131),X13129)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13130),X13128))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__less__mono])])])). 4.46/4.71 fof(c_0_7402, plain, ![X2733, X2734, X2735]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2735),X2734))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2733),X2735))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2735),X2733)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2734),X2733))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__less__mono])])])). 4.46/4.71 fof(c_0_7403, plain, ![X11179, X11180, X11181]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11181),X11180))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11181),X11179))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11179),X11180)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11179),X11181))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono2])])). 4.46/4.71 fof(c_0_7404, plain, ![X9571, X9572, X9573, X9574]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9574),X9573))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9572),X9571))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9574),X9572)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9573),X9571))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono])])). 4.46/4.71 fof(c_0_7405, plain, ![X8819, X8820, X8821]:(~class_Groups_Oordered__comm__monoid__add(X8821)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8821),X8820),c_Groups_Ozero__class_Ozero(X8821)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8821),X8819),c_Groups_Ozero__class_Ozero(X8821)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8821),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8821),X8820),X8819)),c_Groups_Ozero__class_Ozero(X8821)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__nonpos__neg])])])). 4.46/4.71 fof(c_0_7406, plain, ![X374, X375, X376]:(~class_Groups_Oordered__comm__monoid__add(X376)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X376),X375),c_Groups_Ozero__class_Ozero(X376)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X376),X374),c_Groups_Ozero__class_Ozero(X376)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X376),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X376),X375),X374)),c_Groups_Ozero__class_Ozero(X376)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__neg__nonpos])])])). 4.46/4.71 fof(c_0_7407, plain, ![X13932, X13933, X13934]:(~class_Groups_Oordered__comm__monoid__add(X13934)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13934),X13933),c_Groups_Ozero__class_Ozero(X13934)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13934),X13932),c_Groups_Ozero__class_Ozero(X13934)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13934),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13934),X13933),X13932)),c_Groups_Ozero__class_Ozero(X13934)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__nonpos__nonpos])])])). 4.46/4.71 fof(c_0_7408, plain, ![X6482, X6483, X6484]:(~class_Rings_Olinordered__semidom(X6484)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6484),c_Groups_Oone__class_Oone(X6484)),X6483))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6484),c_Groups_Oone__class_Oone(X6484)),X6482))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6484),c_Groups_Oone__class_Oone(X6484)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6484),X6483),X6482)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__1__mult])])])). 4.46/4.71 fof(c_0_7409, plain, ![X14029, X14030, X14031, X14032]:(~class_Fields_Ofield__inverse__zero(X14032)|(c_Groups_Ozero__class_Ozero(X14032)=X14031|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14032),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14032),X14031),X14030)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14032),X14031),X14029))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14032),X14030),X14029))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__divide__mult__cancel__left])])])). 4.46/4.71 fof(c_0_7410, plain, ![X2047, X2048, X2049, X2050]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2050),X2049))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2048),X2047))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2050),X2048)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2049),X2047))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono])])). 4.46/4.71 fof(c_0_7411, plain, ![X5146, X5147, X5148, X5149]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5149),X5148))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5147),X5146))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5149),X5147)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5148),X5146))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__mono])])])). 4.46/4.71 fof(c_0_7412, plain, ![X8979, X8980, X8981]:(~class_Rings_Olinordered__semiring__strict(X8981)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8981),c_Groups_Ozero__class_Ozero(X8981)),X8980))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8981),c_Groups_Ozero__class_Ozero(X8981)),X8979))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8981),c_Groups_Ozero__class_Ozero(X8981)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8981),X8980),X8979)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__pos__pos])])])). 4.46/4.71 fof(c_0_7413, plain, ![X6796, X6797, X6798]:(~class_Fields_Olinordered__field(X6798)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6798),c_Groups_Ozero__class_Ozero(X6798)),X6797))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6798),c_Groups_Ozero__class_Ozero(X6798)),X6796))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6798),c_Groups_Ozero__class_Ozero(X6798)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6798),X6797),X6796)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__pos])])). 4.46/4.71 fof(c_0_7414, plain, ![X12904, X12905, X12906]:(~class_Groups_Oordered__comm__monoid__add(X12906)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12906),c_Groups_Ozero__class_Ozero(X12906)),X12905))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12906),c_Groups_Ozero__class_Ozero(X12906)),X12904))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12906),c_Groups_Ozero__class_Ozero(X12906)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12906),X12905),X12904)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__pos__pos])])])). 4.46/4.71 fof(c_0_7415, plain, ![X15315, X15316]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X15316|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X15315,X15316),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X15315),X15316)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X15315,X15316))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div__mod])])). 4.46/4.71 fof(c_0_7416, plain, ![X1701, X1702, X1703, X1704, X1705, X1706]:(~hBOOL(hAPP(hAPP(c_member(X1706),X1705),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1704,tc_fun(X1706,tc_HOL_Obool)),X1703),X1702)))|(~hBOOL(hAPP(hAPP(c_member(X1704),X1701),X1703))|hBOOL(hAPP(hAPP(c_member(X1706),X1705),hAPP(X1702,X1701))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INT__D])])])). 4.46/4.71 fof(c_0_7417, plain, ![X2438, X2439, X2440]:(~class_Rings_Oring__1(X2440)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2439),X2438))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2440),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2440),X2438)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2440),X2439))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2440),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2438),X2439)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__diff])])). 4.46/4.71 fof(c_0_7418, plain, ![X10612, X10613]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X10613)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X10612)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X10613),X10612)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X10613),X10612))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X10613)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X10612))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I4_J])])). 4.46/4.71 fof(c_0_7419, plain, ![X11424, X11425, X11426]:(X11426=c_List_Olist_ONil(X11425)|hBOOL(hAPP(hAPP(c_member(X11425),hAPP(c_Product__Type_Ofst(X11425,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X11425,X11426),X11424))),hAPP(c_List_Oset(X11425),X11426)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_select])])])). 4.46/4.71 fof(c_0_7420, plain, ![X8851, X8852, X8853]:(~class_Rings_Oordered__cancel__semiring(X8853)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8853),c_Groups_Ozero__class_Ozero(X8853)),X8852))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8853),c_Groups_Ozero__class_Ozero(X8853)),X8851))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8853),c_Groups_Ozero__class_Ozero(X8853)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8853),X8852),X8851)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg])])). 4.46/4.71 fof(c_0_7421, plain, ![X9990, X9991, X9992]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9992),X9990),c_Groups_Ozero__class_Ozero(X9992)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9992),X9991),c_Groups_Ozero__class_Ozero(X9992)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9992),c_Groups_Ozero__class_Ozero(X9992)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9992),X9991),X9990)))|~class_Rings_Olinordered__ring__strict(X9992))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9992),c_Groups_Ozero__class_Ozero(X9992)),X9990))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9992),c_Groups_Ozero__class_Ozero(X9992)),X9991))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9992),c_Groups_Ozero__class_Ozero(X9992)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9992),X9991),X9990)))|~class_Rings_Olinordered__ring__strict(X9992)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9992),c_Groups_Ozero__class_Ozero(X9992)),X9990))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9992),X9990),c_Groups_Ozero__class_Ozero(X9992)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9992),c_Groups_Ozero__class_Ozero(X9992)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9992),X9991),X9990)))|~class_Rings_Olinordered__ring__strict(X9992))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9992),c_Groups_Ozero__class_Ozero(X9992)),X9991))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9992),X9990),c_Groups_Ozero__class_Ozero(X9992)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9992),c_Groups_Ozero__class_Ozero(X9992)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9992),X9991),X9990)))|~class_Rings_Olinordered__ring__strict(X9992)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9992),c_Groups_Ozero__class_Ozero(X9992)),X9990))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9992),X9991),c_Groups_Ozero__class_Ozero(X9992)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9992),c_Groups_Ozero__class_Ozero(X9992)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9992),X9991),X9990)))|~class_Rings_Olinordered__ring__strict(X9992))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9992),c_Groups_Ozero__class_Ozero(X9992)),X9991))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9992),X9991),c_Groups_Ozero__class_Ozero(X9992)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9992),c_Groups_Ozero__class_Ozero(X9992)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9992),X9991),X9990)))|~class_Rings_Olinordered__ring__strict(X9992))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff])])])). 4.46/4.71 fof(c_0_7422, plain, ![X6043, X6044, X6045]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6045),c_Groups_Ozero__class_Ozero(X6045)),X6043))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6045),c_Groups_Ozero__class_Ozero(X6045)),X6044))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6045),c_Groups_Ozero__class_Ozero(X6045)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6045),X6044),X6043)))|~class_Rings_Oordered__ring(X6045))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6045),X6043),c_Groups_Ozero__class_Ozero(X6045)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6045),X6044),c_Groups_Ozero__class_Ozero(X6045)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6045),c_Groups_Ozero__class_Ozero(X6045)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6045),X6044),X6043)))|~class_Rings_Oordered__ring(X6045))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_split__mult__pos__le])])])])). 4.46/4.71 fof(c_0_7423, plain, ![X14664, X14665, X14666, X14667]:(~class_Divides_Osemiring__div(X14667)|(X14666=c_Groups_Ozero__class_Ozero(X14667)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X14667),X14665),X14664)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X14667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14667),X14666),X14665)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14667),X14666),X14664)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__mult1])])])). 4.46/4.71 fof(c_0_7424, plain, ![X17544, X17545, X17546, X17547, X17548, X17550, X17551, X17552, X17553, X17554, X17555]:(((X17547=hAPP(c_Set_Oimage(X17546,X17548,X17545),esk525_5(X17544,X17545,X17546,X17547,X17548))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17548,tc_HOL_Obool)),X17547),hAPP(c_Set_Oimage(X17546,X17548,X17545),X17544))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17546,tc_HOL_Obool)),esk525_5(X17544,X17545,X17546,X17547,X17548)),X17544))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17548,tc_HOL_Obool)),X17547),hAPP(c_Set_Oimage(X17546,X17548,X17545),X17544)))))&(X17553!=hAPP(c_Set_Oimage(X17552,X17554,X17551),X17555)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17552,tc_HOL_Obool)),X17555),X17550))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17554,tc_HOL_Obool)),X17553),hAPP(c_Set_Oimage(X17552,X17554,X17551),X17550))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__image__iff])])])])])])). 4.46/4.71 fof(c_0_7425, plain, ![X16355, X16356, X16357]:(~class_Fields_Olinordered__field(X16357)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16357),c_Groups_Ozero__class_Ozero(X16357)),X16356))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16357),c_Groups_Ozero__class_Ozero(X16357)),X16355))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16357),c_Groups_Ozero__class_Ozero(X16357)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16357),X16356),X16355)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__nonneg__pos])])])). 4.46/4.71 fof(c_0_7426, plain, ![X12838, X12839, X12840]:(~class_Rings_Olinordered__ring__strict(X12840)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12840),X12839),c_Groups_Ozero__class_Ozero(X12840)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12840),X12838),c_Groups_Ozero__class_Ozero(X12840)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12840),c_Groups_Ozero__class_Ozero(X12840)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12840),X12839),X12838)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__neg__neg])])])). 4.46/4.71 fof(c_0_7427, plain, ![X7430, X7431, X7432]:(~class_Fields_Olinordered__field(X7432)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7432),X7431),c_Groups_Ozero__class_Ozero(X7432)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7432),X7430),c_Groups_Ozero__class_Ozero(X7432)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7432),c_Groups_Ozero__class_Ozero(X7432)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7432),X7431),X7430)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__neg__neg])])])). 4.46/4.71 fof(c_0_7428, plain, ![X16974, X16975, X16976, X16977]:(~class_Fields_Ofield__inverse__zero(X16977)|(X16976=c_Groups_Ozero__class_Ozero(X16977)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16977),X16975),X16974)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16977),X16975),X16976)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16977),X16974),X16976)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__right])])). 4.46/4.71 fof(c_0_7429, plain, ![X12558, X12559, X12560, X12561]:((X12560=hAPP(c_Relation_OImage(X12561,X12561,X12558),hAPP(hAPP(c_Set_Oinsert(X12561),esk371_4(X12558,X12559,X12560,X12561)),c_Orderings_Obot__class_Obot(tc_fun(X12561,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X12561,tc_HOL_Obool)),X12560),hAPP(hAPP(c_Equiv__Relations_Oquotient(X12561),X12559),X12558))))&(hBOOL(hAPP(hAPP(c_member(X12561),esk371_4(X12558,X12559,X12560,X12561)),X12559))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X12561,tc_HOL_Obool)),X12560),hAPP(hAPP(c_Equiv__Relations_Oquotient(X12561),X12559),X12558))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_quotientE])])])])])). 4.46/4.71 fof(c_0_7430, plain, ![X6802, X6803, X6804]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X6804)),X6803)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X6804)),X6802)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6803),X6802)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6803),X6802))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X6804)),X6803)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X6804)),X6802))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1])])). 4.46/4.71 fof(c_0_7431, plain, ![X8215, X8216, X8217, X8218]:(~class_Fields_Olinordered__field(X8218)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8217,X8218),hAPP(hAPP(c_COMBB(X8218,X8218,X8217),c_Groups_Oabs__class_Oabs(X8218)),X8216)),X8215)=hAPP(c_Groups_Oabs__class_Oabs(X8218),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8217,X8218),X8216),X8215))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__setprod])])])). 4.46/4.71 fof(c_0_7432, plain, ![X716, X717, X718]:(~class_Fields_Olinordered__field(X718)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X718),X717),c_Groups_Ozero__class_Ozero(X718)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X718),X716),c_Groups_Ozero__class_Ozero(X718)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X718),c_Groups_Ozero__class_Ozero(X718)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X718),X717),X716)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__nonpos__neg])])])). 4.46/4.71 fof(c_0_7433, plain, ![X5275, X5276, X5277, X5278]:(~class_Rings_Oring__1(X5278)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5277,X5278),hAPP(hAPP(c_COMBB(tc_Int_Oint,X5278,X5277),c_Int_Oring__1__class_Oof__int(X5278)),X5276)),X5275)=hAPP(c_Int_Oring__1__class_Oof__int(X5278),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5277,tc_Int_Oint),X5276),X5275))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__setsum])])). 4.46/4.71 cnf(c_0_7434, plain, (X2=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))|~class_Int_Onumber__ring(X1)|~class_Fields_Ofield(X1)), inference(rw,[status(thm)],[c_0_5298, c_0_4471])). 4.46/4.71 fof(c_0_7435, plain, ![X6039, X6040, X6041]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6041))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X6040),X6039)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6041),X6040)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6041),X6039))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel1])])). 4.46/4.71 fof(c_0_7436, plain, ![X17172, X17173, X17174, X17175]:(~class_Rings_Ocomm__semiring__1(X17175)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17175),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17175),X17174),X17172)),X17173)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17175),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17175),X17174),X17173)),X17172)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])])])). 4.46/4.71 fof(c_0_7437, plain, ![X8603, X8604]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8604),X8603))|c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X8603),c_Lazy__Sequence_Osmall__lazy_H(X8604,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8603),c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Lazy__Sequence_Osmall__lazy_H(X8604,X8603))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8604),X8603))|c_Lazy__Sequence_Osmall__lazy_H(X8604,X8603)=c_Lazy__Sequence_Oempty(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_small__lazy_H_Osimps])])])). 4.46/4.71 fof(c_0_7438, plain, ![X2957, X2958, X2959, X2961, X2962, X2963]:(((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk75_2(X2957,X2958)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2958)))|(~hBOOL(hAPP(X2957,X2959))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2959),X2958))))&(hBOOL(hAPP(X2957,esk75_2(X2957,X2958)))|(~hBOOL(hAPP(X2957,X2959))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2959),X2958)))))&((hBOOL(hAPP(X2961,esk76_2(X2961,X2962)))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2963),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2962)))|~hBOOL(hAPP(X2961,X2963))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk76_2(X2961,X2962)),X2962))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2963),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2962)))|~hBOOL(hAPP(X2961,X2963)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__nat__less])])])])])])). 4.46/4.71 fof(c_0_7439, plain, ![X6854, X6855, X6856]:(~class_Lattices_Oab__semigroup__idem__mult(X6856)|(c_Orderings_Obot__class_Obot(tc_fun(X6856,tc_HOL_Obool))=X6855|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6856),X6855))|hAPP(c_Finite__Set_Ofold1(X6856,c_Groups_Otimes__class_Otimes(X6856)),hAPP(hAPP(c_Set_Oinsert(X6856),X6854),X6855))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6856),X6854),hAPP(c_Finite__Set_Ofold1(X6856,c_Groups_Otimes__class_Otimes(X6856)),X6855))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__insert__idem])])). 4.46/4.71 fof(c_0_7440, plain, ![X15204, X15205, X15206, X15207]:(~class_Rings_Ocomm__semiring__1(X15207)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15207),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15207),X15206),X15204)),X15205)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15207),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15207),X15206),X15205)),X15204)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])])). 4.46/4.71 fof(c_0_7441, plain, ![X8929, X8930]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X8930),X8929))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X8930)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X8929)))|~c_Nat__Transfer_Onat__set(X8929)|~c_Nat__Transfer_Onat__set(X8930))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X8930)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X8929)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X8930),X8929))|~c_Nat__Transfer_Onat__set(X8929)|~c_Nat__Transfer_Onat__set(X8930))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I4_J])])])). 4.46/4.71 fof(c_0_7442, plain, ![X4197, X4198, X4199, X4200, X4201, X4202]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4202,X4201)),hAPP(hAPP(c_Product__Type_OPair(X4202,X4201),X4200),X4199)),hAPP(c_List_Oset(tc_prod(X4202,X4201)),hAPP(hAPP(c_List_Ozip(X4202,X4201),X4198),X4197))))|hBOOL(hAPP(hAPP(c_member(X4202),X4200),hAPP(c_List_Oset(X4202),X4198)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__zip__leftD])])). 4.46/4.71 fof(c_0_7443, plain, ![X14866, X14867, X14868, X14869, X14870, X14871]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X14871,X14870)),hAPP(hAPP(c_Product__Type_OPair(X14871,X14870),X14869),X14868)),hAPP(c_List_Oset(tc_prod(X14871,X14870)),hAPP(hAPP(c_List_Ozip(X14871,X14870),X14867),X14866))))|hBOOL(hAPP(hAPP(c_member(X14870),X14868),hAPP(c_List_Oset(X14870),X14866)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__zip__rightD])])])). 4.46/4.71 fof(c_0_7444, plain, ![X10791, X10792, X10793]:((hBOOL(hAPP(hAPP(c_member(X10793),esk319_3(X10791,X10792,X10793)),hAPP(c_List_Oset(X10793),X10792)))|(~c_List_Olinorder__class_Osorted(X10793,X10792)|c_List_Olinorder__class_Osorted(X10793,hAPP(hAPP(c_List_Olist_OCons(X10793),X10791),X10792)))|~class_Orderings_Olinorder(X10793))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10793),X10791),esk319_3(X10791,X10792,X10793)))|(~c_List_Olinorder__class_Osorted(X10793,X10792)|c_List_Olinorder__class_Osorted(X10793,hAPP(hAPP(c_List_Olist_OCons(X10793),X10791),X10792)))|~class_Orderings_Olinorder(X10793))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted_OCons])])])])])). 4.46/4.71 fof(c_0_7445, plain, ![X7301, X7302, X7303, X7305]:(((hBOOL(hAPP(hAPP(c_member(X7303),esk212_3(X7301,X7302,X7303)),hAPP(c_List_Oset(X7303),X7301)))|~c_List_Olinorder__class_Osorted(X7303,X7301)|c_List_Olinorder__class_Osorted(X7303,hAPP(hAPP(c_List_Olist_OCons(X7303),X7302),X7301))|~class_Orderings_Olinorder(X7303))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7303),X7302),esk212_3(X7301,X7302,X7303)))|~c_List_Olinorder__class_Osorted(X7303,X7301)|c_List_Olinorder__class_Osorted(X7303,hAPP(hAPP(c_List_Olist_OCons(X7303),X7302),X7301))|~class_Orderings_Olinorder(X7303)))&((c_List_Olinorder__class_Osorted(X7303,X7301)|~c_List_Olinorder__class_Osorted(X7303,hAPP(hAPP(c_List_Olist_OCons(X7303),X7302),X7301))|~class_Orderings_Olinorder(X7303))&(~hBOOL(hAPP(hAPP(c_member(X7303),X7305),hAPP(c_List_Oset(X7303),X7301)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7303),X7302),X7305))|~c_List_Olinorder__class_Osorted(X7303,hAPP(hAPP(c_List_Olist_OCons(X7303),X7302),X7301))|~class_Orderings_Olinorder(X7303)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted_Oequations_I2_J])])])])])])). 4.46/4.71 fof(c_0_7446, plain, ![X13418, X13419, X13420]:(c_List_Olist_ONil(X13419)=X13420|hAPP(hAPP(c_List_Olist_OCons(X13419),hAPP(c_List_Ohd(X13419),X13420)),hAPP(hAPP(c_List_Otake(X13419),X13418),hAPP(c_List_Otl(X13419),X13420)))=hAPP(hAPP(c_List_Otake(X13419),hAPP(c_Nat_OSuc,X13418)),X13420)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_take__Suc])])])). 4.46/4.71 cnf(c_0_7447, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4,X1,X5),X2)),hAPP(c_Set_Ovimage(X4,X1,X5),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5299])). 4.46/4.71 fof(c_0_7448, plain, ![X7124, X7125, X7126, X7127]:(((c_List_Olinorder__class_Osorted(X7126,X7124)|~c_List_Olinorder__class_Osorted(X7126,hAPP(hAPP(c_List_Olist_OCons(X7126),X7125),X7124))|~class_Orderings_Olinorder(X7126))&(~hBOOL(hAPP(hAPP(c_member(X7126),X7127),hAPP(c_List_Oset(X7126),X7124)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7126),X7125),X7127))|~c_List_Olinorder__class_Osorted(X7126,hAPP(hAPP(c_List_Olist_OCons(X7126),X7125),X7124))|~class_Orderings_Olinorder(X7126)))&((hBOOL(hAPP(hAPP(c_member(X7126),esk208_3(X7124,X7125,X7126)),hAPP(c_List_Oset(X7126),X7124)))|~c_List_Olinorder__class_Osorted(X7126,X7124)|c_List_Olinorder__class_Osorted(X7126,hAPP(hAPP(c_List_Olist_OCons(X7126),X7125),X7124))|~class_Orderings_Olinorder(X7126))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7126),X7125),esk208_3(X7124,X7125,X7126)))|~c_List_Olinorder__class_Osorted(X7126,X7124)|c_List_Olinorder__class_Osorted(X7126,hAPP(hAPP(c_List_Olist_OCons(X7126),X7125),X7124))|~class_Orderings_Olinorder(X7126)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__Cons])])])])])])). 4.46/4.71 fof(c_0_7449, plain, ![X11874, X11875, X11876, X11877]:(~class_Divides_Osemiring__div(X11877)|c_Divides_Odiv__class_Omod(X11877,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11877),X11876),X11875),X11874)=c_Divides_Odiv__class_Omod(X11877,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11877),c_Divides_Odiv__class_Omod(X11877,X11876,X11874)),c_Divides_Odiv__class_Omod(X11877,X11875,X11874)),X11874)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__eq])])). 4.46/4.71 fof(c_0_7450, plain, ![X12175, X12176, X12177, X12178]:(~class_Divides_Osemiring__div(X12178)|c_Divides_Odiv__class_Omod(X12178,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12178),X12177),X12176),X12175)=c_Divides_Odiv__class_Omod(X12178,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12178),c_Divides_Odiv__class_Omod(X12178,X12177,X12175)),c_Divides_Odiv__class_Omod(X12178,X12176,X12175)),X12175)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__eq])])). 4.46/4.71 fof(c_0_7451, plain, ![X16510, X16511, X16512, X16513, X16514]:((~c_Relation_Oirrefl(X16511,X16510)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16511,X16511)),hAPP(hAPP(c_Product__Type_OPair(X16511,X16511),X16512),X16512)),X16510)))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X16514,X16514)),hAPP(hAPP(c_Product__Type_OPair(X16514,X16514),esk482_2(X16513,X16514)),esk482_2(X16513,X16514))),X16513))|c_Relation_Oirrefl(X16514,X16513))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_irrefl__def])])])])])])). 4.46/4.71 fof(c_0_7452, plain, ![X10922, X10923, X10924, X10925]:((X10925!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X10923=hAPP(hAPP(c_List_Onth(X10924),hAPP(hAPP(c_List_Olist_OCons(X10924),X10923),X10922)),X10925))&(X10925=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Onth(X10924),X10922),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10925),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_List_Onth(X10924),hAPP(hAPP(c_List_Olist_OCons(X10924),X10923),X10922)),X10925))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__Cons_H])])])). 4.46/4.71 cnf(c_0_7453, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5300])). 4.46/4.71 cnf(c_0_7454, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))=hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_5301]), ['final']). 4.46/4.71 cnf(c_0_7455, plain, (X1=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5302]), ['final']). 4.46/4.71 cnf(c_0_7456, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_5303])). 4.46/4.71 fof(c_0_7457, plain, ![X5293, X5294, X5295]:(~class_Orderings_Olinorder(X5295)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5295,tc_HOL_Obool)),X5294),X5293))|(X5294=c_Orderings_Obot__class_Obot(tc_fun(X5295,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5295),X5293))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5295),c_Big__Operators_Olinorder__class_OMax(X5295,X5294)),c_Big__Operators_Olinorder__class_OMax(X5295,X5293))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max__mono])])])). 4.46/4.71 fof(c_0_7458, plain, ![X13393, X13394, X13395]:(~class_Orderings_Olinorder(X13395)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13395,tc_HOL_Obool)),X13394),X13393))|(X13394=c_Orderings_Obot__class_Obot(tc_fun(X13395,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13395),X13393))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13395),c_Big__Operators_Olinorder__class_OMin(X13395,X13393)),c_Big__Operators_Olinorder__class_OMin(X13395,X13394))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min__antimono])])])). 4.46/4.71 fof(c_0_7459, plain, ![X5133, X5134, X5135, X5136]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X5134),X5133))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5136),X5135))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5136),X5135)),hAPP(c_Finite__Set_Ocard(X5134),X5133))=hAPP(c_Finite__Set_Ocard(tc_sum(X5136,X5134)),c_Sum__Type_OPlus(X5136,X5134,X5135,X5133)))&((hBOOL(hAPP(c_Finite__Set_Ofinite(X5134),X5133))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(tc_sum(X5136,X5134)),c_Sum__Type_OPlus(X5136,X5134,X5135,X5133)))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X5136),X5135))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(tc_sum(X5136,X5134)),c_Sum__Type_OPlus(X5136,X5134,X5135,X5133))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Plus__conv__if])])])])). 4.46/4.71 fof(c_0_7460, plain, ![X8656, X8657, X8658, X8659, X8660, X8661, X8662, X8663]:(~c_Finite__Set_Ofolding__image__simple__idem(X8663,X8662,X8661,X8660,X8659,X8658)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8662),X8657))|(~hBOOL(hAPP(hAPP(c_member(X8662),X8656),X8657))|hAPP(hAPP(X8661,hAPP(X8659,X8656)),hAPP(X8658,X8657))=hAPP(X8658,X8657)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oin__idem])])). 4.46/4.71 fof(c_0_7461, plain, ![X14372, X14373, X14374, X14375, X14376, X14377, X14378]:((~c_List_Olist__all2(X14375,X14377,hAPP(hAPP(c_COMBB(X14378,tc_fun(X14377,tc_HOL_Obool),X14375),X14376),X14374),X14373,X14372)|c_List_Olist__all2(X14378,X14377,X14376,hAPP(hAPP(c_List_Omap(X14375,X14378),X14374),X14373),X14372))&(~c_List_Olist__all2(X14378,X14377,X14376,hAPP(hAPP(c_List_Omap(X14375,X14378),X14374),X14373),X14372)|c_List_Olist__all2(X14375,X14377,hAPP(hAPP(c_COMBB(X14378,tc_fun(X14377,tc_HOL_Obool),X14375),X14376),X14374),X14373,X14372))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__map1])])). 4.46/4.71 cnf(c_0_7462, plain, (X1=hAPP(hAPP(c_List_Omap(tc_prod(X2,X3),X2),c_Product__Type_Ofst(X2,X3)),X4)|X4!=hAPP(hAPP(c_List_Ozip(X2,X3),X1),X5)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)), inference(split_conjunct,[status(thm)],[c_0_5304])). 4.46/4.71 cnf(c_0_7463, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5305])). 4.46/4.71 cnf(c_0_7464, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5306]), ['final']). 4.46/4.71 cnf(c_0_7465, plain, (X1=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X1)), inference(split_conjunct,[status(thm)],[c_0_5307]), ['final']). 4.46/4.71 fof(c_0_7466, plain, ![X2551, X2552, X2553, X2554]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X2553,tc_HOL_Obool)),esk70_4(X2551,X2552,X2553,X2554)),X2554))|c_Fun_Oinj__on(X2553,X2552,X2551,c_Complete__Lattice_OInf__class_OInf(tc_fun(X2553,tc_HOL_Obool),X2554))|c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2553,tc_HOL_Obool),tc_HOL_Obool))=X2554)&(~c_Fun_Oinj__on(X2553,X2552,X2551,esk70_4(X2551,X2552,X2553,X2554))|c_Fun_Oinj__on(X2553,X2552,X2551,c_Complete__Lattice_OInf__class_OInf(tc_fun(X2553,tc_HOL_Obool),X2554))|c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2553,tc_HOL_Obool),tc_HOL_Obool))=X2554)), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__Inter])])])])])). 4.46/4.71 fof(c_0_7467, plain, ![X16069, X16070]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X16070),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X16069),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16069),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X16070)))))|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X16069),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16069),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X16070)))=X16070), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__card__intvl__is__intvl])])). 4.46/4.71 cnf(c_0_7468, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5308])). 4.46/4.71 cnf(c_0_7469, plain, (c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),X4)|~c_Fun_Oinj__on(X1,X2,X3,c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),c_List_Oset(X1)),X4)))), inference(split_conjunct,[status(thm)],[c_0_5309])). 4.46/4.71 cnf(c_0_7470, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)=c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_Oimage(X1,tc_fun(X2,tc_HOL_Obool),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_5310]), ['final']). 4.46/4.71 fof(c_0_7471, plain, ![X15944, X15945, X15946, X15947]:(~class_Divides_Osemiring__div(X15947)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15947),c_Divides_Odiv__class_Omod(X15947,X15946,X15944)),X15945)=c_Divides_Odiv__class_Omod(X15947,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15947),X15946),X15945),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15947),X15944),X15945))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__mult__mult2])])])). 4.46/4.71 cnf(c_0_7472, plain, (X1=hAPP(hAPP(c_List_Omap(tc_prod(X2,X3),X3),c_Product__Type_Osnd(X2,X3)),X4)|X4!=hAPP(hAPP(c_List_Ozip(X2,X3),X5),X1)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)), inference(split_conjunct,[status(thm)],[c_0_5304])). 4.46/4.71 cnf(c_0_7473, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5311])). 4.46/4.71 cnf(c_0_7474, plain, (X1=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1))|~c_Nat__Transfer_Onat__set(X1)), inference(split_conjunct,[status(thm)],[c_0_5312])). 4.46/4.71 cnf(c_0_7475, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X1,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),X2))|~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),X1),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),X2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),X2))), inference(split_conjunct,[status(thm)],[c_0_5313])). 4.46/4.71 fof(c_0_7476, plain, ![X9751, X9752, X9753, X9754]:(~class_Divides_Osemiring__div(X9754)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9754),X9753),c_Divides_Odiv__class_Omod(X9754,X9752,X9751))=c_Divides_Odiv__class_Omod(X9754,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9754),X9753),X9752),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9754),X9753),X9751))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__mult__mult1])])])). 4.46/4.71 fof(c_0_7477, plain, ![X13195, X13196, X13197, X13198]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X13198),tc_List_Olist(X13198))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X13198),tc_List_Olist(X13198)),X13197),X13196)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X13198),c_List_Olistrel1(X13198,X13195))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13198)),X13197)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13198)),X13196)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__listrel1__eq__len])])])). 4.46/4.71 cnf(c_0_7478, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk67_4(X2,X1,X3,X4)),hAPP(c_List_Oset(X1),X3)))|c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,X3)|hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)!=X2|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5314])). 4.46/4.71 fof(c_0_7479, plain, ![X5243, X5244, X5245, X5246, X5247, X5248, X5249]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5246),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5243)),X5245)))|hAPP(hAPP(c_List_Onth(X5243),X5245),X5246)=hAPP(hAPP(c_List_Onth(X5243),X5244),X5246)|X5245!=X5244)&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5243)),X5244)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5243)),X5245)|X5245!=X5244))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk161_3(X5247,X5248,X5249)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5247)),X5249)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5247)),X5248)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5247)),X5249)|X5249=X5248)&(hAPP(hAPP(c_List_Onth(X5247),X5249),esk161_3(X5247,X5248,X5249))!=hAPP(hAPP(c_List_Onth(X5247),X5248),esk161_3(X5247,X5248,X5249))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5247)),X5248)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5247)),X5249)|X5249=X5248))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__eq__iff__nth__eq])])])])])])])). 4.46/4.71 fof(c_0_7480, plain, ![X9957, X9958, X9959]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9959),X9957),c_Groups_Ozero__class_Ozero(X9959)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9959),X9958),c_Groups_Ozero__class_Ozero(X9959)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9959),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9959),X9958),X9957)),c_Groups_Ozero__class_Ozero(X9959)))|~class_Fields_Olinordered__field__inverse__zero(X9959))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9959),c_Groups_Ozero__class_Ozero(X9959)),X9958))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9959),X9958),c_Groups_Ozero__class_Ozero(X9959)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9959),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9959),X9958),X9957)),c_Groups_Ozero__class_Ozero(X9959)))|~class_Fields_Olinordered__field__inverse__zero(X9959)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9959),X9957),c_Groups_Ozero__class_Ozero(X9959)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9959),c_Groups_Ozero__class_Ozero(X9959)),X9957))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9959),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9959),X9958),X9957)),c_Groups_Ozero__class_Ozero(X9959)))|~class_Fields_Olinordered__field__inverse__zero(X9959))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9959),c_Groups_Ozero__class_Ozero(X9959)),X9958))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9959),c_Groups_Ozero__class_Ozero(X9959)),X9957))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9959),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9959),X9958),X9957)),c_Groups_Ozero__class_Ozero(X9959)))|~class_Fields_Olinordered__field__inverse__zero(X9959))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9959),X9958),c_Groups_Ozero__class_Ozero(X9959)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9959),c_Groups_Ozero__class_Ozero(X9959)),X9957))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9959),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9959),X9958),X9957)),c_Groups_Ozero__class_Ozero(X9959)))|~class_Fields_Olinordered__field__inverse__zero(X9959))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9959),X9957),c_Groups_Ozero__class_Ozero(X9959)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9959),c_Groups_Ozero__class_Ozero(X9959)),X9958))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9959),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9959),X9958),X9957)),c_Groups_Ozero__class_Ozero(X9959)))|~class_Fields_Olinordered__field__inverse__zero(X9959)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__less__0__iff])])])])). 4.46/4.71 fof(c_0_7481, plain, ![X12294, X12295]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12295),X12294))|c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X12294,X12295))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12295),X12294))|hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X12294),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12294),c_Groups_Oone__class_Oone(tc_Int_Oint)),X12295))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X12294,X12295))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_simp__from__to])])])). 4.46/4.71 fof(c_0_7482, plain, ![X15291, X15292, X15293, X15294]:(~class_Groups_Ocomm__monoid__add(X15294)|(~hBOOL(hAPP(c_List_Odistinct(X15293),X15292))|hAPP(c_List_Omonoid__add__class_Olistsum(X15294),hAPP(hAPP(c_List_Omap(X15293,X15294),X15291),X15292))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15293,X15294),X15291),hAPP(c_List_Oset(X15293),X15292)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__distinct__conv__setsum__set])])])). 4.46/4.71 cnf(c_0_7483, plain, (hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X1,X3)),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_5315])). 4.46/4.71 fof(c_0_7484, plain, ![X4458, X4459, X4460, X4461, X4462]:(~hBOOL(hAPP(hAPP(c_member(X4462),X4461),X4460))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4459,tc_HOL_Obool)),hAPP(X4458,X4461)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4462,tc_fun(X4459,tc_HOL_Obool)),X4460),X4458))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4462,tc_fun(X4459,tc_HOL_Obool)),X4460),X4458)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__absorb])])). 4.46/4.71 cnf(c_0_7485, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(c_Nat_OSuc,X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5316, c_0_5317]), c_0_5317])). 4.46/4.71 fof(c_0_7486, plain, ![X4076, X4077, X4078]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4078),c_Groups_Ozero__class_Ozero(X4078)),X4077))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4078),c_Groups_Ozero__class_Ozero(X4078)),X4076))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4078),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4078),X4077),X4076)),c_Groups_Ozero__class_Ozero(X4078)))|~class_Fields_Olinordered__field__inverse__zero(X4078))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4078),X4076),c_Groups_Ozero__class_Ozero(X4078)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4078),c_Groups_Ozero__class_Ozero(X4078)),X4076))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4078),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4078),X4077),X4076)),c_Groups_Ozero__class_Ozero(X4078)))|~class_Fields_Olinordered__field__inverse__zero(X4078)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4078),c_Groups_Ozero__class_Ozero(X4078)),X4077))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4078),X4077),c_Groups_Ozero__class_Ozero(X4078)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4078),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4078),X4077),X4076)),c_Groups_Ozero__class_Ozero(X4078)))|~class_Fields_Olinordered__field__inverse__zero(X4078))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4078),X4076),c_Groups_Ozero__class_Ozero(X4078)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4078),X4077),c_Groups_Ozero__class_Ozero(X4078)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4078),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4078),X4077),X4076)),c_Groups_Ozero__class_Ozero(X4078)))|~class_Fields_Olinordered__field__inverse__zero(X4078))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4078),c_Groups_Ozero__class_Ozero(X4078)),X4076))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4078),X4077),c_Groups_Ozero__class_Ozero(X4078)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4078),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4078),X4077),X4076)),c_Groups_Ozero__class_Ozero(X4078)))|~class_Fields_Olinordered__field__inverse__zero(X4078))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4078),c_Groups_Ozero__class_Ozero(X4078)),X4077))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4078),X4076),c_Groups_Ozero__class_Ozero(X4078)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4078),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4078),X4077),X4076)),c_Groups_Ozero__class_Ozero(X4078)))|~class_Fields_Olinordered__field__inverse__zero(X4078)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__le__0__iff])])])])). 4.46/4.71 fof(c_0_7487, plain, ![X6920, X6921, X6922]:(~class_Rings_Oring__1(X6922)|(~hBOOL(hAPP(hAPP(c_member(X6922),X6921),c_Int_Oring__1__class_OInts(X6922)))|(~hBOOL(hAPP(hAPP(c_member(X6922),X6920),c_Int_Oring__1__class_OInts(X6922)))|hBOOL(hAPP(hAPP(c_member(X6922),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6922),X6921),X6920)),c_Int_Oring__1__class_OInts(X6922)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__mult])])])). 4.46/4.71 fof(c_0_7488, plain, ![X4831, X4832, X4833]:(~class_Rings_Osemiring__1(X4833)|(~hBOOL(hAPP(hAPP(c_member(X4833),X4832),c_Nat_Osemiring__1__class_ONats(X4833)))|(~hBOOL(hAPP(hAPP(c_member(X4833),X4831),c_Nat_Osemiring__1__class_ONats(X4833)))|hBOOL(hAPP(hAPP(c_member(X4833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4833),X4832),X4831)),c_Nat_Osemiring__1__class_ONats(X4833)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nats__mult])])])). 4.46/4.71 fof(c_0_7489, plain, ![X7229, X7230]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X7230|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7230),X7229)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7229),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7230),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X7229)))&(X7230!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7230),X7229))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__if])])). 4.46/4.71 fof(c_0_7490, plain, ![X17186, X17187, X17188, X17189, X17190]:(~hBOOL(hAPP(hAPP(c_member(X17190),X17189),X17188))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17190,tc_fun(X17187,tc_HOL_Obool)),X17188),X17186)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17187,tc_HOL_Obool)),hAPP(X17186,X17189)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17190,tc_fun(X17187,tc_HOL_Obool)),X17188),X17186))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__absorb])])])). 4.46/4.71 cnf(c_0_7491, plain, (c_List_Olist__ex1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~c_List_Olist__all(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2))),hAPP(c_fequal,X3)),X4)|~c_List_Olist__ex1(X1,X2,X4)), inference(split_conjunct,[status(thm)],[c_0_5229])). 4.46/4.71 fof(c_0_7492, plain, ![X9139, X9140]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9140),X9139))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X9140),X9139)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X9140),X9139)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9140),X9139)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__nat__trancl__eq__le])])). 4.46/4.71 fof(c_0_7493, plain, ![X13291, X13292]:(X13292=c_List_Olist_ONil(X13291)|hAPP(hAPP(c_List_Oappend(X13291),hAPP(c_List_Otl(X13291),X13292)),hAPP(hAPP(c_List_Olist_OCons(X13291),hAPP(c_List_Ohd(X13291),X13292)),c_List_Olist_ONil(X13291)))=hAPP(c_List_Orotate1(X13291),X13292)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rotate1__hd__tl])])])). 4.46/4.71 fof(c_0_7494, plain, ![X16548, X16549, X16550]:(~class_Rings_Oring__1(X16550)|(~hBOOL(hAPP(hAPP(c_member(X16550),X16549),c_Int_Oring__1__class_OInts(X16550)))|(~hBOOL(hAPP(hAPP(c_member(X16550),X16548),c_Int_Oring__1__class_OInts(X16550)))|hBOOL(hAPP(hAPP(c_member(X16550),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16550),X16549),X16548)),c_Int_Oring__1__class_OInts(X16550)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__add])])])). 4.46/4.71 fof(c_0_7495, plain, ![X16430, X16431, X16432]:(~class_Rings_Osemiring__1(X16432)|(~hBOOL(hAPP(hAPP(c_member(X16432),X16431),c_Nat_Osemiring__1__class_ONats(X16432)))|(~hBOOL(hAPP(hAPP(c_member(X16432),X16430),c_Nat_Osemiring__1__class_ONats(X16432)))|hBOOL(hAPP(hAPP(c_member(X16432),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16432),X16431),X16430)),c_Nat_Osemiring__1__class_ONats(X16432)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nats__add])])])). 4.46/4.71 fof(c_0_7496, plain, ![X13608, X13609, X13610]:(~class_Rings_Oring__1(X13610)|(~hBOOL(hAPP(hAPP(c_member(X13610),X13609),c_Int_Oring__1__class_OInts(X13610)))|(~hBOOL(hAPP(hAPP(c_member(X13610),X13608),c_Int_Oring__1__class_OInts(X13610)))|hBOOL(hAPP(hAPP(c_member(X13610),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13610),X13609),X13608)),c_Int_Oring__1__class_OInts(X13610)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__diff])])])). 4.46/4.71 fof(c_0_7497, plain, ![X11547, X11548, X11549]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11549),X11548),c_Groups_Ozero__class_Ozero(X11549)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11549),X11547),c_Groups_Ozero__class_Ozero(X11549)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11549),c_Groups_Ozero__class_Ozero(X11549)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11549),X11548),X11547)))|~class_Fields_Olinordered__field__inverse__zero(X11549))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11549),c_Groups_Ozero__class_Ozero(X11549)),X11548))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11549),c_Groups_Ozero__class_Ozero(X11549)),X11547))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11549),c_Groups_Ozero__class_Ozero(X11549)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11549),X11548),X11547)))|~class_Fields_Olinordered__field__inverse__zero(X11549)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11549),c_Groups_Ozero__class_Ozero(X11549)),X11548))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11549),X11548),c_Groups_Ozero__class_Ozero(X11549)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11549),c_Groups_Ozero__class_Ozero(X11549)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11549),X11548),X11547)))|~class_Fields_Olinordered__field__inverse__zero(X11549))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11549),c_Groups_Ozero__class_Ozero(X11549)),X11547))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11549),X11548),c_Groups_Ozero__class_Ozero(X11549)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11549),c_Groups_Ozero__class_Ozero(X11549)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11549),X11548),X11547)))|~class_Fields_Olinordered__field__inverse__zero(X11549)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11549),c_Groups_Ozero__class_Ozero(X11549)),X11548))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11549),X11547),c_Groups_Ozero__class_Ozero(X11549)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11549),c_Groups_Ozero__class_Ozero(X11549)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11549),X11548),X11547)))|~class_Fields_Olinordered__field__inverse__zero(X11549))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11549),c_Groups_Ozero__class_Ozero(X11549)),X11547))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11549),X11547),c_Groups_Ozero__class_Ozero(X11549)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11549),c_Groups_Ozero__class_Ozero(X11549)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11549),X11548),X11547)))|~class_Fields_Olinordered__field__inverse__zero(X11549))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__divide__iff])])])])). 4.46/4.71 fof(c_0_7498, plain, ![X15104, X15105, X15106]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15106))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15106),X15105)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15106),X15104))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15105),X15104))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15106),X15105)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15106),X15104)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15106),X15105)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15106),X15104)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15106))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15105),X15104))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__cancel1])])])])). 4.46/4.71 fof(c_0_7499, plain, ![X6886, X6887, X6888, X6889]:(~hBOOL(hAPP(hAPP(c_member(X6889),X6888),X6887))|hAPP(hAPP(c_Set_Oinsert(X6889),X6888),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6889,tc_HOL_Obool)),X6887),X6886))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6889,tc_HOL_Obool)),X6887),hAPP(hAPP(c_Set_Oinsert(X6889),X6888),X6886))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__insert__right__if1])])])). 4.46/4.71 fof(c_0_7500, plain, ![X6789, X6790, X6791, X6792, X6793]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6792,tc_HOL_Obool)),hAPP(c_Set_Oimage(X6793,X6792,X6791),X6790)),hAPP(c_Set_Oimage(X6793,X6792,X6791),X6789)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6793,tc_HOL_Obool)),X6790),X6789))|~c_Fun_Oinj__on(X6793,X6792,X6791,c_Orderings_Otop__class_Otop(tc_fun(X6793,tc_HOL_Obool))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6793,tc_HOL_Obool)),X6790),X6789))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6792,tc_HOL_Obool)),hAPP(c_Set_Oimage(X6793,X6792,X6791),X6790)),hAPP(c_Set_Oimage(X6793,X6792,X6791),X6789)))|~c_Fun_Oinj__on(X6793,X6792,X6791,c_Orderings_Otop__class_Otop(tc_fun(X6793,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__subset__iff])])])). 4.46/4.71 fof(c_0_7501, plain, ![X9605, X9606, X9607]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9607),X9606)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9605),X9606)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9606))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9607),X9605))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9606))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9607),X9606)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9605),X9606))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9607),X9605))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9607),X9606)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9605),X9606)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__cancel2])])])])). 4.46/4.71 fof(c_0_7502, plain, ![X9764, X9765, X9766]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9766),c_Groups_Ozero__class_Ozero(X9766)),X9764))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9766),c_Groups_Ozero__class_Ozero(X9766)),X9765))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9766),c_Groups_Ozero__class_Ozero(X9766)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9766),X9765),X9764)))|~class_Fields_Olinordered__field__inverse__zero(X9766))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9766),X9765),c_Groups_Ozero__class_Ozero(X9766)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9766),X9764),c_Groups_Ozero__class_Ozero(X9766)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9766),c_Groups_Ozero__class_Ozero(X9766)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9766),X9765),X9764)))|~class_Fields_Olinordered__field__inverse__zero(X9766)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9766),X9765),c_Groups_Ozero__class_Ozero(X9766)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9766),c_Groups_Ozero__class_Ozero(X9766)),X9764))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9766),c_Groups_Ozero__class_Ozero(X9766)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9766),X9765),X9764)))|~class_Fields_Olinordered__field__inverse__zero(X9766))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9766),X9764),c_Groups_Ozero__class_Ozero(X9766)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9766),c_Groups_Ozero__class_Ozero(X9766)),X9764))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9766),c_Groups_Ozero__class_Ozero(X9766)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9766),X9765),X9764)))|~class_Fields_Olinordered__field__inverse__zero(X9766)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9766),X9765),c_Groups_Ozero__class_Ozero(X9766)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9766),c_Groups_Ozero__class_Ozero(X9766)),X9765))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9766),c_Groups_Ozero__class_Ozero(X9766)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9766),X9765),X9764)))|~class_Fields_Olinordered__field__inverse__zero(X9766))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9766),X9764),c_Groups_Ozero__class_Ozero(X9766)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9766),c_Groups_Ozero__class_Ozero(X9766)),X9765))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9766),c_Groups_Ozero__class_Ozero(X9766)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9766),X9765),X9764)))|~class_Fields_Olinordered__field__inverse__zero(X9766))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__divide__iff])])])])). 4.46/4.71 fof(c_0_7503, plain, ![X6651, X6652, X6653, X6654]:((~hBOOL(hAPP(hAPP(c_member(X6654),X6653),hAPP(c_List_Oset(X6654),X6652)))|hAPP(hAPP(c_List_Oappend(X6654),c_List_Oremove1(X6654,X6653,X6652)),X6651)=c_List_Oremove1(X6654,X6653,hAPP(hAPP(c_List_Oappend(X6654),X6652),X6651)))&(hBOOL(hAPP(hAPP(c_member(X6654),X6653),hAPP(c_List_Oset(X6654),X6652)))|hAPP(hAPP(c_List_Oappend(X6654),X6652),c_List_Oremove1(X6654,X6653,X6651))=c_List_Oremove1(X6654,X6653,hAPP(hAPP(c_List_Oappend(X6654),X6652),X6651)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_remove1__append])])])). 4.46/4.71 fof(c_0_7504, plain, ![X13334, X13335, X13336]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X13336,X13336),tc_HOL_Obool)),X13335),c_Transitive__Closure_Ortrancl(X13336,X13334)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X13336,X13336),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X13336,X13335)),c_Transitive__Closure_Ortrancl(X13336,X13334)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__subset__rtrancl])])])). 4.46/4.71 fof(c_0_7505, plain, ![X2671, X2672, X2673]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2673),X2672))|hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X2673),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2673,tc_HOL_Obool)),X2672),hAPP(hAPP(c_Set_Oinsert(X2673),X2671),c_Orderings_Obot__class_Obot(tc_fun(X2673,tc_HOL_Obool))))))=hAPP(c_Finite__Set_Ocard(X2673),hAPP(hAPP(c_Set_Oinsert(X2673),X2671),X2672))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__insert])])])). 4.46/4.71 fof(c_0_7506, plain, ![X6423, X6424, X6425]:(~class_Complete__Lattice_Ocomplete__lattice(X6425)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6425),X6424))|hAPP(hAPP(c_Finite__Set_Ofold(X6425,X6425,c_Lattices_Osemilattice__inf__class_Oinf(X6425)),X6423),X6424)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6425),X6423),c_Complete__Lattice_OInf__class_OInf(X6425,X6424)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__Inf__fold__inf])])])). 4.46/4.71 fof(c_0_7507, plain, ![X15507, X15508, X15509, X15510, X15511]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15511),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15510)),X15509)))|hAPP(hAPP(c_List_Onth(X15508),hAPP(hAPP(c_List_Omap(X15510,X15508),X15507),X15509)),X15511)=hAPP(X15507,hAPP(hAPP(c_List_Onth(X15510),X15509),X15511))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__map])])). 4.46/4.71 cnf(c_0_7508, plain, (hAPP(c_List_Ofilter(X3,X1),X4)=hAPP(c_List_Ofilter(X3,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),hAPP(c_fequal,X2))),hAPP(c_List_Ofilter(X3,X1),X4))|hBOOL(hAPP(X1,X2))), inference(rw,[status(thm)],[c_0_5318, c_0_5035])). 4.46/4.71 cnf(c_0_7509, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Ofilter(X1,X3),X4))=hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)),X4)), inference(rw,[status(thm)],[c_0_5319, c_0_5320]), ['final']). 4.46/4.71 fof(c_0_7510, plain, ![X1862, X1863]:(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1863),hAPP(c_List_Oset(tc_Nat_Onat),X1862)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1863),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1862)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_elem__le__sum])])])). 4.46/4.71 cnf(c_0_7511, plain, (esk496_4(X1,X2,X4,X5)=X3|X1!=hAPP(X2,X3)|~hBOOL(hAPP(hAPP(c_member(X4),X1),hAPP(c_Set_Oimage(X5,X4,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5321])). 4.46/4.71 cnf(c_0_7512, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_5322]), ['final']). 4.46/4.71 fof(c_0_7513, plain, ![X1427, X1428, X1429]:(~c_Wellfounded_Owf(X1429,X1428)|(~c_Wellfounded_Owf(X1429,X1427)|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1429,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1429,X1429),X1428)),hAPP(c_Relation_ORange(X1429,X1429),X1427))!=c_Orderings_Obot__class_Obot(tc_fun(X1429,tc_HOL_Obool))|c_Wellfounded_Owf(X1429,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1429,X1429),tc_HOL_Obool)),X1428),X1427))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__Un])])])). 4.46/4.71 cnf(c_0_7514, plain, (hAPP(X1,X2)=hAPP(c_Option_Ooption_OSome(X3),esk87_7(X4,X2,X1,X5,X6,X7,X3))|c_Map_Omap__comp(X3,X7,X6,X5,X1,X2)!=hAPP(c_Option_Ooption_OSome(X7),X4)), inference(split_conjunct,[status(thm)],[c_0_5256])). 4.46/4.71 fof(c_0_7515, plain, ![X16552, X16553, X16554, X16555, X16556]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16553),hAPP(X16552,X16556)))|~hBOOL(hAPP(hAPP(c_member(X16555),X16556),X16554))|hBOOL(hAPP(c_Finite__Set_Ofinite(X16553),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16555,tc_fun(X16553,tc_HOL_Obool)),X16554),X16552)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__INT])])])])). 4.46/4.71 cnf(c_0_7516, plain, (c_List_Olist_ONil(X1)=c_List_OdropWhile(X1,X2,X3)|~hBOOL(hAPP(X2,hAPP(c_List_Ohd(X1),c_List_OdropWhile(X1,X2,X3))))), inference(split_conjunct,[status(thm)],[c_0_5323])). 4.46/4.71 fof(c_0_7517, plain, ![X8626, X8627, X8628, X8629, X8630]:(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X8630,X8630,X8629,X8628,X8627),X8626))|(hBOOL(hAPP(hAPP(c_member(X8630),X8628),X8627))|hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8630,X8629,hAPP(hAPP(c_Set_Oinsert(X8630),X8628),X8627)),X8626)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1Set_Ointros])])])). 4.46/4.71 fof(c_0_7518, plain, ![X1135, X1136, X1137, X1138, X1139]:((~hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1139,X1138,X1137),X1136),X1135))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1139,X1138)),hAPP(hAPP(c_Product__Type_OPair(X1139,X1138),X1136),X1135)),X1137)))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X1139,X1138)),hAPP(hAPP(c_Product__Type_OPair(X1139,X1138),X1136),X1135)),X1137))|hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1139,X1138,X1137),X1136),X1135)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])])). 4.46/4.71 fof(c_0_7519, plain, ![X5862, X5863, X5864, X5865]:((X5865=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Odrop(X5864),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5865),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X5862)=hAPP(hAPP(c_List_Odrop(X5864),X5865),hAPP(hAPP(c_List_Olist_OCons(X5864),X5863),X5862)))&(X5865!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Olist_OCons(X5864),X5863),X5862)=hAPP(hAPP(c_List_Odrop(X5864),X5865),hAPP(hAPP(c_List_Olist_OCons(X5864),X5863),X5862)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_drop__Cons_H])])])). 4.46/4.71 cnf(c_0_7520, plain, (c_Relation_Ototal__on(X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Relation_OId(X1)))|~c_Relation_Ototal__on(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_5324])). 4.46/4.71 fof(c_0_7521, plain, ![X3908, X3909]:(((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X3909),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X3909),tc_HOL_Obool,X3909),X3908),c_Option_Ooption_OSome(X3909))))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X3909)),X3908))|~class_Enum_Oenum(X3909))&(~hBOOL(hAPP(X3908,c_Option_Ooption_ONone(X3909)))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X3909)),X3908))|~class_Enum_Oenum(X3909)))&(~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X3909)),X3908))|(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X3909),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X3909),tc_HOL_Obool,X3909),X3908),c_Option_Ooption_OSome(X3909))))|hBOOL(hAPP(X3908,c_Option_Ooption_ONone(X3909))))|~class_Enum_Oenum(X3909))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_enum__ex__option__def])])])])). 4.46/4.71 fof(c_0_7522, plain, ![X2382, X2383, X2384, X2385]:(~class_Rings_Olinordered__semidom(X2385)|(hAPP(hAPP(c_Power_Opower__class_Opower(X2385),X2384),hAPP(c_Nat_OSuc,X2383))!=hAPP(hAPP(c_Power_Opower__class_Opower(X2385),X2382),hAPP(c_Nat_OSuc,X2383))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2385),c_Groups_Ozero__class_Ozero(X2385)),X2384))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2385),c_Groups_Ozero__class_Ozero(X2385)),X2382))|X2384=X2382)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__inject__base])])])). 4.46/4.71 fof(c_0_7523, plain, ![X17383, X17384, X17385]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17384),X17385)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17383),X17385)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17384),X17383))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17385),X17383))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17385),X17384)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17384),X17383))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17384),X17385)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17383),X17385)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17385),X17383))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17385),X17384)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__diff__iff])])])])). 4.46/4.71 cnf(c_0_7524, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X1),X2),c_List_Oupto(X3,X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X3,X4)))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5325])). 4.46/4.71 cnf(c_0_7525, plain, (hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1,X2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5326]), ['final']). 4.46/4.71 fof(c_0_7526, plain, ![X16324, X16325]:(~class_Groups_Ocomm__monoid__add(X16325)|hAPP(c_List_Omonoid__add__class_Olistsum(X16325),X16324)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X16325),hAPP(c_List_Onth(X16325),X16324)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16325)),X16324)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__setsum__nth])])])). 4.46/4.71 fof(c_0_7527, plain, ![X14117, X14118, X14119]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14118),X14117))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14118),X14119)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14117),X14119)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14119),X14117))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14119),X14118)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14118),X14119)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14117),X14119)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14118),X14117))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14119),X14117))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14119),X14118)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__diff__iff])])])])). 4.46/4.71 cnf(c_0_7528, plain, (X2=esk92_3(X4,X3,X1)|hAPP(X4,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_5222])). 4.46/4.71 fof(c_0_7529, plain, ![X16381, X16382, X16383, X16384, X16385, X16386, X16387]:((hBOOL(hAPP(hAPP(c_member(X16387),esk477_7(X16381,X16382,X16383,X16384,X16385,X16386,X16387)),X16384))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16387,tc_fun(X16386,tc_fun(X16385,tc_HOL_Obool))),X16384),X16383),X16382),X16381)))&(hBOOL(hAPP(hAPP(hAPP(X16383,esk477_7(X16381,X16382,X16383,X16384,X16385,X16386,X16387)),X16382),X16381))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16387,tc_fun(X16386,tc_fun(X16385,tc_HOL_Obool))),X16384),X16383),X16382),X16381)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUP2__E])])])])])). 4.46/4.71 fof(c_0_7530, plain, ![X14704, X14705, X14706, X14707, X14708, X14709, X14710, X14712, X14713, X14714, X14715, X14716, X14717, X14718, X14719]:(((hBOOL(hAPP(hAPP(c_member(X14710),esk430_7(X14704,X14705,X14706,X14707,X14708,X14709,X14710)),X14707))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14710,tc_fun(X14709,tc_fun(X14708,tc_HOL_Obool))),X14707),X14706),X14705),X14704)))&(hBOOL(hAPP(hAPP(hAPP(X14706,esk430_7(X14704,X14705,X14706,X14707,X14708,X14709,X14710)),X14705),X14704))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14710,tc_fun(X14709,tc_fun(X14708,tc_HOL_Obool))),X14707),X14706),X14705),X14704))))&(~hBOOL(hAPP(hAPP(c_member(X14718),X14719),X14715))|~hBOOL(hAPP(hAPP(hAPP(X14714,X14719),X14713),X14712))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14718,tc_fun(X14717,tc_fun(X14716,tc_HOL_Obool))),X14715),X14714),X14713),X14712)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP2__iff])])])])])])). 4.46/4.71 cnf(c_0_7531, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_5297])). 4.46/4.71 cnf(c_0_7532, plain, (hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5327])). 4.46/4.71 cnf(c_0_7533, plain, (c_List_Olist__ex1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~c_List_Olist__all(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2))),hAPP(c_fequal,X3)),X4)|~hBOOL(hAPP(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_5229])). 4.46/4.71 fof(c_0_7534, plain, ![X17624, X17625, X17626, X17627]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17627,tc_HOL_Obool)),X17624),X17626))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17627,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17627,tc_HOL_Obool)),X17626),X17625)),X17624)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17627,tc_HOL_Obool)),X17626),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17627,tc_HOL_Obool)),X17625),X17624)))&(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17627,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17627,tc_HOL_Obool)),X17626),X17625)),X17624)!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17627,tc_HOL_Obool)),X17626),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17627,tc_HOL_Obool)),X17625),X17624))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17627,tc_HOL_Obool)),X17624),X17626)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__Int__assoc__eq])])). 4.46/4.71 fof(c_0_7535, plain, ![X5866, X5867, X5868, X5869, X5870, X5871, X5872, X5873]:(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5873,tc_fun(X5872,tc_fun(X5871,tc_HOL_Obool))),X5870),X5869),X5868),X5867))|(~hBOOL(hAPP(hAPP(c_member(X5873),X5866),X5870))|hBOOL(hAPP(hAPP(hAPP(X5869,X5866),X5868),X5867)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF2__D])])). 4.46/4.71 fof(c_0_7536, plain, ![X10319, X10320, X10321, X10322]:(~class_Rings_Olinordered__semidom(X10322)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10322),hAPP(hAPP(c_Power_Opower__class_Opower(X10322),X10321),hAPP(c_Nat_OSuc,X10320))),hAPP(hAPP(c_Power_Opower__class_Opower(X10322),X10319),hAPP(c_Nat_OSuc,X10320))))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10322),c_Groups_Ozero__class_Ozero(X10322)),X10319))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10322),X10321),X10319))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__le__imp__le__base])])])). 4.46/4.71 cnf(c_0_7537, plain, (c_Option_Ooption_ONone(X1)=hAPP(X2,esk519_6(X3,X4,X2,X5,X1,X6))|c_Option_Ooption_ONone(X6)=hAPP(X4,X3)|c_Option_Ooption_ONone(X1)!=c_Map_Omap__comp(X6,X1,X5,X2,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_5286])). 4.46/4.71 fof(c_0_7538, plain, ![X14311, X14312, X14313, X14314, X14315, X14317, X14318, X14319, X14320, X14321, X14322]:(((hBOOL(hAPP(hAPP(c_member(X14313),esk421_5(X14311,X14312,X14313,X14314,X14315)),X14312))|~hBOOL(hAPP(hAPP(c_member(X14315),X14314),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14313,tc_fun(X14315,tc_HOL_Obool)),X14312),X14311))))&(hBOOL(hAPP(hAPP(c_member(X14315),X14314),hAPP(X14311,esk421_5(X14311,X14312,X14313,X14314,X14315))))|~hBOOL(hAPP(hAPP(c_member(X14315),X14314),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14313,tc_fun(X14315,tc_HOL_Obool)),X14312),X14311)))))&(~hBOOL(hAPP(hAPP(c_member(X14319),X14322),X14318))|~hBOOL(hAPP(hAPP(c_member(X14321),X14320),hAPP(X14317,X14322)))|hBOOL(hAPP(hAPP(c_member(X14321),X14320),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14319,tc_fun(X14321,tc_HOL_Obool)),X14318),X14317))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__iff])])])])])])). 4.46/4.71 fof(c_0_7539, plain, ![X14550, X14551, X14552, X14553]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X14553)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14553),X14552),X14551))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14553),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14553),X14552),X14550)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14553),X14551),X14550))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__right__mono])])])). 4.46/4.71 fof(c_0_7540, plain, ![X16456, X16457, X16458, X16459]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16459),X16458),X16456))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16459),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16459),X16458),X16457)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16459),X16456),X16457)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X16459))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16459),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16459),X16458),X16457)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16459),X16456),X16457)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16459),X16458),X16456))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X16459))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__less__cancel__right])])])])). 4.46/4.71 fof(c_0_7541, plain, ![X16194, X16195, X16196, X16197]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X16197)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16197),X16196),X16195))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16197),X16194),X16196)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16197),X16194),X16195))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__left__mono])])])). 4.46/4.71 fof(c_0_7542, plain, ![X8063, X8064, X8065, X8066]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8066),X8064),X8063))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8066),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8066),X8065),X8064)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8066),X8065),X8063)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X8066))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8066),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8066),X8065),X8064)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8066),X8065),X8063)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8066),X8064),X8063))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X8066))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__less__cancel__left])])])])). 4.46/4.71 fof(c_0_7543, plain, ![X10622, X10623, X10624]:(~class_Groups_Omonoid__add(X10624)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10624),X10623),hAPP(c_List_Ofoldl(X10624,X10624,c_Groups_Oplus__class_Oplus(X10624),c_Groups_Ozero__class_Ozero(X10624)),X10622))=hAPP(c_List_Ofoldl(X10624,X10624,c_Groups_Oplus__class_Oplus(X10624),X10623),X10622)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_foldl__absorb0])])])). 4.46/4.71 cnf(c_0_7544, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_5328])). 4.46/4.71 fof(c_0_7545, plain, ![X1387, X1388, X1389, X1390]:(~class_Groups_Oordered__ab__semigroup__add(X1390)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1390),X1389),X1388))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1390),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1390),X1389),X1387)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1390),X1388),X1387))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__right__mono])])])). 4.46/4.71 fof(c_0_7546, plain, ![X6323, X6324, X6325, X6326]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6326),X6325),X6323))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6326),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6326),X6325),X6324)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6326),X6323),X6324)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X6326))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6326),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6326),X6325),X6324)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6326),X6323),X6324)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6326),X6325),X6323))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X6326))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])])). 4.46/4.71 fof(c_0_7547, plain, ![X14814, X14815, X14816, X14817]:(~class_Groups_Oordered__ab__semigroup__add(X14817)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14817),X14816),X14815))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14817),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14817),X14814),X14816)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14817),X14814),X14815))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__left__mono])])])). 4.46/4.71 cnf(c_0_7548, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X5,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X2)!=X4|~hBOOL(hAPP(X5,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4,X1)))), inference(split_conjunct,[status(thm)],[c_0_5242])). 4.46/4.71 cnf(c_0_7549, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))|c_Groups_Ozero__class_Ozero(X1)!=X2|X3!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_5329])). 4.46/4.71 fof(c_0_7550, plain, ![X15062, X15063, X15064, X15065]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15065),X15063),X15062))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15065),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15065),X15064),X15063)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15065),X15064),X15062)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X15065))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15065),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15065),X15064),X15063)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15065),X15064),X15062)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15065),X15063),X15062))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X15065))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__cancel__left])])])])). 4.46/4.71 fof(c_0_7551, plain, ![X7399, X7400, X7401]:(~class_Fields_Ofield__inverse__zero(X7401)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7401),c_Groups_Oone__class_Oone(X7401)),hAPP(hAPP(c_Power_Opower__class_Opower(X7401),X7400),X7399))=hAPP(hAPP(c_Power_Opower__class_Opower(X7401),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7401),c_Groups_Oone__class_Oone(X7401)),X7400)),X7399)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__one__over])])])). 4.46/4.71 fof(c_0_7552, plain, ![X16290, X16291, X16292, X16293, X16294, X16295, X16296]:(((hBOOL(hAPP(hAPP(X16294,X16293),X16291))|~c_List_Olist__all2(X16296,X16295,X16294,hAPP(hAPP(c_List_Olist_OCons(X16296),X16293),X16292),hAPP(hAPP(c_List_Olist_OCons(X16295),X16291),X16290)))&(c_List_Olist__all2(X16296,X16295,X16294,X16292,X16290)|~c_List_Olist__all2(X16296,X16295,X16294,hAPP(hAPP(c_List_Olist_OCons(X16296),X16293),X16292),hAPP(hAPP(c_List_Olist_OCons(X16295),X16291),X16290))))&(~hBOOL(hAPP(hAPP(X16294,X16293),X16291))|~c_List_Olist__all2(X16296,X16295,X16294,X16292,X16290)|c_List_Olist__all2(X16296,X16295,X16294,hAPP(hAPP(c_List_Olist_OCons(X16296),X16293),X16292),hAPP(hAPP(c_List_Olist_OCons(X16295),X16291),X16290)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Cons])])])). 4.46/4.71 fof(c_0_7553, plain, ![X649, X650, X651, X652, X653, X654, X655]:(~c_Finite__Set_Ofolding__image(X655,X654,X653,X652,X651)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X654),X650))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X655,X654,X653),X649),X652),X650)=hAPP(hAPP(X651,X649),X650))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Oeq__fold])])). 4.46/4.71 fof(c_0_7554, plain, ![X11783, X11784, X11785, X11786, X11787, X11788, X11789]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X11788),X11784))|hAPP(hAPP(X11785,X11783),X11784)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X11789,X11788,X11787),X11783),X11786),X11784)|~c_Big__Operators_Ocomm__monoid__big(X11789,X11788,X11787,X11786,X11785))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X11788),X11784))|hAPP(hAPP(X11785,X11783),X11784)=X11786|~c_Big__Operators_Ocomm__monoid__big(X11789,X11788,X11787,X11786,X11785))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__monoid__big_OF__eq])])])])). 4.46/4.71 cnf(c_0_7555, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[c_0_5330, c_0_4471])). 4.46/4.71 cnf(c_0_7556, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5303])). 4.46/4.71 cnf(c_0_7557, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X2|X3!=c_Groups_Ozero__class_Ozero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Groups_Oordered__comm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5331])). 4.46/4.71 fof(c_0_7558, plain, ![X2772, X2773, X2774, X2775]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2775),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2774)),X2773)))|hBOOL(hAPP(hAPP(c_member(X2774),X2772),hAPP(c_List_Oset(X2774),hAPP(hAPP(c_List_Olist__update(X2774,X2773),X2775),X2772))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__update__memI])])). 4.46/4.71 cnf(c_0_7559, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_5165])). 4.46/4.71 fof(c_0_7560, plain, ![X795, X796, X797]:(~class_Lattices_Olattice(X797)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X797),X796))|hAPP(hAPP(c_Finite__Set_Ofold(X797,X797,c_Lattices_Osemilattice__sup__class_Osup(X797)),X795),X796)=c_Big__Operators_Olattice__class_OSup__fin(X797,hAPP(hAPP(c_Set_Oinsert(X797),X795),X796)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oeq__fold__idem_H])])])). 4.46/4.71 fof(c_0_7561, plain, ![X13766, X13767, X13768]:(~class_Lattices_Olattice(X13768)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13768),X13767))|hAPP(hAPP(c_Finite__Set_Ofold(X13768,X13768,c_Lattices_Osemilattice__inf__class_Oinf(X13768)),X13766),X13767)=c_Big__Operators_Olattice__class_OInf__fin(X13768,hAPP(hAPP(c_Set_Oinsert(X13768),X13766),X13767)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold__idem_H])])). 4.46/4.71 fof(c_0_7562, plain, ![X3499, X3500, X3501, X3502, X3503, X3504]:(~c_Relation_Osingle__valued(X3504,X3503,X3502)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X3504,X3503)),hAPP(hAPP(c_Product__Type_OPair(X3504,X3503),X3501),X3500)),X3502))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X3504,X3503)),hAPP(hAPP(c_Product__Type_OPair(X3504,X3503),X3501),X3499)),X3502))|X3499=X3500))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valuedD])])). 4.46/4.71 fof(c_0_7563, plain, ![X3900, X3901]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X3901))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(X3901),X3900))),X3901))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range])])). 4.46/4.71 fof(c_0_7564, plain, ![X7852, X7853, X7854]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X7854,tc_HOL_Obool)),esk222_3(X7852,X7853,X7854)),X7853))|(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7854,tc_HOL_Obool),tc_HOL_Obool))=X7853|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7854,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7854,tc_HOL_Obool),X7853)),X7852))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7854,tc_HOL_Obool)),esk222_3(X7852,X7853,X7854)),X7852))|(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7854,tc_HOL_Obool),tc_HOL_Obool))=X7853|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7854,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7854,tc_HOL_Obool),X7853)),X7852))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inter__subset])])])])])). 4.46/4.71 fof(c_0_7565, plain, ![X12062, X12063, X12064, X12065, X12066]:((~c_List_Olinorder__class_Osorted(X12066,hAPP(hAPP(c_List_Omap(X12065,X12066),X12064),X12062))|c_List_Olinorder__class_Osorted(X12066,hAPP(hAPP(c_List_Omap(X12065,X12066),X12064),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X12065,X12066,X12064),X12063),X12062)))|~class_Orderings_Olinorder(X12066))&(~c_List_Olinorder__class_Osorted(X12066,hAPP(hAPP(c_List_Omap(X12065,X12066),X12064),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X12065,X12066,X12064),X12063),X12062)))|c_List_Olinorder__class_Osorted(X12066,hAPP(hAPP(c_List_Omap(X12065,X12066),X12064),X12062))|~class_Orderings_Olinorder(X12066))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__insort__key])])])])). 4.46/4.71 fof(c_0_7566, plain, ![X2716, X2717, X2718]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2718),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2717)),X2716)))|c_List_Obutlast(X2717,hAPP(hAPP(c_List_Otake(X2717),X2718),X2716))=hAPP(hAPP(c_List_Otake(X2717),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2718),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2716)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_butlast__take])])])). 4.46/4.71 cnf(c_0_7567, plain, (hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X1)))), inference(split_conjunct,[status(thm)],[c_0_5332])). 4.46/4.71 cnf(c_0_7568, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(rw,[status(thm)],[c_0_5333, c_0_5334]), ['final']). 4.46/4.71 fof(c_0_7569, plain, ![X9081, X9082, X9083, X9084]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9084,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9084,tc_HOL_Obool)),X9083),hAPP(hAPP(c_Set_Oinsert(X9084),X9082),c_Orderings_Obot__class_Obot(tc_fun(X9084,tc_HOL_Obool))))),X9081))|(~hBOOL(hAPP(hAPP(c_member(X9084),X9082),X9083))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9084,tc_HOL_Obool)),X9083),hAPP(hAPP(c_Set_Oinsert(X9084),X9082),X9081))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__single__insert])])])). 4.46/4.71 fof(c_0_7570, plain, ![X14671, X14672, X14673, X14674, X14675]:(~c_Finite__Set_Ofolding__one__idem(X14675,X14674,X14673)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14675),X14672))|hAPP(hAPP(c_Finite__Set_Ofold(X14675,X14675,X14674),X14671),X14672)=hAPP(X14673,hAPP(hAPP(c_Set_Oinsert(X14675),X14671),X14672)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oeq__fold__idem_H])])). 4.46/4.71 fof(c_0_7571, plain, ![X1333, X1334, X1335]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1335))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1334),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1333),X1335))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1334),X1333)),X1335)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zmult2__eq])])). 4.46/4.71 cnf(c_0_7572, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),X2)=X2|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5335, c_0_4471])). 4.46/4.71 cnf(c_0_7573, plain, (hAPP(X1,esk87_7(X2,X3,X4,X1,X5,X6,X7))=hAPP(c_Option_Ooption_OSome(X6),X2)|c_Map_Omap__comp(X7,X6,X5,X1,X4,X3)!=hAPP(c_Option_Ooption_OSome(X6),X2)), inference(split_conjunct,[status(thm)],[c_0_5256])). 4.46/4.71 fof(c_0_7574, plain, ![X13704, X13705, X13706, X13707, X13708, X13709, X13710]:(~c_List_Olist__all2(X13710,X13709,X13708,X13707,X13706)|(~c_List_Olist__all2(X13710,X13709,X13708,X13705,X13704)|c_List_Olist__all2(X13710,X13709,X13708,hAPP(hAPP(c_List_Oappend(X13710),X13707),X13705),hAPP(hAPP(c_List_Oappend(X13709),X13706),X13704)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__appendI])])). 4.46/4.71 cnf(c_0_7575, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))=X2|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5336, c_0_4471])). 4.46/4.71 cnf(c_0_7576, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_5264])). 4.46/4.71 cnf(c_0_7577, plain, (hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),hAPP(c_Int_Onat,X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5337])). 4.46/4.71 fof(c_0_7578, plain, ![X4691, X4692]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4691),X4692)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4691),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4692)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4691),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4691),X4692)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4692)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__imp__zdiv__neg__iff])])])])). 4.46/4.71 fof(c_0_7579, plain, ![X15664, X15665]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15664))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X15664),X15665)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15665),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X15664),X15665)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15664))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15665),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__imp__zdiv__neg__iff])])])])). 4.46/4.71 cnf(c_0_7580, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk452_2(X1,X2)),hAPP(c_List_Oset(tc_Nat_Onat),X1)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2), inference(split_conjunct,[status(thm)],[c_0_5338])). 4.46/4.71 fof(c_0_7581, plain, ![X10890, X10891, X10892, X10893, X10894]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10894),X10891),X10893))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10894),X10892),X10893))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10894,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10894,X10893),X10892)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10894,X10891),X10890)))|~class_Orderings_Olinorder(X10894))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10894),X10892),X10890))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10894),X10892),X10893))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10894,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10894,X10893),X10892)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10894,X10891),X10890)))|~class_Orderings_Olinorder(X10894))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__subset__iff])])])])). 4.46/4.71 fof(c_0_7582, plain, ![X9141, X9142]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9142),hAPP(c_Int_Onumber__class_Onumber__of(X9142),X9141)),c_Groups_Ozero__class_Ozero(X9142)))|hAPP(c_Groups_Oabs__class_Oabs(X9142),hAPP(c_Int_Onumber__class_Onumber__of(X9142),X9141))=hAPP(c_Groups_Ouminus__class_Ouminus(X9142),hAPP(c_Int_Onumber__class_Onumber__of(X9142),X9141))|(~class_Rings_Olinordered__idom(X9142)|~class_Int_Onumber__ring(X9142)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9142),hAPP(c_Int_Onumber__class_Onumber__of(X9142),X9141)),c_Groups_Ozero__class_Ozero(X9142)))|hAPP(c_Groups_Oabs__class_Oabs(X9142),hAPP(c_Int_Onumber__class_Onumber__of(X9142),X9141))=hAPP(c_Int_Onumber__class_Onumber__of(X9142),X9141)|(~class_Rings_Olinordered__idom(X9142)|~class_Int_Onumber__ring(X9142)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__number__of])])])])). 4.46/4.71 fof(c_0_7583, plain, ![X7947, X7948]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7948))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7947),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X7948),X7947)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__nonneg__neg__le0])])])). 4.46/4.71 fof(c_0_7584, plain, ![X9400, X9401]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9401),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9400))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X9401),X9400)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__nonpos__pos__le0])])). 4.46/4.71 fof(c_0_7585, plain, ![X12634, X12635]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12635))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12634))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12635),X12634))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12635))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12635),X12634))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12634))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12635),X12634)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])])). 4.46/4.71 fof(c_0_7586, plain, ![X17366, X17367]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X17366),X17367)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17366))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17367)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17366))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X17366),X17367)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17367)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff])])])])). 4.46/4.71 fof(c_0_7587, plain, ![X3823, X3824, X3825]:(~class_Orderings_Olinorder(X3825)|(hBOOL(hAPP(hAPP(c_member(X3825),X3824),hAPP(c_List_Oset(X3825),X3823)))|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3825,X3825,c_COMBI(X3825)),X3824),X3823)=c_List_Olinorder__class_Oinsort__insert__key(X3825,X3825,c_COMBI(X3825),X3824,X3823))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__insert__insort])])])). 4.46/4.71 fof(c_0_7588, plain, ![X6067, X6068, X6069, X6070]:(~class_Divides_Oring__div(X6070)|(c_Divides_Odiv__class_Omod(X6070,X6067,X6068)!=c_Divides_Odiv__class_Omod(X6070,X6069,X6068)|c_Divides_Odiv__class_Omod(X6070,hAPP(c_Groups_Ouminus__class_Ouminus(X6070),X6069),X6068)=c_Divides_Odiv__class_Omod(X6070,hAPP(c_Groups_Ouminus__class_Ouminus(X6070),X6067),X6068))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__cong])])). 4.46/4.71 fof(c_0_7589, plain, ![X16672, X16673]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16673))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16672))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16673),X16672))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I1_J])])])). 4.46/4.71 fof(c_0_7590, plain, ![X12704, X12705]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12705))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12704))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12705),X12704))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])])])). 4.46/4.71 fof(c_0_7591, plain, ![X748, X749]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X749))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X748))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X749),X748))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])])). 4.46/4.71 fof(c_0_7592, plain, ![X11530, X11531]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11530),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11530),X11531)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11531),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11530),X11531)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11530),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11531),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__imp__zdiv__nonneg__iff])])])])). 4.46/4.71 fof(c_0_7593, plain, ![X5027, X5028, X5029, X5031]:((hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X5029)),esk151_3(X5027,X5028,X5029)),X5028))|(~hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X5029)),X5031),X5028))|c_Hoare__Mirabelle_Otriple__valid(X5029,X5027,X5031)))&(~c_Hoare__Mirabelle_Otriple__valid(X5029,hAPP(c_Nat_OSuc,X5027),esk151_3(X5027,X5028,X5029))|(~hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X5029)),X5031),X5028))|c_Hoare__Mirabelle_Otriple__valid(X5029,X5027,X5031)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_triples__valid__Suc])])])])])])). 4.46/4.71 fof(c_0_7594, plain, ![X11323]:(~class_Enum_Oenum(X11323)|hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(X11323)),c_Option_Ooption_ONone(X11323)),hAPP(hAPP(c_List_Omap(X11323,tc_Option_Ooption(X11323)),c_Option_Ooption_OSome(X11323)),c_Enum_Oenum__class_Oenum(X11323)))=c_Enum_Oenum__class_Oenum(tc_Option_Ooption(X11323))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__option__def])])). 4.46/4.71 cnf(c_0_7595, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Orev(X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))=X4|hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=hAPP(c_List_Orev(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_5339])). 4.46/4.71 cnf(c_0_7596, plain, (hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Orev(X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))), inference(split_conjunct,[status(thm)],[c_0_5340]), ['final']). 4.46/4.71 cnf(c_0_7597, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[c_0_5341, c_0_4471])). 4.46/4.71 cnf(c_0_7598, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[c_0_5342, c_0_4471])). 4.46/4.71 cnf(c_0_7599, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(rw,[status(thm)],[c_0_5343, c_0_4471])). 4.46/4.71 cnf(c_0_7600, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[c_0_5344, c_0_4471])). 4.46/4.71 cnf(c_0_7601, plain, (hAPP(X6,hAPP(c_Product__Type_Osnd(X3,X1),X5))=hAPP(X4,hAPP(c_Product__Type_Osnd(X3,X1),X5))|hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X4),X5)!=hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X6),X5)), inference(split_conjunct,[status(thm)],[c_0_5189])). 4.46/4.71 fof(c_0_7602, plain, ![X16259, X16260, X16261]:(~class_Groups_Oordered__ab__group__add(X16261)|c_SetInterval_Oord__class_OgreaterThanAtMost(X16261,hAPP(c_Groups_Ouminus__class_Ouminus(X16261),X16259),hAPP(c_Groups_Ouminus__class_Ouminus(X16261),X16260))=hAPP(c_Set_Oimage(X16261,X16261,c_Groups_Ouminus__class_Ouminus(X16261)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X16261,X16260),X16259))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__uminus__atLeastLessThan])])])). 4.46/4.71 cnf(c_0_7603, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(rw,[status(thm)],[c_0_5345, c_0_4471])). 4.46/4.71 cnf(c_0_7604, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[c_0_5346, c_0_4471])). 4.46/4.71 cnf(c_0_7605, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[c_0_5347, c_0_4471])). 4.46/4.71 cnf(c_0_7606, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[c_0_5348, c_0_4471])). 4.46/4.71 fof(c_0_7607, plain, ![X5531, X5532]:(X5532=c_List_Olist_ONil(X5531)|c_Random_Oselect__weight(X5531,hAPP(hAPP(c_List_Omap(X5531,tc_prod(tc_Code__Numeral_Ocode__numeral,X5531)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X5531),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X5532))=c_Random_Oselect(X5531,X5532)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select__weigth__select])])). 4.46/4.71 cnf(c_0_7608, plain, (hAPP(X6,hAPP(c_Product__Type_Ofst(X1,X3),X5))=hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X3),X5))|hAPP(c_Product__Type_Oapfst(X1,X2,X3,X4),X5)!=hAPP(c_Product__Type_Oapfst(X1,X2,X3,X6),X5)), inference(split_conjunct,[status(thm)],[c_0_5190])). 4.46/4.71 fof(c_0_7609, plain, ![X11460, X11461, X11462, X11463, X11464, X11465, X11466, X11467]:(((c_List_Olist_ONil(X11462)!=X11461|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X11462)),X11461),c_List_Olists(X11462,X11460))))&(hAPP(hAPP(c_List_Olist_OCons(X11462),X11463),X11464)!=X11461|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X11462)),X11464),c_List_Olists(X11462,X11460)))|~hBOOL(hAPP(hAPP(c_member(X11462),X11463),X11460))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X11462)),X11461),c_List_Olists(X11462,X11460)))))&(((hAPP(hAPP(c_List_Olist_OCons(X11467),esk335_3(X11465,X11466,X11467)),esk336_3(X11465,X11466,X11467))=X11466|c_List_Olist_ONil(X11467)=X11466|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X11467)),X11466),c_List_Olists(X11467,X11465))))&(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X11467)),esk336_3(X11465,X11466,X11467)),c_List_Olists(X11467,X11465)))|c_List_Olist_ONil(X11467)=X11466|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X11467)),X11466),c_List_Olists(X11467,X11465)))))&(hBOOL(hAPP(hAPP(c_member(X11467),esk335_3(X11465,X11466,X11467)),X11465))|c_List_Olist_ONil(X11467)=X11466|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X11467)),X11466),c_List_Olists(X11467,X11465)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists_Osimps])])])])])])). 4.46/4.71 fof(c_0_7610, plain, ![X15801, X15802, X15803, X15804]:(~class_Groups_Ocomm__monoid__add(X15804)|(~c_Fun_Oinj__on(X15803,X15804,X15802,X15801)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15804,X15804),c_Fun_Oid(X15804)),hAPP(c_Set_Oimage(X15803,X15804,X15802),X15801))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15803,X15804),X15802),X15801))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__reindex__id])])])). 4.46/4.71 cnf(c_0_7611, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))), inference(rw,[status(thm)],[c_0_5349, c_0_4471])). 4.46/4.71 cnf(c_0_7612, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[c_0_5350, c_0_4471])). 4.46/4.71 cnf(c_0_7613, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))), inference(rw,[status(thm)],[c_0_5351, c_0_4471])). 4.46/4.71 fof(c_0_7614, plain, ![X8183, X8184, X8185, X8186]:(~class_Groups_Ocomm__monoid__mult(X8186)|(~c_Fun_Oinj__on(X8185,X8186,X8184,X8183)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8185,X8186),X8184),X8183)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8186,X8186),c_Fun_Oid(X8186)),hAPP(c_Set_Oimage(X8185,X8186,X8184),X8183)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__reindex__id])])])). 4.46/4.71 fof(c_0_7615, plain, ![X12275, X12276, X12278]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X12276)),X12275))|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X12276)),X12278),X12275))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12276)),X12278)),esk359_2(X12275,X12276))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__maxlen])])])])])). 4.46/4.71 fof(c_0_7616, plain, ![X3805, X3806, X3807, X3808]:(((c_List_Olinorder__class_Osorted(X3808,hAPP(hAPP(c_List_Olist_OCons(X3808),X3806),X3805))|~c_List_Olinorder__class_Osorted(X3808,hAPP(hAPP(c_List_Olist_OCons(X3808),X3807),hAPP(hAPP(c_List_Olist_OCons(X3808),X3806),X3805)))|~class_Orderings_Olinorder(X3808))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3808),X3807),X3806))|~c_List_Olinorder__class_Osorted(X3808,hAPP(hAPP(c_List_Olist_OCons(X3808),X3807),hAPP(hAPP(c_List_Olist_OCons(X3808),X3806),X3805)))|~class_Orderings_Olinorder(X3808)))&(~c_List_Olinorder__class_Osorted(X3808,hAPP(hAPP(c_List_Olist_OCons(X3808),X3806),X3805))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3808),X3807),X3806))|c_List_Olinorder__class_Osorted(X3808,hAPP(hAPP(c_List_Olist_OCons(X3808),X3807),hAPP(hAPP(c_List_Olist_OCons(X3808),X3806),X3805)))|~class_Orderings_Olinorder(X3808))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__many__eq])])])). 4.46/4.71 fof(c_0_7617, plain, ![X15566, X15567, X15568, X15569]:(~class_Orderings_Olinorder(X15569)|c_SetInterval_Oord__class_OatLeastAtMost(X15569,hAPP(hAPP(c_Orderings_Oord__class_Omax(X15569),X15568),X15566),X15567)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15569,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X15569,X15568,X15567)),hAPP(c_SetInterval_Oord__class_OatLeast(X15569),X15566))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL2])])). 4.46/4.71 cnf(c_0_7618, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5352])). 4.46/4.71 cnf(c_0_7619, plain, (hAPP(c_Finite__Set_Ocard(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,X2),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5353])). 4.46/4.71 fof(c_0_7620, plain, ![X7667, X7668, X7669, X7670]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7670,X7669),tc_HOL_Obool)),X7668),X7667))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7670,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X7670,X7669),X7668)),hAPP(c_Relation_ODomain(X7670,X7669),X7667)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__mono])])). 4.46/4.71 fof(c_0_7621, plain, ![X999, X1000, X1001, X1002]:(~class_Orderings_Olinorder(X1002)|c_SetInterval_Oord__class_OatLeastAtMost(X1002,X1001,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1002),X1000),X999))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1002,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1002,X1001,X1000)),hAPP(c_SetInterval_Oord__class_OatMost(X1002),X999))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__atLeastAtMostL1])])])). 4.46/4.71 fof(c_0_7622, plain, ![X5591, X5592, X5593, X5594]:(~class_Orderings_Olinorder(X5594)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5594,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X5594),X5593)),c_SetInterval_Oord__class_OatLeastAtMost(X5594,X5592,X5591))=c_SetInterval_Oord__class_OatLeastAtMost(X5594,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5594),X5593),X5592),X5591)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__atLeastAtMostR2])])])). 4.46/4.71 fof(c_0_7623, plain, ![X14763, X14764, X14765, X14766, X14767]:(c_Option_Ooption_ONone(X14765)!=hAPP(X14767,X14766)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14764,tc_HOL_Obool)),c_Map_Odom(X14764,X14765,X14767)),hAPP(hAPP(c_Set_Oinsert(X14764),X14766),X14763))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14764,tc_HOL_Obool)),c_Map_Odom(X14764,X14765,X14767)),X14763)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__minus])])). 4.46/4.71 fof(c_0_7624, plain, ![X9461, X9462]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9462),X9461))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X9461)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X9462))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9461),X9462))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiff__int])])])). 4.46/4.71 cnf(c_0_7625, plain, (hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(c_fequal,X2))),X3)=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[c_0_5354, c_0_4531])). 4.46/4.71 fof(c_0_7626, plain, ![X7708, X7709, X7710, X7711]:(~class_Orderings_Olinorder(X7711)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7711,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X7711),X7710)),c_SetInterval_Oord__class_OatLeastAtMost(X7711,X7709,X7708))=c_SetInterval_Oord__class_OatLeastAtMost(X7711,X7709,hAPP(hAPP(c_Orderings_Oord__class_Omin(X7711),X7710),X7708))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR1])])). 4.46/4.71 cnf(c_0_7627, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))), inference(rw,[status(thm)],[c_0_5355, c_0_4471])). 4.46/4.71 cnf(c_0_7628, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))), inference(rw,[status(thm)],[c_0_5356, c_0_4471])). 4.46/4.71 fof(c_0_7629, plain, ![X1055, X1056, X1057, X1058, X1059]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X1059,X1058)),hAPP(hAPP(c_Product__Type_OPair(X1059,X1058),X1057),X1056)),X1055))|hBOOL(hAPP(hAPP(c_member(X1059),X1057),hAPP(c_Relation_ODomain(X1059,X1058),X1055)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_DomainI])])])). 4.46/4.71 cnf(c_0_7630, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X4)),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_5357])). 4.46/4.71 cnf(c_0_7631, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2)),X4)),X3))), inference(split_conjunct,[status(thm)],[c_0_5357])). 4.46/4.71 cnf(c_0_7632, plain, (hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(c_fequal,X2))),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[c_0_5358, c_0_4531])). 4.46/4.71 fof(c_0_7633, plain, ![X10768, X10769, X10770, X10771, X10772]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10772,X10771)),hAPP(hAPP(c_Product__Type_OPair(X10772,X10771),X10770),X10769)),X10768))|hBOOL(hAPP(hAPP(c_member(X10771),X10769),hAPP(c_Relation_ORange(X10772,X10771),X10768)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_RangeI])])])). 4.46/4.71 cnf(c_0_7634, plain, (c_Option_Ooption_ONone(X5)=c_Map_Omap__comp(X1,X5,X7,X6,X3,X4)|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(X3,X4)|c_Option_Ooption_ONone(X5)!=hAPP(X6,X2)), inference(split_conjunct,[status(thm)],[c_0_5286])). 4.46/4.71 fof(c_0_7635, plain, ![X5572, X5573, X5574]:((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5574,tc_HOL_Obool)),hAPP(c_List_Oset(X5574),X5573)),hAPP(c_List_Oset(X5574),X5572))!=c_Orderings_Obot__class_Obot(tc_fun(X5574,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(X5574),X5572))|~hBOOL(hAPP(c_List_Odistinct(X5574),X5573))|hBOOL(hAPP(c_List_Odistinct(X5574),hAPP(hAPP(c_List_Oappend(X5574),X5573),X5572))))&(((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5574,tc_HOL_Obool)),hAPP(c_List_Oset(X5574),X5573)),hAPP(c_List_Oset(X5574),X5572))=c_Orderings_Obot__class_Obot(tc_fun(X5574,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(X5574),hAPP(hAPP(c_List_Oappend(X5574),X5573),X5572))))&(hBOOL(hAPP(c_List_Odistinct(X5574),X5572))|~hBOOL(hAPP(c_List_Odistinct(X5574),hAPP(hAPP(c_List_Oappend(X5574),X5573),X5572)))))&(hBOOL(hAPP(c_List_Odistinct(X5574),X5573))|~hBOOL(hAPP(c_List_Odistinct(X5574),hAPP(hAPP(c_List_Oappend(X5574),X5573),X5572)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__append])])])). 4.46/4.71 cnf(c_0_7636, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X4)|X1!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),X4)|hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)!=c_Groups_Ozero__class_Ozero(X2)|~class_Fields_Ofield__inverse__zero(X2)|~class_Int_Onumber(X2)), inference(split_conjunct,[status(thm)],[c_0_5359])). 4.46/4.71 fof(c_0_7637, plain, ![X6917, X6918, X6919]:(~class_Orderings_Olinorder(X6919)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6919),X6918),X6917))|hAPP(c_SetInterval_Oord__class_OatLeast(X6919),X6918)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6919,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X6919,X6918),X6917)),hAPP(c_SetInterval_Oord__class_OatLeast(X6919),X6917)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I14_J])])). 4.46/4.71 fof(c_0_7638, plain, ![X13694, X13695, X13696]:(~class_Orderings_Olinorder(X13696)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13696),X13695),X13694))|hAPP(c_SetInterval_Oord__class_OlessThan(X13696),X13694)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13696,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X13696),X13695)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X13696,X13695),X13694)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I8_J])])])). 4.46/4.71 cnf(c_0_7639, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X1),hAPP(c_Int_Onat,X2))=hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5360])). 4.46/4.71 fof(c_0_7640, plain, ![X809, X810]:(~class_Rings_Ocomm__semiring__1(X810)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X810),X809),X809)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X810),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X810),c_Groups_Oone__class_Oone(X810)),c_Groups_Oone__class_Oone(X810))),X809)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])])). 4.46/4.71 fof(c_0_7641, plain, ![X17597, X17598, X17599]:(~class_Orderings_Olinorder(X17599)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17599),X17598),X17597))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17599,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X17599,X17598,X17597)),hAPP(c_SetInterval_Oord__class_OatLeast(X17599),X17597))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X17599),X17598))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I12_J])])])). 4.46/4.71 fof(c_0_7642, plain, ![X14848, X14849, X14850, X14851]:((~hBOOL(hAPP(X14851,X14850))|hAPP(c_List_Ofilter(X14849,X14851),hAPP(hAPP(c_List_Olist_OCons(X14849),X14850),X14848))=hAPP(hAPP(c_List_Olist_OCons(X14849),X14850),hAPP(c_List_Ofilter(X14849,X14851),X14848)))&(hBOOL(hAPP(X14851,X14850))|hAPP(c_List_Ofilter(X14849,X14851),hAPP(hAPP(c_List_Olist_OCons(X14849),X14850),X14848))=hAPP(c_List_Ofilter(X14849,X14851),X14848))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter_Osimps_I2_J])])])). 4.46/4.71 fof(c_0_7643, plain, ![X7908, X7909, X7910]:(~class_Orderings_Olinorder(X7910)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7910),X7909),X7908))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7910,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X7910,X7909,X7908)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X7910),X7908))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X7910),X7909))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I11_J])])])). 4.46/4.71 fof(c_0_7644, plain, ![X13116, X13117, X13118]:(~class_Orderings_Olinorder(X13118)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13118),X13117),X13116))|hAPP(c_SetInterval_Oord__class_OatLeast(X13118),X13117)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13118,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X13118,X13117,X13116)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X13118),X13116)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I13_J])])])). 4.46/4.71 fof(c_0_7645, plain, ![X7475, X7476, X7477]:(~class_Orderings_Olinorder(X7477)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7477),X7476),X7475))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7477,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X7477),X7476)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7477,X7476,X7475))=hAPP(c_SetInterval_Oord__class_OlessThan(X7477),X7475))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I7_J])])). 4.46/4.71 fof(c_0_7646, plain, ![X9131, X9132, X9133]:(~class_Orderings_Olinorder(X9133)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9133),X9132),X9131))|hAPP(c_SetInterval_Oord__class_OatMost(X9133),X9131)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9133,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X9133),X9132)),c_SetInterval_Oord__class_OatLeastAtMost(X9133,X9132,X9131)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I10_J])])])). 4.46/4.71 fof(c_0_7647, plain, ![X11710, X11711, X11712]:(~class_Divides_Osemiring__div(X11712)|X11711=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11712),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11712),X11711),X11710)),X11710)),c_Divides_Odiv__class_Omod(X11712,X11711,X11710))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__equality])])). 4.46/4.71 fof(c_0_7648, plain, ![X903, X904, X905]:(~class_Divides_Osemiring__div(X905)|X904=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X905),c_Divides_Odiv__class_Omod(X905,X904,X903)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X905),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X905),X904),X903)),X903))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__div__class_Omod__div__equality_H])])). 4.46/4.71 fof(c_0_7649, plain, ![X1296, X1297, X1298]:(~class_Orderings_Olinorder(X1298)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1298),X1297),X1296))|hAPP(c_SetInterval_Oord__class_OatMost(X1298),X1296)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1298,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1298),X1297)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1298,X1297,X1296)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I9_J])])])). 4.46/4.71 fof(c_0_7650, plain, ![X6269, X6270, X6271, X6272]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6271,X6272)),X6269),X6270))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6271,X6272)),X6270),X6269))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X6271,X6272)),X6270),X6269))|~class_Orderings_Oord(X6272))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6271,X6272)),X6269),X6270))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X6271,X6272)),X6270),X6269))|~class_Orderings_Oord(X6272))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6271,X6272)),X6270),X6269))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X6271,X6272)),X6270),X6269))|~class_Orderings_Oord(X6272)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__fun__def])])])])). 4.46/4.71 fof(c_0_7651, plain, ![X542, X543, X544]:(c_List_Olist_ONil(X543)=X544|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X542),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X543)),X544)))|hAPP(c_List_Ohd(X543),hAPP(hAPP(c_List_Odrop(X543),X542),X544))=hAPP(hAPP(c_List_Onth(X543),X544),X542))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__drop__conv__nth])])])). 4.46/4.71 fof(c_0_7652, plain, ![X2886, X2887, X2888, X2889, X2890]:(~c_Finite__Set_Ofolding__one__idem(X2890,X2889,X2888)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2890),X2887))|(c_Orderings_Obot__class_Obot(tc_fun(X2890,tc_HOL_Obool))=X2887|hAPP(hAPP(X2889,X2886),hAPP(X2888,X2887))=hAPP(X2888,hAPP(hAPP(c_Set_Oinsert(X2890),X2886),X2887))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one__idem_Oinsert__idem])])])). 4.46/4.71 fof(c_0_7653, plain, ![X7800, X7801, X7802]:(~class_Divides_Osemiring__div(X7802)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7802),X7801),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X7802),X7800),X7801))),c_Divides_Odiv__class_Omod(X7802,X7800,X7801))=X7800), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__div__equality2])])])). 4.46/4.71 cnf(c_0_7654, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_5361])). 4.46/4.71 fof(c_0_7655, plain, ![X527, X528, X529, X530]:(~class_Orderings_Olinorder(X530)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X530),X528),hAPP(hAPP(c_Orderings_Oord__class_Omax(X530),X529),X527))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X530),X529),hAPP(hAPP(c_Orderings_Oord__class_Omax(X530),X528),X527))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup_Oleft__commute])])])). 4.46/4.71 fof(c_0_7656, plain, ![X10776, X10777, X10778]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10778,X10778),tc_HOL_Obool)),X10777),X10776))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10778,X10778),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X10778,X10777)),c_Transitive__Closure_Ortrancl(X10778,X10776)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__mono])])). 4.46/4.71 cnf(c_0_7657, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5362])). 4.46/4.71 cnf(c_0_7658, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)!=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_5363])). 4.46/4.71 fof(c_0_7659, plain, ![X3902, X3903]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3903),X3902))|c_List_Oupto(X3903,X3902)=c_List_Olist_ONil(tc_Int_Oint))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3903),X3902))|c_List_Oupto(X3903,X3902)=hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X3903),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3903),c_Groups_Oone__class_Oone(tc_Int_Oint)),X3902)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_upto_Osimps])])])). 4.46/4.71 fof(c_0_7660, plain, ![X9450, X9451]:(~class_Groups_Olinordered__ab__group__add(X9451)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9451),X9450))|(X9450=c_Orderings_Obot__class_Obot(tc_fun(X9451,tc_HOL_Obool))|hAPP(c_Groups_Ouminus__class_Ouminus(X9451),c_Big__Operators_Olinorder__class_OMax(X9451,X9450))=c_Big__Operators_Olinorder__class_OMin(X9451,hAPP(c_Set_Oimage(X9451,X9451,c_Groups_Ouminus__class_Ouminus(X9451)),X9450))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__Max__eq__Min])])])). 4.46/4.71 fof(c_0_7661, plain, ![X5551, X5552, X5553, X5554]:((~hBOOL(hAPP(hAPP(c_member(X5554),X5553),X5552))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5554,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5554),X5553),X5551)),X5552)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5554,tc_HOL_Obool)),X5551),X5552))&(hBOOL(hAPP(hAPP(c_member(X5554),X5553),X5552))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5554,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5554),X5553),X5551)),X5552)=hAPP(hAPP(c_Set_Oinsert(X5554),X5553),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5554,tc_HOL_Obool)),X5551),X5552)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insert__Diff__if])])])). 4.46/4.71 fof(c_0_7662, plain, ![X2831, X2832]:(~class_Groups_Olinordered__ab__group__add(X2832)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2832),X2831))|(X2831=c_Orderings_Obot__class_Obot(tc_fun(X2832,tc_HOL_Obool))|hAPP(c_Groups_Ouminus__class_Ouminus(X2832),c_Big__Operators_Olinorder__class_OMin(X2832,X2831))=c_Big__Operators_Olinorder__class_OMax(X2832,hAPP(c_Set_Oimage(X2832,X2832,c_Groups_Ouminus__class_Ouminus(X2832)),X2831))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__Min__eq__Max])])])). 4.46/4.71 fof(c_0_7663, plain, ![X16137, X16138, X16139, X16140]:(~class_Groups_Oordered__comm__monoid__add(X16140)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16140),c_Groups_Ozero__class_Ozero(X16140)),X16139))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16140),X16138),X16137))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16140),X16138),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16140),X16139),X16137)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])])). 4.46/4.71 fof(c_0_7664, plain, ![X3258, X3259, X3260, X3261]:(~class_Groups_Oordered__comm__monoid__add(X3261)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3261),c_Groups_Ozero__class_Ozero(X3261)),X3260))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3261),X3259),X3258))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3261),X3259),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3261),X3260),X3258)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__increasing])])])). 4.46/4.71 cnf(c_0_7665, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X3))))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)!=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))), inference(split_conjunct,[status(thm)],[c_0_5363])). 4.46/4.71 fof(c_0_7666, plain, ![X12279, X12280, X12281]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12281),X12280))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12279),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12280),X12281))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12279),X12280)),X12281)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__add__assoc])])])). 4.46/4.71 fof(c_0_7667, plain, ![X13691, X13692, X13693]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13693),X13692))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13691),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13692),X13693))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13691),X13693)),X13692)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__right])])). 4.46/4.71 fof(c_0_7668, plain, ![X3534, X3535]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3534))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3535),X3534))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3535))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3535),X3534)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3535),X3534)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3534))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3535))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])])). 4.46/4.71 fof(c_0_7669, plain, ![X16406, X16407, X16408, X16409]:(~class_Rings_Olinordered__semidom(X16409)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16409),c_Groups_Ozero__class_Ozero(X16409)),X16408))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16409),X16407),X16406))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16409),X16407),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16409),X16408),X16406)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__add__strict])])])). 4.46/4.71 fof(c_0_7670, plain, ![X13574, X13575, X13576, X13577]:(~class_Groups_Oordered__comm__monoid__add(X13577)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13577),c_Groups_Ozero__class_Ozero(X13577)),X13576))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13577),X13575),X13574))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13577),X13575),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13577),X13576),X13574)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__increasing])])])). 4.46/4.71 fof(c_0_7671, plain, ![X12003, X12004, X12005, X12006]:(~class_Groups_Oordered__comm__monoid__add(X12006)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12006),c_Groups_Ozero__class_Ozero(X12006)),X12005))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12006),X12004),X12003))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12006),X12004),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12006),X12003),X12005)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__increasing2])])])). 4.46/4.71 fof(c_0_7672, plain, ![X15878, X15879, X15880]:(~class_Lattices_Oab__semigroup__idem__mult(X15880)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15880),X15879))|hAPP(hAPP(c_Finite__Set_Ofold(X15880,X15880,c_Groups_Otimes__class_Otimes(X15880)),X15878),X15879)=hAPP(c_Finite__Set_Ofold1(X15880,c_Groups_Otimes__class_Otimes(X15880)),hAPP(hAPP(c_Set_Oinsert(X15880),X15878),X15879)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__eq__fold__idem])])])). 4.46/4.71 cnf(c_0_7673, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4))=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Divides_Osemiring__div(X2)), inference(split_conjunct,[status(thm)],[c_0_5364])). 4.46/4.71 fof(c_0_7674, plain, ![X8997, X8998, X8999, X9000]:(~hBOOL(hAPP(hAPP(c_member(tc_fun(X9000,tc_HOL_Obool)),X8999),X8998))|(~hBOOL(hAPP(hAPP(c_member(X9000),X8997),X8999))|hBOOL(hAPP(hAPP(c_member(X9000),X8997),c_Complete__Lattice_OSup__class_OSup(tc_fun(X9000,tc_HOL_Obool),X8998))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnionI])])). 4.46/4.71 fof(c_0_7675, plain, ![X10854, X10855, X10856, X10857, X10858, X10859]:((X10855!=X10854|hAPP(hAPP(c_Product__Type_OSigma(X10856,X10859),X10854),hAPP(c_COMBK(tc_fun(X10859,tc_HOL_Obool),X10856),X10857))=hAPP(hAPP(c_Product__Type_OSigma(X10856,X10859),X10855),hAPP(c_COMBK(tc_fun(X10859,tc_HOL_Obool),X10856),X10857))|~hBOOL(hAPP(hAPP(c_member(X10859),X10858),X10857)))&(hAPP(hAPP(c_Product__Type_OSigma(X10856,X10859),X10854),hAPP(c_COMBK(tc_fun(X10859,tc_HOL_Obool),X10856),X10857))!=hAPP(hAPP(c_Product__Type_OSigma(X10856,X10859),X10855),hAPP(c_COMBK(tc_fun(X10859,tc_HOL_Obool),X10856),X10857))|X10855=X10854|~hBOOL(hAPP(hAPP(c_member(X10859),X10858),X10857)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Times__eq__cancel2])])])])). 4.46/4.71 fof(c_0_7676, plain, ![X3635, X3636]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3636))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3635))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X3636,X3635))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I2_J])])])). 4.46/4.71 fof(c_0_7677, plain, ![X4708, X4709, X4710, X4711, X4712, X4713, X4714]:(((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4708),X4711)!=X4709|hBOOL(hAPP(X4710,X4711))|~hBOOL(hAPP(X4710,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4709),X4708))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4709),X4708))|hBOOL(hAPP(X4710,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X4710,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4709),X4708)))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4713),X4712))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4712),esk135_3(X4712,X4713,X4714))=X4713|hBOOL(hAPP(X4714,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4713),X4712))))&(~hBOOL(hAPP(X4714,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4712),esk135_3(X4712,X4713,X4714))=X4713|hBOOL(hAPP(X4714,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4713),X4712)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4713),X4712))|~hBOOL(hAPP(X4714,esk135_3(X4712,X4713,X4714)))|hBOOL(hAPP(X4714,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4713),X4712))))&(~hBOOL(hAPP(X4714,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X4714,esk135_3(X4712,X4713,X4714)))|hBOOL(hAPP(X4714,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4713),X4712))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__diff__split__asm])])])])])])])). 4.46/4.71 fof(c_0_7678, plain, ![X1646, X1647, X1648, X1649]:(~class_Orderings_Olinorder(X1649)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1649),X1648),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1649),X1647),X1646))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1649),X1647),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1649),X1648),X1646))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__commute])])). 4.46/4.71 fof(c_0_7679, plain, ![X14452, X14453]:(~hBOOL(hAPP(c_List_Odistinct(X14453),X14452))|hBOOL(hAPP(c_List_Odistinct(tc_fun(X14453,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X14453),tc_fun(X14453,tc_HOL_Obool)),c_List_Oset(X14453)),c_Enum_Osublists(X14453,X14452))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__set__sublists])])). 4.46/4.71 fof(c_0_7680, plain, ![X7306, X7307, X7308, X7309]:((hBOOL(hAPP(hAPP(c_member(X7309),esk213_4(X7306,X7307,X7308,X7309)),X7307))|hAPP(c_Nat_OSuc,X7306)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7309,tc_Nat_Onat),X7308),X7307))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X7308,esk213_4(X7306,X7307,X7308,X7309))))|hAPP(c_Nat_OSuc,X7306)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7309,tc_Nat_Onat),X7308),X7307))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__SucD])])])])])). 4.46/4.71 fof(c_0_7681, plain, ![X9762, X9763]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9763),X9762))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X9762),X9763)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9763)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X9762),X9763)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9763),X9762))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9763)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__imp__zdiv__pos__iff])])])])). 4.46/4.71 cnf(c_0_7682, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,X1)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5365])). 4.46/4.71 fof(c_0_7683, plain, ![X3399, X3400, X3401, X3402, X3403, X3404, X3405]:(((X3400!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3399),X3402)|hBOOL(hAPP(X3401,X3402))|~hBOOL(hAPP(X3401,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3400),X3399))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3400),X3399))|hBOOL(hAPP(X3401,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X3401,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3400),X3399)))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3404),X3403))|X3404=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3403),esk90_3(X3403,X3404,X3405))|hBOOL(hAPP(X3405,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3404),X3403))))&(~hBOOL(hAPP(X3405,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|X3404=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3403),esk90_3(X3403,X3404,X3405))|hBOOL(hAPP(X3405,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3404),X3403)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3404),X3403))|~hBOOL(hAPP(X3405,esk90_3(X3403,X3404,X3405)))|hBOOL(hAPP(X3405,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3404),X3403))))&(~hBOOL(hAPP(X3405,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X3405,esk90_3(X3403,X3404,X3405)))|hBOOL(hAPP(X3405,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3404),X3403))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__split])])])])])])). 4.46/4.71 fof(c_0_7684, plain, ![X4310, X4311, X4312, X4313, X4314]:((hBOOL(hAPP(hAPP(c_member(X4312),esk119_5(X4310,X4311,X4312,X4313,X4314)),X4310))|~hBOOL(hAPP(hAPP(c_member(X4314),X4313),c_Map_Oran(X4312,X4314,c_Map_Orestrict__map(X4312,X4314,X4311,X4310)))))&(hAPP(X4311,esk119_5(X4310,X4311,X4312,X4313,X4314))=hAPP(c_Option_Ooption_OSome(X4314),X4313)|~hBOOL(hAPP(hAPP(c_member(X4314),X4313),c_Map_Oran(X4312,X4314,c_Map_Orestrict__map(X4312,X4314,X4311,X4310)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ran__restrictD])])])])). 4.46/4.71 cnf(c_0_7685, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),c_Transitive__Closure_Otrancl(X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_5366])). 4.46/4.71 fof(c_0_7686, plain, ![X12088, X12089]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12089,tc_HOL_Obool)),esk353_2(X12088,X12089)),hAPP(c_Relation_OImage(X12089,X12089,X12088),esk353_2(X12088,X12089))))|c_Wellfounded_Owf(X12089,X12088))&(esk353_2(X12088,X12089)!=c_Orderings_Obot__class_Obot(tc_fun(X12089,tc_HOL_Obool))|c_Wellfounded_Owf(X12089,X12088))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wfI__pf])])])])])). 4.46/4.71 fof(c_0_7687, plain, ![X15248, X15249, X15250, X15251]:(~class_Rings_Ocomm__semiring__1(X15251)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15251),X15250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15251),X15249),X15248))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15251),X15249),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15251),X15250),X15248))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])])). 4.46/4.71 cnf(c_0_7688, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5367])). 4.46/4.71 cnf(c_0_7689, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_5368]), ['final']). 4.46/4.71 fof(c_0_7690, plain, ![X10764, X10765, X10766, X10767]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10767),X10766))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10765),hAPP(c_Set_Oimage(X10767,X10765,X10764),X10766))),hAPP(c_Finite__Set_Ocard(X10767),X10766)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__image__le])])])). 4.46/4.71 fof(c_0_7691, plain, ![X975, X976, X977, X979, X980, X981, X982]:(((hBOOL(hAPP(hAPP(c_member(X977),esk24_3(X975,X976,X977)),hAPP(c_List_Oset(X977),X976)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X977)),X976),c_List_Olists(X977,X975))))&(~hBOOL(hAPP(hAPP(c_member(X977),esk24_3(X975,X976,X977)),X975))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X977)),X976),c_List_Olists(X977,X975)))))&(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X981)),X980),c_List_Olists(X981,X979)))|(~hBOOL(hAPP(hAPP(c_member(X981),X982),hAPP(c_List_Oset(X981),X980)))|hBOOL(hAPP(hAPP(c_member(X981),X982),X979))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lists__conv__set])])])])])])). 4.46/4.71 fof(c_0_7692, plain, ![X2429, X2430, X2431, X2432]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X2431),X2430))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2431,X2432),X2429),X2430)=c_Groups_Ozero__class_Ozero(X2432)|~class_Groups_Ocomm__monoid__add(X2432))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2431),X2430))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2431,X2432),X2429),X2430)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X2432,X2431,c_Groups_Oplus__class_Oplus(X2432)),X2429),c_Groups_Ozero__class_Ozero(X2432)),X2430)|~class_Groups_Ocomm__monoid__add(X2432))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum_OF__eq])])])])). 4.46/4.71 fof(c_0_7693, plain, ![X1309, X1310]:((c_Divides_Odiv__class_Omod(tc_Int_Oint,X1310,X1309)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1310,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1309))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1310,X1309)),X1309))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1310,X1309)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1310,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1309)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmod__zminus2__eq__if])])])). 4.46/4.71 fof(c_0_7694, plain, ![X17414, X17415, X17416, X17417]:(~class_Rings_Ocomm__semiring__1(X17417)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17417),X17416),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17417),X17415),X17414))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17417),X17415),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17417),X17416),X17414))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])])])). 4.46/4.71 fof(c_0_7695, plain, ![X11692, X11693, X11694, X11695]:(~hBOOL(hAPP(hAPP(c_member(X11695),X11694),X11693))|(hBOOL(hAPP(hAPP(c_member(X11695),X11694),X11692))|hBOOL(hAPP(hAPP(c_member(X11695),X11694),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11695,tc_HOL_Obool)),X11693),X11692))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_DiffI])])])). 4.46/4.71 cnf(c_0_7696, plain, (hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X3),X1))))|~hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_5369])). 4.46/4.71 fof(c_0_7697, plain, ![X12757, X12758, X12759, X12760, X12761, X12762]:(hBOOL(hAPP(hAPP(c_member(X12762),X12761),hAPP(c_List_Oset(X12762),X12760)))|hAPP(X12758,X12761)=hAPP(c_Map_Omap__upds(X12762,X12759,X12758,X12760,X12757),X12761)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__upds__apply__nontin])])])). 4.46/4.71 fof(c_0_7698, plain, ![X11032, X11033, X11034, X11035]:(~class_Groups_Ocomm__monoid__mult(X11035)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11034),X11033))|hAPP(hAPP(c_Power_Opower__class_Opower(X11035),X11032),hAPP(c_Finite__Set_Ocard(X11034),X11033))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X11034,X11035),hAPP(c_COMBK(X11035,X11034),X11032)),X11033))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__constant])])])). 4.46/4.71 fof(c_0_7699, plain, ![X12336, X12337, X12338, X12339, X12340, X12341]:((~hBOOL(hAPP(c_List_Odistinct(X12337),X12336))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12338),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12337)),X12336)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12339),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12337)),X12336)))|(X12338=X12339|hAPP(hAPP(c_List_Onth(X12337),X12336),X12339)!=hAPP(hAPP(c_List_Onth(X12337),X12336),X12338)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk360_2(X12340,X12341)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12341)),X12340)))|hBOOL(hAPP(c_List_Odistinct(X12341),X12340)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk361_2(X12340,X12341)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12341)),X12340)))|hBOOL(hAPP(c_List_Odistinct(X12341),X12340)))&((esk360_2(X12340,X12341)!=esk361_2(X12340,X12341)|hBOOL(hAPP(c_List_Odistinct(X12341),X12340)))&(hAPP(hAPP(c_List_Onth(X12341),X12340),esk361_2(X12340,X12341))=hAPP(hAPP(c_List_Onth(X12341),X12340),esk360_2(X12340,X12341))|hBOOL(hAPP(c_List_Odistinct(X12341),X12340))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__conv__nth])])])])])])])). 4.46/4.71 cnf(c_0_7700, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5370])). 4.46/4.71 fof(c_0_7701, plain, ![X13472, X13473, X13474, X13475]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X13475),tc_List_Olist(X13475))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X13475),tc_List_Olist(X13475)),X13474),X13473)),c_List_Olistrel1(X13475,X13472)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13475)),X13473)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13475)),X13474)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel1__eq__len])])])). 4.46/4.71 fof(c_0_7702, plain, ![X2078, X2079, X2080, X2081]:(~class_Lattices_Osemilattice__sup(X2081)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2081),X2079),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2081),X2080),X2078))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2081),X2080),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2081),X2079),X2078))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup_Oleft__commute])])])). 4.46/4.71 cnf(c_0_7703, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_4636])). 4.46/4.71 cnf(c_0_7704, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)=hAPP(c_Nat_OSuc,X1)), inference(split_conjunct,[status(thm)],[c_0_5371]), ['final']). 4.46/4.71 fof(c_0_7705, plain, ![X11723, X11724, X11725, X11726]:(~class_Lattices_Olattice(X11726)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X11726),X11725),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X11726),X11724),X11723))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X11726),X11724),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X11726),X11725),X11723))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__aci_I7_J])])])). 4.46/4.71 cnf(c_0_7706, plain, (hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_5372])). 4.46/4.71 fof(c_0_7707, plain, ![X1099, X1100, X1101, X1102, X1103]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1103,tc_HOL_Obool)),X1102),X1101))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1100,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1103,X1100,X1099),X1102)),hAPP(c_Set_Oimage(X1103,X1100,X1099),X1101)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__mono])])])). 4.46/4.71 fof(c_0_7708, plain, ![X17355, X17356, X17357, X17358]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17358),X17356),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17358),X17355),X17357)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17358),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17358),X17356),X17357)),X17355))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17358),c_Groups_Ozero__class_Ozero(X17358)),X17357))|~class_Fields_Olinordered__field(X17358))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17358),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17358),X17356),X17357)),X17355))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17358),X17356),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17358),X17355),X17357)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17358),c_Groups_Ozero__class_Ozero(X17358)),X17357))|~class_Fields_Olinordered__field(X17358))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__divide__less__eq])])])])). 4.46/4.71 fof(c_0_7709, plain, ![X13680, X13681, X13682, X13683]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13683),X13681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13683),X13680),X13682)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13683),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13683),X13681),X13682)),X13680))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13683),c_Groups_Ozero__class_Ozero(X13683)),X13682))|~class_Fields_Olinordered__field(X13683))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13683),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13683),X13681),X13682)),X13680))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13683),X13681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13683),X13680),X13682)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13683),c_Groups_Ozero__class_Ozero(X13683)),X13682))|~class_Fields_Olinordered__field(X13683))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq])])])). 4.46/4.71 fof(c_0_7710, plain, ![X7443, X7444, X7445, X7446, X7447]:(~class_Complete__Lattice_Ocomplete__lattice(X7447)|(~hBOOL(hAPP(hAPP(c_member(X7446),X7445),X7444))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7447),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7446,X7447),X7444),X7443)),hAPP(X7443,X7445))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF__leI])])])). 4.46/4.71 fof(c_0_7711, plain, ![X7459, X7460, X7461, X7462]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7462),X7460),X7461)),X7459))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7462),X7460),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7462),X7459),X7461)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7462),c_Groups_Ozero__class_Ozero(X7462)),X7461))|~class_Fields_Olinordered__field(X7462))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7462),X7460),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7462),X7459),X7461)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7462),X7460),X7461)),X7459))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7462),c_Groups_Ozero__class_Ozero(X7462)),X7461))|~class_Fields_Olinordered__field(X7462))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__less__divide__eq])])])])). 4.46/4.71 fof(c_0_7712, plain, ![X11702, X11703, X11704, X11705]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11705),X11703),X11704)),X11702))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11705),X11703),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11705),X11702),X11704)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11705),c_Groups_Ozero__class_Ozero(X11705)),X11704))|~class_Fields_Olinordered__field(X11705))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11705),X11703),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11705),X11702),X11704)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11705),X11703),X11704)),X11702))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11705),c_Groups_Ozero__class_Ozero(X11705)),X11704))|~class_Fields_Olinordered__field(X11705))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq])])])). 4.46/4.71 fof(c_0_7713, plain, ![X7647, X7648, X7649, X7650]:(~class_Lattices_Osemilattice__inf(X7650)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7650),X7648),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7650),X7649),X7647))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7650),X7649),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7650),X7648),X7647))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__left__commute])])])). 4.46/4.71 fof(c_0_7714, plain, ![X8624, X8625]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8625),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X8624)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X8624),X8625)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X8624)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__le__listsum__nat])])). 4.46/4.71 fof(c_0_7715, plain, ![X6298, X6299, X6300, X6301, X6302]:(~class_Complete__Lattice_Ocomplete__lattice(X6302)|(~hBOOL(hAPP(hAPP(c_member(X6301),X6300),X6299))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6302),hAPP(X6298,X6300)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6301,X6302),X6299),X6298))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__SUPI])])])). 4.46/4.71 fof(c_0_7716, plain, ![X12140, X12141, X12142]:(~hBOOL(hAPP(hAPP(c_member(X12142),X12141),hAPP(c_List_Oset(X12142),X12140)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12142)),X12140)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_length__pos__if__in__set])])])). 4.46/4.71 fof(c_0_7717, plain, ![X8274, X8275, X8276, X8277, X8278, X8280, X8281, X8282, X8283, X8284, X8285]:(((hBOOL(hAPP(hAPP(c_member(X8278),esk235_5(X8274,X8275,X8276,X8277,X8278)),X8276))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8278,tc_fun(X8277,tc_HOL_Obool)),X8276),X8275),X8274)))&(~hBOOL(hAPP(hAPP(X8275,esk235_5(X8274,X8275,X8276,X8277,X8278)),X8274))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8278,tc_fun(X8277,tc_HOL_Obool)),X8276),X8275),X8274))))&(~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8284,tc_fun(X8283,tc_HOL_Obool)),X8282),X8281),X8280))|(~hBOOL(hAPP(hAPP(c_member(X8284),X8285),X8282))|hBOOL(hAPP(hAPP(X8281,X8285),X8280))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF1__iff])])])])])])])). 4.46/4.71 fof(c_0_7718, plain, ![X839, X840, X841, X842]:(~class_Lattices_Olattice(X842)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X842),X841),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X842),X840),X839))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X842),X840),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X842),X841),X839))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I3_J])])). 4.46/4.71 fof(c_0_7719, plain, ![X10354, X10355, X10356]:(~class_Rings_Olinordered__semidom(X10356)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10356),c_Groups_Oone__class_Oone(X10356)),X10355))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10356),c_Groups_Oone__class_Oone(X10356)),hAPP(hAPP(c_Power_Opower__class_Opower(X10356),X10355),hAPP(c_Nat_OSuc,X10354)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1])])). 4.46/4.71 fof(c_0_7720, plain, ![X9128, X9129, X9130]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9130),X9129))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9130,tc_HOL_Obool)),X9128),X9129))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X9130),X9128)),hAPP(c_Finite__Set_Ocard(X9130),X9129)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9130,tc_HOL_Obool)),X9128),X9129))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__psubset])])])). 4.46/4.71 fof(c_0_7721, plain, ![X6743, X6744, X6745, X6746, X6747, X6748]:(~hBOOL(hAPP(hAPP(X6748,X6747),X6746))|(~c_List_Olistrelp(X6745,X6748,X6744,X6743)|c_List_Olistrelp(X6745,X6748,hAPP(hAPP(c_List_Olist_OCons(X6745),X6747),X6744),hAPP(hAPP(c_List_Olist_OCons(X6745),X6746),X6743)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrelp_OCons])])])). 4.46/4.71 fof(c_0_7722, plain, ![X4344, X4345, X4346]:(~c_Fun_Oinj__on(X4346,X4345,X4344,c_Orderings_Otop__class_Otop(tc_fun(X4346,tc_HOL_Obool)))|c_Fun_Oinj__on(tc_List_Olist(X4346),tc_List_Olist(X4345),hAPP(c_List_Omap(X4346,X4345),X4344),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X4346),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__mapI])])). 4.46/4.71 cnf(c_0_7723, plain, (hAPP(X3,X5)=hAPP(X4,X5)|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X1,X2)),X3),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1))))|~class_Enum_Oenum(X1)|~class_HOL_Oequal(X2)), inference(split_conjunct,[status(thm)],[c_0_5373])). 4.46/4.71 cnf(c_0_7724, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1))))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_5374]), ['final']). 4.46/4.71 cnf(c_0_7725, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omin(X1),X2),X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5375])). 4.46/4.71 cnf(c_0_7726, plain, (hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_5376]), ['final']). 4.46/4.71 cnf(c_0_7727, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omax(X1),X2),X3)=c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5377])). 4.46/4.71 fof(c_0_7728, plain, ![X8401, X8402, X8403]:((hBOOL(hAPP(hAPP(c_member(X8403),X8402),hAPP(c_List_Oset(X8403),X8401)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8403)),X8401)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8403)),c_List_Oremove1(X8403,X8402,X8401)))&(~hBOOL(hAPP(hAPP(c_member(X8403),X8402),hAPP(c_List_Oset(X8403),X8401)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8403)),c_List_Oremove1(X8403,X8402,X8401))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8403)),X8401)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_length__remove1])])])). 4.46/4.71 cnf(c_0_7729, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,X1),hAPP(c_Int_Onat,X2)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)|~c_Nat__Transfer_Ois__nat(X1)|~c_Nat__Transfer_Ois__nat(X2)), inference(split_conjunct,[status(thm)],[c_0_5378])). 4.46/4.71 cnf(c_0_7730, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_5303])). 4.46/4.71 fof(c_0_7731, plain, ![X7028, X7029, X7030, X7031, X7032]:(~class_Lattices_Olattice(X7032)|hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7031,X7032)),X7030),X7029),X7028)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7032),hAPP(X7030,X7028)),hAPP(X7029,X7028))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__fun__def])])])). 4.46/4.71 fof(c_0_7732, plain, ![X9162, X9163, X9164, X9165, X9166]:(~class_Groups_Ominus(X9166)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9166),hAPP(X9164,X9162)),hAPP(X9163,X9162))=hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9165,X9166)),X9164),X9163),X9162)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__apply])])])). 4.46/4.71 cnf(c_0_7733, plain, (c_List_Olist_ONil(X3)=c_List_OdropWhile(X3,X1,X2)|~hBOOL(hAPP(X1,esk193_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_5284])). 4.46/4.71 cnf(c_0_7734, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))), inference(rw,[status(thm)],[c_0_5379, c_0_4443])). 4.46/4.71 fof(c_0_7735, plain, ![X6018, X6019, X6020, X6021, X6022]:(~class_Lattices_Olattice(X6022)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6022),hAPP(X6020,X6018)),hAPP(X6019,X6018))=hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6021,X6022)),X6020),X6019),X6018)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__fun__def])])])). 4.46/4.71 cnf(c_0_7736, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)=hAPP(c_Groups_Ouminus__class_Ouminus(X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Oring__1(X2)), inference(split_conjunct,[status(thm)],[c_0_5380])). 4.46/4.71 fof(c_0_7737, plain, ![X1972, X1973, X1974, X1975]:(~class_Lattices_Osemilattice__sup(X1975)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1975),X1974),X1973))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1975),X1972),X1973))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1975),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1975),X1974),X1972)),X1973))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__supI])])])). 4.46/4.71 cnf(c_0_7738, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3))))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5381])). 4.46/4.71 fof(c_0_7739, plain, ![X12820, X12821]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X12820),c_Orderings_Otop__class_Otop(tc_fun(X12820,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12821),c_Orderings_Otop__class_Otop(tc_fun(X12821,tc_HOL_Obool))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X12821,X12820)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X12821,X12820),tc_HOL_Obool)))))&((hBOOL(hAPP(c_Finite__Set_Ofinite(X12820),c_Orderings_Otop__class_Otop(tc_fun(X12820,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X12821,X12820)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X12821,X12820),tc_HOL_Obool)))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X12821),c_Orderings_Otop__class_Otop(tc_fun(X12821,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X12821,X12820)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X12821,X12820),tc_HOL_Obool))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__UNIV__iff])])])). 4.46/4.71 fof(c_0_7740, plain, ![X9965, X9966]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9966),c_Orderings_Otop__class_Otop(tc_fun(X9966,tc_HOL_Obool))))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9965),c_Orderings_Otop__class_Otop(tc_fun(X9965,tc_HOL_Obool))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X9966,X9965)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X9966,X9965),tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Prod__UNIV])])])). 4.46/4.71 fof(c_0_7741, plain, ![X5426, X5427, X5428]:((hBOOL(hAPP(hAPP(c_member(X5428),X5427),hAPP(c_List_Oset(X5428),X5426)))|~hBOOL(hAPP(c_List_Odistinct(X5428),X5426))|hBOOL(hAPP(c_List_Odistinct(X5428),hAPP(hAPP(c_List_Olist_OCons(X5428),X5427),X5426))))&((~hBOOL(hAPP(hAPP(c_member(X5428),X5427),hAPP(c_List_Oset(X5428),X5426)))|~hBOOL(hAPP(c_List_Odistinct(X5428),hAPP(hAPP(c_List_Olist_OCons(X5428),X5427),X5426))))&(hBOOL(hAPP(c_List_Odistinct(X5428),X5426))|~hBOOL(hAPP(c_List_Odistinct(X5428),hAPP(hAPP(c_List_Olist_OCons(X5428),X5427),X5426)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct_Osimps_I2_J])])])])). 4.46/4.71 cnf(c_0_7742, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate(X1,X3),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5382])). 4.46/4.71 fof(c_0_7743, plain, ![X10979, X10980, X10981, X10982]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10982),X10981),X10979))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10982),X10981),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10982),X10980),X10979)))|~class_Lattices_Osemilattice__inf(X10982))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10982),X10981),X10980))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10982),X10981),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10982),X10980),X10979)))|~class_Lattices_Osemilattice__inf(X10982)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10982),X10981),X10979))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10982),X10981),X10980))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10982),X10981),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10982),X10980),X10979)))|~class_Lattices_Osemilattice__inf(X10982))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__inf__iff])])])). 4.46/4.71 fof(c_0_7744, plain, ![X3690, X3691, X3692]:(~class_Rings_Olinordered__idom(X3692)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3692),c_Groups_Ozero__class_Ozero(X3692)),X3691))|hAPP(c_Groups_Oabs__class_Oabs(X3692),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3692),X3690),X3691))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3692),hAPP(c_Groups_Oabs__class_Oabs(X3692),X3690)),X3691))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__mult__pos])])])). 4.46/4.71 fof(c_0_7745, plain, ![X9659, X9660, X9661, X9662, X9663]:(~c_Finite__Set_Ofun__left__comm(X9663,X9662,X9661)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9663),X9660))|hBOOL(hAPP(c_Finite__Set_Ofold__graph(X9663,X9662,X9661,X9659,X9660),hAPP(hAPP(c_Finite__Set_Ofold(X9663,X9662,X9661),X9659),X9660))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__graph__fold])])])). 4.46/4.71 fof(c_0_7746, plain, ![X14421, X14422, X14423]:((hBOOL(hAPP(hAPP(c_member(X14423),X14422),hAPP(c_List_Oset(X14423),X14421)))|hAPP(hAPP(c_List_Olist_OCons(X14423),X14422),c_List_Oremdups(X14423,X14421))=c_List_Oremdups(X14423,hAPP(hAPP(c_List_Olist_OCons(X14423),X14422),X14421)))&(~hBOOL(hAPP(hAPP(c_member(X14423),X14422),hAPP(c_List_Oset(X14423),X14421)))|c_List_Oremdups(X14423,hAPP(hAPP(c_List_Olist_OCons(X14423),X14422),X14421))=c_List_Oremdups(X14423,X14421))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_remdups_Osimps_I2_J])])])). 4.46/4.71 cnf(c_0_7747, plain, (hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_List_Oset(X2),X3)))|X1!=hAPP(hAPP(c_List_Onth(X2),X3),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_5383])). 4.46/4.71 cnf(c_0_7748, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OPls))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5384, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 fof(c_0_7749, plain, ![X2002, X2003, X2004, X2005]:((~hBOOL(hAPP(hAPP(c_member(X2003),X2005),hAPP(c_List_Oset(X2003),c_List_Oremove1(X2003,X2004,X2002))))|hBOOL(hAPP(hAPP(c_member(X2003),X2005),hAPP(c_List_Oset(X2003),X2002)))|X2005=X2004)&(~hBOOL(hAPP(hAPP(c_member(X2003),X2005),hAPP(c_List_Oset(X2003),X2002)))|hBOOL(hAPP(hAPP(c_member(X2003),X2005),hAPP(c_List_Oset(X2003),c_List_Oremove1(X2003,X2004,X2002))))|X2005=X2004)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__set__remove1])])])])). 4.46/4.71 fof(c_0_7750, plain, ![X11146, X11147, X11148, X11149]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11149),X11148))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11147),X11148)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11149),X11146)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11147),X11146)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__add__eq__less])])])). 4.46/4.71 cnf(c_0_7751, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_Opred(X2))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5385])). 4.46/4.71 cnf(c_0_7752, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OPls))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5386, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 cnf(c_0_7753, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5387, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 cnf(c_0_7754, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5388, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 cnf(c_0_7755, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OPls))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5389, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 fof(c_0_7756, plain, ![X13786, X13787]:(~class_Rings_Osemiring__1(X13787)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X13787),X13786)=c_Nat_Osemiring__1__class_Oof__nat__aux(X13787,hAPP(hAPP(c_COMBC(X13787,X13787,X13787),c_Groups_Oplus__class_Oplus(X13787)),c_Groups_Oone__class_Oone(X13787)),X13786,c_Groups_Ozero__class_Ozero(X13787))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__1__class_Oof__nat__code])])). 4.46/4.71 fof(c_0_7757, plain, ![X6771, X6772, X6773]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk199_3(X6771,X6772,X6773)),X6773))|(~hBOOL(hAPP(X6772,X6771))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6771),X6773))|hBOOL(hAPP(X6772,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))&((hBOOL(hAPP(X6772,esk199_3(X6771,X6772,X6773)))|(~hBOOL(hAPP(X6772,X6771))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6771),X6773))|hBOOL(hAPP(X6772,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))&(~hBOOL(hAPP(X6772,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,esk199_3(X6771,X6772,X6773)),X6773)))|(~hBOOL(hAPP(X6772,X6771))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6771),X6773))|hBOOL(hAPP(X6772,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__induct__0])])])])])). 4.46/4.71 fof(c_0_7758, plain, ![X15940, X15941, X15942, X15943]:((hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15943)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Olist_OCons(X15942),X15941),X15940)=hAPP(hAPP(c_List_Odrop(X15942),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15943)),hAPP(hAPP(c_List_Olist_OCons(X15942),X15941),X15940)))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15943)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Odrop(X15942),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15943)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X15940)=hAPP(hAPP(c_List_Odrop(X15942),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15943)),hAPP(hAPP(c_List_Olist_OCons(X15942),X15941),X15940)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_drop__Cons__number__of])])])). 4.46/4.71 cnf(c_0_7759, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5390, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 cnf(c_0_7760, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X1))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5391, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 cnf(c_0_7761, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5392, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 cnf(c_0_7762, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5393, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 cnf(c_0_7763, plain, (hAPP(c_List_Orotate(X1,X3),X2)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5394])). 4.46/4.71 fof(c_0_7764, plain, ![X3886, X3887, X3888, X3889, X3890, X3891]:(~class_Orderings_Olinorder(X3891)|(hBOOL(hAPP(X3890,X3889))|hAPP(c_List_Ofilter(X3888,X3890),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3888,X3891,X3887),X3889),X3886))=hAPP(c_List_Ofilter(X3888,X3890),X3886))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__insort__triv])])])). 4.46/4.71 cnf(c_0_7765, plain, (hAPP(X5,X2)=c_Map_Omap__comp(X1,X6,X7,X5,X3,X4)|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_5395])). 4.46/4.71 fof(c_0_7766, plain, ![X16480, X16481, X16482]:(~class_Fields_Olinordered__field(X16482)|(X16481=c_Groups_Ozero__class_Ozero(X16482)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16482),hAPP(c_Groups_Oabs__class_Oabs(X16482),X16480)),hAPP(c_Groups_Oabs__class_Oabs(X16482),X16481))=hAPP(c_Groups_Oabs__class_Oabs(X16482),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16482),X16480),X16481)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nonzero__abs__divide])])])). 4.46/4.71 cnf(c_0_7767, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5396, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 cnf(c_0_7768, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5397, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 fof(c_0_7769, plain, ![X9048, X9049, X9050]:(~class_Groups_Omonoid__mult(X9050)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9050),hAPP(hAPP(c_Power_Opower__class_Opower(X9050),X9049),X9048)),X9049)=hAPP(hAPP(c_Power_Opower__class_Opower(X9050),X9049),hAPP(c_Nat_OSuc,X9048))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__Suc2])])])). 4.46/4.71 fof(c_0_7770, plain, ![X6618, X6619, X6620]:(~class_Rings_Ocomm__semiring__1(X6620)|hAPP(hAPP(c_Power_Opower__class_Opower(X6620),X6619),hAPP(c_Nat_OSuc,X6618))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6620),hAPP(hAPP(c_Power_Opower__class_Opower(X6620),X6619),X6618)),X6619)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J])])])). 4.46/4.71 fof(c_0_7771, plain, ![X6189, X6190]:(c_List_Olist_ONil(X6189)=X6190|c_List_Olast(X6189,X6190)=hAPP(hAPP(c_List_Onth(X6189),X6190),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6189)),X6190)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__conv__nth])])). 4.46/4.71 cnf(c_0_7772, plain, (c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Otrancl(X1,X2)))|~c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5398])). 4.46/4.71 fof(c_0_7773, plain, ![X13423, X13424, X13425, X13426, X13427]:((~c_Hoare__Mirabelle_Otriple__valid(X13427,X13426,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X13427),X13425),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X13424))),X13423))|c_Hoare__Mirabelle_Otriple__valid(X13427,hAPP(c_Nat_OSuc,X13426),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X13427),X13425),hAPP(c_Com_Ocom_OBODY,X13424)),X13423)))&(~c_Hoare__Mirabelle_Otriple__valid(X13427,hAPP(c_Nat_OSuc,X13426),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X13427),X13425),hAPP(c_Com_Ocom_OBODY,X13424)),X13423))|c_Hoare__Mirabelle_Otriple__valid(X13427,X13426,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X13427),X13425),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X13424))),X13423)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Body__triple__valid__Suc])])). 4.46/4.71 fof(c_0_7774, plain, ![X13167, X13168]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X13168))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13167))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X13167),X13168)),X13167)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__less__dividend])])])). 4.46/4.71 fof(c_0_7775, plain, ![X15629, X15630]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15630))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15629))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15629),X15630)),X15629)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__less])])])). 4.46/4.71 fof(c_0_7776, plain, ![X5214, X5215]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5215))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X5214))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X5215),X5214)),X5215)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__div__less__self])])). 4.46/4.71 fof(c_0_7777, plain, ![X14735, X14736, X14737, X14738]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14738),X14737),X14735))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14738),hAPP(hAPP(c_Orderings_Oord__class_Omax(X14738),X14737),X14736)),X14735))|~class_Orderings_Olinorder(X14738))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14738),X14736),X14735))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14738),hAPP(hAPP(c_Orderings_Oord__class_Omax(X14738),X14737),X14736)),X14735))|~class_Orderings_Olinorder(X14738)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14738),X14737),X14735))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14738),X14736),X14735))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14738),hAPP(hAPP(c_Orderings_Oord__class_Omax(X14738),X14737),X14736)),X14735))|~class_Orderings_Olinorder(X14738))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__less__iff__conj])])])). 4.46/4.71 fof(c_0_7778, plain, ![X15993, X15994, X15995, X15996]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15996),X15994),X15993))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15996),X15995),X15993))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15996),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15996),X15995),X15994)),X15993))|~class_Orderings_Olinorder(X15996))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15996),X15994),X15993))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15996),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15996),X15995),X15994)),X15993))|~class_Orderings_Olinorder(X15996))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15996),X15995),X15993))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15996),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15996),X15995),X15994)),X15993))|~class_Orderings_Olinorder(X15996)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ole__sup__iff])])])])). 4.46/4.71 fof(c_0_7779, plain, ![X6367, X6368, X6369]:(~class_Orderings_Olinorder(X6369)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6369),X6368))|(c_Orderings_Obot__class_Obot(tc_fun(X6369,tc_HOL_Obool))=X6368|hAPP(hAPP(c_Orderings_Oord__class_Omin(X6369),X6367),c_Big__Operators_Olinorder__class_OMin(X6369,X6368))=c_Big__Operators_Olinorder__class_OMin(X6369,hAPP(hAPP(c_Set_Oinsert(X6369),X6367),X6368))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min__insert])])])). 4.46/4.71 cnf(c_0_7780, plain, (hBOOL(hAPP(c_Predicate_OPowp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_5399])). 4.46/4.71 fof(c_0_7781, plain, ![X13366, X13367, X13368]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13368),X13367))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13366),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13367),X13366)),X13368)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__add__diff])])])). 4.46/4.71 fof(c_0_7782, plain, ![X14835, X14836, X14837]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14837),X14836))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14837),X14835)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14836),X14835)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])])). 4.46/4.71 fof(c_0_7783, plain, ![X2336, X2337, X2338, X2339]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2339),X2338),X2336))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2339),X2338),X2337))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2339),X2338),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2339),X2337),X2336)))|~class_Orderings_Olinorder(X2339))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2339),X2338),X2336))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2339),X2338),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2339),X2337),X2336)))|~class_Orderings_Olinorder(X2339))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2339),X2338),X2337))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2339),X2338),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2339),X2337),X2336)))|~class_Orderings_Olinorder(X2339)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__conj])])])). 4.46/4.71 fof(c_0_7784, plain, ![X1180, X1181, X1182, X1183]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1183),X1182),X1180))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1183),X1182),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1183),X1181),X1180)))|~class_Orderings_Olinorder(X1183))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1183),X1182),X1181))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1183),X1182),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1183),X1181),X1180)))|~class_Orderings_Olinorder(X1183)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1183),X1182),X1180))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1183),X1182),X1181))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1183),X1182),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1183),X1181),X1180)))|~class_Orderings_Olinorder(X1183))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ole__inf__iff])])])])). 4.46/4.71 fof(c_0_7785, plain, ![X11970, X11971, X11972]:(~class_Lattices_Olattice(X11972)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11972),X11971))|(c_Orderings_Obot__class_Obot(tc_fun(X11972,tc_HOL_Obool))=X11971|c_Big__Operators_Olattice__class_OSup__fin(X11972,hAPP(hAPP(c_Set_Oinsert(X11972),X11970),X11971))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X11972),X11970),c_Big__Operators_Olattice__class_OSup__fin(X11972,X11971))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oinsert__idem])])])). 4.46/4.71 fof(c_0_7786, plain, ![X3347, X3348, X3349]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3349),X3348)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3349),X3347)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3348),X3347)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3348),X3347))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3349),X3348)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3349),X3347))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])])). 4.46/4.71 fof(c_0_7787, plain, ![X16741, X16742, X16743]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16743),X16742))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16743),X16741)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16742),X16741)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])])). 4.46/4.71 fof(c_0_7788, plain, ![X2115, X2116, X2117]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2117),X2116))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2117),X2115)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2116),X2115)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono])])). 4.46/4.71 fof(c_0_7789, plain, ![X16655, X16656, X16657]:(~class_Fields_Olinordered__field__inverse__zero(X16657)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16657),c_Groups_Ozero__class_Ozero(X16657)),X16656))|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16657),hAPP(c_Groups_Oabs__class_Oabs(X16657),X16655)),X16656)=hAPP(c_Groups_Oabs__class_Oabs(X16657),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16657),X16655),X16656)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__div__pos])])). 4.46/4.71 cnf(c_0_7790, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5400, c_0_4436]), c_0_4500]), c_0_4760]), c_0_4436])). 4.46/4.71 fof(c_0_7791, plain, ![X16557, X16558, X16559]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16559),hAPP(c_Int_Onumber__class_Onumber__of(X16559),X16558)),hAPP(c_Int_Onumber__class_Onumber__of(X16559),X16557)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16558),X16557))|(~class_Rings_Olinordered__idom(X16559)|~class_Int_Onumber__ring(X16559)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16558),X16557))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16559),hAPP(c_Int_Onumber__class_Onumber__of(X16559),X16558)),hAPP(c_Int_Onumber__class_Onumber__of(X16559),X16557)))|(~class_Rings_Olinordered__idom(X16559)|~class_Int_Onumber__ring(X16559)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__number__of])])])])). 4.46/4.71 fof(c_0_7792, plain, ![X16691, X16692, X16693]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16693),hAPP(c_Int_Onumber__class_Onumber__of(X16693),X16692)),hAPP(c_Int_Onumber__class_Onumber__of(X16693),X16691)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16692),X16691))|(~class_Rings_Olinordered__idom(X16693)|~class_Int_Onumber__ring(X16693)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16692),X16691))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16693),hAPP(c_Int_Onumber__class_Onumber__of(X16693),X16692)),hAPP(c_Int_Onumber__class_Onumber__of(X16693),X16691)))|(~class_Rings_Olinordered__idom(X16693)|~class_Int_Onumber__ring(X16693)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__number__of])])])])). 4.46/4.71 fof(c_0_7793, plain, ![X15285, X15286, X15287]:(~class_Orderings_Olinorder(X15287)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15287),X15286))|(~hBOOL(hAPP(hAPP(c_member(X15287),X15285),X15286))|c_Big__Operators_Olattice_OInf__fin(X15287,c_Orderings_Oord__class_Omin(X15287),X15286)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X15287),X15285),c_Big__Operators_Olattice_OInf__fin(X15287,c_Orderings_Oord__class_Omin(X15287),X15286))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oin__idem])])])). 4.46/4.71 fof(c_0_7794, plain, ![X12179, X12180, X12181]:(~class_Orderings_Olinorder(X12181)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12181),X12180))|(~hBOOL(hAPP(hAPP(c_member(X12181),X12179),X12180))|c_Big__Operators_Olattice_OSup__fin(X12181,c_Orderings_Oord__class_Omax(X12181),X12180)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X12181),X12179),c_Big__Operators_Olattice_OSup__fin(X12181,c_Orderings_Oord__class_Omax(X12181),X12180))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oin__idem])])])). 4.46/4.71 fof(c_0_7795, plain, ![X1732, X1733, X1734]:(~class_Lattices_Olattice(X1734)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1734),X1733))|(X1733=c_Orderings_Obot__class_Obot(tc_fun(X1734,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1734),X1732),c_Big__Operators_Olattice__class_OInf__fin(X1734,X1733))=c_Big__Operators_Olattice__class_OInf__fin(X1734,hAPP(hAPP(c_Set_Oinsert(X1734),X1732),X1733))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__idem])])). 4.46/4.71 fof(c_0_7796, plain, ![X14481, X14482, X14483]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14483),X14482))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14481),X14483)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14481),X14482)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__mono2])])])). 4.46/4.71 fof(c_0_7797, plain, ![X918, X919, X920]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X920),X919))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X920),X918)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X919),X918)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__mono1])])])). 4.46/4.71 cnf(c_0_7798, plain, (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2)|hAPP(X1,esk93_4(X1,X2,X3,X4))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X3),X4),X2))|hAPP(X1,X4)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5222])). 4.46/4.71 fof(c_0_7799, plain, ![X4875, X4876, X4877, X4878, X4879, X4880, X4881]:(~c_Finite__Set_Ofolding__image__simple(X4881,X4880,X4879,X4878,X4877,X4876)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4880),X4875))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4881,X4880,X4879),X4877),X4878),X4875)=hAPP(X4876,X4875))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oeq__fold__g])])). 4.46/4.71 cnf(c_0_7800, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)|~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5401, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.71 fof(c_0_7801, plain, ![X6203, X6204, X6205]:(~class_Orderings_Olinorder(X6205)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6205),X6204))|(X6204=c_Orderings_Obot__class_Obot(tc_fun(X6205,tc_HOL_Obool))|c_Big__Operators_Olinorder__class_OMax(X6205,hAPP(hAPP(c_Set_Oinsert(X6205),X6203),X6204))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X6205),X6203),c_Big__Operators_Olinorder__class_OMax(X6205,X6204))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max__insert])])])). 4.46/4.71 fof(c_0_7802, plain, ![X3350, X3351, X3352]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3351),X3350))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3352),X3351)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3352),X3350))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3352),X3351)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3352),X3350)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3351),X3350)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])])). 4.46/4.71 fof(c_0_7803, plain, ![X15245, X15246, X15247]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15247),X15246))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15247),X15245)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15246),X15245)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__le__mono])])])). 4.46/4.71 fof(c_0_7804, plain, ![X11289, X11290, X11291]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11291),X11290))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11289),X11290)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11289),X11291)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono2])])). 4.46/4.71 fof(c_0_7805, plain, ![X5330, X5331, X5332]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5332),X5331))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5330),X5332)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5330),X5331)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zadd__left__mono])])])). 4.46/4.71 fof(c_0_7806, plain, ![X5105, X5106, X5107, X5108, X5109]:(hBOOL(hAPP(X5109,X5108))|c_List_OtakeWhile(X5107,X5109,X5106)=c_List_OtakeWhile(X5107,X5109,hAPP(hAPP(c_List_Oappend(X5107),X5106),hAPP(hAPP(c_List_Olist_OCons(X5107),X5108),X5105)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile__tail])])])). 4.46/4.71 fof(c_0_7807, plain, ![X5740, X5741, X5742, X5743]:((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5742,tc_Nat_Onat),X5740),X5741)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|(~hBOOL(hAPP(hAPP(c_member(X5742),X5743),X5741))|hAPP(X5740,X5743)=c_Groups_Oone__class_Oone(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5742),X5741)))&((hBOOL(hAPP(hAPP(c_member(X5742),esk177_3(X5740,X5741,X5742)),X5741))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5742,tc_Nat_Onat),X5740),X5741)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5742),X5741)))&(hAPP(X5740,esk177_3(X5740,X5741,X5742))!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5742,tc_Nat_Onat),X5740),X5741)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5742),X5741))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__eq__1__iff])])])])])])). 4.46/4.71 fof(c_0_7808, plain, ![X9038, X9039, X9040, X9042]:(((hBOOL(hAPP(hAPP(c_member(X9040),esk260_3(X9038,X9039,X9040)),X9039))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9040,tc_Nat_Onat),X9038),X9039)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9040),X9039)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(X9038,esk260_3(X9038,X9039,X9040))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9040,tc_Nat_Onat),X9038),X9039)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9040),X9039))))&(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9040,tc_Nat_Onat),X9038),X9039)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(~hBOOL(hAPP(hAPP(c_member(X9040),X9042),X9039))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(X9038,X9042))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9040),X9039)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__eq__0__iff])])])])])])). 4.46/4.71 fof(c_0_7809, plain, ![X8487, X8488, X8489, X8490]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8489),X8490),X8487))|~hBOOL(hAPP(hAPP(c_member(X8489),X8490),X8488))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8489),c_Complete__Lattice_OInf__class_OInf(X8489,X8488)),X8487))|(~class_Complete__Lattice_Ocomplete__lattice(X8489)|~class_Orderings_Olinorder(X8489)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8489),esk239_3(X8487,X8488,X8489)),X8487))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8489),c_Complete__Lattice_OInf__class_OInf(X8489,X8488)),X8487))|(~class_Complete__Lattice_Ocomplete__lattice(X8489)|~class_Orderings_Olinorder(X8489)))&(hBOOL(hAPP(hAPP(c_member(X8489),esk239_3(X8487,X8488,X8489)),X8488))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8489),c_Complete__Lattice_OInf__class_OInf(X8489,X8488)),X8487))|(~class_Complete__Lattice_Ocomplete__lattice(X8489)|~class_Orderings_Olinorder(X8489))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__less__iff])])])])])])). 4.46/4.71 cnf(c_0_7810, plain, (c_Groups_Ozero__class_Ozero(X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(c_Nat_OSuc,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~class_Groups_Ocomm__monoid__add(X3)), inference(split_conjunct,[status(thm)],[c_0_5137])). 4.46/4.71 fof(c_0_7811, plain, ![X12364, X12365, X12366, X12367]:((~hBOOL(hAPP(hAPP(c_member(X12366),X12367),X12364))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12366),X12365),X12367))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12366),X12365),c_Complete__Lattice_OSup__class_OSup(X12366,X12364)))|(~class_Complete__Lattice_Ocomplete__lattice(X12366)|~class_Orderings_Olinorder(X12366)))&((hBOOL(hAPP(hAPP(c_member(X12366),esk364_3(X12364,X12365,X12366)),X12364))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12366),X12365),c_Complete__Lattice_OSup__class_OSup(X12366,X12364)))|(~class_Complete__Lattice_Ocomplete__lattice(X12366)|~class_Orderings_Olinorder(X12366)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12366),X12365),esk364_3(X12364,X12365,X12366)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12366),X12365),c_Complete__Lattice_OSup__class_OSup(X12366,X12364)))|(~class_Complete__Lattice_Ocomplete__lattice(X12366)|~class_Orderings_Olinorder(X12366))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Sup__iff])])])])])). 4.46/4.71 fof(c_0_7812, plain, ![X508, X509, X510]:(~class_Groups_Olinordered__ab__group__add(X510)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X510),hAPP(c_Groups_Ouminus__class_Ouminus(X510),X509)),hAPP(c_Groups_Ouminus__class_Ouminus(X510),X508))=hAPP(c_Groups_Ouminus__class_Ouminus(X510),hAPP(hAPP(c_Orderings_Oord__class_Omin(X510),X509),X508))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__min__eq__max])])])). 4.46/4.71 fof(c_0_7813, plain, ![X16057, X16058, X16059]:(~class_Groups_Olinordered__ab__group__add(X16059)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X16059),hAPP(c_Groups_Ouminus__class_Ouminus(X16059),X16058)),hAPP(c_Groups_Ouminus__class_Ouminus(X16059),X16057))=hAPP(c_Groups_Ouminus__class_Ouminus(X16059),hAPP(hAPP(c_Orderings_Oord__class_Omax(X16059),X16058),X16057))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__max__eq__min])])). 4.46/4.71 fof(c_0_7814, plain, ![X6191, X6192, X6193]:(~class_Orderings_Olinorder(X6193)|(~hBOOL(hAPP(hAPP(c_member(X6193),X6192),hAPP(c_List_Oset(X6193),X6191)))|(~c_List_Olinorder__class_Osorted(X6193,X6191)|X6191=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X6193,X6193,c_COMBI(X6193)),X6192),c_List_Oremove1(X6193,X6192,X6191))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__remove1])])])). 4.46/4.71 fof(c_0_7815, plain, ![X11159, X11160, X11161]:(~class_Groups_Oab__group__add(X11161)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11161),hAPP(c_Groups_Ouminus__class_Ouminus(X11161),X11160)),hAPP(c_Groups_Ouminus__class_Ouminus(X11161),X11159))=hAPP(c_Groups_Ouminus__class_Ouminus(X11161),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11161),X11160),X11159))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__distrib])])). 4.46/4.71 fof(c_0_7816, plain, ![X1246, X1247, X1248]:(~class_Groups_Ogroup__add(X1248)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1248),hAPP(c_Groups_Ouminus__class_Ouminus(X1248),X1246)),hAPP(c_Groups_Ouminus__class_Ouminus(X1248),X1247))=hAPP(c_Groups_Ouminus__class_Ouminus(X1248),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1248),X1247),X1246))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add])])). 4.46/4.71 fof(c_0_7817, plain, ![X5068, X5069, X5070]:(~class_Lattices_Oboolean__algebra(X5070)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5070),hAPP(c_Groups_Ouminus__class_Ouminus(X5070),X5069)),hAPP(c_Groups_Ouminus__class_Ouminus(X5070),X5068))=hAPP(c_Groups_Ouminus__class_Ouminus(X5070),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5070),X5069),X5068))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__inf])])). 4.46/4.71 fof(c_0_7818, plain, ![X1713, X1714, X1715]:(~class_Lattices_Oboolean__algebra(X1715)|hAPP(c_Groups_Ouminus__class_Ouminus(X1715),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1715),X1714),X1713))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1715),hAPP(c_Groups_Ouminus__class_Ouminus(X1715),X1714)),hAPP(c_Groups_Ouminus__class_Ouminus(X1715),X1713))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_compl__sup])])])). 4.46/4.71 fof(c_0_7819, plain, ![X10755, X10756, X10757]:((hBOOL(hAPP(hAPP(c_member(X10757),esk318_3(X10755,X10756,X10757)),X10756))|(~hBOOL(hAPP(hAPP(c_member(X10757),X10755),X10756))|c_Big__Operators_Olinorder__class_OMax(X10757,X10756)=X10755)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10757),X10756))|~class_Orderings_Olinorder(X10757))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10757),esk318_3(X10755,X10756,X10757)),X10755))|(~hBOOL(hAPP(hAPP(c_member(X10757),X10755),X10756))|c_Big__Operators_Olinorder__class_OMax(X10757,X10756)=X10755)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10757),X10756))|~class_Orderings_Olinorder(X10757))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max__eqI])])])])])). 4.46/4.71 fof(c_0_7820, plain, ![X12679, X12680, X12681, X12682, X12683, X12684, X12685, X12686, X12687, X12688, X12689]:((~hBOOL(hAPP(hAPP(X12680,X12684),X12679))|~hBOOL(hAPP(hAPP(c_member(X12683),X12684),X12681))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12683,tc_fun(X12682,tc_HOL_Obool)),X12681),X12680),X12679)))&((hBOOL(hAPP(hAPP(X12686,esk374_5(X12685,X12686,X12687,X12688,X12689)),X12685))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12689,tc_fun(X12688,tc_HOL_Obool)),X12687),X12686),X12685)))&(hBOOL(hAPP(hAPP(c_member(X12689),esk374_5(X12685,X12686,X12687,X12688,X12689)),X12687))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12689,tc_fun(X12688,tc_HOL_Obool)),X12687),X12686),X12685))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP1__iff])])])])])])). 4.46/4.71 cnf(c_0_7821, plain, (c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))|~c_Predicate_Oreflp(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5402])). 4.46/4.71 fof(c_0_7822, plain, ![X11673, X11674, X11675]:((hBOOL(hAPP(hAPP(c_member(X11675),esk343_3(X11673,X11674,X11675)),X11674))|(~hBOOL(hAPP(hAPP(c_member(X11675),X11673),X11674))|c_Big__Operators_Olinorder__class_OMin(X11675,X11674)=X11673)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11675),X11674))|~class_Orderings_Olinorder(X11675))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11675),X11673),esk343_3(X11673,X11674,X11675)))|(~hBOOL(hAPP(hAPP(c_member(X11675),X11673),X11674))|c_Big__Operators_Olinorder__class_OMin(X11675,X11674)=X11673)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11675),X11674))|~class_Orderings_Olinorder(X11675))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min__eqI])])])])])). 4.46/4.71 fof(c_0_7823, plain, ![X7589, X7590, X7591, X7592]:(~class_Divides_Oring__div(X7592)|c_Divides_Odiv__class_Omod(X7592,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7592),c_Divides_Odiv__class_Omod(X7592,X7591,X7589)),X7590),X7589)=c_Divides_Odiv__class_Omod(X7592,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7592),X7591),X7590),X7589)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__left__eq])])). 4.46/4.71 fof(c_0_7824, plain, ![X2131, X2132]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X2132,X2131)|c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2132),X2131)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2131),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2132,X2131)))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X2132,X2131)|c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2132),X2131)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmod__zminus1__eq__if])])])). 4.46/4.71 fof(c_0_7825, plain, ![X3960, X3961, X3962, X3963]:(~hBOOL(hAPP(hAPP(c_member(X3963),X3962),c_Complete__Lattice_OInf__class_OInf(tc_fun(X3963,tc_HOL_Obool),X3961)))|(~hBOOL(hAPP(hAPP(c_member(tc_fun(X3963,tc_HOL_Obool)),X3960),X3961))|hBOOL(hAPP(hAPP(c_member(X3963),X3962),X3960)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_InterE])])])). 4.46/4.71 fof(c_0_7826, plain, ![X3135, X3136, X3137, X3138, X3139]:(hBOOL(hAPP(hAPP(c_member(X3139),X3138),c_Map_Odom(X3139,X3137,X3136)))|hAPP(c_Map_Omap__add(X3139,X3137,X3136,X3135),X3138)=hAPP(X3135,X3138)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__add__dom__app__simps_I2_J])])])). 4.46/4.71 fof(c_0_7827, plain, ![X5660, X5661, X5662, X5663]:(~class_Divides_Osemiring__div(X5663)|c_Divides_Odiv__class_Omod(X5663,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5663),X5662),X5660),X5661)=c_Divides_Odiv__class_Omod(X5663,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5663),c_Divides_Odiv__class_Omod(X5663,X5662,X5661)),X5660),X5661)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmod__simps_I4_J])])])). 4.46/4.71 fof(c_0_7828, plain, ![X12100, X12101, X12102, X12103]:(~class_Divides_Osemiring__div(X12103)|c_Divides_Odiv__class_Omod(X12103,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12103),X12102),X12101),X12100)=c_Divides_Odiv__class_Omod(X12103,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12103),c_Divides_Odiv__class_Omod(X12103,X12102,X12100)),X12101),X12100)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__add__left__eq])])])). 4.46/4.71 fof(c_0_7829, plain, ![X9364, X9365, X9366, X9367]:(~class_Divides_Osemiring__div(X9367)|c_Divides_Odiv__class_Omod(X9367,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9367),X9366),c_Divides_Odiv__class_Omod(X9367,X9365,X9364)),X9364)=c_Divides_Odiv__class_Omod(X9367,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9367),X9366),X9365),X9364)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__right__eq])])). 4.46/4.71 fof(c_0_7830, plain, ![X13378, X13379, X13380, X13381, X13382]:(hBOOL(hAPP(hAPP(c_member(X13382),X13381),c_Map_Odom(X13382,X13380,X13379)))|hAPP(c_Map_Omap__add(X13382,X13380,X13378,X13379),X13381)=hAPP(X13378,X13381)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__add__dom__app__simps_I3_J])])])). 4.46/4.71 cnf(c_0_7831, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))), inference(split_conjunct,[status(thm)],[c_0_5403])). 4.46/4.71 fof(c_0_7832, plain, ![X9543, X9544]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X9544),X9543)),c_Wellfounded_Oless__than))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9544),X9543)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9544),X9543))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X9544),X9543)),c_Wellfounded_Oless__than)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__than__iff])])). 4.46/4.71 fof(c_0_7833, plain, ![X3570, X3571, X3572, X3573]:(~class_Divides_Oring__div(X3573)|c_Divides_Odiv__class_Omod(X3573,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3573),X3572),c_Divides_Odiv__class_Omod(X3573,X3571,X3570)),X3570)=c_Divides_Odiv__class_Omod(X3573,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3573),X3572),X3571),X3570)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__diff__right__eq])])])). 4.46/4.71 fof(c_0_7834, plain, ![X1046, X1047, X1048, X1049]:(~class_Divides_Osemiring__div(X1049)|c_Divides_Odiv__class_Omod(X1049,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1049),X1048),X1047),X1046)=c_Divides_Odiv__class_Omod(X1049,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1049),X1048),c_Divides_Odiv__class_Omod(X1049,X1047,X1046)),X1046)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__right__eq])])). 4.46/4.71 fof(c_0_7835, plain, ![X9556, X9557, X9558]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9558),X9557))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9558,tc_HOL_Obool)),X9556),X9557))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X9558),X9556)),hAPP(c_Finite__Set_Ocard(X9558),X9557))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__card__mono])])). 4.46/4.71 fof(c_0_7836, plain, ![X1215, X1216, X1217]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1217),X1216))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1217,tc_HOL_Obool)),X1215),X1216))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1217),X1215)),hAPP(c_Finite__Set_Ocard(X1217),X1216))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__mono])])])). 4.46/4.71 cnf(c_0_7837, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Ois__nat(X1)), inference(split_conjunct,[status(thm)],[c_0_5404])). 4.46/4.71 cnf(c_0_7838, plain, (c_Nat__Transfer_Ois__nat(X2)|~c_Nat__Transfer_Onat__set(X1)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_5405]), ['final']). 4.46/4.71 fof(c_0_7839, plain, ![X16620, X16621, X16622, X16623]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16623,tc_HOL_Obool)),X16622),X16621))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16623,tc_HOL_Obool)),X16620),X16621))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16623,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16623,tc_HOL_Obool)),X16622),X16620)),X16621)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__least])])). 4.46/4.71 fof(c_0_7840, plain, ![X14987, X14988, X14989]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14989))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X14989),X14988)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X14989),X14987)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14988),X14987)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__power__less__imp__less])])])). 4.46/4.71 fof(c_0_7841, plain, ![X13752, X13753, X13754]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13753),X13752))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13754),X13753)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13754),X13752)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13754)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13754),X13753)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13754),X13752)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13753),X13752))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13754)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__mult__le__cancel1])])])])). 4.46/4.71 fof(c_0_7842, plain, ![X8746, X8747, X8748, X8749, X8750]:((hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8750),X8747),X8749)!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8750),X8746),X8748)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8750),X8747),X8748)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8750),X8746),X8749)|X8748=c_Groups_Ozero__class_Ozero(X8750)|X8749=c_Groups_Ozero__class_Ozero(X8750)|~class_Fields_Ofield(X8750))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8750),X8747),X8748)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8750),X8746),X8749)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8750),X8747),X8749)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8750),X8746),X8748)|X8748=c_Groups_Ozero__class_Ozero(X8750)|X8749=c_Groups_Ozero__class_Ozero(X8750)|~class_Fields_Ofield(X8750))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_frac__eq__eq])])])])). 4.46/4.71 fof(c_0_7843, plain, ![X11317, X11318, X11319, X11320]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11320,tc_HOL_Obool)),X11319),X11318))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11320,tc_HOL_Obool)),X11319),X11317))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11320,tc_HOL_Obool)),X11319),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11320,tc_HOL_Obool)),X11318),X11317))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__greatest])])])). 4.46/4.71 fof(c_0_7844, plain, ![X5736, X5737, X5738, X5739]:(~class_Groups_Oab__semigroup__mult(X5739)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5739),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5739),X5738),X5737)),X5736)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5739),X5738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5739),X5737),X5736))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])])). 4.46/4.71 fof(c_0_7845, plain, ![X12080, X12081, X12082, X12083]:(~class_Rings_Odivision__ring(X12083)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12083),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12083),X12082),X12081)),X12080)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12083),X12082),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12083),X12081),X12080))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_times__divide__eq__right])])])). 4.46/4.71 fof(c_0_7846, plain, ![X8014, X8015, X8016, X8017, X8018, X8019]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X8019,X8018),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X8017),X8016)))|(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X8019,X8018),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X8015),X8014)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X8018|X8017=X8015))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_unique__quotient])])])). 4.46/4.71 fof(c_0_7847, plain, ![X4803, X4804, X4805, X4806, X4807, X4808]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4808,X4807),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4806),X4805)))|(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4808,X4807),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4804),X4803)))|(X4807=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X4803=X4805))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__remainder])])). 4.46/4.71 fof(c_0_7848, plain, ![X800, X801, X802, X803]:(~class_Lattices_Osemilattice__inf(X803)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X803),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X803),X802),X801)),X800)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X803),X802),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X803),X801),X800))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oassoc])])). 4.46/4.71 cnf(c_0_7849, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2))=hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5406])). 4.46/4.71 fof(c_0_7850, plain, ![X11818, X11819]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11819))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11818))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11819),X11818)=hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X11819,X11818)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__pos__pos])])])). 4.46/4.71 fof(c_0_7851, plain, ![X4406, X4407]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4407),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4406))|hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X4407,X4406))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4407),X4406))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__pos])])). 4.46/4.71 fof(c_0_7852, plain, ![X8124, X8125, X8126, X8127]:(~class_Rings_Ocomm__semiring__1(X8127)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8127),X8126),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8127),X8125),X8124))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8127),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8127),X8126),X8125)),X8124)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])])])). 4.46/4.71 fof(c_0_7853, plain, ![X15973, X15974, X15975]:(~class_Groups_Omonoid__mult(X15975)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15975),X15974),hAPP(hAPP(c_Power_Opower__class_Opower(X15975),X15974),X15973))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15975),hAPP(hAPP(c_Power_Opower__class_Opower(X15975),X15974),X15973)),X15974)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__commutes])])])). 4.46/4.71 fof(c_0_7854, plain, ![X12143, X12144, X12145, X12146]:(~class_Groups_Oab__semigroup__add(X12146)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12146),X12145),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12146),X12144),X12143))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12146),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12146),X12145),X12144)),X12143)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])])])). 4.46/4.71 fof(c_0_7855, plain, ![X11342, X11343, X11344, X11345]:(~class_Rings_Ocomm__semiring__1(X11345)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11345),X11344),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11345),X11343),X11342))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11345),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11345),X11344),X11343)),X11342)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])])). 4.46/4.71 fof(c_0_7856, plain, ![X13781, X13782, X13783, X13784, X13785]:(~class_Rings_Ocomm__semiring__1(X13784)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13783),X13782))|(~hBOOL(hAPP(hAPP(c_member(X13783),X13785),X13782))|hAPP(X13781,X13785)!=c_Groups_Ozero__class_Ozero(X13784)|c_Groups_Ozero__class_Ozero(X13784)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X13783,X13784),X13781),X13782)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__zero])])])). 4.46/4.71 fof(c_0_7857, plain, ![X12524, X12525, X12526, X12527]:(~class_Rings_Olinordered__semiring(X12527)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12527),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12527),X12526),X12525)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12527),X12524),X12525)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12527),c_Groups_Ozero__class_Ozero(X12527)),X12525))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12527),X12526),X12524))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right__less__imp__less])])])). 4.46/4.71 fof(c_0_7858, plain, ![X9893, X9894, X9895, X9896]:(~class_Rings_Olinordered__semiring__strict(X9896)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9896),X9895),X9894)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9896),X9893),X9894)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9896),c_Groups_Ozero__class_Ozero(X9896)),X9894))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9896),X9895),X9893))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__imp__less__right])])])). 4.46/4.71 fof(c_0_7859, plain, ![X12825, X12826, X12827, X12828]:(~class_Rings_Olinordered__semiring(X12828)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12828),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12828),X12827),X12826)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12828),X12827),X12825)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12828),c_Groups_Ozero__class_Ozero(X12828)),X12827))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12828),X12826),X12825))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left__less__imp__less])])])). 4.46/4.71 fof(c_0_7860, plain, ![X14888, X14889, X14890, X14891]:(~class_Lattices_Osemilattice__sup(X14891)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X14891),X14890),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X14891),X14889),X14888))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X14891),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X14891),X14890),X14889)),X14888)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oassoc])])). 4.46/4.71 fof(c_0_7861, plain, ![X13700, X13701, X13702, X13703]:(~class_Lattices_Olattice(X13703)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13703),X13702),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13703),X13701),X13700))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13703),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13703),X13702),X13701)),X13700)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__aci_I6_J])])])). 4.46/4.71 fof(c_0_7862, plain, ![X7455, X7456, X7457, X7458]:(~class_Lattices_Olattice(X7458)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7458),X7457),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7458),X7456),X7455))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7458),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7458),X7457),X7456)),X7455)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__aci_I2_J])])])). 4.46/4.71 fof(c_0_7863, plain, ![X9855, X9856, X9857, X9858]:(~class_Groups_Omonoid__mult(X9858)|hAPP(hAPP(c_Power_Opower__class_Opower(X9858),X9857),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9856),X9855))=hAPP(hAPP(c_Power_Opower__class_Opower(X9858),hAPP(hAPP(c_Power_Opower__class_Opower(X9858),X9857),X9856)),X9855)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])])). 4.46/4.71 fof(c_0_7864, plain, ![X1003, X1004, X1005, X1006]:(~class_Rings_Olinordered__semiring__strict(X1006)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1006),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1006),X1005),X1004)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1006),X1005),X1003)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1006),c_Groups_Ozero__class_Ozero(X1006)),X1005))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1006),X1004),X1003))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__imp__less__left])])])). 4.46/4.71 fof(c_0_7865, plain, ![X15367, X15368, X15369, X15370]:(~class_Rings_Olinordered__semiring__strict(X15370)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15370),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15370),X15369),X15368)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15370),X15367),X15368)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15370),c_Groups_Ozero__class_Ozero(X15370)),X15368))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15370),X15369),X15367))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right__le__imp__le])])])). 4.46/4.71 fof(c_0_7866, plain, ![X2776, X2777, X2778]:(~class_Rings_Osemiring__1(X2778)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2778),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2778),X2777)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2778),X2776))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2778),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2777),X2776))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__add])])])). 4.46/4.71 fof(c_0_7867, plain, ![X14626, X14627, X14628, X14629]:(~class_Rings_Ocomm__semiring__1(X14629)|hAPP(hAPP(c_Power_Opower__class_Opower(X14629),X14628),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14627),X14626))=hAPP(hAPP(c_Power_Opower__class_Opower(X14629),hAPP(hAPP(c_Power_Opower__class_Opower(X14629),X14628),X14627)),X14626)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])])). 4.46/4.71 fof(c_0_7868, plain, ![X5449, X5450, X5451]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5451),X5450))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5451),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5450),X5449)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_start__le__sum])])])). 4.46/4.71 fof(c_0_7869, plain, ![X16978, X16979, X16980, X16981]:(~class_Rings_Olinordered__semiring__strict(X16981)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16981),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16981),X16980),X16979)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16981),X16980),X16978)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16981),c_Groups_Ozero__class_Ozero(X16981)),X16980))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16981),X16979),X16978))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left__le__imp__le])])])). 4.46/4.71 fof(c_0_7870, plain, ![X15024, X15025, X15026, X15027]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15027),X15024),X15025))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15027),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15027),X15026),X15025)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15027),X15026),X15024)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15027),X15026),c_Groups_Ozero__class_Ozero(X15027)))|~class_Rings_Olinordered__ring__strict(X15027))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15027),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15027),X15026),X15025)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15027),X15026),X15024)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15027),X15024),X15025))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15027),X15026),c_Groups_Ozero__class_Ozero(X15027)))|~class_Rings_Olinordered__ring__strict(X15027))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__cancel__left__neg])])])])). 4.46/4.71 fof(c_0_7871, plain, ![X1290, X1291, X1292]:(~class_Int_Onumber__ring(X1292)|hAPP(c_Int_Onumber__class_Onumber__of(X1292),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1291),X1290))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1292),hAPP(c_Int_Onumber__class_Onumber__of(X1292),X1291)),hAPP(c_Int_Onumber__class_Onumber__of(X1292),X1290))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I32_J])])). 4.46/4.71 fof(c_0_7872, plain, ![X10951, X10952, X10953]:(~class_Orderings_Olinorder(X10953)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10953),X10952))|c_Big__Operators_Olattice_OInf__fin(X10953,c_Orderings_Oord__class_Omin(X10953),hAPP(hAPP(c_Set_Oinsert(X10953),X10951),X10952))=hAPP(hAPP(c_Finite__Set_Ofold(X10953,X10953,c_Orderings_Oord__class_Omin(X10953)),X10951),X10952))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold__idem_H])])])). 4.46/4.71 fof(c_0_7873, plain, ![X13057, X13058, X13059]:(~class_Orderings_Olinorder(X13059)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13059),X13058))|hAPP(hAPP(c_Finite__Set_Ofold(X13059,X13059,c_Orderings_Oord__class_Omax(X13059)),X13057),X13058)=c_Big__Operators_Olattice_OSup__fin(X13059,c_Orderings_Oord__class_Omax(X13059),hAPP(hAPP(c_Set_Oinsert(X13059),X13057),X13058)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold__idem_H])])). 4.46/4.71 fof(c_0_7874, plain, ![X10404, X10405, X10406, X10407]:(~class_Divides_Osemiring__div(X10407)|c_Divides_Odiv__class_Omod(X10407,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10407),X10406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10407),X10405),X10404)),X10405)=c_Divides_Odiv__class_Omod(X10407,X10406,X10405)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2])])). 4.46/4.71 fof(c_0_7875, plain, ![X17092, X17093]:((X17093=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17093),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X17092))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17093),X17092))&(X17093!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17093),X17092)=X17092)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__if])])). 4.46/4.71 fof(c_0_7876, plain, ![X15272, X15273, X15274]:(~class_Int_Onumber__ring(X15274)|hAPP(c_Int_Onumber__class_Onumber__of(X15274),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15273),X15272))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15274),hAPP(c_Int_Onumber__class_Onumber__of(X15274),X15273)),hAPP(c_Int_Onumber__class_Onumber__of(X15274),X15272))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__number__of__eq])])])). 4.46/4.71 fof(c_0_7877, plain, ![X5705, X5706]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X5706,tc_HOL_Obool)),esk176_2(X5705,X5706)),X5705))|hBOOL(hAPP(c_Finite__Set_Ofinite(X5706),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5706,tc_HOL_Obool),X5705)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5706,tc_HOL_Obool)),X5705)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5706),esk176_2(X5705,X5706)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X5706),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5706,tc_HOL_Obool),X5705)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5706,tc_HOL_Obool)),X5705)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Union])])])])])). 4.46/4.71 fof(c_0_7878, plain, ![X8196, X8197]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8197),X8196),c_Groups_Ozero__class_Ozero(X8197)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8197),X8196),X8196)),c_Groups_Ozero__class_Ozero(X8197)))|~class_Rings_Olinordered__idom(X8197))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8197),X8196),X8196)),c_Groups_Ozero__class_Ozero(X8197)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8197),X8196),c_Groups_Ozero__class_Ozero(X8197)))|~class_Rings_Olinordered__idom(X8197))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_even__less__0__iff])])])])). 4.46/4.71 fof(c_0_7879, plain, ![X16985, X16986]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16986),X16985),X16985)),c_Groups_Ozero__class_Ozero(X16986)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16986),X16985),c_Groups_Ozero__class_Ozero(X16986)))|~class_Groups_Olinordered__ab__group__add(X16986))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16986),X16985),c_Groups_Ozero__class_Ozero(X16986)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16986),X16985),X16985)),c_Groups_Ozero__class_Ozero(X16986)))|~class_Groups_Olinordered__ab__group__add(X16986))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_double__add__less__zero__iff__single__add__less__zero])])])])). 4.46/4.71 fof(c_0_7880, plain, ![X13721, X13722, X13723, X13724]:(~class_Divides_Osemiring__div(X13724)|c_Divides_Odiv__class_Omod(X13724,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13724),X13723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13724),X13722),X13721)),X13721)=c_Divides_Odiv__class_Omod(X13724,X13723,X13721)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1])])). 4.46/4.71 fof(c_0_7881, plain, ![X10209, X10210, X10211, X10212, X10213, X10214]:(~c_List_Olist__all2(X10214,X10213,X10212,X10211,X10210)|c_List_Olist__all2(X10214,X10213,X10212,hAPP(hAPP(c_List_Odrop(X10214),X10209),X10211),hAPP(hAPP(c_List_Odrop(X10213),X10209),X10210))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2__dropI])])])). 4.46/4.71 fof(c_0_7882, plain, ![X8246, X8247, X8248, X8249, X8250, X8251]:(~c_List_Olist__all2(X8251,X8250,X8249,X8248,X8247)|c_List_Olist__all2(X8251,X8250,X8249,hAPP(hAPP(c_List_Otake(X8251),X8246),X8248),hAPP(hAPP(c_List_Otake(X8250),X8246),X8247))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__takeI])])). 4.46/4.71 cnf(c_0_7883, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_fequal),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X4))))|X3!=X4), inference(split_conjunct,[status(thm)],[c_0_5407])). 4.46/4.71 fof(c_0_7884, plain, ![X5366, X5367]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5367),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5367),X5366),X5366)),c_Groups_Ozero__class_Ozero(X5367)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5367),X5366),c_Groups_Ozero__class_Ozero(X5367)))|~class_Groups_Olinordered__ab__group__add(X5367))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5367),X5366),c_Groups_Ozero__class_Ozero(X5367)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5367),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5367),X5366),X5366)),c_Groups_Ozero__class_Ozero(X5367)))|~class_Groups_Olinordered__ab__group__add(X5367))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero])])])])). 4.46/4.71 fof(c_0_7885, plain, ![X15483, X15484, X15485]:(~class_Rings_Olinordered__semidom(X15485)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15485),c_Groups_Ozero__class_Ozero(X15485)),X15484))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15485),c_Groups_Ozero__class_Ozero(X15485)),hAPP(hAPP(c_Power_Opower__class_Opower(X15485),X15484),X15483))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__power])])])). 4.46/4.71 fof(c_0_7886, plain, ![X15037, X15038]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15038),c_Groups_Ozero__class_Ozero(X15038)),X15037))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15038),c_Groups_Ozero__class_Ozero(X15038)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15038),X15037),X15037)))|~class_Groups_Olinordered__ab__group__add(X15038))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15038),c_Groups_Ozero__class_Ozero(X15038)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15038),X15037),X15037)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15038),c_Groups_Ozero__class_Ozero(X15038)),X15037))|~class_Groups_Olinordered__ab__group__add(X15038))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__double__add__iff__zero__less__single__add])])])])). 4.46/4.71 fof(c_0_7887, plain, ![X9256, X9257, X9258]:(~class_Rings_Olinordered__semidom(X9258)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9258),c_Groups_Oone__class_Oone(X9258)),X9257))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9258),c_Groups_Oone__class_Oone(X9258)),hAPP(hAPP(c_Power_Opower__class_Opower(X9258),X9257),X9256))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__power])])). 4.46/4.71 fof(c_0_7888, plain, ![X9167, X9168, X9169]:(~class_Int_Onumber__ring(X9169)|hAPP(c_Int_Onumber__class_Onumber__of(X9169),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9168),X9167))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9169),hAPP(c_Int_Onumber__class_Onumber__of(X9169),X9168)),hAPP(c_Int_Onumber__class_Onumber__of(X9169),X9167))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__diff])])). 4.46/4.71 fof(c_0_7889, plain, ![X8534, X8535, X8536]:(~class_Rings_Olinordered__semidom(X8536)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8536),c_Groups_Ozero__class_Ozero(X8536)),X8535))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8536),c_Groups_Ozero__class_Ozero(X8536)),hAPP(hAPP(c_Power_Opower__class_Opower(X8536),X8535),X8534))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__power])])])). 4.46/4.71 fof(c_0_7890, plain, ![X1466, X1467]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1467),c_Groups_Ozero__class_Ozero(X1467)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1467),X1466),X1466)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1467),c_Groups_Ozero__class_Ozero(X1467)),X1466))|~class_Groups_Olinordered__ab__group__add(X1467))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1467),c_Groups_Ozero__class_Ozero(X1467)),X1466))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1467),c_Groups_Ozero__class_Ozero(X1467)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1467),X1466),X1466)))|~class_Groups_Olinordered__ab__group__add(X1467))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__double__add__iff__zero__le__single__add])])])])). 4.46/4.71 fof(c_0_7891, plain, ![X7025, X7026]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7026),hAPP(c_Nat_OSuc,X7025)))|hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X7025)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X7026,X7025))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X7026,hAPP(c_Nat_OSuc,X7025))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMostSuc__conv])])). 4.46/4.71 fof(c_0_7892, plain, ![X6950, X6951, X6952]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6952),X6951))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X6952),X6951)),hAPP(c_Finite__Set_Ocard(X6952),hAPP(hAPP(c_Set_Oinsert(X6952),X6950),X6951))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert__le])])). 4.46/4.71 fof(c_0_7893, plain, ![X12675, X12676, X12677, X12678]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12678),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12677)),c_List_OtakeWhile(X12677,X12676,X12675))))|hAPP(hAPP(c_List_Onth(X12677),c_List_OtakeWhile(X12677,X12676,X12675)),X12678)=hAPP(hAPP(c_List_Onth(X12677),X12675),X12678)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile__nth])])])). 4.46/4.71 fof(c_0_7894, plain, ![X11735, X11736, X11737]:(~class_Rings_Osemiring__1(X11737)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X11737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11736),X11735))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11737),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X11737),X11736)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X11737),X11735))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__mult])])). 4.46/4.71 cnf(c_0_7895, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(X1),X2))=hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5408])). 4.46/4.71 fof(c_0_7896, plain, ![X7911, X7912]:(~class_Lattices_Olattice(X7912)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7912),X7911))|(X7911=c_Orderings_Obot__class_Obot(tc_fun(X7912,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7912),c_Big__Operators_Olattice__class_OInf__fin(X7912,X7911)),c_Big__Operators_Olattice__class_OSup__fin(X7912,X7911)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__le__Sup])])])). 4.46/4.71 fof(c_0_7897, plain, ![X14382, X14383, X14384]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14384),X14383))|(hBOOL(hAPP(hAPP(c_member(X14384),X14382),X14383))|hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X14384),X14383))=hAPP(c_Finite__Set_Ocard(X14384),hAPP(hAPP(c_Set_Oinsert(X14384),X14382),X14383)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__insert__disjoint])])])). 4.46/4.71 fof(c_0_7898, plain, ![X1604, X1605]:((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk37_2(X1604,X1605)),X1605))|c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1604),X1605))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1604),esk37_2(X1604,X1605)))|c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1604),X1605))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__diff__nat])])])])). 4.46/4.71 fof(c_0_7899, plain, ![X15395, X15396]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15396))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15395))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X15396,X15395))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J])])])). 4.46/4.71 fof(c_0_7900, plain, ![X11334, X11335, X11336, X11337, X11338, X11339]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11339)),X11338)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11337)),X11336)|c_Map_Omap__upds(X11339,X11337,X11335,hAPP(hAPP(c_List_Oappend(X11339),X11338),X11334),X11336)=c_Map_Omap__upds(X11339,X11337,X11335,X11338,X11336)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upds__append__drop])])). 4.46/4.71 fof(c_0_7901, plain, ![X5874, X5875]:(~class_Fields_Ofield__inverse__zero(X5875)|~class_Int_Onumber__ring(X5875)|hAPP(c_Groups_Ouminus__class_Ouminus(X5875),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5875),c_Groups_Oone__class_Oone(X5875)),X5874))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5875),hAPP(c_Int_Onumber__class_Onumber__of(X5875),c_Int_OMin)),X5874)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus1__divide])])])). 4.46/4.71 cnf(c_0_7902, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk309_2(X2,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5409])). 4.46/4.71 fof(c_0_7903, plain, ![X16177, X16178, X16179, X16180, X16181, X16182]:(~c_Finite__Set_Ofun__left__comm(X16182,X16181,X16180)|hAPP(hAPP(X16180,X16178),hAPP(hAPP(X16180,X16179),X16177))=hAPP(hAPP(X16180,X16179),hAPP(hAPP(X16180,X16178),X16177))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofun__left__comm])])])). 4.46/4.71 fof(c_0_7904, plain, ![X16174, X16175, X16176]:(~class_Rings_Olinordered__idom(X16176)|hAPP(c_Groups_Oabs__class_Oabs(X16176),hAPP(hAPP(c_Power_Opower__class_Opower(X16176),hAPP(c_Groups_Ouminus__class_Ouminus(X16176),X16175)),X16174))=hAPP(c_Groups_Oabs__class_Oabs(X16176),hAPP(hAPP(c_Power_Opower__class_Opower(X16176),X16175),X16174))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus])])). 4.46/4.71 fof(c_0_7905, plain, ![X5037, X5038, X5039, X5040, X5041, X5042]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5040)),X5039)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5042)),X5041)|c_Map_Omap__upds(X5042,X5040,X5038,X5041,hAPP(hAPP(c_List_Oappend(X5040),X5039),X5037))=c_Map_Omap__upds(X5042,X5040,X5038,X5041,X5039)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upds__append2__drop])])). 4.46/4.71 fof(c_0_7906, plain, ![X4557, X4558, X4559, X4560, X4561]:(~class_Orderings_Olinorder(X4561)|c_List_Olinorder__class_Osort__key(X4560,X4561,X4559,hAPP(hAPP(c_List_Olist_OCons(X4560),X4558),X4557))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4560,X4561,X4559),X4558),c_List_Olinorder__class_Osort__key(X4560,X4561,X4559,X4557))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sort__key__simps_I2_J])])])). 4.46/4.71 fof(c_0_7907, plain, ![X3578, X3579, X3580]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3580),hAPP(c_Groups_Ouminus__class_Ouminus(X3580),X3579)),X3578))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3580),hAPP(c_Groups_Oabs__class_Oabs(X3580),X3579)),X3578))|~class_Rings_Olinordered__idom(X3580))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3580),X3579),X3578))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3580),hAPP(c_Groups_Oabs__class_Oabs(X3580),X3579)),X3578))|~class_Rings_Olinordered__idom(X3580)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3580),hAPP(c_Groups_Ouminus__class_Ouminus(X3580),X3579)),X3578))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3580),X3579),X3578))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3580),hAPP(c_Groups_Oabs__class_Oabs(X3580),X3579)),X3578))|~class_Rings_Olinordered__idom(X3580))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__less__iff])])])). 4.46/4.71 fof(c_0_7908, plain, ![X8616, X8617, X8618]:(~class_Rings_Olinordered__idom(X8618)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8618),hAPP(c_Groups_Oabs__class_Oabs(X8618),X8617)),hAPP(c_Groups_Oabs__class_Oabs(X8618),X8616))=hAPP(c_Groups_Oabs__class_Oabs(X8618),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8618),X8617),X8616))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult])])). 4.46/4.71 cnf(c_0_7909, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(rw,[status(thm)],[c_0_5410, c_0_4431])). 4.46/4.71 fof(c_0_7910, plain, ![X12744, X12745, X12746, X12747]:((~hBOOL(hAPP(hAPP(c_member(X12747),X12746),X12745))|hAPP(hAPP(c_Set_Oinsert(X12747),X12746),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12747,tc_HOL_Obool)),X12744),X12745))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12747,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X12747),X12746),X12744)),X12745))&(hBOOL(hAPP(hAPP(c_member(X12747),X12746),X12745))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12747,tc_HOL_Obool)),X12744),X12745)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12747,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X12747),X12746),X12744)),X12745))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__insert__left])])])). 4.46/4.71 fof(c_0_7911, plain, ![X17440, X17441, X17442]:(hBOOL(hAPP(hAPP(c_member(X17442),X17441),X17440))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17442,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17442),X17441),X17440)),hAPP(hAPP(c_Set_Oinsert(X17442),X17441),c_Orderings_Obot__class_Obot(tc_fun(X17442,tc_HOL_Obool))))=X17440), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Diff__insert__absorb])])])). 4.46/4.71 fof(c_0_7912, plain, ![X14668, X14669, X14670]:(~class_Groups_Omonoid__add(X14670)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14670),hAPP(c_List_Omonoid__add__class_Olistsum(X14670),X14669)),hAPP(c_List_Omonoid__add__class_Olistsum(X14670),X14668))=hAPP(c_List_Omonoid__add__class_Olistsum(X14670),hAPP(hAPP(c_List_Oappend(X14670),X14669),X14668))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__append])])])). 4.46/4.71 fof(c_0_7913, plain, ![X8269, X8270, X8271]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8271),hAPP(c_Groups_Ouminus__class_Ouminus(X8271),X8270)),X8269))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8271),X8270),X8269))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8271),hAPP(c_Groups_Oabs__class_Oabs(X8271),X8270)),X8269))|~class_Groups_Oordered__ab__group__add__abs(X8271))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8271),hAPP(c_Groups_Ouminus__class_Ouminus(X8271),X8270)),X8269))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8271),hAPP(c_Groups_Oabs__class_Oabs(X8271),X8270)),X8269))|~class_Groups_Oordered__ab__group__add__abs(X8271))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8271),X8270),X8269))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8271),hAPP(c_Groups_Oabs__class_Oabs(X8271),X8270)),X8269))|~class_Groups_Oordered__ab__group__add__abs(X8271)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__le__iff])])])])). 4.46/4.71 fof(c_0_7914, plain, ![X7038, X7039, X7040]:((~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7040))|hAPP(hAPP(c_List_Olist_OCons(X7039),X7038),c_List_Olist_ONil(X7039))=c_List_Osublist(X7039,hAPP(hAPP(c_List_Olist_OCons(X7039),X7038),c_List_Olist_ONil(X7039)),X7040))&(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7040))|c_List_Osublist(X7039,hAPP(hAPP(c_List_Olist_OCons(X7039),X7038),c_List_Olist_ONil(X7039)),X7040)=c_List_Olist_ONil(X7039))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sublist__singleton])])])). 4.46/4.71 fof(c_0_7915, plain, ![X15724, X15725, X15726]:(~class_Fields_Olinordered__field__inverse__zero(X15726)|hAPP(c_Groups_Oabs__class_Oabs(X15726),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15726),X15725),X15724))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15726),hAPP(c_Groups_Oabs__class_Oabs(X15726),X15725)),hAPP(c_Groups_Oabs__class_Oabs(X15726),X15724))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__divide])])). 4.46/4.71 cnf(c_0_7916, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),X4)=X3|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)!=X2|X4!=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_5411])). 4.46/4.71 cnf(c_0_7917, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Ovimage(X1,X2,X3),X4))=X4|hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5412])). 4.46/4.71 cnf(c_0_7918, plain, (hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Set_Oimage(X1,X2,X3),X4))=X4|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5413])). 4.46/4.71 cnf(c_0_7919, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Ovimage(X1,X2,X3),X4)))|c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5414])). 4.46/4.71 fof(c_0_7920, plain, ![X11501, X11502, X11503]:(~class_Rings_Oring__1(X11503)|hAPP(c_Int_Oring__1__class_Oof__int(X11503),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11502),X11501))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11503),hAPP(c_Int_Oring__1__class_Oof__int(X11503),X11502)),hAPP(c_Int_Oring__1__class_Oof__int(X11503),X11501))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__mult])])])). 4.46/4.71 fof(c_0_7921, plain, ![X15911, X15912, X15913]:(~class_Orderings_Olinorder(X15913)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15913),X15912))|(~hBOOL(hAPP(hAPP(c_member(X15913),X15911),X15912))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15913),hAPP(c_Finite__Set_Ofold1(X15913,c_Orderings_Oord__class_Omin(X15913)),X15912)),X15911))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ofold1__belowI])])])). 4.46/4.71 fof(c_0_7922, plain, ![X14090, X14091, X14092]:(~class_Lattices_Osemilattice__inf(X14092)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14092),X14091))|(~hBOOL(hAPP(hAPP(c_member(X14092),X14090),X14091))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14092),hAPP(c_Finite__Set_Ofold1(X14092,c_Lattices_Osemilattice__inf__class_Oinf(X14092)),X14091)),X14090))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__belowI])])])). 4.46/4.71 fof(c_0_7923, plain, ![X8058, X8059, X8060]:(~class_Rings_Oring__1(X8060)|hAPP(c_Int_Oring__1__class_Oof__int(X8060),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8059),X8058))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8060),hAPP(c_Int_Oring__1__class_Oof__int(X8060),X8059)),hAPP(c_Int_Oring__1__class_Oof__int(X8060),X8058))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__add])])])). 4.46/4.71 cnf(c_0_7924, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Ovimage(X3,X1,X4),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Fun_Oinj__on(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5415])). 4.46/4.71 cnf(c_0_7925, plain, (hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_Set_Ovimage(X5,X1,X2),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_5416])). 4.46/4.71 cnf(c_0_7926, plain, (hBOOL(hAPP(hAPP(c_member(X3),hAPP(X4,X2)),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Ovimage(X1,X3,X4),X5)))), inference(split_conjunct,[status(thm)],[c_0_5417])). 4.46/4.71 cnf(c_0_7927, plain, (X5=hAPP(X4,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Ovimage(X1,X3,X4),hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_4803])). 4.46/4.71 fof(c_0_7928, plain, ![X16933, X16934, X16935]:(~class_Rings_Oring__1(X16935)|hAPP(c_Int_Oring__1__class_Oof__int(X16935),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X16934),X16933))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X16935),hAPP(c_Int_Oring__1__class_Oof__int(X16935),X16934)),hAPP(c_Int_Oring__1__class_Oof__int(X16935),X16933))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__diff])])])). 4.46/4.71 fof(c_0_7929, plain, ![X636, X637, X638]:((hBOOL(hAPP(hAPP(c_member(X638),esk16_3(X636,X637,X638)),X636))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X638,X638)),X637),c_Relation_OId__on(X638,X636))))&(X637=hAPP(hAPP(c_Product__Type_OPair(X638,X638),esk16_3(X636,X637,X638)),esk16_3(X636,X637,X638))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X638,X638)),X637),c_Relation_OId__on(X638,X636))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Id__onE])])])])])). 4.46/4.71 cnf(c_0_7930, plain, (c_List_Olast(tc_Nat_Onat,c_List_Oupt(X1,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5418])). 4.46/4.71 cnf(c_0_7931, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X4,X1,hAPP(c_COMBK(X1,X4),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_5419])). 4.46/4.71 cnf(c_0_7932, plain, (c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X4,X1,hAPP(c_COMBK(X1,X4),X2)),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5419])). 4.46/4.71 fof(c_0_7933, plain, ![X10593, X10594, X10595, X10596]:(~class_Rings_Olinordered__semidom(X10596)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10596),hAPP(hAPP(c_Power_Opower__class_Opower(X10596),X10595),X10594)),hAPP(hAPP(c_Power_Opower__class_Opower(X10596),X10593),X10594)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10596),c_Groups_Ozero__class_Ozero(X10596)),X10593))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10596),X10595),X10593))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__less__imp__less__base])])])). 4.46/4.71 fof(c_0_7934, plain, ![X13826, X13827, X13828]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13828),c_Map_Odom(X13828,X13827,X13826)))|(hBOOL(hAPP(c_Finite__Set_Ofinite(X13828),c_Orderings_Otop__class_Otop(tc_fun(X13828,tc_HOL_Obool))))|c_Option_Ooption_ONone(X13827)=hAPP(X13826,esk402_3(X13826,X13827,X13828)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__map__freshness])])])])). 4.46/4.71 fof(c_0_7935, plain, ![X11488, X11489, X11490]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X11490,tc_HOL_Obool)),esk338_3(X11488,X11489,X11490)),X11489))|hBOOL(hAPP(hAPP(c_member(X11490),X11488),c_Complete__Lattice_OInf__class_OInf(tc_fun(X11490,tc_HOL_Obool),X11489))))&(~hBOOL(hAPP(hAPP(c_member(X11490),X11488),esk338_3(X11488,X11489,X11490)))|hBOOL(hAPP(hAPP(c_member(X11490),X11488),c_Complete__Lattice_OInf__class_OInf(tc_fun(X11490,tc_HOL_Obool),X11489))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_InterI])])])])])). 4.46/4.71 fof(c_0_7936, plain, ![X16402, X16403, X16404, X16405]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X16405,X16404)),hAPP(hAPP(c_Product__Type_OSigma(X16405,X16404),X16403),hAPP(c_COMBK(tc_fun(X16404,tc_HOL_Obool),X16405),X16402))))|(c_Orderings_Obot__class_Obot(tc_fun(X16404,tc_HOL_Obool))=X16402|hBOOL(hAPP(c_Finite__Set_Ofinite(X16405),X16403)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__cartesian__productD1])])])). 4.46/4.71 cnf(c_0_7937, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=X4|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)|X5!=X6|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_5420])). 4.46/4.71 fof(c_0_7938, plain, ![X10489, X10490, X10491, X10492]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10492,X10491)),hAPP(hAPP(c_Product__Type_OSigma(X10492,X10491),X10490),hAPP(c_COMBK(tc_fun(X10491,tc_HOL_Obool),X10492),X10489))))|(X10490=c_Orderings_Obot__class_Obot(tc_fun(X10492,tc_HOL_Obool))|hBOOL(hAPP(c_Finite__Set_Ofinite(X10491),X10489)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__cartesian__productD2])])])). 4.46/4.71 cnf(c_0_7939, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5421])). 4.46/4.71 fof(c_0_7940, plain, ![X5082, X5083, X5084]:(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5084)),X5083),c_Wellfounded_Oacc(tc_List_Olist(X5084),c_List_Olistrel1(X5084,X5082))))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5084)),X5083),c_List_Olists(X5084,c_Wellfounded_Oacc(X5084,X5082))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lists__accI])])])). 4.46/4.71 fof(c_0_7941, plain, ![X10819, X10820, X10821, X10822, X10823, X10824]:(~c_Finite__Set_Ofolding(X10824,X10823,X10822,X10821)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10824),X10820))|hAPP(hAPP(c_Finite__Set_Ofold(X10824,X10823,X10822),X10819),X10820)=hAPP(hAPP(X10821,X10820),X10819))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Oeq__fold])])])). 4.46/4.71 cnf(c_0_7942, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))=c_Divides_OnegDivAlg(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_4528])). 4.46/4.71 fof(c_0_7943, plain, ![X11474, X11475, X11476, X11477, X11479, X11480, X11481, X11482, X11483]:(((hBOOL(hAPP(hAPP(c_member(X11477),esk337_4(X11474,X11475,X11476,X11477)),X11475))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11477,tc_fun(X11476,tc_HOL_Obool)),X11475),X11474)=c_Orderings_Otop__class_Otop(tc_fun(X11476,tc_HOL_Obool)))&(c_Orderings_Otop__class_Otop(tc_fun(X11476,tc_HOL_Obool))!=hAPP(X11474,esk337_4(X11474,X11475,X11476,X11477))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11477,tc_fun(X11476,tc_HOL_Obool)),X11475),X11474)=c_Orderings_Otop__class_Otop(tc_fun(X11476,tc_HOL_Obool))))&(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11482,tc_fun(X11481,tc_HOL_Obool)),X11480),X11479)!=c_Orderings_Otop__class_Otop(tc_fun(X11481,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_member(X11482),X11483),X11480))|c_Orderings_Otop__class_Otop(tc_fun(X11481,tc_HOL_Obool))=hAPP(X11479,X11483)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INTER__UNIV__conv_I2_J])])])])])])). 4.46/4.71 fof(c_0_7944, plain, ![X14699, X14700]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X14700),X14699))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X14700)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X14699)))|~c_Nat__Transfer_Onat__set(X14699)|~c_Nat__Transfer_Onat__set(X14700))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X14700)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X14699)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X14700),X14699))|~c_Nat__Transfer_Onat__set(X14699)|~c_Nat__Transfer_Onat__set(X14700))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__int__nat__set__relations_I5_J])])])])). 4.46/4.71 fof(c_0_7945, plain, ![X5095, X5096, X5097]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5097),X5096))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5096),X5095))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X5097)),X5095)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__trans__Suc])])])). 4.46/4.71 fof(c_0_7946, plain, ![X9213, X9214, X9215, X9216, X9218, X9219, X9220, X9221, X9222]:(((hBOOL(hAPP(hAPP(c_member(X9215),esk266_4(X9213,X9214,X9215,X9216)),X9214))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9215,tc_fun(X9216,tc_HOL_Obool)),X9214),X9213)=c_Orderings_Otop__class_Otop(tc_fun(X9216,tc_HOL_Obool)))&(c_Orderings_Otop__class_Otop(tc_fun(X9216,tc_HOL_Obool))!=hAPP(X9213,esk266_4(X9213,X9214,X9215,X9216))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9215,tc_fun(X9216,tc_HOL_Obool)),X9214),X9213)=c_Orderings_Otop__class_Otop(tc_fun(X9216,tc_HOL_Obool))))&(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9220,tc_fun(X9221,tc_HOL_Obool)),X9219),X9218)!=c_Orderings_Otop__class_Otop(tc_fun(X9221,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_member(X9220),X9222),X9219))|c_Orderings_Otop__class_Otop(tc_fun(X9221,tc_HOL_Obool))=hAPP(X9218,X9222)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INTER__UNIV__conv_I1_J])])])])])])). 4.46/4.71 fof(c_0_7947, plain, ![X2506, X2507, X2508, X2509, X2510, X2511, X2512, X2513, X2514]:(hAPP(c_Fun_Ocomp(X2508,X2512,X2511,X2507),X2506)!=hAPP(c_Fun_Ocomp(X2513,X2512,X2511,X2510),X2509)|hAPP(X2507,hAPP(X2506,X2514))=hAPP(X2510,hAPP(X2509,X2514))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__elim])])])). 4.46/4.71 fof(c_0_7948, plain, ![X13087, X13088, X13089, X13090, X13091]:(~c_Fun_Oinj__on(X13091,X13090,X13089,X13088)|(~hBOOL(hAPP(hAPP(c_member(X13090),X13087),hAPP(c_Set_Oimage(X13091,X13090,X13089),X13088)))|X13087=hAPP(X13089,hAPP(c_Fun_Othe__inv__into(X13091,X13090,X13088,X13089),X13087)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__the__inv__into__f])])). 4.46/4.71 cnf(c_0_7949, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X2))|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1))), inference(split_conjunct,[status(thm)],[c_0_5031])). 4.46/4.71 fof(c_0_7950, plain, ![X2021, X2022]:((((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2022),X2021))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2022))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2022),X2021)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2021),X2022))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2022),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2022),X2021)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X2021|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2022),X2021)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2021),X2022))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2022),X2021))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2021|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2022),X2021)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2022),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2022),X2021))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2021|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2022),X2021)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2021),X2022))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2022))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2021|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2022),X2021)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2022),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2022))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2021|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2022),X2021)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__eq__0__iff])])])). 4.46/4.71 cnf(c_0_7951, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))|c_Groups_Ozero__class_Ozero(X1)!=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5422])). 4.46/4.71 cnf(c_0_7952, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)=X1), inference(rw,[status(thm)],[c_0_5423, c_0_4436]), ['final']). 4.46/4.71 cnf(c_0_7953, plain, (c_Nitpick_Oless__eq__frac(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_5424, c_0_5003])). 4.46/4.71 cnf(c_0_7954, plain, (c_Nitpick_Oless__frac(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_5425, c_0_5003])). 4.46/4.71 fof(c_0_7955, plain, ![X1406, X1407, X1408, X1409, X1410]:(~class_Orderings_Olinorder(X1410)|(~c_List_Olinorder__class_Osorted(X1410,hAPP(hAPP(c_List_Omap(X1409,X1410),X1408),X1407))|c_List_Olinorder__class_Osorted(X1410,hAPP(hAPP(c_List_Omap(X1409,X1410),X1408),c_List_Olinorder__class_Oinsort__insert__key(X1409,X1410,X1408,X1406,X1407))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__insort__insert__key])])])). 4.46/4.71 fof(c_0_7956, plain, ![X12474, X12475, X12476, X12477, X12478, X12479, X12480, X12481, X12482, X12483, X12484]:((~hBOOL(hAPP(hAPP(c_member(X12476),X12478),X12474))|X12477!=hAPP(X12475,X12478)|hBOOL(hAPP(hAPP(c_member(X12479),X12477),hAPP(c_Set_Oimage(X12476,X12479,X12475),X12474))))&((hBOOL(hAPP(hAPP(c_member(X12482),esk367_4(X12480,X12481,X12482,X12483)),X12480))|~hBOOL(hAPP(hAPP(c_member(X12484),X12483),hAPP(c_Set_Oimage(X12482,X12484,X12481),X12480))))&(X12483=hAPP(X12481,esk367_4(X12480,X12481,X12482,X12483))|~hBOOL(hAPP(hAPP(c_member(X12484),X12483),hAPP(c_Set_Oimage(X12482,X12484,X12481),X12480)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__iff])])])])])])). 4.46/4.71 cnf(c_0_7957, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5426])). 4.46/4.71 cnf(c_0_7958, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5427, c_0_4436]), c_0_4436]), ['final']). 4.46/4.71 fof(c_0_7959, plain, ![X6236, X6237, X6238, X6239]:((~hBOOL(hAPP(hAPP(c_member(X6239),X6238),X6237))|~hBOOL(hAPP(hAPP(c_member(X6239),X6238),X6236))|hBOOL(hAPP(hAPP(c_member(X6239),X6238),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6239,tc_HOL_Obool)),X6237),X6236))))&((hBOOL(hAPP(hAPP(c_member(X6239),X6238),X6237))|~hBOOL(hAPP(hAPP(c_member(X6239),X6238),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6239,tc_HOL_Obool)),X6237),X6236))))&(hBOOL(hAPP(hAPP(c_member(X6239),X6238),X6236))|~hBOOL(hAPP(hAPP(c_member(X6239),X6238),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6239,tc_HOL_Obool)),X6237),X6236)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__iff])])])). 4.46/4.71 cnf(c_0_7960, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))|~c_Wellfounded_Oacyclic(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_Predicate_Oconversep(X1,X1,X2))))), inference(split_conjunct,[status(thm)],[c_0_5293])). 4.46/4.71 fof(c_0_7961, plain, ![X11852, X11853, X11854, X11856]:(((hBOOL(hAPP(hAPP(c_member(X11854),esk351_3(X11852,X11853,X11854)),X11853))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11854),c_Complete__Lattice_OSup__class_OSup(X11854,X11853)),X11852))|~class_Complete__Lattice_Ocomplete__lattice(X11854))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11854),esk351_3(X11852,X11853,X11854)),X11852))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11854),c_Complete__Lattice_OSup__class_OSup(X11854,X11853)),X11852))|~class_Complete__Lattice_Ocomplete__lattice(X11854)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11854),c_Complete__Lattice_OSup__class_OSup(X11854,X11853)),X11852))|(~hBOOL(hAPP(hAPP(c_member(X11854),X11856),X11853))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11854),X11856),X11852)))|~class_Complete__Lattice_Ocomplete__lattice(X11854))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__le__iff])])])])])])). 4.46/4.71 fof(c_0_7962, plain, ![X1943, X1944, X1945, X1947]:(((hBOOL(hAPP(hAPP(c_member(X1945),esk48_3(X1943,X1944,X1945)),X1943))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1945),X1944),c_Complete__Lattice_OInf__class_OInf(X1945,X1943)))|~class_Complete__Lattice_Ocomplete__lattice(X1945))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1945),X1944),esk48_3(X1943,X1944,X1945)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1945),X1944),c_Complete__Lattice_OInf__class_OInf(X1945,X1943)))|~class_Complete__Lattice_Ocomplete__lattice(X1945)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1945),X1944),c_Complete__Lattice_OInf__class_OInf(X1945,X1943)))|(~hBOOL(hAPP(hAPP(c_member(X1945),X1947),X1943))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1945),X1944),X1947)))|~class_Complete__Lattice_Ocomplete__lattice(X1945))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__Inf__iff])])])])])])). 4.46/4.71 cnf(c_0_7963, plain, (X3=hAPP(c_List_Orotate(X2,X1),X3)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_5428])). 4.46/4.71 fof(c_0_7964, plain, ![X16310, X16311, X16312, X16313, X16314]:(~c_Finite__Set_Ofolding__one__idem(X16314,X16313,X16312)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16314),X16311))|(~hBOOL(hAPP(hAPP(c_member(X16314),X16310),X16311))|hAPP(hAPP(X16313,X16310),hAPP(X16312,X16311))=hAPP(X16312,X16311)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oin__idem])])). 4.46/4.71 cnf(c_0_7965, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))), inference(split_conjunct,[status(thm)],[c_0_5429])). 4.46/4.71 fof(c_0_7966, plain, ![X6466, X6467, X6468, X6469]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6469,tc_HOL_Obool)),X6468),X6467))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6469,tc_HOL_Obool)),X6467),X6466))|X6468=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6469,tc_HOL_Obool)),X6467),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6469,tc_HOL_Obool)),X6466),X6468)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_double__diff])])])). 4.46/4.71 fof(c_0_7967, plain, ![X1502, X1503, X1504, X1505, X1506]:(~hBOOL(hAPP(hAPP(c_member(X1506),X1505),X1504))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1503,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1506,tc_fun(X1503,tc_HOL_Obool)),X1504),X1502)),hAPP(X1502,X1505)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INT__lower])])])). 4.46/4.71 fof(c_0_7968, plain, ![X8327, X8328, X8329, X8330, X8331, X8332]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X8332,X8331)),hAPP(hAPP(c_Product__Type_OPair(X8332,X8331),X8330),X8329)),hAPP(hAPP(c_Product__Type_OSigma(X8332,X8331),X8328),X8327)))|hBOOL(hAPP(hAPP(c_member(X8331),X8329),hAPP(X8327,X8330)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD2])])). 4.46/4.71 fof(c_0_7969, plain, ![X13079, X13080, X13081, X13082]:((~c_Fun_Oinj__on(X13081,X13082,X13080,hAPP(c_List_Oset(X13081),X13079))|~hBOOL(hAPP(c_List_Odistinct(X13081),X13079))|hBOOL(hAPP(c_List_Odistinct(X13082),hAPP(hAPP(c_List_Omap(X13081,X13082),X13080),X13079))))&((c_Fun_Oinj__on(X13081,X13082,X13080,hAPP(c_List_Oset(X13081),X13079))|~hBOOL(hAPP(c_List_Odistinct(X13082),hAPP(hAPP(c_List_Omap(X13081,X13082),X13080),X13079))))&(hBOOL(hAPP(c_List_Odistinct(X13081),X13079))|~hBOOL(hAPP(c_List_Odistinct(X13082),hAPP(hAPP(c_List_Omap(X13081,X13082),X13080),X13079)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__map])])])). 4.46/4.71 fof(c_0_7970, plain, ![X5575, X5576, X5577, X5578, X5579]:((~hBOOL(hAPP(hAPP(c_member(X5577),X5579),X5576))|hAPP(X5575,X5579)!=c_Groups_Ozero__class_Ozero(X5578)|c_Groups_Ozero__class_Ozero(X5578)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5577,X5578),X5575),X5576)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5577),X5576))|(~class_Rings_Ono__zero__divisors(X5578)|~class_Rings_Ocomm__semiring__1(X5578)))&((hBOOL(hAPP(hAPP(c_member(X5577),esk169_4(X5575,X5576,X5577,X5578)),X5576))|c_Groups_Ozero__class_Ozero(X5578)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5577,X5578),X5575),X5576)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5577),X5576))|(~class_Rings_Ono__zero__divisors(X5578)|~class_Rings_Ocomm__semiring__1(X5578)))&(hAPP(X5575,esk169_4(X5575,X5576,X5577,X5578))=c_Groups_Ozero__class_Ozero(X5578)|c_Groups_Ozero__class_Ozero(X5578)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5577,X5578),X5575),X5576)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5577),X5576))|(~class_Rings_Ono__zero__divisors(X5578)|~class_Rings_Ocomm__semiring__1(X5578))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__zero__iff])])])])])])). 4.46/4.71 cnf(c_0_7971, plain, (X4=c_List_Olast(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))|X2=c_List_Olist_ONil(X1)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X3), inference(split_conjunct,[status(thm)],[c_0_5430])). 4.46/4.71 fof(c_0_7972, plain, ![X2540, X2541, X2542, X2543, X2544]:(~hBOOL(hAPP(hAPP(c_member(X2544),X2543),X2542))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2541,tc_HOL_Obool)),hAPP(X2540,X2543)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2544,tc_fun(X2541,tc_HOL_Obool)),X2542),X2540)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__upper])])). 4.46/4.71 fof(c_0_7973, plain, ![X1547, X1548, X1549, X1550]:(~c_Wellfounded_Owf(X1550,X1549)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X1550,X1550)),hAPP(hAPP(c_Product__Type_OPair(X1550,X1550),X1548),X1547)),X1549))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1550,X1550)),hAPP(hAPP(c_Product__Type_OPair(X1550,X1550),X1547),X1548)),X1549)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__not__sym])])])). 4.46/4.71 cnf(c_0_7974, plain, (X3=hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X2))),X3)|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(rw,[status(thm)],[c_0_5431, c_0_5035])). 4.46/4.71 cnf(c_0_7975, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_5361])). 4.46/4.71 fof(c_0_7976, plain, ![X7553, X7554, X7555, X7556, X7557]:(~c_Relation_Orefl__on(X7557,X7556,X7555)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X7557,X7557)),hAPP(hAPP(c_Product__Type_OPair(X7557,X7557),X7554),X7553)),X7555))|hBOOL(hAPP(hAPP(c_member(X7557),X7554),X7556)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD1])])). 4.46/4.71 fof(c_0_7977, plain, ![X9973, X9974, X9975, X9976, X9977]:(~c_Relation_Orefl__on(X9977,X9976,X9975)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9977,X9977)),hAPP(hAPP(c_Product__Type_OPair(X9977,X9977),X9974),X9973)),X9975))|hBOOL(hAPP(hAPP(c_member(X9977),X9973),X9976)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__onD2])])])). 4.46/4.71 cnf(c_0_7978, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5432])). 4.46/4.71 fof(c_0_7979, plain, ![X12528]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12528))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X12528)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__imp__0__less])])])). 4.46/4.71 fof(c_0_7980, plain, ![X16927, X16928, X16929, X16930, X16931]:((c_List_Olist_ONil(tc_List_Olist(X16928))!=c_List_Otranspose(X16928,X16927)|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X16928)),X16929),hAPP(c_List_Oset(tc_List_Olist(X16928)),X16927)))|c_List_Olist_ONil(X16928)=X16929))&((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X16931)),esk504_2(X16930,X16931)),hAPP(c_List_Oset(tc_List_Olist(X16931)),X16930)))|c_List_Olist_ONil(tc_List_Olist(X16931))=c_List_Otranspose(X16931,X16930))&(c_List_Olist_ONil(X16931)!=esk504_2(X16930,X16931)|c_List_Olist_ONil(tc_List_Olist(X16931))=c_List_Otranspose(X16931,X16930)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transpose__empty])])])])])])])). 4.46/4.71 cnf(c_0_7981, plain, (hBOOL(hAPP(X2,X4))|c_List_Olist_ONil(X1)!=c_List_OdropWhile(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_5284])). 4.46/4.71 fof(c_0_7982, plain, ![X11042, X11043, X11044, X11045, X11046]:((~c_Nitpick_Orefl_H(X11043,X11042)|hBOOL(hAPP(hAPP(c_member(tc_prod(X11043,X11043)),hAPP(hAPP(c_Product__Type_OPair(X11043,X11043),X11044),X11044)),X11042)))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X11046,X11046)),hAPP(hAPP(c_Product__Type_OPair(X11046,X11046),esk330_2(X11045,X11046)),esk330_2(X11045,X11046))),X11045))|c_Nitpick_Orefl_H(X11046,X11045))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Orefl_H__def])])])])])). 4.46/4.71 fof(c_0_7983, plain, ![X15591, X15592, X15593, X15594]:(~class_Orderings_Olinorder(X15594)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X15594),X15593),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15594),X15592),X15591))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X15594),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15594),X15593),X15592)),X15591)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oassoc])])). 4.46/4.71 fof(c_0_7984, plain, ![X5055, X5056, X5057, X5058]:(~class_Orderings_Olinorder(X5058)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X5058),X5057),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5058),X5056),X5055))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5058),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5058),X5057),X5056)),X5055)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__assoc])])). 4.46/4.71 cnf(c_0_7985, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_5279])). 4.46/4.71 fof(c_0_7986, plain, ![X8323, X8324, X8325, X8326]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X8326),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8326,tc_HOL_Obool)),X8325),X8323)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X8326),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8326,tc_HOL_Obool)),X8325),hAPP(hAPP(c_Set_Oinsert(X8326),X8324),X8323)))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8326),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8326,tc_HOL_Obool)),X8325),hAPP(hAPP(c_Set_Oinsert(X8326),X8324),X8323))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X8326),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8326,tc_HOL_Obool)),X8325),X8323))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff__insert])])). 4.46/4.71 fof(c_0_7987, plain, ![X4492, X4493]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4492))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4493),X4492)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4493)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4492),X4493))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4493),X4492)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4493))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4492))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4492),X4493))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4493),X4492)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4493)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff])])])])). 4.46/4.71 fof(c_0_7988, plain, ![X10184, X10185, X10186]:((~hBOOL(hAPP(hAPP(c_member(X10186),X10185),hAPP(c_List_Oset(X10186),X10184)))|X10184=c_List_Oinsert(X10186,X10185,X10184))&(hBOOL(hAPP(hAPP(c_member(X10186),X10185),hAPP(c_List_Oset(X10186),X10184)))|c_List_Oinsert(X10186,X10185,X10184)=hAPP(hAPP(c_List_Olist_OCons(X10186),X10185),X10184))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_List_Oinsert__def])])])). 4.46/4.71 fof(c_0_7989, plain, ![X7712, X7713, X7714, X7715, X7716]:(~hBOOL(hAPP(hAPP(c_member(X7716),X7715),X7714))|hAPP(c_Set_Oimage(X7716,X7713,hAPP(c_COMBK(X7713,X7716),X7712)),X7714)=hAPP(hAPP(c_Set_Oinsert(X7713),X7712),c_Orderings_Obot__class_Obot(tc_fun(X7713,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__constant])])])). 4.46/4.71 fof(c_0_7990, plain, ![X640, X641, X642]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X642),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X642),X641),X640)),c_Groups_Ozero__class_Ozero(X642)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X642),X641),X640))|~class_Groups_Oordered__ab__group__add(X642))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X642),X641),X640))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X642),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X642),X641),X640)),c_Groups_Ozero__class_Ozero(X642)))|~class_Groups_Oordered__ab__group__add(X642))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0])])])). 4.46/4.71 fof(c_0_7991, plain, ![X4151, X4152, X4153, X4154, X4155, X4156, X4157, X4158, X4159]:((hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4154,tc_fun(X4153,tc_HOL_Obool)),X4152),X4151)!=c_Orderings_Obot__class_Obot(tc_fun(X4153,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_member(X4154),X4155),X4152))|hAPP(X4151,X4155)=c_Orderings_Obot__class_Obot(tc_fun(X4153,tc_HOL_Obool))))&((hBOOL(hAPP(hAPP(c_member(X4159),esk114_4(X4156,X4157,X4158,X4159)),X4157))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4159,tc_fun(X4158,tc_HOL_Obool)),X4157),X4156)=c_Orderings_Obot__class_Obot(tc_fun(X4158,tc_HOL_Obool)))&(hAPP(X4156,esk114_4(X4156,X4157,X4158,X4159))!=c_Orderings_Obot__class_Obot(tc_fun(X4158,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4159,tc_fun(X4158,tc_HOL_Obool)),X4157),X4156)=c_Orderings_Obot__class_Obot(tc_fun(X4158,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UNION__empty__conv_I2_J])])])])])])])). 4.46/4.71 fof(c_0_7992, plain, ![X4451, X4452, X4453]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4453),hAPP(c_Groups_Ouminus__class_Ouminus(X4453),X4452)),X4451))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4453),hAPP(c_Groups_Ouminus__class_Ouminus(X4453),X4451)),X4452))|~class_Groups_Oordered__ab__group__add(X4453))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4453),hAPP(c_Groups_Ouminus__class_Ouminus(X4453),X4451)),X4452))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4453),hAPP(c_Groups_Ouminus__class_Ouminus(X4453),X4452)),X4451))|~class_Groups_Oordered__ab__group__add(X4453))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])])). 4.46/4.71 fof(c_0_7993, plain, ![X13072, X13073, X13074]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13074),hAPP(c_Groups_Ouminus__class_Ouminus(X13074),X13073)),X13072))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13074),hAPP(c_Groups_Ouminus__class_Ouminus(X13074),X13072)),X13073))|~class_Groups_Oordered__ab__group__add(X13074))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13074),hAPP(c_Groups_Ouminus__class_Ouminus(X13074),X13072)),X13073))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13074),hAPP(c_Groups_Ouminus__class_Ouminus(X13074),X13073)),X13072))|~class_Groups_Oordered__ab__group__add(X13074))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__le__iff])])])])). 4.46/4.71 fof(c_0_7994, plain, ![X7098, X7099, X7100, X7101, X7103, X7104, X7105, X7106, X7107]:(((hBOOL(hAPP(hAPP(c_member(X7100),esk207_4(X7098,X7099,X7100,X7101)),X7099))|c_Orderings_Obot__class_Obot(tc_fun(X7101,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7100,tc_fun(X7101,tc_HOL_Obool)),X7099),X7098))&(hAPP(X7098,esk207_4(X7098,X7099,X7100,X7101))!=c_Orderings_Obot__class_Obot(tc_fun(X7101,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X7101,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7100,tc_fun(X7101,tc_HOL_Obool)),X7099),X7098)))&(c_Orderings_Obot__class_Obot(tc_fun(X7106,tc_HOL_Obool))!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7105,tc_fun(X7106,tc_HOL_Obool)),X7104),X7103)|(~hBOOL(hAPP(hAPP(c_member(X7105),X7107),X7104))|hAPP(X7103,X7107)=c_Orderings_Obot__class_Obot(tc_fun(X7106,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UNION__empty__conv_I1_J])])])])])])])). 4.46/4.71 fof(c_0_7995, plain, ![X16854, X16855, X16856]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16856),X16855),X16854))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16856),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X16856),X16855),X16854)),c_Groups_Ozero__class_Ozero(X16856)))|~class_Groups_Oordered__ab__group__add(X16856))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16856),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X16856),X16855),X16854)),c_Groups_Ozero__class_Ozero(X16856)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16856),X16855),X16854))|~class_Groups_Oordered__ab__group__add(X16856))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__iff__diff__le__0])])])])). 4.46/4.71 fof(c_0_7996, plain, ![X6820, X6821, X6822]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6822),hAPP(c_Groups_Ouminus__class_Ouminus(X6822),X6821)),hAPP(c_Groups_Ouminus__class_Ouminus(X6822),X6820)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6822),X6820),X6821))|~class_Groups_Oordered__ab__group__add(X6822))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6822),X6820),X6821))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6822),hAPP(c_Groups_Ouminus__class_Ouminus(X6822),X6821)),hAPP(c_Groups_Ouminus__class_Ouminus(X6822),X6820)))|~class_Groups_Oordered__ab__group__add(X6822))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__less__iff__less])])])])). 4.46/4.71 fof(c_0_7997, plain, ![X13409, X13410, X13411]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13411),hAPP(c_Groups_Ouminus__class_Ouminus(X13411),X13410)),hAPP(c_Groups_Ouminus__class_Ouminus(X13411),X13409)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13411),X13409),X13410))|~class_Lattices_Oboolean__algebra(X13411))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13411),X13409),X13410))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13411),hAPP(c_Groups_Ouminus__class_Ouminus(X13411),X13410)),hAPP(c_Groups_Ouminus__class_Ouminus(X13411),X13409)))|~class_Lattices_Oboolean__algebra(X13411))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff])])])). 4.46/4.71 fof(c_0_7998, plain, ![X1896, X1897, X1898]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1898),c_Groups_Ozero__class_Ozero(X1898)),esk47_3(X1896,X1897,X1898)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1898),X1897),X1896))|~class_Fields_Olinordered__field__inverse__zero(X1898))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1898),esk47_3(X1896,X1897,X1898)),c_Groups_Oone__class_Oone(X1898)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1898),X1897),X1896))|~class_Fields_Olinordered__field__inverse__zero(X1898))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1898),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1898),esk47_3(X1896,X1897,X1898)),X1897)),X1896))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1898),X1897),X1896))|~class_Fields_Olinordered__field__inverse__zero(X1898)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_field__le__mult__one__interval])])])])])). 4.46/4.71 fof(c_0_7999, plain, ![X12636, X12637, X12638]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12638),X12637),hAPP(c_Groups_Ouminus__class_Ouminus(X12638),X12636)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12638),X12636),hAPP(c_Groups_Ouminus__class_Ouminus(X12638),X12637)))|~class_Groups_Oordered__ab__group__add(X12638))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12638),X12636),hAPP(c_Groups_Ouminus__class_Ouminus(X12638),X12637)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12638),X12637),hAPP(c_Groups_Ouminus__class_Ouminus(X12638),X12636)))|~class_Groups_Oordered__ab__group__add(X12638))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__minus__iff])])])])). 4.46/4.71 fof(c_0_8000, plain, ![X13948, X13949, X13950]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13950),X13948),hAPP(c_Groups_Ouminus__class_Ouminus(X13950),X13949)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13950),X13949),hAPP(c_Groups_Ouminus__class_Ouminus(X13950),X13948)))|~class_Groups_Oordered__ab__group__add(X13950))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13950),X13949),hAPP(c_Groups_Ouminus__class_Ouminus(X13950),X13948)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13950),X13948),hAPP(c_Groups_Ouminus__class_Ouminus(X13950),X13949)))|~class_Groups_Oordered__ab__group__add(X13950))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__minus__iff])])])])). 4.46/4.71 fof(c_0_8001, plain, ![X15922, X15923, X15924]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15924),c_Groups_Ozero__class_Ozero(X15924)),esk461_3(X15922,X15923,X15924)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15924),X15923),X15922))|~class_Fields_Olinordered__field(X15924))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15924),X15923),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15924),X15922),esk461_3(X15922,X15923,X15924))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15924),X15923),X15922))|~class_Fields_Olinordered__field(X15924))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_field__le__epsilon])])])])])). 4.46/4.71 fof(c_0_8002, plain, ![X897, X898, X899]:(~class_Groups_Oordered__ab__group__add(X899)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X899),X898),X897))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X899),hAPP(c_Groups_Ouminus__class_Ouminus(X899),X897)),hAPP(c_Groups_Ouminus__class_Ouminus(X899),X898))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__imp__neg__le])])])). 4.46/4.71 fof(c_0_8003, plain, ![X8039, X8040, X8041]:(~class_Rings_Oring__1(X8041)|(~hBOOL(hAPP(hAPP(c_member(X8041),X8040),c_Int_Oring__1__class_OInts(X8041)))|hBOOL(hAPP(hAPP(c_member(X8041),hAPP(hAPP(c_Power_Opower__class_Opower(X8041),X8040),X8039)),c_Int_Oring__1__class_OInts(X8041))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__power])])])). 4.46/4.71 fof(c_0_8004, plain, ![X12253, X12254, X12255, X12256]:(~hBOOL(hAPP(c_List_Olistsp(X12256,X12255),X12254))|(~hBOOL(hAPP(c_List_Olistsp(X12256,X12253),X12254))|hBOOL(hAPP(c_List_Olistsp(X12256,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12256,tc_HOL_Obool)),X12255),X12253)),X12254)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsp__infI])])])). 4.46/4.71 fof(c_0_8005, plain, ![X14915, X14916, X14917, X14918, X14919, X14920]:(((hAPP(X14917,X14916)=c_Option_Ooption_ONone(X14919)|hAPP(X14917,X14916)=hAPP(c_Option_Ooption_OSome(X14919),X14915)|hAPP(c_Option_Ooption_OSome(X14919),X14915)!=hAPP(c_Map_Omap__add(X14920,X14919,X14918,X14917),X14916))&(hAPP(c_Option_Ooption_OSome(X14919),X14915)=hAPP(X14918,X14916)|hAPP(X14917,X14916)=hAPP(c_Option_Ooption_OSome(X14919),X14915)|hAPP(c_Option_Ooption_OSome(X14919),X14915)!=hAPP(c_Map_Omap__add(X14920,X14919,X14918,X14917),X14916)))&((hAPP(X14917,X14916)!=hAPP(c_Option_Ooption_OSome(X14919),X14915)|hAPP(c_Option_Ooption_OSome(X14919),X14915)=hAPP(c_Map_Omap__add(X14920,X14919,X14918,X14917),X14916))&(hAPP(X14917,X14916)!=c_Option_Ooption_ONone(X14919)|hAPP(c_Option_Ooption_OSome(X14919),X14915)!=hAPP(X14918,X14916)|hAPP(c_Option_Ooption_OSome(X14919),X14915)=hAPP(c_Map_Omap__add(X14920,X14919,X14918,X14917),X14916)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__Some__iff])])])). 4.46/4.71 fof(c_0_8006, plain, ![X2226, X2227, X2228, X2229, X2230]:(~class_Orderings_Olinorder(X2230)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2229)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2229,X2230,X2228),X2227),X2226))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2229)),X2226))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_length__insort])])])). 4.46/4.71 fof(c_0_8007, plain, ![X9714, X9715, X9716, X9717]:((~hBOOL(hAPP(hAPP(c_member(X9717),X9716),X9715))|hAPP(hAPP(c_Set_Oinsert(X9717),X9716),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9717,tc_HOL_Obool)),X9715),X9714))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9717,tc_HOL_Obool)),X9715),hAPP(hAPP(c_Set_Oinsert(X9717),X9716),X9714)))&(hBOOL(hAPP(hAPP(c_member(X9717),X9716),X9715))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9717,tc_HOL_Obool)),X9715),X9714)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9717,tc_HOL_Obool)),X9715),hAPP(hAPP(c_Set_Oinsert(X9717),X9716),X9714)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__insert__right])])])). 4.46/4.71 fof(c_0_8008, plain, ![X15078, X15079, X15080, X15081]:(~c_Fun_Oinj__on(X15081,X15080,X15079,X15078)|hAPP(c_Set_Oimage(X15080,X15081,c_Fun_Othe__inv__into(X15081,X15080,X15078,X15079)),hAPP(c_Set_Oimage(X15081,X15080,X15079),X15078))=X15078), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_the__inv__into__onto])])])). 4.46/4.71 fof(c_0_8009, plain, ![X661, X662, X663, X664]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X664),hAPP(hAPP(c_Orderings_Oord__class_Omin(X664),X663),X662)),X661))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X664),X662),X661))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X664),X663),X661)))|~class_Orderings_Olinorder(X664))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X664),X662),X661))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X664),hAPP(hAPP(c_Orderings_Oord__class_Omin(X664),X663),X662)),X661))|~class_Orderings_Olinorder(X664))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X664),X663),X661))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X664),hAPP(hAPP(c_Orderings_Oord__class_Omin(X664),X663),X662)),X661))|~class_Orderings_Olinorder(X664)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__less__iff__disj])])])])). 4.46/4.71 fof(c_0_8010, plain, ![X8233, X8234, X8235, X8236]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8236),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8236),X8235),X8234)),X8233))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8236),X8235),X8233))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8236),X8234),X8233)))|~class_Orderings_Olinorder(X8236))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8236),X8235),X8233))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8236),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8236),X8235),X8234)),X8233))|~class_Orderings_Olinorder(X8236))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8236),X8234),X8233))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8236),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8236),X8235),X8234)),X8233))|~class_Orderings_Olinorder(X8236)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__le__iff__disj])])])])). 4.46/4.71 fof(c_0_8011, plain, ![X16800, X16801, X16802, X16803]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16803),X16802),hAPP(hAPP(c_Orderings_Oord__class_Omax(X16803),X16801),X16800)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16803),X16802),X16800))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16803),X16802),X16801)))|~class_Orderings_Olinorder(X16803))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16803),X16802),X16800))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16803),X16802),hAPP(hAPP(c_Orderings_Oord__class_Omax(X16803),X16801),X16800)))|~class_Orderings_Olinorder(X16803))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16803),X16802),X16801))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16803),X16802),hAPP(hAPP(c_Orderings_Oord__class_Omax(X16803),X16801),X16800)))|~class_Orderings_Olinorder(X16803)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__max__iff__disj])])])])). 4.46/4.71 fof(c_0_8012, plain, ![X10799, X10800, X10801, X10802, X10804]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10802),hAPP(X10800,esk320_4(X10799,X10800,X10801,X10802))),hAPP(X10799,esk320_4(X10799,X10800,X10801,X10802))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10801,X10802)),X10800),X10799))|~class_Orderings_Oord(X10802))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10801,X10802)),X10800),X10799))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10802),hAPP(X10800,X10804)),hAPP(X10799,X10804)))|~class_Orderings_Oord(X10802))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__fun__def])])])])])])). 4.46/4.71 fof(c_0_8013, plain, ![X12242, X12243, X12244, X12245]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12245),X12244),hAPP(hAPP(c_Orderings_Oord__class_Omax(X12245),X12243),X12242)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12245),X12244),X12243))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12245),X12244),X12242)))|~class_Orderings_Olinorder(X12245))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12245),X12244),X12243))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12245),X12244),hAPP(hAPP(c_Orderings_Oord__class_Omax(X12245),X12243),X12242)))|~class_Orderings_Olinorder(X12245))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12245),X12244),X12242))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12245),X12244),hAPP(hAPP(c_Orderings_Oord__class_Omax(X12245),X12243),X12242)))|~class_Orderings_Olinorder(X12245)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__max__iff__disj])])])])). 4.46/4.71 fof(c_0_8014, plain, ![X13144, X13145, X13146]:(~class_Groups_Oordered__ab__group__add(X13146)|hAPP(c_Set_Oimage(X13146,X13146,c_Groups_Ouminus__class_Ouminus(X13146)),c_SetInterval_Oord__class_OgreaterThanAtMost(X13146,X13145,X13144))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X13146,hAPP(c_Groups_Ouminus__class_Ouminus(X13146),X13144)),hAPP(c_Groups_Ouminus__class_Ouminus(X13146),X13145))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanAtMost])])). 4.46/4.71 fof(c_0_8015, plain, ![X8097, X8098, X8099, X8100, X8101, X8102, X8103, X8105, X8106, X8107, X8108, X8109, X8110, X8111, X8112]:(((hBOOL(hAPP(hAPP(X8100,X8098),esk231_4(X8097,X8098,X8099,X8100)))|~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X8103,X8102,X8101,X8100,X8099),X8098),X8097)))&(hBOOL(hAPP(hAPP(X8099,esk231_4(X8097,X8098,X8099,X8100)),X8097))|~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X8103,X8102,X8101,X8100,X8099),X8098),X8097))))&(~hBOOL(hAPP(hAPP(X8108,X8106),X8109))|~hBOOL(hAPP(hAPP(X8107,X8109),X8105))|hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X8112,X8111,X8110,X8108,X8107),X8106),X8105)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__comp_Oequations])])])])])])). 4.46/4.71 fof(c_0_8016, plain, ![X17135, X17136, X17137, X17138, X17139]:((X17135=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17139)),X17138)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17139),tc_List_Olist(X17139))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17139),tc_List_Olist(X17139)),X17138),X17137)),hAPP(c_List_Olexn(X17139,X17136),X17135))))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17139)),X17137)=X17135|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17139),tc_List_Olist(X17139))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17139),tc_List_Olist(X17139)),X17138),X17137)),hAPP(c_List_Olexn(X17139,X17136),X17135))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexn__length])])])). 4.46/4.71 fof(c_0_8017, plain, ![X7396, X7397, X7398]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7398,X7398),tc_HOL_Obool)),X7397),X7396))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7398,tc_HOL_Obool)),hAPP(c_Relation_OField(X7398),X7397)),hAPP(c_Relation_OField(X7398),X7396)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mono__Field])])])). 4.46/4.71 fof(c_0_8018, plain, ![X16744, X16745, X16746, X16747, X16748]:(~class_Orderings_Olinorder(X16748)|(~c_List_Olinorder__class_Osorted(X16748,hAPP(hAPP(c_List_Omap(X16747,X16748),X16746),X16745))|c_List_Olinorder__class_Osorted(X16748,hAPP(hAPP(c_List_Omap(X16747,X16748),X16746),hAPP(c_List_Ofilter(X16747,X16744),X16745))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__filter])])])). 4.46/4.71 cnf(c_0_8019, plain, (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2)|esk93_4(X1,X2,X3,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X3),X4),X2))|hAPP(X1,X4)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5222])). 4.46/4.71 fof(c_0_8020, plain, ![X343, X344]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X344))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X343))|hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X344,X343))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X344,X343))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__pos__pos])])])). 4.46/4.71 fof(c_0_8021, plain, ![X14042, X14043, X14044]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X14044,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X14044),X14043)),hAPP(c_SetInterval_Oord__class_OlessThan(X14044),X14042)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14044),X14043),X14042))|~class_Orderings_Olinorder(X14044))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14044),X14043),X14042))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X14044,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X14044),X14043)),hAPP(c_SetInterval_Oord__class_OlessThan(X14044),X14042)))|~class_Orderings_Olinorder(X14044))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lessThan__strict__subset__iff])])])])). 4.46/4.71 fof(c_0_8022, plain, ![X16982, X16983, X16984]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16984,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X16984),X16983)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X16984),X16982)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16984),X16982),X16983))|~class_Orderings_Olinorder(X16984))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16984),X16982),X16983))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16984,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X16984),X16983)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X16984),X16982)))|~class_Orderings_Olinorder(X16984))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_greaterThan__subset__iff])])])])). 4.46/4.71 fof(c_0_8023, plain, ![X13684, X13685, X13686]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13686,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X13686),X13685)),hAPP(c_SetInterval_Oord__class_OlessThan(X13686),X13684)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13686),X13685),X13684))|~class_Orderings_Olinorder(X13686))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13686),X13685),X13684))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13686,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X13686),X13685)),hAPP(c_SetInterval_Oord__class_OlessThan(X13686),X13684)))|~class_Orderings_Olinorder(X13686))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lessThan__subset__iff])])])])). 4.46/4.71 fof(c_0_8024, plain, ![X10583, X10584, X10585]:(~class_Groups_Omonoid__add(X10585)|hAPP(c_List_Omonoid__add__class_Olistsum(X10585),hAPP(hAPP(c_List_Omap(X10584,X10585),hAPP(c_COMBK(X10585,X10584),c_Groups_Ozero__class_Ozero(X10585))),X10583))=c_Groups_Ozero__class_Ozero(X10585)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__0])])). 4.46/4.71 fof(c_0_8025, plain, ![X9621, X9622]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9622),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9621))|hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X9622,X9621))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X9622,X9621))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__pos])])). 4.46/4.71 fof(c_0_8026, plain, ![X14060, X14061, X14062]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14062,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X14062),X14061)),hAPP(c_SetInterval_Oord__class_OatMost(X14062),X14060)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14062),X14061),X14060))|~class_Orderings_Oorder(X14062))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14062),X14061),X14060))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14062,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X14062),X14061)),hAPP(c_SetInterval_Oord__class_OatMost(X14062),X14060)))|~class_Orderings_Oorder(X14062))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atMost__subset__iff])])])])). 4.46/4.71 fof(c_0_8027, plain, ![X1914, X1915, X1916]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1916),X1914),X1915))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1916,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1916),X1915)),hAPP(c_SetInterval_Oord__class_OatLeast(X1916),X1914)))|~class_Orderings_Oorder(X1916))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1916,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1916),X1915)),hAPP(c_SetInterval_Oord__class_OatLeast(X1916),X1914)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1916),X1914),X1915))|~class_Orderings_Oorder(X1916))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__subset__iff])])])). 4.46/4.71 fof(c_0_8028, plain, ![X5544, X5545, X5546]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5546,tc_HOL_Obool)),X5545),X5544))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X5546),tc_HOL_Obool)),c_List_Olistsp(X5546,X5545)),c_List_Olistsp(X5546,X5544)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsp__mono])])])). 4.46/4.71 fof(c_0_8029, plain, ![X11842, X11843, X11844, X11845]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X11845,X11845)),X11844),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X11845,X11845),tc_HOL_Obool),X11843),X11842)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X11845,X11845)),X11844),c_Transitive__Closure_Ortrancl(X11845,X11842)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__pow__imp__rtrancl])])])). 4.46/4.71 cnf(c_0_8030, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_5433])). 4.46/4.71 fof(c_0_8031, plain, ![X2068, X2069, X2070]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2070,tc_HOL_Obool)),X2069),X2068))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X2070),tc_HOL_Obool)),c_List_Olists(X2070,X2069)),c_List_Olists(X2070,X2068)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__mono])])). 4.46/4.71 fof(c_0_8032, plain, ![X16144, X16145]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X16145),X16144))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X16145)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X16144))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X16145)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X16144)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X16145),X16144)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I5_J])])). 4.46/4.71 fof(c_0_8033, plain, ![X514]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X514|hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X514),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__0])])). 4.46/4.71 cnf(c_0_8034, plain, (c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omin(X1),X2),X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5434])). 4.46/4.71 cnf(c_0_8035, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omax(X1),X2),X3)=c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5435])). 4.46/4.71 cnf(c_0_8036, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)=c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_5436])). 4.46/4.71 cnf(c_0_8037, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_5264])). 4.46/4.71 fof(c_0_8038, plain, ![X1305, X1306, X1307, X1308]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1308,tc_HOL_Obool)),X1307),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1308,tc_HOL_Obool)),X1306),X1305)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1308,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1308,tc_HOL_Obool)),X1307),X1306)),X1305)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1308,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1308,tc_HOL_Obool)),X1307),X1306)),X1305))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1308,tc_HOL_Obool)),X1307),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1308,tc_HOL_Obool)),X1306),X1305))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__subset__conv])])). 4.46/4.71 cnf(c_0_8039, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_5297])). 4.46/4.71 fof(c_0_8040, plain, ![X4926, X4927, X4928, X4929, X4930, X4931, X4932]:((~c_List_Olist__all(X4928,X4927,X4926)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4929),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4928)),X4926)))|hBOOL(hAPP(X4927,hAPP(hAPP(c_List_Onth(X4928),X4926),X4929)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk145_3(X4930,X4931,X4932)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4932)),X4930)))|c_List_Olist__all(X4932,X4931,X4930))&(~hBOOL(hAPP(X4931,hAPP(hAPP(c_List_Onth(X4932),X4930),esk145_3(X4930,X4931,X4932))))|c_List_Olist__all(X4932,X4931,X4930)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__length])])])])])])). 4.46/4.71 fof(c_0_8041, plain, ![X4323, X4324, X4325, X4326, X4327, X4328, X4329]:((~hBOOL(hAPP(c_List_Olistsp(X4325,X4324),X4323))|(~hBOOL(hAPP(hAPP(c_member(X4325),X4326),hAPP(c_List_Oset(X4325),X4323)))|hBOOL(hAPP(X4324,X4326))))&((hBOOL(hAPP(hAPP(c_member(X4329),esk120_3(X4327,X4328,X4329)),hAPP(c_List_Oset(X4329),X4327)))|hBOOL(hAPP(c_List_Olistsp(X4329,X4328),X4327)))&(~hBOOL(hAPP(X4328,esk120_3(X4327,X4328,X4329)))|hBOOL(hAPP(c_List_Olistsp(X4329,X4328),X4327))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__listsp__conv__set])])])])])])). 4.46/4.71 cnf(c_0_8042, plain, (X4=X5|hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)!=hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X5)),hAPP(c_List_Oset(X1),X4)))), inference(split_conjunct,[status(thm)],[c_0_5437])). 4.46/4.71 cnf(c_0_8043, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4926])). 4.46/4.71 fof(c_0_8044, plain, ![X7928, X7929, X7930, X7931]:(~hBOOL(hAPP(hAPP(c_member(X7931),X7930),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7931,tc_HOL_Obool)),X7929),X7928)))|(hBOOL(hAPP(hAPP(c_member(X7931),X7930),X7929))|hBOOL(hAPP(hAPP(c_member(X7931),X7930),X7928)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UnE])])])). 4.46/4.71 fof(c_0_8045, plain, ![X3828, X3829, X3830, X3832, X3833, X3834, X3835]:(((hBOOL(hAPP(hAPP(c_member(X3830),esk97_3(X3828,X3829,X3830)),hAPP(c_List_Oset(X3830),X3828)))|hAPP(c_List_Ofilter(X3830,X3829),X3828)=c_List_Olist_ONil(X3830))&(hBOOL(hAPP(X3829,esk97_3(X3828,X3829,X3830)))|hAPP(c_List_Ofilter(X3830,X3829),X3828)=c_List_Olist_ONil(X3830)))&(hAPP(c_List_Ofilter(X3834,X3833),X3832)!=c_List_Olist_ONil(X3834)|(~hBOOL(hAPP(hAPP(c_member(X3834),X3835),hAPP(c_List_Oset(X3834),X3832)))|~hBOOL(hAPP(X3833,X3835))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__empty__conv])])])])])])])). 4.46/4.71 fof(c_0_8046, plain, ![X7108, X7109, X7110]:(~class_Rings_Olinordered__semiring__strict(X7110)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7110),c_Groups_Ozero__class_Ozero(X7110)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7110),X7109),X7108)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7110),c_Groups_Ozero__class_Ozero(X7110)),X7108))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7110),c_Groups_Ozero__class_Ozero(X7110)),X7109))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__mult__pos2])])])). 4.46/4.71 fof(c_0_8047, plain, ![X12010, X12011, X12012]:(~class_Rings_Olinordered__semiring__strict(X12012)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12012),c_Groups_Ozero__class_Ozero(X12012)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12012),X12011),X12010)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12012),c_Groups_Ozero__class_Ozero(X12012)),X12011))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12012),c_Groups_Ozero__class_Ozero(X12012)),X12010))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__mult__pos])])])). 4.46/4.71 fof(c_0_8048, plain, ![X5183, X5184, X5185, X5186, X5187]:(~class_Orderings_Olinorder(X5187)|hAPP(hAPP(c_Set_Oinsert(X5186),X5184),hAPP(c_List_Oset(X5186),X5183))=hAPP(c_List_Oset(X5186),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5186,X5187,X5185),X5184),X5183))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__insort])])). 4.46/4.71 fof(c_0_8049, plain, ![X13745, X13746, X13747]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X13747,X13747),tc_HOL_Obool)),X13746),X13745))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13747,tc_HOL_Obool)),c_Wellfounded_Oacc(X13747,X13745)),c_Wellfounded_Oacc(X13747,X13746)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__subset])])). 4.46/4.71 fof(c_0_8050, plain, ![X2135, X2136, X2137, X2138]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2138),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2137)),X2136)))|hAPP(hAPP(c_List_Onth(X2137),hAPP(hAPP(c_List_Olist__update(X2137,X2136),X2138),X2135)),X2138)=X2135), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update__eq])])). 4.46/4.71 fof(c_0_8051, plain, ![X17276, X17277]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X17277),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X17277),tc_HOL_Obool,X17277),X17276),c_Option_Ooption_OSome(X17277))))|~hBOOL(hAPP(X17276,c_Option_Ooption_ONone(X17277)))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X17277)),X17276))|~class_Enum_Oenum(X17277))&((hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X17277),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X17277),tc_HOL_Obool,X17277),X17276),c_Option_Ooption_OSome(X17277))))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X17277)),X17276))|~class_Enum_Oenum(X17277))&(hBOOL(hAPP(X17276,c_Option_Ooption_ONone(X17277)))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X17277)),X17276))|~class_Enum_Oenum(X17277)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__all__option__def])])])). 4.46/4.71 fof(c_0_8052, plain, ![X17368, X17369, X17370]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17369),X17368))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17370)),X17369)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17370)),X17368))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17370)),X17369)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17370)),X17368)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17369),X17368)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1])])). 4.46/4.71 fof(c_0_8053, plain, ![X4211]:(~class_Rings_Olinordered__semidom(X4211)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4211),c_Groups_Ozero__class_Ozero(X4211)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4211),c_Groups_Oone__class_Oone(X4211)),c_Groups_Oone__class_Oone(X4211))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])])). 4.46/4.71 fof(c_0_8054, plain, ![X9862, X9863, X9864, X9865, X9866, X9867]:((~c_Fun_Oinj__on(X9867,X9863,hAPP(c_Fun_Ocomp(X9866,X9863,X9867,X9862),X9865),X9864)|c_Fun_Oinj__on(X9866,X9863,X9862,hAPP(c_Set_Oimage(X9867,X9866,X9865),X9864))|~c_Fun_Oinj__on(X9867,X9866,X9865,X9864))&(~c_Fun_Oinj__on(X9866,X9863,X9862,hAPP(c_Set_Oimage(X9867,X9866,X9865),X9864))|c_Fun_Oinj__on(X9867,X9863,hAPP(c_Fun_Ocomp(X9866,X9863,X9867,X9862),X9865),X9864)|~c_Fun_Oinj__on(X9867,X9866,X9865,X9864))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comp__inj__on__iff])])])])). 4.46/4.71 cnf(c_0_8055, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_member(X2),X4),X3))|hAPP(c_Nat_OSuc,X1)=hAPP(c_Finite__Set_Ocard(X2),X5)|hAPP(c_Finite__Set_Ocard(X2),X3)!=X1|hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)!=X5), inference(split_conjunct,[status(thm)],[c_0_5438])). 4.46/4.71 fof(c_0_8056, plain, ![X12651, X12652, X12653, X12654]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12654,tc_HOL_Obool)),X12653),X12652))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12654,tc_HOL_Obool)),X12652),X12651))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12654,tc_HOL_Obool)),X12653),X12651)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__trans])])). 4.46/4.71 fof(c_0_8057, plain, ![X17403, X17404, X17405, X17406]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17406,tc_HOL_Obool)),X17405),X17404))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17406,tc_HOL_Obool)),X17404),X17403))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17406,tc_HOL_Obool)),X17405),X17403)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__psubset__trans])])])). 4.46/4.71 fof(c_0_8058, plain, ![X2366, X2367, X2368, X2369]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2369,tc_HOL_Obool)),X2368),X2367))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2369,tc_HOL_Obool)),X2367),X2366))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2369,tc_HOL_Obool)),X2368),X2366)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])])). 4.46/4.71 fof(c_0_8059, plain, ![X7262, X7263, X7264, X7265]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7265,tc_HOL_Obool)),X7264),X7263))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7265,tc_HOL_Obool)),X7263),X7262))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7265,tc_HOL_Obool)),X7264),X7262)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__trans])])])). 4.46/4.71 fof(c_0_8060, plain, ![X6228, X6229]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk191_2(X6228,X6229)),esk192_2(X6228,X6229)))|c_List_Olinorder__class_Osorted(X6229,X6228)|~class_Orderings_Olinorder(X6229))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk192_2(X6228,X6229)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6229)),X6228)))|c_List_Olinorder__class_Osorted(X6229,X6228)|~class_Orderings_Olinorder(X6229))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6229),hAPP(hAPP(c_List_Onth(X6229),X6228),esk191_2(X6228,X6229))),hAPP(hAPP(c_List_Onth(X6229),X6228),esk192_2(X6228,X6229))))|c_List_Olinorder__class_Osorted(X6229,X6228)|~class_Orderings_Olinorder(X6229)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__nth__monoI])])])])])). 4.46/4.71 fof(c_0_8061, plain, ![X16053, X16054, X16055, X16056]:((X16054!=X16053|hAPP(hAPP(c_Set_Oinsert(X16056),X16055),X16054)=hAPP(hAPP(c_Set_Oinsert(X16056),X16055),X16053)|hBOOL(hAPP(hAPP(c_member(X16056),X16055),X16053))|hBOOL(hAPP(hAPP(c_member(X16056),X16055),X16054)))&(hAPP(hAPP(c_Set_Oinsert(X16056),X16055),X16054)!=hAPP(hAPP(c_Set_Oinsert(X16056),X16055),X16053)|X16054=X16053|hBOOL(hAPP(hAPP(c_member(X16056),X16055),X16053))|hBOOL(hAPP(hAPP(c_member(X16056),X16055),X16054)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insert__ident])])])])). 4.46/4.71 fof(c_0_8062, plain, ![X11831, X11832, X11833, X11834, X11835]:(~hBOOL(hAPP(hAPP(c_member(X11835),X11834),X11833))|hAPP(hAPP(c_Set_Oinsert(X11832),hAPP(X11831,X11834)),hAPP(c_Set_Oimage(X11835,X11832,X11831),X11833))=hAPP(c_Set_Oimage(X11835,X11832,X11831),X11833)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__image])])). 4.46/4.71 fof(c_0_8063, plain, ![X5324, X5325, X5326, X5327, X5328, X5329]:(~c_Equiv__Relations_Ocongruent(X5329,X5328,X5327,X5326)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X5329,X5329)),hAPP(hAPP(c_Product__Type_OPair(X5329,X5329),X5325),X5324)),X5327))|hAPP(X5326,X5324)=hAPP(X5326,X5325))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_congruentD])])])). 4.46/4.71 fof(c_0_8064, plain, ![X10236, X10237, X10238, X10239]:((hBOOL(hAPP(X10239,esk294_4(X10236,X10237,X10238,X10239)))|c_Wellfounded_Owf(tc_prod(X10236,X10238),c_Recdef_Osame__fst(X10236,X10238,X10239,X10237)))&(~c_Wellfounded_Owf(X10238,hAPP(X10237,esk294_4(X10236,X10237,X10238,X10239)))|c_Wellfounded_Owf(tc_prod(X10236,X10238),c_Recdef_Osame__fst(X10236,X10238,X10239,X10237)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__same__fst])])])])])). 4.46/4.71 fof(c_0_8065, plain, ![X8377, X8378, X8379, X8381, X8382, X8383, X8384]:(((hBOOL(hAPP(X8378,hAPP(hAPP(c_List_Onth(X8379),X8377),esk236_3(X8377,X8378,X8379))))|~c_List_Olist__ex(X8379,X8378,X8377))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk236_3(X8377,X8378,X8379)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8379)),X8377)))|~c_List_Olist__ex(X8379,X8378,X8377)))&(~hBOOL(hAPP(X8382,hAPP(hAPP(c_List_Onth(X8383),X8381),X8384)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8384),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8383)),X8381)))|c_List_Olist__ex(X8383,X8382,X8381))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__length])])])])])])). 4.46/4.71 fof(c_0_8066, plain, ![X2303, X2304, X2305]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2304),X2303))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2305),hAPP(c_Int_Oring__1__class_Oof__int(X2305),X2304)),hAPP(c_Int_Oring__1__class_Oof__int(X2305),X2303)))|~class_Rings_Olinordered__idom(X2305))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2305),hAPP(c_Int_Oring__1__class_Oof__int(X2305),X2304)),hAPP(c_Int_Oring__1__class_Oof__int(X2305),X2303)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2304),X2303))|~class_Rings_Olinordered__idom(X2305))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__less__iff])])])). 4.46/4.71 fof(c_0_8067, plain, ![X14447, X14448, X14449]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14449),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X14449),X14448)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X14449),X14447)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14448),X14447))|~class_Rings_Olinordered__semidom(X14449))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14448),X14447))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14449),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X14449),X14448)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X14449),X14447)))|~class_Rings_Olinordered__semidom(X14449))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__iff])])])). 4.46/4.71 fof(c_0_8068, plain, ![X11609, X11610, X11611]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11611),hAPP(c_Int_Oring__1__class_Oof__int(X11611),X11610)),hAPP(c_Int_Oring__1__class_Oof__int(X11611),X11609)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11610),X11609))|~class_Rings_Olinordered__idom(X11611))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11610),X11609))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11611),hAPP(c_Int_Oring__1__class_Oof__int(X11611),X11610)),hAPP(c_Int_Oring__1__class_Oof__int(X11611),X11609)))|~class_Rings_Olinordered__idom(X11611))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__le__iff])])])). 4.46/4.71 cnf(c_0_8069, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_5439])). 4.46/4.71 cnf(c_0_8070, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_5440])). 4.46/4.71 cnf(c_0_8071, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_5441])). 4.46/4.71 fof(c_0_8072, plain, ![X9406, X9407, X9408]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9407),X9406))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9408),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X9408),X9407)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X9408),X9406)))|~class_Rings_Olinordered__semidom(X9408))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9408),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X9408),X9407)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X9408),X9406)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9407),X9406))|~class_Rings_Olinordered__semidom(X9408))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__le__iff])])])])). 4.46/4.71 cnf(c_0_8073, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2))=hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5442])). 4.46/4.71 cnf(c_0_8074, plain, (hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5443])). 4.46/4.71 cnf(c_0_8075, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_5444])). 4.46/4.71 fof(c_0_8076, plain, ![X14938, X14939, X14940, X14941, X14942, X14943, X14944]:((~hBOOL(hAPP(hAPP(c_member(X14942),X14943),hAPP(c_List_Oset(X14942),X14938)))|~hBOOL(hAPP(X14941,X14943))|c_List_Opartition(X14942,X14941,X14940)!=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14942),tc_List_Olist(X14942)),X14939),X14938))&(~hBOOL(hAPP(hAPP(c_member(X14942),X14944),hAPP(c_List_Oset(X14942),X14939)))|hBOOL(hAPP(X14941,X14944))|c_List_Opartition(X14942,X14941,X14940)!=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14942),tc_List_Olist(X14942)),X14939),X14938))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_partition__P])])])])])). 4.46/4.71 fof(c_0_8077, plain, ![X16521, X16522, X16523]:(~class_Groups_Oordered__ab__group__add(X16523)|hAPP(c_Set_Oimage(X16523,X16523,c_Groups_Ouminus__class_Ouminus(X16523)),c_SetInterval_Oord__class_OgreaterThanLessThan(X16523,X16522,X16521))=c_SetInterval_Oord__class_OgreaterThanLessThan(X16523,hAPP(c_Groups_Ouminus__class_Ouminus(X16523),X16521),hAPP(c_Groups_Ouminus__class_Ouminus(X16523),X16522))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__uminus__greaterThanLessThan])])])). 4.46/4.71 cnf(c_0_8078, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_5328])). 4.46/4.71 cnf(c_0_8079, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5445])). 4.46/4.71 fof(c_0_8080, plain, ![X17304, X17305, X17306]:(~class_Groups_Oordered__ab__group__add(X17306)|hAPP(c_Set_Oimage(X17306,X17306,c_Groups_Ouminus__class_Ouminus(X17306)),c_SetInterval_Oord__class_OatLeastAtMost(X17306,X17305,X17304))=c_SetInterval_Oord__class_OatLeastAtMost(X17306,hAPP(c_Groups_Ouminus__class_Ouminus(X17306),X17304),hAPP(c_Groups_Ouminus__class_Ouminus(X17306),X17305))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__uminus__atLeastAtMost])])])). 4.46/4.71 fof(c_0_8081, plain, ![X17494, X17495, X17496]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17496,tc_HOL_Obool)),hAPP(c_Relation_OImage(X17496,X17496,X17495),X17494)),X17494))|hAPP(c_Relation_OImage(X17496,X17496,c_Transitive__Closure_Ortrancl(X17496,X17495)),X17494)=X17494), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Image__closed__trancl])])])). 4.46/4.71 fof(c_0_8082, plain, ![X17430, X17431, X17432, X17433, X17434]:((~hBOOL(hAPP(hAPP(c_member(X17434),X17431),X17430))|hBOOL(hAPP(hAPP(c_member(X17433),hAPP(X17432,X17431)),hAPP(c_Set_Oimage(X17434,X17433,X17432),X17430)))|~c_Fun_Oinj__on(X17434,X17433,X17432,c_Orderings_Otop__class_Otop(tc_fun(X17434,tc_HOL_Obool))))&(~hBOOL(hAPP(hAPP(c_member(X17433),hAPP(X17432,X17431)),hAPP(c_Set_Oimage(X17434,X17433,X17432),X17430)))|hBOOL(hAPP(hAPP(c_member(X17434),X17431),X17430))|~c_Fun_Oinj__on(X17434,X17433,X17432,c_Orderings_Otop__class_Otop(tc_fun(X17434,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__mem__iff])])])). 4.46/4.71 cnf(c_0_8083, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5446, c_0_4471])). 4.46/4.71 cnf(c_0_8084, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5447])). 4.46/4.71 fof(c_0_8085, plain, ![X12386, X12387, X12388, X12389, X12390, X12391]:(~hBOOL(hAPP(hAPP(X12391,X12390),X12389))|(~hBOOL(hAPP(hAPP(X12388,X12390),X12389))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12387,tc_fun(X12386,tc_HOL_Obool))),X12391),X12388),X12390),X12389)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf2I])])])). 4.46/4.71 fof(c_0_8086, plain, ![X3928, X3929, X3930, X3931, X3932, X3933]:(~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3933,tc_fun(X3932,tc_HOL_Obool)),X3931),X3930),X3929))|(~hBOOL(hAPP(hAPP(c_member(X3933),X3928),X3931))|hBOOL(hAPP(hAPP(X3930,X3928),X3929)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF1__D])])])). 4.46/4.71 fof(c_0_8087, plain, ![X11223, X11224]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11224))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11224),X11223)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X11224,X11223)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11224),X11223))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__pos__neg__trivial])])])). 4.46/4.71 fof(c_0_8088, plain, ![X14796, X14797, X14798, X14799]:((hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14799)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Olist_ONil(X14798)=hAPP(hAPP(c_List_Otake(X14798),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14799)),hAPP(hAPP(c_List_Olist_OCons(X14798),X14797),X14796)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14799)|hAPP(hAPP(c_List_Olist_OCons(X14798),X14797),hAPP(hAPP(c_List_Otake(X14798),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14799)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X14796))=hAPP(hAPP(c_List_Otake(X14798),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14799)),hAPP(hAPP(c_List_Olist_OCons(X14798),X14797),X14796)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_take__Cons__number__of])])])). 4.46/4.71 fof(c_0_8089, plain, ![X6515, X6516, X6517, X6518]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6518),X6517))|hAPP(hAPP(c_List_Onth(X6516),hAPP(hAPP(c_List_Otake(X6516),X6517),X6515)),X6518)=hAPP(hAPP(c_List_Onth(X6516),X6515),X6518)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__take])])). 4.46/4.71 fof(c_0_8090, plain, ![X12213, X12214, X12215, X12216]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12216,tc_HOL_Obool)),X12214),X12213))|~hBOOL(hAPP(hAPP(c_member(X12216),X12215),X12213))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12216,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X12216),X12215),X12214)),X12213)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12216,tc_HOL_Obool)),X12214),X12213))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12216,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X12216),X12215),X12214)),X12213)))&(hBOOL(hAPP(hAPP(c_member(X12216),X12215),X12213))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12216,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X12216),X12215),X12214)),X12213))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])])). 4.46/4.71 fof(c_0_8091, plain, ![X14509, X14510, X14511]:(~class_Orderings_Olinorder(X14511)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14511),X14510))|c_Big__Operators_Olinorder__class_OMax(X14511,hAPP(hAPP(c_Set_Oinsert(X14511),X14509),X14510))=hAPP(hAPP(c_Finite__Set_Ofold(X14511,X14511,c_Orderings_Oord__class_Omax(X14511)),X14509),X14510))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Oeq__fold__idem_H])])])). 4.46/4.71 fof(c_0_8092, plain, ![X7328, X7329, X7330]:(~class_Orderings_Olinorder(X7330)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7330),X7329))|c_Big__Operators_Olinorder__class_OMin(X7330,hAPP(hAPP(c_Set_Oinsert(X7330),X7328),X7329))=hAPP(hAPP(c_Finite__Set_Ofold(X7330,X7330,c_Orderings_Oord__class_Omin(X7330)),X7328),X7329))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Oeq__fold__idem_H])])])). 4.46/4.71 fof(c_0_8093, plain, ![X13288, X13289, X13290]:(~class_Complete__Lattice_Ocomplete__lattice(X13290)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13290),X13289))|hAPP(hAPP(c_Finite__Set_Ofold(X13290,X13290,c_Lattices_Osemilattice__sup__class_Osup(X13290)),X13288),X13289)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13290),X13288),c_Complete__Lattice_OSup__class_OSup(X13290,X13289)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__Sup__fold__sup])])])). 4.46/4.71 fof(c_0_8094, plain, ![X11431, X11432, X11433]:(~class_Orderings_Olinorder(X11433)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11433),X11432))|(~hBOOL(hAPP(hAPP(c_member(X11433),X11431),X11432))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X11433),X11431),c_Big__Operators_Olattice_OInf__fin(X11433,c_Orderings_Oord__class_Omin(X11433),X11432))=X11431))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__Inf__absorb])])])). 4.46/4.71 fof(c_0_8095, plain, ![X14284, X14285, X14286]:(~class_Groups_Oordered__ab__group__add__abs(X14286)|hAPP(c_Groups_Oabs__class_Oabs(X14286),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X14286),X14284),X14285))=hAPP(c_Groups_Oabs__class_Oabs(X14286),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X14286),X14285),X14284))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__commute])])). 4.46/4.71 fof(c_0_8096, plain, ![X769, X770, X771]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X771,tc_HOL_Obool)),X769),X770))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X771,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X771,tc_HOL_Obool)),X770)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X771,tc_HOL_Obool)),X769))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X771,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X771,tc_HOL_Obool)),X770)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X771,tc_HOL_Obool)),X769)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X771,tc_HOL_Obool)),X769),X770)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__subset__Compl__iff])])). 4.46/4.71 fof(c_0_8097, plain, ![X10175, X10176, X10177, X10178]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10178,tc_HOL_Obool)),X10177),X10176))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10178,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10178),X10175),X10177)),hAPP(hAPP(c_Set_Oinsert(X10178),X10175),X10176)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insert__mono])])])). 4.46/4.71 fof(c_0_8098, plain, ![X13894, X13895]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X13895),X13894)))|(X13894=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13895))))&((X13894!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X13895),X13894))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13895))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X13895),X13894)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])])). 4.46/4.71 fof(c_0_8099, plain, ![X6993, X6994, X6995]:(~class_Orderings_Olinorder(X6995)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6995),X6994))|(~hBOOL(hAPP(hAPP(c_member(X6995),X6993),X6994))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X6995),X6993),c_Big__Operators_Olattice_OSup__fin(X6995,c_Orderings_Oord__class_Omax(X6995),X6994))=X6993))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__Sup__absorb])])])). 4.46/4.71 fof(c_0_8100, plain, ![X17144, X17145, X17146]:(~class_Rings_Oring__1(X17146)|hAPP(hAPP(c_Power_Opower__class_Opower(X17146),hAPP(c_Int_Oring__1__class_Oof__int(X17146),X17145)),X17144)=hAPP(c_Int_Oring__1__class_Oof__int(X17146),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X17145),X17144))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__power])])). 4.46/4.71 cnf(c_0_8101, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),hAPP(X2,X3))),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5448])). 4.46/4.71 fof(c_0_8102, plain, ![X5290, X5291, X5292]:(~class_Rings_Olinordered__idom(X5292)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5292),c_Groups_Ozero__class_Ozero(X5292)),hAPP(hAPP(c_Power_Opower__class_Opower(X5292),hAPP(c_Groups_Oabs__class_Oabs(X5292),X5291)),X5290)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__power__abs])])])). 4.46/4.71 fof(c_0_8103, plain, ![X9742, X9743]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9742))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9743),c_Groups_Ozero__class_Ozero(X9743)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X9743),X9742)))|~class_Rings_Olinordered__semidom(X9743))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9743),c_Groups_Ozero__class_Ozero(X9743)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X9743),X9742)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9742))|~class_Rings_Olinordered__semidom(X9743))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0__less__iff])])])). 4.46/4.71 fof(c_0_8104, plain, ![X3416, X3417, X3418]:(~class_Rings_Osemiring__1(X3418)|hAPP(hAPP(c_Power_Opower__class_Opower(X3418),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3418),X3417)),X3416)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3418),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3417),X3416))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__power])])])). 4.46/4.71 cnf(c_0_8105, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5449])). 4.46/4.71 fof(c_0_8106, plain, ![X6923, X6924, X6925, X6926, X6927, X6928]:((~hBOOL(hAPP(hAPP(X6925,X6927),X6923))|~hBOOL(hAPP(hAPP(X6926,X6924),X6927))|hBOOL(hAPP(hAPP(c_member(X6928),X6927),c_SetInterval_Oord_OatLeastLessThan(X6928,X6926,X6925,X6924,X6923))))&((hBOOL(hAPP(hAPP(X6925,X6927),X6923))|~hBOOL(hAPP(hAPP(c_member(X6928),X6927),c_SetInterval_Oord_OatLeastLessThan(X6928,X6926,X6925,X6924,X6923))))&(hBOOL(hAPP(hAPP(X6926,X6924),X6927))|~hBOOL(hAPP(hAPP(c_member(X6928),X6927),c_SetInterval_Oord_OatLeastLessThan(X6928,X6926,X6925,X6924,X6923)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastLessThan__iff])])])). 4.46/4.71 fof(c_0_8107, plain, ![X2844, X2845, X2846, X2847, X2848, X2849]:(((hBOOL(hAPP(hAPP(X2846,X2845),X2848))|~hBOOL(hAPP(hAPP(c_member(X2849),X2848),c_SetInterval_Oord_OgreaterThanAtMost(X2849,X2847,X2846,X2845,X2844))))&(hBOOL(hAPP(hAPP(X2847,X2848),X2844))|~hBOOL(hAPP(hAPP(c_member(X2849),X2848),c_SetInterval_Oord_OgreaterThanAtMost(X2849,X2847,X2846,X2845,X2844)))))&(~hBOOL(hAPP(hAPP(X2846,X2845),X2848))|~hBOOL(hAPP(hAPP(X2847,X2848),X2844))|hBOOL(hAPP(hAPP(c_member(X2849),X2848),c_SetInterval_Oord_OgreaterThanAtMost(X2849,X2847,X2846,X2845,X2844))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanAtMost__iff])])])). 4.46/4.71 fof(c_0_8108, plain, ![X13215, X13216, X13217, X13218, X13219, X13220, X13221]:((hAPP(c_List_Ofilter(X13217,X13216),X13215)!=X13215|(~hBOOL(hAPP(hAPP(c_member(X13217),X13218),hAPP(c_List_Oset(X13217),X13215)))|hBOOL(hAPP(X13216,X13218))))&((hBOOL(hAPP(hAPP(c_member(X13221),esk386_3(X13219,X13220,X13221)),hAPP(c_List_Oset(X13221),X13219)))|hAPP(c_List_Ofilter(X13221,X13220),X13219)=X13219)&(~hBOOL(hAPP(X13220,esk386_3(X13219,X13220,X13221)))|hAPP(c_List_Ofilter(X13221,X13220),X13219)=X13219))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__id__conv])])])])])])])). 4.46/4.71 fof(c_0_8109, plain, ![X7297, X7298, X7299, X7300]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7300,tc_HOL_Obool)),X7299),X7298))|(~hBOOL(hAPP(hAPP(c_member(X7300),X7297),X7299))|hBOOL(hAPP(hAPP(c_member(X7300),X7297),X7298)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_psubsetD])])])). 4.46/4.71 fof(c_0_8110, plain, ![X13325, X13326, X13327]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13327),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13326)),X13325)))|hAPP(hAPP(c_List_Otake(X13326),X13327),X13325)=hAPP(hAPP(c_List_Otake(X13326),X13327),c_List_Obutlast(X13326,X13325))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__butlast])])). 4.46/4.71 fof(c_0_8111, plain, ![X6343, X6344]:(~class_Orderings_Oorder(X6344)|hAPP(hAPP(c_Set_Oinsert(X6344),X6343),c_Orderings_Obot__class_Obot(tc_fun(X6344,tc_HOL_Obool)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6344,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X6344),X6343),c_Orderings_Obot__class_Obot(tc_fun(X6344,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X6344),X6343))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_single__Diff__lessThan])])])). 4.46/4.71 fof(c_0_8112, plain, ![X10642, X10643]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X10643))|c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10643),X10642)),X10643)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__times__mod__eq])])])). 4.46/4.71 cnf(c_0_8113, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|X1=X2|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_5303])). 4.46/4.71 fof(c_0_8114, plain, ![X9248, X9249, X9250]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X9250,tc_HOL_Obool),tc_HOL_Obool)),X9249),X9248))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9250,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X9250,tc_HOL_Obool),X9248)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X9250,tc_HOL_Obool),X9249)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__anti__mono])])). 4.46/4.71 cnf(c_0_8115, plain, (X3=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X4),X1),hAPP(c_List_Oset(X4),c_List_Oreplicate(X4,X3,X2))))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5450])). 4.46/4.71 fof(c_0_8116, plain, ![X10086, X10087, X10088, X10089, X10090]:(~class_Orderings_Olinorder(X10090)|(~hBOOL(hAPP(hAPP(c_member(X10090),hAPP(X10089,X10088)),hAPP(c_Set_Oimage(X10087,X10090,X10089),hAPP(c_List_Oset(X10087),X10086))))|c_List_Olinorder__class_Oinsort__insert__key(X10087,X10090,X10089,X10088,X10086)=X10086)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__insert__key__triv])])])). 4.46/4.71 fof(c_0_8117, plain, ![X4289, X4290, X4291]:(~class_Orderings_Olinorder(X4291)|hAPP(hAPP(c_Set_Oinsert(X4291),X4290),hAPP(c_List_Oset(X4291),X4289))=hAPP(c_List_Oset(X4291),c_List_Olinorder__class_Oinsort__insert__key(X4291,X4291,c_COMBI(X4291),X4290,X4289))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__insort__insert])])). 4.46/4.71 fof(c_0_8118, plain, ![X7251, X7252]:(~class_Groups_Ocomm__monoid__add(X7252)|(~hBOOL(hAPP(c_List_Odistinct(X7252),X7251))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7252,X7252),c_COMBI(X7252)),hAPP(c_List_Oset(X7252),X7251))=hAPP(c_List_Omonoid__add__class_Olistsum(X7252),X7251))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__listsum__conv__Setsum])])])). 4.46/4.71 fof(c_0_8119, plain, ![X11434, X11435, X11436]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X11436,tc_HOL_Obool),tc_HOL_Obool)),X11435),X11434))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11436,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X11436,tc_HOL_Obool),X11435)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X11436,tc_HOL_Obool),X11434)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__mono])])). 4.46/4.71 fof(c_0_8120, plain, ![X7503, X7504, X7505]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7505,tc_fun(X7505,tc_HOL_Obool))),X7504),X7503))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7505,tc_HOL_Obool)),c_Wellfounded_Oaccp(X7505,X7503)),c_Wellfounded_Oaccp(X7505,X7504)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_accp__subset])])])). 4.46/4.71 fof(c_0_8121, plain, ![X8582, X8583, X8584, X8585]:(~class_Orderings_Oorder(X8585)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8585,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X8585,X8584),X8583)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X8585,X8583),X8582))=c_Orderings_Obot__class_Obot(tc_fun(X8585,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I11_J])])])). 4.46/4.71 fof(c_0_8122, plain, ![X7470, X7471, X7472, X7473, X7474]:(hAPP(X7474,X7473)!=hAPP(c_Option_Ooption_OSome(X7472),X7471)|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7470,tc_Option_Ooption(X7472)),X7474),X7473),hAPP(c_Option_Ooption_OSome(X7472),X7471))=X7474), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upd__triv])])). 4.46/4.71 fof(c_0_8123, plain, ![X6053, X6054, X6055]:(~class_Power_Opower(X6055)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6055),X6054),hAPP(hAPP(c_Power_Opower__class_Opower(X6055),X6054),X6053))=hAPP(hAPP(c_Power_Opower__class_Opower(X6055),X6054),hAPP(c_Nat_OSuc,X6053))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__Suc])])])). 4.46/4.71 fof(c_0_8124, plain, ![X4625, X4626]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4626))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4626),hAPP(c_Nat_OSuc,X4625))),X4626))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__less])])). 4.46/4.71 cnf(c_0_8125, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X1)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5451])). 4.46/4.71 fof(c_0_8126, plain, ![X14063, X14064, X14065, X14066]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14066,tc_HOL_Obool)),X14064),hAPP(hAPP(c_Set_Oinsert(X14066),X14065),X14063)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14066,tc_HOL_Obool)),X14064),X14063))|hBOOL(hAPP(hAPP(c_member(X14066),X14065),X14064)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14066,tc_HOL_Obool)),X14064),X14063))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14066,tc_HOL_Obool)),X14064),hAPP(hAPP(c_Set_Oinsert(X14066),X14065),X14063)))|hBOOL(hAPP(hAPP(c_member(X14066),X14065),X14064)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__insert])])])])). 4.46/4.71 cnf(c_0_8127, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_5452])). 4.46/4.71 fof(c_0_8128, plain, ![X6898, X6899, X6900, X6901, X6902, X6903]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X6903,X6902)),hAPP(hAPP(c_Product__Type_OPair(X6903,X6902),X6901),X6900)),hAPP(hAPP(c_Product__Type_OSigma(X6903,X6902),X6899),X6898)))|hBOOL(hAPP(hAPP(c_member(X6903),X6901),X6899))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD1])])). 4.46/4.71 fof(c_0_8129, plain, ![X14906, X14907, X14908]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14908,tc_HOL_Obool)),X14907),X14906))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X14908,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X14908),X14907)),hAPP(c_Set_OPow(X14908),X14906)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Pow__mono])])])). 4.46/4.71 fof(c_0_8130, plain, ![X17595, X17596]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17596),c_Groups_Ozero__class_Ozero(X17596)),X17595))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17596),hAPP(c_Groups_Ouminus__class_Ouminus(X17596),X17595)),c_Groups_Ozero__class_Ozero(X17596)))|~class_Groups_Oordered__ab__group__add(X17596))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17596),hAPP(c_Groups_Ouminus__class_Ouminus(X17596),X17595)),c_Groups_Ozero__class_Ozero(X17596)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17596),c_Groups_Ozero__class_Ozero(X17596)),X17595))|~class_Groups_Oordered__ab__group__add(X17596))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__less__0__iff__less])])])])). 4.46/4.71 fof(c_0_8131, plain, ![X12202, X12203]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12203),hAPP(c_Groups_Ouminus__class_Ouminus(X12203),X12202)),c_Groups_Ozero__class_Ozero(X12203)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12203),c_Groups_Ozero__class_Ozero(X12203)),X12202))|~class_Groups_Oordered__ab__group__add(X12203))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12203),c_Groups_Ozero__class_Ozero(X12203)),X12202))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12203),hAPP(c_Groups_Ouminus__class_Ouminus(X12203),X12202)),c_Groups_Ozero__class_Ozero(X12203)))|~class_Groups_Oordered__ab__group__add(X12203))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__le__0__iff__le])])])])). 4.46/4.71 fof(c_0_8132, plain, ![X3154, X3155, X3156, X3157]:(~class_Orderings_Opreorder(X3157)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3157),X3156),X3155))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3157),X3155),X3154))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3157),X3156),X3154))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__trans])])])). 4.46/4.71 fof(c_0_8133, plain, ![X15692, X15693, X15694, X15695]:(~class_Orderings_Opreorder(X15695)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15695),X15694),X15693))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15695),X15693),X15692))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15695),X15694),X15692))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__le__less__trans])])])). 4.46/4.71 fof(c_0_8134, plain, ![X5032, X5033, X5034]:(~class_Rings_Ocomm__semiring__1(X5034)|hAPP(hAPP(c_Power_Opower__class_Opower(X5034),X5033),hAPP(c_Nat_OSuc,X5032))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5034),X5033),hAPP(hAPP(c_Power_Opower__class_Opower(X5034),X5033),X5032))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J])])])). 4.46/4.71 fof(c_0_8135, plain, ![X10039, X10040, X10041, X10042]:(~class_Orderings_Oorder(X10042)|c_Orderings_Obot__class_Obot(tc_fun(X10042,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10042,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10042,X10041,X10040)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10042,X10040),X10039))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I9_J])])). 4.46/4.71 fof(c_0_8136, plain, ![X2966, X2967, X2968, X2969]:(~class_Orderings_Oorder(X2969)|c_Orderings_Obot__class_Obot(tc_fun(X2969,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2969,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X2969,X2968),X2967)),c_SetInterval_Oord__class_OatLeastAtMost(X2969,X2967,X2966))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I15_J])])])). 4.46/4.71 fof(c_0_8137, plain, ![X14955, X14956, X14957, X14958]:(~class_Orderings_Opreorder(X14958)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14958),X14957),X14956))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14958),X14956),X14955))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14958),X14957),X14955))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__le__trans])])])). 4.46/4.71 fof(c_0_8138, plain, ![X832, X833, X834, X835]:(~class_Orderings_Oorder(X835)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X835),X834),X833))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X835),X832),X834))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X835),X832),X833))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I10_J])])])). 4.46/4.71 fof(c_0_8139, plain, ![X6434, X6435, X6436, X6437]:(~class_Orderings_Oorder(X6437)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6437),X6436),X6435))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6437),X6434),X6436))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6437),X6434),X6435))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I8_J])])])). 4.46/4.71 fof(c_0_8140, plain, ![X2878, X2879, X2880, X2881]:(~class_Orderings_Oorder(X2881)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2881),X2880),X2879))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2881),X2878),X2880))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2881),X2878),X2879))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I7_J])])])). 4.46/4.71 cnf(c_0_8141, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Ozero__class_Ozero(X2)|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_5452])). 4.46/4.71 fof(c_0_8142, plain, ![X4786, X4787]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4787))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4787),X4786)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])])])). 4.46/4.71 fof(c_0_8143, plain, ![X17179, X17180, X17181]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17181),X17179)),X17180))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17181),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17180),X17179))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17181),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17180),X17179)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17181),X17179)),X17180)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])])). 4.46/4.71 fof(c_0_8144, plain, ![X5834, X5835, X5836]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5836),X5835)),X5834))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5836),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5834),X5835))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5836),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5834),X5835)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5836),X5835)),X5834)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])])). 4.46/4.71 fof(c_0_8145, plain, ![X9193, X9194, X9195, X9196]:(~class_Orderings_Opreorder(X9196)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9196),X9195),X9194))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9196),X9194),X9193))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9196),X9195),X9193))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__trans])])])). 4.46/4.71 fof(c_0_8146, plain, ![X6293, X6294, X6295, X6296]:(~class_Orderings_Oorder(X6296)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6296),X6295),X6294))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6296),X6293),X6295))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6296),X6293),X6294))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I6_J])])])). 4.46/4.71 fof(c_0_8147, plain, ![X1513, X1514]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1514),c_Groups_Ozero__class_Ozero(X1514)),hAPP(c_Groups_Ouminus__class_Ouminus(X1514),X1513)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1514),X1513),c_Groups_Ozero__class_Ozero(X1514)))|~class_Groups_Oordered__ab__group__add(X1514))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1514),X1513),c_Groups_Ozero__class_Ozero(X1514)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1514),c_Groups_Ozero__class_Ozero(X1514)),hAPP(c_Groups_Ouminus__class_Ouminus(X1514),X1513)))|~class_Groups_Oordered__ab__group__add(X1514))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less])])])). 4.46/4.71 fof(c_0_8148, plain, ![X12999, X13000]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13000),c_Groups_Ozero__class_Ozero(X13000)),hAPP(c_Groups_Ouminus__class_Ouminus(X13000),X12999)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13000),X12999),c_Groups_Ozero__class_Ozero(X13000)))|~class_Groups_Oordered__ab__group__add(X13000))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13000),X12999),c_Groups_Ozero__class_Ozero(X13000)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13000),c_Groups_Ozero__class_Ozero(X13000)),hAPP(c_Groups_Ouminus__class_Ouminus(X13000),X12999)))|~class_Groups_Oordered__ab__group__add(X13000))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__0__le__iff__le])])])])). 4.46/4.71 cnf(c_0_8149, plain, (c_Fun_Oinj__on(X1,X2,esk170_4(X3,X2,X1,X4),X4)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X4|X4!=hAPP(c_Set_Oimage(X2,X1,X5),X3)), inference(split_conjunct,[status(thm)],[c_0_5259])). 4.46/4.71 cnf(c_0_8150, plain, (hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X3))),X2)=c_List_Oremove1(X1,X3,X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(rw,[status(thm)],[c_0_5453, c_0_5035])). 4.46/4.71 cnf(c_0_8151, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5454])). 4.46/4.71 fof(c_0_8152, plain, ![X7235, X7236, X7237, X7238]:(~class_Lattices_Osemilattice__inf(X7238)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7238),X7237),X7236))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7238),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7238),X7237),X7235)),X7236)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__infI1])])])). 4.46/4.71 fof(c_0_8153, plain, ![X16832, X16833, X16834]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16834),X16832),X16833))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16834),X16833),X16832))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16834),X16833),X16832))|~class_Orderings_Opreorder(X16834))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16834),X16832),X16833))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16834),X16833),X16832))|~class_Orderings_Opreorder(X16834))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16834),X16833),X16832))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16834),X16833),X16832))|~class_Orderings_Opreorder(X16834)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__le__not__le])])])])). 4.46/4.71 fof(c_0_8154, plain, ![X3867, X3868, X3870, X3871]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk100_1(X3867)))|~hBOOL(hAPP(X3867,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3868))))&(hBOOL(hAPP(X3867,esk100_1(X3867)))|~hBOOL(hAPP(X3867,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3868)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3871))|~hBOOL(hAPP(X3870,X3871))|hBOOL(hAPP(X3870,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk101_1(X3870)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I2_J])])])])])])). 4.46/4.71 fof(c_0_8155, plain, ![X10860, X10861, X10862]:(~class_Rings_Odivision__ring(X10862)|(c_Groups_Ozero__class_Ozero(X10862)=X10861|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10862),X10860),X10861)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10862),hAPP(c_Groups_Ouminus__class_Ouminus(X10862),X10860)),hAPP(c_Groups_Ouminus__class_Ouminus(X10862),X10861)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nonzero__minus__divide__divide])])])). 4.46/4.71 fof(c_0_8156, plain, ![X12118, X12119, X12120, X12121]:(~class_Lattices_Osemilattice__inf(X12121)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12121),X12120),X12119))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12121),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12121),X12118),X12120)),X12119)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__infI2])])])). 4.46/4.71 fof(c_0_8157, plain, ![X17516, X17517, X17518, X17519]:(~class_Lattices_Osemilattice__inf(X17519)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17519),X17518),X17517))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17519),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17519),X17518),X17516)),X17517)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI1])])). 4.46/4.71 fof(c_0_8158, plain, ![X5850, X5851, X5852, X5853]:(~class_Lattices_Osemilattice__inf(X5853)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5853),X5852),X5851))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5853),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5853),X5850),X5852)),X5851)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI2])])). 4.46/4.71 fof(c_0_8159, plain, ![X15954, X15955, X15956, X15957]:(~class_Orderings_Oorder(X15957)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15957,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X15957,X15956,X15955)),c_SetInterval_Oord__class_OgreaterThanLessThan(X15957,X15955,X15954))=c_Orderings_Obot__class_Obot(tc_fun(X15957,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I10_J])])). 4.46/4.71 fof(c_0_8160, plain, ![X9409, X9410, X9411, X9412, X9413, X9414]:((hAPP(c_Option_Ooption_OSome(X9413),X9409)=hAPP(X9412,X9410)|hAPP(X9411,X9410)=hAPP(c_Option_Ooption_OSome(X9413),X9409)|hAPP(c_Option_Ooption_OSome(X9413),X9409)!=hAPP(c_Map_Omap__add(X9414,X9413,X9412,X9411),X9410))&(hAPP(X9411,X9410)=c_Option_Ooption_ONone(X9413)|hAPP(X9411,X9410)=hAPP(c_Option_Ooption_OSome(X9413),X9409)|hAPP(c_Option_Ooption_OSome(X9413),X9409)!=hAPP(c_Map_Omap__add(X9414,X9413,X9412,X9411),X9410))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__add__SomeD])])])])). 4.46/4.71 cnf(c_0_8161, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5455, c_0_4471]), c_0_4471])). 4.46/4.71 cnf(c_0_8162, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))|~hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_5372])). 4.46/4.71 fof(c_0_8163, plain, ![X5377, X5378, X5379, X5380]:(~class_Orderings_Oorder(X5380)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5380,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5380,X5379,X5378)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5380,X5378,X5377))=c_Orderings_Obot__class_Obot(tc_fun(X5380,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I12_J])])])). 4.46/4.71 fof(c_0_8164, plain, ![X8792, X8793, X8794, X8795]:(~class_Orderings_Oorder(X8795)|c_Orderings_Obot__class_Obot(tc_fun(X8795,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8795,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X8795,X8794,X8793)),c_SetInterval_Oord__class_OatLeastAtMost(X8795,X8793,X8792))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I13_J])])). 4.46/4.71 fof(c_0_8165, plain, ![X6645, X6646, X6647, X6648]:(~class_Orderings_Oorder(X6648)|c_Orderings_Obot__class_Obot(tc_fun(X6648,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6648,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X6648,X6647,X6646)),c_SetInterval_Oord__class_OgreaterThanAtMost(X6648,X6646,X6645))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I14_J])])])). 4.46/4.71 fof(c_0_8166, plain, ![X13896, X13897, X13898, X13899]:(~class_Orderings_Oorder(X13899)|c_Orderings_Obot__class_Obot(tc_fun(X13899,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13899,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X13899,X13898,X13897)),c_SetInterval_Oord__class_OgreaterThanAtMost(X13899,X13897,X13896))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I16_J])])). 4.46/4.71 cnf(c_0_8167, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_Divides_Odivmod__nat(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5010])). 4.46/4.71 cnf(c_0_8168, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))|X3!=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_5456])). 4.46/4.71 fof(c_0_8169, plain, ![X7000, X7001, X7002, X7003]:(~class_Lattices_Osemilattice__sup(X7003)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7003),X7002),X7001))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7003),X7002),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7003),X7001),X7000))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__supI1])])])). 4.46/4.71 fof(c_0_8170, plain, ![X5776, X5777, X5778, X5779]:(~class_Lattices_Osemilattice__sup(X5779)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5779),X5778),X5777))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5779),X5778),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5779),X5776),X5777))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__supI2])])])). 4.46/4.71 fof(c_0_8171, plain, ![X15120, X15121, X15122, X15123]:(~class_Lattices_Osemilattice__sup(X15123)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15123),X15122),X15121))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15123),X15122),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15123),X15121),X15120))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI1])])). 4.46/4.71 fof(c_0_8172, plain, ![X1540, X1541, X1542, X1543]:(~class_Lattices_Osemilattice__sup(X1543)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1543),X1542),X1541))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1543),X1542),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1543),X1540),X1541))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI2])])). 4.46/4.71 fof(c_0_8173, plain, ![X8707, X8708, X8709]:(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8709)),X8708),c_List_Olists(X8709,c_Wellfounded_Oacc(X8709,X8707))))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8709)),X8708),c_Wellfounded_Oacc(tc_List_Olist(X8709),c_List_Olistrel1(X8709,X8707))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accD])])). 4.46/4.71 fof(c_0_8174, plain, ![X2891, X2892, X2893]:(~class_Rings_Olinordered__idom(X2893)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2893),c_Groups_Osgn__class_Osgn(X2893,X2892)),c_Groups_Osgn__class_Osgn(X2893,X2891))=c_Groups_Osgn__class_Osgn(X2893,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2893),X2892),X2891))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__times])])])). 4.46/4.71 fof(c_0_8175, plain, ![X13929, X13930, X13931]:(~class_Rings_Oring(X13931)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13931),hAPP(c_Groups_Ouminus__class_Ouminus(X13931),X13930)),hAPP(c_Groups_Ouminus__class_Ouminus(X13931),X13929))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13931),X13930),X13929)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__mult__minus])])])). 4.46/4.71 cnf(c_0_8176, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Set_OPow(X1),X2)))|~hBOOL(hAPP(c_Predicate_OPowp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_5399])). 4.46/4.71 fof(c_0_8177, plain, ![X11820, X11821, X11822, X11823]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X11823)|X11821=hAPP(hAPP(c_List_Onth(X11822),hAPP(hAPP(c_List_Olist_OCons(X11822),X11821),X11820)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X11823)))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X11823)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Onth(X11822),X11820),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X11823)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_List_Onth(X11822),hAPP(hAPP(c_List_Olist_OCons(X11822),X11821),X11820)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X11823)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__Cons__number__of])])). 4.46/4.71 fof(c_0_8178, plain, ![X7133, X7134, X7135]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7135,tc_HOL_Obool)),X7134),X7133))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X7135,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X7135,X7134)),c_Predicate_OPowp(X7135,X7133)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Powp__mono])])])). 4.46/4.71 fof(c_0_8179, plain, ![X3437, X3438, X3439, X3440, X3441]:(~class_Orderings_Olinorder(X3441)|(~c_List_Olinorder__class_Osorted(X3441,hAPP(hAPP(c_List_Omap(X3440,X3441),X3439),X3438))|c_List_Olinorder__class_Osorted(X3441,hAPP(hAPP(c_List_Omap(X3440,X3441),X3439),c_List_Oremove1(X3440,X3437,X3438))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__map__remove1])])])). 4.46/4.71 fof(c_0_8180, plain, ![X12344, X12345, X12346, X12347]:(((hBOOL(hAPP(c_List_Olistsp(X12347,X12346),X12345))|~hBOOL(hAPP(c_List_Olistsp(X12347,X12346),hAPP(hAPP(c_List_Oappend(X12347),X12345),X12344))))&(hBOOL(hAPP(c_List_Olistsp(X12347,X12346),X12344))|~hBOOL(hAPP(c_List_Olistsp(X12347,X12346),hAPP(hAPP(c_List_Oappend(X12347),X12345),X12344)))))&(~hBOOL(hAPP(c_List_Olistsp(X12347,X12346),X12345))|~hBOOL(hAPP(c_List_Olistsp(X12347,X12346),X12344))|hBOOL(hAPP(c_List_Olistsp(X12347,X12346),hAPP(hAPP(c_List_Oappend(X12347),X12345),X12344))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__listsp__conv])])])). 4.46/4.71 fof(c_0_8181, plain, ![X14033, X14034, X14035]:(~class_Fields_Ofield__inverse__zero(X14035)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14035),hAPP(c_Groups_Ouminus__class_Ouminus(X14035),X14034)),hAPP(c_Groups_Ouminus__class_Ouminus(X14035),X14033))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14035),X14034),X14033)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__divide__divide])])])). 4.46/4.71 fof(c_0_8182, plain, ![X13520, X13521, X13523, X13524, X13525]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk397_2(X13520,X13521)),X13520))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X13521|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13521),hAPP(c_Nat_OSuc,X13520))))&(hAPP(c_Nat_OSuc,esk397_2(X13520,X13521))=X13521|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X13521|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13521),hAPP(c_Nat_OSuc,X13520)))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X13524|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13524),hAPP(c_Nat_OSuc,X13523))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13525),X13523))|hAPP(c_Nat_OSuc,X13525)!=X13524|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13524),hAPP(c_Nat_OSuc,X13523)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__0__disj])])])])])])). 4.46/4.71 cnf(c_0_8183, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2))=hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5457])). 4.46/4.71 cnf(c_0_8184, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_5352])). 4.46/4.71 fof(c_0_8185, plain, ![X14720, X14721, X14722]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14722),X14721))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14721),X14720))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14722),X14720)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])])). 4.46/4.71 fof(c_0_8186, plain, ![X15881, X15882, X15883]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15883),X15882))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15882),X15881))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15883),X15881)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zle__trans])])])). 4.46/4.71 fof(c_0_8187, plain, ![X10616, X10617, X10618]:(~class_Rings_Odivision__ring(X10618)|(X10617=c_Groups_Ozero__class_Ozero(X10618)|hAPP(c_Groups_Ouminus__class_Ouminus(X10618),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10618),X10616),X10617))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10618),X10616),hAPP(c_Groups_Ouminus__class_Ouminus(X10618),X10617)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nonzero__minus__divide__right])])])). 4.46/4.71 fof(c_0_8188, plain, ![X13916, X13917]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13916),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13917),hAPP(c_Int_Oring__1__class_Oof__int(X13917),X13916)),c_Groups_Ozero__class_Ozero(X13917)))|~class_Rings_Olinordered__idom(X13917))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13917),hAPP(c_Int_Oring__1__class_Oof__int(X13917),X13916)),c_Groups_Ozero__class_Ozero(X13917)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13916),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X13917))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__less__0__iff])])])])). 4.46/4.71 fof(c_0_8189, plain, ![X6507, X6508]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6507),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6508),hAPP(c_Int_Oring__1__class_Oof__int(X6508),X6507)),c_Groups_Ozero__class_Ozero(X6508)))|~class_Rings_Olinordered__idom(X6508))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6508),hAPP(c_Int_Oring__1__class_Oof__int(X6508),X6507)),c_Groups_Ozero__class_Ozero(X6508)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6507),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X6508))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__le__0__iff])])])])). 4.46/4.71 fof(c_0_8190, plain, ![X14039, X14040]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14039))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14040),c_Groups_Ozero__class_Ozero(X14040)),hAPP(c_Int_Oring__1__class_Oof__int(X14040),X14039)))|~class_Rings_Olinordered__idom(X14040))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14040),c_Groups_Ozero__class_Ozero(X14040)),hAPP(c_Int_Oring__1__class_Oof__int(X14040),X14039)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14039))|~class_Rings_Olinordered__idom(X14040))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__0__less__iff])])])])). 4.46/4.71 fof(c_0_8191, plain, ![X7773, X7774]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7774),c_Groups_Ozero__class_Ozero(X7774)),hAPP(c_Int_Oring__1__class_Oof__int(X7774),X7773)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7773))|~class_Rings_Olinordered__idom(X7774))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7773))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7774),c_Groups_Ozero__class_Ozero(X7774)),hAPP(c_Int_Oring__1__class_Oof__int(X7774),X7773)))|~class_Rings_Olinordered__idom(X7774))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__0__le__iff])])])])). 4.46/4.71 fof(c_0_8192, plain, ![X12621, X12622]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12622),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12621,X12622)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__sign])])). 4.46/4.71 fof(c_0_8193, plain, ![X9727, X9728, X9729, X9731, X9732, X9733, X9734]:(((hBOOL(hAPP(hAPP(c_member(X9729),esk277_3(X9727,X9728,X9729)),hAPP(c_List_Oset(X9729),X9727)))|X9727=c_List_OtakeWhile(X9729,X9728,X9727))&(~hBOOL(hAPP(X9728,esk277_3(X9727,X9728,X9729)))|X9727=c_List_OtakeWhile(X9729,X9728,X9727)))&(X9731!=c_List_OtakeWhile(X9733,X9732,X9731)|(~hBOOL(hAPP(hAPP(c_member(X9733),X9734),hAPP(c_List_Oset(X9733),X9731)))|hBOOL(hAPP(X9732,X9734))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__eq__all__conv])])])])])])). 4.46/4.71 cnf(c_0_8194, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk92_3(X2,X3,X1)),X3))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_5222])). 4.46/4.71 fof(c_0_8195, plain, ![X9373, X9374, X9375, X9376]:((~hBOOL(hAPP(X9376,X9375))|c_List_OtakeWhile(X9374,X9376,hAPP(hAPP(c_List_Olist_OCons(X9374),X9375),X9373))=hAPP(hAPP(c_List_Olist_OCons(X9374),X9375),c_List_OtakeWhile(X9374,X9376,X9373)))&(hBOOL(hAPP(X9376,X9375))|c_List_Olist_ONil(X9374)=c_List_OtakeWhile(X9374,X9376,hAPP(hAPP(c_List_Olist_OCons(X9374),X9375),X9373)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile_Osimps_I2_J])])])). 4.46/4.71 cnf(c_0_8196, plain, (X3=c_List_Olist_ONil(X1)|c_List_Oconcat(X1,X2)!=c_List_Olist_ONil(X1)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))), inference(split_conjunct,[status(thm)],[c_0_5204])). 4.46/4.71 fof(c_0_8197, plain, ![X13437, X13438]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13438))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X13437,X13438)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__sign])])). 4.46/4.71 fof(c_0_8198, plain, ![X16751, X16752, X16753, X16754]:(~hBOOL(hAPP(hAPP(c_member(X16754),X16753),X16752))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16754,tc_HOL_Obool)),X16751),X16752)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16754,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X16754),X16753),X16751)),X16752)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insert__Diff1])])])). 4.46/4.71 fof(c_0_8199, plain, ![X1720, X1721]:(~class_Rings_Oring__1(X1721)|(~hBOOL(hAPP(hAPP(c_member(X1721),X1720),c_Int_Oring__1__class_OInts(X1721)))|hBOOL(hAPP(hAPP(c_member(X1721),hAPP(c_Groups_Ouminus__class_Ouminus(X1721),X1720)),c_Int_Oring__1__class_OInts(X1721))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__minus])])])). 4.46/4.71 cnf(c_0_8200, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1))=c_Divides_OnegDivAlg(X2,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_4528])). 4.46/4.71 fof(c_0_8201, plain, ![X5311, X5312]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5312),X5311))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5312,X5311)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5312),X5311),X5311)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__geq])])])). 4.46/4.71 fof(c_0_8202, plain, ![X2297, X2298, X2299]:(~class_Rings_Olinordered__idom(X2299)|(X2297=X2298|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2299),X2298),X2297))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2299),X2297),X2298))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom])])])). 4.46/4.71 cnf(c_0_8203, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))), inference(rw,[status(thm)],[c_0_5458, c_0_4471])). 4.46/4.71 cnf(c_0_8204, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))), inference(rw,[status(thm)],[c_0_5459, c_0_4471])). 4.46/4.71 cnf(c_0_8205, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OPls))), inference(rw,[status(thm)],[c_0_5460, c_0_4471])). 4.46/4.71 cnf(c_0_8206, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OPls))), inference(rw,[status(thm)],[c_0_5461, c_0_4471])). 4.46/4.71 fof(c_0_8207, plain, ![X4389, X4390]:(~class_Rings_Olinordered__idom(X4390)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4390),X4389),X4389)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4390),hAPP(c_Groups_Oabs__class_Oabs(X4390),X4389)),hAPP(c_Groups_Oabs__class_Oabs(X4390),X4389))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__mult__self])])])). 4.46/4.71 cnf(c_0_8208, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))), inference(rw,[status(thm)],[c_0_5462, c_0_4471])). 4.46/4.71 cnf(c_0_8209, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))))), inference(rw,[status(thm)],[c_0_5463, c_0_4471])). 4.46/4.71 cnf(c_0_8210, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))), inference(rw,[status(thm)],[c_0_5464, c_0_4471])). 4.46/4.71 cnf(c_0_8211, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))), inference(rw,[status(thm)],[c_0_5465, c_0_4471])). 4.46/4.71 fof(c_0_8212, plain, ![X9916, X9917, X9918, X9919, X9920, X9921, X9922]:(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X9922,tc_Option_Ooption(X9921)),X9917),X9919),hAPP(c_Option_Ooption_OSome(X9921),X9916))!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X9922,tc_Option_Ooption(X9921)),X9920),X9919),hAPP(c_Option_Ooption_OSome(X9921),X9918))|X9916=X9918), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__upd__eqD1])])])). 4.46/4.71 cnf(c_0_8213, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))), inference(rw,[status(thm)],[c_0_5466, c_0_4471])). 4.46/4.71 cnf(c_0_8214, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))), inference(rw,[status(thm)],[c_0_5467, c_0_4471])). 4.46/4.71 cnf(c_0_8215, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))), inference(rw,[status(thm)],[c_0_5468, c_0_4471])). 4.46/4.71 fof(c_0_8216, plain, ![X7626, X7627, X7628]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7628))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7628),X7627)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7628),X7626))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7627),X7626))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7628),X7627)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7628),X7626)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7628))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7627),X7626))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7628),X7627)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7628),X7626))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])])). 4.46/4.71 fof(c_0_8217, plain, ![X11666, X11667, X11668, X11669, X11670, X11671, X11672]:((~c_List_Olist__all2(X11672,X11670,X11668,X11671,X11669)|~c_List_Olist__all2(X11672,X11670,X11668,X11667,X11666)|c_List_Olist__all2(X11672,X11670,X11668,hAPP(hAPP(c_List_Oappend(X11672),X11671),X11667),hAPP(hAPP(c_List_Oappend(X11670),X11669),X11666))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11670)),X11669)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11672)),X11671))&((c_List_Olist__all2(X11672,X11670,X11668,X11671,X11669)|~c_List_Olist__all2(X11672,X11670,X11668,hAPP(hAPP(c_List_Oappend(X11672),X11671),X11667),hAPP(hAPP(c_List_Oappend(X11670),X11669),X11666))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11670)),X11669)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11672)),X11671))&(c_List_Olist__all2(X11672,X11670,X11668,X11667,X11666)|~c_List_Olist__all2(X11672,X11670,X11668,hAPP(hAPP(c_List_Oappend(X11672),X11671),X11667),hAPP(hAPP(c_List_Oappend(X11670),X11669),X11666))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11670)),X11669)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11672)),X11671)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2__append])])])])). 4.46/4.71 fof(c_0_8218, plain, ![X16722, X16723, X16724, X16725, X16726]:(~c_Fun_Oinj__on(X16726,X16725,X16724,X16723)|(~c_Fun_Oinj__on(X16726,X16725,X16724,X16722)|c_Fun_Oinj__on(X16726,X16725,X16724,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16726,tc_HOL_Obool)),X16723),X16722)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__Int])])])). 4.46/4.71 fof(c_0_8219, plain, ![X448, X449, X450, X451, X452, X453, X454]:((~c_List_Olist__all(X450,X448,X449)|(~hBOOL(hAPP(hAPP(c_member(X450),X451),hAPP(c_List_Oset(X450),X449)))|hBOOL(hAPP(X448,X451))))&((hBOOL(hAPP(hAPP(c_member(X454),esk6_3(X452,X453,X454)),hAPP(c_List_Oset(X454),X453)))|c_List_Olist__all(X454,X452,X453))&(~hBOOL(hAPP(X452,esk6_3(X452,X453,X454)))|c_List_Olist__all(X454,X452,X453)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ball__set__list__all])])])])])])). 4.46/4.71 cnf(c_0_8220, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_5272])). 4.46/4.71 cnf(c_0_8221, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_5272])). 4.46/4.71 fof(c_0_8222, plain, ![X15676]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15676),c_Orderings_Otop__class_Otop(tc_fun(X15676,tc_HOL_Obool))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X15676),c_Orderings_Otop__class_Otop(tc_fun(X15676,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0])])). 4.46/4.71 fof(c_0_8223, plain, ![X17234, X17235, X17236, X17237, X17238, X17239, X17240]:((~c_List_Olist__all(X17236,X17235,X17234)|(~hBOOL(hAPP(hAPP(c_member(X17236),X17237),hAPP(c_List_Oset(X17236),X17234)))|hBOOL(hAPP(X17235,X17237))))&((hBOOL(hAPP(hAPP(c_member(X17240),esk517_3(X17238,X17239,X17240)),hAPP(c_List_Oset(X17240),X17238)))|c_List_Olist__all(X17240,X17239,X17238))&(~hBOOL(hAPP(X17239,esk517_3(X17238,X17239,X17240)))|c_List_Olist__all(X17240,X17239,X17238)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all__iff])])])])])])])). 4.46/4.71 fof(c_0_8224, plain, ![X9664, X9665, X9666, X9667]:(~hBOOL(hAPP(c_List_Odistinct(X9667),X9666))|hBOOL(hAPP(c_List_Odistinct(tc_prod(X9667,X9665)),hAPP(hAPP(c_List_Ozip(X9667,X9665),X9666),X9664)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__zipI1])])). 4.46/4.71 fof(c_0_8225, plain, ![X8675, X8676, X8677, X8678]:(~hBOOL(hAPP(c_List_Odistinct(X8678),X8677))|hBOOL(hAPP(c_List_Odistinct(tc_prod(X8676,X8678)),hAPP(hAPP(c_List_Ozip(X8676,X8678),X8675),X8677)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__zipI2])])])). 4.46/4.71 fof(c_0_8226, plain, ![X4104, X4105, X4106]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4106),esk113_3(X4104,X4105,X4106)))|hBOOL(hAPP(X4104,X4105))|~hBOOL(hAPP(X4104,c_Orderings_Obot__class_Obot(tc_fun(X4106,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4106),X4105)))&((~hBOOL(hAPP(hAPP(c_member(X4106),esk112_3(X4104,X4105,X4106)),esk113_3(X4104,X4105,X4106)))|hBOOL(hAPP(X4104,X4105))|~hBOOL(hAPP(X4104,c_Orderings_Obot__class_Obot(tc_fun(X4106,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4106),X4105)))&((hBOOL(hAPP(X4104,esk113_3(X4104,X4105,X4106)))|hBOOL(hAPP(X4104,X4105))|~hBOOL(hAPP(X4104,c_Orderings_Obot__class_Obot(tc_fun(X4106,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4106),X4105)))&(~hBOOL(hAPP(X4104,hAPP(hAPP(c_Set_Oinsert(X4106),esk112_3(X4104,X4105,X4106)),esk113_3(X4104,X4105,X4106))))|hBOOL(hAPP(X4104,X4105))|~hBOOL(hAPP(X4104,c_Orderings_Obot__class_Obot(tc_fun(X4106,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4106),X4105)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__induct])])])])])). 4.46/4.71 fof(c_0_8227, plain, ![X8861, X8862, X8863, X8865, X8866, X8867, X8868]:(((hBOOL(hAPP(hAPP(c_member(X8863),esk252_3(X8861,X8862,X8863)),hAPP(c_List_Oset(X8863),X8861)))|c_List_Olist__all(X8863,X8862,X8861))&(~hBOOL(hAPP(X8862,esk252_3(X8861,X8862,X8863)))|c_List_Olist__all(X8863,X8862,X8861)))&(~c_List_Olist__all(X8867,X8866,X8865)|(~hBOOL(hAPP(hAPP(c_member(X8867),X8868),hAPP(c_List_Oset(X8867),X8865)))|hBOOL(hAPP(X8866,X8868))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__iff__raw])])])])])])). 4.46/4.71 cnf(c_0_8228, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5449])). 4.46/4.71 fof(c_0_8229, plain, ![X3996, X3997, X3998, X3999, X4000, X4001, X4002, X4003]:(~c_Equiv__Relations_Oequiv(X4003,X4002,X4001)|(~c_Equiv__Relations_Ocongruent2(X4003,X4000,X3999,X4001,X3998,X3997)|(~hBOOL(hAPP(hAPP(c_member(X4003),X3996),X4002))|c_Equiv__Relations_Ocongruent(X4000,X3999,X3998,hAPP(X3997,X3996))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent])])). 4.46/4.71 fof(c_0_8230, plain, ![X3374, X3375, X3376]:((X3375!=X3374|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3376),X3374),X3375))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3376),X3375),X3374))|~class_Orderings_Olinorder(X3376))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3376),X3374),X3375))|X3375=X3374|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3376),X3375),X3374))|~class_Orderings_Olinorder(X3376))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3])])])])). 4.46/4.71 fof(c_0_8231, plain, ![X17503, X17504]:(~class_Orderings_Oorder(X17504)|hAPP(hAPP(c_Set_Oinsert(X17504),X17503),c_Orderings_Obot__class_Obot(tc_fun(X17504,tc_HOL_Obool)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17504,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X17504),X17503)),hAPP(c_SetInterval_Oord__class_OatLeast(X17504),X17503))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atMost__Int__atLeast])])])). 4.46/4.71 fof(c_0_8232, plain, ![X13906, X13907, X13908, X13909, X13910]:(~hBOOL(hAPP(hAPP(c_member(X13910),X13909),X13908))|hBOOL(hAPP(hAPP(c_member(X13907),hAPP(X13906,X13909)),hAPP(c_Set_Oimage(X13910,X13907,X13906),X13908)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])])). 4.46/4.71 fof(c_0_8233, plain, ![X14640, X14641]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X14641),c_Orderings_Otop__class_Otop(tc_fun(X14641,tc_HOL_Obool))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X14641),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X14641,tc_HOL_Obool)),X14640)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14641),X14640)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14641),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X14641,tc_HOL_Obool)),X14640)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X14641),c_Orderings_Otop__class_Otop(tc_fun(X14641,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14641),X14640)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__compl])])])])). 4.46/4.71 fof(c_0_8234, plain, ![X10788, X10789, X10790]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10790),X10789))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10790,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10790,X10790,X10788),X10789)),X10789))|(~c_Fun_Oinj__on(X10790,X10790,X10788,X10789)|hAPP(c_Set_Oimage(X10790,X10790,X10788),X10789)=X10789))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_endo__inj__surj])])])). 4.46/4.71 fof(c_0_8235, plain, ![X3366, X3367, X3368]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3368,X3368),tc_HOL_Obool)),X3367),X3366))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3368,X3368),tc_HOL_Obool)),X3366),c_Transitive__Closure_Ortrancl(X3368,X3367)))|c_Transitive__Closure_Ortrancl(X3368,X3367)=c_Transitive__Closure_Ortrancl(X3368,X3366))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__subset])])])). 4.46/4.71 fof(c_0_8236, plain, ![X4815, X4816, X4817, X4818]:((~c_Fun_Oinj__on(X4818,tc_Option_Ooption(X4817),X4815,c_Map_Odom(X4818,X4817,X4815))|c_Fun_Oinj__on(X4818,tc_Option_Ooption(X4817),c_Map_Omap__add(X4818,X4817,X4816,X4815),c_Map_Odom(X4818,X4817,X4815)))&(~c_Fun_Oinj__on(X4818,tc_Option_Ooption(X4817),c_Map_Omap__add(X4818,X4817,X4816,X4815),c_Map_Odom(X4818,X4817,X4815))|c_Fun_Oinj__on(X4818,tc_Option_Ooption(X4817),X4815,c_Map_Odom(X4818,X4817,X4815)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__map__add__dom])])). 4.46/4.71 fof(c_0_8237, plain, ![X17206, X17207, X17208, X17209, X17210]:((~hBOOL(hAPP(hAPP(X17208,X17209),X17206))|~hBOOL(hAPP(hAPP(X17208,X17207),X17209))|hBOOL(hAPP(hAPP(c_member(X17210),X17209),c_SetInterval_Oord_OatLeastAtMost(X17210,X17208,X17207,X17206))))&((hBOOL(hAPP(hAPP(X17208,X17209),X17206))|~hBOOL(hAPP(hAPP(c_member(X17210),X17209),c_SetInterval_Oord_OatLeastAtMost(X17210,X17208,X17207,X17206))))&(hBOOL(hAPP(hAPP(X17208,X17207),X17209))|~hBOOL(hAPP(hAPP(c_member(X17210),X17209),c_SetInterval_Oord_OatLeastAtMost(X17210,X17208,X17207,X17206)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastAtMost__iff])])])). 4.46/4.71 cnf(c_0_8238, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Oappend(X2),X3),hAPP(hAPP(c_List_Olist_OCons(X2),X4),c_List_Olist_ONil(X2)))=X1|X3!=c_List_Obutlast(X2,X1)|c_List_Olast(X2,X1)!=X4), inference(split_conjunct,[status(thm)],[c_0_5469])). 4.46/4.71 fof(c_0_8239, plain, ![X8858, X8859, X8860]:(~class_Rings_Oring(X8860)|hAPP(c_Groups_Ouminus__class_Ouminus(X8860),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8860),X8859),X8858))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8860),hAPP(c_Groups_Ouminus__class_Ouminus(X8860),X8859)),X8858)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__mult__left])])])). 4.46/4.71 fof(c_0_8240, plain, ![X14512, X14513, X14514]:(~class_Rings_Odivision__ring(X14514)|hAPP(c_Groups_Ouminus__class_Ouminus(X14514),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14514),X14513),X14512))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14514),hAPP(c_Groups_Ouminus__class_Ouminus(X14514),X14513)),X14512)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__divide__left])])])). 4.46/4.71 fof(c_0_8241, plain, ![X16326, X16327, X16328]:(~class_Rings_Oring(X16328)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16328),hAPP(c_Groups_Ouminus__class_Ouminus(X16328),X16327)),X16326)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16328),X16327),hAPP(c_Groups_Ouminus__class_Ouminus(X16328),X16326))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__commute])])). 4.46/4.71 fof(c_0_8242, plain, ![X5966, X5967, X5968, X5969, X5970]:(((hBOOL(hAPP(hAPP(X5968,X5967),X5969))|~hBOOL(hAPP(hAPP(c_member(X5970),X5969),c_SetInterval_Oord_OgreaterThanLessThan(X5970,X5968,X5967,X5966))))&(hBOOL(hAPP(hAPP(X5968,X5969),X5966))|~hBOOL(hAPP(hAPP(c_member(X5970),X5969),c_SetInterval_Oord_OgreaterThanLessThan(X5970,X5968,X5967,X5966)))))&(~hBOOL(hAPP(hAPP(X5968,X5967),X5969))|~hBOOL(hAPP(hAPP(X5968,X5969),X5966))|hBOOL(hAPP(hAPP(c_member(X5970),X5969),c_SetInterval_Oord_OgreaterThanLessThan(X5970,X5968,X5967,X5966))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanLessThan__iff])])])). 4.46/4.71 fof(c_0_8243, plain, ![X6180, X6181, X6182]:(~class_Orderings_Olinorder(X6182)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6182),X6181))|(~hBOOL(hAPP(hAPP(c_member(X6182),X6180),X6181))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X6182),X6180),c_Big__Operators_Olinorder__class_OMax(X6182,X6181))=c_Big__Operators_Olinorder__class_OMax(X6182,X6181)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Oin__idem])])])). 4.46/4.71 fof(c_0_8244, plain, ![X10739, X10740, X10741]:(~hBOOL(hAPP(hAPP(c_member(tc_fun(X10740,tc_HOL_Obool)),X10741),X10739))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10740),X10741))|hBOOL(hAPP(c_Finite__Set_Ofinite(X10740),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10740,tc_HOL_Obool),X10739)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Inter])])])])). 4.46/4.71 fof(c_0_8245, plain, ![X11764, X11765, X11766, X11767]:(~c_Fun_Oinj__on(X11767,X11766,X11765,c_Orderings_Otop__class_Otop(tc_fun(X11767,tc_HOL_Obool)))|hAPP(c_Fun_Othe__inv__into(X11767,X11766,c_Orderings_Otop__class_Otop(tc_fun(X11767,tc_HOL_Obool)),X11765),hAPP(X11765,X11764))=X11764), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__f__f])])). 4.46/4.71 fof(c_0_8246, plain, ![X1537, X1538, X1539]:(~class_Orderings_Olinorder(X1539)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1539),X1538))|(~hBOOL(hAPP(hAPP(c_member(X1539),X1537),X1538))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1539),X1537),c_Big__Operators_Olinorder__class_OMin(X1539,X1538))=c_Big__Operators_Olinorder__class_OMin(X1539,X1538)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Oin__idem])])])). 4.46/4.71 fof(c_0_8247, plain, ![X13328, X13329, X13330]:(~class_Lattices_Olattice(X13330)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13330),X13329))|(~hBOOL(hAPP(hAPP(c_member(X13330),X13328),X13329))|c_Big__Operators_Olattice__class_OInf__fin(X13330,X13329)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X13330),X13328),c_Big__Operators_Olattice__class_OInf__fin(X13330,X13329))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oin__idem])])])). 4.46/4.71 fof(c_0_8248, plain, ![X5837, X5838, X5839]:(~class_Lattices_Olattice(X5839)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5839),X5838))|(~hBOOL(hAPP(hAPP(c_member(X5839),X5837),X5838))|c_Big__Operators_Olattice__class_OSup__fin(X5839,X5838)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5839),X5837),c_Big__Operators_Olattice__class_OSup__fin(X5839,X5838))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oin__idem])])])). 4.46/4.71 cnf(c_0_8249, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk449_2(X2,X1)),X2))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X1),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5470])). 4.46/4.71 cnf(c_0_8250, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5471]), ['final']). 4.46/4.71 fof(c_0_8251, plain, ![X12932, X12933, X12934, X12935, X12936]:(X12935=X12936|hAPP(hAPP(c_List_Onth(X12934),hAPP(hAPP(c_List_Olist__update(X12934,X12933),X12936),X12932)),X12935)=hAPP(hAPP(c_List_Onth(X12934),X12933),X12935)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__list__update__neq])])])). 4.46/4.71 fof(c_0_8252, plain, ![X3561, X3562]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3562),X3561))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3562),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3561))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zless__imp__add1__zle])])])). 4.46/4.71 fof(c_0_8253, plain, ![X15197, X15198]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15198),X15197))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X15198),X15197)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X15198),X15197)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15198),X15197)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__bin__lemma])])). 4.46/4.71 fof(c_0_8254, plain, ![X14774, X14775, X14776]:(~class_Orderings_Olinorder(X14776)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14776),X14775),X14774))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14776),X14774),X14775)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__le__cases])])])). 4.46/4.71 fof(c_0_8255, plain, ![X1766, X1767]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1767)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1766)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1767),X1766)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1767),X1766))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1767)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1766))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I2_J])])). 4.46/4.71 cnf(c_0_8256, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk206_2(X1,X2))=X1|hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1)))), inference(split_conjunct,[status(thm)],[c_0_5472])). 4.46/4.71 fof(c_0_8257, plain, ![X11167, X11168, X11169, X11170]:(~hBOOL(hAPP(hAPP(c_member(X11170),X11169),hAPP(c_List_Oset(X11170),hAPP(hAPP(c_List_Odrop(X11170),X11168),X11167))))|hBOOL(hAPP(hAPP(c_member(X11170),X11169),hAPP(c_List_Oset(X11170),X11167)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__set__dropD])])])). 4.46/4.71 fof(c_0_8258, plain, ![X1317, X1318, X1319, X1320]:(~hBOOL(hAPP(hAPP(c_member(X1320),X1319),hAPP(c_List_Oset(X1320),hAPP(hAPP(c_List_Otake(X1320),X1318),X1317))))|hBOOL(hAPP(hAPP(c_member(X1320),X1319),hAPP(c_List_Oset(X1320),X1317)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__set__takeD])])])). 4.46/4.71 fof(c_0_8259, plain, ![X1021, X1022]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1022),X1021))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1021,X1022)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1021),X1022),X1022)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__mod__geq])])])). 4.46/4.71 fof(c_0_8260, plain, ![X774, X775]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X775))|c_SMT_Oz3div(X774,X775)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X774),X775))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X775))|c_SMT_Oz3div(X774,X775)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X774),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X775))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_z3div__def])])])). 4.46/4.71 fof(c_0_8261, plain, ![X5085, X5086, X5087]:(~class_Rings_Oring(X5087)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5087),X5086),hAPP(c_Groups_Ouminus__class_Ouminus(X5087),X5085))=hAPP(c_Groups_Ouminus__class_Ouminus(X5087),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5087),X5086),X5085))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__right])])). 4.46/4.71 fof(c_0_8262, plain, ![X3855, X3856]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3856),X3855))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3856)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3855))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3856)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3855)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3856),X3855)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I3_J])])). 4.46/4.71 fof(c_0_8263, plain, ![X5609, X5610, X5611]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X5611|hAPP(c_List_Otl(X5610),c_List_Oreplicate(X5610,X5611,X5609))=c_List_Oreplicate(X5610,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5611),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5609)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tl__replicate])])). 4.46/4.71 fof(c_0_8264, plain, ![X2933, X2934, X2935]:(~class_Fields_Ofield__inverse__zero(X2935)|hAPP(c_Groups_Ouminus__class_Ouminus(X2935),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2935),X2934),X2933))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2935),X2934),hAPP(c_Groups_Ouminus__class_Ouminus(X2935),X2933))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__right])])). 4.46/4.71 fof(c_0_8265, plain, ![X17107, X17108]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17108),X17107)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17107),X17108)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17107),X17108))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17108),X17107))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])])). 4.46/4.71 fof(c_0_8266, plain, ![X3566, X3567]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3567),X3566))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3567),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3566),c_Groups_Oone__class_Oone(tc_Int_Oint)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3567),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3566),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3567),X3566)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le])])). 4.46/4.71 cnf(c_0_8267, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5473])). 4.46/4.71 fof(c_0_8268, plain, ![X2426, X2427, X2428]:(c_List_Olist_ONil(X2427)=X2428|hAPP(c_List_Otl(X2427),hAPP(hAPP(c_List_Oappend(X2427),X2428),X2426))=hAPP(hAPP(c_List_Oappend(X2427),hAPP(c_List_Otl(X2427),X2428)),X2426)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tl__append2])])). 4.46/4.71 fof(c_0_8269, plain, ![X14580, X14581, X14582, X14583]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14583,tc_HOL_Obool)),c_Map_Odom(X14583,X14582,X14581)),c_Map_Odom(X14583,X14582,X14580))!=c_Orderings_Obot__class_Obot(tc_fun(X14583,tc_HOL_Obool))|c_Map_Omap__add(X14583,X14582,X14580,X14581)=c_Map_Omap__add(X14583,X14582,X14581,X14580)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__add__comm])])])). 4.46/4.71 fof(c_0_8270, plain, ![X15555, X15556, X15557]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15557)),c_List_OtakeWhile(X15557,X15556,X15555))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15557)),X15555)))|~hBOOL(hAPP(X15556,hAPP(hAPP(c_List_Onth(X15557),X15555),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15557)),c_List_OtakeWhile(X15557,X15556,X15555)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__length__takeWhile])])])). 4.46/4.71 cnf(c_0_8271, plain, (c_Wellfounded_Owf(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X1))))|~class_Orderings_Owellorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5474])). 4.46/4.71 cnf(c_0_8272, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_5429])). 4.46/4.71 fof(c_0_8273, plain, ![X4412, X4413, X4414]:((hBOOL(hAPP(hAPP(c_member(X4414),X4413),esk121_3(X4412,X4413,X4414)))|~hBOOL(hAPP(hAPP(c_member(X4414),X4413),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4414,tc_HOL_Obool),X4412))))&(hBOOL(hAPP(hAPP(c_member(tc_fun(X4414,tc_HOL_Obool)),esk121_3(X4412,X4413,X4414)),X4412))|~hBOOL(hAPP(hAPP(c_member(X4414),X4413),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4414,tc_HOL_Obool),X4412))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UnionE])])])])])). 4.46/4.71 fof(c_0_8274, plain, ![X1237, X1238, X1239, X1240]:(~class_Groups_Oordered__ab__semigroup__add__imp__le(X1240)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1240),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1240),X1239),X1238)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1240),X1237),X1238)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1240),X1239),X1237)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__less__imp__less__right])])])). 4.46/4.71 fof(c_0_8275, plain, ![X2929, X2930, X2931, X2932]:(~class_Groups_Oordered__ab__semigroup__add__imp__le(X2932)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2932),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2932),X2931),X2930)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2932),X2931),X2929)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2932),X2930),X2929)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__less__imp__less__left])])])). 4.46/4.71 cnf(c_0_8276, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5475, c_0_4431])). 4.46/4.71 fof(c_0_8277, plain, ![X13661, X13662]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X13662),X13661))|c_Orderings_Obot__class_Obot(tc_fun(X13662,tc_HOL_Obool))=X13661|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X13662),X13661))))&((hBOOL(hAPP(c_Finite__Set_Ofinite(X13662),X13661))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X13662),X13661))))&(c_Orderings_Obot__class_Obot(tc_fun(X13662,tc_HOL_Obool))!=X13661|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X13662),X13661)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__gt__0__iff])])])). 4.46/4.71 fof(c_0_8278, plain, ![X8952, X8953, X8954, X8955]:(~class_Groups_Oordered__ab__semigroup__add__imp__le(X8955)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8955),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8955),X8954),X8953)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8955),X8954),X8952)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8955),X8953),X8952)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__imp__le__left])])])). 4.46/4.71 cnf(c_0_8279, plain, (X1=c_List_Oembed__list(c_List_Oreturn__list(X1))|~c_List_Onat__list(X1)), inference(split_conjunct,[status(thm)],[c_0_5476])). 4.46/4.71 fof(c_0_8280, plain, ![X531, X532, X533, X534, X535]:(~c_Finite__Set_Ofolding__idem(X535,X534,X533,X532)|hAPP(c_Fun_Ocomp(X534,X534,X534,hAPP(X533,X531)),hAPP(X533,X531))=hAPP(X533,X531)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__idem_Oidem__comp])])])). 4.46/4.71 fof(c_0_8281, plain, ![X1012, X1013, X1014]:(~class_Divides_Oring__div(X1014)|c_Divides_Odiv__class_Omod(X1014,hAPP(c_Groups_Ouminus__class_Ouminus(X1014),X1013),X1012)=c_Divides_Odiv__class_Omod(X1014,hAPP(c_Groups_Ouminus__class_Ouminus(X1014),c_Divides_Odiv__class_Omod(X1014,X1013,X1012)),X1012)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__minus__eq])])])). 4.46/4.71 fof(c_0_8282, plain, ![X10468, X10469, X10470]:(~c_Wellfounded_Owf(X10470,X10469)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X10470,X10470)),hAPP(hAPP(c_Product__Type_OPair(X10470,X10470),hAPP(X10468,hAPP(c_Nat_OSuc,esk305_3(X10468,X10469,X10470)))),hAPP(X10468,esk305_3(X10468,X10469,X10470)))),X10469))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__no__infinite__down__chainE])])])). 4.46/4.71 fof(c_0_8283, plain, ![X2034, X2036, X2037, X2039]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk52_1(X2034)))|hBOOL(hAPP(X2034,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2036))))&(~hBOOL(hAPP(X2034,esk52_1(X2034)))|hBOOL(hAPP(X2034,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2036)))))&(~hBOOL(hAPP(X2037,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk53_1(X2037))))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2039))|hBOOL(hAPP(X2037,X2039))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I1_J])])])])])])). 4.46/4.71 fof(c_0_8284, plain, ![X11016, X11017, X11018, X11019]:((~hBOOL(hAPP(c_List_Olistsp(X11019,X11018),X11016))|~hBOOL(hAPP(X11018,X11017))|hBOOL(hAPP(c_List_Olistsp(X11019,X11018),hAPP(hAPP(c_List_Olist_OCons(X11019),X11017),X11016))))&((hBOOL(hAPP(c_List_Olistsp(X11019,X11018),X11016))|~hBOOL(hAPP(c_List_Olistsp(X11019,X11018),hAPP(hAPP(c_List_Olist_OCons(X11019),X11017),X11016))))&(hBOOL(hAPP(X11018,X11017))|~hBOOL(hAPP(c_List_Olistsp(X11019,X11018),hAPP(hAPP(c_List_Olist_OCons(X11019),X11017),X11016)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp_Oequations_I2_J])])])). 4.46/4.71 fof(c_0_8285, plain, ![X1689, X1690, X1691, X1692]:(~class_Orderings_Olinorder(X1692)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1692),X1691),X1690))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1692),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1692),X1689),X1691)),X1690)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI2])])). 4.46/4.71 fof(c_0_8286, plain, ![X16666, X16667, X16668, X16669]:(~class_Orderings_Olinorder(X16669)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16669),X16668),X16667))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16669),X16668),hAPP(hAPP(c_Orderings_Oord__class_Omax(X16669),X16667),X16666))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oless__supI1])])])). 4.46/4.71 fof(c_0_8287, plain, ![X7780, X7781, X7782, X7783, X7784]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7784),X7783),X7782))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7784),X7781),X7780))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7784),X7781),X7780)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7784),X7783),X7782)|~class_Groups_Oordered__ab__group__add(X7784))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7784),X7781),X7780))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7784),X7783),X7782))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7784),X7781),X7780)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7784),X7783),X7782)|~class_Groups_Oordered__ab__group__add(X7784))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less])])])). 4.46/4.71 fof(c_0_8288, plain, ![X15816, X15817, X15818, X15819, X15820]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15820),X15817),X15816))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15820),X15819),X15818))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15820),X15819),X15818)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15820),X15817),X15816)|~class_Groups_Oordered__ab__group__add(X15820))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15820),X15819),X15818))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15820),X15817),X15816))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15820),X15819),X15818)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15820),X15817),X15816)|~class_Groups_Oordered__ab__group__add(X15820))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__eq__diff__less__eq])])])])). 4.46/4.71 fof(c_0_8289, plain, ![X1753, X1754, X1755, X1756]:(~class_Orderings_Olinorder(X1756)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1756),X1755),X1754))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1756),X1755),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1756),X1753),X1754))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oless__supI2])])])). 4.46/4.71 fof(c_0_8290, plain, ![X6538, X6539, X6540, X6541]:(~class_Orderings_Olinorder(X6541)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6541),X6540),X6539))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6541),X6540),hAPP(hAPP(c_Orderings_Oord__class_Omax(X6541),X6539),X6538))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ole__supI1])])])). 4.46/4.71 fof(c_0_8291, plain, ![X12816, X12817, X12818, X12819]:(~class_Rings_Osemiring__1(X12819)|c_Nat_Osemiring__1__class_Oof__nat__aux(X12819,X12818,X12817,hAPP(X12818,X12816))=c_Nat_Osemiring__1__class_Oof__nat__aux(X12819,X12818,hAPP(c_Nat_OSuc,X12817),X12816)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I2_J])])). 4.46/4.71 fof(c_0_8292, plain, ![X8431, X8432]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8432),c_Orderings_Otop__class_Otop(tc_fun(X8432,tc_HOL_Obool))))|(c_Orderings_Otop__class_Otop(tc_fun(X8432,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X8432,X8432,X8431),c_Orderings_Otop__class_Otop(tc_fun(X8432,tc_HOL_Obool)))|c_Fun_Oinj__on(X8432,X8432,X8431,c_Orderings_Otop__class_Otop(tc_fun(X8432,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__UNIV__surj__inj])])])). 4.46/4.71 fof(c_0_8293, plain, ![X3143, X3144, X3145, X3146, X3147, X3148, X3149]:(hAPP(hAPP(c_List_Omap(X3145,X3148),X3144),X3143)!=hAPP(hAPP(c_List_Omap(X3149,X3148),X3147),X3146)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3145)),X3143)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3149)),X3146)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__eq__imp__length__eq])])])). 4.46/4.71 cnf(c_0_8294, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Ois__nat(X1)), inference(split_conjunct,[status(thm)],[c_0_5404])). 4.46/4.71 cnf(c_0_8295, plain, (c_Nitpick_Onorm__frac(X1,X2)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X1!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_5477])). 4.46/4.71 fof(c_0_8296, plain, ![X13792, X13793, X13794]:((hBOOL(hAPP(hAPP(c_member(X13794),X13792),X13793))|hAPP(c_Finite__Set_Ocard(X13794),hAPP(hAPP(c_Set_Oinsert(X13794),X13792),X13793))=hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X13794),X13793))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13794),X13793)))&(~hBOOL(hAPP(hAPP(c_member(X13794),X13792),X13793))|hAPP(c_Finite__Set_Ocard(X13794),X13793)=hAPP(c_Finite__Set_Ocard(X13794),hAPP(hAPP(c_Set_Oinsert(X13794),X13792),X13793))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13794),X13793)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__insert__if])])])])). 4.46/4.71 cnf(c_0_8297, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X2))), inference(split_conjunct,[status(thm)],[c_0_5478])). 4.46/4.71 fof(c_0_8298, plain, ![X14222, X14223, X14224]:(~class_Complete__Lattice_Ocomplete__lattice(X14224)|c_Complete__Lattice_OInf__class_OInf(X14224,hAPP(hAPP(c_Set_Oinsert(X14224),X14223),hAPP(hAPP(c_Set_Oinsert(X14224),X14222),c_Orderings_Obot__class_Obot(tc_fun(X14224,tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X14224),X14223),X14222)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__binary])])])). 4.46/4.71 fof(c_0_8299, plain, ![X11938, X11939, X11940, X11942, X11943, X11944, X11945]:(((hBOOL(hAPP(hAPP(c_member(X11940),esk352_3(X11938,X11939,X11940)),hAPP(c_List_Oset(X11940),X11938)))|~c_List_Olist__ex(X11940,X11939,X11938))&(hBOOL(hAPP(X11939,esk352_3(X11938,X11939,X11940)))|~c_List_Olist__ex(X11940,X11939,X11938)))&(~hBOOL(hAPP(hAPP(c_member(X11944),X11945),hAPP(c_List_Oset(X11944),X11942)))|~hBOOL(hAPP(X11943,X11945))|c_List_Olist__ex(X11944,X11943,X11942))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__iff])])])])])])). 4.46/4.71 fof(c_0_8300, plain, ![X17536, X17537, X17538]:(~c_Equiv__Relations_Oequiv(X17538,X17537,X17536)|hAPP(hAPP(c_Relation_Orel__comp(X17538,X17538,X17538),hAPP(c_Relation_Oconverse(X17538,X17538),X17536)),X17536)=X17536), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equiv__comp__eq])])])). 4.46/4.71 fof(c_0_8301, plain, ![X10884, X10885]:(~class_Groups_Oordered__ab__group__add(X10885)|hAPP(c_Set_Oimage(X10885,X10885,c_Groups_Ouminus__class_Ouminus(X10885)),hAPP(c_SetInterval_Oord__class_OlessThan(X10885),X10884))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X10885),hAPP(c_Groups_Ouminus__class_Ouminus(X10885),X10884))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__uminus__lessThan])])])). 4.46/4.71 fof(c_0_8302, plain, ![X16209, X16210, X16211]:(~class_Lattices_Oboolean__algebra(X16211)|(c_Orderings_Obot__class_Obot(X16211)!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16211),X16210),X16209)|(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X16211),X16210),X16209)!=c_Orderings_Otop__class_Otop(X16211)|X16209=hAPP(c_Groups_Ouminus__class_Ouminus(X16211),X16210)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_compl__unique])])])). 4.46/4.71 fof(c_0_8303, plain, ![X8476, X8477, X8478]:(~class_Complete__Lattice_Ocomplete__lattice(X8478)|c_Complete__Lattice_OSup__class_OSup(X8478,hAPP(hAPP(c_Set_Oinsert(X8478),X8477),hAPP(hAPP(c_Set_Oinsert(X8478),X8476),c_Orderings_Obot__class_Obot(tc_fun(X8478,tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8478),X8477),X8476)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__binary])])). 4.46/4.71 cnf(c_0_8304, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X2)=hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5479])). 4.46/4.71 fof(c_0_8305, plain, ![X17348, X17349, X17350]:(~class_Lattices_Oab__semigroup__idem__mult(X17350)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17350),X17349),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17350),X17349),X17348))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17350),X17349),X17348)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left__idem])])])). 4.46/4.71 fof(c_0_8306, plain, ![X16066, X16067]:(~class_Groups_Oordered__ab__group__add(X16067)|hAPP(c_Set_Oimage(X16067,X16067,c_Groups_Ouminus__class_Ouminus(X16067)),hAPP(c_SetInterval_Oord__class_OatMost(X16067),X16066))=hAPP(c_SetInterval_Oord__class_OatLeast(X16067),hAPP(c_Groups_Ouminus__class_Ouminus(X16067),X16066))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__uminus__atMost])])])). 4.46/4.71 fof(c_0_8307, plain, ![X6640, X6641]:(~class_Complete__Lattice_Ocomplete__lattice(X6641)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6641),X6640))|hAPP(hAPP(c_Finite__Set_Ofold(X6641,X6641,c_Lattices_Osemilattice__inf__class_Oinf(X6641)),c_Orderings_Otop__class_Otop(X6641)),X6640)=c_Complete__Lattice_OInf__class_OInf(X6641,X6640))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fold__inf])])])). 4.46/4.71 fof(c_0_8308, plain, ![X1010, X1011]:(~class_Complete__Lattice_Ocomplete__lattice(X1011)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1011),X1010))|c_Complete__Lattice_OSup__class_OSup(X1011,X1010)=hAPP(hAPP(c_Finite__Set_Ofold(X1011,X1011,c_Lattices_Osemilattice__sup__class_Osup(X1011)),c_Orderings_Obot__class_Obot(X1011)),X1010))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fold__sup])])])). 4.46/4.71 fof(c_0_8309, plain, ![X10056, X10057, X10058, X10059, X10060, X10061, X10062]:((X10057!=X10056|hAPP(X10059,X10057)=hAPP(X10059,X10056)|~hBOOL(hAPP(hAPP(c_member(X10061),X10056),X10058))|~hBOOL(hAPP(hAPP(c_member(X10061),X10057),X10058))|~c_Typedef_Otype__definition(X10062,X10061,X10060,X10059,X10058))&(hAPP(X10059,X10057)!=hAPP(X10059,X10056)|X10057=X10056|~hBOOL(hAPP(hAPP(c_member(X10061),X10056),X10058))|~hBOOL(hAPP(hAPP(c_member(X10061),X10057),X10058))|~c_Typedef_Otype__definition(X10062,X10061,X10060,X10059,X10058))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_type__definition_OAbs__inject])])])])). 4.46/4.71 fof(c_0_8310, plain, ![X4169, X4170]:(~class_Groups_Oordered__ab__group__add(X4170)|hAPP(c_Set_Oimage(X4170,X4170,c_Groups_Ouminus__class_Ouminus(X4170)),hAPP(c_SetInterval_Oord__class_OatLeast(X4170),X4169))=hAPP(c_SetInterval_Oord__class_OatMost(X4170),hAPP(c_Groups_Ouminus__class_Ouminus(X4170),X4169))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__uminus__atLeast])])])). 4.46/4.71 fof(c_0_8311, plain, ![X2859, X2860, X2861]:(~class_Lattices_Olattice(X2861)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2861),X2860),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2861),X2860),X2859))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2861),X2860),X2859)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I8_J])])). 4.46/4.71 fof(c_0_8312, plain, ![X16086, X16087, X16088]:(~class_Lattices_Olattice(X16088)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16088),X16087),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16088),X16087),X16086))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16088),X16087),X16086)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I4_J])])). 4.46/4.71 fof(c_0_8313, plain, ![X674, X675]:(~class_Groups_Oordered__ab__group__add(X675)|hAPP(c_SetInterval_Oord__class_OlessThan(X675),hAPP(c_Groups_Ouminus__class_Ouminus(X675),X674))=hAPP(c_Set_Oimage(X675,X675,c_Groups_Ouminus__class_Ouminus(X675)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X675),X674))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__uminus__greaterThan])])])). 4.46/4.71 fof(c_0_8314, plain, ![X5925, X5926, X5927]:(~class_Lattices_Osemilattice__sup(X5927)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5927),X5926),X5925)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5927),X5926),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5927),X5926),X5925))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__left__idem])])])). 4.46/4.71 fof(c_0_8315, plain, ![X9849, X9850, X9851]:(~class_Lattices_Osemilattice__inf(X9851)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9851),X9850),X9849)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9851),X9850),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9851),X9850),X9849))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__idem])])). 4.46/4.71 fof(c_0_8316, plain, ![X811, X812]:(~class_Orderings_Olinorder(X812)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X812),X811))|(c_Orderings_Obot__class_Obot(tc_fun(X812,tc_HOL_Obool))=X811|hBOOL(hAPP(hAPP(c_member(X812),c_Big__Operators_Olinorder__class_OMin(X812,X811)),X811))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__in])])). 4.46/4.71 fof(c_0_8317, plain, ![X9551, X9552]:(~class_Orderings_Olinorder(X9552)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9552),X9551))|(X9551=c_Orderings_Obot__class_Obot(tc_fun(X9552,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X9552),c_Big__Operators_Olinorder__class_OMax(X9552,X9551)),X9551))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max__in])])])). 4.46/4.71 fof(c_0_8318, plain, ![X4568, X4569, X4570, X4571]:(~c_Fun_Oinj__on(X4571,X4570,X4569,X4568)|c_Fun_Oinj__on(X4570,X4571,c_Fun_Othe__inv__into(X4571,X4570,X4568,X4569),hAPP(c_Set_Oimage(X4571,X4570,X4569),X4568))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__the__inv__into])])])). 4.46/4.71 fof(c_0_8319, plain, ![X12554, X12555, X12556, X12557]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X12556),X12554))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12557),X12555))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X12557,X12556)),c_Sum__Type_OPlus(X12557,X12556,X12555,X12554))))&((hBOOL(hAPP(c_Finite__Set_Ofinite(X12556),X12554))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X12557,X12556)),c_Sum__Type_OPlus(X12557,X12556,X12555,X12554))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X12557),X12555))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X12557,X12556)),c_Sum__Type_OPlus(X12557,X12556,X12555,X12554)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff])])])). 4.46/4.71 fof(c_0_8320, plain, ![X11136, X11137]:(~class_Rings_Olinordered__idom(X11137)|~class_Int_Onumber__ring(X11137)|c_Groups_Oone__class_Oone(X11137)=hAPP(c_Groups_Oabs__class_Oabs(X11137),hAPP(hAPP(c_Power_Opower__class_Opower(X11137),hAPP(c_Int_Onumber__class_Onumber__of(X11137),c_Int_OMin)),X11136))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__power__minus__one])])])). 4.46/4.71 fof(c_0_8321, plain, ![X6153, X6154, X6155]:(~class_Groups_Ogroup__add(X6155)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6155),X6154),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6155),hAPP(c_Groups_Ouminus__class_Ouminus(X6155),X6154)),X6153))=X6153), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__minus__cancel])])). 4.46/4.71 fof(c_0_8322, plain, ![X7830, X7831, X7832]:(~class_Groups_Ogroup__add(X7832)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7832),hAPP(c_Groups_Ouminus__class_Ouminus(X7832),X7831)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7832),X7831),X7830))=X7830), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__cancel])])). 4.46/4.71 fof(c_0_8323, plain, ![X4203, X4204, X4205, X4206, X4207, X4208]:(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4208,tc_fun(X4207,tc_HOL_Obool))),X4206),X4205),X4204),X4203))|(hBOOL(hAPP(hAPP(X4206,X4204),X4203))|hBOOL(hAPP(hAPP(X4205,X4204),X4203)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup2E])])])). 4.46/4.71 fof(c_0_8324, plain, ![X13468, X13469, X13470, X13471]:(~hBOOL(hAPP(c_List_Odistinct(X13471),X13470))|(~hBOOL(hAPP(c_List_Odistinct(X13469),X13468))|hBOOL(hAPP(c_List_Odistinct(tc_prod(X13471,X13469)),c_Enum_Oproduct(X13471,X13469,X13470,X13468))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__product])])])). 4.46/4.71 fof(c_0_8325, plain, ![X5564, X5565, X5566]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X5566,X5566)),X5565),X5564))|hBOOL(hAPP(hAPP(c_member(tc_prod(X5566,X5566)),X5565),c_Transitive__Closure_Ortrancl(X5566,X5564)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl])])). 4.46/4.71 cnf(c_0_8326, plain, (c_List_Oconcat(X2,X1)=c_List_Olist_ONil(X2)|esk357_2(X1,X2)!=c_List_Olist_ONil(X2)), inference(split_conjunct,[status(thm)],[c_0_5202])). 4.46/4.71 cnf(c_0_8327, plain, (c_List_Oconcat(X2,X1)=c_List_Olist_ONil(X2)|esk195_2(X1,X2)!=c_List_Olist_ONil(X2)), inference(split_conjunct,[status(thm)],[c_0_5204])). 4.46/4.71 fof(c_0_8328, plain, ![X14305, X14306, X14307, X14308, X14309, X14310]:(~c_Fun_Oinj__on(X14310,X14309,hAPP(c_Fun_Ocomp(X14308,X14309,X14310,X14307),X14306),X14305)|c_Fun_Oinj__on(X14308,X14309,X14307,hAPP(c_Set_Oimage(X14310,X14308,X14306),X14305))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__imageI])])])). 4.46/4.71 fof(c_0_8329, plain, ![X6551, X6552, X6553, X6554]:(~c_Finite__Set_Ofun__left__comm__idem(X6554,X6553,X6552)|hAPP(X6552,X6551)=hAPP(c_Fun_Ocomp(X6553,X6553,X6553,hAPP(X6552,X6551)),hAPP(X6552,X6551))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__comp__idem])])). 4.46/4.71 fof(c_0_8330, plain, ![X657, X658]:(X657=X658|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X658),X657))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X657),X658)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat])])])). 4.46/4.71 fof(c_0_8331, plain, ![X798, X799]:(X798=X799|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X798),X799))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X799),X798))), inference(variable_rename,[status(thm)],[fact_zless__linear])). 4.46/4.71 fof(c_0_8332, plain, ![X2647, X2648, X2649, X2650, X2651, X2652]:(~hBOOL(hAPP(hAPP(X2652,X2651),X2650))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2649,tc_fun(X2648,tc_HOL_Obool))),X2652),X2647))|hBOOL(hAPP(hAPP(X2647,X2651),X2650)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rev__predicate2D])])])). 4.46/4.71 fof(c_0_8333, plain, ![X1727, X1728, X1729]:(~class_Divides_Osemiring__div(X1729)|(c_Groups_Ozero__class_Ozero(X1729)=X1728|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1729),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1729),X1728),X1727)),X1728)=X1727)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__id])])). 4.46/4.71 fof(c_0_8334, plain, ![X14001, X14002, X14003]:(~class_Divides_Osemiring__div(X14003)|(c_Groups_Ozero__class_Ozero(X14003)=X14002|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X14003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14003),X14001),X14002)),X14002)=X14001)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__self2__is__id])])])). 4.46/4.71 fof(c_0_8335, plain, ![X10372, X10373]:((hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk301_2(X10372,X10373)),c_Int_OInteg))|hBOOL(hAPP(X10373,X10372)))&(~hBOOL(hAPP(X10373,hAPP(c_Int_OAbs__Integ,esk301_2(X10372,X10373))))|hBOOL(hAPP(X10373,X10372)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Abs__Integ__induct])])])])])). 4.46/4.71 cnf(c_0_8336, plain, (c_Option_Ooption_ONone(X4)=c_Map_Omap__comp(X1,X4,X5,X6,X2,X3)|c_Option_Ooption_ONone(X1)!=hAPP(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_5286])). 4.46/4.71 fof(c_0_8337, plain, ![X17222, X17223]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17223),c_Groups_Ozero__class_Ozero(X17223)),X17222))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17223),hAPP(c_Groups_Ouminus__class_Ouminus(X17223),X17222)),X17222))|~class_Groups_Olinordered__ab__group__add(X17223))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17223),hAPP(c_Groups_Ouminus__class_Ouminus(X17223),X17222)),X17222))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17223),c_Groups_Ozero__class_Ozero(X17223)),X17222))|~class_Groups_Olinordered__ab__group__add(X17223))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg])])])). 4.46/4.71 fof(c_0_8338, plain, ![X11514, X11515]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11515),X11514))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11514),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11515),X11514))=X11515), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__diff__inverse])])])). 4.46/4.71 fof(c_0_8339, plain, ![X849, X850, X851]:(~class_Rings_Olinordered__idom(X851)|hAPP(c_Groups_Oabs__class_Oabs(X851),hAPP(hAPP(c_Power_Opower__class_Opower(X851),X850),X849))=hAPP(hAPP(c_Power_Opower__class_Opower(X851),hAPP(c_Groups_Oabs__class_Oabs(X851),X850)),X849)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__abs])])). 4.46/4.71 fof(c_0_8340, plain, ![X8091, X8092, X8093]:(~class_Groups_Omonoid__add(X8093)|hAPP(c_List_Omonoid__add__class_Olistsum(X8093),hAPP(hAPP(c_List_Olist_OCons(X8093),X8092),X8091))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8093),X8092),hAPP(c_List_Omonoid__add__class_Olistsum(X8093),X8091))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__simps_I2_J])])). 4.46/4.71 fof(c_0_8341, plain, ![X14927, X14928, X14929, X14930]:(~class_Complete__Lattice_Ocomplete__lattice(X14930)|(c_Orderings_Obot__class_Obot(tc_fun(X14928,tc_HOL_Obool))=X14929|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14928,X14930),X14929),hAPP(c_COMBK(X14930,X14928),X14927))=X14927)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF__const])])])). 4.46/4.71 fof(c_0_8342, plain, ![X3428, X3429]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3429),c_Groups_Ozero__class_Ozero(X3429)),X3428))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3429),hAPP(c_Groups_Ouminus__class_Ouminus(X3429),X3428)),X3428))|~class_Groups_Olinordered__ab__group__add(X3429))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3429),hAPP(c_Groups_Ouminus__class_Ouminus(X3429),X3428)),X3428))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3429),c_Groups_Ozero__class_Ozero(X3429)),X3428))|~class_Groups_Olinordered__ab__group__add(X3429))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__le__self__iff])])])])). 4.46/4.71 fof(c_0_8343, plain, ![X1991, X1992]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1992),X1991),hAPP(c_Groups_Ouminus__class_Ouminus(X1992),X1991)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1992),X1991),c_Groups_Ozero__class_Ozero(X1992)))|~class_Rings_Olinordered__idom(X1992))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1992),X1991),c_Groups_Ozero__class_Ozero(X1992)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1992),X1991),hAPP(c_Groups_Ouminus__class_Ouminus(X1992),X1991)))|~class_Rings_Olinordered__idom(X1992))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff])])])). 4.46/4.71 fof(c_0_8344, plain, ![X11458, X11459]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11459),X11458),hAPP(c_Groups_Ouminus__class_Ouminus(X11459),X11458)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11459),X11458),c_Groups_Ozero__class_Ozero(X11459)))|~class_Groups_Olinordered__ab__group__add(X11459))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11459),X11458),c_Groups_Ozero__class_Ozero(X11459)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11459),X11458),hAPP(c_Groups_Ouminus__class_Ouminus(X11459),X11458)))|~class_Groups_Olinordered__ab__group__add(X11459))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__minus__self__iff])])])])). 4.46/4.71 cnf(c_0_8345, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Ozero__class_Ozero(X2)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_5480])). 4.46/4.71 fof(c_0_8346, plain, ![X1652, X1653]:((X1652!=c_Groups_Ozero__class_Ozero(X1653)|c_Groups_Osgn__class_Osgn(X1653,X1652)=c_Groups_Ozero__class_Ozero(X1653)|~class_Groups_Osgn__if(X1653))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1653),c_Groups_Ozero__class_Ozero(X1653)),X1652))|c_Groups_Oone__class_Oone(X1653)=c_Groups_Osgn__class_Osgn(X1653,X1652)|c_Groups_Ozero__class_Ozero(X1653)=X1652|~class_Groups_Osgn__if(X1653))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1653),c_Groups_Ozero__class_Ozero(X1653)),X1652))|hAPP(c_Groups_Ouminus__class_Ouminus(X1653),c_Groups_Oone__class_Oone(X1653))=c_Groups_Osgn__class_Osgn(X1653,X1652)|c_Groups_Ozero__class_Ozero(X1653)=X1652|~class_Groups_Osgn__if(X1653)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__if])])])])). 4.46/4.71 fof(c_0_8347, plain, ![X5620, X5621, X5622, X5623]:(~class_Complete__Lattice_Ocomplete__lattice(X5623)|(X5622=c_Orderings_Obot__class_Obot(tc_fun(X5621,tc_HOL_Obool))|X5620=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5621,X5623),X5622),hAPP(c_COMBK(X5623,X5621),X5620)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUP__const])])])). 4.46/4.71 fof(c_0_8348, plain, ![X2611, X2612]:(~class_Groups_Oordered__ab__group__add__abs(X2612)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2612),hAPP(c_Groups_Ouminus__class_Ouminus(X2612),hAPP(c_Groups_Oabs__class_Oabs(X2612),X2611))),c_Groups_Ozero__class_Ozero(X2612)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__minus__le__zero])])])). 4.46/4.71 fof(c_0_8349, plain, ![X14140, X14141, X14142]:(~class_Orderings_Oorder(X14142)|c_Orderings_Obot__class_Obot(tc_fun(X14142,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14142,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X14142,X14141),X14140)),hAPP(c_SetInterval_Oord__class_OatLeast(X14142),X14140))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I8_J])])). 4.46/4.71 fof(c_0_8350, plain, ![X6225, X6226, X6227]:(~class_Orderings_Oorder(X6227)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6227,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X6227),X6226)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X6227,X6226),X6225))=c_Orderings_Obot__class_Obot(tc_fun(X6227,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I2_J])])])). 4.46/4.71 fof(c_0_8351, plain, ![X579, X580, X581, X582, X583]:(((X580=X582|hAPP(hAPP(c_List_Oappend(X583),X580),hAPP(hAPP(c_List_Olist_OCons(X583),X579),c_List_Olist_ONil(X583)))!=hAPP(hAPP(c_List_Oappend(X583),X582),hAPP(hAPP(c_List_Olist_OCons(X583),X581),c_List_Olist_ONil(X583))))&(X579=X581|hAPP(hAPP(c_List_Oappend(X583),X580),hAPP(hAPP(c_List_Olist_OCons(X583),X579),c_List_Olist_ONil(X583)))!=hAPP(hAPP(c_List_Oappend(X583),X582),hAPP(hAPP(c_List_Olist_OCons(X583),X581),c_List_Olist_ONil(X583)))))&(X580!=X582|X579!=X581|hAPP(hAPP(c_List_Oappend(X583),X580),hAPP(hAPP(c_List_Olist_OCons(X583),X579),c_List_Olist_ONil(X583)))=hAPP(hAPP(c_List_Oappend(X583),X582),hAPP(hAPP(c_List_Olist_OCons(X583),X581),c_List_Olist_ONil(X583))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append1__eq__conv])])])). 4.46/4.71 fof(c_0_8352, plain, ![X8452, X8453, X8454, X8455]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X8455,X8454),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X8453),X8452)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X8454|X8453=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8455),X8454))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__div])])])). 4.46/4.71 cnf(c_0_8353, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))|~c_Wellfounded_OwfP(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5481])). 4.46/4.71 cnf(c_0_8354, plain, (c_Wellfounded_Owf(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))|~c_Wellfounded_OwfP(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5482])). 4.46/4.71 fof(c_0_8355, plain, ![X8690, X8691]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8691))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8690))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X8691,X8690),c_Divides_OposDivAlg(X8691,X8690))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_posDivAlg__correct])])])). 4.46/4.71 fof(c_0_8356, plain, ![X14259, X14260, X14261, X14262, X14263, X14264, X14265, X14268]:(((hAPP(X14259,X14261)!=hAPP(X14259,X14262)|hBOOL(hAPP(hAPP(X14259,X14261),X14262))|~c_Equiv__Relations_Oequivp(X14260,X14259))&(~hBOOL(hAPP(hAPP(X14259,X14263),X14264))|hAPP(X14259,X14263)=hAPP(X14259,X14264)|~c_Equiv__Relations_Oequivp(X14260,X14259)))&((hAPP(X14265,esk417_1(X14265))!=hAPP(X14265,esk418_1(X14265))|~hBOOL(hAPP(hAPP(X14265,esk417_1(X14265)),esk418_1(X14265)))|c_Equiv__Relations_Oequivp(X14268,X14265))&(hAPP(X14265,esk417_1(X14265))=hAPP(X14265,esk418_1(X14265))|hBOOL(hAPP(hAPP(X14265,esk417_1(X14265)),esk418_1(X14265)))|c_Equiv__Relations_Oequivp(X14268,X14265)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__def])])])])])])). 4.46/4.71 fof(c_0_8357, plain, ![X4421, X4422, X4423]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4423),X4422))|hAPP(hAPP(c_Finite__Set_Ofold(X4423,tc_fun(X4423,tc_HOL_Obool),c_Set_Oinsert(X4423)),X4421),X4422)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4423,tc_HOL_Obool)),X4422),X4421)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_union__fold__insert])])])). 4.46/4.71 fof(c_0_8358, plain, ![X8415, X8416]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8416),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8415))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X8416,X8415),c_Divides_OnegDivAlg(X8416,X8415))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_negDivAlg__correct])])])). 4.46/4.71 fof(c_0_8359, plain, ![X14881, X14882, X14883, X14884]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X14884,X14884)),hAPP(hAPP(c_Product__Type_OPair(X14884,X14884),X14883),X14882)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X14884,X14884),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14881)))|X14883=X14882), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__pow__0__E])])])). 4.46/4.71 fof(c_0_8360, plain, ![X16390, X16391, X16392]:(~class_Orderings_Oorder(X16392)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16392,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X16392,X16391,X16390)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X16392),X16390))=c_Orderings_Obot__class_Obot(tc_fun(X16392,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I7_J])])). 4.46/4.71 fof(c_0_8361, plain, ![X11213, X11214, X11215]:(~class_Orderings_Oorder(X11215)|c_Orderings_Obot__class_Obot(tc_fun(X11215,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11215,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X11215,X11214,X11213)),hAPP(c_SetInterval_Oord__class_OatLeast(X11215),X11213))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I6_J])])). 4.46/4.71 fof(c_0_8362, plain, ![X1710, X1711, X1712]:(~class_Orderings_Oorder(X1712)|c_Orderings_Obot__class_Obot(tc_fun(X1712,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1712,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1712,X1711,X1710)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1712),X1710))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I5_J])])])). 4.46/4.71 fof(c_0_8363, plain, ![X10863, X10864, X10865]:(~class_Orderings_Oorder(X10865)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10865,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X10865),X10864)),c_SetInterval_Oord__class_OatLeastAtMost(X10865,X10864,X10863))=c_Orderings_Obot__class_Obot(tc_fun(X10865,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I4_J])])])). 4.46/4.71 fof(c_0_8364, plain, ![X13307, X13308, X13309]:(~class_Orderings_Oorder(X13309)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13309,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X13309),X13308)),c_SetInterval_Oord__class_OgreaterThanAtMost(X13309,X13308,X13307))=c_Orderings_Obot__class_Obot(tc_fun(X13309,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I3_J])])). 4.46/4.71 fof(c_0_8365, plain, ![X4004, X4005, X4006]:(~class_Orderings_Oorder(X4006)|c_Orderings_Obot__class_Obot(tc_fun(X4006,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4006,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X4006),X4005)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4006,X4005,X4004))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I1_J])])). 4.46/4.71 cnf(c_0_8366, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5483])). 4.46/4.71 cnf(c_0_8367, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5483])). 4.46/4.71 fof(c_0_8368, plain, ![X2824, X2825, X2826, X2827, X2828, X2829, X2830]:(~c_Big__Operators_Ocomm__monoid__big(X2830,X2829,X2828,X2827,X2826)|(hBOOL(hAPP(c_Finite__Set_Ofinite(X2829),X2825))|hAPP(hAPP(X2826,X2824),X2825)=X2827)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__monoid__big_Oinfinite])])])). 4.46/4.71 cnf(c_0_8369, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3))))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5381])). 4.46/4.71 fof(c_0_8370, plain, ![X2621, X2622, X2623]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2623),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2622)),X2621)))|c_List_Olast(X2622,X2621)=c_List_Olast(X2622,hAPP(hAPP(c_List_Odrop(X2622),X2623),X2621))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__drop])])). 4.46/4.71 fof(c_0_8371, plain, ![X13653, X13654, X13655]:(~class_Orderings_Olinorder(X13655)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13655),X13654))|(~hBOOL(hAPP(hAPP(c_member(X13655),X13653),X13654))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13655),c_Big__Operators_Olinorder__class_OMin(X13655,X13654)),X13653))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min__le])])])). 4.46/4.71 fof(c_0_8372, plain, ![X16183, X16184, X16185]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X16185),X16183))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16185),X16184))|hBOOL(hAPP(c_Finite__Set_Ofinite(X16185),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16185,tc_HOL_Obool)),X16184),X16183))))&((hBOOL(hAPP(c_Finite__Set_Ofinite(X16185),X16183))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16185),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16185,tc_HOL_Obool)),X16184),X16183))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X16185),X16184))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16185),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16185,tc_HOL_Obool)),X16184),X16183)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Un])])])). 4.46/4.71 cnf(c_0_8373, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5484])). 4.46/4.71 fof(c_0_8374, plain, ![X14965, X14966, X14967, X14968]:((c_Orderings_Obot__class_Obot(tc_fun(X14967,tc_HOL_Obool))=X14968|hAPP(hAPP(c_Set_Oinsert(X14966),X14965),c_Orderings_Obot__class_Obot(tc_fun(X14966,tc_HOL_Obool)))=hAPP(c_Set_Oimage(X14967,X14966,hAPP(c_COMBK(X14966,X14967),X14965)),X14968))&(X14968!=c_Orderings_Obot__class_Obot(tc_fun(X14967,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X14966,tc_HOL_Obool))=hAPP(c_Set_Oimage(X14967,X14966,hAPP(c_COMBK(X14966,X14967),X14965)),X14968))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__constant__conv])])])). 4.46/4.71 fof(c_0_8375, plain, ![X4183, X4184, X4185]:(~class_Orderings_Olinorder(X4185)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4185),X4184))|(~hBOOL(hAPP(hAPP(c_member(X4185),X4183),X4184))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4185),X4183),c_Big__Operators_Olinorder__class_OMax(X4185,X4184)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max__ge])])])). 4.46/4.71 fof(c_0_8376, plain, ![X6847, X6848]:((~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X6848),X6847))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6848)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X6847))))&(~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6848)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X6847)))|hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X6848),X6847)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I2_J])])). 4.46/4.71 cnf(c_0_8377, plain, (hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X1))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5485])). 4.46/4.71 cnf(c_0_8378, plain, (hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X1,X2))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5486])). 4.46/4.71 fof(c_0_8379, plain, ![X11055, X11056, X11057, X11058]:(c_List_Olist_ONil(X11057)=X11058|hAPP(c_List_Ohd(X11056),hAPP(hAPP(c_List_Omap(X11057,X11056),X11055),X11058))=hAPP(X11055,hAPP(c_List_Ohd(X11057),X11058))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__map])])). 4.46/4.71 fof(c_0_8380, plain, ![X1678, X1679, X1680, X1681, X1682, X1683]:(~c_Fun_Oinj__on(X1683,X1682,X1681,X1680)|(X1678=X1679|(~hBOOL(hAPP(hAPP(c_member(X1683),X1679),X1680))|(~hBOOL(hAPP(hAPP(c_member(X1683),X1678),X1680))|hAPP(X1681,X1678)!=hAPP(X1681,X1679))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__contraD])])])). 4.46/4.71 cnf(c_0_8381, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_5480])). 4.46/4.71 fof(c_0_8382, plain, ![X12078, X12079]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12079),X12078))|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12078),X12079))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12078)),X12079)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__le])])). 4.46/4.71 cnf(c_0_8383, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3))|X4!=X5), inference(split_conjunct,[status(thm)],[c_0_5487])). 4.46/4.71 cnf(c_0_8384, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onat,X1))=hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)|~class_Rings_Oring__1(X2)), inference(split_conjunct,[status(thm)],[c_0_5380])). 4.46/4.71 fof(c_0_8385, plain, ![X16847, X16848, X16849]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16849),tc_List_Olist(X16849))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16849),tc_List_Olist(X16849)),c_List_Olist_ONil(X16849)),X16848)),c_List_Olistrel(X16849,X16847)))|X16848=c_List_Olist_ONil(X16849)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil1])])). 4.46/4.71 fof(c_0_8386, plain, ![X16368, X16369, X16370]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16370),tc_List_Olist(X16370))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16370),tc_List_Olist(X16370)),X16369),c_List_Olist_ONil(X16370))),c_List_Olistrel(X16370,X16368)))|X16369=c_List_Olist_ONil(X16370)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel__Nil2])])])). 4.46/4.71 fof(c_0_8387, plain, ![X8502, X8503, X8504, X8505, X8506]:(~class_Orderings_Olinorder(X8506)|c_List_Olinorder__class_Osort__key(X8505,X8506,X8503,hAPP(c_List_Ofilter(X8505,X8504),X8502))=hAPP(c_List_Ofilter(X8505,X8504),c_List_Olinorder__class_Osort__key(X8505,X8506,X8503,X8502))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__sort])])])). 4.46/4.71 fof(c_0_8388, plain, ![X13961, X13962]:(~c_Nat__Transfer_Onat__set(X13962)|(~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X13961),X13962))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13961)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J])])). 4.46/4.71 fof(c_0_8389, plain, ![X2595]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2595))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2595))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2595)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2595)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__int__conv])])). 4.46/4.71 cnf(c_0_8390, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5488])). 4.46/4.71 fof(c_0_8391, plain, ![X12050, X12051]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12051),X12050),c_Groups_Ozero__class_Ozero(X12051)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12051),c_Groups_Osgn__class_Osgn(X12051,X12050)),c_Groups_Ozero__class_Ozero(X12051)))|~class_Rings_Olinordered__idom(X12051))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12051),c_Groups_Osgn__class_Osgn(X12051,X12050)),c_Groups_Ozero__class_Ozero(X12051)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12051),X12050),c_Groups_Ozero__class_Ozero(X12051)))|~class_Rings_Olinordered__idom(X12051))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__less])])])). 4.46/4.71 fof(c_0_8392, plain, ![X6532, X6533]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6533),c_Groups_Ozero__class_Ozero(X6533)),c_Groups_Osgn__class_Osgn(X6533,X6532)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6533),c_Groups_Ozero__class_Ozero(X6533)),X6532))|~class_Rings_Olinordered__idom(X6533))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6533),c_Groups_Ozero__class_Ozero(X6533)),X6532))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6533),c_Groups_Ozero__class_Ozero(X6533)),c_Groups_Osgn__class_Osgn(X6533,X6532)))|~class_Rings_Olinordered__idom(X6533))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__greater])])])])). 4.46/4.71 fof(c_0_8393, plain, ![X16958, X16959, X16960]:((c_List_Olist_ONil(X16959)=X16960|hAPP(hAPP(c_List_Oappend(X16959),X16958),c_List_Obutlast(X16959,X16960))=c_List_Obutlast(X16959,hAPP(hAPP(c_List_Oappend(X16959),X16958),X16960)))&(c_List_Olist_ONil(X16959)!=X16960|c_List_Obutlast(X16959,hAPP(hAPP(c_List_Oappend(X16959),X16958),X16960))=c_List_Obutlast(X16959,X16958))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_butlast__append])])])). 4.46/4.71 fof(c_0_8394, plain, ![X13594, X13595]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13595),c_Orderings_Otop__class_Otop(tc_fun(X13595,tc_HOL_Obool))))|(~c_Fun_Oinj__on(X13595,X13595,X13594,c_Orderings_Otop__class_Otop(tc_fun(X13595,tc_HOL_Obool)))|hAPP(c_Set_Oimage(X13595,X13595,X13594),c_Orderings_Otop__class_Otop(tc_fun(X13595,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X13595,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__UNIV__inj__surj])])])). 4.46/4.71 fof(c_0_8395, plain, ![X1026, X1027, X1028]:(~class_Lattices_Olattice(X1028)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1028),X1027))|(~hBOOL(hAPP(hAPP(c_member(X1028),X1026),X1027))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1028),X1026),c_Big__Operators_Olattice__class_OInf__fin(X1028,X1027))=X1026))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__Inf__absorb])])])). 4.46/4.71 fof(c_0_8396, plain, ![X8203, X8204, X8205]:(~class_Lattices_Olattice(X8205)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8205),X8204))|(~hBOOL(hAPP(hAPP(c_member(X8205),X8203),X8204))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8205),X8203),c_Big__Operators_Olattice__class_OSup__fin(X8205,X8204))=X8203))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__Sup__absorb])])])). 4.46/4.71 cnf(c_0_8397, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))=hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[c_0_5489, c_0_4431])). 4.46/4.71 fof(c_0_8398, plain, ![X8982, X8983, X8984]:(~class_Orderings_Olinorder(X8984)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X8984),X8983),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8984),X8983),X8982))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X8984),X8983),X8982)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__idem])])). 4.46/4.71 fof(c_0_8399, plain, ![X8314, X8315, X8316]:(~class_Orderings_Olinorder(X8316)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X8316),X8315),X8314)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X8316),X8315),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8316),X8315),X8314))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__idem])])). 4.46/4.71 cnf(c_0_8400, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2)))=c_List_Olist_ONil(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[c_0_5490, c_0_4517])). 4.46/4.71 fof(c_0_8401, plain, ![X9061, X9062, X9063, X9064, X9065, X9066, X9067, X9068, X9069, X9070]:((~c_Fun_Oinj__on(X9064,X9063,X9062,X9061)|(~hBOOL(hAPP(hAPP(c_member(X9064),X9065),X9061))|(~hBOOL(hAPP(hAPP(c_member(X9064),X9066),X9061))|(hAPP(X9062,X9065)!=hAPP(X9062,X9066)|X9065=X9066))))&((hBOOL(hAPP(hAPP(c_member(X9070),esk261_4(X9067,X9068,X9069,X9070)),X9067))|c_Fun_Oinj__on(X9070,X9069,X9068,X9067))&((hBOOL(hAPP(hAPP(c_member(X9070),esk262_4(X9067,X9068,X9069,X9070)),X9067))|c_Fun_Oinj__on(X9070,X9069,X9068,X9067))&((hAPP(X9068,esk261_4(X9067,X9068,X9069,X9070))=hAPP(X9068,esk262_4(X9067,X9068,X9069,X9070))|c_Fun_Oinj__on(X9070,X9069,X9068,X9067))&(esk261_4(X9067,X9068,X9069,X9070)!=esk262_4(X9067,X9068,X9069,X9070)|c_Fun_Oinj__on(X9070,X9069,X9068,X9067)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__def])])])])])])])). 4.46/4.71 fof(c_0_8402, plain, ![X8987, X8988]:(~class_Rings_Osemiring__1(X8988)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8988),hAPP(c_Nat_OSuc,X8987))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8988),c_Groups_Oone__class_Oone(X8988)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8988),X8987))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__Suc])])). 4.46/4.71 fof(c_0_8403, plain, ![X5463, X5464, X5465]:(hBOOL(hAPP(hAPP(c_member(X5465),X5464),X5463))|hBOOL(hAPP(hAPP(c_member(X5465),X5464),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5465,tc_HOL_Obool)),X5463)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ComplI])])])). 4.46/4.71 fof(c_0_8404, plain, ![X1929, X1930]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1930))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1929,X1930)),X1930))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__less__divisor])])])). 4.46/4.71 cnf(c_0_8405, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_5491])). 4.46/4.71 cnf(c_0_8406, plain, (hAPP(X1,esk92_3(X1,X2,X3))=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5222])). 4.46/4.71 fof(c_0_8407, plain, ![X2167, X2168]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2168))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2167,X2168)),X2168))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__bound])])). 4.46/4.71 fof(c_0_8408, plain, ![X871, X872]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X872))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X871,X872)),X872))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__le__divisor])])). 4.46/4.71 fof(c_0_8409, plain, ![X6814, X6815]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6815))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6815,X6814)),X6815))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmod__le__nonneg__dividend])])])). 4.46/4.71 fof(c_0_8410, plain, ![X15192, X15193, X15194, X15195, X15196]:(hAPP(X15196,X15195)!=hAPP(c_Option_Ooption_OSome(X15194),X15193)|hBOOL(hAPP(hAPP(c_member(X15194),X15193),c_Map_Oran(X15192,X15194,X15196)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ranI])])). 4.46/4.71 fof(c_0_8411, plain, ![X8211, X8212, X8213, X8214]:(~class_Orderings_Olinorder(X8214)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8213,X8214,X8212),X8211),c_List_Olist_ONil(X8213))=hAPP(hAPP(c_List_Olist_OCons(X8213),X8211),c_List_Olist_ONil(X8213))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__key_Osimps_I1_J])])])). 4.46/4.71 fof(c_0_8412, plain, ![X5599, X5600, X5601, X5602, X5603]:(~c_Finite__Set_Ofun__left__comm(X5603,X5602,X5601)|c_Finite__Set_Ofun__left__comm(X5600,X5602,hAPP(hAPP(c_COMBB(X5603,tc_fun(X5602,X5602),X5600),X5601),X5599))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofun__left__comm__apply])])])). 4.46/4.71 fof(c_0_8413, plain, ![X10930, X10931, X10932]:(hBOOL(hAPP(hAPP(c_member(X10932),X10931),hAPP(c_List_Oset(X10932),X10930)))|c_List_Oremove1(X10932,X10931,X10930)=X10930), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_remove1__idem])])])). 4.46/4.71 fof(c_0_8414, plain, ![X5035, X5036]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5036),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5036),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5035,X5036)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__mod__bound])])])). 4.46/4.71 fof(c_0_8415, plain, ![X10159, X10160, X10161, X10162, X10163]:(~c_Finite__Set_Ofun__left__comm__idem(X10163,X10162,X10161)|c_Finite__Set_Ofun__left__comm__idem(X10160,X10162,hAPP(hAPP(c_COMBB(X10163,tc_fun(X10162,X10162),X10160),X10161),X10159))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__comm__idem__apply])])). 4.46/4.71 fof(c_0_8416, plain, ![X14788, X14789, X14790]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X14789,X14790)),X14788))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X14790,X14789)),hAPP(c_Relation_Oconverse(X14789,X14790),X14788))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X14790,X14789)),hAPP(c_Relation_Oconverse(X14789,X14790),X14788)))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X14789,X14790)),X14788)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__converse])])). 4.46/4.71 fof(c_0_8417, plain, ![X760, X761, X763, X764]:(((hBOOL(hAPP(X760,esk19_2(X760,X761)))|~c_List_Olist__ex1(X761,X760,c_Enum_Oenum__class_Oenum(X761))|~class_Enum_Oenum(X761))&(~hBOOL(hAPP(X760,X763))|X763=esk19_2(X760,X761)|~c_List_Olist__ex1(X761,X760,c_Enum_Oenum__class_Oenum(X761))|~class_Enum_Oenum(X761)))&((hBOOL(hAPP(X760,esk20_3(X760,X761,X764)))|~hBOOL(hAPP(X760,X764))|c_List_Olist__ex1(X761,X760,c_Enum_Oenum__class_Oenum(X761))|~class_Enum_Oenum(X761))&(esk20_3(X760,X761,X764)!=X764|~hBOOL(hAPP(X760,X764))|c_List_Olist__ex1(X761,X760,c_Enum_Oenum__class_Oenum(X761))|~class_Enum_Oenum(X761)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_exists1__code])])])])])])). 4.46/4.71 fof(c_0_8418, plain, ![X425, X426, X427, X428]:((~hBOOL(hAPP(hAPP(c_member(X428),X427),X426))|hBOOL(hAPP(hAPP(c_member(X428),X427),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X428,tc_HOL_Obool)),X425),X426))))&(~hBOOL(hAPP(hAPP(c_member(X428),X427),X425))|hBOOL(hAPP(hAPP(c_member(X428),X427),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X428,tc_HOL_Obool)),X425),X426))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UnCI])])])])). 4.46/4.71 cnf(c_0_8419, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X1)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~hBOOL(hAPP(hAPP(c_member(X2),X1),c_Int_Oring__1__class_OInts(X2)))|~class_Int_Oring__char__0(X2)), inference(split_conjunct,[status(thm)],[c_0_5492])). 4.46/4.71 fof(c_0_8420, plain, ![X860, X861, X862, X863, X864, X865]:((hBOOL(hAPP(hAPP(c_member(X865),X864),X863))|hAPP(X861,X864)=hAPP(c_Fun_Ooverride__on(X865,X862,X861,X860,X863),X864))&(~hBOOL(hAPP(hAPP(c_member(X865),X864),X863))|hAPP(X860,X864)=hAPP(c_Fun_Ooverride__on(X865,X862,X861,X860,X863),X864))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_override__on__def])])])). 4.46/4.71 fof(c_0_8421, plain, ![X10164, X10165, X10166, X10167]:(~hBOOL(hAPP(hAPP(c_member(X10167),X10166),hAPP(c_List_Oset(X10167),c_List_Osublist(X10167,X10165,X10164))))|hBOOL(hAPP(hAPP(c_member(X10167),X10166),hAPP(c_List_Oset(X10167),X10165)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__sublistD])])). 4.46/4.71 fof(c_0_8422, plain, ![X6056, X6057, X6058, X6059]:(hBOOL(hAPP(hAPP(c_member(X6059),X6058),hAPP(c_List_Oset(X6059),X6057)))|~hBOOL(hAPP(hAPP(c_member(X6059),X6058),hAPP(c_List_Oset(X6059),c_List_Oremove1(X6059,X6056,X6057))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_notin__set__remove1])])])). 4.46/4.71 fof(c_0_8423, plain, ![X4737, X4738, X4739]:(~class_Groups_Ocomm__monoid__mult(X4739)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4738,X4739),hAPP(c_COMBK(X4739,X4738),c_Groups_Oone__class_Oone(X4739))),X4737)=c_Groups_Oone__class_Oone(X4739)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__1])])])). 4.46/4.71 fof(c_0_8424, plain, ![X3801, X3802, X3803]:(~class_Groups_Ocomm__monoid__add(X3803)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3802,X3803),hAPP(c_COMBK(X3803,X3802),c_Groups_Ozero__class_Ozero(X3803))),X3801)=c_Groups_Ozero__class_Ozero(X3803)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__0])])). 4.46/4.71 fof(c_0_8425, plain, ![X13356, X13357, X13358, X13359]:((hBOOL(hAPP(X13357,X13358))|~hBOOL(hAPP(hAPP(c_member(X13359),X13358),hAPP(c_List_Oset(X13359),c_List_OtakeWhile(X13359,X13357,X13356)))))&(hBOOL(hAPP(hAPP(c_member(X13359),X13358),hAPP(c_List_Oset(X13359),X13356)))|~hBOOL(hAPP(hAPP(c_member(X13359),X13358),hAPP(c_List_Oset(X13359),c_List_OtakeWhile(X13359,X13357,X13356)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__takeWhileD])])])])). 4.46/4.71 cnf(c_0_8426, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4678])). 4.46/4.71 fof(c_0_8427, plain, ![X10640, X10641]:(X10641=c_List_Olist_ONil(X10640)|hBOOL(hAPP(hAPP(c_member(X10640),hAPP(c_List_Ohd(X10640),X10641)),hAPP(c_List_Oset(X10640),X10641)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__in__set])])). 4.46/4.71 fof(c_0_8428, plain, ![X15822, X15823]:(~class_Rings_Olinordered__idom(X15823)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15823),X15822),c_Groups_Ozero__class_Ozero(X15823)))|c_Groups_Osgn__class_Osgn(X15823,X15822)=hAPP(c_Groups_Ouminus__class_Ouminus(X15823),c_Groups_Oone__class_Oone(X15823)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__neg])])])). 4.46/4.71 cnf(c_0_8429, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4680])). 4.46/4.71 cnf(c_0_8430, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X4)), inference(split_conjunct,[status(thm)],[c_0_5493])). 4.46/4.71 cnf(c_0_8431, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),X4)!=c_Option_Ooption_ONone(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))))), inference(split_conjunct,[status(thm)],[c_0_5214])). 4.46/4.71 fof(c_0_8432, plain, ![X12776, X12777, X12778, X12779]:(((X12777=X12778|~hBOOL(hAPP(hAPP(c_member(tc_prod(X12779,X12779)),hAPP(hAPP(c_Product__Type_OPair(X12779,X12779),X12778),X12777)),c_Relation_OId__on(X12779,X12776))))&(hBOOL(hAPP(hAPP(c_member(X12779),X12778),X12776))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X12779,X12779)),hAPP(hAPP(c_Product__Type_OPair(X12779,X12779),X12778),X12777)),c_Relation_OId__on(X12779,X12776)))))&(X12777!=X12778|~hBOOL(hAPP(hAPP(c_member(X12779),X12778),X12776))|hBOOL(hAPP(hAPP(c_member(tc_prod(X12779,X12779)),hAPP(hAPP(c_Product__Type_OPair(X12779,X12779),X12778),X12777)),c_Relation_OId__on(X12779,X12776))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__iff])])])). 4.46/4.71 fof(c_0_8433, plain, ![X17371, X17372, X17373]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17373),X17372))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17373,tc_HOL_Obool)),X17371),X17372))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X17373),X17372)),hAPP(c_Finite__Set_Ocard(X17373),X17371)))|X17371=X17372))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__seteq])])])). 4.46/4.71 fof(c_0_8434, plain, ![X17160, X17161, X17162, X17163, X17164]:(hAPP(X17164,X17163)!=hAPP(c_Option_Ooption_OSome(X17162),X17161)|hAPP(hAPP(c_Set_Oinsert(X17160),X17163),c_Map_Odom(X17160,X17162,X17164))=c_Map_Odom(X17160,X17162,X17164)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__dom])])). 4.46/4.71 fof(c_0_8435, plain, ![X10954, X10955, X10956, X10957]:((c_Orderings_Obot__class_Obot(tc_fun(X10956,tc_HOL_Obool))!=X10957|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10956,tc_fun(X10955,tc_HOL_Obool)),X10957),hAPP(c_COMBK(tc_fun(X10955,tc_HOL_Obool),X10956),X10954))=c_Orderings_Otop__class_Otop(tc_fun(X10955,tc_HOL_Obool)))&(X10957=c_Orderings_Obot__class_Obot(tc_fun(X10956,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10956,tc_fun(X10955,tc_HOL_Obool)),X10957),hAPP(c_COMBK(tc_fun(X10955,tc_HOL_Obool),X10956),X10954))=X10954)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__constant])])). 4.46/4.71 fof(c_0_8436, plain, ![X7422, X7423, X7424, X7425, X7426]:(~hBOOL(hAPP(hAPP(c_member(X7426),X7425),c_Map_Odom(X7426,X7424,X7423)))|hAPP(X7423,X7425)=hAPP(c_Map_Omap__add(X7426,X7424,X7422,X7423),X7425)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__dom__app__simps_I1_J])])). 4.46/4.71 fof(c_0_8437, plain, ![X17122, X17123, X17124, X17127, X17128, X17129, X17130, X17132, X17133]:((~hBOOL(hAPP(X17124,hAPP(hAPP(c_Product__Type_OPair(X17123,X17122),esk512_3(X17122,X17123,X17124)),esk513_3(X17122,X17123,X17124))))|hBOOL(hAPP(X17124,X17127)))&(~hBOOL(hAPP(X17130,esk514_3(X17128,X17129,X17130)))|hBOOL(hAPP(X17130,hAPP(hAPP(c_Product__Type_OPair(X17129,X17128),X17132),X17133))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__paired__All])])])])])). 4.46/4.71 fof(c_0_8438, plain, ![X7884, X7885]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7885))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7884),X7885)),X7885)=X7884), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__self__is__m])])])). 4.46/4.71 fof(c_0_8439, plain, ![X6510, X6511]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6511))|X6510=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6511),X6510)),X6511)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__self1__is__m])])])). 4.46/4.71 fof(c_0_8440, plain, ![X8992, X8993, X8994, X8995, X8996]:(~c_Equiv__Relations_Oequivp(X8996,X8995)|(~hBOOL(hAPP(hAPP(X8995,X8994),X8993))|(~hBOOL(hAPP(hAPP(X8995,X8993),X8992))|hBOOL(hAPP(hAPP(X8995,X8994),X8992))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equivp__transp])])])). 4.46/4.71 fof(c_0_8441, plain, ![X14685, X14686]:((hAPP(c_Groups_Ouminus__class_Ouminus(X14686),c_Groups_Oone__class_Oone(X14686))!=c_Groups_Osgn__class_Osgn(X14686,X14685)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14686),X14685),c_Groups_Ozero__class_Ozero(X14686)))|~class_Rings_Olinordered__idom(X14686))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14686),X14685),c_Groups_Ozero__class_Ozero(X14686)))|hAPP(c_Groups_Ouminus__class_Ouminus(X14686),c_Groups_Oone__class_Oone(X14686))=c_Groups_Osgn__class_Osgn(X14686,X14685)|~class_Rings_Olinordered__idom(X14686))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__1__neg])])])])). 4.46/4.71 fof(c_0_8442, plain, ![X6629, X6630]:(~class_Groups_Oordered__ab__group__add__abs(X6630)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6630),hAPP(c_Groups_Ouminus__class_Ouminus(X6630),X6629)),hAPP(c_Groups_Oabs__class_Oabs(X6630),X6629)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__ge__minus__self])])])). 4.46/4.71 fof(c_0_8443, plain, ![X14800, X14801]:(~class_Rings_Olinordered__ring(X14801)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14801),c_Groups_Ozero__class_Ozero(X14801)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14801),X14800),X14800)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__square])])). 4.46/4.71 fof(c_0_8444, plain, ![X9295, X9296]:(~class_Rings_Olinordered__semidom(X9296)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9296),X9295),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9296),X9295),c_Groups_Oone__class_Oone(X9296))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__add__one])])])). 4.46/4.71 fof(c_0_8445, plain, ![X15888, X15889, X15890, X15891, X15892]:((~c_List_Olist__all2(X15892,X15891,X15890,hAPP(c_List_Orev(X15892),X15889),hAPP(c_List_Orev(X15891),X15888))|c_List_Olist__all2(X15892,X15891,X15890,X15889,X15888))&(~c_List_Olist__all2(X15892,X15891,X15890,X15889,X15888)|c_List_Olist__all2(X15892,X15891,X15890,hAPP(c_List_Orev(X15892),X15889),hAPP(c_List_Orev(X15891),X15888)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__rev])])). 4.46/4.71 cnf(c_0_8446, plain, (X3=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X4)|X1!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)|X3!=c_Groups_Ozero__class_Ozero(X2)|~class_Fields_Ofield__inverse__zero(X2)), inference(split_conjunct,[status(thm)],[c_0_5494])). 4.46/4.71 fof(c_0_8447, plain, ![X3357, X3358, X3359, X3360, X3361]:(hAPP(c_Option_Ooption_OSome(X3359),X3358)!=hAPP(X3361,X3360)|hBOOL(hAPP(hAPP(c_member(X3357),X3360),c_Map_Odom(X3357,X3359,X3361)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_domI])])). 4.46/4.71 fof(c_0_8448, plain, ![X9287, X9288, X9289]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9289),X9288))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9289),X9287)),X9288))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less])])). 4.46/4.71 fof(c_0_8449, plain, ![X8739, X8740]:((hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X8740,X8739))=X8739|hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X8740,X8739))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X8740),X8739))&(hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X8740,X8739))!=X8739|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X8740),X8739))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__Suc])])). 4.46/4.71 fof(c_0_8450, plain, ![X586, X587, X588, X589, X590]:(~c_Fun_Oinj__on(X590,X589,X588,X587)|(~hBOOL(hAPP(hAPP(c_member(X590),X586),X587))|hAPP(c_Fun_Othe__inv__into(X590,X589,X587,X588),hAPP(X588,X586))=X586)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_the__inv__into__f__f])])])). 4.46/4.71 fof(c_0_8451, plain, ![X3897, X3898, X3899]:(~class_Orderings_Olinorder(X3899)|X3897=c_List_Oremove1(X3899,X3898,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3899,X3899,c_COMBI(X3899)),X3898),X3897))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_remove1__insort])])])). 4.46/4.71 cnf(c_0_8452, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5495])). 4.46/4.71 fof(c_0_8453, plain, ![X4834, X4835, X4836]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4836),X4835))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4836),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4835),X4834)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_termination__basic__simps_I1_J])])])). 4.46/4.71 fof(c_0_8454, plain, ![X3608, X3609, X3610, X3612, X3613, X3614, X3615]:(((hBOOL(hAPP(hAPP(c_member(X3610),esk96_3(X3608,X3609,X3610)),X3608))|hBOOL(hAPP(c_Predicate_OPowp(X3610,X3609),X3608)))&(~hBOOL(hAPP(X3609,esk96_3(X3608,X3609,X3610)))|hBOOL(hAPP(c_Predicate_OPowp(X3610,X3609),X3608))))&(~hBOOL(hAPP(c_Predicate_OPowp(X3614,X3613),X3612))|(~hBOOL(hAPP(hAPP(c_member(X3614),X3615),X3612))|hBOOL(hAPP(X3613,X3615))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Powp__def])])])])])])])). 4.46/4.71 fof(c_0_8455, plain, ![X8374, X8375, X8376]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8375),X8376)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8374),X8376)|X8374=X8375|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8376),X8374))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8376),X8375)))&(X8374!=X8375|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8375),X8376)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8374),X8376)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8376),X8374))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8376),X8375)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__diff__iff])])])])). 4.46/4.71 fof(c_0_8456, plain, ![X14723, X14724, X14725, X14726, X14727, X14729, X14730, X14731, X14732, X14733, X14734]:(((X14723=hAPP(X14725,esk431_5(X14723,X14724,X14725,X14726,X14727))|hAPP(hAPP(c_Option_Omap(X14727,X14726),X14725),X14724)!=hAPP(c_Option_Ooption_OSome(X14726),X14723))&(hAPP(c_Option_Ooption_OSome(X14727),esk431_5(X14723,X14724,X14725,X14726,X14727))=X14724|hAPP(hAPP(c_Option_Omap(X14727,X14726),X14725),X14724)!=hAPP(c_Option_Ooption_OSome(X14726),X14723)))&(X14729!=hAPP(X14731,X14734)|hAPP(c_Option_Ooption_OSome(X14733),X14734)!=X14730|hAPP(hAPP(c_Option_Omap(X14733,X14732),X14731),X14730)=hAPP(c_Option_Ooption_OSome(X14732),X14729))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_option__map__eq__Some])])])])])])). 4.46/4.71 fof(c_0_8457, plain, ![X359, X360, X361]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X361),X360))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X361),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X359),X360)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trans__less__add2])])])). 4.46/4.71 fof(c_0_8458, plain, ![X15631, X15632, X15633]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15633),X15632))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15633),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15632),X15631)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])])). 4.46/4.71 fof(c_0_8459, plain, ![X13876, X13877, X13878]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13878),X13877))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13878),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13876),X13877)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trans__le__add2])])])). 4.46/4.71 fof(c_0_8460, plain, ![X13830, X13831, X13832]:(~c_Relation_Osingle__valued(X13832,X13832,X13831)|c_Relation_Osingle__valued(X13832,X13832,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X13832,X13832),tc_HOL_Obool),X13830),X13831))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_single__valued__rel__pow])])])). 4.46/4.71 fof(c_0_8461, plain, ![X12034, X12035]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12035),X12034))|(hAPP(c_Nat_OSuc,X12035)=X12034|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12035)),X12034)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__lessI])])])). 4.46/4.71 fof(c_0_8462, plain, ![X13213]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13213),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X13213=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk385_1(X13213))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_negD])])])])). 4.46/4.71 fof(c_0_8463, plain, ![X3482, X3483, X3484]:(~c_Fun_Oinj__on(tc_List_Olist(X3484),tc_List_Olist(X3483),hAPP(c_List_Omap(X3484,X3483),X3482),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X3484),tc_HOL_Obool)))|c_Fun_Oinj__on(X3484,X3483,X3482,c_Orderings_Otop__class_Otop(tc_fun(X3484,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__mapD])])])). 4.46/4.71 fof(c_0_8464, plain, ![X703, X704, X705]:(~class_Groups_Oordered__ab__group__add__abs(X705)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X705),hAPP(c_Groups_Oabs__class_Oabs(X705),X704)),X703))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X705),hAPP(c_Groups_Ouminus__class_Ouminus(X705),X704)),X703)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__le__D2])])])). 4.46/4.71 cnf(c_0_8465, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1)=X4|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)!=X3|~class_Fields_Ofield__inverse__zero(X2)), inference(split_conjunct,[status(thm)],[c_0_5496])). 4.46/4.71 fof(c_0_8466, plain, ![X13428, X13429, X13430]:(~hBOOL(hAPP(hAPP(c_member(X13430),X13429),hAPP(c_List_Oset(X13430),c_List_Obutlast(X13430,X13428))))|hBOOL(hAPP(hAPP(c_member(X13430),X13429),hAPP(c_List_Oset(X13430),X13428)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__butlastD])])). 4.46/4.71 fof(c_0_8467, plain, ![X15340, X15341, X15342, X15343, X15344]:(~c_Fun_Oinj__on(X15344,X15343,X15342,X15341)|c_Fun_Oinj__on(X15344,X15343,X15342,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15344,tc_HOL_Obool)),X15341),X15340))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__diff])])). 4.46/4.71 fof(c_0_8468, plain, ![X15348, X15349, X15350, X15351]:(~class_Orderings_Olinorder(X15351)|c_List_Olinorder__class_Osorted(X15351,hAPP(hAPP(c_List_Omap(X15350,X15351),X15349),c_List_Olinorder__class_Osort__key(X15350,X15351,X15349,X15348)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__sort__key])])])). 4.46/4.71 fof(c_0_8469, plain, ![X14435, X14436]:(~class_Complete__Lattice_Ocomplete__lattice(X14436)|hAPP(c_List_Ofoldl(X14436,X14436,c_Lattices_Osemilattice__sup__class_Osup(X14436),c_Orderings_Obot__class_Obot(X14436)),X14435)=c_Complete__Lattice_OSup__class_OSup(X14436,hAPP(c_List_Oset(X14436),X14435))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__set__fold])])). 4.46/4.71 fof(c_0_8470, plain, ![X12832, X12833]:(~class_Complete__Lattice_Ocomplete__lattice(X12833)|hAPP(c_List_Ofoldl(X12833,X12833,c_Lattices_Osemilattice__inf__class_Oinf(X12833),c_Orderings_Otop__class_Otop(X12833)),X12832)=c_Complete__Lattice_OInf__class_OInf(X12833,hAPP(c_List_Oset(X12833),X12832))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__set__fold])])). 4.46/4.71 fof(c_0_8471, plain, ![X12763, X12764, X12765]:(~class_Rings_Olinordered__ring(X12765)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12765),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12765),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12765),X12764),X12764)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12765),X12763),X12763))),c_Groups_Ozero__class_Ozero(X12765)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero])])])). 4.46/4.71 fof(c_0_8472, plain, ![X6012, X6013]:(~class_Rings_Ocomm__ring__1(X6013)|hAPP(c_Groups_Ouminus__class_Ouminus(X6013),X6012)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6013),hAPP(c_Groups_Ouminus__class_Ouminus(X6013),c_Groups_Oone__class_Oone(X6013))),X6012)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J])])). 4.46/4.71 cnf(c_0_8473, plain, (c_Equiv__Relations_Oequiv(X1,X3,X2)|hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X2)),X2)!=X2|X3!=hAPP(c_Relation_ODomain(X1,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5497])). 4.46/4.71 fof(c_0_8474, plain, ![X325, X326, X327, X328, X329, X330]:((~hBOOL(hAPP(hAPP(X330,X329),X328))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X326,tc_fun(X325,tc_HOL_Obool))),X327),X330),X329),X328)))&(~hBOOL(hAPP(hAPP(X327,X329),X328))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X326,tc_fun(X325,tc_HOL_Obool))),X327),X330),X329),X328)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup2CI])])])])). 4.46/4.71 fof(c_0_8475, plain, ![X16674, X16675, X16676]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X16674)|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X16675),hAPP(c_List_Oset(tc_Nat_Onat),X16674)))|X16675=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk490_1(X16676)),hAPP(c_List_Oset(tc_Nat_Onat),X16676)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X16676))&(esk490_1(X16676)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X16676)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__eq__0__nat__iff__nat])])])])])])). 4.46/4.71 cnf(c_0_8476, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),X2)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X1), inference(split_conjunct,[status(thm)],[c_0_5498])). 4.46/4.71 cnf(c_0_8477, plain, (hBOOL(hAPP(X1,X2))|hAPP(c_List_Ofilter(X3,X1),X4)=c_List_Oremove1(X3,X2,hAPP(c_List_Ofilter(X3,X1),X4))), inference(split_conjunct,[status(thm)],[c_0_5499])). 4.46/4.71 cnf(c_0_8478, plain, (hAPP(c_List_Ofilter(X1,X2),c_List_Oremove1(X1,X3,X4))=c_List_Oremove1(X1,X3,hAPP(c_List_Ofilter(X1,X2),X4))), inference(split_conjunct,[status(thm)],[c_0_5500]), ['final']). 4.46/4.71 fof(c_0_8479, plain, ![X15777, X15778, X15779, X15780]:((hAPP(hAPP(c_Power_Opower__class_Opower(X15780),X15779),X15777)!=hAPP(hAPP(c_Power_Opower__class_Opower(X15780),X15779),X15778)|X15778=X15777|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15780),c_Groups_Oone__class_Oone(X15780)),X15779))|~class_Rings_Olinordered__semidom(X15780))&(X15778!=X15777|hAPP(hAPP(c_Power_Opower__class_Opower(X15780),X15779),X15777)=hAPP(hAPP(c_Power_Opower__class_Opower(X15780),X15779),X15778)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15780),c_Groups_Oone__class_Oone(X15780)),X15779))|~class_Rings_Olinordered__semidom(X15780))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__exp])])])). 4.46/4.71 cnf(c_0_8480, plain, (~c_Wellfounded_Oacyclic(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),c_Transitive__Closure_Otrancl(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_5141])). 4.46/4.71 fof(c_0_8481, plain, ![X4408, X4409]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4409),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4408),X4409))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4409),X4408))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__neg__neg__trivial])])])). 4.46/4.71 fof(c_0_8482, plain, ![X12822, X12823, X12824]:((~hBOOL(hAPP(hAPP(c_member(X12824),X12823),hAPP(c_SetInterval_Oord__class_OlessThan(X12824),X12822)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12824),X12823),X12822))|~class_Orderings_Oord(X12824))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12824),X12823),X12822))|hBOOL(hAPP(hAPP(c_member(X12824),X12823),hAPP(c_SetInterval_Oord__class_OlessThan(X12824),X12822)))|~class_Orderings_Oord(X12824))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__iff])])])). 4.46/4.71 cnf(c_0_8483, plain, (X2=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Relation_OId(X1)))), inference(split_conjunct,[status(thm)],[c_0_5501])). 4.46/4.71 fof(c_0_8484, plain, ![X9586, X9587, X9588, X9589]:((X9587!=hAPP(hAPP(c_List_Olist__update(X9588,X9587),X9589),X9586)|X9586=hAPP(hAPP(c_List_Onth(X9588),X9587),X9589)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9589),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9588)),X9587))))&(X9586!=hAPP(hAPP(c_List_Onth(X9588),X9587),X9589)|X9587=hAPP(hAPP(c_List_Olist__update(X9588,X9587),X9589),X9586)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9589),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9588)),X9587))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__update__same__conv])])])])). 4.46/4.71 fof(c_0_8485, plain, ![X8775, X8776, X8777, X8778]:(X8778=c_List_Olist_ONil(X8777)|hAPP(X8775,c_List_Olast(X8777,X8778))=c_List_Olast(X8776,hAPP(hAPP(c_List_Omap(X8777,X8776),X8775),X8778))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__map])])). 4.46/4.71 fof(c_0_8486, plain, ![X11630, X11631, X11632]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11632),X11631),X11630))|hBOOL(hAPP(hAPP(c_member(X11632),X11631),hAPP(c_SetInterval_Oord__class_OatMost(X11632),X11630)))|~class_Orderings_Oord(X11632))&(~hBOOL(hAPP(hAPP(c_member(X11632),X11631),hAPP(c_SetInterval_Oord__class_OatMost(X11632),X11630)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11632),X11631),X11630))|~class_Orderings_Oord(X11632))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atMost__iff])])])])). 4.46/4.71 fof(c_0_8487, plain, ![X5349, X5350, X5351]:((~hBOOL(hAPP(hAPP(c_member(X5351),X5350),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5351),X5349)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5351),X5349),X5350))|~class_Orderings_Oord(X5351))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5351),X5349),X5350))|hBOOL(hAPP(hAPP(c_member(X5351),X5350),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5351),X5349)))|~class_Orderings_Oord(X5351))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_greaterThan__iff])])])])). 4.46/4.71 fof(c_0_8488, plain, ![X9630, X9631, X9632]:((~hBOOL(hAPP(hAPP(c_member(X9632),X9631),hAPP(c_SetInterval_Oord__class_OatLeast(X9632),X9630)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9632),X9630),X9631))|~class_Orderings_Oord(X9632))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9632),X9630),X9631))|hBOOL(hAPP(hAPP(c_member(X9632),X9631),hAPP(c_SetInterval_Oord__class_OatLeast(X9632),X9630)))|~class_Orderings_Oord(X9632))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeast__iff])])])])). 4.46/4.71 fof(c_0_8489, plain, ![X15714, X15715, X15716, X15717]:(~c_Fun_Oinj__on(X15717,X15716,X15715,X15714)|hAPP(c_Finite__Set_Ocard(X15716),hAPP(c_Set_Oimage(X15717,X15716,X15715),X15714))=hAPP(c_Finite__Set_Ocard(X15717),X15714)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__image])])])). 4.46/4.71 cnf(c_0_8490, plain, (c_Relation_Ototal__on(X1,X2,X3)|~c_Relation_Ototal__on(X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Relation_OId(X1)))), inference(split_conjunct,[status(thm)],[c_0_5324])). 4.46/4.71 cnf(c_0_8491, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),c_Transitive__Closure_Otrancl(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_5366])). 4.46/4.71 fof(c_0_8492, plain, ![X4463, X4464, X4465, X4466, X4467]:(~c_Relation_Osingle__valued(X4467,X4466,X4465)|(~c_Relation_Osingle__valued(X4466,X4464,X4463)|c_Relation_Osingle__valued(X4467,X4464,hAPP(hAPP(c_Relation_Orel__comp(X4467,X4466,X4464),X4465),X4463)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_single__valued__rel__comp])])])). 4.46/4.71 fof(c_0_8493, plain, ![X9284, X9285, X9286]:(~class_Complete__Lattice_Ocomplete__lattice(X9286)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9286),X9285),c_Complete__Lattice_OInf__class_OInf(X9286,X9284))=c_Complete__Lattice_OInf__class_OInf(X9286,hAPP(hAPP(c_Set_Oinsert(X9286),X9285),X9284))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__insert])])])). 4.46/4.71 cnf(c_0_8494, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5439])). 4.46/4.71 cnf(c_0_8495, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_5440])). 4.46/4.71 cnf(c_0_8496, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5441])). 4.46/4.71 cnf(c_0_8497, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_5444])). 4.46/4.71 fof(c_0_8498, plain, ![X6161, X6162, X6163]:(~class_Complete__Lattice_Ocomplete__lattice(X6163)|c_Complete__Lattice_OSup__class_OSup(X6163,hAPP(hAPP(c_Set_Oinsert(X6163),X6162),X6161))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6163),X6162),c_Complete__Lattice_OSup__class_OSup(X6163,X6161))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__insert])])])). 4.46/4.71 fof(c_0_8499, plain, ![X1851, X1852, X1853, X1854, X1855]:(((X1853!=X1851|X1854!=X1852|hAPP(hAPP(c_Set_Oinsert(X1855),X1852),hAPP(hAPP(c_Set_Oinsert(X1855),X1851),c_Orderings_Obot__class_Obot(tc_fun(X1855,tc_HOL_Obool))))=hAPP(hAPP(c_Set_Oinsert(X1855),X1854),hAPP(hAPP(c_Set_Oinsert(X1855),X1853),c_Orderings_Obot__class_Obot(tc_fun(X1855,tc_HOL_Obool)))))&(X1851!=X1854|X1852!=X1853|hAPP(hAPP(c_Set_Oinsert(X1855),X1852),hAPP(hAPP(c_Set_Oinsert(X1855),X1851),c_Orderings_Obot__class_Obot(tc_fun(X1855,tc_HOL_Obool))))=hAPP(hAPP(c_Set_Oinsert(X1855),X1854),hAPP(hAPP(c_Set_Oinsert(X1855),X1853),c_Orderings_Obot__class_Obot(tc_fun(X1855,tc_HOL_Obool))))))&(((X1851=X1854|X1853=X1851|hAPP(hAPP(c_Set_Oinsert(X1855),X1852),hAPP(hAPP(c_Set_Oinsert(X1855),X1851),c_Orderings_Obot__class_Obot(tc_fun(X1855,tc_HOL_Obool))))!=hAPP(hAPP(c_Set_Oinsert(X1855),X1854),hAPP(hAPP(c_Set_Oinsert(X1855),X1853),c_Orderings_Obot__class_Obot(tc_fun(X1855,tc_HOL_Obool)))))&(X1852=X1853|X1853=X1851|hAPP(hAPP(c_Set_Oinsert(X1855),X1852),hAPP(hAPP(c_Set_Oinsert(X1855),X1851),c_Orderings_Obot__class_Obot(tc_fun(X1855,tc_HOL_Obool))))!=hAPP(hAPP(c_Set_Oinsert(X1855),X1854),hAPP(hAPP(c_Set_Oinsert(X1855),X1853),c_Orderings_Obot__class_Obot(tc_fun(X1855,tc_HOL_Obool))))))&((X1851=X1854|X1854=X1852|hAPP(hAPP(c_Set_Oinsert(X1855),X1852),hAPP(hAPP(c_Set_Oinsert(X1855),X1851),c_Orderings_Obot__class_Obot(tc_fun(X1855,tc_HOL_Obool))))!=hAPP(hAPP(c_Set_Oinsert(X1855),X1854),hAPP(hAPP(c_Set_Oinsert(X1855),X1853),c_Orderings_Obot__class_Obot(tc_fun(X1855,tc_HOL_Obool)))))&(X1852=X1853|X1854=X1852|hAPP(hAPP(c_Set_Oinsert(X1855),X1852),hAPP(hAPP(c_Set_Oinsert(X1855),X1851),c_Orderings_Obot__class_Obot(tc_fun(X1855,tc_HOL_Obool))))!=hAPP(hAPP(c_Set_Oinsert(X1855),X1854),hAPP(hAPP(c_Set_Oinsert(X1855),X1853),c_Orderings_Obot__class_Obot(tc_fun(X1855,tc_HOL_Obool)))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff])])])). 4.46/4.71 fof(c_0_8500, plain, ![X14805, X14806, X14807]:((X14806!=X14805|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14807),X14805)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14807),X14806)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14807)))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14807),X14805)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14807),X14806)|X14806=X14805|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14807)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])])). 4.46/4.71 fof(c_0_8501, plain, ![X8741, X8742, X8743]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X8743),X8742))|c_Random_Ominus__shift(X8741,X8743,X8742)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X8743),X8742))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X8743),X8742))|c_Random_Ominus__shift(X8741,X8743,X8742)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X8741),X8743)),X8742))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__shift__def])])])). 4.46/4.71 fof(c_0_8502, plain, ![X10094, X10095, X10096]:(~class_Lazy__Sequence_Osmall__lazy(X10095)|~class_Lazy__Sequence_Osmall__lazy(X10096)|c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X10096,X10095),X10094)=c_Lazy__Sequence_Oproduct(X10096,X10095,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X10096,X10094),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X10095,X10094))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_small__lazy__prod__def])])])). 4.46/4.71 fof(c_0_8503, plain, ![X8312, X8313]:(c_List_Olist_ONil(X8312)=X8313|hBOOL(hAPP(hAPP(c_member(X8312),c_List_Olast(X8312,X8313)),hAPP(c_List_Oset(X8312),X8313)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_last__in__set])])])). 4.46/4.71 fof(c_0_8504, plain, ![X4631, X4632, X4633]:(~class_Orderings_Olinorder(X4633)|(~c_List_Olinorder__class_Osorted(X4633,X4632)|(~hBOOL(hAPP(c_List_Odistinct(X4633),X4632))|(~c_List_Olinorder__class_Osorted(X4633,X4631)|(~hBOOL(hAPP(c_List_Odistinct(X4633),X4631))|(hAPP(c_List_Oset(X4633),X4631)!=hAPP(c_List_Oset(X4633),X4632)|X4631=X4632)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__distinct__set__unique])])])). 4.46/4.71 fof(c_0_8505, plain, ![X13855, X13856, X13857, X13859, X13860, X13861, X13862, X13863]:(((~hBOOL(hAPP(X13857,X13859))|X13859=esk403_3(X13855,X13856,X13857)|X13855=c_FunDef_OTHE__default(X13856,X13855,X13857))&(hBOOL(hAPP(X13857,esk403_3(X13855,X13856,X13857)))|X13855=c_FunDef_OTHE__default(X13856,X13855,X13857)))&((hBOOL(hAPP(X13862,esk404_4(X13860,X13861,X13862,X13863)))|~hBOOL(hAPP(X13862,X13863))|c_FunDef_OTHE__default(X13861,X13860,X13862)=c_HOL_OThe(X13861,X13862))&(X13863!=esk404_4(X13860,X13861,X13862,X13863)|~hBOOL(hAPP(X13862,X13863))|c_FunDef_OTHE__default(X13861,X13860,X13862)=c_HOL_OThe(X13861,X13862)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_THE__default__def])])])])])])])). 4.46/4.71 fof(c_0_8506, plain, ![X1785, X1786]:((X1785=c_List_Olist_ONil(X1786)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1786)),X1785))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1786)),X1785)))|X1785!=c_List_Olist_ONil(X1786))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__greater__0__conv])])). 4.46/4.71 cnf(c_0_8507, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk190_3(X2,X3,X1)),X2)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5502])). 4.46/4.71 fof(c_0_8508, plain, ![X4627, X4628, X4629, X4630]:(~class_Orderings_Olinorder(X4630)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4629)),X4627)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4629)),c_List_Olinorder__class_Osort__key(X4629,X4630,X4628,X4627))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__sort])])). 4.46/4.71 fof(c_0_8509, plain, ![X4524, X4525, X4526, X4527, X4528]:((~c_List_Olist__all2(X4528,X4527,X4526,hAPP(c_List_Orev(X4528),X4525),X4524)|c_List_Olist__all2(X4528,X4527,X4526,X4525,hAPP(c_List_Orev(X4527),X4524)))&(~c_List_Olist__all2(X4528,X4527,X4526,X4525,hAPP(c_List_Orev(X4527),X4524))|c_List_Olist__all2(X4528,X4527,X4526,hAPP(c_List_Orev(X4528),X4525),X4524))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__rev1])])). 4.46/4.71 cnf(c_0_8510, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X4)=X3|X4=c_Groups_Ozero__class_Ozero(X2)|X1!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)|~class_Rings_Odivision__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_5503])). 4.46/4.71 fof(c_0_8511, plain, ![X12658, X12659, X12660]:(~class_Groups_Oab__group__add(X12660)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12660),X12658),X12659)=hAPP(c_Groups_Ouminus__class_Ouminus(X12660),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12660),X12659),X12658))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__diff__eq])])). 4.46/4.71 cnf(c_0_8512, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1)))|~hBOOL(hAPP(X2,esk206_2(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_5472])). 4.46/4.71 cnf(c_0_8513, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk206_2(X2,X1))=X2|hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5472])). 4.46/4.71 fof(c_0_8514, plain, ![X3846, X3848, X3849, X3850]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X3846))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3848),X3846))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3848),esk98_1(X3846)))))&((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk99_2(X3849,X3850)),X3849))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X3849)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk99_2(X3849,X3850)),X3850))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X3849))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__nat__set__iff__bounded])])])])])])])). 4.46/4.71 fof(c_0_8515, plain, ![X14488, X14490, X14491, X14492]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X14488))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X14490),X14488))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14490),esk423_1(X14488)))))&((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk424_2(X14491,X14492)),X14491))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X14491)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk424_2(X14491,X14492)),X14492))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X14491))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__nat__set__iff__bounded__le])])])])])])])). 4.46/4.71 fof(c_0_8516, plain, ![X13635, X13636, X13637, X13638, X13639]:(~c_Typedef_Otype__definition(X13639,X13638,X13637,X13636,X13635)|hAPP(c_Set_Oimage(X13639,X13638,X13637),c_Orderings_Otop__class_Otop(tc_fun(X13639,tc_HOL_Obool)))=X13635), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_type__definition_ORep__range])])])). 4.46/4.71 cnf(c_0_8517, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(rw,[status(thm)],[c_0_5504, c_0_4443])). 4.46/4.71 fof(c_0_8518, plain, ![X1140, X1141, X1142]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1142),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1141)),X1140))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1142,X1141),hAPP(c_Divides_OnegateSnd,X1140)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__neg])])])). 4.46/4.71 cnf(c_0_8519, plain, (X2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)|X3=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)!=X4|~class_Rings_Odivision__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5503])). 4.46/4.71 fof(c_0_8520, plain, ![X3239, X3240]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3240),X3239))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3239),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3239),X3240))=X3240), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__diff__cancel])])])). 4.46/4.71 fof(c_0_8521, plain, ![X12219, X12220]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12220),X12219))|X12219=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12220),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12219),X12220))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__add__diff__inverse])])])). 4.46/4.71 fof(c_0_8522, plain, ![X3072, X3073, X3074]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3074),hAPP(c_Groups_Ouminus__class_Ouminus(X3074),X3073)),hAPP(c_Groups_Ouminus__class_Ouminus(X3074),X3072)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3074),X3072),X3073))|~class_Groups_Oordered__ab__group__add(X3074))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3074),X3072),X3073))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3074),hAPP(c_Groups_Ouminus__class_Ouminus(X3074),X3073)),hAPP(c_Groups_Ouminus__class_Ouminus(X3074),X3072)))|~class_Groups_Oordered__ab__group__add(X3074))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__le__iff__le])])])])). 4.46/4.71 fof(c_0_8523, plain, ![X3447, X3448]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3447),X3448))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3448),X3447))), inference(variable_rename,[status(thm)],[fact_nat__le__linear])). 4.46/4.71 fof(c_0_8524, plain, ![X6134, X6135]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6134),X6135))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6135),X6134))), inference(variable_rename,[status(thm)],[fact_zle__linear])). 4.46/4.71 fof(c_0_8525, plain, ![X6331, X6332, X6333, X6334, X6335]:(hAPP(hAPP(c_List_Omap(X6335,X6334),X6333),X6331)!=hAPP(hAPP(c_List_Omap(X6335,X6334),X6333),X6332)|(~c_Fun_Oinj__on(X6335,X6334,X6333,c_Orderings_Otop__class_Otop(tc_fun(X6335,tc_HOL_Obool)))|X6331=X6332)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__injective])])])). 4.46/4.71 cnf(c_0_8526, plain, (X4=c_Groups_Ozero__class_Ozero(X2)|X3=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X4)|X1!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)|~class_Fields_Ofield__inverse__zero(X2)), inference(split_conjunct,[status(thm)],[c_0_5494])). 4.46/4.71 fof(c_0_8527, plain, ![X8116, X8117, X8118, X8119]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X8119,X8118),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X8117),X8116)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X8118|c_Divides_Odiv__class_Omod(tc_Int_Oint,X8119,X8118)=X8116)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__mod])])])). 4.46/4.71 fof(c_0_8528, plain, ![X437, X438, X439]:(~class_Rings_Olinordered__semidom(X439)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X439),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X439),X438)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X439),X437)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X438),X437)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__less__imp__less])])])). 4.46/4.71 fof(c_0_8529, plain, ![X15288, X15289, X15290]:(~class_Groups_Oab__group__add(X15290)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15290),X15289),hAPP(c_Groups_Ouminus__class_Ouminus(X15290),X15288))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15290),X15289),X15288)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ab__diff__minus])])])). 4.46/4.71 fof(c_0_8530, plain, ![X15671, X15672, X15673, X15674, X15675]:(~c_Finite__Set_Ofun__left__comm__idem(X15675,X15674,X15673)|hAPP(hAPP(X15673,X15672),hAPP(hAPP(X15673,X15672),X15671))=hAPP(hAPP(X15673,X15672),X15671)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__idem])])). 4.46/4.71 fof(c_0_8531, plain, ![X12192, X12193, X12194, X12195]:((c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X12195,X12194),tc_HOL_Obool))!=hAPP(hAPP(c_Product__Type_OSigma(X12195,X12194),X12193),hAPP(c_COMBK(tc_fun(X12194,tc_HOL_Obool),X12195),X12192))|(c_Orderings_Obot__class_Obot(tc_fun(X12194,tc_HOL_Obool))=X12192|c_Orderings_Obot__class_Obot(tc_fun(X12195,tc_HOL_Obool))=X12193))&((c_Orderings_Obot__class_Obot(tc_fun(X12194,tc_HOL_Obool))!=X12192|c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X12195,X12194),tc_HOL_Obool))=hAPP(hAPP(c_Product__Type_OSigma(X12195,X12194),X12193),hAPP(c_COMBK(tc_fun(X12194,tc_HOL_Obool),X12195),X12192)))&(c_Orderings_Obot__class_Obot(tc_fun(X12195,tc_HOL_Obool))!=X12193|c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X12195,X12194),tc_HOL_Obool))=hAPP(hAPP(c_Product__Type_OSigma(X12195,X12194),X12193),hAPP(c_COMBK(tc_fun(X12194,tc_HOL_Obool),X12195),X12192))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__empty])])])). 4.46/4.71 cnf(c_0_8532, plain, (c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X2))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5505])). 4.46/4.71 fof(c_0_8533, plain, ![X6046, X6047, X6048]:((X6048!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Obot__class_Obot(tc_fun(X6047,tc_HOL_Obool))=hAPP(c_List_Oset(X6047),c_List_Oreplicate(X6047,X6048,X6046)))&(X6048=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_List_Oset(X6047),c_List_Oreplicate(X6047,X6048,X6046))=hAPP(hAPP(c_Set_Oinsert(X6047),X6046),c_Orderings_Obot__class_Obot(tc_fun(X6047,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__replicate__conv__if])])])). 4.46/4.71 fof(c_0_8534, plain, ![X5412, X5413, X5414]:(~class_Groups_Ogroup__add(X5414)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5414),X5413),hAPP(c_Groups_Ouminus__class_Ouminus(X5414),X5412))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5414),X5413),X5412)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__def])])). 4.46/4.71 cnf(c_0_8535, plain, (esk407_2(X3,X1)=X2|hAPP(c_List_Oset(X1),X2)!=X3|~hBOOL(hAPP(c_List_Odistinct(X1),X2))|~c_List_Olinorder__class_Osorted(X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5506])). 4.46/4.71 cnf(c_0_8536, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_5507]), ['final']). 4.46/4.71 fof(c_0_8537, plain, ![X2907, X2908, X2909, X2910, X2911, X2912, X2913]:(~c_Finite__Set_Ofun__left__comm(X2913,X2912,X2911)|(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X2913,X2912,X2911,X2910,X2909),X2908))|(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X2913,X2912,X2911,X2910,X2909),X2907))|X2908=X2907))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__graph__determ])])])). 4.46/4.71 fof(c_0_8538, plain, ![X13331, X13332, X13333]:(~class_Groups_Ogroup__add(X13333)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13333),X13332),hAPP(c_Groups_Ouminus__class_Ouminus(X13333),X13331))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13333),X13332),X13331)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add])])). 4.46/4.71 fof(c_0_8539, plain, ![X3082, X3083, X3084, X3085]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3085,tc_HOL_Obool)),X3084),X3083))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3085,tc_HOL_Obool)),X3084),hAPP(hAPP(c_Set_Oinsert(X3085),X3082),X3083)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])])). 4.46/4.71 fof(c_0_8540, plain, ![X4781, X4782, X4783, X4784, X4785]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4785),X4784))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4783,tc_HOL_Obool)),X4782),hAPP(c_Set_Oimage(X4785,X4783,X4781),X4784)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X4783),X4782)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__surj])])])). 4.46/4.71 fof(c_0_8541, plain, ![X16593, X16594, X16595]:((~c_List_Olinorder__class_Osorted(X16595,X16593)|c_List_Olinorder__class_Osorted(X16595,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16595,X16595,c_COMBI(X16595)),X16594),X16593))|~class_Orderings_Olinorder(X16595))&(~c_List_Olinorder__class_Osorted(X16595,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16595,X16595,c_COMBI(X16595)),X16594),X16593))|c_List_Olinorder__class_Osorted(X16595,X16593)|~class_Orderings_Olinorder(X16595))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort])])])). 4.46/4.71 fof(c_0_8542, plain, ![X2276, X2277, X2278]:(~class_Lattices_Oboolean__algebra(X2278)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2278),X2277),hAPP(c_Groups_Ouminus__class_Ouminus(X2278),X2276))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2278),X2277),X2276)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq])])). 4.46/4.71 fof(c_0_8543, plain, ![X5935, X5936, X5937]:(~class_Orderings_Olinorder(X5937)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5937),X5936),X5935))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5937),X5935),X5936)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_leI])])])). 4.46/4.71 cnf(c_0_8544, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5508])). 4.46/4.71 cnf(c_0_8545, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|c_List_Oupt(X1,X2)!=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_4649])). 4.46/4.71 cnf(c_0_8546, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X2),X1),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X2),X1),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5509])). 4.46/4.71 fof(c_0_8547, plain, ![X8420, X8421, X8422]:((c_Orderings_Obot__class_Obot(tc_fun(X8422,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8422,tc_HOL_Obool)),X8421),X8420)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8422,tc_HOL_Obool)),X8421),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8422,tc_HOL_Obool)),X8420))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8422,tc_HOL_Obool)),X8421),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8422,tc_HOL_Obool)),X8420)))|c_Orderings_Obot__class_Obot(tc_fun(X8422,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8422,tc_HOL_Obool)),X8421),X8420))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_disjoint__eq__subset__Compl])])). 4.46/4.71 fof(c_0_8548, plain, ![X5527, X5528, X5529, X5530]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5530),X5529))|hAPP(hAPP(c_List_Onth(X5528),c_List_Oreplicate(X5528,X5529,X5527)),X5530)=X5527), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__replicate])])])). 4.46/4.71 cnf(c_0_8549, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))|c_List_Olist_ONil(tc_Nat_Onat)!=c_List_Oupt(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5510])). 4.46/4.71 fof(c_0_8550, plain, ![X7568, X7569, X7570]:(~class_Rings_Ocomm__ring__1(X7570)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7570),X7569),X7568)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7570),X7569),hAPP(c_Groups_Ouminus__class_Ouminus(X7570),X7568))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J])])). 4.46/4.71 fof(c_0_8551, plain, ![X4374, X4375, X4376]:(~hBOOL(hAPP(hAPP(c_member(tc_fun(X4376,tc_HOL_Obool)),X4375),X4374))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4376,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4376,tc_HOL_Obool),X4374)),X4375))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inter__lower])])])). 4.46/4.71 fof(c_0_8552, plain, ![X4166, X4167, X4168]:(~hBOOL(hAPP(hAPP(c_member(tc_fun(X4168,tc_HOL_Obool)),X4167),X4166))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4168,tc_HOL_Obool)),X4167),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4168,tc_HOL_Obool),X4166)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__upper])])). 4.46/4.71 cnf(c_0_8553, plain, (hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_5511])). 4.46/4.71 fof(c_0_8554, plain, ![X17520]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk524_1(X17520)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17520)))&(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk524_1(X17520))=X17520|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17520)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__imp__eq__int])])])])])). 4.46/4.71 fof(c_0_8555, plain, ![X11923, X11924, X11925]:(~class_Complete__Lattice_Ocomplete__lattice(X11925)|(~hBOOL(hAPP(hAPP(c_member(X11925),X11924),X11923))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11925),c_Complete__Lattice_OInf__class_OInf(X11925,X11923)),X11924)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__lower])])])). 4.46/4.71 fof(c_0_8556, plain, ![X1212, X1213, X1214]:(~class_Complete__Lattice_Ocomplete__lattice(X1214)|(~hBOOL(hAPP(hAPP(c_member(X1214),X1213),X1212))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1214),X1213),c_Complete__Lattice_OSup__class_OSup(X1214,X1212))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__upper])])). 4.46/4.71 fof(c_0_8557, plain, ![X5766, X5767, X5768, X5769]:(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5769)),X5768),hAPP(c_List_Oset(tc_List_Olist(X5769)),c_Enum_On__lists(X5769,X5767,X5766))))|X5767=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5769)),X5768)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__n__lists__elem])])). 4.46/4.71 fof(c_0_8558, plain, ![X5670, X5671]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5671),X5670),c_Groups_Ozero__class_Ozero(X5671)))|hAPP(c_Groups_Oabs__class_Oabs(X5671),X5670)=hAPP(c_Groups_Ouminus__class_Ouminus(X5671),X5670)|~class_Groups_Oabs__if(X5671))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5671),X5670),c_Groups_Ozero__class_Ozero(X5671)))|hAPP(c_Groups_Oabs__class_Oabs(X5671),X5670)=X5670|~class_Groups_Oabs__if(X5671))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__if])])])])). 4.46/4.71 cnf(c_0_8559, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5426])). 4.46/4.71 cnf(c_0_8560, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5422])). 4.46/4.71 fof(c_0_8561, plain, ![X6548, X6549, X6550]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6550,tc_HOL_Obool)),X6549),X6548))|hBOOL(hAPP(hAPP(c_member(tc_fun(X6550,tc_HOL_Obool)),X6549),hAPP(c_Set_OPow(X6550),X6548)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_PowI])])). 4.46/4.71 cnf(c_0_8562, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),X1))|~c_Com_OWT__bodies|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),X1),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))), inference(split_conjunct,[status(thm)],[c_0_5512])). 4.46/4.71 fof(c_0_8563, plain, ![X15875, X15876, X15877]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15877,tc_HOL_Obool)),X15876),hAPP(hAPP(c_Set_Oinsert(X15877),X15875),c_Orderings_Obot__class_Obot(tc_fun(X15877,tc_HOL_Obool)))))|(c_Orderings_Obot__class_Obot(tc_fun(X15877,tc_HOL_Obool))=X15876|hAPP(hAPP(c_Set_Oinsert(X15877),X15875),c_Orderings_Obot__class_Obot(tc_fun(X15877,tc_HOL_Obool)))=X15876)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__singletonD])])])). 4.46/4.71 fof(c_0_8564, plain, ![X13383, X13384, X13385]:(~class_Divides_Osemiring__div(X13385)|c_Divides_Odiv__class_Omod(X13385,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13385),X13384),X13383),X13383)=c_Divides_Odiv__class_Omod(X13385,X13384,X13383)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__add__self2])])])). 4.46/4.71 fof(c_0_8565, plain, ![X13154, X13155, X13156]:(~class_Divides_Osemiring__div(X13156)|c_Divides_Odiv__class_Omod(X13156,X13154,X13155)=c_Divides_Odiv__class_Omod(X13156,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13156),X13155),X13154),X13155)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self1])])). 4.46/4.71 cnf(c_0_8566, plain, (hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),esk283_2(X1,X2)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))|c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))|~hBOOL(hAPP(c_Com_OWT,X1))|~c_Hoare__Mirabelle_Ostate__not__singleton), inference(split_conjunct,[status(thm)],[c_0_5513])). 4.46/4.71 fof(c_0_8567, plain, ![X7833, X7834, X7835, X7836, X7837]:(((hBOOL(hAPP(hAPP(X7836,X7834),X7833))|~hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X7837,X7836,X7835),X7834),X7833)))&(hBOOL(hAPP(X7835,X7833))|~hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X7837,X7836,X7835),X7834),X7833))))&(~hBOOL(hAPP(hAPP(X7836,X7834),X7833))|~hBOOL(hAPP(X7835,X7833))|hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X7837,X7836,X7835),X7834),X7833)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_peek__and__def])])])). 4.46/4.71 fof(c_0_8568, plain, ![X15455, X15456, X15457, X15459, X15460, X15461, X15462]:(((hBOOL(hAPP(hAPP(X15456,esk453_3(X15455,X15456,X15457)),X15455))|hBOOL(hAPP(c_Wellfounded_Oaccp(X15457,X15456),X15455)))&(~hBOOL(hAPP(c_Wellfounded_Oaccp(X15457,X15456),esk453_3(X15455,X15456,X15457)))|hBOOL(hAPP(c_Wellfounded_Oaccp(X15457,X15456),X15455))))&(~hBOOL(hAPP(c_Wellfounded_Oaccp(X15461,X15460),X15459))|(~hBOOL(hAPP(hAPP(X15460,X15462),X15459))|hBOOL(hAPP(c_Wellfounded_Oaccp(X15461,X15460),X15462))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_accp_Osimps])])])])])])])). 4.46/4.71 fof(c_0_8569, plain, ![X3842, X3843, X3844, X3845]:(((X3843!=X3844|hBOOL(hAPP(hAPP(c_member(X3845),X3844),hAPP(hAPP(c_Set_Oinsert(X3845),X3843),X3842))))&(~hBOOL(hAPP(hAPP(c_member(X3845),X3844),X3842))|hBOOL(hAPP(hAPP(c_member(X3845),X3844),hAPP(hAPP(c_Set_Oinsert(X3845),X3843),X3842)))))&(~hBOOL(hAPP(hAPP(c_member(X3845),X3844),hAPP(hAPP(c_Set_Oinsert(X3845),X3843),X3842)))|(X3843=X3844|hBOOL(hAPP(hAPP(c_member(X3845),X3844),X3842))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])])). 4.46/4.71 fof(c_0_8570, plain, ![X8569, X8570, X8571, X8573, X8574, X8575, X8576]:(((hBOOL(hAPP(hAPP(X8570,esk240_3(X8569,X8570,X8571)),X8569))|hBOOL(hAPP(c_Wellfounded_Oaccp(X8571,X8570),X8569)))&(~hBOOL(hAPP(c_Wellfounded_Oaccp(X8571,X8570),esk240_3(X8569,X8570,X8571)))|hBOOL(hAPP(c_Wellfounded_Oaccp(X8571,X8570),X8569))))&(~hBOOL(hAPP(c_Wellfounded_Oaccp(X8575,X8574),X8573))|(~hBOOL(hAPP(hAPP(X8574,X8576),X8573))|hBOOL(hAPP(c_Wellfounded_Oaccp(X8575,X8574),X8576))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp_Oequations])])])])])])). 4.46/4.71 fof(c_0_8571, plain, ![X11171, X11172, X11173]:((hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X11173,X11172),X11171)!=c_Orderings_Obot__class_Obot(tc_fun(X11173,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11173),X11172),X11171))|~class_Orderings_Oorder(X11173))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11173),X11172),X11171))|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X11173,X11172),X11171)=c_Orderings_Obot__class_Obot(tc_fun(X11173,tc_HOL_Obool))|~class_Orderings_Oorder(X11173))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff2])])])])). 4.46/4.71 fof(c_0_8572, plain, ![X14339, X14340, X14341]:(~class_Lattices_Osemilattice__inf(X14341)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14341),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X14341),X14340),X14339)),X14340))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__le1])])])). 4.46/4.71 fof(c_0_8573, plain, ![X11839, X11840, X11841]:(~class_Lattices_Olattice(X11841)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11841),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X11841),X11840),X11839)),X11840))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__ord_I1_J])])])). 4.46/4.71 fof(c_0_8574, plain, ![X10149, X10150]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10150))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X10149,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X10150))=c_SMT_Oz3mod(X10149,X10150))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10150))|c_SMT_Oz3mod(X10149,X10150)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X10149,X10150))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_z3mod__def])])])). 4.46/4.71 fof(c_0_8575, plain, ![X1840, X1841, X1842]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1842),X1841),X1840))|X1840=X1841|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1842),X1841),X1840))|~class_Orderings_Olinorder(X1842))&(X1840!=X1841|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1842),X1841),X1840))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1842),X1841),X1840))|~class_Orderings_Olinorder(X1842))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2])])])])). 4.46/4.71 fof(c_0_8576, plain, ![X1007, X1008, X1009]:(~class_Orderings_Oorder(X1009)|(X1008=X1007|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1009),X1007),X1008))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1009),X1007),X1008))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I12_J])])])). 4.46/4.71 cnf(c_0_8577, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)!=X3|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_5514])). 4.46/4.71 fof(c_0_8578, plain, ![X2613, X2614, X2615]:(~class_Lattices_Osemilattice__inf(X2615)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2615),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2615),X2614),X2613)),X2613))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le2])])). 4.46/4.71 fof(c_0_8579, plain, ![X11256, X11257, X11258]:(~class_Lattices_Olattice(X11258)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11258),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X11258),X11257),X11256)),X11256))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__ord_I2_J])])])). 4.46/4.71 fof(c_0_8580, plain, ![X14250, X14251, X14252]:(~class_Lattices_Osemilattice__sup(X14252)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14252),X14251),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X14252),X14251),X14250)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__ge1])])])). 4.46/4.71 fof(c_0_8581, plain, ![X10631, X10632, X10633]:(~class_Lattices_Olattice(X10633)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10633),X10632),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10633),X10632),X10631)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I3_J])])). 4.46/4.71 fof(c_0_8582, plain, ![X7143, X7144, X7145, X7146, X7147]:(~class_Orderings_Olinorder(X7147)|(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7147,X7146),X7145)!=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7147,X7144),X7143)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7147),X7146),X7145))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7147),X7144),X7143))|X7146=X7144)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__inj_I1_J])])])). 4.46/4.71 fof(c_0_8583, plain, ![X2802, X2803, X2804, X2805, X2806]:(~class_Orderings_Olinorder(X2806)|(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X2806,X2805),X2804)!=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X2806,X2803),X2802)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2806),X2805),X2804))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2806),X2803),X2802))|X2802=X2804)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__inj_I2_J])])])). 4.46/4.71 fof(c_0_8584, plain, ![X15612, X15613, X15614]:(~class_Lattices_Osemilattice__sup(X15614)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15614),X15613),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15614),X15612),X15613)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__ge2])])). 4.46/4.71 fof(c_0_8585, plain, ![X11131, X11132, X11133]:(~class_Lattices_Olattice(X11133)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11133),X11132),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X11133),X11131),X11132)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__ord_I4_J])])])). 4.46/4.71 fof(c_0_8586, plain, ![X14478, X14479, X14480]:(~c_Wellfounded_Owf(X14480,X14479)|c_Wellfounded_Owf(X14480,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X14480,X14480),tc_HOL_Obool)),X14479),X14478))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Int1])])). 4.46/4.71 fof(c_0_8587, plain, ![X9781, X9782, X9783]:(~c_Wellfounded_Owf(X9783,X9782)|c_Wellfounded_Owf(X9783,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X9783,X9783),tc_HOL_Obool)),X9781),X9782))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Int2])])). 4.46/4.71 fof(c_0_8588, plain, ![X2144, X2145, X2146, X2147, X2148, X2149]:(~c_Finite__Set_Ofun__left__comm(X2149,X2148,X2147)|(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X2149,X2148,X2147,X2146,X2145),X2144))|X2144=hAPP(hAPP(c_Finite__Set_Ofold(X2149,X2148,X2147),X2146),X2145))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__equality])])])). 4.46/4.71 fof(c_0_8589, plain, ![X6585, X6586, X6587, X6588, X6589]:(~class_Orderings_Olinorder(X6589)|(~hBOOL(hAPP(c_List_Odistinct(X6588),X6587))|hBOOL(hAPP(c_List_Odistinct(X6588),c_List_Olinorder__class_Oinsort__insert__key(X6588,X6589,X6586,X6585,X6587))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__insort__insert])])])). 4.46/4.71 cnf(c_0_8590, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1), inference(split_conjunct,[status(thm)],[c_0_5515])). 4.46/4.71 cnf(c_0_8591, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))|~hBOOL(hAPP(X1,esk394_1(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5516])). 4.46/4.71 fof(c_0_8592, plain, ![X13562, X13563]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13563),c_Groups_Oone__class_Oone(tc_Int_Oint))),X13562))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13563),X13562)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13563),X13562))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13563),c_Groups_Oone__class_Oone(tc_Int_Oint))),X13562)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])])). 4.46/4.71 fof(c_0_8593, plain, ![X3766, X3767, X3768, X3769, X3770, X3771]:(~c_Typedef_Otype__definition(X3771,X3770,X3769,X3768,X3767)|(~hBOOL(hAPP(hAPP(c_member(X3770),X3766),X3767))|X3766=hAPP(X3769,hAPP(X3768,X3766)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_type__definition_OAbs__inverse])])])). 4.46/4.71 fof(c_0_8594, plain, ![X7769, X7770, X7771, X7772]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7772),X7771),X7769))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7772),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7772),X7771),X7770)),X7769))|~class_Lattices_Osemilattice__sup(X7772))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7772),X7770),X7769))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7772),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7772),X7771),X7770)),X7769))|~class_Lattices_Osemilattice__sup(X7772))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__supE])])])])). 4.46/4.71 fof(c_0_8595, plain, ![X3290, X3291, X3292, X3293]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3293),X3292),X3291))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3293),X3292),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3293),X3291),X3290)))|~class_Lattices_Osemilattice__inf(X3293))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3293),X3292),X3290))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3293),X3292),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3293),X3291),X3290)))|~class_Lattices_Osemilattice__inf(X3293))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__infE])])])])). 4.46/4.71 fof(c_0_8596, plain, ![X3046, X3047, X3048, X3049, X3050]:(hBOOL(hAPP(hAPP(c_member(X3050),X3049),X3048))|c_Option_Ooption_ONone(X3047)=hAPP(c_Map_Orestrict__map(X3050,X3047,X3046,X3048),X3049)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_restrict__out])])])). 4.46/4.71 cnf(c_0_8597, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1))), inference(split_conjunct,[status(thm)],[c_0_5517])). 4.46/4.71 fof(c_0_8598, plain, ![X17522, X17523, X17524, X17525]:((~hBOOL(hAPP(hAPP(c_member(X17525),X17524),c_SetInterval_Oord_OlessThan(X17525,X17523,X17522)))|hBOOL(hAPP(hAPP(X17523,X17524),X17522)))&(~hBOOL(hAPP(hAPP(X17523,X17524),X17522))|hBOOL(hAPP(hAPP(c_member(X17525),X17524),c_SetInterval_Oord_OlessThan(X17525,X17523,X17522))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OlessThan__iff])])). 4.46/4.71 fof(c_0_8599, plain, ![X9311, X9312, X9313, X9314]:((~hBOOL(hAPP(hAPP(c_member(X9314),X9313),c_SetInterval_Oord_OatMost(X9314,X9312,X9311)))|hBOOL(hAPP(hAPP(X9312,X9313),X9311)))&(~hBOOL(hAPP(hAPP(X9312,X9313),X9311))|hBOOL(hAPP(hAPP(c_member(X9314),X9313),c_SetInterval_Oord_OatMost(X9314,X9312,X9311))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatMost__iff])])). 4.46/4.71 fof(c_0_8600, plain, ![X16116, X16117, X16118, X16119]:((~hBOOL(hAPP(hAPP(c_member(X16119),X16118),c_SetInterval_Oord_OgreaterThan(X16119,X16117,X16116)))|hBOOL(hAPP(hAPP(X16117,X16116),X16118)))&(~hBOOL(hAPP(hAPP(X16117,X16116),X16118))|hBOOL(hAPP(hAPP(c_member(X16119),X16118),c_SetInterval_Oord_OgreaterThan(X16119,X16117,X16116))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThan__iff])])). 4.46/4.71 fof(c_0_8601, plain, ![X2493, X2494]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2494),X2493))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2493),hAPP(c_Nat_OSuc,X2494))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2493),hAPP(c_Nat_OSuc,X2494)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2494),X2493)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__less__eq])])])). 4.46/4.71 cnf(c_0_8602, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)|c_Groups_Ozero__class_Ozero(X1)!=X2|hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber(X1)), inference(split_conjunct,[status(thm)],[c_0_5359])). 4.46/4.71 cnf(c_0_8603, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))), inference(split_conjunct,[status(thm)],[c_0_5473])). 4.46/4.71 cnf(c_0_8604, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5289])). 4.46/4.71 fof(c_0_8605, plain, ![X4088, X4089, X4090, X4091]:((~hBOOL(hAPP(hAPP(c_member(X4091),X4090),c_SetInterval_Oord_OatLeast(X4091,X4089,X4088)))|hBOOL(hAPP(hAPP(X4089,X4088),X4090)))&(~hBOOL(hAPP(hAPP(X4089,X4088),X4090))|hBOOL(hAPP(hAPP(c_member(X4091),X4090),c_SetInterval_Oord_OatLeast(X4091,X4089,X4088))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeast__iff])])). 4.46/4.71 cnf(c_0_8606, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,X1)))), inference(split_conjunct,[status(thm)],[c_0_5484])). 4.46/4.71 fof(c_0_8607, plain, ![X2210, X2211]:(((hAPP(c_Nat_OSuc,X2210)!=X2211|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2211),hAPP(c_Nat_OSuc,X2210))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2211),X2210))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2211),hAPP(c_Nat_OSuc,X2210)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2211),hAPP(c_Nat_OSuc,X2210)))|(hAPP(c_Nat_OSuc,X2210)=X2211|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2211),X2210))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])])). 4.46/4.71 cnf(c_0_8608, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5518])). 4.46/4.71 cnf(c_0_8609, plain, (X3=c_Divides_Odivmod__nat(X1,X2)|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5519])). 4.46/4.71 fof(c_0_8610, plain, ![X13018, X13019, X13020, X13021, X13022, X13023]:((X13022!=X13023|X13018=hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13021,X13020),X13019),X13022),X13018),X13023))&(X13023=X13022|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13021,X13020),X13019),X13022),X13018),X13023)=hAPP(X13019,X13023))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__upd__def])])])). 4.46/4.71 fof(c_0_8611, plain, ![X6775, X6776]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X6776),X6775))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X6776)),hAPP(c_Code__Numeral_Onat__of,X6775))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X6776)),hAPP(c_Code__Numeral_Onat__of,X6775)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X6776),X6775)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__code__numeral__def])])). 4.46/4.71 fof(c_0_8612, plain, ![X7086, X7087]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7087),X7086))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X7087)),hAPP(c_Nat_OSuc,X7086)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__mono])])])). 4.46/4.71 cnf(c_0_8613, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5520])). 4.46/4.71 cnf(c_0_8614, plain, (X1=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5521])). 4.46/4.71 fof(c_0_8615, plain, ![X5886, X5887]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X5887)),hAPP(c_Code__Numeral_Onat__of,X5886)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X5887),X5886)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X5887),X5886))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X5887)),hAPP(c_Code__Numeral_Onat__of,X5886))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__def])])). 4.46/4.71 cnf(c_0_8616, plain, (~hBOOL(hAPP(X1,X2))|hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)!=c_List_OdropWhile(X3,X1,X5)), inference(split_conjunct,[status(thm)],[c_0_5127])). 4.46/4.71 cnf(c_0_8617, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X3))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate(X1,X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_5382])). 4.46/4.71 fof(c_0_8618, plain, ![X2689, X2690, X2691]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2691),X2690))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2691,tc_HOL_Obool)),X2690),hAPP(c_Set_Oimage(X2691,X2691,X2689),X2690)))|c_Fun_Oinj__on(X2691,X2691,X2689,X2690))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__surj__inj])])])). 4.46/4.71 fof(c_0_8619, plain, ![X14362, X14363]:(~class_Int_Oring__char__0(X14363)|(~hBOOL(hAPP(hAPP(c_member(X14363),X14362),c_Int_Oring__1__class_OInts(X14363)))|c_Groups_Ozero__class_Ozero(X14363)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14363),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14363),c_Groups_Oone__class_Oone(X14363)),X14362)),X14362))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__odd__nonzero])])])). 4.46/4.71 fof(c_0_8620, plain, ![X5516, X5517]:(~class_Orderings_Olinorder(X5517)|c_List_Olinorder__class_Osorted__list__of__set(X5517,hAPP(c_List_Oset(X5517),X5516))=c_List_Olinorder__class_Osort__key(X5517,X5517,c_COMBI(X5517),c_List_Oremdups(X5517,X5516))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__sort__remdups])])). 4.46/4.71 fof(c_0_8621, plain, ![X11071, X11072]:(~hBOOL(hAPP(c_List_Odistinct(X11072),X11071))|hAPP(c_Finite__Set_Ocard(X11072),hAPP(c_List_Oset(X11072),X11071))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11072)),X11071)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__card])])). 4.46/4.71 cnf(c_0_8622, plain, (c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X2,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5522])). 4.46/4.71 cnf(c_0_8623, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2))=hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5523])). 4.46/4.71 cnf(c_0_8624, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)|~class_Fields_Ofield__inverse__zero(X2)|~class_Int_Onumber(X2)), inference(split_conjunct,[status(thm)],[c_0_5359])). 4.46/4.71 fof(c_0_8625, plain, ![X6690, X6691, X6692]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6692),X6691),X6690))|c_SetInterval_Oord__class_OatLeastAtMost(X6692,X6691,X6690)=c_Orderings_Obot__class_Obot(tc_fun(X6692,tc_HOL_Obool))|~class_Orderings_Oorder(X6692))&(c_SetInterval_Oord__class_OatLeastAtMost(X6692,X6691,X6690)!=c_Orderings_Obot__class_Obot(tc_fun(X6692,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6692),X6691),X6690))|~class_Orderings_Oorder(X6692))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty__iff])])])])). 4.46/4.72 fof(c_0_8626, plain, ![X12513]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X12513),c_Orderings_Otop__class_Otop(tc_fun(X12513,tc_HOL_Obool))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X12513)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X12513),tc_HOL_Obool)))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X12513)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X12513),tc_HOL_Obool))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X12513),c_Orderings_Otop__class_Otop(tc_fun(X12513,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])])). 4.46/4.72 fof(c_0_8627, plain, ![X15914, X15915, X15916, X15917, X15918, X15919]:(~c_Typedef_Otype__definition(X15919,X15918,X15917,X15916,X15915)|hBOOL(hAPP(hAPP(c_member(X15918),hAPP(X15917,X15914)),X15915))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep])])). 4.46/4.72 fof(c_0_8628, plain, ![X11138, X11139]:(~class_Fields_Ofield__inverse__zero(X11139)|~class_Int_Onumber__ring(X11139)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11139),X11138),hAPP(c_Int_Onumber__class_Onumber__of(X11139),c_Int_OMin))=hAPP(c_Groups_Ouminus__class_Ouminus(X11139),X11138)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__minus1])])). 4.46/4.72 fof(c_0_8629, plain, ![X4030]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4030))|X4030=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4030),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__pred_H])])])). 4.46/4.72 fof(c_0_8630, plain, ![X9398, X9399]:(~class_Groups_Oordered__ab__group__add__abs(X9399)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9399),c_Groups_Ozero__class_Ozero(X9399)),hAPP(c_Groups_Oabs__class_Oabs(X9399),X9398)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__zero])])). 4.46/4.72 fof(c_0_8631, plain, ![X9939, X9940]:(~class_Rings_Olinordered__semidom(X9940)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9940),c_Groups_Ozero__class_Ozero(X9940)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X9940),X9939)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__0__le__iff])])])). 4.46/4.72 fof(c_0_8632, plain, ![X4212, X4213]:(~class_Int_Onumber__ring(X4213)|hAPP(c_Groups_Ouminus__class_Ouminus(X4213),X4212)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4213),hAPP(c_Int_Onumber__class_Onumber__of(X4213),c_Int_OMin)),X4212)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__minus1])])])). 4.46/4.72 cnf(c_0_8633, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5524])). 4.46/4.72 fof(c_0_8634, plain, ![X3492, X3493, X3494, X3495]:((~hBOOL(hAPP(hAPP(c_member(X3495),X3494),c_Map_Odom(X3495,X3493,X3492)))|hAPP(X3492,X3494)!=c_Option_Ooption_ONone(X3493))&(hAPP(X3492,X3494)=c_Option_Ooption_ONone(X3493)|hBOOL(hAPP(hAPP(c_member(X3495),X3494),c_Map_Odom(X3495,X3493,X3492))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_domIff])])). 4.46/4.72 fof(c_0_8635, plain, ![X1551, X1552]:(~class_Rings_Oring__1(X1552)|hAPP(c_Groups_Ouminus__class_Ouminus(X1552),hAPP(c_Int_Oring__1__class_Oof__int(X1552),X1551))=hAPP(c_Int_Oring__1__class_Oof__int(X1552),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1551))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__minus])])). 4.46/4.72 cnf(c_0_8636, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onat,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_5525])). 4.46/4.72 fof(c_0_8637, plain, ![X1846, X1847]:(~class_Int_Onumber__ring(X1847)|hAPP(c_Groups_Ouminus__class_Ouminus(X1847),hAPP(c_Int_Onumber__class_Onumber__of(X1847),X1846))=hAPP(c_Int_Onumber__class_Onumber__of(X1847),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1846))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I30_J])])). 4.46/4.72 fof(c_0_8638, plain, ![X9668, X9669]:(~class_Groups_Oordered__ab__group__add__abs(X9669)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9669),X9668),c_Groups_Ozero__class_Ozero(X9669)))|hAPP(c_Groups_Oabs__class_Oabs(X9669),X9668)=hAPP(c_Groups_Ouminus__class_Ouminus(X9669),X9668))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__of__neg])])])). 4.46/4.72 fof(c_0_8639, plain, ![X7509, X7510]:(~class_Groups_Oordered__ab__group__add__abs(X7510)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7510),X7509),c_Groups_Ozero__class_Ozero(X7510)))|hAPP(c_Groups_Ouminus__class_Ouminus(X7510),X7509)=hAPP(c_Groups_Oabs__class_Oabs(X7510),X7509))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos])])). 4.46/4.72 fof(c_0_8640, plain, ![X1243, X1244, X1245]:((X1243!=hAPP(c_COMBK(tc_Option_Ooption(X1244),X1245),c_Option_Ooption_ONone(X1244))|c_Orderings_Obot__class_Obot(tc_fun(X1245,tc_HOL_Obool))=c_Map_Odom(X1245,X1244,X1243))&(c_Orderings_Obot__class_Obot(tc_fun(X1245,tc_HOL_Obool))!=c_Map_Odom(X1245,X1244,X1243)|X1243=hAPP(c_COMBK(tc_Option_Ooption(X1244),X1245),c_Option_Ooption_ONone(X1244)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__eq__empty__conv])])). 4.46/4.72 cnf(c_0_8641, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5521])). 4.46/4.72 cnf(c_0_8642, plain, (X1=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5521])). 4.46/4.72 fof(c_0_8643, plain, ![X10483, X10484]:(((X10484=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10484)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10483)))))&(X10483=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10484)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10483))))))&(X10484!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X10483!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10484)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10483)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__zle__neg])])])). 4.46/4.72 fof(c_0_8644, plain, ![X4282, X4283, X4284, X4285]:(~c_Big__Operators_Osemilattice__big(X4285,X4284,X4283)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4285),X4282))|hAPP(c_Finite__Set_Ofold1(X4285,X4284),X4282)=hAPP(X4283,X4282))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_semilattice__big_OF__eq])])])). 4.46/4.72 fof(c_0_8645, plain, ![X16576, X16577, X16578, X16579]:(~c_Finite__Set_Ofolding__one(X16579,X16578,X16577)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16579),X16576))|hAPP(c_Finite__Set_Ofold1(X16579,X16578),X16576)=hAPP(X16577,X16576))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold])])). 4.46/4.72 fof(c_0_8646, plain, ![X12729, X12730]:(~class_Int_Onumber__ring(X12730)|hAPP(c_Groups_Ouminus__class_Ouminus(X12730),X12729)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12730),X12729),hAPP(c_Int_Onumber__class_Onumber__of(X12730),c_Int_OMin))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__minus1__right])])])). 4.46/4.72 fof(c_0_8647, plain, ![X14841, X14842, X14843, X14844]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14844)),X14843)),X14842))|X14843=hAPP(hAPP(c_List_Olist__update(X14844,X14843),X14842),X14841)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__update__beyond])])])). 4.46/4.72 cnf(c_0_8648, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))), inference(split_conjunct,[status(thm)],[c_0_5454])). 4.46/4.72 fof(c_0_8649, plain, ![X9073, X9074, X9075, X9076]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9076),X9075),X9073))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9076),hAPP(hAPP(c_Orderings_Oord__class_Omax(X9076),X9075),X9074)),X9073))|~class_Orderings_Olinorder(X9076))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9076),X9074),X9073))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9076),hAPP(hAPP(c_Orderings_Oord__class_Omax(X9076),X9075),X9074)),X9073))|~class_Orderings_Olinorder(X9076))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ole__supE])])])])). 4.46/4.72 fof(c_0_8650, plain, ![X13369, X13370, X13371]:(X13371=c_List_Olist_ONil(X13370)|hAPP(c_List_Ohd(X13370),hAPP(hAPP(c_List_Oappend(X13370),X13371),X13369))=hAPP(c_List_Ohd(X13370),X13371)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__append2])])])). 4.46/4.72 fof(c_0_8651, plain, ![X855, X856, X857]:(~class_Rings_Ocomm__semiring__1(X857)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X857),X856),X855)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X857),X855),X856)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])])). 4.46/4.72 cnf(c_0_8652, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|X2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_5209])). 4.46/4.72 cnf(c_0_8653, plain, (X1=hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X1))), inference(split_conjunct,[status(thm)],[c_0_5526])). 4.46/4.72 fof(c_0_8654, plain, ![X8784, X8785, X8786]:(~class_Rings_Ocomm__semiring__1(X8786)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8786),X8784),X8785)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8786),X8785),X8784)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])])). 4.46/4.72 fof(c_0_8655, plain, ![X2529, X2530, X2531, X2532]:(~class_Groups_Ouminus(X2532)|hAPP(c_Groups_Ouminus__class_Ouminus(X2532),hAPP(X2530,X2529))=hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2531,X2532)),X2530),X2529)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__Compl__def])])). 4.46/4.72 fof(c_0_8656, plain, ![X2876, X2877]:(~class_Rings_Olinordered__idom(X2877)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2877),c_Groups_Osgn__class_Osgn(X2877,X2876)),hAPP(c_Groups_Oabs__class_Oabs(X2877),X2876))=X2876), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__sgn__abs])])])). 4.46/4.72 fof(c_0_8657, plain, ![X3497, X3498]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3498),c_Orderings_Otop__class_Otop(tc_fun(X3498,tc_HOL_Obool))))|(hAPP(c_Finite__Set_Ocard(X3498),X3497)!=hAPP(c_Finite__Set_Ocard(X3498),c_Orderings_Otop__class_Otop(tc_fun(X3498,tc_HOL_Obool)))|X3497=c_Orderings_Otop__class_Otop(tc_fun(X3498,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV])])])). 4.46/4.72 fof(c_0_8658, plain, ![X16678, X16679, X16680]:(~class_Groups_Ogroup__add(X16680)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16680),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X16680),X16679),X16678)),X16678)=X16679), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__add__cancel])])])). 4.46/4.72 fof(c_0_8659, plain, ![X10449, X10450, X10451]:(~class_Groups_Ogroup__add(X10451)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10451),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10451),X10450),X10449)),X10449)=X10450), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__diff__cancel])])])). 4.46/4.72 fof(c_0_8660, plain, ![X9028, X9029, X9030]:(~class_Lattices_Olattice(X9030)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9030),X9029),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9030),X9029),X9028))=X9029), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__inf__absorb])])])). 4.46/4.72 fof(c_0_8661, plain, ![X14556, X14557, X14558]:(~class_Lattices_Olattice(X14558)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X14558),X14557),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X14558),X14557),X14556))=X14557), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__absorb])])])). 4.46/4.72 fof(c_0_8662, plain, ![X11123, X11124, X11125]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11125),X11124))|hBOOL(hAPP(c_Finite__Set_Ofinite(X11125),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11125,tc_HOL_Obool)),X11124),X11123)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff])])). 4.46/4.72 fof(c_0_8663, plain, ![X17263, X17264, X17265]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X17265),X17263))|hBOOL(hAPP(c_Finite__Set_Ofinite(X17265),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17265,tc_HOL_Obool)),X17264),X17263))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17265),X17264))|hBOOL(hAPP(c_Finite__Set_Ofinite(X17265),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17265,tc_HOL_Obool)),X17264),X17263))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Int])])])])). 4.46/4.72 fof(c_0_8664, plain, ![X2894, X2895, X2896]:(~class_Lattices_Osemilattice__sup(X2896)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2896),X2895),X2894)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2896),X2894),X2895)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__commute])])])). 4.46/4.72 fof(c_0_8665, plain, ![X8286, X8287, X8288]:(~class_Orderings_Olinorder(X8288)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8288),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8288),X8287),X8286)),X8287))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__le1])])])). 4.46/4.72 fof(c_0_8666, plain, ![X12093, X12094, X12095]:(~class_Orderings_Olinorder(X12095)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12095),hAPP(hAPP(c_Orderings_Oord__class_Omin(X12095),X12094),X12093)),X12093))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le2])])). 4.46/4.72 fof(c_0_8667, plain, ![X5386, X5387, X5388]:(~class_Lattices_Olattice(X5388)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5388),X5386),X5387)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5388),X5387),X5386)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__aci_I5_J])])])). 4.46/4.72 fof(c_0_8668, plain, ![X1132, X1133, X1134]:(~class_Orderings_Olinorder(X1134)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1134),X1133),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1134),X1133),X1132)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__maxI1])])])). 4.46/4.72 fof(c_0_8669, plain, ![X12000, X12001, X12002]:(~class_Orderings_Olinorder(X12002)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12002),X12001),hAPP(hAPP(c_Orderings_Oord__class_Omax(X12002),X12000),X12001)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__maxI2])])). 4.46/4.72 fof(c_0_8670, plain, ![X13124, X13125, X13126, X13127]:(~hBOOL(hAPP(X13127,X13126))|(~hBOOL(hAPP(X13125,X13126))|hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13124,tc_HOL_Obool)),X13127),X13125),X13126)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1I])])). 4.46/4.72 fof(c_0_8671, plain, ![X8638, X8639, X8640]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X8640),X8638))|hBOOL(hAPP(c_Finite__Set_Ofinite(X8640),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8640,tc_HOL_Obool)),X8638),X8639)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8640),X8639)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8640),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8640,tc_HOL_Obool)),X8638),X8639)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X8640),X8638))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8640),X8639)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff2])])])). 4.46/4.72 fof(c_0_8672, plain, ![X17540, X17541, X17542, X17543]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X17543,X17542),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X17541),X17540)))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X17543),X17542)=X17541), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__eq])])])). 4.46/4.72 fof(c_0_8673, plain, ![X14779, X14780, X14781, X14782, X14783]:(((c_Option_Ooption_ONone(X14782)=hAPP(X14780,X14779)|hAPP(c_Map_Omap__add(X14783,X14782,X14781,X14780),X14779)!=c_Option_Ooption_ONone(X14782))&(c_Option_Ooption_ONone(X14782)=hAPP(X14781,X14779)|hAPP(c_Map_Omap__add(X14783,X14782,X14781,X14780),X14779)!=c_Option_Ooption_ONone(X14782)))&(c_Option_Ooption_ONone(X14782)!=hAPP(X14780,X14779)|c_Option_Ooption_ONone(X14782)!=hAPP(X14781,X14779)|hAPP(c_Map_Omap__add(X14783,X14782,X14781,X14780),X14779)=c_Option_Ooption_ONone(X14782))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__None])])])). 4.46/4.72 fof(c_0_8674, plain, ![X2608, X2609, X2610]:(~class_Orderings_Olinorder(X2610)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X2610),X2609),X2608)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X2610),X2608),X2609)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__commute])])])). 4.46/4.72 fof(c_0_8675, plain, ![X6173, X6174, X6175]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X6175,X6174)),X6173))|hBOOL(hAPP(c_Finite__Set_Ofinite(X6175),hAPP(c_Relation_ODomain(X6175,X6174),X6173)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Domain])])). 4.46/4.72 fof(c_0_8676, plain, ![X5092, X5093, X5094]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5094,X5093)),X5092))|hBOOL(hAPP(c_Finite__Set_Ofinite(X5093),hAPP(c_Relation_ORange(X5094,X5093),X5092)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Range])])])). 4.46/4.72 fof(c_0_8677, plain, ![X1593, X1594, X1595]:(~class_Orderings_Olinorder(X1595)|(~hBOOL(hAPP(hAPP(c_member(X1595),X1594),hAPP(c_List_Oset(X1595),X1593)))|X1593=c_List_Olinorder__class_Oinsort__insert__key(X1595,X1595,c_COMBI(X1595),X1594,X1593))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__insert__triv])])). 4.46/4.72 fof(c_0_8678, plain, ![X1630, X1631, X1632]:(~class_Orderings_Olinorder(X1632)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1632),X1630),X1631)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1632),X1631),X1630)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__commute])])])). 4.46/4.72 fof(c_0_8679, plain, ![X1488, X1489, X1490]:(~class_Lattices_Osemilattice__inf(X1490)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1490),X1489),X1488)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1490),X1488),X1489)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__commute])])])). 4.46/4.72 cnf(c_0_8680, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X3),X1))))), inference(split_conjunct,[status(thm)],[c_0_5369])). 4.46/4.72 fof(c_0_8681, plain, ![X6420, X6421, X6422]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X6422,X6422),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X6421),X6420)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X6422|X6421=c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient])])). 4.46/4.72 fof(c_0_8682, plain, ![X792, X793, X794]:(~class_Lattices_Olattice(X794)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X794),X792),X793)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X794),X793),X792)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I1_J])])). 4.46/4.72 fof(c_0_8683, plain, ![X1430, X1431, X1432, X1433]:(~hBOOL(hAPP(hAPP(c_member(X1433),X1432),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1433,tc_HOL_Obool)),X1431),X1430)))|hBOOL(hAPP(hAPP(c_member(X1433),X1432),X1431))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_DiffD1])])])). 4.46/4.72 fof(c_0_8684, plain, ![X4488, X4489, X4490, X4491]:((hBOOL(hAPP(hAPP(c_member(X4491),X4490),X4489))|~hBOOL(hAPP(hAPP(c_member(X4491),X4490),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4491,tc_HOL_Obool)),X4489),X4488))))&(hBOOL(hAPP(hAPP(c_member(X4491),X4490),X4488))|~hBOOL(hAPP(hAPP(c_member(X4491),X4490),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4491,tc_HOL_Obool)),X4489),X4488))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_IntE])])])])). 4.46/4.72 fof(c_0_8685, plain, ![X2449, X2450, X2451]:((c_Orderings_Obot__class_Obot(tc_fun(X2451,tc_HOL_Obool))!=c_SetInterval_Oord__class_OgreaterThanAtMost(X2451,X2450,X2449)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2451),X2450),X2449))|~class_Orderings_Oorder(X2451))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2451),X2450),X2449))|c_Orderings_Obot__class_Obot(tc_fun(X2451,tc_HOL_Obool))=c_SetInterval_Oord__class_OgreaterThanAtMost(X2451,X2450,X2449)|~class_Orderings_Oorder(X2451))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_greaterThanAtMost__empty__iff2])])])])). 4.46/4.72 fof(c_0_8686, plain, ![X4611, X4612, X4613]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4613,X4613),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4612),X4611)))|(X4613=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X4611=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_self__remainder])])])). 4.46/4.72 cnf(c_0_8687, plain, (hBOOL(hAPP(X2,esk205_1(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1)))), inference(split_conjunct,[status(thm)],[c_0_5527])). 4.46/4.72 fof(c_0_8688, plain, ![X1271, X1272, X1273, X1274]:(~hBOOL(hAPP(hAPP(c_member(X1274),X1273),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1274,tc_HOL_Obool)),X1272),X1271)))|hBOOL(hAPP(hAPP(c_member(X1274),X1273),X1271))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_IntD2])])])). 4.46/4.72 fof(c_0_8689, plain, ![X3396, X3397]:(~class_Rings_Oring__1(X3397)|hBOOL(hAPP(hAPP(c_member(X3397),hAPP(c_Int_Oring__1__class_Oof__int(X3397),X3396)),c_Int_Oring__1__class_OInts(X3397)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__of__int])])). 4.46/4.72 fof(c_0_8690, plain, ![X8333, X8334]:(~class_Int_Onumber__ring(X8334)|hBOOL(hAPP(hAPP(c_member(X8334),hAPP(c_Int_Onumber__class_Onumber__of(X8334),X8333)),c_Int_Oring__1__class_OInts(X8334)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__number__of])])). 4.46/4.72 cnf(c_0_8691, plain, (c_Divides_Odivmod__int(X2,X1)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X1!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_4494])). 4.46/4.72 fof(c_0_8692, plain, ![X11921, X11922]:(~class_Rings_Oring__1(X11922)|hBOOL(hAPP(hAPP(c_member(X11922),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X11922),X11921)),c_Int_Oring__1__class_OInts(X11922)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__of__nat])])])). 4.46/4.72 fof(c_0_8693, plain, ![X14578, X14579]:(~class_Rings_Osemiring__1(X14579)|hBOOL(hAPP(hAPP(c_member(X14579),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X14579),X14578)),c_Nat_Osemiring__1__class_ONats(X14579)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__in__Nats])])). 4.46/4.72 fof(c_0_8694, plain, ![X6042]:(~c_Nat__Transfer_Onat__set(X6042)|hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X6042))=hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X6042)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J])])])). 4.46/4.72 fof(c_0_8695, plain, ![X8692, X8693, X8694]:(~c_Wellfounded_Owf(X8694,X8693)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8694,tc_HOL_Obool)),X8692),hAPP(c_Relation_OImage(X8694,X8694,X8693),X8692)))|X8692=c_Orderings_Obot__class_Obot(tc_fun(X8694,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wfE__pf])])])). 4.46/4.72 fof(c_0_8696, plain, ![X1340, X1341, X1342, X1343, X1344]:((X1341!=X1340|hAPP(c_Set_Oimage(X1344,X1343,X1342),X1341)=hAPP(c_Set_Oimage(X1344,X1343,X1342),X1340)|~c_Fun_Oinj__on(X1344,X1343,X1342,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1344,tc_HOL_Obool)),X1341),X1340)))&(hAPP(c_Set_Oimage(X1344,X1343,X1342),X1341)!=hAPP(c_Set_Oimage(X1344,X1343,X1342),X1340)|X1341=X1340|~c_Fun_Oinj__on(X1344,X1343,X1342,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1344,tc_HOL_Obool)),X1341),X1340)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Un__image__eq__iff])])])). 4.46/4.72 fof(c_0_8697, plain, ![X10672, X10673, X10674, X10675, X10676]:(~c_Fun_Oinj__on(X10676,X10675,X10674,X10673)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10676,tc_HOL_Obool)),X10672),X10673))|c_Fun_Oinj__on(X10676,X10675,X10674,X10672))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__inj__on])])). 4.46/4.72 fof(c_0_8698, plain, ![X7111, X7112, X7113, X7114, X7115, X7116]:((~c_List_Olistrelp(X7116,X7115,X7113,X7111)|~hBOOL(hAPP(hAPP(X7115,X7114),X7112))|c_List_Olistrelp(X7116,X7115,hAPP(hAPP(c_List_Olist_OCons(X7116),X7114),X7113),hAPP(hAPP(c_List_Olist_OCons(X7116),X7112),X7111)))&((c_List_Olistrelp(X7116,X7115,X7113,X7111)|~c_List_Olistrelp(X7116,X7115,hAPP(hAPP(c_List_Olist_OCons(X7116),X7114),X7113),hAPP(hAPP(c_List_Olist_OCons(X7116),X7112),X7111)))&(hBOOL(hAPP(hAPP(X7115,X7114),X7112))|~c_List_Olistrelp(X7116,X7115,hAPP(hAPP(c_List_Olist_OCons(X7116),X7114),X7113),hAPP(hAPP(c_List_Olist_OCons(X7116),X7112),X7111))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_Oequations_I2_J])])])). 4.46/4.72 fof(c_0_8699, plain, ![X10815, X10816, X10817, X10818]:((hBOOL(hAPP(X10818,X10817))|hAPP(c_List_Ofilter(X10816,X10818),c_List_Oreplicate(X10816,X10815,X10817))=c_List_Olist_ONil(X10816))&(~hBOOL(hAPP(X10818,X10817))|hAPP(c_List_Ofilter(X10816,X10818),c_List_Oreplicate(X10816,X10815,X10817))=c_List_Oreplicate(X10816,X10815,X10817))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__replicate])])])). 4.46/4.72 cnf(c_0_8700, plain, (c_List_Olinorder__class_Osorted(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk67_4(X3,X1,X4,X2)))|~c_List_Olinorder__class_Osorted(X1,X4)|hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)!=X3|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5314])). 4.46/4.72 fof(c_0_8701, plain, ![X3697, X3698, X3699]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3699)),X3697)),X3698))|c_List_Olist_ONil(X3699)=hAPP(hAPP(c_List_Odrop(X3699),X3698),X3697))&(c_List_Olist_ONil(X3699)!=hAPP(hAPP(c_List_Odrop(X3699),X3698),X3697)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3699)),X3697)),X3698)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__eq__Nil])])). 4.46/4.72 fof(c_0_8702, plain, ![X7408, X7409, X7410, X7411, X7412, X7413, X7414, X7415, X7416]:((~hBOOL(hAPP(hAPP(X7409,X7410),X7408))|hBOOL(hAPP(c_Predicate_ORangeP(X7412,X7411,X7409),X7408)))&(~hBOOL(hAPP(c_Predicate_ORangeP(X7416,X7415,X7414),X7413))|hBOOL(hAPP(hAPP(X7414,esk215_2(X7413,X7414)),X7413)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP_Oequations])])])])])). 4.46/4.72 fof(c_0_8703, plain, ![X1957, X1958, X1959, X1960, X1962, X1963, X1964, X1965, X1966]:((~hBOOL(hAPP(c_Predicate_ODomainP(X1960,X1959,X1958),X1957))|hBOOL(hAPP(hAPP(X1958,X1957),esk51_2(X1957,X1958))))&(~hBOOL(hAPP(hAPP(X1963,X1962),X1964))|hBOOL(hAPP(c_Predicate_ODomainP(X1966,X1965,X1963),X1962)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP_Oequations])])])])])). 4.46/4.72 fof(c_0_8704, plain, ![X11828, X11829, X11830]:(~class_Divides_Osemiring__div(X11830)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11830),c_Divides_Odiv__class_Omod(X11830,X11829,X11828)),X11828)=c_Groups_Ozero__class_Ozero(X11830)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__trivial])])). 4.46/4.72 fof(c_0_8705, plain, ![X4533, X4534, X4535]:(~class_Divides_Osemiring__div(X4535)|c_Divides_Odiv__class_Omod(X4535,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4535),X4534),X4533),X4533)=c_Groups_Ozero__class_Ozero(X4535)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2__is__0])])). 4.46/4.72 cnf(c_0_8706, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)=c_Groups_Oone__class_Oone(X1)|hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))!=X2|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_5528])). 4.46/4.72 fof(c_0_8707, plain, ![X14544, X14545, X14546]:(~class_Divides_Osemiring__div(X14546)|c_Groups_Ozero__class_Ozero(X14546)=c_Divides_Odiv__class_Omod(X14546,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14546),X14545),X14544),X14545)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1__is__0])])). 4.46/4.72 fof(c_0_8708, plain, ![X2566, X2567, X2568, X2569, X2570]:((X2566!=X2567|hAPP(c_Set_Oimage(X2570,X2569,X2568),X2567)=hAPP(c_Set_Oimage(X2570,X2569,X2568),X2566)|~c_Fun_Oinj__on(X2570,X2569,X2568,c_Orderings_Otop__class_Otop(tc_fun(X2570,tc_HOL_Obool))))&(hAPP(c_Set_Oimage(X2570,X2569,X2568),X2567)!=hAPP(c_Set_Oimage(X2570,X2569,X2568),X2566)|X2566=X2567|~c_Fun_Oinj__on(X2570,X2569,X2568,c_Orderings_Otop__class_Otop(tc_fun(X2570,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__eq__iff])])])). 4.46/4.72 fof(c_0_8709, plain, ![X1521, X1522, X1523, X1524]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1524),X1523))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1522),hAPP(c_Set_Oimage(X1524,X1522,X1521),X1523)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__imageI])])])). 4.46/4.72 fof(c_0_8710, plain, ![X5900, X5901, X5902]:(~hBOOL(hAPP(c_List_Odistinct(X5902),X5901))|hBOOL(hAPP(c_List_Odistinct(X5902),hAPP(hAPP(c_List_Odrop(X5902),X5900),X5901)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__drop])])])). 4.46/4.72 fof(c_0_8711, plain, ![X3760, X3761, X3762]:(~hBOOL(hAPP(c_List_Odistinct(X3762),X3761))|hBOOL(hAPP(c_List_Odistinct(X3762),hAPP(hAPP(c_List_Otake(X3762),X3760),X3761)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__take])])). 4.46/4.72 fof(c_0_8712, plain, ![X8252, X8253, X8255, X8256, X8257]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8253),X8252))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8253),esk234_2(X8252,X8253))=X8252)&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8256),X8257)!=X8255|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8256),X8255)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__add])])])])])). 4.46/4.72 fof(c_0_8713, plain, ![X14416, X14417, X14418, X14419]:((~c_List_Olist__all(X14419,X14418,X14416)|~hBOOL(hAPP(X14418,X14417))|c_List_Olist__all(X14419,X14418,hAPP(hAPP(c_List_Olist_OCons(X14419),X14417),X14416)))&((c_List_Olist__all(X14419,X14418,X14416)|~c_List_Olist__all(X14419,X14418,hAPP(hAPP(c_List_Olist_OCons(X14419),X14417),X14416)))&(hBOOL(hAPP(X14418,X14417))|~c_List_Olist__all(X14419,X14418,hAPP(hAPP(c_List_Olist_OCons(X14419),X14417),X14416))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__simps_I1_J])])])). 4.46/4.72 cnf(c_0_8714, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_5529])). 4.46/4.72 fof(c_0_8715, plain, ![X11654, X11655]:(~class_Power_Opower(X11655)|~class_Rings_Osemiring__0(X11655)|hAPP(hAPP(c_Power_Opower__class_Opower(X11655),c_Groups_Ozero__class_Ozero(X11655)),hAPP(c_Nat_OSuc,X11654))=c_Groups_Ozero__class_Ozero(X11655)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__Suc])])). 4.46/4.72 cnf(c_0_8716, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),hAPP(c_Int_Onat,X1))=hAPP(c_Int_Onat,X2)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(split_conjunct,[status(thm)],[c_0_4987])). 4.46/4.72 cnf(c_0_8717, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls))|~class_Int_Onumber__ring(X1)|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_5530])). 4.46/4.72 fof(c_0_8718, plain, ![X1751, X1752]:(~class_Orderings_Olinorder(X1752)|c_Big__Operators_Olattice_OInf__fin(X1752,c_Orderings_Oord__class_Omin(X1752),hAPP(hAPP(c_Set_Oinsert(X1752),X1751),c_Orderings_Obot__class_Obot(tc_fun(X1752,tc_HOL_Obool))))=X1751), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Osingleton])])])). 4.46/4.72 fof(c_0_8719, plain, ![X6649, X6650]:(~class_Orderings_Olinorder(X6650)|c_Big__Operators_Olattice_OSup__fin(X6650,c_Orderings_Oord__class_Omax(X6650),hAPP(hAPP(c_Set_Oinsert(X6650),X6649),c_Orderings_Obot__class_Obot(tc_fun(X6650,tc_HOL_Obool))))=X6649), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osingleton])])). 4.46/4.72 fof(c_0_8720, plain, ![X1979, X1980]:((c_Groups_Osgn__class_Osgn(X1980,X1979)!=c_Groups_Oone__class_Oone(X1980)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1980),c_Groups_Ozero__class_Ozero(X1980)),X1979))|~class_Rings_Olinordered__idom(X1980))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1980),c_Groups_Ozero__class_Ozero(X1980)),X1979))|c_Groups_Osgn__class_Osgn(X1980,X1979)=c_Groups_Oone__class_Oone(X1980)|~class_Rings_Olinordered__idom(X1980))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__pos])])])). 4.46/4.72 fof(c_0_8721, plain, ![X15019, X15020]:(((c_Groups_Oone__class_Oone(tc_Int_Oint)=X15019|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15020),X15019)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15020)))&(c_Groups_Oone__class_Oone(tc_Int_Oint)=X15020|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15020),X15019)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15020))))&(c_Groups_Oone__class_Oone(tc_Int_Oint)!=X15019|c_Groups_Oone__class_Oone(tc_Int_Oint)!=X15020|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15020),X15019)=c_Groups_Oone__class_Oone(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15020)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff])])])). 4.46/4.72 fof(c_0_8722, plain, ![X13322, X13323, X13324]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13324),X13323)),X13322))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13324),X13322))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])])). 4.46/4.72 fof(c_0_8723, plain, ![X6843, X6844, X6845, X6846]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6846,X6845),tc_HOL_Obool)),X6844),X6843))|(~c_Relation_Osingle__valued(X6846,X6845,X6843)|c_Relation_Osingle__valued(X6846,X6845,X6844))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__subset])])). 4.46/4.72 fof(c_0_8724, plain, ![X15317, X15318, X15319, X15320]:((~hBOOL(hAPP(c_List_Odistinct(X15319),X15317))|hBOOL(hAPP(c_List_Odistinct(X15319),c_List_Olinorder__class_Osort__key(X15319,X15320,X15318,X15317)))|~class_Orderings_Olinorder(X15320))&(~hBOOL(hAPP(c_List_Odistinct(X15319),c_List_Olinorder__class_Osort__key(X15319,X15320,X15318,X15317)))|hBOOL(hAPP(c_List_Odistinct(X15319),X15317))|~class_Orderings_Olinorder(X15320))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__sort])])])). 4.46/4.72 fof(c_0_8725, plain, ![X440, X441, X442]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X442),X441)),X440))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X442),X440))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])])). 4.46/4.72 cnf(c_0_8726, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_5495])). 4.46/4.72 cnf(c_0_8727, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),hAPP(c_Int_Onat,X1)))), inference(split_conjunct,[status(thm)],[c_0_5445])). 4.46/4.72 fof(c_0_8728, plain, ![X10733, X10734, X10735, X10736]:(((c_List_Olist__all(X10736,X10735,X10733)|~c_List_Olist__all(X10736,X10735,hAPP(hAPP(c_List_Oappend(X10736),X10734),X10733)))&(c_List_Olist__all(X10736,X10735,X10734)|~c_List_Olist__all(X10736,X10735,hAPP(hAPP(c_List_Oappend(X10736),X10734),X10733))))&(~c_List_Olist__all(X10736,X10735,X10733)|~c_List_Olist__all(X10736,X10735,X10734)|c_List_Olist__all(X10736,X10735,hAPP(hAPP(c_List_Oappend(X10736),X10734),X10733)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__append])])])). 4.46/4.72 fof(c_0_8729, plain, ![X10228, X10229]:(c_List_Olist_ONil(X10228)=X10229|(~hBOOL(hAPP(c_List_Odistinct(X10228),X10229))|hBOOL(hAPP(c_List_Odistinct(X10228),c_List_Obutlast(X10228,X10229))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__butlast])])])). 4.46/4.72 cnf(c_0_8730, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onat,X2)))), inference(split_conjunct,[status(thm)],[c_0_5525])). 4.46/4.72 cnf(c_0_8731, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))|~hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5511])). 4.46/4.72 cnf(c_0_8732, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X1)))), inference(split_conjunct,[status(thm)],[c_0_5508])). 4.46/4.72 fof(c_0_8733, plain, ![X11621, X11622]:(~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X11622),c_Int_OInteg))|(~hBOOL(hAPP(X11621,hAPP(c_Int_ORep__Integ,esk342_2(X11621,X11622))))|hBOOL(hAPP(X11621,X11622)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Rep__Integ__induct])])])])). 4.46/4.72 cnf(c_0_8734, plain, (X1=X2|hAPP(c_Int_Onat,X1)!=hAPP(c_Int_Onat,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5531])). 4.46/4.72 cnf(c_0_8735, plain, (X3=c_Groups_Ozero__class_Ozero(X1)|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))!=X3|~class_Int_Onumber(X1)|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_5532])). 4.46/4.72 fof(c_0_8736, plain, ![X4410, X4411]:((X4411!=X4410|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4411),hAPP(c_Nat_OSuc,X4410)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4411),X4410)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4411),hAPP(c_Nat_OSuc,X4410)))|X4411=X4410|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4411),X4410)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq])])])])). 4.46/4.72 fof(c_0_8737, plain, ![X5352, X5353, X5354, X5355, X5356]:(hAPP(hAPP(c_List_Olist_OCons(X5356),X5353),X5352)!=hAPP(hAPP(c_List_Odrop(X5356),X5355),X5354)|hAPP(hAPP(c_List_Onth(X5356),X5354),X5355)=X5353), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__via__drop])])])). 4.46/4.72 fof(c_0_8738, plain, ![X13687, X13688]:(~class_Complete__Lattice_Ocomplete__lattice(X13688)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13688),X13687))|(c_Orderings_Obot__class_Obot(tc_fun(X13688,tc_HOL_Obool))=X13687|c_Big__Operators_Olattice__class_OSup__fin(X13688,X13687)=c_Complete__Lattice_OSup__class_OSup(X13688,X13687)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin__Sup])])). 4.46/4.72 fof(c_0_8739, plain, ![X4588]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4588))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X4588)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X4588))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4588)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])])). 4.46/4.72 fof(c_0_8740, plain, ![X2676, X2677]:(~class_Lattices_Oboolean__algebra(X2677)|c_Orderings_Otop__class_Otop(X2677)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2677),hAPP(c_Groups_Ouminus__class_Ouminus(X2677),X2676)),X2676)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_compl__sup__top])])])). 4.46/4.72 fof(c_0_8741, plain, ![X13305, X13306]:(~class_Groups_Oab__group__add(X13306)|c_Groups_Ozero__class_Ozero(X13306)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13306),hAPP(c_Groups_Ouminus__class_Ouminus(X13306),X13305)),X13305)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__left__minus])])). 4.46/4.72 fof(c_0_8742, plain, ![X2139, X2140]:(~class_Complete__Lattice_Ocomplete__lattice(X2140)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2140),X2139))|(X2139=c_Orderings_Obot__class_Obot(tc_fun(X2140,tc_HOL_Obool))|c_Complete__Lattice_OInf__class_OInf(X2140,X2139)=c_Big__Operators_Olattice__class_OInf__fin(X2140,X2139)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin__Inf])])])). 4.46/4.72 fof(c_0_8743, plain, ![X8423, X8424]:(~class_Groups_Ogroup__add(X8424)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8424),X8423),hAPP(c_Groups_Ouminus__class_Ouminus(X8424),X8423))=c_Groups_Ozero__class_Ozero(X8424)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus])])). 4.46/4.72 fof(c_0_8744, plain, ![X8567, X8568]:(~class_Lattices_Oboolean__algebra(X8568)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8568),X8567),hAPP(c_Groups_Ouminus__class_Ouminus(X8568),X8567))=c_Orderings_Otop__class_Otop(X8568)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__compl__top])])). 4.46/4.72 fof(c_0_8745, plain, ![X4791, X4792, X4793]:(~class_Orderings_Olinorder(X4793)|X4792=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4793),X4792),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4793),X4792),X4791))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__absorb])])). 4.46/4.72 fof(c_0_8746, plain, ![X852, X853, X854]:(~class_Orderings_Olinorder(X854)|X853=hAPP(hAPP(c_Orderings_Oord__class_Omin(X854),X853),hAPP(hAPP(c_Orderings_Oord__class_Omax(X854),X853),X852))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__absorb])])). 4.46/4.72 fof(c_0_8747, plain, ![X728, X729]:(~class_Orderings_Oorder(X729)|hAPP(hAPP(c_Set_Oinsert(X729),X728),c_Orderings_Obot__class_Obot(tc_fun(X729,tc_HOL_Obool)))=c_SetInterval_Oord__class_OatLeastAtMost(X729,X728,X728)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton])])). 4.46/4.72 fof(c_0_8748, plain, ![X2855, X2856, X2857]:(~class_Groups_Oordered__ab__group__add__abs(X2857)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2857),hAPP(c_Groups_Oabs__class_Oabs(X2857),X2856)),X2855))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2857),X2856),X2855)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__le__D1])])])). 4.46/4.72 fof(c_0_8749, plain, ![X9796, X9797, X9798]:((c_List_Olist_ONil(X9797)!=X9798|c_List_Olast(X9797,X9796)=c_List_Olast(X9797,hAPP(hAPP(c_List_Oappend(X9797),X9796),X9798)))&(X9798=c_List_Olist_ONil(X9797)|c_List_Olast(X9797,X9798)=c_List_Olast(X9797,hAPP(hAPP(c_List_Oappend(X9797),X9796),X9798)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__append])])). 4.46/4.72 fof(c_0_8750, plain, ![X12950, X12951, X12952]:(X12952=c_List_Olist_ONil(X12951)|c_List_Olast(X12951,X12952)=c_List_Olast(X12951,hAPP(hAPP(c_List_Olist_OCons(X12951),X12950),X12952))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsR])])). 4.46/4.72 fof(c_0_8751, plain, ![X9026, X9027]:(((~c_Nitpick_Ounknown(tc_HOL_Obool)|~c_Wellfounded_Oacyclic(X9027,X9026)|c_Nitpick_Owf_H(X9027,X9026))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X9027,X9027)),X9026))|~c_Wellfounded_Oacyclic(X9027,X9026)|c_Nitpick_Owf_H(X9027,X9026)))&((c_Wellfounded_Oacyclic(X9027,X9026)|~c_Nitpick_Owf_H(X9027,X9026))&(c_Nitpick_Ounknown(tc_HOL_Obool)|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X9027,X9027)),X9026))|~c_Nitpick_Owf_H(X9027,X9026)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Owf_H__def])])])). 4.46/4.72 fof(c_0_8752, plain, ![X17507]:(~class_Orderings_Olinorder(X17507)|c_Orderings_Oord_Omin(X17507,hAPP(c_COMBC(X17507,X17507,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X17507)))=c_Orderings_Oord__class_Omax(X17507)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dual__min])])). 4.46/4.72 fof(c_0_8753, plain, ![X3092, X3093]:((X3092=X3093|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3093),X3092))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3093),X3092)))&((X3092!=X3093|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3093),X3092)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3093),X3092))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3093),X3092))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])])). 4.46/4.72 fof(c_0_8754, plain, ![X1374]:(~class_Orderings_Olinorder(X1374)|c_Orderings_Oord_Omax(X1374,hAPP(c_COMBC(X1374,X1374,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1374)))=c_Orderings_Oord__class_Omin(X1374)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dual__max])])])). 4.46/4.72 fof(c_0_8755, plain, ![X9846, X9847, X9848]:(~hBOOL(hAPP(c_List_Odistinct(X9848),X9847))|hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X9848)),c_Enum_On__lists(X9848,X9846,X9847)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__n__lists])])). 4.46/4.72 fof(c_0_8756, plain, ![X10887, X10888, X10889]:(~hBOOL(hAPP(c_List_Odistinct(X10889),X10888))|hBOOL(hAPP(c_List_Odistinct(X10889),hAPP(c_List_Ofilter(X10889,X10887),X10888)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__filter])])])). 4.46/4.72 fof(c_0_8757, plain, ![X14345, X14346, X14347, X14348]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X14348),hAPP(c_Set_Oimage(X14347,X14348,X14346),X14345))),hAPP(c_Finite__Set_Ocard(X14347),X14345)))|~c_Fun_Oinj__on(X14347,X14348,X14346,X14345)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pigeonhole])])])). 4.46/4.72 fof(c_0_8758, plain, ![X8262, X8263]:(~class_Rings_Olinordered__idom(X8263)|hAPP(c_Groups_Oabs__class_Oabs(X8263),X8262)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8263),X8262),c_Groups_Osgn__class_Osgn(X8263,X8262))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__sgn])])). 4.46/4.72 cnf(c_0_8759, plain, (X3=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Ono__zero__divisors(X1)|~class_Rings_Ozero__neq__one(X1)|~class_Rings_Omult__zero(X1)|~class_Power_Opower(X1)), inference(split_conjunct,[status(thm)],[c_0_5533])). 4.46/4.72 fof(c_0_8760, plain, ![X1218, X1219, X1220, X1221]:(~class_Orderings_Olinorder(X1221)|hAPP(c_List_Oset(X1220),c_List_Olinorder__class_Osort__key(X1220,X1221,X1219,X1218))=hAPP(c_List_Oset(X1220),X1218)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__sort])])])). 4.46/4.72 fof(c_0_8761, plain, ![X9876, X9877, X9878, X9879]:(~c_Hoare__Mirabelle_Ohoare__derivs(X9879,X9878,X9877)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X9879),tc_HOL_Obool)),X9876),X9877))|c_Hoare__Mirabelle_Ohoare__derivs(X9879,X9878,X9876))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_weaken])])). 4.46/4.72 fof(c_0_8762, plain, ![X4454, X4455, X4456, X4457]:(~c_Hoare__Mirabelle_Ohoare__derivs(X4457,X4456,X4455)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X4457),tc_HOL_Obool)),X4456),X4454))|c_Hoare__Mirabelle_Ohoare__derivs(X4457,X4454,X4455))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_thin])])])). 4.46/4.72 cnf(c_0_8763, plain, (X1=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5534])). 4.46/4.72 fof(c_0_8764, plain, ![X9197, X9198, X9199]:(~c_Equiv__Relations_Oequiv(X9199,X9198,X9197)|c_Complete__Lattice_OSup__class_OSup(tc_fun(X9199,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X9199),X9198),X9197))=X9198), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__quotient])])). 4.46/4.72 fof(c_0_8765, plain, ![X750, X751, X752, X753, X754]:((hBOOL(hAPP(hAPP(c_member(X754),X753),X752))|hAPP(c_Map_Orestrict__map(X754,X751,X750,X752),X753)=c_Option_Ooption_ONone(X751))&(~hBOOL(hAPP(hAPP(c_member(X754),X753),X752))|hAPP(X750,X753)=hAPP(c_Map_Orestrict__map(X754,X751,X750,X752),X753))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_restrict__map__def])])])). 4.46/4.72 fof(c_0_8766, plain, ![X2561, X2562, X2563, X2564, X2565]:(~hBOOL(hAPP(hAPP(X2565,X2564),X2563))|hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X2562,X2561,X2565),X2563),X2564))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep_Ointros])])). 4.46/4.72 fof(c_0_8767, plain, ![X15608, X15609, X15610, X15611]:(~hBOOL(hAPP(X15611,X15610))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15609,tc_HOL_Obool)),X15611),X15608))|hBOOL(hAPP(X15608,X15610)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rev__predicate1D])])])). 4.46/4.72 cnf(c_0_8768, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5521])). 4.46/4.72 fof(c_0_8769, plain, ![X478, X479]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X479,X479)),X478))|hBOOL(hAPP(c_Finite__Set_Ofinite(X479),hAPP(c_Relation_OField(X479),X478)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Field])])])). 4.46/4.72 fof(c_0_8770, plain, ![X5438, X5439]:(~class_Orderings_Olinorder(X5439)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5439),X5438))|c_Big__Operators_Olattice_OInf__fin(X5439,c_Orderings_Oord__class_Omin(X5439),X5438)=hAPP(c_Finite__Set_Ofold1(X5439,c_Orderings_Oord__class_Omin(X5439)),X5438))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_OF__eq])])])). 4.46/4.72 cnf(c_0_8771, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X1|c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5535])). 4.46/4.72 fof(c_0_8772, plain, ![X13454, X13455]:(~class_Orderings_Olinorder(X13455)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13455),X13454))|c_Big__Operators_Olattice_OSup__fin(X13455,c_Orderings_Oord__class_Omax(X13455),X13454)=hAPP(c_Finite__Set_Ofold1(X13455,c_Orderings_Oord__class_Omax(X13455)),X13454))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_OF__eq])])])). 4.46/4.72 cnf(c_0_8773, plain, (~class_Int_Onumber__ring(X1)|~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))), inference(rw,[status(thm)],[c_0_5536, c_0_4471])). 4.46/4.72 cnf(c_0_8774, plain, (X1=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)|c_Groups_Oone__class_Oone(tc_Int_Oint)=X2|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_5535])). 4.46/4.72 fof(c_0_8775, plain, ![X13293, X13294]:(~class_Enum_Oenum(X13293)|~class_Enum_Oenum(X13294)|c_Enum_Oenum__class_Oenum(tc_prod(X13294,X13293))=c_Enum_Oproduct(X13294,X13293,c_Enum_Oenum__class_Oenum(X13294),c_Enum_Oenum__class_Oenum(X13293))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_enum__prod__def])])])). 4.46/4.72 fof(c_0_8776, plain, ![X14962, X14963, X14964]:(((X14962=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~epred2_3(X14964,X14962,X14963)|hBOOL(hAPP(X14964,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14963),X14962))))&(~hBOOL(hAPP(X14964,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~epred2_3(X14964,X14962,X14963)|hBOOL(hAPP(X14964,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14963),X14962)))))&((epred2_3(X14964,X14962,X14963)|~hBOOL(hAPP(X14964,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14963),X14962))))&(X14962!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(X14964,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X14964,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14963),X14962)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_5537])])])])). 4.46/4.72 fof(c_0_8777, plain, ![X14109, X14110, X14111]:(~hBOOL(hAPP(c_List_Odistinct(X14111),X14110))|c_List_Oremdups(X14111,c_List_Oremove1(X14111,X14109,X14110))=c_List_Oremove1(X14111,X14109,c_List_Oremdups(X14111,X14110))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_remove1__remdups])])])). 4.46/4.72 cnf(c_0_8778, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X1|X2=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5535])). 4.46/4.72 fof(c_0_8779, plain, ![X12032, X12033]:(~class_Groups_Oordered__ab__group__add__abs(X12033)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12033),X12032),hAPP(c_Groups_Oabs__class_Oabs(X12033),X12032)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__ge__self])])])). 4.46/4.72 fof(c_0_8780, plain, ![X14661, X14662, X14663]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14661),X14662)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14663),X14662)|(X14663=X14661|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X14662))&((X14663!=X14661|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14661),X14662)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14663),X14662))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X14662|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14661),X14662)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14663),X14662)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])])). 4.46/4.72 fof(c_0_8781, plain, ![X15521, X15522, X15523]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15523),X15521)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15523),X15522)|(X15522=X15521|X15523=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&((X15522!=X15521|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15523),X15521)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15523),X15522))&(X15523!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15523),X15521)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15523),X15522)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])])). 4.46/4.72 cnf(c_0_8782, plain, (c_Predicate_Oreflp(X1,X2)|~c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))), inference(split_conjunct,[status(thm)],[c_0_5402])). 4.46/4.72 cnf(c_0_8783, plain, (X1=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)|X1=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_5535])). 4.46/4.72 fof(c_0_8784, plain, ![X8037, X8038]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8038),hAPP(c_Nat_OSuc,X8037)))|(X8037=X8038|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8038),X8037))))&((X8037!=X8038|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8038),hAPP(c_Nat_OSuc,X8037))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8038),X8037))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8038),hAPP(c_Nat_OSuc,X8037)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])])). 4.46/4.72 cnf(c_0_8785, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=esk452_2(X1,X2)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2), inference(split_conjunct,[status(thm)],[c_0_5338])). 4.46/4.72 fof(c_0_8786, plain, ![X15589, X15590]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15590),X15589))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15590),hAPP(c_Nat_OSuc,X15589))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15590),hAPP(c_Nat_OSuc,X15589)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15590),X15589)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])])). 4.46/4.72 cnf(c_0_8787, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)=c_Groups_Ozero__class_Ozero(X2)|X1!=hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)|~class_Groups_Ogroup__add(X2)), inference(split_conjunct,[status(thm)],[c_0_5538])). 4.46/4.72 fof(c_0_8788, plain, ![X12628, X12629, X12630, X12631, X12632, X12633]:(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12633,tc_fun(X12632,tc_HOL_Obool))),X12631),X12630),X12629),X12628))|hBOOL(hAPP(hAPP(X12631,X12629),X12628))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D1])])). 4.46/4.72 fof(c_0_8789, plain, ![X9774, X9775]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9775))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9775),X9774))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X9775,X9774)=X9775)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__trivial])])). 4.46/4.72 fof(c_0_8790, plain, ![X4174, X4175]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4175),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4174),X4175))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X4175,X4174)=X4175)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__neg__neg__trivial])])])). 4.46/4.72 fof(c_0_8791, plain, ![X4934, X4935, X4936, X4937, X4938, X4939]:(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4939,tc_fun(X4938,tc_HOL_Obool))),X4937),X4936),X4935),X4934))|hBOOL(hAPP(hAPP(X4936,X4935),X4934))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf2D2])])])). 4.46/4.72 fof(c_0_8792, plain, ![X8937, X8938]:((hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X8938)!=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X8937)|X8938=X8937|~c_Nat__Transfer_Onat__set(X8937)|~c_Nat__Transfer_Onat__set(X8938))&(X8938!=X8937|hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X8938)=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X8937)|~c_Nat__Transfer_Onat__set(X8937)|~c_Nat__Transfer_Onat__set(X8938))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I3_J])])])). 4.46/4.72 fof(c_0_8793, plain, ![X1860, X1861]:((~c_Wellfounded_Owf(X1861,X1860)|c_Wellfounded_Owf(X1861,hAPP(hAPP(c_Relation_Orel__comp(X1861,X1861,X1861),X1860),X1860)))&(~c_Wellfounded_Owf(X1861,hAPP(hAPP(c_Relation_Orel__comp(X1861,X1861,X1861),X1860),X1860))|c_Wellfounded_Owf(X1861,X1860))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__comp__self])])). 4.46/4.72 cnf(c_0_8794, plain, (~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))), inference(rw,[status(thm)],[c_0_5539, c_0_4471])). 4.46/4.72 fof(c_0_8795, plain, ![X16077, X16078, X16079, X16080, X16081]:((~hBOOL(hAPP(hAPP(c_member(X16078),X16079),X16077))|c_Orderings_Obot__class_Obot(tc_fun(X16078,tc_HOL_Obool))!=X16077)&(c_Orderings_Obot__class_Obot(tc_fun(X16081,tc_HOL_Obool))=X16080|hBOOL(hAPP(hAPP(c_member(X16081),esk468_2(X16080,X16081)),X16080)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__in__conv])])])])])). 4.46/4.72 fof(c_0_8796, plain, ![X7321, X7322, X7323]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7323,tc_HOL_Obool)),X7322),X7321))|hBOOL(hAPP(hAPP(c_member(tc_fun(X7323,tc_HOL_Obool)),X7322),hAPP(c_Set_OPow(X7323),X7321))))&(~hBOOL(hAPP(hAPP(c_member(tc_fun(X7323,tc_HOL_Obool)),X7322),hAPP(c_Set_OPow(X7323),X7321)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7323,tc_HOL_Obool)),X7322),X7321)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pow__iff])])). 4.46/4.72 fof(c_0_8797, plain, ![X14202, X14203, X14204]:(~class_Orderings_Oorder(X14204)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14204),X14203),X14202))|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X14204,X14202),X14203)=c_Orderings_Obot__class_Obot(tc_fun(X14204,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty])])])). 4.46/4.72 fof(c_0_8798, plain, ![X4809, X4810, X4811, X4812, X4813]:((c_Orderings_Obot__class_Obot(tc_fun(X4810,tc_HOL_Obool))!=X4809|~hBOOL(hAPP(hAPP(c_member(X4810),X4811),X4809)))&(hBOOL(hAPP(hAPP(c_member(X4813),esk139_2(X4812,X4813)),X4812))|c_Orderings_Obot__class_Obot(tc_fun(X4813,tc_HOL_Obool))=X4812)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_all__not__in__conv])])])])])])). 4.46/4.72 fof(c_0_8799, plain, ![X5480]:(~class_Groups_Omonoid__add(X5480)|c_List_Ofoldl(X5480,X5480,c_Groups_Oplus__class_Oplus(X5480),c_Groups_Ozero__class_Ozero(X5480))=c_List_Omonoid__add__class_Olistsum(X5480)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__foldl])])). 4.46/4.72 fof(c_0_8800, plain, ![X10634, X10635, X10636]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10634,tc_HOL_Obool)),X10635),X10636))|X10636!=X10635)&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10634,tc_HOL_Obool)),X10636),X10635))|X10636!=X10635))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10634,tc_HOL_Obool)),X10635),X10636))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10634,tc_HOL_Obool)),X10636),X10635))|X10636=X10635)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])])). 4.46/4.72 fof(c_0_8801, plain, ![X10295, X10296]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10296,X10295)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10296,X10295),tc_HOL_Obool))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X10295),c_Orderings_Otop__class_Otop(tc_fun(X10295,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__fun__UNIVD2])])])). 4.46/4.72 fof(c_0_8802, plain, ![X11883, X11884, X11885, X11886]:(~c_Equiv__Relations_Oequivp(X11886,X11885)|(~hBOOL(hAPP(hAPP(X11885,X11884),X11883))|hBOOL(hAPP(hAPP(X11885,X11883),X11884)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__symp])])). 4.46/4.72 fof(c_0_8803, plain, ![X14177, X14178]:(~class_Orderings_Olinorder(X14178)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14178),X14177))|hAPP(c_Finite__Set_Ofold1(X14178,c_Orderings_Oord__class_Omax(X14178)),X14177)=c_Big__Operators_Olinorder__class_OMax(X14178,X14177))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_OF__eq])])])). 4.46/4.72 fof(c_0_8804, plain, ![X16224, X16225]:(~class_Lattices_Olattice(X16225)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16225),X16224))|hAPP(c_Finite__Set_Ofold1(X16225,c_Lattices_Osemilattice__sup__class_Osup(X16225)),X16224)=c_Big__Operators_Olattice__class_OSup__fin(X16225,X16224))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_OF__eq])])). 4.46/4.72 fof(c_0_8805, plain, ![X16506, X16507, X16508, X16509]:(~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16509,tc_HOL_Obool)),X16508),X16507),X16506))|(hBOOL(hAPP(X16508,X16506))|hBOOL(hAPP(X16507,X16506)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup1E])])])). 4.46/4.72 cnf(c_0_8806, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))))), inference(rw,[status(thm)],[c_0_5540, c_0_4443])). 4.46/4.72 fof(c_0_8807, plain, ![X11007, X11008, X11009]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11009)),X11008)),X11007))|X11008=hAPP(hAPP(c_List_Otake(X11009),X11007),X11008)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__all])])). 4.46/4.72 fof(c_0_8808, plain, ![X10012, X10013]:(~class_Lattices_Olattice(X10013)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10013),X10012))|hAPP(c_Finite__Set_Ofold1(X10013,c_Lattices_Osemilattice__inf__class_Oinf(X10013)),X10012)=c_Big__Operators_Olattice__class_OInf__fin(X10013,X10012))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_OF__eq])])])). 4.46/4.72 fof(c_0_8809, plain, ![X3513, X3514]:(~class_Orderings_Olinorder(X3514)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3514),X3513))|c_Big__Operators_Olinorder__class_OMin(X3514,X3513)=hAPP(c_Finite__Set_Ofold1(X3514,c_Orderings_Oord__class_Omin(X3514)),X3513))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_OF__eq])])])). 4.46/4.72 fof(c_0_8810, plain, ![X1829, X1830, X1831, X1832]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1832),X1831))|(hAPP(c_Finite__Set_Ocard(X1832),X1831)!=hAPP(c_Finite__Set_Ocard(X1830),hAPP(c_Set_Oimage(X1832,X1830,X1829),X1831))|c_Fun_Oinj__on(X1832,X1830,X1829,X1831))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on])])). 4.46/4.72 fof(c_0_8811, plain, ![X13947]:(~class_Rings_Olinordered__semidom(X13947)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13947),c_Groups_Ozero__class_Ozero(X13947)),c_Groups_Oone__class_Oone(X13947)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__one])])])). 4.46/4.72 cnf(c_0_8812, plain, (c_List_Oremdups(X1,X2)=X2|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremdups(X1,X2))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_5541])). 4.46/4.72 cnf(c_0_8813, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremdups(X1,X2))=hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5542]), ['final']). 4.46/4.72 fof(c_0_8814, plain, ![X1491, X1492, X1493]:(~class_Lattices_Osemilattice__inf(X1493)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1493),X1492),X1491))|X1492=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1493),X1492),X1491))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__absorb1])])])). 4.46/4.72 fof(c_0_8815, plain, ![X15648, X15649, X15650]:(~class_Lattices_Osemilattice__inf(X15650)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15650),X15649),X15648))|X15649=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15650),X15648),X15649))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__absorb2])])])). 4.46/4.72 fof(c_0_8816, plain, ![X4702, X4703, X4704]:((X4702!=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4704),X4703),X4702)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4704),X4703),X4702))|~class_Lattices_Osemilattice__sup(X4704))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4704),X4703),X4702))|X4702=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4704),X4703),X4702)|~class_Lattices_Osemilattice__sup(X4704))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__sup])])])). 4.46/4.72 fof(c_0_8817, plain, ![X16973]:(~class_Rings_Olinordered__semidom(X16973)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16973),c_Groups_Ozero__class_Ozero(X16973)),c_Groups_Oone__class_Oone(X16973)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])])). 4.46/4.72 fof(c_0_8818, plain, ![X3554, X3555, X3556, X3557]:(~c_Wellfounded_Owf(X3557,X3556)|(~c_Wellfounded_Owf(X3555,X3554)|c_Wellfounded_Owf(tc_prod(X3557,X3555),c_Wellfounded_Olex__prod(X3557,X3555,X3556,X3554)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__lex__prod])])])). 4.46/4.72 fof(c_0_8819, plain, ![X9612]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X9612)))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X9612))|~c_Nat__Transfer_Onat__set(X9612))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X9612))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X9612)))|~c_Nat__Transfer_Onat__set(X9612))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I1_J])])])). 4.46/4.72 fof(c_0_8820, plain, ![X1206, X1207, X1208]:(~class_Lattices_Osemilattice__sup(X1208)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1208),X1207),X1206))|X1206=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1208),X1206),X1207))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__absorb1])])])). 4.46/4.72 fof(c_0_8821, plain, ![X4429, X4430]:(~class_Groups_Oordered__ab__group__add__abs(X4430)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4430),c_Groups_Ozero__class_Ozero(X4430)),X4429))|hAPP(c_Groups_Oabs__class_Oabs(X4430),X4429)=X4429)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__of__nonneg])])])). 4.46/4.72 fof(c_0_8822, plain, ![X4549, X4550]:(~class_Groups_Oordered__ab__group__add__abs(X4550)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4550),c_Groups_Ozero__class_Ozero(X4550)),X4549))|X4549=hAPP(c_Groups_Oabs__class_Oabs(X4550),X4549))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__of__pos])])])). 4.46/4.72 fof(c_0_8823, plain, ![X9392, X9393, X9394]:(~class_Groups_Ogroup__add(X9394)|(c_Groups_Ozero__class_Ozero(X9394)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9394),X9393),X9392)|hAPP(c_Groups_Ouminus__class_Ouminus(X9394),X9393)=X9392)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__unique])])])). 4.46/4.72 cnf(c_0_8824, plain, (c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=esk34_3(X1,X3,X2)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|hAPP(c_Nat_OSuc,X1)!=hAPP(c_Finite__Set_Ocard(X2),X3)), inference(split_conjunct,[status(thm)],[c_0_5438])). 4.46/4.72 cnf(c_0_8825, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2)))), inference(split_conjunct,[status(thm)],[c_0_5518])). 4.46/4.72 fof(c_0_8826, plain, ![X10147, X10148]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X10148)),hAPP(c_Nat_OSuc,X10147)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10148),X10147))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])])). 4.46/4.72 cnf(c_0_8827, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))), inference(split_conjunct,[status(thm)],[c_0_5445])). 4.46/4.72 fof(c_0_8828, plain, ![X2952, X2953]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2953,X2953)),X2952))|(~c_Wellfounded_Oacyclic(X2953,X2952)|c_Wellfounded_Owf(X2953,hAPP(c_Relation_Oconverse(X2953,X2953),X2952)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__acyclic__wf__converse])])])). 4.46/4.72 fof(c_0_8829, plain, ![X6953, X6954, X6955]:((~hBOOL(hAPP(c_Com_OWT,X6954))|~hBOOL(hAPP(c_Com_OWT,X6953))|hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X6955,X6954,X6953))))&((hBOOL(hAPP(c_Com_OWT,X6954))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X6955,X6954,X6953))))&(hBOOL(hAPP(c_Com_OWT,X6953))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X6955,X6954,X6953)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I5_J])])])). 4.46/4.72 fof(c_0_8830, plain, ![X14088, X14089]:(~class_Groups_Ogroup__add(X14089)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X14089),c_Groups_Ozero__class_Ozero(X14089)),X14088)=hAPP(c_Groups_Ouminus__class_Ouminus(X14089),X14088)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0])])). 4.46/4.72 cnf(c_0_8831, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2)))), inference(split_conjunct,[status(thm)],[c_0_5520])). 4.46/4.72 fof(c_0_8832, plain, ![X14470, X14471, X14472, X14473]:(((~hBOOL(hAPP(X14472,X14471))|c_List_Olist__ex(X14473,X14472,hAPP(hAPP(c_List_Olist_OCons(X14473),X14471),X14470)))&(~c_List_Olist__ex(X14473,X14472,X14470)|c_List_Olist__ex(X14473,X14472,hAPP(hAPP(c_List_Olist_OCons(X14473),X14471),X14470))))&(~c_List_Olist__ex(X14473,X14472,hAPP(hAPP(c_List_Olist_OCons(X14473),X14471),X14470))|(hBOOL(hAPP(X14472,X14471))|c_List_Olist__ex(X14473,X14472,X14470)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__simps_I1_J])])])). 4.46/4.72 fof(c_0_8833, plain, ![X9656, X9657, X9658]:(~c_Wellfounded_Owf(X9658,X9657)|hBOOL(hAPP(hAPP(c_member(X9658),X9656),c_Wellfounded_Oacc(X9658,X9657)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__wfD])])). 4.46/4.72 fof(c_0_8834, plain, ![X4052, X4053, X4054]:(~class_Orderings_Olinorder(X4054)|(~c_List_Olinorder__class_Osorted(X4054,X4053)|c_List_Olinorder__class_Osorted(X4054,c_List_Olinorder__class_Oinsort__insert__key(X4054,X4054,c_COMBI(X4054),X4052,X4053)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__insort__insert])])])). 4.46/4.72 fof(c_0_8835, plain, ![X10156, X10157, X10158]:(~c_Wellfounded_Oacyclic(X10158,X10157)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10158,X10158),tc_HOL_Obool)),X10156),X10157))|c_Wellfounded_Oacyclic(X10158,X10156))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acyclic__subset])])])). 4.46/4.72 fof(c_0_8836, plain, ![X8398, X8399, X8400]:(~c_Wellfounded_Owf(X8400,X8399)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X8400,X8400),tc_HOL_Obool)),X8398),X8399))|c_Wellfounded_Owf(X8400,X8398))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__subset])])])). 4.46/4.72 fof(c_0_8837, plain, ![X17600, X17601, X17602]:(~c_Wellfounded_OwfP(X17602,X17601)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17602,tc_fun(X17602,tc_HOL_Obool))),X17600),X17601))|c_Wellfounded_OwfP(X17602,X17600))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__subset])])). 4.46/4.72 fof(c_0_8838, plain, ![X7418, X7419, X7420, X7421]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X7421,X7420),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X7419),X7418)))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X7421,X7420)=X7418), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__eq])])). 4.46/4.72 fof(c_0_8839, plain, ![X4716, X4717]:((X4716=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(X4717),c_Groups_Ozero__class_Ozero(X4717)),X4716)=c_Groups_Ozero__class_Ozero(X4717)|(~class_Rings_Osemiring__0(X4717)|~class_Power_Opower(X4717)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X4716|hAPP(hAPP(c_Power_Opower__class_Opower(X4717),c_Groups_Ozero__class_Ozero(X4717)),X4716)=c_Groups_Oone__class_Oone(X4717)|(~class_Rings_Osemiring__0(X4717)|~class_Power_Opower(X4717)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__0__left])])])])). 4.46/4.72 fof(c_0_8840, plain, ![X15082, X15083]:(~class_Lattices_Oboolean__algebra(X15083)|c_Orderings_Obot__class_Obot(X15083)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15083),hAPP(c_Groups_Ouminus__class_Ouminus(X15083),X15082)),X15082)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__inf__bot])])). 4.46/4.72 fof(c_0_8841, plain, ![X16484, X16485]:(~class_Lattices_Oboolean__algebra(X16485)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16485),X16484),hAPP(c_Groups_Ouminus__class_Ouminus(X16485),X16484))=c_Orderings_Obot__class_Obot(X16485)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__compl__bot])])). 4.46/4.72 fof(c_0_8842, plain, ![X12007, X12008, X12009]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12009)),X12007)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12009)),X12008)|X12008=X12007)&(X12008!=X12007|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12009)),X12007)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12009)),X12008))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1])])). 4.46/4.72 cnf(c_0_8843, plain, (hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1)))), inference(split_conjunct,[status(thm)],[c_0_5472])). 4.46/4.72 fof(c_0_8844, plain, ![X4859, X4860, X4861, X4862]:(((~c_List_Olist__ex(X4862,X4861,X4860)|c_List_Olist__ex(X4862,X4861,hAPP(hAPP(c_List_Oappend(X4862),X4860),X4859)))&(~c_List_Olist__ex(X4862,X4861,X4859)|c_List_Olist__ex(X4862,X4861,hAPP(hAPP(c_List_Oappend(X4862),X4860),X4859))))&(~c_List_Olist__ex(X4862,X4861,hAPP(hAPP(c_List_Oappend(X4862),X4860),X4859))|(c_List_Olist__ex(X4862,X4861,X4860)|c_List_Olist__ex(X4862,X4861,X4859)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__append])])])). 4.46/4.72 fof(c_0_8845, plain, ![X7994, X7995]:(~class_Groups_Oordered__ab__group__add__abs(X7995)|hAPP(c_Groups_Oabs__class_Oabs(X7995),hAPP(c_Groups_Ouminus__class_Ouminus(X7995),X7994))=hAPP(c_Groups_Oabs__class_Oabs(X7995),X7994)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel])])). 4.46/4.72 fof(c_0_8846, plain, ![X17048, X17049]:(~class_Orderings_Olinorder(X17049)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17049,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X17049),X17048))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X17049),X17048)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__atMost])])). 4.46/4.72 fof(c_0_8847, plain, ![X1782, X1783]:(~class_Orderings_Olinorder(X1783)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1783,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1783),X1782))=hAPP(c_SetInterval_Oord__class_OlessThan(X1783),X1782)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__atLeast])])). 4.46/4.72 fof(c_0_8848, plain, ![X2150, X2151]:(~class_Orderings_Olinorder(X2151)|hAPP(c_SetInterval_Oord__class_OatMost(X2151),X2150)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2151,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X2151),X2150))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Compl__greaterThan])])])). 4.46/4.72 fof(c_0_8849, plain, ![X5947, X5948]:(~class_Orderings_Olinorder(X5948)|hAPP(c_SetInterval_Oord__class_OatLeast(X5948),X5947)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5948,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5948),X5947))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__lessThan])])). 4.46/4.72 fof(c_0_8850, plain, ![X13275, X13276, X13277]:(~c_Equiv__Relations_Oequiv(X13277,X13276,X13275)|c_Equiv__Relations_Oequiv(tc_List_Olist(X13277),c_List_Olists(X13277,X13276),c_List_Olistrel(X13277,X13275))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equiv__listrel])])])). 4.46/4.72 fof(c_0_8851, plain, ![X14041]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X14041))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X14041))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X14041)))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X14041)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I1_J])])). 4.46/4.72 fof(c_0_8852, plain, ![X1510, X1511, X1512]:(~c_Relation_Orefl__on(X1512,X1511,X1510)|c_Relation_Orefl__on(tc_List_Olist(X1512),c_List_Olists(X1512,X1511),c_List_Olistrel(X1512,X1510))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__refl__on])])). 4.46/4.72 fof(c_0_8853, plain, ![X8972, X8973, X8974, X8975]:(((hAPP(c_Product__Type_Osnd(X8973,X8972),X8974)=hAPP(c_Product__Type_Osnd(X8973,X8972),X8975)|X8974!=X8975)&(hAPP(c_Product__Type_Ofst(X8973,X8972),X8975)=hAPP(c_Product__Type_Ofst(X8973,X8972),X8974)|X8974!=X8975))&(hAPP(c_Product__Type_Osnd(X8973,X8972),X8974)!=hAPP(c_Product__Type_Osnd(X8973,X8972),X8975)|hAPP(c_Product__Type_Ofst(X8973,X8972),X8975)!=hAPP(c_Product__Type_Ofst(X8973,X8972),X8974)|X8974=X8975)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__fst__snd__eq])])])). 4.46/4.72 cnf(c_0_8854, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)),X2)=X2|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5543])). 4.46/4.72 cnf(c_0_8855, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls))=X2|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5544])). 4.46/4.72 fof(c_0_8856, plain, ![X13482, X13483, X13484, X13485, X13486]:(~c_List_Olist__all2(X13486,X13485,X13484,X13483,X13482)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13486)),X13483)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13485)),X13482)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__lengthD])])). 4.46/4.72 fof(c_0_8857, plain, ![X11073, X11074, X11075, X11076]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11076),hAPP(c_Set_Oimage(X11075,X11076,X11074),X11073)))|(~c_Fun_Oinj__on(X11075,X11076,X11074,X11073)|hBOOL(hAPP(c_Finite__Set_Ofinite(X11075),X11073)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])])). 4.46/4.72 fof(c_0_8858, plain, ![X4863, X4864, X4865]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4865),X4864))|hBOOL(hAPP(c_Finite__Set_Ofinite(X4865),hAPP(hAPP(c_Set_Oinsert(X4865),X4863),X4864)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite_OinsertI])])])). 4.46/4.72 fof(c_0_8859, plain, ![X6965, X6966]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X6966,tc_HOL_Obool)),hAPP(c_Set_OPow(X6966),X6965)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X6966),X6965)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6966),X6965))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X6966,tc_HOL_Obool)),hAPP(c_Set_OPow(X6966),X6965))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Pow__iff])])). 4.46/4.72 fof(c_0_8860, plain, ![X4163, X4164, X4165]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4165),X4164))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4165,tc_HOL_Obool)),X4163),X4164))|hBOOL(hAPP(c_Finite__Set_Ofinite(X4165),X4163)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])])). 4.46/4.72 cnf(c_0_8861, plain, (X1=c_Int_OMin|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)!=c_Int_OMin), inference(rw,[status(thm)],[c_0_5545, c_0_4471])). 4.46/4.72 fof(c_0_8862, plain, ![X6307, X6308]:(c_List_Olist_ONil(X6307)=X6308|c_List_Olast(X6307,X6308)=hAPP(c_List_Ohd(X6307),hAPP(c_List_Orev(X6307),X6308))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__rev])])])). 4.46/4.72 cnf(c_0_8863, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2!=hAPP(c_Int_Onat,X1)), inference(split_conjunct,[status(thm)],[c_0_5546])). 4.46/4.72 fof(c_0_8864, plain, ![X5071, X5072, X5073]:(~class_Groups_Ocomm__monoid__add(X5073)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5072,X5073),X5071),c_Orderings_Obot__class_Obot(tc_fun(X5072,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(X5073)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oempty])])). 4.46/4.72 cnf(c_0_8865, plain, (hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|~hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))), inference(split_conjunct,[status(thm)],[c_0_5209])). 4.46/4.72 cnf(c_0_8866, plain, (hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|~hBOOL(hAPP(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_5242])). 4.46/4.72 fof(c_0_8867, plain, ![X1956]:(~class_Nat_Osemiring__char__0(X1956)|c_Fun_Oinj__on(tc_Nat_Onat,X1956,c_Nat_Osemiring__1__class_Oof__nat(X1956),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__of__nat])])])). 4.46/4.72 fof(c_0_8868, plain, ![X7152]:(~class_Rings_Oring__1(X7152)|hBOOL(hAPP(hAPP(c_member(X7152),c_Groups_Oone__class_Oone(X7152)),c_Int_Oring__1__class_OInts(X7152)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__1])])). 4.46/4.72 fof(c_0_8869, plain, ![X8516]:(~class_Rings_Osemiring__1(X8516)|hBOOL(hAPP(hAPP(c_member(X8516),c_Groups_Oone__class_Oone(X8516)),c_Nat_Osemiring__1__class_ONats(X8516)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__1])])). 4.46/4.72 fof(c_0_8870, plain, ![X6868, X6869, X6870]:(~class_Orderings_Oorder(X6870)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6870),X6869),X6868))|c_SetInterval_Oord__class_OatLeastAtMost(X6870,X6868,X6869)=c_Orderings_Obot__class_Obot(tc_fun(X6870,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty])])])). 4.46/4.72 fof(c_0_8871, plain, ![X4133, X4134, X4135]:(~class_Divides_Osemiring__div(X4135)|c_Divides_Odiv__class_Omod(X4135,c_Divides_Odiv__class_Omod(X4135,X4134,X4133),X4133)=c_Divides_Odiv__class_Omod(X4135,X4134,X4133)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__mod__trivial])])])). 4.46/4.72 fof(c_0_8872, plain, ![X15696, X15697]:((hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X15696)!=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X15697)|X15697=X15696)&(X15697!=X15696|hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X15696)=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X15697))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I3_J])])). 4.46/4.72 fof(c_0_8873, plain, ![X17462]:(~class_Rings_Oring__1(X17462)|hBOOL(hAPP(hAPP(c_member(X17462),c_Groups_Ozero__class_Ozero(X17462)),c_Int_Oring__1__class_OInts(X17462)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__0])])])). 4.46/4.72 fof(c_0_8874, plain, ![X3035]:(~class_Rings_Osemiring__1(X3035)|hBOOL(hAPP(hAPP(c_member(X3035),c_Groups_Ozero__class_Ozero(X3035)),c_Nat_Osemiring__1__class_ONats(X3035)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__0])])). 4.46/4.72 fof(c_0_8875, plain, ![X6016, X6017]:(~class_Orderings_Olinorder(X6017)|c_List_Olinorder__class_Osorted(X6017,hAPP(hAPP(c_List_Olist_OCons(X6017),X6016),c_List_Olist_ONil(X6017)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__single])])])). 4.46/4.72 fof(c_0_8876, plain, ![X4427, X4428]:(~class_Groups_Ocomm__monoid__add(X4428)|hAPP(c_List_Omonoid__add__class_Olistsum(X4428),X4427)=hAPP(c_List_Omonoid__add__class_Olistsum(X4428),hAPP(c_List_Orev(X4428),X4427))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__rev])])). 4.46/4.72 fof(c_0_8877, plain, ![X9054, X9055, X9056, X9057, X9058, X9059, X9060]:((X9055!=X9058|X9054!=X9057|X9056!=X9059|hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X9060),X9056),X9055),X9054)=hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X9060),X9059),X9058),X9057))&(((X9055=X9058|hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X9060),X9056),X9055),X9054)!=hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X9060),X9059),X9058),X9057))&(X9054=X9057|hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X9060),X9056),X9055),X9054)!=hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X9060),X9059),X9058),X9057)))&(X9056=X9059|hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X9060),X9056),X9055),X9054)!=hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X9060),X9059),X9058),X9057)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_triple_Oinject])])])). 4.46/4.72 fof(c_0_8878, plain, ![X2730, X2731, X2732]:(~hBOOL(hAPP(c_List_Odistinct(X2732),X2731))|hBOOL(hAPP(c_List_Odistinct(X2732),c_List_Osublist(X2732,X2731,X2730)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__sublistI])])). 4.46/4.72 fof(c_0_8879, plain, ![X6490, X6491]:(~class_Groups_Oordered__ab__group__add__abs(X6491)|hAPP(c_Groups_Oabs__class_Oabs(X6491),X6490)=hAPP(c_Groups_Oabs__class_Oabs(X6491),hAPP(c_Groups_Oabs__class_Oabs(X6491),X6490))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__idempotent])])])). 4.46/4.72 fof(c_0_8880, plain, ![X16105, X16106]:(~class_Rings_Olinordered__idom(X16106)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X16106),X16105)=hAPP(c_Groups_Oabs__class_Oabs(X16106),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X16106),X16105))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__of__nat])])])). 4.46/4.72 fof(c_0_8881, plain, ![X14947, X14948]:(~class_Rings_Oring__1(X14948)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X14948),X14947)=hAPP(c_Int_Oring__1__class_Oof__int(X14948),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14947))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__of__nat__eq])])])). 4.46/4.72 fof(c_0_8882, plain, ![X9343, X9344, X9345]:(~hBOOL(hAPP(c_List_Odistinct(X9345),X9344))|hBOOL(hAPP(c_List_Odistinct(X9345),c_List_Oremove1(X9345,X9343,X9344)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__remove1])])])). 4.46/4.72 fof(c_0_8883, plain, ![X5949, X5950, X5951]:(~hBOOL(hAPP(c_List_Odistinct(X5951),X5950))|hBOOL(hAPP(c_List_Odistinct(X5951),c_List_OtakeWhile(X5951,X5949,X5950)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__takeWhile])])). 4.46/4.72 fof(c_0_8884, plain, ![X8390, X8391, X8392]:(~hBOOL(hAPP(c_List_Odistinct(X8392),X8391))|hBOOL(hAPP(c_List_Odistinct(X8392),c_List_Oinsert(X8392,X8390,X8391)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__insert])])])). 4.46/4.72 fof(c_0_8885, plain, ![X13801, X13802, X13803, X13804]:(~c_FunDef_Oreduction__pair(X13804,X13803)|c_FunDef_Oreduction__pair(X13802,hAPP(hAPP(c_FunDef_Orp__inv__image(X13804,X13802),X13803),X13801))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rp__inv__image__rp])])). 4.46/4.72 fof(c_0_8886, plain, ![X14689, X14690, X14691, X14692]:(~c_Wellfounded_Owf(X14692,X14691)|c_Wellfounded_Owf(X14690,hAPP(hAPP(c_Relation_Oinv__image(X14692,X14690),X14691),X14689))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__inv__image])])). 4.46/4.72 fof(c_0_8887, plain, ![X1573]:(~class_Rings_Olinordered__idom(X1573)|~class_Int_Onumber__ring(X1573)|hAPP(c_Groups_Oabs__class_Oabs(X1573),hAPP(c_Int_Onumber__class_Onumber__of(X1573),c_Int_OMin))=c_Groups_Oone__class_Oone(X1573)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__minus__one])])])). 4.46/4.72 cnf(c_0_8888, plain, (hBOOL(hAPP(X1,esk376_1(X1)))|c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=hAPP(c_Set_OCollect(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_5547])). 4.46/4.72 fof(c_0_8889, plain, ![X9290, X9291, X9292, X9293, X9294]:(~c_Typedef_Otype__definition(X9294,X9293,X9292,X9291,X9290)|hAPP(c_Set_Oimage(X9293,X9294,X9291),X9290)=c_Orderings_Otop__class_Otop(tc_fun(X9294,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_type__definition_OAbs__image])])])). 4.46/4.72 fof(c_0_8890, plain, ![X8174, X8175]:(X8175=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X8174,X8175),c_Divides_Odivmod__int(X8174,X8175)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__correct])])). 4.46/4.72 cnf(c_0_8891, plain, (hBOOL(hAPP(X1,esk109_1(X1)))|c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=hAPP(c_Set_OCollect(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_5548])). 4.46/4.72 fof(c_0_8892, plain, ![X10091, X10092, X10093]:(~class_Orderings_Olinorder(X10093)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10093),X10092),X10091))|X10092=hAPP(hAPP(c_Orderings_Oord__class_Omin(X10093),X10092),X10091))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__absorb1])])])). 4.46/4.72 fof(c_0_8893, plain, ![X691, X692, X693]:(~class_Orderings_Oorder(X693)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X693),X692),X691))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X693),X691),X692))|X691=X692))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__antisym])])])). 4.46/4.72 fof(c_0_8894, plain, ![X9590, X9591]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X9591),X9590)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X9591),X9590))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__ge__0__finite])])])). 4.46/4.72 fof(c_0_8895, plain, ![X6594, X6595, X6596]:(~class_Orderings_Olinorder(X6596)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6596),X6595),X6594))|X6595=hAPP(hAPP(c_Orderings_Oord__class_Omin(X6596),X6594),X6595))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb2])])). 4.46/4.72 fof(c_0_8896, plain, ![X2987, X2988, X2989]:(~class_Orderings_Olinorder(X2989)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2989),X2988),X2987))|X2987=hAPP(hAPP(c_Orderings_Oord__class_Omax(X2989),X2988),X2987))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb2])])). 4.46/4.72 fof(c_0_8897, plain, ![X7155, X7156, X7157]:(~class_Orderings_Olinorder(X7157)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7157),X7156),X7155))|X7155=hAPP(hAPP(c_Orderings_Oord__class_Omax(X7157),X7155),X7156))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__absorb1])])])). 4.46/4.72 fof(c_0_8898, plain, ![X937, X938]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X938),X937)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X937),X938)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X937=X938)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal])])). 4.46/4.72 fof(c_0_8899, plain, ![X14810, X14811, X14812, X14813]:(~hBOOL(hAPP(hAPP(c_member(X14813),X14812),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14813,tc_HOL_Obool)),X14811),X14810)))|~hBOOL(hAPP(hAPP(c_member(X14813),X14812),X14810))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_DiffD2])])])). 4.46/4.72 fof(c_0_8900, plain, ![X12331, X12332]:((~hBOOL(hAPP(c_List_Odistinct(X12332),X12331))|hBOOL(hAPP(c_List_Odistinct(X12332),hAPP(c_List_Orotate1(X12332),X12331))))&(~hBOOL(hAPP(c_List_Odistinct(X12332),hAPP(c_List_Orotate1(X12332),X12331)))|hBOOL(hAPP(c_List_Odistinct(X12332),X12331)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct1__rotate])])). 4.46/4.72 fof(c_0_8901, plain, ![X8337, X8338]:(~hBOOL(hAPP(c_List_Odistinct(X8338),X8337))|hBOOL(hAPP(c_List_Odistinct(X8338),hAPP(c_List_Otl(X8338),X8337)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__tl])])])). 4.46/4.72 fof(c_0_8902, plain, ![X14220, X14221]:(c_List_Olist_ONil(X14220)=X14221|hAPP(c_List_Ohd(X14220),X14221)=c_List_Olast(X14220,hAPP(c_List_Orev(X14220),X14221))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_last__rev])])])). 4.46/4.72 fof(c_0_8903, plain, ![X8931, X8932]:(((hAPP(c_List_Oset(X8932),c_List_Olinorder__class_Osorted__list__of__set(X8932,X8931))=X8931|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8932),X8931))|~class_Orderings_Olinorder(X8932))&(hBOOL(hAPP(c_List_Odistinct(X8932),c_List_Olinorder__class_Osorted__list__of__set(X8932,X8931)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8932),X8931))|~class_Orderings_Olinorder(X8932)))&(c_List_Olinorder__class_Osorted(X8932,c_List_Olinorder__class_Osorted__list__of__set(X8932,X8931))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8932),X8931))|~class_Orderings_Olinorder(X8932))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set])])])). 4.46/4.72 fof(c_0_8904, plain, ![X14342, X14343, X14344]:(~class_Orderings_Olinorder(X14344)|(~c_List_Olinorder__class_Osorted(X14344,X14343)|c_List_Olinorder__class_Osorted(X14344,hAPP(hAPP(c_List_Odrop(X14344),X14342),X14343)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__drop])])])). 4.46/4.72 fof(c_0_8905, plain, ![X4529, X4530]:((~hBOOL(hAPP(c_List_Odistinct(X4530),X4529))|hBOOL(hAPP(c_List_Odistinct(X4530),hAPP(c_List_Orev(X4530),X4529))))&(~hBOOL(hAPP(c_List_Odistinct(X4530),hAPP(c_List_Orev(X4530),X4529)))|hBOOL(hAPP(c_List_Odistinct(X4530),X4529)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__rev])])). 4.46/4.72 fof(c_0_8906, plain, ![X12308, X12309, X12310, X12311]:(~c_Finite__Set_Ofolding__one(X12311,X12310,X12309)|hAPP(X12309,hAPP(hAPP(c_Set_Oinsert(X12311),X12308),c_Orderings_Obot__class_Obot(tc_fun(X12311,tc_HOL_Obool))))=X12308), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Osingleton])])])). 4.46/4.72 fof(c_0_8907, plain, ![X12530, X12531, X12532]:(~class_Orderings_Olinorder(X12532)|(~c_List_Olinorder__class_Osorted(X12532,X12531)|c_List_Olinorder__class_Osorted(X12532,hAPP(hAPP(c_List_Otake(X12532),X12530),X12531)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__take])])). 4.46/4.72 cnf(c_0_8908, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)=c_Groups_Oone__class_Oone(X1)|c_Groups_Oone__class_Oone(X1)!=X2|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_5528])). 4.46/4.72 cnf(c_0_8909, plain, (X3=X4|X1!=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X2),X1)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X4),X3)|~class_Groups_Oab__group__add(X5)), inference(split_conjunct,[status(thm)],[c_0_5549])). 4.46/4.72 fof(c_0_8910, plain, ![X3568, X3569]:(c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3569),X3568))|c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X3569)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zmult__eq__1])])). 4.46/4.72 fof(c_0_8911, plain, ![X4362, X4363, X4364]:(~class_Orderings_Oorder(X4364)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4364),X4363),X4362))|c_Orderings_Obot__class_Obot(tc_fun(X4364,tc_HOL_Obool))=c_SetInterval_Oord__class_OgreaterThanLessThan(X4364,X4362,X4363))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_greaterThanLessThan__empty])])])). 4.46/4.72 fof(c_0_8912, plain, ![X13731, X13732, X13733]:(~class_Orderings_Oorder(X13733)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13733),X13732),X13731))|c_SetInterval_Oord__class_OgreaterThanAtMost(X13733,X13731,X13732)=c_Orderings_Obot__class_Obot(tc_fun(X13733,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty])])). 4.46/4.72 fof(c_0_8913, plain, ![X12312]:(~class_Orderings_Olinorder(X12312)|c_Finite__Set_Ofun__left__comm(X12312,tc_List_Olist(X12312),c_List_Olinorder__class_Oinsort__key(X12312,X12312,c_COMBI(X12312)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm__insort])])])). 4.46/4.72 fof(c_0_8914, plain, ![X12623, X12624, X12625, X12626]:(~hBOOL(hAPP(X12626,X12625))|hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12624,tc_HOL_Obool)),X12626),X12623),X12625))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup1I1])])])). 4.46/4.72 fof(c_0_8915, plain, ![X13604, X13605, X13606, X13607]:((~hBOOL(hAPP(X13607,X13606))|hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13604,tc_HOL_Obool)),X13605),X13607),X13606)))&(~hBOOL(hAPP(X13605,X13606))|hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13604,tc_HOL_Obool)),X13605),X13607),X13606)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup1CI])])])])). 4.46/4.72 cnf(c_0_8916, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,esk283_2(X2,X1)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))|~hBOOL(hAPP(c_Com_OWT,X2))|~c_Hoare__Mirabelle_Ostate__not__singleton), inference(split_conjunct,[status(thm)],[c_0_5513])). 4.46/4.72 fof(c_0_8917, plain, ![X3034]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3034),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X3034)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3034))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3034),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X3034)=X3034)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zabs__def])])])). 4.46/4.72 fof(c_0_8918, plain, ![X4698, X4699]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4699)),X4698)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|X4698=hAPP(c_List_Orotate1(X4699),X4698)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rotate1__length01])])])). 4.46/4.72 cnf(c_0_8919, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Oring__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_5550])). 4.46/4.72 fof(c_0_8920, plain, ![X9352, X9353]:(~class_Divides_Osemiring__div(X9353)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X9353),c_Groups_Ozero__class_Ozero(X9353)),X9352)=c_Groups_Ozero__class_Ozero(X9353)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__0])])). 4.46/4.72 fof(c_0_8921, plain, ![X13647, X13648, X13649]:(~class_Orderings_Opreorder(X13649)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13649),X13648),X13647))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13649),X13648),X13647)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__imp__le])])])). 4.46/4.72 fof(c_0_8922, plain, ![X16198, X16199]:(~class_Rings_Ocomm__semiring__1(X16199)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16199),c_Groups_Ozero__class_Ozero(X16199)),X16198)=c_Groups_Ozero__class_Ozero(X16199)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])])])). 4.46/4.72 fof(c_0_8923, plain, ![X9565, X9566]:(~class_Groups_Omonoid__mult(X9566)|hAPP(hAPP(c_Power_Opower__class_Opower(X9566),c_Groups_Oone__class_Oone(X9566)),X9565)=c_Groups_Oone__class_Oone(X9566)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__one])])])). 4.46/4.72 fof(c_0_8924, plain, ![X16027, X16028]:(~class_Lattices_Obounded__lattice__top(X16028)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X16028),c_Orderings_Otop__class_Otop(X16028)),X16027)=c_Orderings_Otop__class_Otop(X16028)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__top__left])])). 4.46/4.72 fof(c_0_8925, plain, ![X1533, X1534]:(~class_Rings_Omult__zero(X1534)|c_Groups_Ozero__class_Ozero(X1534)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1534),c_Groups_Ozero__class_Ozero(X1534)),X1533)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])])). 4.46/4.72 fof(c_0_8926, plain, ![X8565, X8566]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8566),X8565))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X8566),X8565)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less])])). 4.46/4.72 fof(c_0_8927, plain, ![X16580, X16581]:(~class_Rings_Odivision__ring(X16581)|c_Groups_Ozero__class_Ozero(X16581)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16581),c_Groups_Ozero__class_Ozero(X16581)),X16580)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__zero__left])])])). 4.46/4.72 fof(c_0_8928, plain, ![X16758, X16759]:(c_List_Olist_ONil(X16758)=X16759|hAPP(hAPP(c_List_Onth(X16758),X16759),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_List_Ohd(X16758),X16759)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__conv__nth])])])). 4.46/4.72 fof(c_0_8929, plain, ![X7871, X7872]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7872),X7871))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7872),X7871))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7872),X7871)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7872),X7871)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq])])). 4.46/4.72 fof(c_0_8930, plain, ![X5645, X5646]:(~hBOOL(hAPP(c_Com_OWT,X5646))|(~hBOOL(hAPP(c_Com_OWT,X5645))|hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X5646,X5645))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_OSemi])])). 4.46/4.72 fof(c_0_8931, plain, ![X12829, X12830, X12831]:(~class_Rings_Ono__zero__divisors(X12831)|(X12830=c_Groups_Ozero__class_Ozero(X12831)|(X12829=c_Groups_Ozero__class_Ozero(X12831)|c_Groups_Ozero__class_Ozero(X12831)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12831),X12830),X12829)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_no__zero__divisors])])])). 4.46/4.72 cnf(c_0_8932, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_5551])). 4.46/4.72 fof(c_0_8933, plain, ![X17587, X17588, X17589]:((X17588!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17589),X17588),X17587)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17589),X17588),X17587))|~class_Lattices_Osemilattice__inf(X17589))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17589),X17588),X17587))|X17588=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17589),X17588),X17587)|~class_Lattices_Osemilattice__inf(X17589))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__inf])])])). 4.46/4.72 cnf(c_0_8934, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))|~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X1))),X2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5552])). 4.46/4.72 cnf(c_0_8935, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))|~hBOOL(hAPP(c_Com_OWT,X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5553, c_0_5554]), c_0_5555])])). 4.46/4.72 cnf(c_0_8936, plain, (c_List_Olist_ONil(X1)=X3|hAPP(c_List_Orotate(X1,X2),X3)!=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_4811])). 4.46/4.72 fof(c_0_8937, plain, ![X3037, X3038, X3039, X3040]:(((X3038=X3037|c_SetInterval_Oord__class_OatLeastAtMost(X3040,X3039,X3038)!=hAPP(hAPP(c_Set_Oinsert(X3040),X3037),c_Orderings_Obot__class_Obot(tc_fun(X3040,tc_HOL_Obool)))|~class_Orderings_Oorder(X3040))&(X3039=X3038|c_SetInterval_Oord__class_OatLeastAtMost(X3040,X3039,X3038)!=hAPP(hAPP(c_Set_Oinsert(X3040),X3037),c_Orderings_Obot__class_Obot(tc_fun(X3040,tc_HOL_Obool)))|~class_Orderings_Oorder(X3040)))&(X3038!=X3037|X3039!=X3038|c_SetInterval_Oord__class_OatLeastAtMost(X3040,X3039,X3038)=hAPP(hAPP(c_Set_Oinsert(X3040),X3037),c_Orderings_Obot__class_Obot(tc_fun(X3040,tc_HOL_Obool)))|~class_Orderings_Oorder(X3040))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton__iff])])])). 4.46/4.72 fof(c_0_8938, plain, ![X16238, X16239]:(~class_Rings_Olinordered__idom(X16239)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16239),c_Groups_Ozero__class_Ozero(X16239)),X16238))|c_Groups_Oone__class_Oone(X16239)=c_Groups_Osgn__class_Osgn(X16239,X16238))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__pos])])])). 4.46/4.72 cnf(c_0_8939, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5556])). 4.46/4.72 fof(c_0_8940, plain, ![X13211, X13212]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X13212)),X13211))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13212),X13211))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__lessD])])])). 4.46/4.72 cnf(c_0_8941, plain, (hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5031])). 4.46/4.72 cnf(c_0_8942, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,esk206_2(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_5472])). 4.46/4.72 fof(c_0_8943, plain, ![X13251, X13252]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13252),X13251))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Nat__Transfer_Otsub(X13251,X13252))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13252),X13251))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X13251),X13252)=c_Nat__Transfer_Otsub(X13251,X13252))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_tsub__def])])])). 4.46/4.72 fof(c_0_8944, plain, ![X9356, X9357]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9357),X9356))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9356),X9357))|X9357=X9356)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__antisym])])])). 4.46/4.72 cnf(c_0_8945, plain, (c_Groups_Ozero__class_Ozero(X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Oring__no__zero__divisors(X2)), inference(split_conjunct,[status(thm)],[c_0_5550])). 4.46/4.72 fof(c_0_8946, plain, ![X4940, X4941, X4942]:(~class_Groups_Ocomm__monoid__mult(X4942)|c_Groups_Oone__class_Oone(X4942)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4941,X4942),X4940),c_Orderings_Obot__class_Obot(tc_fun(X4941,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod_Oempty])])])). 4.46/4.72 fof(c_0_8947, plain, ![X3774, X3775]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3775),X3774))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3774),X3775))|X3775=X3774)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])])). 4.46/4.72 fof(c_0_8948, plain, ![X12697, X12698]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X12698),X12697)|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X12698),X12697)))&(~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X12698),X12697))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X12698),X12697))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__int__def])])). 4.46/4.72 fof(c_0_8949, plain, ![X11732, X11733, X11734]:(~c_Wellfounded_Owf(X11734,X11733)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X11734,X11734)),hAPP(hAPP(c_Product__Type_OPair(X11734,X11734),X11732),X11732)),X11733))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__not__refl])])])). 4.46/4.72 fof(c_0_8950, plain, ![X7319, X7320]:(~class_Rings_Odivision__ring__inverse__zero(X7320)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7320),X7319),c_Groups_Ozero__class_Ozero(X7320))=c_Groups_Ozero__class_Ozero(X7320)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__zero])])])). 4.46/4.72 fof(c_0_8951, plain, ![X8133, X8134]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8134),X8133)|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X8133|X8134=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X8133|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8134),X8133))&(X8134!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8134),X8133)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__is__0])])])). 4.46/4.72 fof(c_0_8952, plain, ![X11270, X11271]:(~class_Lattices_Obounded__lattice__top(X11271)|c_Orderings_Otop__class_Otop(X11271)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X11271),X11270),c_Orderings_Otop__class_Otop(X11271))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__top__right])])])). 4.46/4.72 cnf(c_0_8953, plain, (X1=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5529])). 4.46/4.72 fof(c_0_8954, plain, ![X13152, X13153]:(~class_Orderings_Otop(X13153)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13153),X13152),c_Orderings_Otop__class_Otop(X13153)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__greatest])])). 4.46/4.72 fof(c_0_8955, plain, ![X3587, X3588]:((X3587!=X3588|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3587),hAPP(c_Nat_OSuc,X3588)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3588),X3587)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3587),hAPP(c_Nat_OSuc,X3588)))|X3587=X3588|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3588),X3587)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])])). 4.46/4.72 fof(c_0_8956, plain, ![X11408, X11409, X11410]:((hAPP(hAPP(c_Orderings_Oord__class_Omax(X11410),X11409),X11408)!=X11408|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11410),X11409),X11408))|~class_Orderings_Olinorder(X11410))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11410),X11409),X11408))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X11410),X11409),X11408)=X11408|~class_Orderings_Olinorder(X11410))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__sup])])])). 4.46/4.72 fof(c_0_8957, plain, ![X15430, X15431]:(~class_Divides_Osemiring__div(X15431)|c_Groups_Ozero__class_Ozero(X15431)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15431),X15430),c_Groups_Ozero__class_Ozero(X15431))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__0])])). 4.46/4.72 fof(c_0_8958, plain, ![X6136, X6137, X6138]:((hAPP(hAPP(c_Orderings_Oord__class_Omin(X6138),X6137),X6136)!=X6137|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6138),X6137),X6136))|~class_Orderings_Olinorder(X6138))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6138),X6137),X6136))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X6138),X6137),X6136)=X6137|~class_Orderings_Olinorder(X6138))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__inf])])])). 4.46/4.72 fof(c_0_8959, plain, ![X2155]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2155)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2155)&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2155|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2155)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__le__0__conv])])). 4.46/4.72 fof(c_0_8960, plain, ![X1869, X1870, X1871]:(X1871=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1869=hAPP(c_List_Ohd(X1870),c_List_Oreplicate(X1870,X1871,X1869))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__replicate])])])). 4.46/4.72 fof(c_0_8961, plain, ![X1588, X1589]:(~class_Rings_Ocomm__semiring__1(X1589)|c_Groups_Ozero__class_Ozero(X1589)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1589),X1588),c_Groups_Ozero__class_Ozero(X1589))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])])])). 4.46/4.72 fof(c_0_8962, plain, ![X7766, X7767, X7768]:(~c_Wellfounded_Owf(X7768,X7767)|c_Wellfounded_Owf(tc_List_Olist(X7768),hAPP(c_List_Olexn(X7768,X7767),X7766))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lexn])])). 4.46/4.72 fof(c_0_8963, plain, ![X3167, X3168]:((X3168!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X3167!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3167)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3168)))&((X3168=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3167)!=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3168)))&(X3167=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3167)!=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3168))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negative__eq__positive])])])). 4.46/4.72 cnf(c_0_8964, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),X1))|X1!=X2|~class_Orderings_Oorder(X3)), inference(split_conjunct,[status(thm)],[c_0_5557])). 4.46/4.72 fof(c_0_8965, plain, ![X772, X773]:(~class_Rings_Omult__zero(X773)|c_Groups_Ozero__class_Ozero(X773)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X773),X772),c_Groups_Ozero__class_Ozero(X773))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])])). 4.46/4.72 cnf(c_0_8966, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X3),X1)=X3|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)), inference(split_conjunct,[status(thm)],[c_0_5558])). 4.46/4.72 cnf(c_0_8967, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X1),X2)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5470])). 4.46/4.72 fof(c_0_8968, plain, ![X10926, X10927, X10928, X10929]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X10929,X10928)),c_Sum__Type_OPlus(X10929,X10928,X10927,X10926)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X10929),X10927))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__PlusD_I1_J])])])). 4.46/4.72 fof(c_0_8969, plain, ![X4377, X4378, X4379]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4379,tc_HOL_Obool)),X4378),X4377))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4379,tc_HOL_Obool)),X4378),X4377)=X4377), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__absorb1])])). 4.46/4.72 fof(c_0_8970, plain, ![X995, X996, X997]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X997,tc_HOL_Obool)),X996),X995))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X997,tc_HOL_Obool)),X995),X996)=X995), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__absorb2])])). 4.46/4.72 fof(c_0_8971, plain, ![X16297, X16298, X16299]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16299,tc_HOL_Obool)),X16298),X16297))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16299,tc_HOL_Obool)),X16297),X16298)=X16298), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb1])])). 4.46/4.72 fof(c_0_8972, plain, ![X16277, X16278]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X16278|c_List_Olist_ONil(tc_List_Olist(X16277))=c_Enum_On__lists(X16277,X16278,c_List_Olist_ONil(X16277)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X16278|c_Enum_On__lists(X16277,X16278,c_List_Olist_ONil(X16277))=hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X16277)),c_List_Olist_ONil(X16277)),c_List_Olist_ONil(tc_List_Olist(X16277))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_n__lists__Nil])])])). 4.46/4.72 fof(c_0_8973, plain, ![X1325, X1326, X1327, X1328]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1328,X1327)),c_Sum__Type_OPlus(X1328,X1327,X1326,X1325)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1327),X1325))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__PlusD_I2_J])])])). 4.46/4.72 fof(c_0_8974, plain, ![X17443, X17444, X17445, X17446, X17447, X17448, X17449]:(~c_Finite__Set_Ofolding__image__simple__idem(X17449,X17448,X17447,X17446,X17445,X17444)|hAPP(hAPP(X17447,X17443),X17443)=X17443), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem])])). 4.46/4.72 fof(c_0_8975, plain, ![X5916, X5917, X5918]:((~c_Relation_Ototal__on(X5918,X5917,X5916)|c_Relation_Ototal__on(X5918,X5917,hAPP(c_Relation_Oconverse(X5918,X5918),X5916)))&(~c_Relation_Ototal__on(X5918,X5917,hAPP(c_Relation_Oconverse(X5918,X5918),X5916))|c_Relation_Ototal__on(X5918,X5917,X5916))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__converse])])). 4.46/4.72 fof(c_0_8976, plain, ![X9739, X9740, X9741]:((~c_Relation_Orefl__on(X9741,X9740,X9739)|c_Relation_Orefl__on(X9741,X9740,hAPP(c_Relation_Oconverse(X9741,X9741),X9739)))&(~c_Relation_Orefl__on(X9741,X9740,hAPP(c_Relation_Oconverse(X9741,X9741),X9739))|c_Relation_Orefl__on(X9741,X9740,X9739))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__converse])])). 4.46/4.72 fof(c_0_8977, plain, ![X8404, X8405]:((c_Groups_Ozero__class_Ozero(X8405)=X8404|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8405),X8404),X8404)=c_Groups_Oone__class_Oone(X8405)|~class_Rings_Odivision__ring__inverse__zero(X8405))&(c_Groups_Ozero__class_Ozero(X8405)!=X8404|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8405),X8404),X8404)=c_Groups_Ozero__class_Ozero(X8405)|~class_Rings_Odivision__ring__inverse__zero(X8405))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__self__if])])])])). 4.46/4.72 fof(c_0_8978, plain, ![X4229, X4230, X4231]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4231,tc_HOL_Obool)),X4230),X4229))|X4230=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4231,tc_HOL_Obool)),X4230),X4229)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb2])])). 4.46/4.72 fof(c_0_8979, plain, ![X3788, X3789, X3790]:(~hBOOL(hAPP(hAPP(c_member(X3790),X3789),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3790,tc_HOL_Obool)),X3788)))|~hBOOL(hAPP(hAPP(c_member(X3790),X3789),X3788))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ComplE])])])). 4.46/4.72 fof(c_0_8980, plain, ![X14164, X14166, X14167]:(((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk412_1(X14164)),X14164))|c_Nat__Transfer_Onat__set(X14164))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk412_1(X14164)))|c_Nat__Transfer_Onat__set(X14164)))&(~c_Nat__Transfer_Onat__set(X14166)|(~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X14167),X14166))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14167))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__set__def])])])])])])])). 4.46/4.72 cnf(c_0_8981, plain, (X1=X2|c_List_Oupt(X1,X3)!=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),X4)), inference(split_conjunct,[status(thm)],[c_0_4649])). 4.46/4.72 fof(c_0_8982, plain, ![X4219, X4220, X4221, X4222]:((X4219!=X4221|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4222),X4221),X4220)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4222),X4219),X4220)|~class_Groups_Ocancel__semigroup__add(X4222))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4222),X4221),X4220)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4222),X4219),X4220)|X4219=X4221|~class_Groups_Ocancel__semigroup__add(X4222))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])])). 4.46/4.72 fof(c_0_8983, plain, ![X6974, X6975]:(~class_Divides_Osemiring__div(X6975)|(c_Groups_Ozero__class_Ozero(X6975)=X6974|c_Groups_Oone__class_Oone(X6975)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X6975),X6974),X6974))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__self])])). 4.46/4.72 cnf(c_0_8984, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk204_1(X1))))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5527])). 4.46/4.72 fof(c_0_8985, plain, ![X9388, X9389, X9390, X9391]:(~class_Groups_Ocancel__ab__semigroup__add(X9391)|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9391),X9390),X9388)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9391),X9390),X9389)|X9389=X9388)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__imp__eq])])])). 4.46/4.72 fof(c_0_8986, plain, ![X14153, X14154, X14155, X14156]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14156),X14155),X14154)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14156),X14155),X14153)|X14154=X14153|~class_Groups_Ocancel__semigroup__add(X14156))&(X14154!=X14153|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14156),X14155),X14154)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14156),X14155),X14153)|~class_Groups_Ocancel__semigroup__add(X14156))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__left__cancel])])])])). 4.46/4.72 fof(c_0_8987, plain, ![X13578, X13579]:(~class_Rings_Odivision__ring(X13579)|(X13578=c_Groups_Ozero__class_Ozero(X13579)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13579),X13578),X13578)=c_Groups_Oone__class_Oone(X13579))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__self])])])). 4.46/4.72 fof(c_0_8988, plain, ![X5909, X5910]:(~c_Nat__Transfer_Onat__set(X5910)|(~c_Nat__Transfer_Onat__set(X5909)|c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X5910),X5909)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J])])])). 4.46/4.72 fof(c_0_8989, plain, ![X15463, X15464]:(~c_Nat__Transfer_Onat__set(X15464)|(~c_Nat__Transfer_Onat__set(X15463)|c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X15464),X15463)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J])])])). 4.46/4.72 fof(c_0_8990, plain, ![X13034]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13034))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X13034)))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,X13034))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13034)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__neg__eq__ge__0])])])). 4.46/4.72 fof(c_0_8991, plain, ![X13514, X13515, X13516]:((~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X13516,X13515,X13514)))|hBOOL(hAPP(c_Com_OWT,X13514)))&(~hBOOL(hAPP(c_Com_OWT,X13514))|hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X13516,X13515,X13514))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I3_J])])). 4.46/4.72 cnf(c_0_8992, plain, (c_Groups_Ozero__class_Ozero(X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X1),X2)|X1!=X2|~class_Groups_Oab__group__add(X3)), inference(split_conjunct,[status(thm)],[c_0_5559])). 4.46/4.72 fof(c_0_8993, plain, ![X8789, X8790]:(hAPP(c_Finite__Set_Ocard(X8790),hAPP(c_List_Oset(X8790),X8789))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8790)),X8789)|hBOOL(hAPP(c_List_Odistinct(X8790),X8789))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__distinct])])). 4.46/4.72 fof(c_0_8994, plain, ![X8471, X8472]:(~class_Orderings_Olinorder(X8472)|(c_List_Olist_ONil(X8472)=X8471|(~c_List_Olinorder__class_Osorted(X8472,X8471)|c_List_Olinorder__class_Osorted(X8472,c_List_Obutlast(X8472,X8471))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__butlast])])])). 4.46/4.72 fof(c_0_8995, plain, ![X17109, X17110, X17111]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X17111|c_List_Olast(X17110,c_List_Oreplicate(X17110,X17111,X17109))=X17109), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_last__replicate])])])). 4.46/4.72 fof(c_0_8996, plain, ![X14802, X14803, X14804]:(((c_List_Olist_ONil(X14804)!=X14802|c_List_Olist_ONil(X14804)=hAPP(hAPP(c_List_Otake(X14804),X14803),X14802))&(X14803!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Olist_ONil(X14804)=hAPP(hAPP(c_List_Otake(X14804),X14803),X14802)))&(c_List_Olist_ONil(X14804)!=hAPP(hAPP(c_List_Otake(X14804),X14803),X14802)|(c_List_Olist_ONil(X14804)=X14802|X14803=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__eq__Nil])])])). 4.46/4.72 fof(c_0_8997, plain, ![X15709, X15710, X15711, X15712, X15713]:(~c_Fun_Oinj__on(X15713,X15712,X15711,c_Orderings_Otop__class_Otop(tc_fun(X15713,tc_HOL_Obool)))|(hAPP(X15711,X15710)!=hAPP(X15711,X15709)|X15709=X15710)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_injD])])])). 4.46/4.72 fof(c_0_8998, plain, ![X6060, X6061]:(~class_Power_Opower(X6061)|hAPP(hAPP(c_Power_Opower__class_Opower(X6061),X6060),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X6061)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__0])])])). 4.46/4.72 fof(c_0_8999, plain, ![X6488, X6489]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6489),X6488)!=X6489|(X6488=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X6489=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__eq__self__implies__10])])])). 4.46/4.72 fof(c_0_9000, plain, ![X3536, X3537]:(~class_Groups_Omonoid__mult(X3537)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3537),c_Groups_Oone__class_Oone(X3537)),X3536)=X3536), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])])). 4.46/4.72 fof(c_0_9001, plain, ![X11484, X11485]:(~class_Groups_Ocomm__monoid__mult(X11485)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11485),c_Groups_Oone__class_Oone(X11485)),X11484)=X11484), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])])). 4.46/4.72 fof(c_0_9002, plain, ![X2862, X2863]:(~class_Groups_Omonoid__add(X2863)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2863),c_Groups_Ozero__class_Ozero(X2863)),X2862)=X2862), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])])). 4.46/4.72 fof(c_0_9003, plain, ![X11065, X11066, X11067, X11068, X11069, X11070]:(((X11065=X11067|hAPP(hAPP(c_Product__Type_OPair(X11070,X11069),X11068),X11067)!=hAPP(hAPP(c_Product__Type_OPair(X11070,X11069),X11066),X11065))&(X11066=X11068|hAPP(hAPP(c_Product__Type_OPair(X11070,X11069),X11068),X11067)!=hAPP(hAPP(c_Product__Type_OPair(X11070,X11069),X11066),X11065)))&(X11065!=X11067|X11066!=X11068|hAPP(hAPP(c_Product__Type_OPair(X11070,X11069),X11068),X11067)=hAPP(hAPP(c_Product__Type_OPair(X11070,X11069),X11066),X11065))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__eq])])])). 4.46/4.72 fof(c_0_9004, plain, ![X16749, X16750]:(~class_Rings_Ocomm__semiring__1(X16750)|hAPP(hAPP(c_Power_Opower__class_Opower(X16750),X16749),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X16750)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])])])). 4.46/4.72 fof(c_0_9005, plain, ![X5605, X5606]:(~class_Groups_Ocomm__monoid__add(X5606)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5606),c_Groups_Ozero__class_Ozero(X5606)),X5605)=X5605), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])])). 4.46/4.72 fof(c_0_9006, plain, ![X8495, X8496]:(~class_Rings_Ocomm__semiring__1(X8496)|X8495=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8496),c_Groups_Oone__class_Oone(X8496)),X8495)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])])])). 4.46/4.72 fof(c_0_9007, plain, ![X7752, X7753]:(~class_Rings_Ocomm__semiring__1(X7753)|X7752=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7753),c_Groups_Ozero__class_Ozero(X7753)),X7752)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])])). 4.46/4.72 fof(c_0_9008, plain, ![X17191, X17192]:(~class_Lattices_Obounded__lattice__top(X17192)|X17191=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17192),c_Orderings_Otop__class_Otop(X17192)),X17191)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__top__left])])). 4.46/4.72 fof(c_0_9009, plain, ![X8362, X8363]:(~class_Divides_Osemiring__div(X8363)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8363),X8362),c_Groups_Oone__class_Oone(X8363))=X8362), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__by__1])])])). 4.46/4.72 fof(c_0_9010, plain, ![X1545, X1546]:(~class_Groups_Ocomm__monoid__mult(X1546)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1546),X1545),c_Groups_Oone__class_Oone(X1546))=X1545), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult_Ocomm__neutral])])])). 4.46/4.72 fof(c_0_9011, plain, ![X4674, X4675]:(~class_Groups_Omonoid__add(X4675)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4675),X4674),c_Groups_Ozero__class_Ozero(X4675))=X4674), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])])). 4.46/4.72 fof(c_0_9012, plain, ![X4801, X4802]:(~class_Groups_Ogroup__add(X4802)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4802),X4801),c_Groups_Ozero__class_Ozero(X4802))=X4801), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__0__right])])])). 4.46/4.72 fof(c_0_9013, plain, ![X1279, X1280]:(~class_Lattices_Obounded__lattice__top(X1280)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1280),X1279),c_Orderings_Otop__class_Otop(X1280))=X1279), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__top__right])])])). 4.46/4.72 fof(c_0_9014, plain, ![X17533, X17534, X17535]:((X17533!=X17534|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17535),X17533),X17534)=c_Groups_Oone__class_Oone(X17535)|c_Groups_Ozero__class_Ozero(X17535)=X17534|~class_Rings_Odivision__ring(X17535))&(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17535),X17533),X17534)!=c_Groups_Oone__class_Oone(X17535)|X17533=X17534|c_Groups_Ozero__class_Ozero(X17535)=X17534|~class_Rings_Odivision__ring(X17535))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse__eq])])])). 4.46/4.72 fof(c_0_9015, plain, ![X4595, X4596]:(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4596,X4596),tc_HOL_Obool))!=hAPP(hAPP(c_Relation_Orel__comp(X4596,X4596,X4596),X4595),X4595)|c_Wellfounded_Owf(X4596,X4595)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__no__loop])])). 4.46/4.72 cnf(c_0_9016, plain, (c_Wellfounded_OwfP(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))), inference(split_conjunct,[status(thm)],[c_0_5482])). 4.46/4.72 fof(c_0_9017, plain, ![X14083, X14084]:(~class_Groups_Omonoid__mult(X14084)|X14083=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14084),X14083),c_Groups_Oone__class_Oone(X14084))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__1__right])])])). 4.46/4.72 fof(c_0_9018, plain, ![X13558, X13559]:(~class_Rings_Ocomm__semiring__1(X13559)|X13558=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13559),X13558),c_Groups_Oone__class_Oone(X13559))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])])). 4.46/4.72 fof(c_0_9019, plain, ![X12766, X12767]:(~class_Rings_Odivision__ring(X12767)|X12766=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12767),X12766),c_Groups_Oone__class_Oone(X12767))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__1])])). 4.46/4.72 fof(c_0_9020, plain, ![X1162, X1163, X1164, X1165, X1166, X1167]:(~c_Typedef_Otype__definition(X1167,X1166,X1165,X1164,X1163)|X1162=hAPP(X1164,hAPP(X1165,X1162))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inverse])])). 4.46/4.72 fof(c_0_9021, plain, ![X3817, X3818]:(~class_Rings_Ocomm__semiring__1(X3818)|X3817=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3818),X3817),c_Groups_Ozero__class_Ozero(X3818))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])])])). 4.46/4.72 fof(c_0_9022, plain, ![X12156, X12157]:(~class_Groups_Ocomm__monoid__add(X12157)|X12156=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12157),X12156),c_Groups_Ozero__class_Ozero(X12157))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])])). 4.46/4.72 fof(c_0_9023, plain, ![X3165, X3166]:(~class_Lattices_Oboolean__algebra(X3166)|X3165=hAPP(c_Groups_Ouminus__class_Ouminus(X3166),hAPP(c_Groups_Ouminus__class_Ouminus(X3166),X3165))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__compl])])). 4.46/4.72 fof(c_0_9024, plain, ![X9489, X9490]:(~class_Groups_Omonoid__mult(X9490)|X9489=hAPP(hAPP(c_Power_Opower__class_Opower(X9490),X9489),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__one__right])])])). 4.46/4.72 fof(c_0_9025, plain, ![X4011, X4012, X4013, X4014, X4015]:(~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4015,X4014,X4013),X4012),X4011))|hBOOL(hAPP(hAPP(X4013,X4011),X4012))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversepD])])). 4.46/4.72 fof(c_0_9026, plain, ![X17374, X17375]:(~class_Rings_Ocomm__semiring__1(X17375)|X17374=hAPP(hAPP(c_Power_Opower__class_Opower(X17375),X17374),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])])])). 4.46/4.72 fof(c_0_9027, plain, ![X12158, X12159, X12161]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X12159),X12158))|hBOOL(hAPP(X12158,esk356_2(X12158,X12159)))|~class_Enum_Oenum(X12159))&(~hBOOL(hAPP(X12158,X12161))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X12159),X12158))|~class_Enum_Oenum(X12159))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exists__code])])])])])). 4.46/4.72 fof(c_0_9028, plain, ![X10599, X10600, X10602]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X10600),X10599))|hBOOL(hAPP(X10599,esk310_2(X10599,X10600)))|~class_Enum_Oenum(X10600))&(~hBOOL(hAPP(X10599,X10602))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X10600),X10599))|~class_Enum_Oenum(X10600))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__ex])])])])])). 4.46/4.72 cnf(c_0_9029, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_4687])). 4.46/4.72 fof(c_0_9030, plain, ![X12748, X12749]:(~class_Complete__Lattice_Ocomplete__lattice(X12749)|c_Complete__Lattice_OInf__class_OInf(X12749,hAPP(hAPP(c_Set_Oinsert(X12749),X12748),c_Orderings_Obot__class_Obot(tc_fun(X12749,tc_HOL_Obool))))=X12748), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__singleton])])). 4.46/4.72 fof(c_0_9031, plain, ![X3865, X3866]:(~class_Orderings_Olinorder(X3866)|c_List_Olinorder__class_Osorted(X3866,c_List_Olinorder__class_Osort__key(X3866,X3866,c_COMBI(X3866),X3865))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__sort])])). 4.46/4.72 fof(c_0_9032, plain, ![X12217, X12218]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12218))|c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X12218,X12217))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__function__closures])])). 4.46/4.72 fof(c_0_9033, plain, ![X12613, X12614]:(~class_Orderings_Olinorder(X12614)|c_Big__Operators_Olinorder__class_OMax(X12614,hAPP(hAPP(c_Set_Oinsert(X12614),X12613),c_Orderings_Obot__class_Obot(tc_fun(X12614,tc_HOL_Obool))))=X12613), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Osingleton])])). 4.46/4.72 fof(c_0_9034, plain, ![X2066, X2067]:(~class_Complete__Lattice_Ocomplete__lattice(X2067)|c_Complete__Lattice_OSup__class_OSup(X2067,hAPP(hAPP(c_Set_Oinsert(X2067),X2066),c_Orderings_Obot__class_Obot(tc_fun(X2067,tc_HOL_Obool))))=X2066), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__singleton])])])). 4.46/4.72 fof(c_0_9035, plain, ![X2196, X2197]:(~class_Lattices_Olattice(X2197)|c_Big__Operators_Olattice__class_OSup__fin(X2197,hAPP(hAPP(c_Set_Oinsert(X2197),X2196),c_Orderings_Obot__class_Obot(tc_fun(X2197,tc_HOL_Obool))))=X2196), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Osingleton])])])). 4.46/4.72 fof(c_0_9036, plain, ![X7468, X7469]:(~class_Lattices_Olattice(X7469)|X7468=c_Big__Operators_Olattice__class_OInf__fin(X7469,hAPP(hAPP(c_Set_Oinsert(X7469),X7468),c_Orderings_Obot__class_Obot(tc_fun(X7469,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Osingleton])])])). 4.46/4.72 fof(c_0_9037, plain, ![X4985]:(~class_Power_Opower(X4985)|c_Power_Opower_Opower(X4985,c_Groups_Oone__class_Oone(X4985),c_Groups_Otimes__class_Otimes(X4985))=c_Power_Opower__class_Opower(X4985)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__power__power])])])). 4.46/4.72 cnf(c_0_9038, plain, (X3=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|X3!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)|~class_Fields_Ofield__inverse__zero(X2)), inference(split_conjunct,[status(thm)],[c_0_5494])). 4.46/4.72 fof(c_0_9039, plain, ![X7996, X7997]:(~class_Orderings_Olinorder(X7997)|X7996=c_Big__Operators_Olinorder__class_OMin(X7997,hAPP(hAPP(c_Set_Oinsert(X7997),X7996),c_Orderings_Obot__class_Obot(tc_fun(X7997,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Osingleton])])). 4.46/4.72 fof(c_0_9040, plain, ![X1525, X1526, X1527]:(~class_Orderings_Opreorder(X1527)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1527),X1526),X1525))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1527),X1525),X1526)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__asym_H])])])). 4.46/4.72 fof(c_0_9041, plain, ![X7593, X7594, X7595]:(~class_Orderings_Oorder(X7595)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7595),X7594),X7593))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7595),X7593),X7594)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I9_J])])])). 4.46/4.72 fof(c_0_9042, plain, ![X8193, X8194, X8195]:(((X8193!=X8194|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8195),X8194),X8193))|~class_Orderings_Olinorder(X8195))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8195),X8193),X8194))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8195),X8194),X8193))|~class_Orderings_Olinorder(X8195)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8195),X8194),X8193))|(X8193=X8194|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8195),X8193),X8194)))|~class_Orderings_Olinorder(X8195))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq])])])])). 4.46/4.72 fof(c_0_9043, plain, ![X8012, X8013]:(~c_Nat__Transfer_Ois__nat(X8013)|(~c_Nat__Transfer_Ois__nat(X8012)|c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8013),X8012)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I1_J])])])). 4.46/4.72 fof(c_0_9044, plain, ![X13262, X13263, X13264]:((X13262!=hAPP(c_Option_Ooption_OSome(X13264),X13263)|hBOOL(hAPP(hAPP(c_member(X13264),X13263),c_Option_Oset(X13264,X13262))))&(~hBOOL(hAPP(hAPP(c_member(X13264),X13263),c_Option_Oset(X13264,X13262)))|X13262=hAPP(c_Option_Ooption_OSome(X13264),X13263))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__set])])). 4.46/4.72 fof(c_0_9045, plain, ![X17100, X17101, X17102, X17103]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X17103,X17102),X17101))|(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X17103,X17102),X17100))|X17101=X17100)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__unique])])). 4.46/4.72 fof(c_0_9046, plain, ![X8939, X8940]:(~c_Nat__Transfer_Ois__nat(X8940)|(~c_Nat__Transfer_Ois__nat(X8939)|c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8940),X8939)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J])])])). 4.46/4.72 fof(c_0_9047, plain, ![X547, X548]:(~c_Nat__Transfer_Ois__nat(X548)|(~c_Nat__Transfer_Ois__nat(X547)|c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X548),X547)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J])])])). 4.46/4.72 fof(c_0_9048, plain, ![X16071, X16072, X16073]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X16073),hAPP(hAPP(c_Set_Oinsert(X16073),X16072),X16071)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X16073),X16071)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16073),X16071))|hBOOL(hAPP(c_Finite__Set_Ofinite(X16073),hAPP(hAPP(c_Set_Oinsert(X16073),X16072),X16071))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__insert])])). 4.46/4.72 cnf(c_0_9049, plain, (X2=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)|hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)!=X3|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5560])). 4.46/4.72 fof(c_0_9050, plain, ![X6829]:(~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X6829),c_Int_OInteg))|X6829=hAPP(c_Int_ORep__Integ,esk200_1(X6829))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Rep__Integ__cases])])])])). 4.46/4.72 cnf(c_0_9051, plain, (X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(X2)!=hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1)|~class_Rings_Ono__zero__divisors(X2)|~class_Rings_Ozero__neq__one(X2)|~class_Rings_Omult__zero(X2)|~class_Power_Opower(X2)), inference(split_conjunct,[status(thm)],[c_0_5533])). 4.46/4.72 cnf(c_0_9052, plain, (X1=X2|hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))!=hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5561, c_0_5562]), c_0_5562])). 4.46/4.72 fof(c_0_9053, plain, ![X11108, X11109, X11110]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11110,tc_HOL_Obool)),X11109),X11108))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11110,tc_HOL_Obool)),X11109),X11108)=X11108)&(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11110,tc_HOL_Obool)),X11109),X11108)!=X11108|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11110,tc_HOL_Obool)),X11109),X11108)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Un__eq])])). 4.46/4.72 fof(c_0_9054, plain, ![X9978, X9979, X9980, X9981, X9982]:((~hBOOL(hAPP(X9979,X9980))|hBOOL(hAPP(X9979,c_Hilbert__Choice_OEps(X9978,X9979))))&(~hBOOL(hAPP(X9982,c_Hilbert__Choice_OEps(X9981,X9982)))|hBOOL(hAPP(X9982,esk286_2(X9981,X9982))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_some__eq__ex])])])])])). 4.46/4.72 fof(c_0_9055, plain, ![X953, X954, X955]:((~c_List_Olist__ex(X955,X954,X953)|c_List_Olist__ex(X955,X954,hAPP(c_List_Orev(X955),X953)))&(~c_List_Olist__ex(X955,X954,hAPP(c_List_Orev(X955),X953))|c_List_Olist__ex(X955,X954,X953))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__rev])])). 4.46/4.72 fof(c_0_9056, plain, ![X12506, X12507, X12508]:((~c_List_Olist__all(X12508,X12507,hAPP(c_List_Orev(X12508),X12506))|c_List_Olist__all(X12508,X12507,X12506))&(~c_List_Olist__all(X12508,X12507,X12506)|c_List_Olist__all(X12508,X12507,hAPP(c_List_Orev(X12508),X12506)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__rev])])). 4.46/4.72 fof(c_0_9057, plain, ![X15492, X15493, X15494, X15495, X15496, X15497]:(~c_Finite__Set_Ofolding__image__simple(X15497,X15496,X15495,X15494,X15493,X15492)|hAPP(X15492,c_Orderings_Obot__class_Obot(tc_fun(X15496,tc_HOL_Obool)))=X15494), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oempty])])])). 4.46/4.72 cnf(c_0_9058, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|X1=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1))), inference(split_conjunct,[status(thm)],[c_0_5563])). 4.46/4.72 fof(c_0_9059, plain, ![X17278, X17279, X17280, X17281, X17282, X17283]:(~c_Fun_Oinj__on(X17283,X17282,hAPP(c_Fun_Ocomp(X17281,X17282,X17283,X17280),X17279),X17278)|c_Fun_Oinj__on(X17283,X17281,X17279,X17278)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__imageI2])])])). 4.46/4.72 fof(c_0_9060, plain, ![X6141, X6142, X6143]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6141),X6142)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6143),X6142)|X6141=X6143)&(X6141!=X6143|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6141),X6142)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6143),X6142))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])])). 4.46/4.72 fof(c_0_9061, plain, ![X14566, X14567, X14568]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14568),X14567)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14568),X14566)|X14566=X14567)&(X14566!=X14567|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14568),X14567)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14568),X14566))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])])). 4.46/4.72 cnf(c_0_9062, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_5564])). 4.46/4.72 cnf(c_0_9063, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(split_conjunct,[status(thm)],[c_0_5565])). 4.46/4.72 fof(c_0_9064, plain, ![X3232, X3233, X3234]:(~class_Orderings_Otop(X3234)|c_Orderings_Otop__class_Otop(X3234)=hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3233,X3234)),X3232)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_top__apply])])])). 4.46/4.72 fof(c_0_9065, plain, ![X9022, X9023]:(~class_Groups_Ogroup__add(X9023)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9023),X9022),X9022)=c_Groups_Ozero__class_Ozero(X9023)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])])). 4.46/4.72 fof(c_0_9066, plain, ![X7654, X7655, X7656]:(c_Orderings_Obot__class_Obot(tc_fun(X7656,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7656,tc_HOL_Obool)),X7655),X7654)|X7655=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7656,tc_HOL_Obool)),X7655),X7654)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Diff__triv])])])). 4.46/4.72 fof(c_0_9067, plain, ![X4351, X4352, X4353, X4354, X4355]:(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X4354|X4354!=X4352|c_List_Oreplicate(X4355,X4354,X4353)=c_List_Oreplicate(X4355,X4352,X4351))&(X4353!=X4351|X4354!=X4352|c_List_Oreplicate(X4355,X4354,X4353)=c_List_Oreplicate(X4355,X4352,X4351)))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X4354|X4353=X4351|c_List_Oreplicate(X4355,X4354,X4353)!=c_List_Oreplicate(X4355,X4352,X4351))&(X4354=X4352|c_List_Oreplicate(X4355,X4354,X4353)!=c_List_Oreplicate(X4355,X4352,X4351)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_replicate__eq__replicate])])])])). 4.46/4.72 fof(c_0_9068, plain, ![X4316, X4317, X4318]:(~class_Orderings_Olinorder(X4318)|c_List_Olist_ONil(X4317)=c_List_Olinorder__class_Osort__key(X4317,X4318,X4316,c_List_Olist_ONil(X4317))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sort__key__simps_I1_J])])). 4.46/4.72 fof(c_0_9069, plain, ![X10809, X10810]:(~class_Rings_Olinordered__ring(X10810)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10810),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10810),X10809),X10809)),c_Groups_Ozero__class_Ozero(X10810)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__square__less__zero])])])). 4.46/4.72 fof(c_0_9070, plain, ![X2407, X2408]:(~class_Orderings_Obot(X2408)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2408),c_Orderings_Obot__class_Obot(X2408)),X2407))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__least])])). 4.46/4.72 fof(c_0_9071, plain, ![X16228, X16229]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16229,tc_HOL_Obool)),X16228),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16229,tc_HOL_Obool)),X16228)))|c_Orderings_Obot__class_Obot(tc_fun(X16229,tc_HOL_Obool))=X16228)&(c_Orderings_Obot__class_Obot(tc_fun(X16229,tc_HOL_Obool))!=X16228|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16229,tc_HOL_Obool)),X16228),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16229,tc_HOL_Obool)),X16228))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Compl__self__eq])])). 4.46/4.72 fof(c_0_9072, plain, ![X5539, X5540, X5541, X5542, X5543]:((X5542!=X5540|X5541!=X5539|hAPP(hAPP(c_List_Olist_OCons(X5543),X5540),X5539)=hAPP(hAPP(c_List_Olist_OCons(X5543),X5542),X5541))&((X5542=X5540|hAPP(hAPP(c_List_Olist_OCons(X5543),X5540),X5539)!=hAPP(hAPP(c_List_Olist_OCons(X5543),X5542),X5541))&(X5541=X5539|hAPP(hAPP(c_List_Olist_OCons(X5543),X5540),X5539)!=hAPP(hAPP(c_List_Olist_OCons(X5543),X5542),X5541)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list_Oinject])])])). 4.46/4.72 fof(c_0_9073, plain, ![X9828, X9829, X9830, X9831]:((X9828!=X9830|hAPP(hAPP(c_List_Oappend(X9831),X9828),X9829)=hAPP(hAPP(c_List_Oappend(X9831),X9830),X9829))&(hAPP(hAPP(c_List_Oappend(X9831),X9828),X9829)!=hAPP(hAPP(c_List_Oappend(X9831),X9830),X9829)|X9828=X9830)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__same__eq])])). 4.46/4.72 cnf(c_0_9074, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk393_1(X1))))), inference(split_conjunct,[status(thm)],[c_0_5516])). 4.46/4.72 fof(c_0_9075, plain, ![X2200, X2201, X2202]:((~hBOOL(hAPP(X2200,X2201))|hBOOL(hAPP(hAPP(c_member(X2202),X2201),X2200)))&(~hBOOL(hAPP(hAPP(c_member(X2202),X2201),X2200))|hBOOL(hAPP(X2200,X2201)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])])). 4.46/4.72 fof(c_0_9076, plain, ![X1660, X1661, X1662, X1663]:((hAPP(hAPP(c_List_Oappend(X1663),X1662),X1660)!=hAPP(hAPP(c_List_Oappend(X1663),X1662),X1661)|X1661=X1660)&(X1661!=X1660|hAPP(hAPP(c_List_Oappend(X1663),X1662),X1660)=hAPP(hAPP(c_List_Oappend(X1663),X1662),X1661))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__append__eq])])). 4.46/4.72 fof(c_0_9077, plain, ![X6621, X6622]:(~class_HOL_Oequal(X6622)|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X6622),X6621),X6621))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__refl])])). 4.46/4.72 fof(c_0_9078, plain, ![X15481, X15482]:(~class_Orderings_Opreorder(X15482)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15482),X15481),X15481))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])])). 4.46/4.72 fof(c_0_9079, plain, ![X14559, X14560]:(~c_Wellfounded_Owf(X14560,X14559)|c_Wellfounded_Owf(tc_fun(X14560,tc_HOL_Obool),c_Wellfounded_Omin__ext(X14560,X14559))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__ext__wf])])])). 4.46/4.72 fof(c_0_9080, plain, ![X2558, X2559]:(~c_Wellfounded_Owf(X2559,X2558)|c_Wellfounded_Owf(tc_fun(X2559,tc_HOL_Obool),c_Wellfounded_Omax__ext(X2559,X2558))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__wf])])). 4.46/4.72 fof(c_0_9081, plain, ![X9725, X9726]:((~c_Wellfounded_Oacyclic(X9726,X9725)|c_Wellfounded_Oacyclic(X9726,hAPP(c_Relation_Oconverse(X9726,X9726),X9725)))&(~c_Wellfounded_Oacyclic(X9726,hAPP(c_Relation_Oconverse(X9726,X9726),X9725))|c_Wellfounded_Oacyclic(X9726,X9725))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__converse])])). 4.46/4.72 fof(c_0_9082, plain, ![X9011, X9012, X9013, X9014, X9015]:((hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X9015,X9014),X9013),X9012),X9011)!=X9013|hAPP(X9013,X9012)=X9011)&(hAPP(X9013,X9012)!=X9011|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X9015,X9014),X9013),X9012),X9011)=X9013)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem__iff])])). 4.46/4.72 fof(c_0_9083, plain, ![X7610, X7611, X7612]:(~hBOOL(hAPP(hAPP(c_member(X7612),X7611),hAPP(hAPP(c_Set_Oinsert(X7612),X7610),c_Orderings_Obot__class_Obot(tc_fun(X7612,tc_HOL_Obool)))))|X7611=X7610), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_singletonE])])])). 4.46/4.72 fof(c_0_9084, plain, ![X9005, X9006, X9007, X9008, X9009, X9010]:(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X9010,X9009,X9008,X9007,X9006),X9005))|hBOOL(hAPP(c_Finite__Set_Ofinite(X9010),X9006))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph__imp__finite])])). 4.46/4.72 fof(c_0_9085, plain, ![X1499, X1500, X1501]:(~class_Rings_Osemiring__1(X1501)|X1499=c_Nat_Osemiring__1__class_Oof__nat__aux(X1501,X1500,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1499)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I1_J])])). 4.46/4.72 fof(c_0_9086, plain, ![X7992, X7993]:((~hBOOL(hAPP(c_Com_OWT,X7992))|hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X7993,X7992))))&(~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X7993,X7992)))|hBOOL(hAPP(c_Com_OWT,X7992)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I6_J])])). 4.46/4.72 fof(c_0_9087, plain, ![X8631, X8633, X8634]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8631))|hAPP(c_Nat_OSuc,esk244_1(X8631))=X8631)&(hAPP(c_Nat_OSuc,X8634)!=X8633|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8633)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc])])])])])). 4.46/4.72 fof(c_0_9088, plain, ![X11357, X11358, X11359, X11360]:(~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11360,tc_HOL_Obool)),X11359),X11358),X11357))|hBOOL(hAPP(X11359,X11357))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D1])])). 4.46/4.72 fof(c_0_9089, plain, ![X7534, X7535, X7536, X7537]:(~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7537,tc_HOL_Obool)),X7536),X7535),X7534))|hBOOL(hAPP(X7535,X7534))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf1D2])])])). 4.46/4.72 fof(c_0_9090, plain, ![X4745, X4746, X4747, X4748]:(~c_Finite__Set_Ofolding__one__idem(X4748,X4747,X4746)|X4745=hAPP(hAPP(X4747,X4745),X4745)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one__idem_Oidem])])])). 4.46/4.72 fof(c_0_9091, plain, ![X5506, X5507]:(~class_Orderings_Olinorder(X5507)|(~c_List_Olinorder__class_Osorted(X5507,X5506)|c_List_Olinorder__class_Osorted(X5507,hAPP(c_List_Otl(X5507),X5506)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__tl])])])). 4.46/4.72 fof(c_0_9092, plain, ![X5604]:(~class_Enum_Oenum(X5604)|c_Orderings_Otop__class_Otop(tc_fun(X5604,tc_HOL_Obool))=hAPP(c_List_Oset(X5604),c_Enum_Oenum__class_Oenum(X5604))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_enum__UNIV])])])). 4.46/4.72 fof(c_0_9093, plain, ![X3442, X3443, X3444]:((X3443!=c_Orderings_Otop__class_Otop(X3444)|X3442!=c_Orderings_Otop__class_Otop(X3444)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3444),X3443),X3442)=c_Orderings_Otop__class_Otop(X3444)|~class_Lattices_Obounded__lattice__top(X3444))&((X3443=c_Orderings_Otop__class_Otop(X3444)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3444),X3443),X3442)!=c_Orderings_Otop__class_Otop(X3444)|~class_Lattices_Obounded__lattice__top(X3444))&(X3442=c_Orderings_Otop__class_Otop(X3444)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3444),X3443),X3442)!=c_Orderings_Otop__class_Otop(X3444)|~class_Lattices_Obounded__lattice__top(X3444)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__eq__top__iff])])])])). 4.46/4.72 cnf(c_0_9094, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_5566])). 4.46/4.72 cnf(c_0_9095, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_5517])). 4.46/4.72 cnf(c_0_9096, plain, (hBOOL(hAPP(X2,X3))|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5242])). 4.46/4.72 cnf(c_0_9097, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Int_Onat,X1)), inference(split_conjunct,[status(thm)],[c_0_5567])). 4.46/4.72 fof(c_0_9098, plain, ![X15968]:(~class_Complete__Lattice_Ocomplete__lattice(X15968)|c_Complete__Lattice_OSup__class_OSup(X15968,c_Orderings_Otop__class_Otop(tc_fun(X15968,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(X15968)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__UNIV])])). 4.46/4.72 fof(c_0_9099, plain, ![X10813, X10814]:(~class_Lattices_Obounded__lattice__bot(X10814)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10814),c_Orderings_Obot__class_Obot(X10814)),X10813)=c_Orderings_Obot__class_Obot(X10814)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__bot__left])])])). 4.46/4.72 fof(c_0_9100, plain, ![X659, X660]:(~class_Lattices_Obounded__lattice__bot(X660)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X660),X659),c_Orderings_Obot__class_Obot(X660))=c_Orderings_Obot__class_Obot(X660)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__bot__right])])])). 4.46/4.72 fof(c_0_9101, plain, ![X10591, X10592]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10592),X10591))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X10592,X10591)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10592),X10591),X10591))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10592),X10591))|X10592=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X10592,X10591))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__if])])])). 4.46/4.72 fof(c_0_9102, plain, ![X3969, X3970, X3971, X3972, X3973]:(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X3973,X3972,X3971,X3970,c_Orderings_Obot__class_Obot(tc_fun(X3973,tc_HOL_Obool))),X3969))|X3970=X3969), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_empty__fold__graphE])])])). 4.46/4.72 fof(c_0_9103, plain, ![X7874, X7875, X7876]:(~c_Wellfounded_Owf(X7876,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7876,X7876),tc_HOL_Obool),X7875),X7874))|c_Wellfounded_Owf(X7876,X7874)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__exp])])])). 4.46/4.72 fof(c_0_9104, plain, ![X10072, X10073, X10074, X10075, X10076]:((~c_Wellfounded_Owf(X10073,X10072)|hBOOL(hAPP(hAPP(c_member(X10073),X10074),c_Wellfounded_Oacc(X10073,X10072))))&(~hBOOL(hAPP(hAPP(c_member(X10076),esk292_2(X10075,X10076)),c_Wellfounded_Oacc(X10076,X10075)))|c_Wellfounded_Owf(X10076,X10075))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__acc__iff])])])])])). 4.46/4.72 fof(c_0_9105, plain, ![X16830, X16831]:(~class_Rings_Olinordered__idom(X16831)|c_Groups_Osgn__class_Osgn(X16831,c_Groups_Osgn__class_Osgn(X16831,X16830))=c_Groups_Osgn__class_Osgn(X16831,X16830)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__sgn])])). 4.46/4.72 fof(c_0_9106, plain, ![X2062, X2063, X2064]:((hAPP(c_Int_Onumber__class_Onumber__of(X2064),X2063)!=hAPP(c_Int_Onumber__class_Onumber__of(X2064),X2062)|X2062=X2063|(~class_Int_Oring__char__0(X2064)|~class_Int_Onumber__ring(X2064)))&(X2062!=X2063|hAPP(c_Int_Onumber__class_Onumber__of(X2064),X2063)=hAPP(c_Int_Onumber__class_Onumber__of(X2064),X2062)|(~class_Int_Oring__char__0(X2064)|~class_Int_Onumber__ring(X2064)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__number__of])])])])). 4.46/4.72 fof(c_0_9107, plain, ![X14687, X14688]:(~class_Lattices_Obounded__lattice__bot(X14688)|X14687=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X14688),c_Orderings_Obot__class_Obot(X14688)),X14687)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__bot__left])])). 4.46/4.72 fof(c_0_9108, plain, ![X6131, X6132, X6133]:(~c_Wellfounded_OwfP(X6133,X6132)|hBOOL(hAPP(c_Wellfounded_Oaccp(X6133,X6132),X6131))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_accp__wfPD])])])). 4.46/4.72 fof(c_0_9109, plain, ![X7601, X7602]:(~class_Divides_Osemiring__div(X7602)|c_Groups_Ozero__class_Ozero(X7602)=c_Divides_Odiv__class_Omod(X7602,c_Groups_Ozero__class_Ozero(X7602),X7601)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__0])])). 4.46/4.72 fof(c_0_9110, plain, ![X15542, X15543]:(~class_Lattices_Obounded__lattice__bot(X15543)|X15542=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15543),X15542),c_Orderings_Obot__class_Obot(X15543))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__bot__right])])])). 4.46/4.72 fof(c_0_9111, plain, ![X17165, X17166]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X17166),X17165))|hAPP(c_Finite__Set_Ocard(X17166),X17165)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_Orderings_Obot__class_Obot(tc_fun(X17166,tc_HOL_Obool))!=X17165|hAPP(c_Finite__Set_Ocard(X17166),X17165)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(hAPP(c_Finite__Set_Ocard(X17166),X17165)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17166),X17165))|c_Orderings_Obot__class_Obot(tc_fun(X17166,tc_HOL_Obool))=X17165))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__eq__0__iff])])])])). 4.46/4.72 fof(c_0_9112, plain, ![X1744, X1745, X1746, X1747]:(~c_Finite__Set_Ofolding(X1747,X1746,X1745,X1744)|c_Fun_Oid(X1746)=hAPP(X1744,c_Orderings_Obot__class_Obot(tc_fun(X1747,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oempty])])). 4.46/4.72 fof(c_0_9113, plain, ![X12043, X12044]:(~class_Divides_Osemiring__div(X12044)|c_Groups_Ozero__class_Ozero(X12044)=c_Divides_Odiv__class_Omod(X12044,X12043,c_Groups_Oone__class_Oone(X12044))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__by__1])])])). 4.46/4.72 fof(c_0_9114, plain, ![X9147]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X9147|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X9147),X9147)=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__self])])). 4.46/4.72 fof(c_0_9115, plain, ![X10117, X10118, X10119]:(~c_Predicate_Oreflp(X10119,X10118)|hBOOL(hAPP(hAPP(X10118,X10117),X10117))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_reflpE])])])). 4.46/4.72 fof(c_0_9116, plain, ![X12449, X12450, X12451]:(~c_Equiv__Relations_Oequivp(X12451,X12450)|hBOOL(hAPP(hAPP(X12450,X12449),X12449))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__reflp])])). 4.46/4.72 fof(c_0_9117, plain, ![X8237, X8238, X8239]:(~hBOOL(hAPP(hAPP(c_member(X8239),X8238),X8237))|hAPP(hAPP(c_Set_Oinsert(X8239),X8238),X8237)=X8237), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insert__absorb])])])). 4.46/4.72 fof(c_0_9118, plain, ![X1544]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1544),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1544)))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1544))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1544),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__def])])). 4.46/4.72 fof(c_0_9119, plain, ![X5882, X5883, X5884]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5883),X5882))|hBOOL(hAPP(X5882,X5884))|~class_Enum_Oenum(X5883))&(~hBOOL(hAPP(X5882,esk182_2(X5882,X5883)))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5883),X5882))|~class_Enum_Oenum(X5883))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_all__code])])])])])). 4.46/4.72 fof(c_0_9120, plain, ![X9305, X9306, X9307, X9308, X9309]:((c_Option_Ooption_ONone(X9305)!=X9306|hAPP(c_Option_Ooption_OSome(X9305),X9307)!=X9306)&(hAPP(c_Option_Ooption_OSome(X9308),esk268_2(X9308,X9309))=X9309|c_Option_Ooption_ONone(X9308)=X9309)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_not__Some__eq])])])])])). 4.46/4.72 fof(c_0_9121, plain, ![X15936, X15937, X15938, X15939]:(~c_Hoare__Mirabelle_Ohoare__derivs(X15939,X15938,X15937)|(~c_Hoare__Mirabelle_Ohoare__derivs(X15939,X15936,X15938)|c_Hoare__Mirabelle_Ohoare__derivs(X15939,X15936,X15937))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_cut])])])). 4.46/4.72 fof(c_0_9122, plain, ![X8915, X8916, X8918, X8919, X8920]:((c_Option_Ooption_ONone(X8915)=X8916|X8916=hAPP(c_Option_Ooption_OSome(X8915),esk259_2(X8915,X8916)))&(X8919!=hAPP(c_Option_Ooption_OSome(X8918),X8920)|c_Option_Ooption_ONone(X8918)!=X8919)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_not__None__eq])])])])])). 4.46/4.72 fof(c_0_9123, plain, ![X6768, X6769, X6770]:(~class_Orderings_Olinorder(X6770)|(~c_List_Olinorder__class_Osorted(X6770,X6769)|c_List_Olinorder__class_Osorted(X6770,c_List_Oremove1(X6770,X6768,X6769)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__remove1])])])). 4.46/4.72 fof(c_0_9124, plain, ![X11081, X11082, X11083]:(~class_Orderings_Olinorder(X11083)|(~c_List_Olinorder__class_Osorted(X11083,X11082)|c_List_Olinorder__class_Osorted(X11083,c_List_OtakeWhile(X11083,X11081,X11082)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__takeWhile])])])). 4.46/4.72 fof(c_0_9125, plain, ![X17211, X17212, X17213, X17214, X17215, X17216, X17217]:((hAPP(X17215,X17211)!=hAPP(X17215,X17212)|X17211=X17212|~c_Typedef_Otype__definition(X17217,X17216,X17215,X17214,X17213))&(X17211!=X17212|hAPP(X17215,X17211)=hAPP(X17215,X17212)|~c_Typedef_Otype__definition(X17217,X17216,X17215,X17214,X17213))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inject])])])). 4.46/4.72 fof(c_0_9126, plain, ![X17080, X17081, X17082]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X17081),X17080))|hBOOL(hAPP(X17080,X17082))|~class_Enum_Oenum(X17081))&(~hBOOL(hAPP(X17080,esk509_2(X17080,X17081)))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X17081),X17080))|~class_Enum_Oenum(X17081))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_enum__all])])])])])])). 4.46/4.72 fof(c_0_9127, plain, ![X16892, X16893]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16893),X16892))|c_List_Olist_ONil(tc_Int_Oint)=c_List_Oupto(X16892,X16893)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_upto__empty])])])). 4.46/4.72 fof(c_0_9128, plain, ![X10458]:(~class_Int_Onumber__ring(X10458)|hAPP(c_Int_Onumber__class_Onumber__of(X10458),c_Int_OMin)=hAPP(c_Groups_Ouminus__class_Ouminus(X10458),c_Groups_Oone__class_Oone(X10458))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_arith__simps_I31_J])])])). 4.46/4.72 fof(c_0_9129, plain, ![X10244, X10245, X10246]:(~class_Rings_Oring__1__no__zero__divisors(X10246)|(c_Groups_Ozero__class_Ozero(X10246)=X10245|c_Groups_Ozero__class_Ozero(X10246)!=hAPP(hAPP(c_Power_Opower__class_Opower(X10246),X10245),X10244))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_field__power__not__zero])])])). 4.46/4.72 cnf(c_0_9130, plain, (hAPP(c_Int_Onat,X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(split_conjunct,[status(thm)],[c_0_5568])). 4.46/4.72 fof(c_0_9131, plain, ![X14653, X14654, X14655]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14655),X14654),X14653))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14655),X14653),X14654))|~class_Orderings_Olinorder(X14655))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14655),X14653),X14654))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14655),X14654),X14653))|~class_Orderings_Olinorder(X14655))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__not__le])])])])). 4.46/4.72 fof(c_0_9132, plain, ![X13596, X13597]:(~c_Wellfounded_Owf(X13597,X13596)|c_Wellfounded_Owf(tc_List_Olist(X13597),c_List_Olex(X13597,X13596))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__lex])])])). 4.46/4.72 fof(c_0_9133, plain, ![X3763, X3764]:(~class_Lattices_Olattice(X3764)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3764),X3763),X3763)=X3763), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oidem])])])). 4.46/4.72 fof(c_0_9134, plain, ![X5023, X5024]:(~class_Lattices_Oab__semigroup__idem__mult(X5024)|X5023=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5024),X5023),X5023)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times_Oidem])])). 4.46/4.72 fof(c_0_9135, plain, ![X9993, X9994]:(~class_Lattices_Osemilattice__sup(X9994)|X9993=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9994),X9993),X9993)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__idem])])). 4.46/4.72 fof(c_0_9136, plain, ![X2340, X2341]:(~c_Wellfounded_Owf(X2341,X2340)|c_Wellfounded_Owf(tc_List_Olist(X2341),c_List_Olenlex(X2341,X2340))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__lenlex])])])). 4.46/4.72 fof(c_0_9137, plain, ![X9334, X9335]:((~c_Wellfounded_Oacyclic(X9335,X9334)|c_Wellfounded_Owf(X9335,X9334)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X9335,X9335)),X9334)))&(~c_Wellfounded_Owf(X9335,X9334)|c_Wellfounded_Oacyclic(X9335,X9334)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X9335,X9335)),X9334)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__iff__acyclic__if__finite])])])). 4.46/4.72 fof(c_0_9138, plain, ![X3667, X3668]:(~class_Lattices_Olattice(X3668)|X3667=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3668),X3667),X3667)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oidem])])). 4.46/4.72 fof(c_0_9139, plain, ![X5699, X5700]:(~class_Lattices_Osemilattice__inf(X5700)|X5699=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5700),X5699),X5699)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__idem])])])). 4.46/4.72 fof(c_0_9140, plain, ![X1519, X1520]:(~class_Groups_Oordered__ab__group__add__abs(X1520)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1520),hAPP(c_Groups_Oabs__class_Oabs(X1520),X1519)),c_Groups_Ozero__class_Ozero(X1520)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__not__less__zero])])])). 4.46/4.72 fof(c_0_9141, plain, ![X11975, X11976]:(~class_Rings_Olinordered__semidom(X11976)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11976),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X11976),X11975)),c_Groups_Ozero__class_Ozero(X11976)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__less__0__iff])])])). 4.46/4.72 fof(c_0_9142, plain, ![X781, X782]:(~c_Nat__Transfer_Ois__nat(X782)|c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X782),X781))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J])])). 4.46/4.72 fof(c_0_9143, plain, ![X8360, X8361]:(~class_Divides_Osemiring__div(X8361)|c_Divides_Odiv__class_Omod(X8361,X8360,c_Groups_Ozero__class_Ozero(X8361))=X8360), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__by__0])])])). 4.46/4.72 fof(c_0_9144, plain, ![X1175]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1175|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1175),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1175),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1175)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__0__eq])])). 4.46/4.72 fof(c_0_9145, plain, ![X757, X758, X759]:((hAPP(c_Int_Oring__1__class_Oof__int(X759),X758)!=hAPP(c_Int_Oring__1__class_Oof__int(X759),X757)|X757=X758|~class_Int_Oring__char__0(X759))&(X757!=X758|hAPP(c_Int_Oring__1__class_Oof__int(X759),X758)=hAPP(c_Int_Oring__1__class_Oof__int(X759),X757)|~class_Int_Oring__char__0(X759))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__eq__iff])])])])). 4.46/4.72 fof(c_0_9146, plain, ![X5508, X5509, X5510]:((X5509!=X5508|hAPP(c_Groups_Ouminus__class_Ouminus(X5510),X5508)=hAPP(c_Groups_Ouminus__class_Ouminus(X5510),X5509)|~class_Lattices_Oboolean__algebra(X5510))&(hAPP(c_Groups_Ouminus__class_Ouminus(X5510),X5508)!=hAPP(c_Groups_Ouminus__class_Ouminus(X5510),X5509)|X5509=X5508|~class_Lattices_Oboolean__algebra(X5510))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_compl__eq__compl__iff])])])])). 4.46/4.72 fof(c_0_9147, plain, ![X1621, X1622, X1623]:(hAPP(hAPP(c_Set_Oinsert(X1623),X1622),c_Orderings_Obot__class_Obot(tc_fun(X1623,tc_HOL_Obool)))!=hAPP(hAPP(c_Set_Oinsert(X1623),X1621),c_Orderings_Obot__class_Obot(tc_fun(X1623,tc_HOL_Obool)))|X1621=X1622), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_singleton__inject])])])). 4.46/4.72 fof(c_0_9148, plain, ![X16050, X16051, X16052]:((hAPP(c_Groups_Ouminus__class_Ouminus(X16052),X16051)!=hAPP(c_Groups_Ouminus__class_Ouminus(X16052),X16050)|X16051=X16050|~class_Groups_Ogroup__add(X16052))&(X16051!=X16050|hAPP(c_Groups_Ouminus__class_Ouminus(X16052),X16051)=hAPP(c_Groups_Ouminus__class_Ouminus(X16052),X16050)|~class_Groups_Ogroup__add(X16052))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal])])])). 4.46/4.72 fof(c_0_9149, plain, ![X13103, X13104, X13105]:((hAPP(c_Nat_Osemiring__1__class_Oof__nat(X13105),X13104)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X13105),X13103)|X13103=X13104|~class_Nat_Osemiring__char__0(X13105))&(X13103!=X13104|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X13105),X13104)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X13105),X13103)|~class_Nat_Osemiring__char__0(X13105))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__eq__iff])])])). 4.46/4.72 fof(c_0_9150, plain, ![X9051, X9052, X9053]:((~hBOOL(hAPP(X9053,c_Divides_Odiv__class_Omod(tc_Int_Oint,X9052,X9051)))|epred1_3(X9053,X9051,X9052))&(~epred1_3(X9053,X9051,X9052)|hBOOL(hAPP(X9053,c_Divides_Odiv__class_Omod(tc_Int_Oint,X9052,X9051))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5569])])). 4.46/4.72 fof(c_0_9151, plain, ![X4397, X4398]:(~hBOOL(X4398)|~hBOOL(X4397)|hBOOL(hAPP(hAPP(c_fconj,X4398),X4397))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fconj__1])])). 4.46/4.72 fof(c_0_9152, plain, ![X1784]:(~class_Enum_Oenum(X1784)|hBOOL(hAPP(c_List_Odistinct(X1784),c_Enum_Oenum__class_Oenum(X1784)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__distinct])])). 4.46/4.72 fof(c_0_9153, plain, ![X6278, X6279]:(~class_Groups_Oordered__ab__group__add(X6279)|c_Fun_Oinj__on(X6279,X6279,c_Groups_Ouminus__class_Ouminus(X6279),X6278)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__uminus])])). 4.46/4.72 fof(c_0_9154, plain, ![X5240, X5241]:(hAPP(X5240,esk160_2(X5240,X5241))!=hAPP(X5241,esk160_2(X5240,X5241))|X5240=X5241), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])). 4.46/4.72 cnf(c_0_9155, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5570])). 4.46/4.72 fof(c_0_9156, plain, ![X15109, X15110]:(~class_Int_Onumber__ring(X15110)|hAPP(c_Int_Oring__1__class_Oof__int(X15110),X15109)=hAPP(c_Int_Onumber__class_Onumber__of(X15110),X15109)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_number__of__eq])])])). 4.46/4.72 fof(c_0_9157, plain, ![X15563, X15564, X15565]:((c_Orderings_Obot__class_Obot(X15565)!=X15563|X15564!=c_Orderings_Obot__class_Obot(X15565)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15565),X15564),X15563)=c_Orderings_Obot__class_Obot(X15565)|~class_Lattices_Obounded__lattice__bot(X15565))&((c_Orderings_Obot__class_Obot(X15565)=X15563|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15565),X15564),X15563)!=c_Orderings_Obot__class_Obot(X15565)|~class_Lattices_Obounded__lattice__bot(X15565))&(X15564=c_Orderings_Obot__class_Obot(X15565)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15565),X15564),X15563)!=c_Orderings_Obot__class_Obot(X15565)|~class_Lattices_Obounded__lattice__bot(X15565)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__eq__bot__iff])])])])). 4.46/4.72 fof(c_0_9158, plain, ![X6947, X6948, X6949]:(~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X6949,X6948,X6947)))|hBOOL(hAPP(c_Com_OWT,X6947))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_WTs__elim__cases_I3_J])])])). 4.46/4.72 fof(c_0_9159, plain, ![X17347]:(~class_Rings_Olinordered__idom(X17347)|c_Groups_Oone__class_Oone(X17347)=hAPP(c_Groups_Oabs__class_Oabs(X17347),c_Groups_Oone__class_Oone(X17347))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__one])])). 4.46/4.72 fof(c_0_9160, plain, ![X1868]:(~class_Groups_Omonoid__add(X1868)|c_Groups_Ozero__class_Ozero(X1868)=hAPP(c_List_Omonoid__add__class_Olistsum(X1868),c_List_Olist_ONil(X1868))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__simps_I1_J])])). 4.46/4.72 fof(c_0_9161, plain, ![X7873]:(~class_Lattices_Oboolean__algebra(X7873)|c_Orderings_Otop__class_Otop(X7873)=hAPP(c_Groups_Ouminus__class_Ouminus(X7873),c_Orderings_Obot__class_Obot(X7873))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_compl__bot__eq])])])). 4.46/4.72 fof(c_0_9162, plain, ![X10787]:(~class_Complete__Lattice_Ocomplete__lattice(X10787)|c_Orderings_Obot__class_Obot(X10787)=c_Complete__Lattice_OInf__class_OInf(X10787,c_Orderings_Otop__class_Otop(tc_fun(X10787,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__UNIV])])])). 4.46/4.72 fof(c_0_9163, plain, ![X1464, X1465]:(~c_Wellfounded_Owf(X1465,X1464)|c_Wellfounded_OwfP(X1465,c_FunDef_Oin__rel(X1465,X1465,X1464))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__in__rel])])). 4.46/4.72 fof(c_0_9164, plain, ![X5624, X5625, X5626]:(~c_Wellfounded_Owf(X5626,X5625)|c_Wellfounded_Owf(X5626,c_Wellfounded_Omlex__prod(X5626,X5624,X5625))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__mlex])])). 4.46/4.72 fof(c_0_9165, plain, ![X15618, X15619]:(~c_Nat__Transfer_Ois__nat(X15619)|(~c_Nat__Transfer_Ois__nat(X15618)|c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X15619,X15618)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I2_J])])])). 4.46/4.72 fof(c_0_9166, plain, ![X13362]:(~class_Groups_Oordered__ab__group__add__abs(X13362)|c_Groups_Ozero__class_Ozero(X13362)=hAPP(c_Groups_Oabs__class_Oabs(X13362),c_Groups_Ozero__class_Ozero(X13362))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zero])])). 4.46/4.72 fof(c_0_9167, plain, ![X1034, X1035]:(~class_Orderings_Olinorder(X1035)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1035),X1034),X1034)=X1034), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup_Oidem])])])). 4.46/4.72 fof(c_0_9168, plain, ![X3681, X3682, X3683, X3684]:((c_List_Olist_ONil(X3684)!=X3681|hAPP(hAPP(c_List_Omap(X3684,X3683),X3682),X3681)=c_List_Olist_ONil(X3683))&(hAPP(hAPP(c_List_Omap(X3684,X3683),X3682),X3681)!=c_List_Olist_ONil(X3683)|c_List_Olist_ONil(X3684)=X3681)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__is__Nil__conv])])). 4.46/4.72 fof(c_0_9169, plain, ![X14358, X14359, X14360, X14361]:((c_List_Olist_ONil(X14361)!=hAPP(hAPP(c_List_Olist__update(X14361,X14360),X14359),X14358)|c_List_Olist_ONil(X14361)=X14360)&(c_List_Olist_ONil(X14361)!=X14360|c_List_Olist_ONil(X14361)=hAPP(hAPP(c_List_Olist__update(X14361,X14360),X14359),X14358))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__nonempty])])). 4.46/4.72 fof(c_0_9170, plain, ![X363]:(~class_Groups_Ogroup__add(X363)|c_Groups_Ozero__class_Ozero(X363)=hAPP(c_Groups_Ouminus__class_Ouminus(X363),c_Groups_Ozero__class_Ozero(X363))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__zero])])). 4.46/4.72 fof(c_0_9171, plain, ![X5137, X5138]:(~class_Orderings_Olinorder(X5138)|X5137=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5138),X5137),X5137)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf_Oidem])])])). 4.46/4.72 fof(c_0_9172, plain, ![X6492, X6493, X6494]:((X6493!=X6492|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6494,tc_HOL_Obool)),X6492)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6494,tc_HOL_Obool)),X6493))&(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6494,tc_HOL_Obool)),X6492)!=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6494,tc_HOL_Obool)),X6493)|X6493=X6492)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__eq__Compl__iff])])). 4.46/4.72 fof(c_0_9173, plain, ![X15926, X15927]:(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X15927|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15927),X15926)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X15926|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15927),X15926)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X15927|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X15926|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15927),X15926)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__0])])])). 4.46/4.72 fof(c_0_9174, plain, ![X2662, X2663, X2664, X2665]:((X2662!=c_Option_Ooption_ONone(X2665)|hAPP(hAPP(c_Option_Omap(X2665,X2664),X2663),X2662)=c_Option_Ooption_ONone(X2664))&(hAPP(hAPP(c_Option_Omap(X2665,X2664),X2663),X2662)!=c_Option_Ooption_ONone(X2664)|X2662=c_Option_Ooption_ONone(X2665))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_option__map__is__None])])). 4.46/4.72 fof(c_0_9175, plain, ![X1516, X1517, X1518]:((X1517!=X1516|hAPP(c_SetInterval_Oord__class_OgreaterThan(X1518),X1517)=hAPP(c_SetInterval_Oord__class_OgreaterThan(X1518),X1516)|~class_Orderings_Olinorder(X1518))&(hAPP(c_SetInterval_Oord__class_OgreaterThan(X1518),X1517)!=hAPP(c_SetInterval_Oord__class_OgreaterThan(X1518),X1516)|X1517=X1516|~class_Orderings_Olinorder(X1518))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__eq__iff])])])). 4.46/4.72 fof(c_0_9176, plain, ![X17182]:(~class_Lattices_Oboolean__algebra(X17182)|c_Orderings_Obot__class_Obot(X17182)=hAPP(c_Groups_Ouminus__class_Ouminus(X17182),c_Orderings_Otop__class_Otop(X17182))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__top__eq])])). 4.46/4.72 fof(c_0_9177, plain, ![X8317, X8318]:((c_Groups_Oone__class_Oone(tc_Nat_Onat)!=X8317|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=X8318|c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8318),X8317))&((c_Groups_Oone__class_Oone(tc_Nat_Onat)=X8317|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8318),X8317))&(c_Groups_Oone__class_Oone(tc_Nat_Onat)=X8318|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8318),X8317)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff])])])). 4.46/4.72 fof(c_0_9178, plain, ![X7868, X7869, X7870]:((hAPP(c_SetInterval_Oord__class_OlessThan(X7870),X7868)!=hAPP(c_SetInterval_Oord__class_OlessThan(X7870),X7869)|X7868=X7869|~class_Orderings_Olinorder(X7870))&(X7868!=X7869|hAPP(c_SetInterval_Oord__class_OlessThan(X7870),X7868)=hAPP(c_SetInterval_Oord__class_OlessThan(X7870),X7869)|~class_Orderings_Olinorder(X7870))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lessThan__eq__iff])])])])). 4.46/4.72 fof(c_0_9179, plain, ![X6247, X6248, X6249]:((X6247!=X6248|hAPP(c_SetInterval_Oord__class_OatMost(X6249),X6247)=hAPP(c_SetInterval_Oord__class_OatMost(X6249),X6248)|~class_Orderings_Olinorder(X6249))&(hAPP(c_SetInterval_Oord__class_OatMost(X6249),X6247)!=hAPP(c_SetInterval_Oord__class_OatMost(X6249),X6248)|X6247=X6248|~class_Orderings_Olinorder(X6249))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atMost__eq__iff])])])])). 4.46/4.72 fof(c_0_9180, plain, ![X2397, X2398, X2399]:((hAPP(c_SetInterval_Oord__class_OatLeast(X2399),X2398)!=hAPP(c_SetInterval_Oord__class_OatLeast(X2399),X2397)|X2398=X2397|~class_Orderings_Olinorder(X2399))&(X2398!=X2397|hAPP(c_SetInterval_Oord__class_OatLeast(X2399),X2398)=hAPP(c_SetInterval_Oord__class_OatLeast(X2399),X2397)|~class_Orderings_Olinorder(X2399))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__eq__iff])])])). 4.46/4.72 fof(c_0_9181, plain, ![X7480, X7481]:(~class_Orderings_Olinorder(X7481)|(~c_List_Olinorder__class_Osorted(X7481,X7480)|c_List_Olinorder__class_Osorted(X7481,c_List_Oremdups(X7481,X7480)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__remdups])])). 4.46/4.72 fof(c_0_9182, plain, ![X11950, X11951]:(((c_Groups_Oone__class_Oone(tc_Nat_Onat)=X11950|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11951),X11950))&(X11951=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11951),X11950)))&(c_Groups_Oone__class_Oone(tc_Nat_Onat)!=X11950|X11951!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11951),X11950))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])])). 4.46/4.72 fof(c_0_9183, plain, ![X1015, X1016]:(hBOOL(X1016)|hBOOL(hAPP(hAPP(c_fimplies,X1016),X1015))), inference(variable_rename,[status(thm)],[help_c__fimplies__1])). 4.46/4.72 cnf(c_0_9184, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~class_Int_Oring__char__0(X2)), inference(split_conjunct,[status(thm)],[c_0_5571])). 4.46/4.72 fof(c_0_9185, plain, ![X12291, X12292, X12293]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X12293),tc_HOL_Obool)),X12292),X12291))|c_Hoare__Mirabelle_Ohoare__derivs(X12293,X12291,X12292)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_asm])])])). 4.46/4.72 fof(c_0_9186, plain, ![X9421, X9423, X9424]:((~hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X9421)))|hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk271_1(X9421))=hAPP(c_Com_Obody,X9421))&(hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X9424)!=hAPP(c_Com_Obody,X9423)|hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X9423))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I7_J])])])])])). 4.46/4.72 fof(c_0_9187, plain, ![X4193, X4194, X4195]:((X4193!=X4194|c_Groups_Ozero__class_Ozero(X4195)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4195),X4194),X4193)|~class_Groups_Ogroup__add(X4195))&(c_Groups_Ozero__class_Ozero(X4195)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4195),X4194),X4193)|X4193=X4194|~class_Groups_Ogroup__add(X4195))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_right__minus__eq])])])])). 4.46/4.72 fof(c_0_9188, plain, ![X6453, X6454]:(~class_Divides_Osemiring__div(X6454)|c_Groups_Ozero__class_Ozero(X6454)=c_Divides_Odiv__class_Omod(X6454,X6453,X6453)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__self])])])). 4.46/4.72 fof(c_0_9189, plain, ![X9337, X9338, X9339, X9340, X9341, X9342]:(((X9340=X9338|c_Nitpick_Opair__box_OPairBox(X9342,X9341,X9340,X9339)!=c_Nitpick_Opair__box_OPairBox(X9342,X9341,X9338,X9337))&(X9339=X9337|c_Nitpick_Opair__box_OPairBox(X9342,X9341,X9340,X9339)!=c_Nitpick_Opair__box_OPairBox(X9342,X9341,X9338,X9337)))&(X9340!=X9338|X9339!=X9337|c_Nitpick_Opair__box_OPairBox(X9342,X9341,X9340,X9339)=c_Nitpick_Opair__box_OPairBox(X9342,X9341,X9338,X9337))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__box_Oinject])])])). 4.46/4.72 fof(c_0_9190, plain, ![X10811, X10812]:((hBOOL(hAPP(c_Com_OWT,X10812))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X10812,X10811))))&(hBOOL(hAPP(c_Com_OWT,X10811))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X10812,X10811))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_WTs__elim__cases_I4_J])])])])). 4.46/4.72 fof(c_0_9191, plain, ![X12224, X12225, X12226]:((~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X12226),X12225),X12224))|X12224=X12225|~class_HOL_Oequal(X12226))&(X12224!=X12225|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X12226),X12225),X12224))|~class_HOL_Oequal(X12226))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__eq])])])). 4.46/4.72 fof(c_0_9192, plain, ![X417]:((~c_Nat__Transfer_Ois__nat(X417)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X417)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X417))|c_Nat__Transfer_Ois__nat(X417))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_is__nat__def])])). 4.46/4.72 fof(c_0_9193, plain, ![X6356]:(~class_Orderings_Olinorder(X6356)|c_List_Olinorder__class_Osorted__list__of__set(X6356,c_Orderings_Obot__class_Obot(tc_fun(X6356,tc_HOL_Obool)))=c_List_Olist_ONil(X6356)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__empty])])). 4.46/4.72 fof(c_0_9194, plain, ![X6290, X6291, X6292]:(((c_List_Olist_ONil(X6292)=X6291|c_List_Olist_ONil(X6292)!=hAPP(hAPP(c_List_Oappend(X6292),X6291),X6290))&(X6290=c_List_Olist_ONil(X6292)|c_List_Olist_ONil(X6292)!=hAPP(hAPP(c_List_Oappend(X6292),X6291),X6290)))&(c_List_Olist_ONil(X6292)!=X6291|X6290!=c_List_Olist_ONil(X6292)|c_List_Olist_ONil(X6292)=hAPP(hAPP(c_List_Oappend(X6292),X6291),X6290))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__append__conv])])])). 4.46/4.72 cnf(c_0_9195, plain, (X1=hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Olinordered__ab__group__add(X2)), inference(split_conjunct,[status(thm)],[c_0_5572])). 4.46/4.72 fof(c_0_9196, plain, ![X13791]:(~class_Complete__Lattice_Ocomplete__lattice(X13791)|c_Complete__Lattice_OInf__class_OInf(X13791,c_Orderings_Obot__class_Obot(tc_fun(X13791,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(X13791)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__empty])])). 4.46/4.72 fof(c_0_9197, plain, ![X8927, X8928]:(~class_Finite__Set_Ofinite(X8928)|hBOOL(hAPP(c_Finite__Set_Ofinite(X8928),X8927))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])])). 4.46/4.72 fof(c_0_9198, plain, ![X4857, X4858]:((X4857!=c_Groups_Ozero__class_Ozero(X4858)|hAPP(c_Groups_Ouminus__class_Ouminus(X4858),X4857)=c_Groups_Ozero__class_Ozero(X4858)|~class_Groups_Ogroup__add(X4858))&(hAPP(c_Groups_Ouminus__class_Ouminus(X4858),X4857)!=c_Groups_Ozero__class_Ozero(X4858)|X4857=c_Groups_Ozero__class_Ozero(X4858)|~class_Groups_Ogroup__add(X4858))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__equal__0__iff__equal])])])])). 4.46/4.72 fof(c_0_9199, plain, ![X5942, X5943]:((c_Groups_Ozero__class_Ozero(X5943)!=hAPP(c_Groups_Oabs__class_Oabs(X5943),X5942)|X5942=c_Groups_Ozero__class_Ozero(X5943)|~class_Groups_Oordered__ab__group__add__abs(X5943))&(X5942!=c_Groups_Ozero__class_Ozero(X5943)|c_Groups_Ozero__class_Ozero(X5943)=hAPP(c_Groups_Oabs__class_Oabs(X5943),X5942)|~class_Groups_Oordered__ab__group__add__abs(X5943))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__0])])])). 4.46/4.72 fof(c_0_9200, plain, ![X8845, X8846, X8848, X8849, X8850]:((~hBOOL(hAPP(c_Wellfounded_Oaccp(X8846,X8845),esk251_2(X8845,X8846)))|c_Wellfounded_OwfP(X8846,X8845))&(~c_Wellfounded_OwfP(X8849,X8848)|hBOOL(hAPP(c_Wellfounded_Oaccp(X8849,X8848),X8850)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__accp__iff])])])])])). 4.46/4.72 fof(c_0_9201, plain, ![X9354]:(~hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X9354)))|hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk269_1(X9354))=hAPP(c_Com_Obody,X9354)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I7_J])])])). 4.46/4.72 fof(c_0_9202, plain, ![X8540, X8541]:(~hBOOL(hAPP(hAPP(c_fdisj,X8541),X8540))|hBOOL(X8541)|hBOOL(X8540)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fdisj__3])])). 4.46/4.72 fof(c_0_9203, plain, ![X9838, X9839]:(~c_Nat__Transfer_Ois__nat(X9839)|c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X9839,X9838))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__function__closures])])). 4.46/4.72 fof(c_0_9204, plain, ![X3113, X3114]:((hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3114)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3113)|X3113=X3114)&(X3113!=X3114|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3114)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3113))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__int__eq])])). 4.46/4.72 fof(c_0_9205, plain, ![X16339]:(~class_Rings_Olinordered__semidom(X16339)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16339),c_Groups_Oone__class_Oone(X16339)),c_Groups_Ozero__class_Ozero(X16339)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__one__less__zero])])])). 4.46/4.72 fof(c_0_9206, plain, ![X5715, X5716, X5717]:(~class_Orderings_Obot(X5717)|hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5716,X5717)),X5715)=c_Orderings_Obot__class_Obot(X5717)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__fun__def])])). 4.46/4.72 fof(c_0_9207, plain, ![X16686, X16687]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16687,tc_HOL_Obool)),X16686),c_Orderings_Obot__class_Obot(tc_fun(X16687,tc_HOL_Obool))))|c_Orderings_Obot__class_Obot(tc_fun(X16687,tc_HOL_Obool))=X16686)&(c_Orderings_Obot__class_Obot(tc_fun(X16687,tc_HOL_Obool))!=X16686|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16687,tc_HOL_Obool)),X16686),c_Orderings_Obot__class_Obot(tc_fun(X16687,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__empty])])). 4.46/4.72 fof(c_0_9208, plain, ![X1913]:(~class_Rings_Olinordered__semidom(X1913)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1913),c_Groups_Oone__class_Oone(X1913)),c_Groups_Ozero__class_Ozero(X1913)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__one__le__zero])])])). 4.46/4.72 fof(c_0_9209, plain, ![X13926, X13927, X13928]:((hAPP(c_Option_Ooption_OSome(X13928),X13927)!=hAPP(c_Option_Ooption_OSome(X13928),X13926)|X13927=X13926)&(X13927!=X13926|hAPP(c_Option_Ooption_OSome(X13928),X13927)=hAPP(c_Option_Ooption_OSome(X13928),X13926))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_option_Oinject])])). 4.46/4.72 cnf(c_0_9210, plain, (c_Groups_Osgn__class_Osgn(X2,X1)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_5573])). 4.46/4.72 fof(c_0_9211, plain, ![X17104, X17105, X17106]:((hAPP(c_List_Orev(X17106),X17104)!=hAPP(c_List_Orev(X17106),X17105)|X17105=X17104)&(X17105!=X17104|hAPP(c_List_Orev(X17106),X17104)=hAPP(c_List_Orev(X17106),X17105))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__is__rev__conv])])). 4.46/4.72 fof(c_0_9212, plain, ![X5429, X5430]:((X5429!=c_List_Olist_ONil(X5430)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5430)),X5429)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5430)),X5429)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X5429=c_List_Olist_ONil(X5430))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__0__conv])])). 4.46/4.72 cnf(c_0_9213, plain, (hBOOL(hAPP(X2,X3))|X1!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~epred1_3(X2,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_5089])). 4.46/4.72 fof(c_0_9214, plain, ![X9515, X9516]:(~hBOOL(hAPP(c_List_Odistinct(X9516),X9515))|X9515=c_List_Oremdups(X9516,X9515)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__remdups__id])])])). 4.46/4.72 fof(c_0_9215, plain, ![X2051, X2052, X2053, X2054]:((X2051!=c_List_Olist_ONil(X2053)|c_List_Olist__all2(X2054,X2053,X2052,c_List_Olist_ONil(X2054),X2051))&(~c_List_Olist__all2(X2054,X2053,X2052,c_List_Olist_ONil(X2054),X2051)|X2051=c_List_Olist_ONil(X2053))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Nil])])). 4.46/4.72 fof(c_0_9216, plain, ![X5088]:(~class_Groups_Oab__semigroup__mult(X5088)|c_Finite__Set_Ofun__left__comm(X5088,X5088,c_Groups_Otimes__class_Otimes(X5088))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm])])). 4.46/4.72 fof(c_0_9217, plain, ![X1735]:(~class_Orderings_Olinorder(X1735)|c_Finite__Set_Ofun__left__comm__idem(X1735,X1735,c_Orderings_Oord__class_Omax(X1735))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__sup])])). 4.46/4.72 fof(c_0_9218, plain, ![X9923]:(~class_Orderings_Olinorder(X9923)|c_Finite__Set_Ofun__left__comm__idem(X9923,X9923,c_Orderings_Oord__class_Omin(X9923))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ofun__left__comm__idem__inf])])])). 4.46/4.72 fof(c_0_9219, plain, ![X10870]:(~class_Lattices_Oab__semigroup__idem__mult(X10870)|c_Finite__Set_Ofun__left__comm__idem(X10870,X10870,c_Groups_Otimes__class_Otimes(X10870))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm__idem])])])). 4.46/4.72 fof(c_0_9220, plain, ![X967]:(~class_Lattices_Osemilattice__sup(X967)|c_Finite__Set_Ofun__left__comm__idem(X967,X967,c_Lattices_Osemilattice__sup__class_Osup(X967))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm__idem__sup])])])). 4.46/4.72 fof(c_0_9221, plain, ![X10429]:(~class_Orderings_Oord(X10429)|c_Orderings_Oord_Omin(X10429,c_Orderings_Oord__class_Oless__eq(X10429))=c_Orderings_Oord__class_Omin(X10429)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ord__min])])). 4.46/4.72 fof(c_0_9222, plain, ![X4180, X4181, X4182]:((X4180!=c_List_Olist_ONil(X4181)|hAPP(hAPP(c_List_Oappend(X4181),X4180),X4182)=X4182)&(hAPP(hAPP(c_List_Oappend(X4181),X4180),X4182)!=X4182|X4180=c_List_Olist_ONil(X4181))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv2])])). 4.46/4.72 fof(c_0_9223, plain, ![X7132]:(~class_Lattices_Osemilattice__inf(X7132)|c_Finite__Set_Ofun__left__comm__idem(X7132,X7132,c_Lattices_Osemilattice__inf__class_Oinf(X7132))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm__idem__inf])])])). 4.46/4.72 fof(c_0_9224, plain, ![X14494, X14495, X14496]:(~c_Hoare__Mirabelle_Otriple__valid(X14496,hAPP(c_Nat_OSuc,X14495),X14494)|c_Hoare__Mirabelle_Otriple__valid(X14496,X14495,X14494)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_triple__valid__Suc])])). 4.46/4.72 fof(c_0_9225, plain, ![X6289]:(~class_Orderings_Oord(X6289)|c_Orderings_Oord_Omax(X6289,c_Orderings_Oord__class_Oless__eq(X6289))=c_Orderings_Oord__class_Omax(X6289)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_max__ord__max])])])). 4.46/4.72 fof(c_0_9226, plain, ![X13581, X13582, X13583]:((X13581!=c_List_Olist_ONil(X13583)|X13582=hAPP(hAPP(c_List_Oappend(X13583),X13582),X13581))&(X13582!=hAPP(hAPP(c_List_Oappend(X13583),X13582),X13581)|X13581=c_List_Olist_ONil(X13583))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv])])). 4.46/4.72 fof(c_0_9227, plain, ![X2240, X2241]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2241),X2240)!=X2241|X2240=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])). 4.46/4.72 fof(c_0_9228, plain, ![X5991, X5992]:(hBOOL(hAPP(hAPP(c_fdisj,X5992),X5991))|~hBOOL(X5992)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fdisj__1])])). 4.46/4.72 fof(c_0_9229, plain, ![X9491, X9492, X9493, X9494, X9495]:(((X9494=X9492|c_Lazy__Sequence_Olazy__sequence_OInsert(X9495,X9492,X9491)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X9495,X9494,X9493))&(X9491=X9493|c_Lazy__Sequence_Olazy__sequence_OInsert(X9495,X9492,X9491)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X9495,X9494,X9493)))&(X9494!=X9492|X9491!=X9493|c_Lazy__Sequence_Olazy__sequence_OInsert(X9495,X9492,X9491)=c_Lazy__Sequence_Olazy__sequence_OInsert(X9495,X9494,X9493))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Oinject])])])). 4.46/4.72 fof(c_0_9230, plain, ![X11597, X11598, X11599, X11600, X11601, X11602]:((X11601!=X11598|X11597!=X11600|X11599!=X11602|c_Com_Ocom_OCond(X11602,X11601,X11600)=c_Com_Ocom_OCond(X11599,X11598,X11597))&(((X11601=X11598|c_Com_Ocom_OCond(X11602,X11601,X11600)!=c_Com_Ocom_OCond(X11599,X11598,X11597))&(X11597=X11600|c_Com_Ocom_OCond(X11602,X11601,X11600)!=c_Com_Ocom_OCond(X11599,X11598,X11597)))&(X11599=X11602|c_Com_Ocom_OCond(X11602,X11601,X11600)!=c_Com_Ocom_OCond(X11599,X11598,X11597)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I4_J])])])). 4.46/4.72 fof(c_0_9231, plain, ![X15051]:(~class_Groups_Osgn__if(X15051)|c_Groups_Ozero__class_Ozero(X15051)=c_Groups_Osgn__class_Osgn(X15051,c_Groups_Ozero__class_Ozero(X15051))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn0])])). 4.46/4.72 fof(c_0_9232, plain, ![X8941, X8942]:(~hBOOL(X8942)|hBOOL(hAPP(hAPP(c_fdisj,X8941),X8942))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fdisj__2])])). 4.46/4.72 fof(c_0_9233, plain, ![X9275, X9276]:(~hBOOL(X9276)|hBOOL(hAPP(hAPP(c_fimplies,X9275),X9276))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fimplies__2])])). 4.46/4.72 fof(c_0_9234, plain, ![X4774, X4775, X4776, X4777, X4778, X4779]:((((X4779=X4776|c_Com_Ocom_OLocal(X4779,X4778,X4777)!=c_Com_Ocom_OLocal(X4776,X4775,X4774))&(X4778=X4775|c_Com_Ocom_OLocal(X4779,X4778,X4777)!=c_Com_Ocom_OLocal(X4776,X4775,X4774)))&(X4777=X4774|c_Com_Ocom_OLocal(X4779,X4778,X4777)!=c_Com_Ocom_OLocal(X4776,X4775,X4774)))&(X4779!=X4776|X4778!=X4775|X4777!=X4774|c_Com_Ocom_OLocal(X4779,X4778,X4777)=c_Com_Ocom_OLocal(X4776,X4775,X4774))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I2_J])])])). 4.46/4.72 fof(c_0_9235, plain, ![X10572, X10573]:((~hBOOL(hAPP(c_List_Odistinct(X10573),X10572))|X10572=c_List_Oremdups(X10573,X10572))&(X10572!=c_List_Oremdups(X10573,X10572)|hBOOL(hAPP(c_List_Odistinct(X10573),X10572)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remdups__id__iff__distinct])])). 4.46/4.72 fof(c_0_9236, plain, ![X16862, X16863, X16864]:((c_Orderings_Obot__class_Obot(tc_fun(X16864,tc_HOL_Obool))!=X16862|X16863!=c_Orderings_Obot__class_Obot(tc_fun(X16864,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16864,tc_HOL_Obool)),X16863),X16862)=c_Orderings_Obot__class_Obot(tc_fun(X16864,tc_HOL_Obool)))&((c_Orderings_Obot__class_Obot(tc_fun(X16864,tc_HOL_Obool))=X16862|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16864,tc_HOL_Obool)),X16863),X16862)!=c_Orderings_Obot__class_Obot(tc_fun(X16864,tc_HOL_Obool)))&(X16863=c_Orderings_Obot__class_Obot(tc_fun(X16864,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16864,tc_HOL_Obool)),X16863),X16862)!=c_Orderings_Obot__class_Obot(tc_fun(X16864,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__empty])])])). 4.46/4.72 fof(c_0_9237, plain, ![X2281, X2282, X2283]:((c_Orderings_Obot__class_Obot(tc_fun(X2283,tc_HOL_Obool))!=X2282|c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2283,tc_HOL_Obool),tc_HOL_Obool))=hAPP(hAPP(c_Equiv__Relations_Oquotient(X2283),X2282),X2281))&(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2283,tc_HOL_Obool),tc_HOL_Obool))!=hAPP(hAPP(c_Equiv__Relations_Oquotient(X2283),X2282),X2281)|c_Orderings_Obot__class_Obot(tc_fun(X2283,tc_HOL_Obool))=X2282)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__is__empty])])). 4.46/4.72 fof(c_0_9238, plain, ![X7142]:(~class_Rings_Oring__1(X7142)|hAPP(c_Int_Oring__1__class_Oof__int(X7142),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(X7142)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__0])])])). 4.46/4.72 fof(c_0_9239, plain, ![X4196]:(~class_Rings_Oring__1(X4196)|c_Groups_Oone__class_Oone(X4196)=hAPP(c_Int_Oring__1__class_Oof__int(X4196),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__1])])])). 4.46/4.72 cnf(c_0_9240, plain, (~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|X2!=X3), inference(split_conjunct,[status(thm)],[c_0_5574])). 4.46/4.72 fof(c_0_9241, plain, ![X15252]:(~class_Rings_Osemiring__1(X15252)|c_Groups_Oone__class_Oone(X15252)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15252),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__1])])). 4.46/4.72 fof(c_0_9242, plain, ![X4651]:(~class_Rings_Osemiring__1(X4651)|c_Groups_Ozero__class_Ozero(X4651)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4651),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__0])])])). 4.46/4.72 cnf(c_0_9243, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|X2!=X3|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5575])). 4.46/4.72 fof(c_0_9244, plain, ![X7240, X7241]:(~class_Lazy__Sequence_Osmall__lazy(X7240)|~class_Lazy__Sequence_Osmall__lazy(X7241)|class_Lazy__Sequence_Osmall__lazy(tc_prod(X7241,X7240))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_prod__Lazy__Sequence_Osmall__lazy])])])). 4.46/4.72 fof(c_0_9245, plain, ![X14746, X14747]:(~class_Enum_Oenum(X14747)|~class_HOL_Oequal(X14746)|class_HOL_Oequal(tc_fun(X14747,X14746))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__HOL_Oequal])])). 4.46/4.72 fof(c_0_9246, plain, ![X4437]:((X4437!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4437)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4437)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X4437=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__0__conv])])). 4.46/4.72 fof(c_0_9247, plain, ![X4309]:(~class_Complete__Lattice_Ocomplete__lattice(X4309)|c_Orderings_Obot__class_Obot(X4309)=c_Complete__Lattice_OSup__class_OSup(X4309,c_Orderings_Obot__class_Obot(tc_fun(X4309,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__empty])])])). 4.46/4.72 fof(c_0_9248, plain, ![X10614, X10615]:(~class_Finite__Set_Ofinite(X10614)|~class_Finite__Set_Ofinite(X10615)|class_Finite__Set_Ofinite(tc_sum(X10615,X10614))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_sum__Finite__Set_Ofinite])])])). 4.46/4.72 fof(c_0_9249, plain, ![X11134, X11135]:(~class_Finite__Set_Ofinite(X11134)|~class_Finite__Set_Ofinite(X11135)|class_Finite__Set_Ofinite(tc_prod(X11135,X11134))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_prod__Finite__Set_Ofinite])])])). 4.46/4.72 fof(c_0_9250, plain, ![X1658, X1659]:(~class_Finite__Set_Ofinite(X1658)|~class_Finite__Set_Ofinite(X1659)|class_Finite__Set_Ofinite(tc_fun(X1659,X1658))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Finite__Set_Ofinite])])])). 4.46/4.72 fof(c_0_9251, plain, ![X1780, X1781]:(~class_Smallcheck_Osmall(X1781)|~class_Smallcheck_Osmall(X1780)|class_Smallcheck_Osmall(tc_prod(X1781,X1780))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Smallcheck_Osmall])])). 4.46/4.72 fof(c_0_9252, plain, ![X1998, X1999, X2000, X2001]:((X1998!=c_Orderings_Obot__class_Obot(tc_fun(X2001,tc_HOL_Obool))|hAPP(c_Set_Oimage(X2001,X2000,X1999),X1998)=c_Orderings_Obot__class_Obot(tc_fun(X2000,tc_HOL_Obool)))&(hAPP(c_Set_Oimage(X2001,X2000,X1999),X1998)!=c_Orderings_Obot__class_Obot(tc_fun(X2000,tc_HOL_Obool))|X1998=c_Orderings_Obot__class_Obot(tc_fun(X2001,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__is__empty])])). 4.46/4.72 fof(c_0_9253, plain, ![X7609]:(hAPP(c_Com_Obody,X7609)=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X7609)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_WT_OBody])])])). 4.46/4.72 fof(c_0_9254, plain, ![X1927, X1928]:(~class_Enum_Oenum(X1928)|~class_Enum_Oenum(X1927)|class_Enum_Oenum(tc_sum(X1928,X1927))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_sum__Enum_Oenum])])])). 4.46/4.72 fof(c_0_9255, plain, ![X13911, X13912]:(~class_Enum_Oenum(X13912)|~class_Enum_Oenum(X13911)|class_Enum_Oenum(tc_prod(X13912,X13911))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_prod__Enum_Oenum])])])). 4.46/4.72 fof(c_0_9256, plain, ![X3877, X3878]:(~class_Enum_Oenum(X3877)|~class_Enum_Oenum(X3878)|class_Enum_Oenum(tc_fun(X3878,X3877))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Enum_Oenum])])). 4.46/4.72 fof(c_0_9257, plain, ![X17418, X17419]:(~c_Nat__Transfer_Ois__nat(X17419)|(~c_Nat__Transfer_Ois__nat(X17418)|c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X17419,X17418)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J])])). 4.46/4.72 cnf(c_0_9258, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~c_Com_OWT__bodies|hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1)!=hAPP(c_Com_Obody,X2)), inference(split_conjunct,[status(thm)],[c_0_5576])). 4.46/4.72 fof(c_0_9259, plain, ![X9170, X9171, X9172, X9173, X9174]:(~class_Orderings_Olinorder(X9174)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X9173,X9174,X9172),X9171),X9170)!=c_List_Olist_ONil(X9173)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__not__Nil])])])). 4.46/4.72 fof(c_0_9260, plain, ![X15393, X15394]:(hBOOL(X15393)|~hBOOL(X15394)|~hBOOL(hAPP(hAPP(c_fimplies,X15394),X15393))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fimplies__3])])). 4.46/4.72 fof(c_0_9261, plain, ![X6412, X6413, X6414]:((c_List_Oreplicate(X6414,X6413,X6412)!=c_List_Olist_ONil(X6414)|X6413=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(X6413!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Oreplicate(X6414,X6413,X6412)=c_List_Olist_ONil(X6414))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__replicate])])). 4.46/4.72 fof(c_0_9262, plain, ![X7036, X7037]:((hAPP(c_List_Oset(X7037),X7036)!=c_Orderings_Obot__class_Obot(tc_fun(X7037,tc_HOL_Obool))|X7036=c_List_Olist_ONil(X7037))&(X7036!=c_List_Olist_ONil(X7037)|hAPP(c_List_Oset(X7037),X7036)=c_Orderings_Obot__class_Obot(tc_fun(X7037,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty2])])). 4.46/4.72 fof(c_0_9263, plain, ![X3515, X3516]:((c_Orderings_Obot__class_Obot(tc_fun(X3516,tc_HOL_Obool))!=c_Option_Oset(X3516,X3515)|c_Option_Ooption_ONone(X3516)=X3515)&(c_Option_Ooption_ONone(X3516)!=X3515|c_Orderings_Obot__class_Obot(tc_fun(X3516,tc_HOL_Obool))=c_Option_Oset(X3516,X3515))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty__eq])])). 4.46/4.72 fof(c_0_9264, plain, ![X8734]:(hBOOL(X8734)|hBOOL(hAPP(c_fNot,X8734))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fNot__2])])). 4.46/4.72 fof(c_0_9265, plain, ![X647, X648]:((X647!=c_List_Olist_ONil(X648)|hAPP(c_List_Orotate1(X648),X647)=c_List_Olist_ONil(X648))&(hAPP(c_List_Orotate1(X648),X647)!=c_List_Olist_ONil(X648)|X647=c_List_Olist_ONil(X648))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__is__Nil__conv])])). 4.46/4.72 fof(c_0_9266, plain, ![X8010, X8011]:((hAPP(c_List_Orev(X8011),X8010)!=c_List_Olist_ONil(X8011)|X8010=c_List_Olist_ONil(X8011))&(X8010!=c_List_Olist_ONil(X8011)|hAPP(c_List_Orev(X8011),X8010)=c_List_Olist_ONil(X8011))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__is__Nil__conv])])). 4.46/4.72 fof(c_0_9267, plain, ![X10009, X10010, X10011]:(~c_Hoare__Mirabelle_Ohoare__derivs(X10011,X10010,X10009)|c_Hoare__Mirabelle_Ohoare__valids(X10011,X10010,X10009)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hoare__sound])])])). 4.46/4.72 cnf(c_0_9268, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5577])). 4.46/4.72 fof(c_0_9269, plain, ![X6506]:(~class_Rings_Osemiring__1(X6506)|c_Int_Oiszero(X6506,c_Groups_Ozero__class_Ozero(X6506))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_iszero__0])])])). 4.46/4.72 fof(c_0_9270, plain, ![X17424, X17425]:(~class_Orderings_Opreorder(X17425)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17425),X17424),X17424))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__irrefl])])])). 4.46/4.72 cnf(c_0_9271, plain, (c_List_Olinorder__class_Osorted(X2,X1)|X1!=c_List_Olist_ONil(X2)|~class_Orderings_Olinorder(X2)), inference(split_conjunct,[status(thm)],[c_0_5314])). 4.46/4.72 fof(c_0_9272, plain, ![X11455, X11456]:(~hBOOL(hAPP(hAPP(c_fequal,X11456),X11455))|X11456=X11455), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fequal__1])])). 4.46/4.72 fof(c_0_9273, plain, ![X15230, X15231, X15232, X15233]:(((X15231=X15233|c_Com_Ocom_OSemi(X15233,X15232)!=c_Com_Ocom_OSemi(X15231,X15230))&(X15232=X15230|c_Com_Ocom_OSemi(X15233,X15232)!=c_Com_Ocom_OSemi(X15231,X15230)))&(X15231!=X15233|X15232!=X15230|c_Com_Ocom_OSemi(X15233,X15232)=c_Com_Ocom_OSemi(X15231,X15230))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I3_J])])])). 4.46/4.72 fof(c_0_9274, plain, ![X7067]:((~c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X7067))|c_List_Onat__list(X7067))&(~c_List_Onat__list(X7067)|c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X7067)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__list__def])])). 4.46/4.72 fof(c_0_9275, plain, ![X8517, X8518]:((X8517!=X8518|hAPP(c_Code__Numeral_Onat__of,X8518)=hAPP(c_Code__Numeral_Onat__of,X8517))&(hAPP(c_Code__Numeral_Onat__of,X8518)!=hAPP(c_Code__Numeral_Onat__of,X8517)|X8517=X8518)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Onat__of__inject])])). 4.46/4.72 fof(c_0_9276, plain, ![X1197, X1198]:((hAPP(c_Int_ORep__Integ,X1197)!=hAPP(c_Int_ORep__Integ,X1198)|X1197=X1198)&(X1197!=X1198|hAPP(c_Int_ORep__Integ,X1197)=hAPP(c_Int_ORep__Integ,X1198))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__inject])])). 4.46/4.72 fof(c_0_9277, plain, ![X7402, X7403, X7404, X7405]:(((X7403=X7405|c_Com_Ocom_OWhile(X7403,X7402)!=c_Com_Ocom_OWhile(X7405,X7404))&(X7402=X7404|c_Com_Ocom_OWhile(X7403,X7402)!=c_Com_Ocom_OWhile(X7405,X7404)))&(X7403!=X7405|X7402!=X7404|c_Com_Ocom_OWhile(X7403,X7402)=c_Com_Ocom_OWhile(X7405,X7404))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I5_J])])])). 4.46/4.72 cnf(c_0_9278, plain, (X2=X1|hAPP(c_Code__Numeral_Oof__nat,X1)!=hAPP(c_Code__Numeral_Oof__nat,X2)), inference(split_conjunct,[status(thm)],[c_0_5578])). 4.46/4.72 fof(c_0_9279, plain, ![X6694, X6695]:((hAPP(c_Nat_OSuc,X6694)!=hAPP(c_Nat_OSuc,X6695)|X6695=X6694)&(X6695!=X6694|hAPP(c_Nat_OSuc,X6694)=hAPP(c_Nat_OSuc,X6695))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])])). 4.46/4.72 fof(c_0_9280, plain, ![X17363, X17364]:(~class_Orderings_Otop(X17364)|class_Orderings_Otop(tc_fun(X17363,X17364))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop])])). 4.46/4.72 fof(c_0_9281, plain, ![X15615, X15616]:(~class_Groups_Ouminus(X15616)|class_Groups_Ouminus(tc_fun(X15615,X15616))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus])])). 4.46/4.72 fof(c_0_9282, plain, ![X3407, X3408]:(~class_Lattices_Odistrib__lattice(X3408)|class_Lattices_Odistrib__lattice(tc_fun(X3407,X3408))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Odistrib__lattice])])). 4.46/4.72 fof(c_0_9283, plain, ![X1827, X1828]:(~class_Orderings_Oord(X1828)|class_Orderings_Oord(tc_fun(X1827,X1828))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Orderings_Oord])])])). 4.46/4.72 fof(c_0_9284, plain, ![X11238, X11239]:(~class_Lattices_Oboolean__algebra(X11239)|class_Lattices_Oboolean__algebra(tc_fun(X11238,X11239))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Lattices_Oboolean__algebra])])])). 4.46/4.72 fof(c_0_9285, plain, ![X8883, X8884]:(~class_Orderings_Opreorder(X8884)|class_Orderings_Opreorder(tc_fun(X8883,X8884))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Orderings_Opreorder])])])). 4.46/4.72 fof(c_0_9286, plain, ![X17469, X17470]:(~class_Lattices_Obounded__lattice(X17470)|class_Lattices_Obounded__lattice__top(tc_fun(X17469,X17470))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Lattices_Obounded__lattice__top])])])). 4.46/4.72 fof(c_0_9287, plain, ![X3958, X3959]:(~class_Lattices_Obounded__lattice(X3959)|class_Lattices_Obounded__lattice(tc_fun(X3958,X3959))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice])])). 4.46/4.72 fof(c_0_9288, plain, ![X5318, X5319]:(~class_Complete__Lattice_Ocomplete__lattice(X5319)|class_Complete__Lattice_Ocomplete__lattice(tc_fun(X5318,X5319))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Complete__Lattice_Ocomplete__lattice])])])). 4.46/4.72 fof(c_0_9289, plain, ![X2279, X2280]:(~hBOOL(hAPP(hAPP(c_fconj,X2280),X2279))|hBOOL(X2280)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fconj__2])])). 4.46/4.72 fof(c_0_9290, plain, ![X13445, X13446]:(~hBOOL(hAPP(hAPP(c_fconj,X13446),X13445))|hBOOL(X13445)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fconj__3])])). 4.46/4.72 fof(c_0_9291, plain, ![X15634, X15635]:(~class_Lattices_Olattice(X15635)|class_Lattices_Osemilattice__sup(tc_fun(X15634,X15635))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__sup])])). 4.46/4.72 fof(c_0_9292, plain, ![X7890, X7891]:(~class_Lattices_Olattice(X7891)|class_Lattices_Osemilattice__inf(tc_fun(X7890,X7891))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Lattices_Osemilattice__inf])])])). 4.46/4.72 fof(c_0_9293, plain, ![X10774, X10775]:(~class_Lattices_Olattice(X10775)|class_Lattices_Olattice(tc_fun(X10774,X10775))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Lattices_Olattice])])])). 4.46/4.72 fof(c_0_9294, plain, ![X14522, X14523]:(~class_Orderings_Obot(X14523)|class_Orderings_Obot(tc_fun(X14522,X14523))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Obot])])). 4.46/4.72 fof(c_0_9295, plain, ![X1443, X1444]:((X1443!=c_List_Olist_ONil(X1444)|c_List_Oremdups(X1444,X1443)=c_List_Olist_ONil(X1444))&(c_List_Oremdups(X1444,X1443)!=c_List_Olist_ONil(X1444)|X1443=c_List_Olist_ONil(X1444))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__right__iff])])). 4.46/4.72 fof(c_0_9296, plain, ![X2527, X2528]:(~class_Orderings_Oorder(X2528)|class_Orderings_Oorder(tc_fun(X2527,X2528))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])])). 4.46/4.72 fof(c_0_9297, plain, ![X14115, X14116]:(~class_Lattices_Obounded__lattice(X14116)|class_Lattices_Obounded__lattice__bot(tc_fun(X14115,X14116))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__bot])])). 4.46/4.72 fof(c_0_9298, plain, ![X8406, X8407]:(~class_Groups_Ominus(X8407)|class_Groups_Ominus(tc_fun(X8406,X8407))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus])])). 4.46/4.72 fof(c_0_9299, plain, ![X6522, X6523]:((~c_Int_Oiszero(X6523,X6522)|c_Groups_Ozero__class_Ozero(X6523)=X6522|~class_Rings_Osemiring__1(X6523))&(c_Groups_Ozero__class_Ozero(X6523)!=X6522|c_Int_Oiszero(X6523,X6522)|~class_Rings_Osemiring__1(X6523))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__def])])])). 4.46/4.72 fof(c_0_9300, plain, ![X13580]:(~class_Lattices_Osemilattice__sup(X13580)|~class_Orderings_Olinorder(X13580)|c_Orderings_Oord__class_Omax(X13580)=c_Lattices_Osemilattice__sup__class_Osup(X13580)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__max])])])). 4.46/4.72 fof(c_0_9301, plain, ![X13354]:(~class_Lattices_Osemilattice__inf(X13354)|~class_Orderings_Olinorder(X13354)|c_Lattices_Osemilattice__inf__class_Oinf(X13354)=c_Orderings_Oord__class_Omin(X13354)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__min])])])). 4.46/4.72 fof(c_0_9302, plain, ![X9237]:(~class_Int_Onumber__ring(X9237)|~c_Int_Oiszero(X9237,hAPP(c_Int_Onumber__class_Onumber__of(X9237),c_Int_OMin))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nonzero__number__of__Min])])])). 4.46/4.72 fof(c_0_9303, plain, ![X17499]:(~class_Lazy__Sequence_Osmall__lazy(X17499)|class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X17499))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_List__Olist__Lazy__Sequence_Osmall__lazy])])). 4.46/4.72 fof(c_0_9304, plain, ![X5025, X5026]:(~c_Wellfounded_Owf(X5026,X5025)|c_Wellfounded_Oacyclic(X5026,X5025)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__acyclic])])). 4.46/4.72 fof(c_0_9305, plain, ![X2748]:(~class_Finite__Set_Ofinite(X2748)|class_Finite__Set_Ofinite(tc_Option_Ooption(X2748))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite])])). 4.46/4.72 fof(c_0_9306, plain, ![X15332]:(~class_Enum_Oenum(X15332)|class_Enum_Oenum(tc_Option_Ooption(X15332))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Enum_Oenum])])). 4.46/4.72 fof(c_0_9307, plain, ![X16516, X16517]:((hAPP(c_Com_Ocom_OBODY,X16516)!=hAPP(c_Com_Ocom_OBODY,X16517)|X16517=X16516)&(X16517!=X16516|hAPP(c_Com_Ocom_OBODY,X16516)=hAPP(c_Com_Ocom_OBODY,X16517))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I6_J])])). 4.46/4.72 fof(c_0_9308, plain, ![X9872]:(~class_HOL_Oequal(X9872)|c_fequal=c_HOL_Oequal__class_Oequal(X9872)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__equal])])])). 4.46/4.72 fof(c_0_9309, plain, ![X11955]:(~hBOOL(hAPP(c_fNot,X11955))|~hBOOL(X11955)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fNot__1])])). 4.46/4.72 fof(c_0_9310, plain, ![X599]:(~class_Rings_Osemiring__1(X599)|~c_Int_Oiszero(X599,c_Groups_Oone__class_Oone(X599))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__iszero__1])])])). 4.46/4.72 fof(c_0_9311, plain, ![X6642]:(~class_Rings_Ozero__neq__one(X6642)|c_Groups_Ozero__class_Ozero(X6642)!=c_Groups_Oone__class_Oone(X6642)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_one__neq__zero])])])). 4.46/4.72 cnf(c_0_9312, negated_conjecture, (~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,v_y)))), inference(rw,[status(thm)],[c_0_5579, c_0_5580])). 4.46/4.72 cnf(c_0_9313, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5581, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9314, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5582, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9315, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5583, c_0_4500]), c_0_4760])). 4.46/4.72 cnf(c_0_9316, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5584, c_0_4500]), c_0_4760])). 4.46/4.72 cnf(c_0_9317, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))!=c_Int_OMin), inference(rw,[status(thm)],[c_0_5585, c_0_4760])). 4.46/4.72 cnf(c_0_9318, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5586, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9319, plain, (X1!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),X1)),c_Wellfounded_Omax__ext(X2,X4)))), inference(split_conjunct,[status(thm)],[c_0_5587])). 4.46/4.72 cnf(c_0_9320, plain, (~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot)),c_fequal)),X2),X3))|X3!=X2), inference(split_conjunct,[status(thm)],[c_0_5588])). 4.46/4.72 fof(c_0_9321, plain, ![X7193, X7194, X7195]:~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7195),tc_List_Olist(X7195))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7195),tc_List_Olist(X7195)),c_List_Olist_ONil(X7195)),X7194)),c_List_Olex(X7195,X7193))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nil__notin__lex])])). 4.46/4.72 fof(c_0_9322, plain, ![X11248, X11249, X11250]:~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X11250),tc_List_Olist(X11250))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X11250),tc_List_Olist(X11250)),c_List_Olist_ONil(X11250)),X11249)),c_List_Olistrel1(X11250,X11248))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__Nil__listrel1])])). 4.46/4.72 fof(c_0_9323, plain, ![X6786, X6787, X6788]:~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6788),tc_List_Olist(X6788))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6788),tc_List_Olist(X6788)),X6787),c_List_Olist_ONil(X6788))),c_List_Olex(X6788,X6786))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nil2__notin__lex])])). 4.46/4.72 fof(c_0_9324, plain, ![X7378, X7379, X7380]:~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X7380),tc_List_Olist(X7380))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X7380),tc_List_Olist(X7380)),X7379),c_List_Olist_ONil(X7380))),c_List_Olexord(X7380,X7378))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lexord__Nil__right])])). 4.46/4.72 fof(c_0_9325, plain, ![X8527, X8528, X8529]:~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X8529),tc_List_Olist(X8529))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X8529),tc_List_Olist(X8529)),X8528),c_List_Olist_ONil(X8529))),c_List_Olistrel1(X8529,X8527))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__listrel1__Nil])])). 4.46/4.72 fof(c_0_9326, plain, ![X9115, X9116, X9117]:~hBOOL(hAPP(hAPP(c_member(tc_prod(X9117,X9117)),hAPP(hAPP(c_Product__Type_OPair(X9117,X9117),X9116),X9115)),c_List_Omeasures(X9117,c_List_Olist_ONil(tc_fun(X9117,tc_Nat_Onat))))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__measures_I1_J])])). 4.46/4.72 cnf(c_0_9327, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OPls))), inference(rw,[status(thm)],[c_0_5589, c_0_4471])). 4.46/4.72 cnf(c_0_9328, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))), inference(rw,[status(thm)],[c_0_5590, c_0_4471])). 4.46/4.72 cnf(c_0_9329, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_5591, c_0_4436])). 4.46/4.72 fof(c_0_9330, plain, ![X9567]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X9567))))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__zle__0__negative])])). 4.46/4.72 fof(c_0_9331, plain, ![X15391, X15392]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X15392)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X15391)))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__int__zless__negative])])). 4.46/4.72 fof(c_0_9332, plain, ![X1050, X1051, X1052, X1053, X1054]:hAPP(c_COMBK(tc_Option_Ooption(X1053),X1054),c_Option_Ooption_ONone(X1053))!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1054,tc_Option_Ooption(X1053)),X1052),X1051),hAPP(c_Option_Ooption_OSome(X1053),X1050)), inference(variable_rename,[status(thm)],[fact_map__upd__nonempty])). 4.46/4.72 cnf(c_0_9333, plain, (X1!=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Oappend(X2),X3),hAPP(hAPP(c_List_Olist_OCons(X2),X4),c_List_Olist_ONil(X2)))!=X1), inference(split_conjunct,[status(thm)],[c_0_5469])). 4.46/4.72 cnf(c_0_9334, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X1))|X1!=hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5526])). 4.46/4.72 fof(c_0_9335, plain, ![X10689, X10690]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10690),X10689)),X10690)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__add__less1])])). 4.46/4.72 fof(c_0_9336, plain, ![X11997, X11998]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11998),X11997)),X11997)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__add__less2])])). 4.46/4.72 fof(c_0_9337, plain, ![X14430]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14430)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__less__0__conv])])). 4.46/4.72 fof(c_0_9338, plain, ![X2342, X2343, X2344]:hAPP(c_Set_OPow(X2343),X2342)!=hAPP(c_Set_Oimage(X2343,tc_fun(X2343,tc_HOL_Obool),X2344),X2342), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cantors__paradox])])). 4.46/4.72 fof(c_0_9339, plain, ![X16483]:~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X16483)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X16483),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_infinite__UNIV__listI])])). 4.46/4.72 cnf(c_0_9340, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(c_Set_OCollect(X1),X2)|~hBOOL(hAPP(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_5548])). 4.46/4.72 cnf(c_0_9341, plain, (X1!=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool)),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5592])). 4.46/4.72 fof(c_0_9342, plain, ![X1156, X1157, X1158]:~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1158,X1157,c_Orderings_Obot__class_Obot(tc_fun(X1158,tc_HOL_Obool))),X1156)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_empty__fold1SetE])])). 4.46/4.72 fof(c_0_9343, plain, ![X8319]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8319),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code])])). 4.46/4.72 cnf(c_0_9344, plain, (X1!=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5593])). 4.46/4.72 fof(c_0_9345, plain, ![X4757, X4758]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4758,tc_HOL_Obool)),X4757),c_Orderings_Obot__class_Obot(tc_fun(X4758,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__psubset__empty])])). 4.46/4.72 fof(c_0_9346, plain, ![X3626, X3627, X3628, X3629]:~hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3629,tc_fun(X3628,tc_HOL_Obool))),X3627),X3626)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bot2E])])). 4.46/4.72 cnf(c_0_9347, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))), inference(rw,[status(thm)],[c_0_5594, c_0_5562])). 4.46/4.72 cnf(c_0_9348, plain, (X1!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~c_Wellfounded_Omax__extp(X2,X3,X4,X1)), inference(split_conjunct,[status(thm)],[c_0_5595])). 4.46/4.72 fof(c_0_9349, plain, ~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(fof_simplification,[status(thm)],[fact_infinite__UNIV__nat])). 4.46/4.72 fof(c_0_9350, plain, ~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))), inference(fof_simplification,[status(thm)],[fact_infinite__UNIV__int])). 4.46/4.72 fof(c_0_9351, plain, ![X502, X503, X504, X505, X506, X507]:c_Com_Ocom_OLocal(X507,X506,X505)!=c_Com_Ocom_OCond(X504,X503,X502), inference(variable_rename,[status(thm)],[fact_com_Osimps_I36_J])). 4.46/4.72 fof(c_0_9352, plain, ![X17218]:~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17218))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__neg__int])])). 4.46/4.72 cnf(c_0_9353, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_5596])). 4.46/4.72 fof(c_0_9354, plain, ![X362]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X362),X362)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat])])). 4.46/4.72 fof(c_0_9355, plain, ![X2616, X2617, X2618]:c_List_Olist_ONil(X2618)!=hAPP(hAPP(c_List_Olist_OCons(X2618),X2617),X2616), inference(variable_rename,[status(thm)],[fact_list_Osimps_I3_J])). 4.46/4.72 cnf(c_0_9356, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_5597])). 4.46/4.72 fof(c_0_9357, plain, ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)), inference(fof_simplification,[status(thm)],[fact_rel__simps_I7_J])). 4.46/4.72 cnf(c_0_9358, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_5598])). 4.46/4.72 fof(c_0_9359, plain, ![X11960, X11961, X11962, X11963, X11964]:c_Com_Ocom_OLocal(X11962,X11961,X11960)!=c_Com_Ocom_OWhile(X11964,X11963), inference(variable_rename,[status(thm)],[fact_com_Osimps_I39_J])). 4.46/4.72 cnf(c_0_9360, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_5599])). 4.46/4.72 fof(c_0_9361, plain, ![X9908, X9909, X9910, X9911, X9912]:c_Com_Ocom_OSemi(X9909,X9908)!=c_Com_Ocom_OCond(X9912,X9911,X9910), inference(variable_rename,[status(thm)],[fact_com_Osimps_I45_J])). 4.46/4.72 fof(c_0_9362, plain, ![X7311, X7312, X7313, X7314, X7315]:c_Com_Ocom_OSemi(X7312,X7311)!=c_Com_Ocom_OLocal(X7315,X7314,X7313), inference(variable_rename,[status(thm)],[fact_com_Osimps_I34_J])). 4.46/4.72 fof(c_0_9363, plain, ![X1067, X1068, X1069, X1070]:c_Com_Ocom_OLocal(X1069,X1068,X1067)!=hAPP(c_Com_Ocom_OBODY,X1070), inference(variable_rename,[status(thm)],[fact_com_Osimps_I41_J])). 4.46/4.72 fof(c_0_9364, plain, ![X11279, X11280, X11281, X11282]:hAPP(c_Com_Ocom_OBODY,X11279)!=c_Com_Ocom_OCond(X11282,X11281,X11280), inference(variable_rename,[status(thm)],[fact_com_Osimps_I54_J])). 4.46/4.72 fof(c_0_9365, plain, ![X10120, X10121, X10122, X10123, X10124]:c_Com_Ocom_OWhile(X10124,X10123)!=c_Com_Ocom_OCond(X10122,X10121,X10120), inference(variable_rename,[status(thm)],[fact_com_Osimps_I53_J])). 4.46/4.72 fof(c_0_9366, plain, ![X7088, X7089, X7090]:X7090!=hAPP(hAPP(c_List_Olist_OCons(X7089),X7088),X7090), inference(variable_rename,[status(thm)],[fact_not__Cons__self])). 4.46/4.72 fof(c_0_9367, plain, ![X9386, X9387]:c_Option_Ooption_ONone(X9387)!=hAPP(c_Option_Ooption_OSome(X9387),X9386), inference(variable_rename,[status(thm)],[fact_option_Osimps_I3_J])). 4.46/4.72 fof(c_0_9368, plain, ![X2707, X2708, X2709]:c_Com_Ocom_OSemi(X2709,X2708)!=hAPP(c_Com_Ocom_OBODY,X2707), inference(variable_rename,[status(thm)],[fact_com_Osimps_I48_J])). 4.46/4.72 fof(c_0_9369, plain, ![X14335, X14336, X14337]:c_Lazy__Sequence_Olazy__sequence_OEmpty(X14337)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X14337,X14336,X14335), inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I3_J])). 4.46/4.72 fof(c_0_9370, plain, ![X7838, X7839, X7840]:c_Com_Ocom_OWhile(X7840,X7839)!=hAPP(c_Com_Ocom_OBODY,X7838), inference(variable_rename,[status(thm)],[fact_com_Osimps_I58_J])). 4.46/4.72 fof(c_0_9371, plain, ![X829, X830, X831]:c_Orderings_Obot__class_Obot(tc_fun(X831,tc_HOL_Obool))!=hAPP(hAPP(c_Set_Oinsert(X831),X830),X829), inference(variable_rename,[status(thm)],[fact_empty__not__insert])). 4.46/4.72 fof(c_0_9372, plain, ![X2633, X2634, X2635, X2636]:c_Com_Ocom_OWhile(X2636,X2635)!=c_Com_Ocom_OSemi(X2634,X2633), inference(variable_rename,[status(thm)],[fact_com_Osimps_I47_J])). 4.46/4.72 fof(c_0_9373, plain, ~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(fof_simplification,[status(thm)],[fact_not__neg__1])). 4.46/4.72 fof(c_0_9374, plain, ~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(fof_simplification,[status(thm)],[fact_not__neg__0])). 4.46/4.72 fof(c_0_9375, plain, ![X9273, X9274]:c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X9274,tc_HOL_Obool),tc_HOL_Obool))!=hAPP(c_Set_OPow(X9274),X9273), inference(variable_rename,[status(thm)],[fact_Pow__not__empty])). 4.46/4.72 fof(c_0_9376, plain, ![X15236, X15237, X15238]:c_Com_Ocom_OSKIP!=c_Com_Ocom_OCond(X15238,X15237,X15236), inference(variable_rename,[status(thm)],[fact_com_Osimps_I15_J])). 4.46/4.72 fof(c_0_9377, plain, ![X8713, X8714, X8715]:c_Com_Ocom_OSKIP!=c_Com_Ocom_OLocal(X8715,X8714,X8713), inference(variable_rename,[status(thm)],[fact_com_Osimps_I10_J])). 4.46/4.72 fof(c_0_9378, hypothesis, ~hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,v_y)),v_F)), inference(fof_simplification,[status(thm)],[conj_3])). 4.46/4.72 fof(c_0_9379, plain, ![X2199]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X2199), inference(variable_rename,[status(thm)],[fact_Suc__not__Zero])). 4.46/4.72 fof(c_0_9380, plain, ![X12296, X12297]:~c_List_Olist__ex(X12297,X12296,c_List_Olist_ONil(X12297)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__ex__simps_I2_J])])). 4.46/4.72 fof(c_0_9381, plain, ![X1602, X1603]:~c_List_Olist__ex1(X1603,X1602,c_List_Olist_ONil(X1603)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__ex1__simps_I1_J])])). 4.46/4.72 fof(c_0_9382, plain, ![X3804]:c_Orderings_Otop__class_Otop(tc_fun(X3804,tc_HOL_Obool))!=c_Orderings_Obot__class_Obot(tc_fun(X3804,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_UNIV__not__empty])). 4.46/4.72 fof(c_0_9383, plain, ![X15297]:c_Com_Ocom_OSKIP!=hAPP(c_Com_Ocom_OBODY,X15297), inference(variable_rename,[status(thm)],[fact_com_Osimps_I18_J])). 4.46/4.72 fof(c_0_9384, plain, ![X8525, X8526]:c_Com_Ocom_OSKIP!=c_Com_Ocom_OSemi(X8526,X8525), inference(variable_rename,[status(thm)],[fact_com_Osimps_I13_J])). 4.46/4.72 fof(c_0_9385, plain, ![X12384, X12385]:c_Com_Ocom_OSKIP!=c_Com_Ocom_OWhile(X12385,X12384), inference(variable_rename,[status(thm)],[fact_com_Osimps_I16_J])). 4.46/4.72 fof(c_0_9386, plain, ![X9548]:X9548!=hAPP(c_Nat_OSuc,X9548), inference(variable_rename,[status(thm)],[fact_Suc__n__not__n])). 4.46/4.72 cnf(c_0_9387, plain, (c_Int_OPls!=c_Int_OMin), inference(split_conjunct,[status(thm)],[fact_rel__simps_I40_J])). 4.46/4.72 fof(c_0_9388, plain, ~hBOOL(c_fFalse), inference(fof_simplification,[status(thm)],[help_c__fFalse__1])). 4.46/4.72 cnf(c_0_9389, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1))),hAPP(hAPP(c_COMBC(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),X3))),c_Transitive__Closure_Ortrancl(X1,X2))))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1))),hAPP(c_Product__Type_OPair(X1,X1),X4))),c_Transitive__Closure_Ortrancl(X1,X2))))))=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5600, c_0_5266]), c_0_5266])). 4.46/4.72 cnf(c_0_9390, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X1,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X2)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))))))=hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X1,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(X1,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X4))),X2)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5601, c_0_4517]), c_0_4517])). 4.46/4.72 cnf(c_0_9391, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5602, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.72 fof(c_0_9392, plain, ![X11586, X11587, X11588, X11589, X11590, X11591]:hAPP(c_Set_Oimage(X11591,tc_prod(X11590,X11589),hAPP(hAPP(c_COMBS(X11591,X11589,tc_prod(X11590,X11589)),hAPP(hAPP(c_COMBB(X11590,tc_fun(X11589,tc_prod(X11590,X11589)),X11591),c_Product__Type_OPair(X11590,X11589)),X11588)),X11587)),X11586)=hAPP(hAPP(c_Product__Type_OSigma(X11590,X11589),hAPP(c_Set_Oimage(X11591,X11590,X11588),X11586)),hAPP(hAPP(c_COMBB(tc_fun(X11591,tc_HOL_Obool),tc_fun(X11589,tc_HOL_Obool),X11590),c_Set_Oimage(X11591,X11589,X11587)),hAPP(hAPP(c_COMBC(X11590,tc_fun(X11591,tc_HOL_Obool),tc_fun(X11591,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11591,tc_HOL_Obool),tc_fun(tc_fun(X11591,tc_HOL_Obool),tc_fun(X11591,tc_HOL_Obool)),X11590),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11591,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X11590,tc_HOL_Obool),tc_fun(X11591,tc_HOL_Obool),X11590),c_Set_Ovimage(X11591,X11590,X11588)),hAPP(hAPP(c_COMBC(X11590,tc_fun(X11590,tc_HOL_Obool),tc_fun(X11590,tc_HOL_Obool)),c_Set_Oinsert(X11590)),c_Orderings_Obot__class_Obot(tc_fun(X11590,tc_HOL_Obool)))))),X11586))), inference(variable_rename,[status(thm)],[fact_image__split__eq__Sigma])). 4.46/4.72 cnf(c_0_9393, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5603, c_0_4470]), c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9394, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_5604])). 4.46/4.72 cnf(c_0_9395, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),hAPP(c_Set_OCollect(X1),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X5)),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X4))))=c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),X1),c_If(tc_Option_Ooption(X2))),X4)),X3)),X5))), inference(split_conjunct,[status(thm)],[c_0_5605])). 4.46/4.72 cnf(c_0_9396, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X2),X5)))),hAPP(c_Set_Oimage(X2,X1,X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2),c_fNot),X5)))))=hAPP(c_Set_Oimage(X2,X1,hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBS(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X5)),X3)),X6)),X4)), inference(split_conjunct,[status(thm)],[c_0_5606])). 4.46/4.72 fof(c_0_9397, plain, ![X4968, X4969, X4970, X4971]:hAPP(hAPP(c_List_Omap(tc_prod(X4971,tc_Nat_Onat),X4971),c_Product__Type_Ofst(X4971,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X4971,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X4971,tc_Nat_Onat)),X4970),c_Product__Type_Osnd(X4971,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X4971,tc_Nat_Onat),X4969),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X4968))))=hAPP(hAPP(c_List_Omap(tc_prod(X4971,tc_Nat_Onat),X4971),c_Product__Type_Ofst(X4971,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X4971,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X4971,tc_Nat_Onat)),X4970),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X4971,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X4971,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X4971,tc_Nat_Onat),X4969),X4968))), inference(variable_rename,[status(thm)],[fact_sublist__shift__lemma__Suc])). 4.46/4.72 fof(c_0_9398, plain, ![X5723, X5724, X5725, X5726, X5727, X5728, X5729, X5730, X5731]:hAPP(hAPP(c_Product__Type_Oscomp(X5731,X5727,X5726,X5728),X5725),hAPP(hAPP(c_COMBC(X5727,tc_fun(X5730,tc_fun(X5729,X5728)),tc_fun(X5726,X5728)),hAPP(hAPP(c_COMBB(tc_fun(X5726,tc_prod(X5730,X5729)),tc_fun(tc_fun(X5730,tc_fun(X5729,X5728)),tc_fun(X5726,X5728)),X5727),c_Product__Type_Oscomp(X5726,X5730,X5729,X5728)),X5724)),X5723))=hAPP(hAPP(c_Product__Type_Oscomp(X5731,X5730,X5729,X5728),hAPP(hAPP(c_Product__Type_Oscomp(X5731,X5727,X5726,tc_prod(X5730,X5729)),X5725),X5724)),X5723), inference(variable_rename,[status(thm)],[fact_scomp__scomp])). 4.46/4.72 cnf(c_0_9399, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X3))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1)))), inference(split_conjunct,[status(thm)],[c_0_5607])). 4.46/4.72 cnf(c_0_9400, plain, (hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X1),hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X1)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X1)),c_List_Otranspose(X1,X2)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1)))),X2))), inference(rw,[status(thm)],[c_0_5608, c_0_4713])). 4.46/4.72 cnf(c_0_9401, plain, (hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X1),hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X1)),c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X1)),X2))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X2))), inference(rw,[status(thm)],[c_0_5609, c_0_5101]), ['final']). 4.46/4.72 fof(c_0_9402, plain, ![X10347, X10348, X10349, X10350, X10351, X10352, X10353]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10351,tc_Option_Ooption(X10352)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X10353),tc_Option_Ooption(X10352),X10351,hAPP(c_Option_Omap(X10353,X10352),X10350)),X10349)),X10348),hAPP(c_Option_Ooption_OSome(X10352),hAPP(X10350,X10347)))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X10353),tc_Option_Ooption(X10352),X10351,hAPP(c_Option_Omap(X10353,X10352),X10350)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10351,tc_Option_Ooption(X10353)),X10349),X10348),hAPP(c_Option_Ooption_OSome(X10353),X10347))), inference(variable_rename,[status(thm)],[fact_option__map__o__map__upd])). 4.46/4.72 cnf(c_0_9403, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin)))),c_Int_OMin)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5610, c_0_4470]), c_0_4443]), c_0_4431]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9404, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5611, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9405, plain, (hAPP(hAPP(c_Product__Type_OSigma(X3,X7),X1),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X3),X10))=hAPP(c_Set_Oimage(tc_prod(X2,X6),tc_prod(X3,X7),c_Product__Type_Omap__pair(X2,X3,X6,X7,X4,X8)),hAPP(hAPP(c_Product__Type_OSigma(X2,X6),X5),hAPP(c_COMBK(tc_fun(X6,tc_HOL_Obool),X2),X9)))|X1!=hAPP(c_Set_Oimage(X2,X3,X4),X5)|hAPP(c_Set_Oimage(X6,X7,X8),X9)!=X10), inference(split_conjunct,[status(thm)],[c_0_5612])). 4.46/4.72 cnf(c_0_9406, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5613, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9407, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_OdropWhile(X1,hAPP(c_Fun_Ocomp(X2,tc_HOL_Obool,X1,X4),X3),X5))=c_List_OdropWhile(X2,X4,hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_5614])). 4.46/4.72 cnf(c_0_9408, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5615, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.72 fof(c_0_9409, plain, ![X5485, X5486, X5487, X5488, X5489]:hAPP(hAPP(c_Product__Type_OSigma(X5489,X5488),X5487),hAPP(hAPP(c_COMBS(X5489,tc_fun(X5488,tc_HOL_Obool),tc_fun(X5488,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5488,tc_HOL_Obool),tc_fun(tc_fun(X5488,tc_HOL_Obool),tc_fun(X5488,tc_HOL_Obool)),X5489),c_Groups_Ominus__class_Ominus(tc_fun(X5488,tc_HOL_Obool))),X5486)),X5485))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5489,X5488),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5489,X5488),X5487),X5486)),hAPP(hAPP(c_Product__Type_OSigma(X5489,X5488),X5487),X5485)), inference(variable_rename,[status(thm)],[fact_Sigma__Diff__distrib2])). 4.46/4.72 fof(c_0_9410, plain, ![X5522, X5523, X5524, X5525, X5526]:hAPP(hAPP(c_Product__Type_OSigma(X5526,X5525),X5524),hAPP(hAPP(c_COMBS(X5526,tc_fun(X5525,tc_HOL_Obool),tc_fun(X5525,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5525,tc_HOL_Obool),tc_fun(tc_fun(X5525,tc_HOL_Obool),tc_fun(X5525,tc_HOL_Obool)),X5526),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5525,tc_HOL_Obool))),X5523)),X5522))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5526,X5525),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5526,X5525),X5524),X5523)),hAPP(hAPP(c_Product__Type_OSigma(X5526,X5525),X5524),X5522)), inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib2])). 4.46/4.72 fof(c_0_9411, plain, ![X13139, X13140, X13141, X13142, X13143]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X13143,X13142),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X13143,X13142),X13141),X13140)),hAPP(hAPP(c_Product__Type_OSigma(X13143,X13142),X13141),X13139))=hAPP(hAPP(c_Product__Type_OSigma(X13143,X13142),X13141),hAPP(hAPP(c_COMBS(X13143,tc_fun(X13142,tc_HOL_Obool),tc_fun(X13142,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13142,tc_HOL_Obool),tc_fun(tc_fun(X13142,tc_HOL_Obool),tc_fun(X13142,tc_HOL_Obool)),X13143),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13142,tc_HOL_Obool))),X13140)),X13139)), inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib2])). 4.46/4.72 cnf(c_0_9412, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X3))))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Osublist(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_5616])). 4.46/4.72 cnf(c_0_9413, plain, (c_List_Ofoldr(X1,X2,hAPP(c_Fun_Ocomp(X3,tc_fun(X2,X2),X1,X4),X5),X6,X7)=c_List_Ofoldr(X3,X2,X4,hAPP(hAPP(c_List_Omap(X1,X3),X5),X6),X7)), inference(split_conjunct,[status(thm)],[c_0_5617])). 4.46/4.72 cnf(c_0_9414, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5618, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9415, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5619, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.72 fof(c_0_9416, plain, ![X5017, X5018, X5019, X5020, X5021]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5020,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5021,tc_fun(X5020,tc_HOL_Obool)),X5019),X5018)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5021,tc_fun(X5020,tc_HOL_Obool)),X5019),X5017))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5021,tc_fun(X5020,tc_HOL_Obool)),X5019),hAPP(hAPP(c_COMBS(X5021,tc_fun(X5020,tc_HOL_Obool),tc_fun(X5020,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5020,tc_HOL_Obool),tc_fun(tc_fun(X5020,tc_HOL_Obool),tc_fun(X5020,tc_HOL_Obool)),X5021),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5020,tc_HOL_Obool))),X5018)),X5017)), inference(variable_rename,[status(thm)],[fact_UN__Un__distrib])). 4.46/4.72 fof(c_0_9417, plain, ![X2186, X2187, X2188, X2189, X2190]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2189,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2190,tc_fun(X2189,tc_HOL_Obool)),X2188),X2187)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2190,tc_fun(X2189,tc_HOL_Obool)),X2188),X2186))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2190,tc_fun(X2189,tc_HOL_Obool)),X2188),hAPP(hAPP(c_COMBS(X2190,tc_fun(X2189,tc_HOL_Obool),tc_fun(X2189,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2189,tc_HOL_Obool),tc_fun(tc_fun(X2189,tc_HOL_Obool),tc_fun(X2189,tc_HOL_Obool)),X2190),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2189,tc_HOL_Obool))),X2187)),X2186)), inference(variable_rename,[status(thm)],[fact_INT__Int__distrib])). 4.46/4.72 cnf(c_0_9418, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X2,X1),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X2,X1))),hAPP(c_Product__Type_OPair(X2,X1),X3))),X4))=hAPP(c_Relation_OImage(X2,X1,X4),hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5620])). 4.46/4.72 cnf(c_0_9419, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X3)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool),tc_Nat_Onat),X4),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2)))), inference(split_conjunct,[status(thm)],[c_0_5621])). 4.46/4.72 fof(c_0_9420, plain, ![X4797, X4798, X4799, X4800]:hAPP(c_Map_Omap__of(X4800,X4799),hAPP(hAPP(c_List_Omap(X4800,tc_prod(X4800,X4799)),hAPP(hAPP(c_COMBS(X4800,X4799,tc_prod(X4800,X4799)),c_Product__Type_OPair(X4800,X4799)),X4798)),X4797))=c_Map_Orestrict__map(X4800,X4799,hAPP(c_Fun_Ocomp(X4799,tc_Option_Ooption(X4799),X4800,c_Option_Ooption_OSome(X4799)),X4798),hAPP(c_List_Oset(X4800),X4797)), inference(variable_rename,[status(thm)],[fact_map__of__map__restrict])). 4.46/4.72 cnf(c_0_9421, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_List_Olist(X1)),hAPP(c_List_Omap(X2,X1),X3)),X4))=hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5622, c_0_4736]), c_0_4736])). 4.46/4.72 cnf(c_0_9422, plain, (hAPP(c_Product__Type_Oapfst(X1,X2,X3,X4),hAPP(c_Product__Type_Oapsnd(X5,X3,X1,X6),X7))=hAPP(c_Product__Type_Oapsnd(X5,X3,X2,X6),hAPP(c_Product__Type_Oapfst(X1,X2,X5,X4),X7))), inference(split_conjunct,[status(thm)],[c_0_5623])). 4.46/4.72 fof(c_0_9423, plain, ![X15805, X15806, X15807, X15808, X15809, X15810, X15811, X15812, X15813, X15814, X15815]:hAPP(c_Product__Type_Omap__pair(X15809,X15814,X15808,X15812,hAPP(c_Fun_Ocomp(X15815,X15814,X15809,X15811),X15807),hAPP(c_Fun_Ocomp(X15813,X15812,X15808,X15810),X15806)),X15805)=hAPP(c_Product__Type_Omap__pair(X15815,X15814,X15813,X15812,X15811,X15810),hAPP(c_Product__Type_Omap__pair(X15809,X15815,X15808,X15813,X15807,X15806),X15805)), inference(variable_rename,[status(thm)],[fact_map__pair_Ocompositionality])). 4.46/4.72 cnf(c_0_9424, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),c_Int_OMin)),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5624, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9425, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5625]), ['final']). 4.46/4.72 cnf(c_0_9426, plain, (hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X4),hAPP(c_Product__Type_Oapfst(X5,X3,X1,X6),X7))=hAPP(hAPP(c_Product__Type_OPair(X3,X2),hAPP(X6,hAPP(c_Product__Type_Ofst(X5,X1),X7))),hAPP(X4,hAPP(c_Product__Type_Osnd(X5,X1),X7)))), inference(split_conjunct,[status(thm)],[c_0_5626])). 4.46/4.72 cnf(c_0_9427, plain, (hAPP(c_Product__Type_Oapfst(X1,X2,X3,X4),hAPP(c_Product__Type_Oapsnd(X5,X3,X1,X6),X7))=hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X5),X7))),hAPP(X6,hAPP(c_Product__Type_Osnd(X1,X5),X7)))), inference(split_conjunct,[status(thm)],[c_0_5627])). 4.46/4.72 cnf(c_0_9428, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),c_Int_OMin)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5628, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9429, plain, (hAPP(hAPP(X1,X2),c_List_Ofoldr(X3,X4,X1,X5,X6))=c_List_Ofoldr(X3,X4,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5),X6)), inference(split_conjunct,[status(thm)],[c_0_5629])). 4.46/4.72 fof(c_0_9430, plain, ![X4642, X4643, X4644, X4645, X4646, X4647, X4648]:hAPP(hAPP(c_List_Ozip(X4648,X4647),hAPP(hAPP(c_List_Olist__update(X4648,X4646),X4645),X4644)),hAPP(hAPP(c_List_Olist__update(X4647,X4643),X4645),X4642))=hAPP(hAPP(c_List_Olist__update(tc_prod(X4648,X4647),hAPP(hAPP(c_List_Ozip(X4648,X4647),X4646),X4643)),X4645),hAPP(hAPP(c_Product__Type_OPair(X4648,X4647),X4644),X4642)), inference(variable_rename,[status(thm)],[fact_zip__update])). 4.46/4.72 cnf(c_0_9431, plain, (hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X4),hAPP(c_Product__Type_Oapsnd(X5,X1,X3,X6),X7))=hAPP(c_Product__Type_Oapsnd(X5,X2,X3,hAPP(c_Fun_Ocomp(X1,X2,X5,X4),X6)),X7)), inference(split_conjunct,[status(thm)],[c_0_5630])). 4.46/4.72 cnf(c_0_9432, plain, (hAPP(c_Product__Type_Oapfst(X1,X2,X3,hAPP(c_Fun_Ocomp(X4,X2,X1,X5),X6)),X7)=hAPP(c_Product__Type_Oapfst(X4,X2,X3,X5),hAPP(c_Product__Type_Oapfst(X1,X4,X3,X6),X7))), inference(split_conjunct,[status(thm)],[c_0_5631])). 4.46/4.72 cnf(c_0_9433, plain, (hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5632, c_0_4470]), c_0_4443]), c_0_4471])). 4.46/4.72 cnf(c_0_9434, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))),c_Int_OMin)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5633, c_0_4470]), c_0_4443]), c_0_4431]), c_0_4431]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9435, plain, (hAPP(c_List_Orotate(X1,X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5))=hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(c_List_Orotate(X3,X2),X5))), inference(split_conjunct,[status(thm)],[c_0_5634])). 4.46/4.72 fof(c_0_9436, plain, ![X10963, X10964, X10965, X10966, X10967, X10968]:hAPP(hAPP(c_List_Olist_OCons(tc_prod(X10968,X10967)),hAPP(hAPP(c_Product__Type_OPair(X10968,X10967),X10966),X10964)),hAPP(hAPP(c_List_Ozip(X10968,X10967),X10965),X10963))=hAPP(hAPP(c_List_Ozip(X10968,X10967),hAPP(hAPP(c_List_Olist_OCons(X10968),X10966),X10965)),hAPP(hAPP(c_List_Olist_OCons(X10967),X10964),X10963)), inference(variable_rename,[status(thm)],[fact_zip__Cons__Cons])). 4.46/4.72 cnf(c_0_9437, plain, (hAPP(c_Set_Oimage(X1,tc_List_Olist(X1),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))),X2)=c_List_Oset__Cons(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5635])). 4.46/4.72 fof(c_0_9438, plain, ![X15765, X15766, X15767]:hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X15767)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X15766),X15765))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15766),X15767)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15765),X15767)), inference(variable_rename,[status(thm)],[fact_image__add__atLeastLessThan])). 4.46/4.72 fof(c_0_9439, plain, ![X10933, X10934, X10935, X10936, X10937, X10938, X10939]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10937,X10938),hAPP(c_Fun_Ocomp(X10939,X10938,X10937,X10936),X10935)),X10934),hAPP(X10936,X10933))=hAPP(c_Fun_Ocomp(X10939,X10938,X10937,X10936),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10937,X10939),X10935),X10934),X10933)), inference(variable_rename,[status(thm)],[fact_fun__upd__comp])). 4.46/4.72 fof(c_0_9440, plain, ![X8289, X8290, X8291, X8292, X8293, X8294]:hAPP(c_Fun_Ocomp(X8292,X8294,tc_prod(X8292,X8291),X8290),c_Product__Type_Ofst(X8292,X8291))=hAPP(c_Fun_Ocomp(tc_prod(X8294,X8293),X8294,tc_prod(X8292,X8291),c_Product__Type_Ofst(X8294,X8293)),c_Product__Type_Omap__pair(X8292,X8294,X8291,X8293,X8290,X8289)), inference(variable_rename,[status(thm)],[fact_fst__comp__map__pair])). 4.46/4.72 fof(c_0_9441, plain, ![X6031, X6032, X6033, X6034, X6035, X6036]:hAPP(c_Fun_Ocomp(X6033,X6035,tc_prod(X6034,X6033),X6031),c_Product__Type_Osnd(X6034,X6033))=hAPP(c_Fun_Ocomp(tc_prod(X6036,X6035),X6035,tc_prod(X6034,X6033),c_Product__Type_Osnd(X6036,X6035)),c_Product__Type_Omap__pair(X6034,X6036,X6033,X6035,X6032,X6031)), inference(variable_rename,[status(thm)],[fact_snd__comp__map__pair])). 4.46/4.72 fof(c_0_9442, plain, ![X13624, X13625, X13626]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13625),X13626),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13624),X13626))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X13626)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X13625,X13624)), inference(variable_rename,[status(thm)],[fact_image__add__atLeastAtMost])). 4.46/4.72 fof(c_0_9443, plain, ![X12995, X12996, X12997, X12998]:c_List_Otranspose(X12998,hAPP(hAPP(c_List_Omap(tc_List_Olist(X12997),tc_List_Olist(X12998)),hAPP(c_List_Omap(X12997,X12998),X12996)),X12995))=hAPP(hAPP(c_List_Omap(tc_List_Olist(X12997),tc_List_Olist(X12998)),hAPP(c_List_Omap(X12997,X12998),X12996)),c_List_Otranspose(X12997,X12995)), inference(variable_rename,[status(thm)],[fact_transpose__map__map])). 4.46/4.72 fof(c_0_9444, plain, ![X2203, X2204, X2205, X2206, X2207, X2208, X2209]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2209,X2208,X2207),hAPP(c_Fun_Ocomp(X2206,tc_fun(X2208,X2207),X2209,X2205),X2204)),X2203)=hAPP(hAPP(X2205,hAPP(X2204,hAPP(c_Product__Type_Ofst(X2209,X2208),X2203))),hAPP(c_Product__Type_Osnd(X2209,X2208),X2203)), inference(variable_rename,[status(thm)],[fact_split__comp])). 4.46/4.72 fof(c_0_9445, plain, ![X7340, X7341, X7342, X7343, X7344]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7344)),hAPP(c_List_Ofilter(X7344,X7343),hAPP(hAPP(c_List_Omap(X7342,X7344),X7341),X7340)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7342)),hAPP(c_List_Ofilter(X7342,hAPP(c_Fun_Ocomp(X7344,tc_HOL_Obool,X7342,X7343),X7341)),X7340)), inference(variable_rename,[status(thm)],[fact_length__filter__map])). 4.46/4.72 cnf(c_0_9446, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oconcat(X1,X2))=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2))), inference(split_conjunct,[status(thm)],[c_0_5636])). 4.46/4.72 fof(c_0_9447, plain, ![X11800, X11801]:hAPP(hAPP(c_List_Omap(X11801,tc_prod(X11801,X11801)),hAPP(hAPP(c_COMBS(X11801,X11801,tc_prod(X11801,X11801)),c_Product__Type_OPair(X11801,X11801)),c_COMBI(X11801))),X11800)=hAPP(hAPP(c_List_Ozip(X11801,X11801),X11800),X11800), inference(variable_rename,[status(thm)],[fact_zip__same__conv__map])). 4.46/4.72 cnf(c_0_9448, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),c_Map_Odom(X3,X1,X4)),hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))=c_Map_Odom(X3,X1,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X1)),X4),X5),X2))|c_Option_Ooption_ONone(X1)!=X2), inference(split_conjunct,[status(thm)],[c_0_5637])). 4.46/4.72 cnf(c_0_9449, plain, (c_List_Olist_Olist__size(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,X3)),c_List_Olist_Olist__size(X1,X2,X4))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5638])). 4.46/4.72 cnf(c_0_9450, plain, (hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X3,X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,X3)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),X4))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5639])). 4.46/4.72 fof(c_0_9451, plain, ![X4605, X4606, X4607, X4608, X4609, X4610]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4610,tc_fun(X4609,tc_HOL_Obool)),X4608),hAPP(c_Fun_Ocomp(X4607,tc_fun(X4609,tc_HOL_Obool),X4610,X4606),X4605))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4607,tc_fun(X4609,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4610,X4607,X4605),X4608)),X4606), inference(variable_rename,[status(thm)],[fact_UN__o])). 4.46/4.72 fof(c_0_9452, plain, ![X4903, X4904, X4905, X4906, X4907, X4908, X4909]:hAPP(c_Fun_Ocomp(X4905,X4908,X4907,hAPP(c_Fun_Ocomp(X4909,X4908,X4905,X4906),X4904)),X4903)=hAPP(c_Fun_Ocomp(X4909,X4908,X4907,X4906),hAPP(c_Fun_Ocomp(X4905,X4909,X4907,X4904),X4903)), inference(variable_rename,[status(thm)],[fact_o__assoc])). 4.46/4.72 fof(c_0_9453, plain, ![X11846, X11847, X11848, X11849, X11850, X11851]:hAPP(hAPP(c_List_Omap(X11851,X11850),X11849),hAPP(hAPP(c_List_Olist__update(X11851,X11848),X11847),X11846))=hAPP(hAPP(c_List_Olist__update(X11850,hAPP(hAPP(c_List_Omap(X11851,X11850),X11849),X11848)),X11847),hAPP(X11849,X11846)), inference(variable_rename,[status(thm)],[fact_map__update])). 4.46/4.72 fof(c_0_9454, plain, ![X393, X394, X395, X396, X397, X398]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X396,tc_fun(X397,tc_HOL_Obool)),X394),hAPP(hAPP(c_COMBB(X398,tc_fun(X397,tc_HOL_Obool),X396),X393),X395))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X398,tc_fun(X397,tc_HOL_Obool)),hAPP(c_Set_Oimage(X396,X398,X395),X394)),X393), inference(variable_rename,[status(thm)],[fact_UN__simps_I10_J])). 4.46/4.72 fof(c_0_9455, plain, ![X11204, X11205, X11206, X11207, X11208, X11209]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11209,tc_fun(X11208,tc_HOL_Obool)),hAPP(c_Set_Oimage(X11207,X11209,X11206),X11205)),X11204)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11207,tc_fun(X11208,tc_HOL_Obool)),X11205),hAPP(hAPP(c_COMBB(X11209,tc_fun(X11208,tc_HOL_Obool),X11207),X11204),X11206)), inference(variable_rename,[status(thm)],[fact_INT__simps_I10_J])). 4.46/4.72 cnf(c_0_9456, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(c_COMBC(X2,X1,tc_HOL_Obool),X3)))=hAPP(c_Relation_ORange(X2,X1),hAPP(c_Set_OCollect(tc_prod(X2,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X1,tc_HOL_Obool),X3)))), inference(split_conjunct,[status(thm)],[c_0_5640])). 4.46/4.72 fof(c_0_9457, plain, ![X13553, X13554, X13555, X13556]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13556,tc_Option_Ooption(X13555)),X13554),X13553),c_Option_Ooption_ONone(X13555))=c_Map_Orestrict__map(X13556,X13555,X13554,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X13556,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X13556),X13553),c_Orderings_Obot__class_Obot(tc_fun(X13556,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_restrict__complement__singleton__eq])). 4.46/4.72 fof(c_0_9458, plain, ![X9745, X9746, X9747, X9748, X9749, X9750]:hAPP(hAPP(c_Option_Omap(X9747,X9749),hAPP(c_Fun_Ocomp(X9750,X9749,X9747,X9748),X9746)),X9745)=hAPP(hAPP(c_Option_Omap(X9750,X9749),X9748),hAPP(hAPP(c_Option_Omap(X9747,X9750),X9746),X9745)), inference(variable_rename,[status(thm)],[fact_option__map__comp])). 4.46/4.72 fof(c_0_9459, plain, ![X16045, X16046, X16047, X16048, X16049]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16049,tc_fun(X16048,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X16049),X16047),X16046)),X16045)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16048,tc_HOL_Obool)),hAPP(X16045,X16047)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16049,tc_fun(X16048,tc_HOL_Obool)),X16046),X16045)), inference(variable_rename,[status(thm)],[fact_INT__insert])). 4.46/4.72 fof(c_0_9460, plain, ![X1281, X1282, X1283, X1284, X1285]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1285,tc_fun(X1284,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1285),X1283),X1282)),X1281)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1284,tc_HOL_Obool)),hAPP(X1281,X1283)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1285,tc_fun(X1284,tc_HOL_Obool)),X1282),X1281)), inference(variable_rename,[status(thm)],[fact_UN__insert])). 4.46/4.72 fof(c_0_9461, plain, ![X1906, X1907, X1908]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X1908,X1907),tc_HOL_Obool),tc_fun(X1907,tc_HOL_Obool)),X1906),c_Relation_ORange(X1908,X1907))=hAPP(c_Relation_ORange(X1908,X1907),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1908,X1907),tc_HOL_Obool),X1906)), inference(variable_rename,[status(thm)],[fact_Range__Union])). 4.46/4.72 fof(c_0_9462, plain, ![X7248, X7249, X7250]:hAPP(c_Relation_ODomain(X7250,X7249),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X7250,X7249),tc_HOL_Obool),X7248))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X7250,X7249),tc_HOL_Obool),tc_fun(X7250,tc_HOL_Obool)),X7248),c_Relation_ODomain(X7250,X7249)), inference(variable_rename,[status(thm)],[fact_Domain__Union])). 4.46/4.72 cnf(c_0_9463, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X1,X2,X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X3))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5641])). 4.46/4.72 cnf(c_0_9464, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)))=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X1,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5642, c_0_4836]), c_0_5643]), c_0_5644]), c_0_5645]), ['final']). 4.46/4.72 cnf(c_0_9465, plain, (hAPP(c_Set_Ovimage(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6)=hAPP(c_Set_Ovimage(X1,X3,X5),hAPP(c_Set_Ovimage(X3,X2,X4),X6))), inference(split_conjunct,[status(thm)],[c_0_5646])). 4.46/4.72 fof(c_0_9466, plain, ![X3158, X3159, X3160, X3161, X3162]:hAPP(hAPP(c_List_Omap(X3162,X3161),X3160),hAPP(hAPP(c_List_Olist_OCons(X3162),X3159),X3158))=hAPP(hAPP(c_List_Olist_OCons(X3161),hAPP(X3160,X3159)),hAPP(hAPP(c_List_Omap(X3162,X3161),X3160),X3158)), inference(variable_rename,[status(thm)],[fact_map_Osimps_I2_J])). 4.46/4.72 fof(c_0_9467, plain, ![X12615, X12616, X12617, X12618, X12619, X12620]:hAPP(c_List_Ofoldl(X12620,X12619,X12618,X12617),hAPP(hAPP(c_List_Olist_OCons(X12619),X12616),X12615))=hAPP(c_List_Ofoldl(X12620,X12619,X12618,hAPP(hAPP(X12618,X12617),X12616)),X12615), inference(variable_rename,[status(thm)],[fact_foldl__Cons])). 4.46/4.72 fof(c_0_9468, plain, ![X9229, X9230, X9231, X9232, X9233]:hAPP(hAPP(c_List_Omap(X9231,X9233),X9230),hAPP(hAPP(c_List_Otake(X9231),X9232),X9229))=hAPP(hAPP(c_List_Otake(X9233),X9232),hAPP(hAPP(c_List_Omap(X9231,X9233),X9230),X9229)), inference(variable_rename,[status(thm)],[fact_take__map])). 4.46/4.72 fof(c_0_9469, plain, ![X4365, X4366, X4367, X4368, X4369]:hAPP(hAPP(c_List_Odrop(X4369),X4368),hAPP(hAPP(c_List_Omap(X4367,X4369),X4366),X4365))=hAPP(hAPP(c_List_Omap(X4367,X4369),X4366),hAPP(hAPP(c_List_Odrop(X4367),X4368),X4365)), inference(variable_rename,[status(thm)],[fact_drop__map])). 4.46/4.72 cnf(c_0_9470, plain, (c_Divides_Odivmod__nat(X1,X2)=hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5647])). 4.46/4.72 fof(c_0_9471, plain, ![X10197, X10198, X10199, X10200, X10201, X10202]:hAPP(c_Set_Oimage(X10202,X10201,hAPP(c_Fun_Ocomp(X10200,X10201,X10202,X10199),X10198)),X10197)=hAPP(c_Set_Oimage(X10200,X10201,X10199),hAPP(c_Set_Oimage(X10202,X10200,X10198),X10197)), inference(variable_rename,[status(thm)],[fact_image__compose])). 4.46/4.72 fof(c_0_9472, plain, ![X14609, X14610, X14611, X14612, X14613]:c_List_Omaps(X14613,X14612,X14611,hAPP(hAPP(c_List_Olist_OCons(X14613),X14610),X14609))=hAPP(hAPP(c_List_Oappend(X14612),hAPP(X14611,X14610)),c_List_Omaps(X14613,X14612,X14611,X14609)), inference(variable_rename,[status(thm)],[fact_maps__simps_I1_J])). 4.46/4.72 fof(c_0_9473, plain, ![X11965, X11966, X11967, X11968]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11968,tc_HOL_Obool)),X11966),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11968,tc_HOL_Obool)),X11967),X11965))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11968,tc_HOL_Obool)),X11967),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11968,tc_HOL_Obool)),X11966),X11965)), inference(variable_rename,[status(thm)],[fact_Un__left__commute])). 4.46/4.72 fof(c_0_9474, plain, ![X11219, X11220, X11221, X11222]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11222,tc_HOL_Obool)),X11220),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11222,tc_HOL_Obool)),X11221),X11219))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11222,tc_HOL_Obool)),X11221),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11222,tc_HOL_Obool)),X11220),X11219)), inference(variable_rename,[status(thm)],[fact_Int__left__commute])). 4.46/4.72 fof(c_0_9475, plain, ![X16541, X16542, X16543, X16544]:hAPP(c_Relation_Oconverse(X16544,X16544),hAPP(hAPP(c_Relation_Oinv__image(X16543,X16544),X16542),X16541))=hAPP(hAPP(c_Relation_Oinv__image(X16543,X16544),hAPP(c_Relation_Oconverse(X16543,X16543),X16542)),X16541), inference(variable_rename,[status(thm)],[fact_converse__inv__image])). 4.46/4.72 fof(c_0_9476, plain, ![X10988, X10989, X10990, X10991, X10992]:c_List_Olist_Olist__size(X10990,hAPP(c_Fun_Ocomp(X10992,tc_Nat_Onat,X10990,X10991),X10989),X10988)=c_List_Olist_Olist__size(X10992,X10991,hAPP(hAPP(c_List_Omap(X10990,X10992),X10989),X10988)), inference(variable_rename,[status(thm)],[fact_list__size__map])). 4.46/4.72 fof(c_0_9477, plain, ![X10305, X10306, X10307, X10308, X10309]:hAPP(hAPP(X10307,X10306),hAPP(hAPP(c_Power_Opower_Opower(X10309,X10308,X10307),X10306),X10305))=hAPP(hAPP(c_Power_Opower_Opower(X10309,X10308,X10307),X10306),hAPP(c_Nat_OSuc,X10305)), inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__Suc])). 4.46/4.72 cnf(c_0_9478, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X1,X2,X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X2)),c_Com_Ocom_Ocom__size(X3))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5648])). 4.46/4.72 cnf(c_0_9479, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X2)))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5649, c_0_4836]), c_0_5643]), c_0_5644]), c_0_5645]), ['final']). 4.46/4.72 cnf(c_0_9480, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),c_Relation_OField(X1)),X2))=hAPP(c_Relation_OField(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2))), inference(split_conjunct,[status(thm)],[c_0_5650])). 4.46/4.72 fof(c_0_9481, plain, ![X8682, X8683, X8684]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X8684,tc_HOL_Obool),tc_fun(X8684,tc_HOL_Obool)),X8682),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8684,tc_HOL_Obool)),X8683))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8684,tc_HOL_Obool)),X8683),c_Complete__Lattice_OInf__class_OInf(tc_fun(X8684,tc_HOL_Obool),X8682)), inference(variable_rename,[status(thm)],[fact_Un__Inter])). 4.46/4.72 fof(c_0_9482, plain, ![X4519, X4520, X4521]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4521,tc_HOL_Obool)),X4520),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4521,tc_HOL_Obool),X4519))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X4521,tc_HOL_Obool),tc_fun(X4521,tc_HOL_Obool)),X4519),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4521,tc_HOL_Obool)),X4520)), inference(variable_rename,[status(thm)],[fact_Int__Union])). 4.46/4.72 fof(c_0_9483, plain, ![X9043, X9044, X9045, X9046, X9047]:hAPP(c_Map_Omap__add(X9047,X9046,X9045,X9044),X9043)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X9046),X9046,hAPP(X9045,X9043),c_Option_Ooption_OSome(X9046)),hAPP(X9044,X9043)), inference(variable_rename,[status(thm)],[fact_map__add__def])). 4.46/4.72 cnf(c_0_9484, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4))=hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X4))), inference(split_conjunct,[status(thm)],[c_0_5651])). 4.46/4.72 fof(c_0_9485, plain, ![X15028, X15029, X15030, X15031, X15032]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X15032,X15031,X15030),X15029),X15028)=hAPP(hAPP(X15029,hAPP(c_Product__Type_Ofst(X15032,X15031),X15028)),hAPP(c_Product__Type_Osnd(X15032,X15031),X15028)), inference(variable_rename,[status(thm)],[fact_prod__case__beta])). 4.46/4.72 fof(c_0_9486, plain, ![X10125, X10126, X10127, X10128]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X10128,tc_HOL_Obool),tc_fun(X10127,tc_HOL_Obool)),X10125),c_Set_Oimage(X10128,X10127,X10126))=hAPP(c_Set_Oimage(X10128,X10127,X10126),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10128,tc_HOL_Obool),X10125)), inference(variable_rename,[status(thm)],[fact_image__Union])). 4.46/4.72 fof(c_0_9487, plain, ![X4304, X4305, X4306, X4307, X4308]:hAPP(c_Set_Oimage(X4308,X4307,X4306),hAPP(hAPP(c_Set_Oinsert(X4308),X4305),X4304))=hAPP(hAPP(c_Set_Oinsert(X4307),hAPP(X4306,X4305)),hAPP(c_Set_Oimage(X4308,X4307,X4306),X4304)), inference(variable_rename,[status(thm)],[fact_image__insert])). 4.46/4.72 cnf(c_0_9488, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X3,X1,X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))=hAPP(c_Set_Oimage(X3,X1,X4),hAPP(c_Set_Ovimage(X3,X1,X4),X2))), inference(split_conjunct,[status(thm)],[c_0_5652])). 4.46/4.72 fof(c_0_9489, plain, ![X11744, X11745, X11746, X11747]:(c_List_Olist_ONil(X11747)=hAPP(c_List_Orotate1(X11747),c_List_Olist_ONil(X11747))&hAPP(c_List_Orotate1(X11746),hAPP(hAPP(c_List_Olist_OCons(X11746),X11745),X11744))=hAPP(hAPP(c_List_Oappend(X11746),X11744),hAPP(hAPP(c_List_Olist_OCons(X11746),X11745),c_List_Olist_ONil(X11746)))), inference(variable_rename,[status(thm)],[fact_rotate__simps])). 4.46/4.72 cnf(c_0_9490, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),X3),c_List_Olist_ONil(X2)),X4)=hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X3,X2,X5),X1),X4)|X1!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[c_0_5653])). 4.46/4.72 fof(c_0_9491, plain, ![X13570, X13571, X13572, X13573]:hAPP(hAPP(c_List_Omap(X13573,X13572),hAPP(c_COMBK(X13572,X13573),X13571)),X13570)=c_List_Oreplicate(X13572,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13573)),X13570),X13571), inference(variable_rename,[status(thm)],[fact_map__replicate__const])). 4.46/4.72 fof(c_0_9492, plain, ![X2547, X2548, X2549, X2550]:hAPP(hAPP(c_List_Omap(X2550,X2549),X2548),hAPP(c_List_Otl(X2550),X2547))=hAPP(c_List_Otl(X2549),hAPP(hAPP(c_List_Omap(X2550,X2549),X2548),X2547)), inference(variable_rename,[status(thm)],[fact_map__tl])). 4.46/4.72 fof(c_0_9493, plain, ![X7136, X7137]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7137),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X7136),X7137))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7136),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X7136,X7137)), inference(variable_rename,[status(thm)],[fact_mult__div__cancel])). 4.46/4.72 fof(c_0_9494, plain, ![X8008, X8009]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8009),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8008),X8009))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X8008),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8008,X8009)), inference(variable_rename,[status(thm)],[fact_zmult__div__cancel])). 4.46/4.72 fof(c_0_9495, plain, ![X4147, X4148, X4149, X4150]:hAPP(c_List_Oset(X4150),hAPP(hAPP(c_List_Omap(X4149,X4150),X4148),X4147))=hAPP(c_Set_Oimage(X4149,X4150,X4148),hAPP(c_List_Oset(X4149),X4147)), inference(variable_rename,[status(thm)],[fact_set__map])). 4.46/4.72 fof(c_0_9496, plain, ![X4031, X4032, X4033, X4034]:c_List_Obutlast(X4033,hAPP(hAPP(c_List_Omap(X4034,X4033),X4032),X4031))=hAPP(hAPP(c_List_Omap(X4034,X4033),X4032),c_List_Obutlast(X4034,X4031)), inference(variable_rename,[status(thm)],[fact_map__butlast])). 4.46/4.72 fof(c_0_9497, plain, ![X12875, X12876, X12877]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12877),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12876),X12875))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12876),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12877),X12875)), inference(variable_rename,[status(thm)],[fact_nat__add__left__commute])). 4.46/4.72 fof(c_0_9498, plain, ![X3992, X3993, X3994, X3995]:hAPP(c_Nat_Onat_Onat__rec(X3995,X3994,X3993),hAPP(c_Nat_OSuc,X3992))=hAPP(hAPP(X3993,X3992),hAPP(c_Nat_Onat_Onat__rec(X3995,X3994,X3993),X3992)), inference(variable_rename,[status(thm)],[fact_nat__rec__Suc])). 4.46/4.72 cnf(c_0_9499, plain, (c_Relation_OId(X1)=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)), inference(split_conjunct,[status(thm)],[c_0_5654])). 4.46/4.72 fof(c_0_9500, plain, ![X13241, X13242]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13241),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13242),X13241))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X13242)),X13241), inference(variable_rename,[status(thm)],[fact_mult__Suc])). 4.46/4.72 fof(c_0_9501, plain, ![X11892, X11893]:hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X11893),tc_List_Olist(X11893)),c_List_Olist_ONil(X11893)),c_List_Olist_ONil(X11893))=c_List_Opartition(X11893,X11892,c_List_Olist_ONil(X11893)), inference(variable_rename,[status(thm)],[fact_partition_Osimps_I1_J])). 4.46/4.72 fof(c_0_9502, plain, ![X15991, X15992]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15992),X15991))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15992),hAPP(c_Nat_OSuc,X15991)), inference(variable_rename,[status(thm)],[fact_mult__Suc__right])). 4.46/4.72 fof(c_0_9503, plain, ![X8961, X8962, X8963, X8964, X8965, X8966]:hAPP(hAPP(hAPP(c_COMBS(X8966,X8965,X8964),X8963),X8962),X8961)=hAPP(hAPP(X8963,X8961),hAPP(X8962,X8961)), inference(variable_rename,[status(thm)],[help_c__COMBS__1])). 4.46/4.72 fof(c_0_9504, plain, ![X6007, X6008, X6009]:hAPP(c_List_Ofilter(X6009,X6008),hAPP(c_List_Orev(X6009),X6007))=hAPP(c_List_Orev(X6009),hAPP(c_List_Ofilter(X6009,X6008),X6007)), inference(variable_rename,[status(thm)],[fact_rev__filter])). 4.46/4.72 cnf(c_0_9505, plain, (hAPP(c_Set_OCollect(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),X2))=hAPP(c_Set_OPow(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5655])). 4.46/4.72 fof(c_0_9506, plain, ![X7613, X7614, X7615, X7616]:hAPP(hAPP(c_Set_Oinsert(X7616),X7614),hAPP(hAPP(c_Set_Oinsert(X7616),X7615),X7613))=hAPP(hAPP(c_Set_Oinsert(X7616),X7615),hAPP(hAPP(c_Set_Oinsert(X7616),X7614),X7613)), inference(variable_rename,[status(thm)],[fact_insert__commute])). 4.46/4.72 fof(c_0_9507, plain, ![X10290, X10291]:hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10291)),c_List_Olist_ONil(X10291)),c_List_Olist_ONil(tc_List_Olist(X10291)))=c_Enum_On__lists(X10291,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10290), inference(variable_rename,[status(thm)],[fact_n__lists_Osimps_I1_J])). 4.46/4.72 fof(c_0_9508, plain, ![X12147, X12148]:c_Fun_Oid(tc_prod(X12148,X12147))=hAPP(c_Product__Type_Oprod_Oprod__case(X12148,X12147,tc_prod(X12148,X12147)),c_Product__Type_OPair(X12148,X12147)), inference(variable_rename,[status(thm)],[fact_split__Pair])). 4.46/4.72 fof(c_0_9509, plain, ![X7806, X7807, X7808, X7809]:c_List_Oremove1(X7809,X7808,c_List_Oremove1(X7809,X7807,X7806))=c_List_Oremove1(X7809,X7807,c_List_Oremove1(X7809,X7808,X7806)), inference(variable_rename,[status(thm)],[fact_remove1__commute])). 4.46/4.72 fof(c_0_9510, plain, ![X7269, X7270, X7271, X7272]:hAPP(c_New__DSequence_Opos__union(X7272,X7271,X7270),X7269)=c_Lazy__Sequence_Oappend(X7272,hAPP(X7271,X7269),hAPP(X7270,X7269)), inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__union__def])). 4.46/4.72 fof(c_0_9511, plain, ![X5933]:c_Enum_Osublists(X5933,c_List_Olist_ONil(X5933))=hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5933)),c_List_Olist_ONil(X5933)),c_List_Olist_ONil(tc_List_Olist(X5933))), inference(variable_rename,[status(thm)],[fact_sublists_Osimps_I1_J])). 4.46/4.72 fof(c_0_9512, plain, ![X17556, X17557]:hAPP(c_List_Olexn(X17557,X17556),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X17557),tc_List_Olist(X17557)),tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_lexn_Osimps_I1_J])). 4.46/4.72 cnf(c_0_9513, plain, (hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X1)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X1)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBC(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X1)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))))),c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1))))),c_List_Olex(X1,X2))))))=c_List_Olenlex(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5656])). 4.46/4.72 cnf(c_0_9514, plain, (hAPP(c_Set_OCollect(tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X1)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),tc_List_Olist(X1)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_List_Olist(X1)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_List_Olist(X1)),c_COMBS(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_List_Olist(X1)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),X1),c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X1)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_List_Olist(X1)),c_COMBB(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_List_Olist(X1),tc_HOL_Obool,tc_List_Olist(X1))),c_fequal))),c_List_Olist_OCons(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X1))),X3))))))=c_List_Oset__Cons(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_5657])). 4.46/4.72 cnf(c_0_9515, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))))=c_Divides_Oadjust(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5658, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9516, plain, (hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X3))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBC(X3,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X1,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X3),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X1,X3)))),c_Product__Type_OPair(X1,X3)))),X4))))),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X3,X2)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X3,X2),tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X3,X2)))),hAPP(c_COMBC(X3,X2,tc_prod(X3,X2)),c_Product__Type_OPair(X3,X2))))),X5)))))=hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_5659])). 4.46/4.72 fof(c_0_9517, plain, ![X12166, X12167]:hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X12167,X12167),tc_HOL_Obool),tc_fun(tc_prod(X12167,X12167),tc_HOL_Obool),tc_fun(tc_fun(X12166,X12167),tc_prod(tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool),tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X12167,X12167),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X12167,X12167),tc_HOL_Obool),tc_fun(tc_fun(X12166,X12167),tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X12167,X12167),tc_HOL_Obool),tc_fun(tc_fun(X12166,X12167),tc_prod(tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool),tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X12166,X12167),tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool)),tc_fun(tc_fun(X12166,X12167),tc_prod(tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool),tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X12167,X12167),tc_HOL_Obool),tc_fun(tc_fun(X12166,X12167),tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X12167,X12167),tc_HOL_Obool),tc_fun(tc_fun(X12166,X12167),tc_prod(tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool),tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool))))),tc_fun(tc_prod(X12167,X12167),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X12166,X12167),tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool)),tc_fun(tc_fun(X12166,X12167),tc_prod(tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool),tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool))),tc_fun(tc_prod(X12167,X12167),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X12166,X12167),tc_fun(tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool),tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X12166,X12167),tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool)),tc_fun(tc_fun(X12166,X12167),tc_prod(tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool),tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool)))),tc_fun(tc_prod(X12167,X12167),tc_HOL_Obool)),c_COMBS(tc_fun(X12166,X12167),tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool),tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X12166,X12167),tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool)),tc_fun(tc_fun(X12166,X12167),tc_fun(tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool),tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool)))),tc_fun(tc_prod(X12167,X12167),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool),tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool))),tc_fun(X12166,X12167)),c_Product__Type_OPair(tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool),tc_fun(tc_prod(X12166,X12166),tc_HOL_Obool)))),c_Relation_Oinv__image(X12167,X12166))))),c_Relation_Oinv__image(X12167,X12166)))=c_FunDef_Orp__inv__image(X12167,X12166), inference(variable_rename,[status(thm)],[fact_rp__inv__image__def])). 4.46/4.72 fof(c_0_9518, plain, ![X5314, X5315, X5316, X5317]:c_List_Opartition(X5317,X5316,hAPP(hAPP(c_List_Olist_OCons(X5317),X5315),X5314))=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5317),tc_List_Olist(X5317),tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317))),hAPP(hAPP(c_COMBS(tc_List_Olist(X5317),tc_fun(tc_List_Olist(X5317),tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317))),tc_fun(tc_List_Olist(X5317),tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5317),tc_fun(tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317)),tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317)))),tc_fun(tc_fun(tc_List_Olist(X5317),tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317))),tc_fun(tc_List_Olist(X5317),tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317)))),tc_List_Olist(X5317)),c_COMBS(tc_List_Olist(X5317),tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317)),tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5317),tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317))),tc_fun(tc_List_Olist(X5317),tc_fun(tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317)),tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317)))),tc_List_Olist(X5317)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317)),tc_fun(tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317)),tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317))),tc_List_Olist(X5317)),hAPP(c_If(tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317))),hAPP(X5316,X5315)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X5317),tc_fun(tc_List_Olist(X5317),tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317))),tc_List_Olist(X5317)),c_Product__Type_OPair(tc_List_Olist(X5317),tc_List_Olist(X5317))),hAPP(c_List_Olist_OCons(X5317),X5315))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5317),tc_fun(tc_List_Olist(X5317),tc_List_Olist(X5317)),tc_fun(tc_List_Olist(X5317),tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5317),tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317))),tc_fun(tc_fun(tc_List_Olist(X5317),tc_List_Olist(X5317)),tc_fun(tc_List_Olist(X5317),tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317)))),tc_List_Olist(X5317)),c_COMBB(tc_List_Olist(X5317),tc_prod(tc_List_Olist(X5317),tc_List_Olist(X5317)),tc_List_Olist(X5317))),c_Product__Type_OPair(tc_List_Olist(X5317),tc_List_Olist(X5317)))),hAPP(c_List_Olist_OCons(X5317),X5315)))),c_List_Opartition(X5317,X5316,X5314)), inference(variable_rename,[status(thm)],[fact_partition_Osimps_I2_J])). 4.46/4.72 cnf(c_0_9519, plain, (hAPP(c_Divides_Oadjust(X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X1)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)),X3)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5660, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.72 fof(c_0_9520, plain, ![X3263]:hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X3263)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3263), inference(variable_rename,[status(thm)],[fact_minus__int__def])). 4.46/4.72 cnf(c_0_9521, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X1,tc_List_Olist(X1)),tc_prod(X1,tc_List_Olist(X1))),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),c_Product__Type_Omap__pair(tc_prod(X1,tc_List_Olist(X1)),tc_List_Olist(X1),tc_prod(X1,tc_List_Olist(X1)),tc_List_Olist(X1),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)))),c_Wellfounded_Olex__prod(X1,tc_List_Olist(X1),X2,hAPP(c_List_Olexn(X1,X2),X3)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),hAPP(c_Nat_OSuc,X3))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),hAPP(c_Nat_OSuc,X3))))))=hAPP(c_List_Olexn(X1,X2),hAPP(c_Nat_OSuc,X3))), inference(split_conjunct,[status(thm)],[c_0_5661])). 4.46/4.72 cnf(c_0_9522, plain, (hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))=hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X1,X2)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X1,X2),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X1,X2)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(X1,X2)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(X1,X2),tc_fun(tc_Nat_Onat,tc_prod(X1,X2)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X1,X2)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X1,X2)),c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X2,tc_prod(X1,X2)),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_prod(X1,X2)),tc_Nat_Onat),c_Product__Type_OPair(X1,X2)),hAPP(c_List_Onth(X1),X3))),hAPP(c_List_Onth(X2),X4)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))))))), inference(split_conjunct,[status(thm)],[c_0_5662])). 4.46/4.72 cnf(c_0_9523, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),c_Nitpick_Oint__lcm(hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X3))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X1),tc_Int_Oint),c_Nitpick_Ofrac(X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X3))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X3)))))),c_COMBI(tc_Int_Oint)))=c_Nitpick_Oplus__frac(X1,X2,X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5663, c_0_5003]), c_0_5003]), c_0_5004]), c_0_5004]), c_0_5004]), c_0_5004])). 4.46/4.72 fof(c_0_9524, plain, ![X11550, X11551, X11552, X11553, X11554]:c_Map_Omap__upds(X11554,X11553,X11552,X11551,X11550)=hAPP(c_List_Ofoldl(tc_fun(X11554,tc_Option_Ooption(X11553)),tc_prod(X11554,X11553),hAPP(hAPP(c_COMBB(tc_fun(X11554,tc_fun(X11553,tc_fun(X11554,tc_Option_Ooption(X11553)))),tc_fun(tc_prod(X11554,X11553),tc_fun(X11554,tc_Option_Ooption(X11553))),tc_fun(X11554,tc_Option_Ooption(X11553))),c_Product__Type_Oprod_Oprod__case(X11554,X11553,tc_fun(X11554,tc_Option_Ooption(X11553)))),hAPP(hAPP(c_COMBC(tc_fun(X11554,tc_Option_Ooption(X11553)),tc_fun(X11553,tc_Option_Ooption(X11553)),tc_fun(X11554,tc_fun(X11553,tc_fun(X11554,tc_Option_Ooption(X11553))))),hAPP(hAPP(c_COMBB(tc_fun(X11554,tc_fun(tc_fun(X11553,tc_Option_Ooption(X11553)),tc_fun(X11553,tc_fun(X11554,tc_Option_Ooption(X11553))))),tc_fun(tc_fun(X11553,tc_Option_Ooption(X11553)),tc_fun(X11554,tc_fun(X11553,tc_fun(X11554,tc_Option_Ooption(X11553))))),tc_fun(X11554,tc_Option_Ooption(X11553))),c_COMBC(X11554,tc_fun(X11553,tc_Option_Ooption(X11553)),tc_fun(X11553,tc_fun(X11554,tc_Option_Ooption(X11553))))),hAPP(hAPP(c_COMBB(tc_fun(X11554,tc_fun(tc_Option_Ooption(X11553),tc_fun(X11554,tc_Option_Ooption(X11553)))),tc_fun(X11554,tc_fun(tc_fun(X11553,tc_Option_Ooption(X11553)),tc_fun(X11553,tc_fun(X11554,tc_Option_Ooption(X11553))))),tc_fun(X11554,tc_Option_Ooption(X11553))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X11553),tc_fun(X11554,tc_Option_Ooption(X11553))),tc_fun(tc_fun(X11553,tc_Option_Ooption(X11553)),tc_fun(X11553,tc_fun(X11554,tc_Option_Ooption(X11553)))),X11554),c_COMBB(tc_Option_Ooption(X11553),tc_fun(X11554,tc_Option_Ooption(X11553)),X11553))),c_Fun_Ofun__upd(X11554,tc_Option_Ooption(X11553))))),c_Option_Ooption_OSome(X11553))),X11552),hAPP(hAPP(c_List_Ozip(X11554,X11553),X11551),X11550)), inference(variable_rename,[status(thm)],[fact_map__upds__fold__map__upd])). 4.46/4.72 cnf(c_0_9525, plain, (c_Map_Omap__add(X1,X2,X3,hAPP(c_Map_Omap__of(X1,X2),X4))=c_List_Ofoldr(tc_prod(X1,X2),tc_fun(X1,tc_Option_Ooption(X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),X1),c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))),X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),X1),c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),X1,tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)))))),c_Option_Ooption_OSome(X2))),X4,X3)), inference(split_conjunct,[status(thm)],[c_0_5664])). 4.46/4.72 fof(c_0_9526, plain, ![X10524, X10525, X10526, X10527]:hAPP(hAPP(c_Product__Type_OSigma(X10527,X10526),X10525),X10524)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10527,tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool)),X10525),hAPP(hAPP(c_COMBS(X10527,tc_fun(X10526,tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool)),tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10526,tc_HOL_Obool),tc_fun(tc_fun(X10526,tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool)),tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool)),X10527),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10526,tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool))),X10524)),hAPP(hAPP(c_COMBC(X10527,tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool),tc_fun(X10526,tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10526,tc_fun(tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool),tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool),tc_fun(X10526,tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool))),X10527),c_COMBC(X10526,tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool),tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10526,tc_prod(X10527,X10526)),tc_fun(X10526,tc_fun(tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool),tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool))),X10527),hAPP(c_COMBB(tc_prod(X10527,X10526),tc_fun(tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool),tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool)),X10526),c_Set_Oinsert(tc_prod(X10527,X10526)))),c_Product__Type_OPair(X10527,X10526)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10527,X10526),tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_Sigma__def])). 4.46/4.72 cnf(c_0_9527, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,X1))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),X2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))))=c_Divides_Odivmod__int__rel(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5665])). 4.46/4.72 cnf(c_0_9528, plain, (hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X2,X2)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X2,X2),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X2,X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X2),tc_fun(X1,tc_prod(X2,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X2,X2)),tc_fun(tc_fun(X1,X2),tc_fun(X1,tc_prod(X2,X2))),X1),c_COMBB(X2,tc_prod(X2,X2),X1)),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_prod(X2,X2)),X1),c_Product__Type_OPair(X2,X2)),X3))),X3)))),X4)))=hAPP(hAPP(c_Relation_Oinv__image(X2,X1),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_5666])). 4.46/4.72 cnf(c_0_9529, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))))),X3)))),c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),X4),hAPP(c_List_Ofoldl(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1)),c_List_Oappend(tc_List_Olist(X1)),c_List_Olist_ONil(tc_List_Olist(X1))),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1)))))),X3)))))=c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5667, c_0_4736]), c_0_4736])). 4.46/4.72 cnf(c_0_9530, plain, (c_List_Omaps(tc_List_Olist(X1),X1,c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1)))),X2)=hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),c_List_Ohd(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X1)))),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5668, c_0_5669]), c_0_5670]), c_0_5580]), c_0_5671]), ['final']). 4.46/4.72 cnf(c_0_9531, plain, (c_List_Omaps(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1))))),X2)=hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Otl(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X1)))),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5672, c_0_5669]), c_0_5670]), c_0_5580]), c_0_5671]), ['final']). 4.46/4.72 cnf(c_0_9532, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X1,tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),hAPP(hAPP(c_COMBC(X1,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),X1),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X1),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),X1),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(X1),X3))=hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_5673])). 4.46/4.72 cnf(c_0_9533, plain, (c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X1,X2,X3,X4,X5)=hAPP(c_Option_Ooption_Ooption__case(X1,tc_prod(X2,tc_Lazy__Sequence_Olazy__sequence(X2)),X3,hAPP(c_Product__Type_Oprod_Oprod__case(X2,tc_Lazy__Sequence_Olazy__sequence(X2),X1),X4)),hAPP(c_Lazy__Sequence_Oyield(X2),X5))), inference(split_conjunct,[status(thm)],[c_0_5674]), ['final']). 4.46/4.72 fof(c_0_9534, plain, ![X7172, X7173, X7174, X7175, X7176, X7177, X7178, X7179]:hAPP(hAPP(c_Product__Type_OSigma(X7177,X7176),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7179,tc_fun(X7177,tc_HOL_Obool)),X7175),X7173)),hAPP(c_COMBK(tc_fun(X7176,tc_HOL_Obool),X7177),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7178,tc_fun(X7176,tc_HOL_Obool)),X7174),X7172)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X7179,X7178),tc_fun(tc_prod(X7177,X7176),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X7179,X7178),X7175),hAPP(c_COMBK(tc_fun(X7178,tc_HOL_Obool),X7179),X7174))),hAPP(c_Product__Type_Oprod_Oprod__case(X7179,X7178,tc_fun(tc_prod(X7177,X7176),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X7179,tc_fun(X7178,tc_fun(X7177,tc_fun(X7176,tc_HOL_Obool))),tc_fun(X7178,tc_fun(tc_prod(X7177,X7176),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7177,tc_fun(X7176,tc_HOL_Obool)),tc_fun(tc_prod(X7177,X7176),tc_HOL_Obool)),tc_fun(tc_fun(X7178,tc_fun(X7177,tc_fun(X7176,tc_HOL_Obool))),tc_fun(X7178,tc_fun(tc_prod(X7177,X7176),tc_HOL_Obool))),X7179),c_COMBB(tc_fun(X7177,tc_fun(X7176,tc_HOL_Obool)),tc_fun(tc_prod(X7177,X7176),tc_HOL_Obool),X7178)),hAPP(hAPP(c_COMBB(tc_fun(X7177,tc_HOL_Obool),tc_fun(tc_fun(X7177,tc_fun(X7176,tc_HOL_Obool)),tc_fun(tc_prod(X7177,X7176),tc_HOL_Obool)),X7179),c_Product__Type_OSigma(X7177,X7176)),X7173))),hAPP(hAPP(c_COMBB(tc_fun(X7176,tc_HOL_Obool),tc_fun(X7177,tc_fun(X7176,tc_HOL_Obool)),X7178),c_COMBK(tc_fun(X7176,tc_HOL_Obool),X7177)),X7172)))), inference(variable_rename,[status(thm)],[fact_UN__Times__distrib])). 4.46/4.72 fof(c_0_9535, plain, ![X10543, X10544, X10545, X10546, X10547]:hAPP(hAPP(c_List_Ozip(X10547,X10546),X10545),hAPP(hAPP(c_List_Olist_OCons(X10546),X10544),X10543))=hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X10547,X10546)),X10547,c_List_Olist_ONil(tc_prod(X10547,X10546)),hAPP(hAPP(c_COMBC(X10547,tc_fun(tc_List_Olist(X10547),tc_List_Olist(tc_prod(X10547,X10546))),tc_fun(tc_List_Olist(X10547),tc_List_Olist(tc_prod(X10547,X10546)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X10547,X10546)),tc_List_Olist(tc_prod(X10547,X10546))),tc_fun(tc_fun(tc_List_Olist(X10547),tc_List_Olist(tc_prod(X10547,X10546))),tc_fun(tc_List_Olist(X10547),tc_List_Olist(tc_prod(X10547,X10546)))),X10547),c_COMBB(tc_List_Olist(tc_prod(X10547,X10546)),tc_List_Olist(tc_prod(X10547,X10546)),tc_List_Olist(X10547))),hAPP(hAPP(c_COMBB(tc_prod(X10547,X10546),tc_fun(tc_List_Olist(tc_prod(X10547,X10546)),tc_List_Olist(tc_prod(X10547,X10546))),X10547),c_List_Olist_OCons(tc_prod(X10547,X10546))),hAPP(hAPP(c_COMBC(X10547,X10546,tc_prod(X10547,X10546)),c_Product__Type_OPair(X10547,X10546)),X10544)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10547),tc_List_Olist(X10546),tc_List_Olist(tc_prod(X10547,X10546))),c_List_Ozip(X10547,X10546)),X10543))),X10545), inference(variable_rename,[status(thm)],[fact_zip__Cons])). 4.46/4.72 cnf(c_0_9536, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X3),hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X3)),X4)))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X3),hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X3)),hAPP(c_List_Ofilter(tc_List_Olist(X3),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X3)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_List_Olist(X3),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X3)))),X4)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5675, c_0_4713]), c_0_4713])). 4.46/4.72 cnf(c_0_9537, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X1),X2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X3)))))=hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_5676])). 4.46/4.72 cnf(c_0_9538, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X1,X3,X4),X5))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X3,X4)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5)))))=hAPP(c_Nat_Onat_Onat__rec(X1,X3,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X5))), inference(rw,[status(thm)],[c_0_5677, c_0_4443])). 4.46/4.72 fof(c_0_9539, plain, ![X2501, X2502, X2503, X2504, X2505]:hAPP(hAPP(c_List_Ozip(X2505,X2504),hAPP(hAPP(c_List_Olist_OCons(X2505),X2503),X2502)),X2501)=hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X2505,X2504)),X2504,c_List_Olist_ONil(tc_prod(X2505,X2504)),hAPP(hAPP(c_COMBC(X2504,tc_fun(tc_List_Olist(X2504),tc_List_Olist(tc_prod(X2505,X2504))),tc_fun(tc_List_Olist(X2504),tc_List_Olist(tc_prod(X2505,X2504)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X2505,X2504)),tc_List_Olist(tc_prod(X2505,X2504))),tc_fun(tc_fun(tc_List_Olist(X2504),tc_List_Olist(tc_prod(X2505,X2504))),tc_fun(tc_List_Olist(X2504),tc_List_Olist(tc_prod(X2505,X2504)))),X2504),c_COMBB(tc_List_Olist(tc_prod(X2505,X2504)),tc_List_Olist(tc_prod(X2505,X2504)),tc_List_Olist(X2504))),hAPP(hAPP(c_COMBB(tc_prod(X2505,X2504),tc_fun(tc_List_Olist(tc_prod(X2505,X2504)),tc_List_Olist(tc_prod(X2505,X2504))),X2504),c_List_Olist_OCons(tc_prod(X2505,X2504))),hAPP(c_Product__Type_OPair(X2505,X2504),X2503)))),hAPP(c_List_Ozip(X2505,X2504),X2502))),X2501), inference(variable_rename,[status(thm)],[fact_zip__Cons1])). 4.46/4.72 cnf(c_0_9540, plain, (hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X2,X1)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X2,X1),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X2,X1)))),hAPP(c_COMBC(X2,X1,tc_prod(X2,X1)),c_Product__Type_OPair(X2,X1))))),X3)))=hAPP(c_Relation_Oconverse(X2,X1),X3)), inference(split_conjunct,[status(thm)],[c_0_5678])). 4.46/4.72 cnf(c_0_9541, plain, (hAPP(c_Set_OCollect(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2)),c_Set_OPow(X1)))))=hAPP(c_Set_OPow(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))), inference(split_conjunct,[status(thm)],[c_0_5679])). 4.46/4.72 fof(c_0_9542, plain, ![X4494, X4495, X4496, X4497, X4498, X4499, X4500, X4501]:hAPP(hAPP(c_List_Omap(tc_prod(X4501,X4496),X4499),hAPP(c_Product__Type_Oprod_Oprod__case(X4501,X4496,X4499),hAPP(hAPP(c_COMBB(tc_fun(X4496,tc_prod(X4501,X4500)),tc_fun(X4496,X4499),X4501),hAPP(c_COMBB(tc_prod(X4501,X4500),X4499,X4496),X4498)),hAPP(hAPP(c_COMBC(X4501,tc_fun(X4496,X4500),tc_fun(X4496,tc_prod(X4501,X4500))),hAPP(hAPP(c_COMBB(tc_fun(X4500,tc_prod(X4501,X4500)),tc_fun(tc_fun(X4496,X4500),tc_fun(X4496,tc_prod(X4501,X4500))),X4501),c_COMBB(X4500,tc_prod(X4501,X4500),X4496)),c_Product__Type_OPair(X4501,X4500))),X4495)))),hAPP(hAPP(c_List_Ozip(X4501,X4496),X4497),X4494))=hAPP(hAPP(c_List_Omap(tc_prod(X4501,X4500),X4499),X4498),hAPP(hAPP(c_List_Ozip(X4501,X4500),X4497),hAPP(hAPP(c_List_Omap(X4496,X4500),X4495),X4494))), inference(variable_rename,[status(thm)],[fact_map__zip__map2])). 4.46/4.72 cnf(c_0_9543, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5680, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9544, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X1),X2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))))=hAPP(c_List_Oset(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5681])). 4.46/4.72 cnf(c_0_9545, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X1,X3,X4,X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))))=c_Nat_Onat_Onat__case(X1,X3,X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X5))), inference(rw,[status(thm)],[c_0_5682, c_0_4443])). 4.46/4.72 cnf(c_0_9546, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)),hAPP(hAPP(c_List_Omap(X6,X2),X7),X8))=hAPP(hAPP(c_List_Omap(tc_prod(X3,X6),tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X6,tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X3,tc_fun(X6,X2),tc_fun(X6,tc_prod(X1,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(tc_fun(X6,X2),tc_fun(X6,tc_prod(X1,X2))),X3),c_COMBB(X2,tc_prod(X1,X2),X6)),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_prod(X1,X2)),X3),c_Product__Type_OPair(X1,X2)),X4))),X7))),hAPP(hAPP(c_List_Ozip(X3,X6),X5),X8))), inference(split_conjunct,[status(thm)],[c_0_5683])). 4.46/4.72 cnf(c_0_9547, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X3,X4)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X4),tc_fun(X2,tc_prod(X3,X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X3,X4)),tc_fun(tc_fun(X2,X4),tc_fun(X2,tc_prod(X3,X4))),X1),c_COMBB(X4,tc_prod(X3,X4),X2)),hAPP(hAPP(c_COMBB(X3,tc_fun(X4,tc_prod(X3,X4)),X1),c_Product__Type_OPair(X3,X4)),X5))),X6))=c_Product__Type_Omap__pair(X1,X3,X2,X4,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_5684]), ['final']). 4.46/4.72 cnf(c_0_9548, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5685, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9549, plain, (hAPP(hAPP(c_Nitpick_Ofrac(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2)),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2)),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X3)))=c_Nitpick_Otimes__frac(X1,X2,X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5686, c_0_5003]), c_0_5003]), c_0_5004]), c_0_5004])). 4.46/4.72 cnf(c_0_9550, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),X2))))), inference(rw,[status(thm)],[c_0_5687, c_0_4443])). 4.46/4.72 cnf(c_0_9551, plain, (c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))=hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X1,X1)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(tc_prod(X1,X1),tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_HOL_Obool)),tc_prod(X1,X1)),c_COMBB(tc_prod(X1,X1),tc_HOL_Obool,X1)),c_fequal)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1)))))), inference(rw,[status(thm)],[c_0_5688, c_0_5689])). 4.46/4.72 cnf(c_0_9552, plain, (hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),X2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X3),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X2,X3)),c_Int_Onat))))), inference(rw,[status(thm)],[c_0_5690, c_0_4443])). 4.46/4.72 fof(c_0_9553, plain, ![X3382, X3383, X3384, X3385, X3386, X3387, X3388]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3387,tc_fun(X3388,tc_HOL_Obool)),X3386),hAPP(hAPP(c_COMBB(tc_fun(X3384,tc_fun(X3388,tc_HOL_Obool)),tc_fun(X3388,tc_HOL_Obool),X3387),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3384,tc_fun(X3388,tc_HOL_Obool)),X3383)),hAPP(hAPP(c_COMBC(X3387,tc_fun(X3384,tc_fun(X3388,tc_HOL_Obool)),tc_fun(X3384,tc_fun(X3388,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3388,tc_HOL_Obool),tc_fun(X3388,tc_HOL_Obool)),tc_fun(tc_fun(X3384,tc_fun(X3388,tc_HOL_Obool)),tc_fun(X3384,tc_fun(X3388,tc_HOL_Obool))),X3387),c_COMBB(tc_fun(X3388,tc_HOL_Obool),tc_fun(X3388,tc_HOL_Obool),X3384)),hAPP(hAPP(c_COMBB(tc_fun(X3388,tc_HOL_Obool),tc_fun(tc_fun(X3388,tc_HOL_Obool),tc_fun(X3388,tc_HOL_Obool)),X3387),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3388,tc_HOL_Obool))),X3385))),X3382)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3388,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3387,tc_fun(X3388,tc_HOL_Obool)),X3386),X3385)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3384,tc_fun(X3388,tc_HOL_Obool)),X3383),X3382)), inference(variable_rename,[status(thm)],[fact_Int__UN__distrib2])). 4.46/4.72 fof(c_0_9554, plain, ![X6731, X6732, X6733, X6734, X6735, X6736, X6737]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6737,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6736,tc_fun(X6737,tc_HOL_Obool)),X6735),X6734)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6733,tc_fun(X6737,tc_HOL_Obool)),X6732),X6731))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6736,tc_fun(X6737,tc_HOL_Obool)),X6735),hAPP(hAPP(c_COMBB(tc_fun(X6733,tc_fun(X6737,tc_HOL_Obool)),tc_fun(X6737,tc_HOL_Obool),X6736),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6733,tc_fun(X6737,tc_HOL_Obool)),X6732)),hAPP(hAPP(c_COMBC(X6736,tc_fun(X6733,tc_fun(X6737,tc_HOL_Obool)),tc_fun(X6733,tc_fun(X6737,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X6737,tc_HOL_Obool),tc_fun(X6737,tc_HOL_Obool)),tc_fun(tc_fun(X6733,tc_fun(X6737,tc_HOL_Obool)),tc_fun(X6733,tc_fun(X6737,tc_HOL_Obool))),X6736),c_COMBB(tc_fun(X6737,tc_HOL_Obool),tc_fun(X6737,tc_HOL_Obool),X6733)),hAPP(hAPP(c_COMBB(tc_fun(X6737,tc_HOL_Obool),tc_fun(tc_fun(X6737,tc_HOL_Obool),tc_fun(X6737,tc_HOL_Obool)),X6736),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6737,tc_HOL_Obool))),X6734))),X6731))), inference(variable_rename,[status(thm)],[fact_Un__INT__distrib2])). 4.46/4.72 cnf(c_0_9555, plain, (c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))))=hAPP(c_Int_Onat,X1)), inference(split_conjunct,[status(thm)],[c_0_5691])). 4.46/4.72 cnf(c_0_9556, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),X2))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))), inference(rw,[status(thm)],[c_0_5692, c_0_4443])). 4.46/4.72 cnf(c_0_9557, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1)),c_List_Oappend(tc_List_Olist(X1)),c_List_Olist_ONil(tc_List_Olist(X1))),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),tc_List_Olist(X1)),c_List_Omap(X1,tc_List_Olist(X1))),hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)))),X2)),c_Enum_On__lists(X1,X3,X2)))=c_Enum_On__lists(X1,hAPP(c_Nat_OSuc,X3),X2)), inference(rw,[status(thm)],[c_0_5693, c_0_4736])). 4.46/4.72 cnf(c_0_9558, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5694, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.72 fof(c_0_9559, plain, ![X443, X444, X445, X446, X447]:hAPP(c_Map_Omap__of(X447,X446),hAPP(hAPP(c_List_Omap(tc_prod(X447,X445),tc_prod(X447,X446)),hAPP(c_Product__Type_Oprod_Oprod__case(X447,X445,tc_prod(X447,X446)),hAPP(hAPP(c_COMBC(X447,tc_fun(X445,X446),tc_fun(X445,tc_prod(X447,X446))),hAPP(hAPP(c_COMBB(tc_fun(X446,tc_prod(X447,X446)),tc_fun(tc_fun(X445,X446),tc_fun(X445,tc_prod(X447,X446))),X447),c_COMBB(X446,tc_prod(X447,X446),X445)),c_Product__Type_OPair(X447,X446))),X444))),X443))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X445),tc_Option_Ooption(X446),X447,hAPP(c_Option_Omap(X445,X446),X444)),hAPP(c_Map_Omap__of(X447,X445),X443)), inference(variable_rename,[status(thm)],[fact_map__of__map])). 4.46/4.72 cnf(c_0_9560, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))=hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_5695])). 4.46/4.72 fof(c_0_9561, plain, ![X3637, X3638, X3639, X3640, X3641, X3642]:hAPP(hAPP(c_List_Omap(tc_prod(X3642,X3639),tc_prod(X3642,X3641)),hAPP(c_Product__Type_Oprod_Oprod__case(X3642,X3639,tc_prod(X3642,X3641)),hAPP(hAPP(c_COMBC(X3642,tc_fun(X3639,X3641),tc_fun(X3639,tc_prod(X3642,X3641))),hAPP(hAPP(c_COMBB(tc_fun(X3641,tc_prod(X3642,X3641)),tc_fun(tc_fun(X3639,X3641),tc_fun(X3639,tc_prod(X3642,X3641))),X3642),c_COMBB(X3641,tc_prod(X3642,X3641),X3639)),c_Product__Type_OPair(X3642,X3641))),X3638))),hAPP(hAPP(c_List_Ozip(X3642,X3639),X3640),X3637))=hAPP(hAPP(c_List_Ozip(X3642,X3641),X3640),hAPP(hAPP(c_List_Omap(X3639,X3641),X3638),X3637)), inference(variable_rename,[status(thm)],[fact_zip__map2])). 4.46/4.72 cnf(c_0_9562, plain, (hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X2,X3))=hAPP(c_Set_OCollect(tc_List_Olist(X1)),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X2))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),c_List_Oset(X1))),hAPP(c_List_Oset(X1),X3))))), inference(split_conjunct,[status(thm)],[c_0_5696])). 4.46/4.72 cnf(c_0_9563, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X1),c_Set_Oinsert(tc_prod(X1,X1))),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))=c_Relation_OId__on(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5697])). 4.46/4.72 cnf(c_0_9564, plain, (hAPP(c_Set_Oimage(X1,X2,X3),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Set_Oinsert(X2)),X3)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5698]), ['final']). 4.46/4.72 fof(c_0_9565, plain, ![X2409, X2410, X2411, X2412, X2413, X2414, X2415]:c_New__DSequence_Oneg__bind(X2415,X2414,hAPP(hAPP(hAPP(X2413,X2411),X2410),X2409),hAPP(hAPP(c_COMBC(X2415,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2414)))),hAPP(hAPP(c_COMBC(X2415,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2414))))),hAPP(hAPP(c_COMBC(X2415,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2414)))))),X2412),X2411)),X2410)),X2409))=hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X2415,X2414,X2413,X2412),X2411),X2410),X2409), inference(variable_rename,[status(thm)],[fact_neg__bind__def])). 4.46/4.72 cnf(c_0_9566, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1)),c_Int_Onat))))), inference(rw,[status(thm)],[c_0_5699, c_0_4443])). 4.46/4.72 cnf(c_0_9567, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X2)),c_Int_Onat))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))), inference(rw,[status(thm)],[c_0_5700, c_0_4443])). 4.46/4.72 cnf(c_0_9568, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X1,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X2)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))))=c_List_Osublist(X1,X3,X2)), inference(rw,[status(thm)],[c_0_5701, c_0_4517])). 4.46/4.72 cnf(c_0_9569, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool))))=c_FunDef_Omin__weak), inference(split_conjunct,[status(thm)],[fact_min__weak__def])). 4.46/4.72 cnf(c_0_9570, plain, (c_FunDef_Omax__weak=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[fact_max__weak__def])). 4.46/4.72 fof(c_0_9571, plain, ![X1627, X1628, X1629]:c_Enum_Osublists(X1629,hAPP(hAPP(c_List_Olist_OCons(X1629),X1628),X1627))=hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(X1629)),tc_List_Olist(tc_List_Olist(X1629))),c_Enum_Osublists(X1629,X1627)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(X1629)),tc_List_Olist(tc_List_Olist(X1629)),tc_List_Olist(tc_List_Olist(X1629))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(X1629)),tc_fun(tc_List_Olist(tc_List_Olist(X1629)),tc_List_Olist(tc_List_Olist(X1629))),tc_List_Olist(tc_List_Olist(X1629))),c_List_Oappend(tc_List_Olist(X1629))),hAPP(c_List_Omap(tc_List_Olist(X1629),tc_List_Olist(X1629)),hAPP(c_List_Olist_OCons(X1629),X1628)))),c_COMBI(tc_List_Olist(tc_List_Olist(X1629))))), inference(variable_rename,[status(thm)],[fact_sublists_Osimps_I2_J])). 4.46/4.72 fof(c_0_9572, plain, ![X3212, X3213, X3214, X3215, X3216, X3217, X3218]:c_New__Random__Sequence_Oneg__decr__bind(X3218,X3217,X3216,X3215,X3214,X3213,X3212)=c_New__DSequence_Oneg__decr__bind(X3218,X3217,hAPP(hAPP(hAPP(X3216,X3214),X3213),X3212),hAPP(hAPP(c_COMBC(X3218,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X3217)))),hAPP(hAPP(c_COMBC(X3218,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X3217))))),hAPP(hAPP(c_COMBC(X3218,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X3217)))))),X3215),X3214)),X3213)),X3212)), inference(variable_rename,[status(thm)],[fact_New__Random__Sequence_Oneg__decr__bind__def])). 4.46/4.72 fof(c_0_9573, plain, ![X6935, X6936, X6937, X6938, X6939, X6940, X6941, X6942]:hAPP(hAPP(c_List_Omap(tc_prod(X6942,X6941),X6940),X6939),hAPP(hAPP(c_List_Ozip(X6942,X6941),hAPP(hAPP(c_List_Omap(X6938,X6942),X6937),X6936)),X6935))=hAPP(hAPP(c_List_Omap(tc_prod(X6938,X6941),X6940),hAPP(c_Product__Type_Oprod_Oprod__case(X6938,X6941,X6940),hAPP(hAPP(c_COMBB(tc_fun(X6941,tc_prod(X6942,X6941)),tc_fun(X6941,X6940),X6938),hAPP(c_COMBB(tc_prod(X6942,X6941),X6940,X6941),X6939)),hAPP(hAPP(c_COMBB(X6942,tc_fun(X6941,tc_prod(X6942,X6941)),X6938),c_Product__Type_OPair(X6942,X6941)),X6937)))),hAPP(hAPP(c_List_Ozip(X6938,X6941),X6936),X6935)), inference(variable_rename,[status(thm)],[fact_map__zip__map])). 4.46/4.72 cnf(c_0_9574, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5702, c_0_4471]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9575, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OAll(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fimplies),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X1,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X2,tc_fun(X1,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2)),c_member(X1))),X4))))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_5703])). 4.46/4.72 cnf(c_0_9576, plain, (c_Map_Odom(X1,X2,c_Fun_Ooverride__on(X1,tc_Option_Ooption(X2),X3,X4,X5))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),c_Map_Odom(X1,X2,X4)))))),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),c_Map_Odom(X1,X2,X4)))))), inference(split_conjunct,[status(thm)],[c_0_5704])). 4.46/4.72 fof(c_0_9577, plain, ![X10725, X10726, X10727, X10728]:c_Lazy__Sequence_Oproduct(X10728,X10727,X10726,X10725)=hAPP(c_Lazy__Sequence_Obind(X10728,tc_prod(X10728,X10727),X10726),hAPP(hAPP(c_COMBB(tc_fun(X10727,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X10728,X10727))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X10728,X10727)),X10728),c_Lazy__Sequence_Obind(X10727,tc_prod(X10728,X10727),X10725)),hAPP(hAPP(c_COMBB(tc_fun(X10727,tc_prod(X10728,X10727)),tc_fun(X10727,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X10728,X10727))),X10728),hAPP(c_COMBB(tc_prod(X10728,X10727),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X10728,X10727)),X10727),c_Lazy__Sequence_Osingle(tc_prod(X10728,X10727)))),c_Product__Type_OPair(X10728,X10727)))), inference(variable_rename,[status(thm)],[fact__02])). 4.46/4.72 fof(c_0_9578, plain, ![X1184, X1185, X1186, X1187, X1188, X1189, X1190]:c_New__DSequence_Opos__bind(X1190,X1189,hAPP(hAPP(hAPP(X1188,X1186),X1185),X1184),hAPP(hAPP(c_COMBC(X1190,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X1189))),hAPP(hAPP(c_COMBC(X1190,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X1189)))),hAPP(hAPP(c_COMBC(X1190,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X1189))))),X1187),X1186)),X1185)),X1184))=hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X1190,X1189,X1188,X1187),X1186),X1185),X1184), inference(variable_rename,[status(thm)],[fact_pos__bind__def])). 4.46/4.72 fof(c_0_9579, plain, ![X3106, X3107, X3108, X3109, X3110, X3111, X3112]:c_New__DSequence_Opos__decr__bind(X3112,X3111,hAPP(hAPP(hAPP(X3110,X3108),X3107),X3106),hAPP(hAPP(c_COMBC(X3112,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X3111))),hAPP(hAPP(c_COMBC(X3112,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X3111)))),hAPP(hAPP(c_COMBC(X3112,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X3111))))),X3109),X3108)),X3107)),X3106))=c_New__Random__Sequence_Opos__decr__bind(X3112,X3111,X3110,X3109,X3108,X3107,X3106), inference(variable_rename,[status(thm)],[fact_New__Random__Sequence_Opos__decr__bind__def])). 4.46/4.72 fof(c_0_9580, plain, ![X12895, X12896, X12897, X12898, X12899, X12900]:hAPP(hAPP(c_Product__Type_OSigma(X12900,X12899),hAPP(hAPP(c_Set_Oinsert(X12900),X12898),X12897)),hAPP(c_COMBK(tc_fun(X12899,tc_HOL_Obool),X12900),hAPP(hAPP(c_Set_Oinsert(X12899),X12896),X12895)))=hAPP(hAPP(c_Set_Oinsert(tc_prod(X12900,X12899)),hAPP(hAPP(c_Product__Type_OPair(X12900,X12899),X12898),X12896)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X12900,X12899),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X12900,X12899),X12897),hAPP(c_COMBK(tc_fun(X12899,tc_HOL_Obool),X12900),hAPP(hAPP(c_Set_Oinsert(X12899),X12896),X12895)))),hAPP(hAPP(c_Product__Type_OSigma(X12900,X12899),hAPP(hAPP(c_Set_Oinsert(X12900),X12898),X12897)),hAPP(c_COMBK(tc_fun(X12899,tc_HOL_Obool),X12900),X12895)))), inference(variable_rename,[status(thm)],[fact_insert__times__insert])). 4.46/4.72 fof(c_0_9581, plain, ![X4038, X4039]:c_Fun_Oinj__on(tc_fun(X4039,X4038),tc_fun(tc_prod(X4039,X4038),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X4039,X4038),tc_HOL_Obool),tc_fun(tc_prod(X4039,X4038),tc_HOL_Obool),tc_fun(X4039,X4038)),c_Set_OCollect(tc_prod(X4039,X4038))),hAPP(hAPP(c_COMBB(tc_fun(X4039,tc_fun(X4038,tc_HOL_Obool)),tc_fun(tc_prod(X4039,X4038),tc_HOL_Obool),tc_fun(X4039,X4038)),c_Product__Type_Oprod_Oprod__case(X4039,X4038,tc_HOL_Obool)),hAPP(c_COMBB(X4038,tc_fun(X4038,tc_HOL_Obool),X4039),hAPP(c_COMBC(X4038,X4038,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X4039,X4038),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_inj__graph])). 4.46/4.72 fof(c_0_9582, plain, ![X7079, X7080, X7081, X7082, X7083, X7084, X7085]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7082,tc_fun(tc_prod(X7085,X7083),tc_HOL_Obool)),X7081),hAPP(hAPP(c_COMBC(X7082,tc_fun(tc_prod(X7084,X7083),tc_HOL_Obool),tc_fun(tc_prod(X7085,X7083),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X7085,X7084),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X7084,X7083),tc_HOL_Obool),tc_fun(tc_prod(X7085,X7083),tc_HOL_Obool)),X7082),c_Relation_Orel__comp(X7085,X7084,X7083)),X7080)),X7079))=hAPP(hAPP(c_Relation_Orel__comp(X7085,X7084,X7083),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7082,tc_fun(tc_prod(X7085,X7084),tc_HOL_Obool)),X7081),X7080)),X7079), inference(variable_rename,[status(thm)],[fact_rel__comp__UNION__distrib2])). 4.46/4.72 fof(c_0_9583, plain, ![X3345, X3346]:c_Random_Oselect__weight(X3346,X3345)=hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X3346,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X3346),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X3346)),X3345)))),hAPP(hAPP(c_COMBB(X3346,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X3346,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X3346,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X3346,X3345))), inference(variable_rename,[status(thm)],[fact_select__weight__def])). 4.46/4.72 fof(c_0_9584, plain, ![X16212, X16213, X16214, X16215, X16216]:c_List_Omap__filter(X16216,X16215,hAPP(hAPP(c_COMBC(X16216,tc_Option_Ooption(X16215),tc_Option_Ooption(X16215)),hAPP(hAPP(c_COMBS(X16216,tc_Option_Ooption(X16215),tc_fun(tc_Option_Ooption(X16215),tc_Option_Ooption(X16215))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X16215),tc_fun(tc_Option_Ooption(X16215),tc_Option_Ooption(X16215))),X16216),c_If(tc_Option_Ooption(X16215))),X16213)),hAPP(hAPP(c_COMBB(X16215,tc_Option_Ooption(X16215),X16216),c_Option_Ooption_OSome(X16215)),X16214))),c_Option_Ooption_ONone(X16215)),X16212)=hAPP(hAPP(c_List_Omap(X16216,X16215),X16214),hAPP(c_List_Ofilter(X16216,X16213),X16212)), inference(variable_rename,[status(thm)],[fact_map__filter__map__filter])). 4.46/4.72 cnf(c_0_9585, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X1)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))),c_List_Olist_ONil(X1))),c_List_Osublist(X1,X4,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X2))))=c_List_Osublist(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4),X2)), inference(split_conjunct,[status(thm)],[c_0_5705])). 4.46/4.72 cnf(c_0_9586, plain, (c_List_Olenlex(X1,X2)=hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X1)),tc_List_Olist(X1)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X1),c_Wellfounded_Oless__than,c_List_Olex(X1,X2))),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_List_Olist(X1),tc_prod(tc_Nat_Onat,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X1),tc_prod(tc_Nat_Onat,tc_List_Olist(X1))),tc_List_Olist(X1)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X1))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_COMBI(tc_List_Olist(X1))))), inference(split_conjunct,[status(thm)],[c_0_5706])). 4.46/4.72 cnf(c_0_9587, plain, (c_Wellfounded_Omlex__prod(X1,X2,X3)=hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X1),X1),c_Wellfounded_Olex__prod(tc_Nat_Onat,X1,c_Wellfounded_Oless__than,X3)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(tc_Nat_Onat,X1)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,tc_prod(tc_Nat_Onat,X1)),X1),c_Product__Type_OPair(tc_Nat_Onat,X1)),X2)),c_COMBI(X1)))), inference(split_conjunct,[status(thm)],[c_0_5707]), ['final']). 4.46/4.72 cnf(c_0_9588, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),X2)=hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X1,tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),X1),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(c_Lazy__Sequence_Oyield(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5708])). 4.46/4.72 cnf(c_0_9589, plain, (c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X1))),c_List_Olists(X1,X2))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X1))),c_List_Olists(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_5709])). 4.46/4.72 fof(c_0_9590, plain, ![X16472, X16473]:c_List_Omeasures(X16473,X16472)=hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),X16473),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(X16473,tc_List_Olist(tc_fun(X16473,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X16473,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(X16473,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),X16473),c_List_Omap(tc_fun(X16473,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(X16473,tc_Nat_Onat),X16473,tc_Nat_Onat),c_COMBI(tc_fun(X16473,tc_Nat_Onat))))),X16472)), inference(variable_rename,[status(thm)],[fact_measures__def])). 4.46/4.72 cnf(c_0_9591, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))),c_Int_OMin)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5710, c_0_4470]), c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9592, plain, (hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X1),X2)),c_Code__Numeral_Onat__of)))=c_Random_Oselect(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5711])). 4.46/4.72 cnf(c_0_9593, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))),c_Int_OMin)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5712, c_0_4470]), c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9594, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5713, c_0_4760]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), c_0_4784]), ['final']). 4.46/4.72 cnf(c_0_9595, plain, (hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OAll(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fimplies),X2))),c_member(X1)))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5715, c_0_4945]), c_0_4531])). 4.46/4.72 cnf(c_0_9596, plain, (c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X3),c_Int_Onat)))), inference(rw,[status(thm)],[c_0_5716, c_0_4443])). 4.46/4.72 cnf(c_0_9597, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))=hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_5717])). 4.46/4.72 cnf(c_0_9598, plain, (c_List_Osublist(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3),X4)=hAPP(hAPP(c_List_Oappend(X1),c_List_Osublist(X1,X2,X4)),c_List_Osublist(X1,X3,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),X4))))), inference(split_conjunct,[status(thm)],[c_0_5718])). 4.46/4.72 cnf(c_0_9599, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5719, c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9600, plain, (hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X1),c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),c_Relation_OImage(X1,X1,X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5720])). 4.46/4.72 cnf(c_0_9601, plain, (X1=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5721, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9602, plain, (hAPP(c_Set_Ovimage(X1,tc_prod(X2,X3),X4),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X5),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X6)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,hAPP(c_Fun_Ocomp(tc_prod(X2,X3),X2,X1,c_Product__Type_Ofst(X2,X3)),X4)),X5)),hAPP(c_Set_Ovimage(X1,X3,hAPP(c_Fun_Ocomp(tc_prod(X2,X3),X3,X1,c_Product__Type_Osnd(X2,X3)),X4)),X6))), inference(split_conjunct,[status(thm)],[c_0_5722])). 4.46/4.72 cnf(c_0_9603, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5723, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9604, plain, (hAPP(c_Set_OCollect(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X1))))=c_Wellfounded_Ofinite__psubset(X1)), inference(split_conjunct,[status(thm)],[c_0_5724])). 4.46/4.72 cnf(c_0_9605, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5725, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9606, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5726, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9607, plain, (c_List_Omap__filter(X1,X2,X3,X4)=hAPP(hAPP(c_List_Omap(X1,X2),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2)),X3)),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3)),c_Option_Ooption_ONone(X2)))),X4))), inference(split_conjunct,[status(thm)],[c_0_5727])). 4.46/4.72 cnf(c_0_9608, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3)),c_Option_Ooption_ONone(X2)))=c_Map_Odom(X1,X2,X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5728, c_0_5671]), c_0_4531]), ['final']). 4.46/4.72 fof(c_0_9609, plain, ![X10191, X10192, X10193, X10194, X10195, X10196]:hAPP(hAPP(c_List_Omap(tc_prod(X10194,X10195),tc_prod(X10196,X10195)),hAPP(c_Product__Type_Oprod_Oprod__case(X10194,X10195,tc_prod(X10196,X10195)),hAPP(hAPP(c_COMBB(X10196,tc_fun(X10195,tc_prod(X10196,X10195)),X10194),c_Product__Type_OPair(X10196,X10195)),X10193))),hAPP(hAPP(c_List_Ozip(X10194,X10195),X10192),X10191))=hAPP(hAPP(c_List_Ozip(X10196,X10195),hAPP(hAPP(c_List_Omap(X10194,X10196),X10193),X10192)),X10191), inference(variable_rename,[status(thm)],[fact_zip__map1])). 4.46/4.72 fof(c_0_9610, plain, ![X1321, X1322, X1323, X1324]:hAPP(c_Set_Oimage(tc_prod(X1324,X1323),tc_prod(X1323,X1324),hAPP(c_Product__Type_Oprod_Oprod__case(X1324,X1323,tc_prod(X1323,X1324)),hAPP(c_COMBC(X1323,X1324,tc_prod(X1323,X1324)),c_Product__Type_OPair(X1323,X1324)))),hAPP(hAPP(c_Product__Type_OSigma(X1324,X1323),X1322),hAPP(c_COMBK(tc_fun(X1323,tc_HOL_Obool),X1324),X1321)))=hAPP(hAPP(c_Product__Type_OSigma(X1323,X1324),X1321),hAPP(c_COMBK(tc_fun(X1324,tc_HOL_Obool),X1323),X1322)), inference(variable_rename,[status(thm)],[fact_swap__product])). 4.46/4.72 cnf(c_0_9611, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)=hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),hAPP(hAPP(c_List_Omap(X1,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X2),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_List_Olist(X2),tc_List_Olist(X2)),X1),c_List_Olist_OCons(X2)),X3)),c_List_Olist_ONil(X2))),X4))), inference(rw,[status(thm)],[c_0_5729, c_0_4736])). 4.46/4.72 cnf(c_0_9612, plain, (hAPP(c_New__DSequence_Opos__not__seq(X1),X2)=c_Lazy__Sequence_Ohb__not__seq(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5730, c_0_4471]), c_0_4471])). 4.46/4.72 fof(c_0_9613, plain, ![X9794, X9795]:hAPP(c_List_Olist_Olist__case(tc_List_Olist(X9795),X9795,c_List_Olist_ONil(X9795),hAPP(hAPP(c_COMBB(tc_List_Olist(X9795),tc_fun(tc_List_Olist(X9795),tc_List_Olist(X9795)),X9795),hAPP(c_COMBC(tc_List_Olist(X9795),tc_List_Olist(X9795),tc_List_Olist(X9795)),c_List_Oappend(X9795))),hAPP(hAPP(c_COMBC(X9795,tc_List_Olist(X9795),tc_List_Olist(X9795)),c_List_Olist_OCons(X9795)),c_List_Olist_ONil(X9795)))),X9794)=hAPP(c_List_Orotate1(X9795),X9794), inference(variable_rename,[status(thm)],[fact_rotate1__def])). 4.46/4.72 fof(c_0_9614, plain, ![X12850, X12851, X12852, X12853, X12854]:hAPP(hAPP(c_List_Ozip(X12854,X12853),X12852),hAPP(hAPP(c_List_Oappend(X12853),X12851),X12850))=hAPP(hAPP(c_List_Oappend(tc_prod(X12854,X12853)),hAPP(hAPP(c_List_Ozip(X12854,X12853),hAPP(hAPP(c_List_Otake(X12854),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12853)),X12851)),X12852)),X12851)),hAPP(hAPP(c_List_Ozip(X12854,X12853),hAPP(hAPP(c_List_Odrop(X12854),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12853)),X12851)),X12852)),X12850)), inference(variable_rename,[status(thm)],[fact_zip__append2])). 4.46/4.72 fof(c_0_9615, plain, ![X8967, X8968, X8969, X8970, X8971]:hAPP(hAPP(c_List_Oappend(tc_prod(X8971,X8970)),hAPP(hAPP(c_List_Ozip(X8971,X8970),X8969),hAPP(hAPP(c_List_Otake(X8970),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8971)),X8969)),X8967))),hAPP(hAPP(c_List_Ozip(X8971,X8970),X8968),hAPP(hAPP(c_List_Odrop(X8970),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8971)),X8969)),X8967)))=hAPP(hAPP(c_List_Ozip(X8971,X8970),hAPP(hAPP(c_List_Oappend(X8971),X8969),X8968)),X8967), inference(variable_rename,[status(thm)],[fact_zip__append1])). 4.46/4.72 fof(c_0_9616, plain, ![X12070, X12071, X12072, X12073, X12074, X12075, X12076, X12077]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X12077,X12076,X12075),X12074),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X12073,X12072,tc_prod(X12077,X12076)),X12071),X12070))=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X12073,X12072,X12075),hAPP(hAPP(c_COMBB(tc_fun(X12072,tc_prod(X12077,X12076)),tc_fun(X12072,X12075),X12073),hAPP(c_COMBB(tc_prod(X12077,X12076),X12075,X12072),hAPP(c_Product__Type_Oprod_Oprod__case(X12077,X12076,X12075),X12074))),X12071)),X12070), inference(variable_rename,[status(thm)],[fact_split__twice])). 4.46/4.72 cnf(c_0_9617, plain, (hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))))=c_List_Oset__Cons(X1,hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_5731])). 4.46/4.72 cnf(c_0_9618, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))=c_Int_Oint__ge__less__than(X1)), inference(rw,[status(thm)],[c_0_5732, c_0_4531])). 4.46/4.72 cnf(c_0_9619, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X3))),X4))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5733, c_0_4531]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_9620, plain, (hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5734, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834])). 4.46/4.72 fof(c_0_9621, plain, ![X2180, X2181, X2182, X2183, X2184, X2185]:hAPP(c_Product__Type_Oprod_Oprod__case(X2185,X2184,X2183),hAPP(hAPP(c_COMBB(X2182,tc_fun(X2184,X2183),X2185),X2181),X2180))=hAPP(hAPP(c_COMBS(tc_prod(X2185,X2184),X2184,X2183),hAPP(hAPP(c_COMBB(X2182,tc_fun(X2184,X2183),tc_prod(X2185,X2184)),X2181),hAPP(hAPP(c_COMBB(X2185,X2182,tc_prod(X2185,X2184)),X2180),c_Product__Type_Ofst(X2185,X2184)))),c_Product__Type_Osnd(X2185,X2184)), inference(variable_rename,[status(thm)],[fact_split__comp__eq])). 4.46/4.72 cnf(c_0_9622, plain, (c_HOL_OThe(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(c_fequal,X3)))),hAPP(c_fequal,X4))))=hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_5735])). 4.46/4.72 cnf(c_0_9623, plain, (c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(c_fequal,X3)))),hAPP(c_fequal,X4))))=hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_5736])). 4.46/4.72 cnf(c_0_9624, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))),c_Int_OMin)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5737, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9625, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat),X3),hAPP(c_List_Onth(X1),X2)))))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5738])). 4.46/4.72 cnf(c_0_9626, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X2))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2)), inference(split_conjunct,[status(thm)],[c_0_5739])). 4.46/4.72 cnf(c_0_9627, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X3,tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool))),X5)),X6))), inference(split_conjunct,[status(thm)],[c_0_5740]), ['final']). 4.46/4.72 cnf(c_0_9628, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_5741])). 4.46/4.72 cnf(c_0_9629, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)), inference(split_conjunct,[status(thm)],[c_0_5742]), ['final']). 4.46/4.72 fof(c_0_9630, plain, ![X13278, X13279, X13280, X13281, X13282, X13283, X13284]:hAPP(c_List_Ofoldl(X13284,X13283,X13282,X13281),hAPP(hAPP(c_List_Omap(X13280,X13283),X13279),X13278))=hAPP(c_List_Ofoldl(X13284,X13280,hAPP(hAPP(c_COMBC(X13284,tc_fun(X13280,X13283),tc_fun(X13280,X13284)),hAPP(hAPP(c_COMBB(tc_fun(X13283,X13284),tc_fun(tc_fun(X13280,X13283),tc_fun(X13280,X13284)),X13284),c_COMBB(X13283,X13284,X13280)),X13282)),X13279),X13281),X13278), inference(variable_rename,[status(thm)],[fact_foldl__map])). 4.46/4.72 cnf(c_0_9631, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3))),X3))), inference(split_conjunct,[status(thm)],[c_0_5743])). 4.46/4.72 cnf(c_0_9632, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))),X3))), inference(split_conjunct,[status(thm)],[c_0_5744])). 4.46/4.72 cnf(c_0_9633, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5745, c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9634, plain, (c_Nitpick_OAbs__Frac(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2))),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2)))=c_Nitpick_Ouminus__frac(X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5746, c_0_5003]), c_0_5004])). 4.46/4.72 fof(c_0_9635, plain, ![X6495, X6496, X6497, X6498, X6499, X6500]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6497,tc_fun(X6499,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6500,tc_fun(X6497,tc_HOL_Obool)),X6498),X6496)),X6495)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6500,tc_fun(X6499,tc_HOL_Obool)),X6498),hAPP(hAPP(c_COMBC(X6500,tc_fun(X6497,tc_fun(X6499,tc_HOL_Obool)),tc_fun(X6499,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6497,tc_HOL_Obool),tc_fun(tc_fun(X6497,tc_fun(X6499,tc_HOL_Obool)),tc_fun(X6499,tc_HOL_Obool)),X6500),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6497,tc_fun(X6499,tc_HOL_Obool))),X6496)),X6495)), inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I9_J])). 4.46/4.72 cnf(c_0_9636, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5747, c_0_5689]), c_0_5266])). 4.46/4.72 cnf(c_0_9637, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))), inference(rw,[status(thm)],[c_0_5748, c_0_5689]), ['final']). 4.46/4.72 cnf(c_0_9638, plain, (c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5749, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9639, plain, (hAPP(c_List_Orev(X1),hAPP(c_List_Orotate(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),X2))=hAPP(c_List_Orotate(X1,X3),hAPP(c_List_Orev(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5750])). 4.46/4.72 fof(c_0_9640, plain, ![X12858, X12859, X12860, X12861, X12862]:hAPP(hAPP(c_List_Olist__update(X12862,hAPP(hAPP(c_List_Olist_OCons(X12862),X12861),X12860)),X12859),X12858)=c_Nat_Onat_Onat__case(tc_List_Olist(X12862),hAPP(hAPP(c_List_Olist_OCons(X12862),X12858),X12860),hAPP(hAPP(c_COMBB(tc_List_Olist(X12862),tc_List_Olist(X12862),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X12862),X12861)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X12862,tc_List_Olist(X12862)),c_List_Olist__update(X12862,X12860)),X12858)),X12859), inference(variable_rename,[status(thm)],[fact_list__update_Osimps_I2_J])). 4.46/4.72 cnf(c_0_9641, plain, (hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),X5)=c_HOL_OThe(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X4)),X5)))), inference(split_conjunct,[status(thm)],[c_0_5751])). 4.46/4.72 cnf(c_0_9642, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBC(X2,tc_Option_Ooption(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool),X2),c_fequal),X3))),c_Option_Ooption_OSome(X1))))=c_Map_Oran(X2,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_5752])). 4.46/4.72 fof(c_0_9643, plain, ![X730, X731, X732, X733, X734, X735, X736]:hAPP(hAPP(c_Relation_Orel__comp(X736,X735,X734),X733),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X732,tc_fun(tc_prod(X735,X734),tc_HOL_Obool)),X731),X730))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X732,tc_fun(tc_prod(X736,X734),tc_HOL_Obool)),X731),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X735,X734),tc_HOL_Obool),tc_fun(tc_prod(X736,X734),tc_HOL_Obool),X732),hAPP(c_Relation_Orel__comp(X736,X735,X734),X733)),X730)), inference(variable_rename,[status(thm)],[fact_rel__comp__UNION__distrib])). 4.46/4.72 cnf(c_0_9644, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X1))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X1))),c_Int_OMin)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5753, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9645, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_5754]), ['final']). 4.46/4.72 fof(c_0_9646, plain, ![X14014, X14015, X14016, X14017, X14018, X14019]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14019,tc_HOL_Obool)),hAPP(c_Relation_OImage(X14018,X14019,X14017),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14016,tc_fun(X14018,tc_HOL_Obool)),X14015),X14014))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14016,tc_fun(X14019,tc_HOL_Obool)),X14015),hAPP(hAPP(c_COMBB(tc_fun(X14018,tc_HOL_Obool),tc_fun(X14019,tc_HOL_Obool),X14016),c_Relation_OImage(X14018,X14019,X14017)),X14014)))), inference(variable_rename,[status(thm)],[fact_Image__INT__subset])). 4.46/4.72 cnf(c_0_9647, plain, (hAPP(c_List_Orotate(X1,X2),X3)=hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3)),hAPP(hAPP(c_List_Otake(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3))), inference(split_conjunct,[status(thm)],[c_0_5755])). 4.46/4.72 fof(c_0_9648, plain, ![X16766, X16767, X16768, X16769, X16770]:hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(X16769),X16769,c_List_Omap__filter(X16770,X16769,X16768,X16766),hAPP(hAPP(c_COMBC(X16769,tc_List_Olist(X16769),tc_List_Olist(X16769)),c_List_Olist_OCons(X16769)),c_List_Omap__filter(X16770,X16769,X16768,X16766))),hAPP(X16768,X16767))=c_List_Omap__filter(X16770,X16769,X16768,hAPP(hAPP(c_List_Olist_OCons(X16770),X16767),X16766)), inference(variable_rename,[status(thm)],[fact_map__filter__simps_I1_J])). 4.46/4.72 fof(c_0_9649, plain, ![X13134, X13135, X13136]:hAPP(c_List_Otl(X13136),hAPP(hAPP(c_List_Oappend(X13136),X13135),X13134))=hAPP(c_List_Olist_Olist__case(tc_List_Olist(X13136),X13136,hAPP(c_List_Otl(X13136),X13134),hAPP(c_COMBK(tc_fun(tc_List_Olist(X13136),tc_List_Olist(X13136)),X13136),hAPP(hAPP(c_COMBC(tc_List_Olist(X13136),tc_List_Olist(X13136),tc_List_Olist(X13136)),c_List_Oappend(X13136)),X13134))),X13135), inference(variable_rename,[status(thm)],[fact_tl__append])). 4.46/4.72 fof(c_0_9650, plain, ![X15997, X15998, X15999, X16000]:hAPP(hAPP(c_List_Otake(X16000),X15999),hAPP(hAPP(c_List_Olist_OCons(X16000),X15998),X15997))=c_Nat_Onat_Onat__case(tc_List_Olist(X16000),c_List_Olist_ONil(X16000),hAPP(hAPP(c_COMBB(tc_List_Olist(X16000),tc_List_Olist(X16000),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X16000),X15998)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X16000),tc_List_Olist(X16000)),c_List_Otake(X16000)),X15997)),X15999), inference(variable_rename,[status(thm)],[fact_take__Cons])). 4.46/4.72 cnf(c_0_9651, plain, (c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5756, c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9652, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),hAPP(c_Relation_OField(X1),X2)),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_Relation_OField(X1),X2)))))), inference(split_conjunct,[status(thm)],[c_0_5757])). 4.46/4.72 fof(c_0_9653, plain, ![X517, X518, X519, X520, X521, X522, X523, X524, X525, X526]:c_Product__Type_Omap__pair(X522,X524,X521,X523,hAPP(c_Fun_Ocomp(X526,X524,X522,X520),X518),hAPP(c_Fun_Ocomp(X525,X523,X521,X519),X517))=hAPP(c_Fun_Ocomp(tc_prod(X526,X525),tc_prod(X524,X523),tc_prod(X522,X521),c_Product__Type_Omap__pair(X526,X524,X525,X523,X520,X519)),c_Product__Type_Omap__pair(X522,X526,X521,X525,X518,X517)), inference(variable_rename,[status(thm)],[fact_map__pair_Ocomp])). 4.46/4.72 fof(c_0_9654, plain, ![X1817, X1818, X1819, X1820, X1821, X1822]:hAPP(hAPP(c_List_Olist__update(tc_prod(X1822,X1821),hAPP(hAPP(c_List_Ozip(X1822,X1821),X1820),X1819)),X1818),X1817)=hAPP(hAPP(c_List_Ozip(X1822,X1821),hAPP(hAPP(c_List_Olist__update(X1822,X1820),X1818),hAPP(c_Product__Type_Ofst(X1822,X1821),X1817))),hAPP(hAPP(c_List_Olist__update(X1821,X1819),X1818),hAPP(c_Product__Type_Osnd(X1822,X1821),X1817))), inference(variable_rename,[status(thm)],[fact_update__zip])). 4.46/4.72 cnf(c_0_9655, plain, (c_Nitpick_Oint__lcm(X1,X2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)))),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)))))), inference(rw,[status(thm)],[c_0_5758, c_0_5759])). 4.46/4.72 cnf(c_0_9656, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5760, c_0_5120]), c_0_5120]), c_0_5120]), ['final']). 4.46/4.72 cnf(c_0_9657, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X1),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),X3))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),X4))),c_Com_Ocom_OWhile(X4,X5)),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5761])). 4.46/4.72 cnf(c_0_9658, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))),c_Int_OMin)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5762, c_0_4470]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.72 cnf(c_0_9659, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5763, c_0_4784]), c_0_5764]), c_0_4500]), c_0_4760]), c_0_5765]), ['final']). 4.46/4.72 cnf(c_0_9660, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),c_Int_OMin))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),c_Int_OMin))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5766, c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.72 fof(c_0_9661, plain, ![X14959, X14960, X14961]:c_Hilbert__Choice_OEps(tc_prod(X14961,X14960),hAPP(c_Product__Type_Oprod_Oprod__case(X14961,X14960,tc_HOL_Obool),X14959))=c_Hilbert__Choice_OEps(tc_prod(X14961,X14960),hAPP(hAPP(c_COMBS(tc_prod(X14961,X14960),X14960,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X14961,tc_fun(X14960,tc_HOL_Obool),tc_prod(X14961,X14960)),X14959),c_Product__Type_Ofst(X14961,X14960))),c_Product__Type_Osnd(X14961,X14960))), inference(variable_rename,[status(thm)],[fact_Eps__split])). 4.46/4.72 fof(c_0_9662, plain, ![X6756, X6757, X6758, X6759, X6760]:c_Map_Orestrict__map(X6760,X6759,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6760,tc_Option_Ooption(X6759)),X6758),X6757),hAPP(c_Option_Ooption_OSome(X6759),X6756)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6760,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X6760),X6757),c_Orderings_Obot__class_Obot(tc_fun(X6760,tc_HOL_Obool)))))=c_Map_Orestrict__map(X6760,X6759,X6758,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6760,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X6760),X6757),c_Orderings_Obot__class_Obot(tc_fun(X6760,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_restrict__upd__same])). 4.46/4.72 fof(c_0_9663, plain, ![X6158, X6159, X6160]:c_HOL_OThe(tc_prod(X6160,X6159),hAPP(c_Product__Type_Oprod_Oprod__case(X6160,X6159,tc_HOL_Obool),X6158))=c_HOL_OThe(tc_prod(X6160,X6159),hAPP(hAPP(c_COMBS(tc_prod(X6160,X6159),X6159,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X6160,tc_fun(X6159,tc_HOL_Obool),tc_prod(X6160,X6159)),X6158),c_Product__Type_Ofst(X6160,X6159))),c_Product__Type_Osnd(X6160,X6159))), inference(variable_rename,[status(thm)],[fact_The__split])). 4.46/4.72 fof(c_0_9664, plain, ![X8206, X8207, X8208, X8209, X8210]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8210,tc_HOL_Obool)),hAPP(c_Relation_OImage(X8209,X8210,X8208),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8209,tc_HOL_Obool)),X8207),X8206))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8210,tc_HOL_Obool)),hAPP(c_Relation_OImage(X8209,X8210,X8208),X8207)),hAPP(c_Relation_OImage(X8209,X8210,X8208),X8206)))), inference(variable_rename,[status(thm)],[fact_Image__Int__subset])). 4.46/4.72 fof(c_0_9665, plain, ![X470, X471, X472, X473, X474]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X472,tc_fun(tc_prod(X473,X474),tc_HOL_Obool)),X471),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X474,X473),tc_HOL_Obool),tc_fun(tc_prod(X473,X474),tc_HOL_Obool),X472),c_Relation_Oconverse(X474,X473)),X470))=hAPP(c_Relation_Oconverse(X474,X473),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X472,tc_fun(tc_prod(X474,X473),tc_HOL_Obool)),X471),X470)), inference(variable_rename,[status(thm)],[fact_converse__INTER])). 4.46/4.72 fof(c_0_9666, plain, ![X4277, X4278, X4279, X4280, X4281]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4279,tc_fun(tc_prod(X4280,X4281),tc_HOL_Obool)),X4278),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X4281,X4280),tc_HOL_Obool),tc_fun(tc_prod(X4280,X4281),tc_HOL_Obool),X4279),c_Relation_Oconverse(X4281,X4280)),X4277))=hAPP(c_Relation_Oconverse(X4281,X4280),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4279,tc_fun(tc_prod(X4281,X4280),tc_HOL_Obool)),X4278),X4277)), inference(variable_rename,[status(thm)],[fact_converse__UNION])). 4.46/4.72 cnf(c_0_9667, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Orev(X1)),hAPP(c_List_Orev(tc_List_Olist(X1)),X2)))=hAPP(c_List_Orev(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5767, c_0_4736]), c_0_4736])). 4.46/4.72 cnf(c_0_9668, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Orev(X1),X4))=hAPP(c_List_Orev(X2),hAPP(hAPP(c_List_Omap(X1,X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5768]), ['final']). 4.46/4.72 fof(c_0_9669, plain, ![X5192, X5193, X5194, X5195]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5194,X5195),tc_HOL_Obool)),hAPP(c_Set_Oimage(X5195,tc_prod(X5194,X5195),esk157_4(X5192,X5193,X5194,X5195)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5194,tc_fun(X5195,tc_HOL_Obool)),X5193),X5192))),hAPP(hAPP(c_Product__Type_OSigma(X5194,X5195),X5193),X5192)))&c_Fun_Oinj__on(X5195,tc_prod(X5194,X5195),esk157_4(X5192,X5193,X5194,X5195),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5194,tc_fun(X5195,tc_HOL_Obool)),X5193),X5192))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_Ex__inj__on__UNION__Sigma])])). 4.46/4.72 cnf(c_0_9670, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))),c_Int_OMin)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5769, c_0_4470]), c_0_4470]), c_0_4443]), c_0_4443]), c_0_4471]), c_0_4471])). 4.46/4.72 fof(c_0_9671, plain, ![X12233, X12234, X12235]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12235),X12234)),X12233)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12235),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X12234),X12233))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12235),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12234,X12233))),X12233)), inference(variable_rename,[status(thm)],[fact_div__mult1__eq])). 4.46/4.72 fof(c_0_9672, plain, ![X6357, X6358, X6359, X6360, X6361]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6361,tc_fun(X6360,tc_HOL_Obool)),X6359),hAPP(hAPP(c_COMBC(X6361,tc_fun(X6360,tc_HOL_Obool),tc_fun(X6360,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6360,tc_HOL_Obool),tc_fun(tc_fun(X6360,tc_HOL_Obool),tc_fun(X6360,tc_HOL_Obool)),X6361),c_Groups_Ominus__class_Ominus(tc_fun(X6360,tc_HOL_Obool))),X6358)),X6357))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6360,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6361,tc_fun(X6360,tc_HOL_Obool)),X6359),X6358)),X6357), inference(variable_rename,[status(thm)],[fact_UN__simps_I6_J])). 4.46/4.72 fof(c_0_9673, plain, ![X1293, X1294, X1295]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1295),X1294)),X1293)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1295),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1294),X1293))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1295),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1294,X1293))),X1293)), inference(variable_rename,[status(thm)],[fact_zdiv__zmult1__eq])). 4.46/4.72 fof(c_0_9674, plain, ![X9646, X9647, X9648, X9649, X9650]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9650,tc_fun(X9649,tc_HOL_Obool)),X9648),hAPP(hAPP(c_COMBC(X9650,tc_fun(X9649,tc_HOL_Obool),tc_fun(X9649,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9649,tc_HOL_Obool),tc_fun(tc_fun(X9649,tc_HOL_Obool),tc_fun(X9649,tc_HOL_Obool)),X9650),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9649,tc_HOL_Obool))),X9647)),X9646))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9649,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9650,tc_fun(X9649,tc_HOL_Obool)),X9648),X9647)),X9646), inference(variable_rename,[status(thm)],[fact_UN__simps_I4_J])). 4.46/4.72 fof(c_0_9675, plain, ![X12443, X12444, X12445, X12446, X12447]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12446,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12447,tc_fun(X12446,tc_HOL_Obool)),X12445),X12444)),X12443)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12447,tc_fun(X12446,tc_HOL_Obool)),X12445),hAPP(hAPP(c_COMBC(X12447,tc_fun(X12446,tc_HOL_Obool),tc_fun(X12446,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12446,tc_HOL_Obool),tc_fun(tc_fun(X12446,tc_HOL_Obool),tc_fun(X12446,tc_HOL_Obool)),X12447),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12446,tc_HOL_Obool))),X12444)),X12443)), inference(variable_rename,[status(thm)],[fact_INT__simps_I6_J])). 4.46/4.72 cnf(c_0_9676, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)=hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_5770])). 4.46/4.72 cnf(c_0_9677, plain, (hAPP(c_List_Orotate(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X4)=hAPP(c_List_Orotate(X1,X2),hAPP(c_List_Orotate(X1,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5771])). 4.46/4.72 fof(c_0_9678, plain, ![X11062, X11063, X11064]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X11064,X11064),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X11064,X11064),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X11064,X11063)),c_Transitive__Closure_Ortrancl(X11064,X11062))),c_Transitive__Closure_Ortrancl(X11064,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X11064,X11064),tc_HOL_Obool)),X11063),X11062)))), inference(variable_rename,[status(thm)],[fact_rtrancl__Un__subset])). 4.46/4.72 fof(c_0_9679, plain, ![X3836, X3837, X3838, X3839, X3840, X3841]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3841,X3839),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X3841,X3840,X3839),X3838),X3836)),hAPP(hAPP(c_Relation_Orel__comp(X3841,X3840,X3839),X3837),X3836))=hAPP(hAPP(c_Relation_Orel__comp(X3841,X3840,X3839),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3841,X3840),tc_HOL_Obool)),X3838),X3837)),X3836), inference(variable_rename,[status(thm)],[fact_rel__comp__distrib2])). 4.46/4.72 fof(c_0_9680, plain, ![X14054, X14055, X14056, X14057, X14058, X14059]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X14059,X14057),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X14059,X14058,X14057),X14056),X14055)),hAPP(hAPP(c_Relation_Orel__comp(X14059,X14058,X14057),X14056),X14054))=hAPP(hAPP(c_Relation_Orel__comp(X14059,X14058,X14057),X14056),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X14058,X14057),tc_HOL_Obool)),X14055),X14054)), inference(variable_rename,[status(thm)],[fact_rel__comp__distrib])). 4.46/4.72 cnf(c_0_9681, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),hAPP(hAPP(c_List_Oappend(X1),X5),X4))),c_List_Olexord(X1,X6)))|hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=X4), inference(split_conjunct,[status(thm)],[c_0_5772])). 4.46/4.72 fof(c_0_9682, plain, ![X16131, X16132, X16133, X16134]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16134,tc_HOL_Obool)),hAPP(c_Relation_ORange(X16133,X16134),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X16133,X16134),tc_HOL_Obool)),X16132),X16131))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16134,tc_HOL_Obool)),hAPP(c_Relation_ORange(X16133,X16134),X16132)),hAPP(c_Relation_ORange(X16133,X16134),X16131)))), inference(variable_rename,[status(thm)],[fact_Range__Int__subset])). 4.46/4.72 fof(c_0_9683, plain, ![X8695, X8696, X8697, X8698]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8698,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X8698,X8697),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X8698,X8697),tc_HOL_Obool)),X8696),X8695))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8698,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X8698,X8697),X8696)),hAPP(c_Relation_ODomain(X8698,X8697),X8695)))), inference(variable_rename,[status(thm)],[fact_Domain__Int__subset])). 4.46/4.72 fof(c_0_9684, plain, ![X15419, X15420, X15421, X15422]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15422,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15422,tc_HOL_Obool)),hAPP(c_Relation_ORange(X15421,X15422),X15420)),hAPP(c_Relation_ORange(X15421,X15422),X15419))),hAPP(c_Relation_ORange(X15421,X15422),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X15421,X15422),tc_HOL_Obool)),X15420),X15419)))), inference(variable_rename,[status(thm)],[fact_Range__Diff__subset])). 4.46/4.72 fof(c_0_9685, plain, ![X8456, X8457, X8458, X8459]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8459,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8459,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X8459,X8458),X8457)),hAPP(c_Relation_ODomain(X8459,X8458),X8456))),hAPP(c_Relation_ODomain(X8459,X8458),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X8459,X8458),tc_HOL_Obool)),X8457),X8456)))), inference(variable_rename,[status(thm)],[fact_Domain__Diff__subset])). 4.46/4.72 fof(c_0_9686, plain, ![X622, X623]:hAPP(c_Product__Type_Oprod_Oprod__case(X623,X623,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X623,tc_HOL_Obool,tc_fun(X623,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X623,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X623,tc_HOL_Obool)),X623),c_COMBC(X623,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X623,tc_HOL_Obool),tc_fun(X623,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X623),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X623),c_fconj)),c_fequal))),X622))=c_Relation_OId__on(X623,X622), inference(variable_rename,[status(thm)],[fact_Id__on__def_H])). 4.46/4.72 fof(c_0_9687, plain, ![X3068, X3069, X3070, X3071]:hAPP(hAPP(c_Product__Type_OSigma(X3071,X3070),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3071,tc_HOL_Obool),X3069)),X3068)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X3071,tc_HOL_Obool),tc_fun(tc_prod(X3071,X3070),tc_HOL_Obool)),X3069),hAPP(hAPP(c_COMBC(tc_fun(X3071,tc_HOL_Obool),tc_fun(X3071,tc_fun(X3070,tc_HOL_Obool)),tc_fun(tc_prod(X3071,X3070),tc_HOL_Obool)),c_Product__Type_OSigma(X3071,X3070)),X3068)), inference(variable_rename,[status(thm)],[fact_Sigma__Union])). 4.46/4.72 fof(c_0_9688, plain, ![X1222, X1223, X1224, X1225]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1225,tc_Option_Ooption(X1224)),hAPP(c_Map_Omap__of(X1225,X1224),X1222)),hAPP(c_Product__Type_Ofst(X1225,X1224),X1223)),hAPP(c_Option_Ooption_OSome(X1224),hAPP(c_Product__Type_Osnd(X1225,X1224),X1223)))=hAPP(c_Map_Omap__of(X1225,X1224),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1225,X1224)),X1223),X1222)), inference(variable_rename,[status(thm)],[fact_map__of_Osimps_I2_J])). 4.46/4.72 cnf(c_0_9689, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Ofilter(X1,X2)),X3))=hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5773, c_0_4736]), c_0_4736])). 4.46/4.72 fof(c_0_9690, plain, ![X6571, X6572]:c_Transitive__Closure_Ortrancl(X6572,X6571)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X6572,X6572),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X6572,X6572),tc_HOL_Obool),tc_fun(tc_prod(X6572,X6572),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X6572,X6572),tc_HOL_Obool)),X6571)), inference(variable_rename,[status(thm)],[fact_rtrancl__is__UN__rel__pow])). 4.46/4.72 cnf(c_0_9691, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_5774])). 4.46/4.72 cnf(c_0_9692, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5775, c_0_5266]), c_0_5266])). 4.46/4.72 cnf(c_0_9693, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),hAPP(hAPP(c_Relation_Orel__comp(X2,X5,X3),X6),X7))=hAPP(hAPP(c_Relation_Orel__comp(X1,X5,X3),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X5),X4),X6)),X7)), inference(split_conjunct,[status(thm)],[c_0_5776]), ['final']). 4.46/4.72 cnf(c_0_9694, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2)=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))), inference(rw,[status(thm)],[c_0_5777, c_0_5266]), ['final']). 4.46/4.72 cnf(c_0_9695, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),esk362_1(X1)),esk363_1(X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))=X1), inference(split_conjunct,[status(thm)],[c_0_5778])). 4.46/4.72 fof(c_0_9696, plain, ![X5840, X5841, X5842, X5843]:hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5843,X5843),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5842),X5841)),X5840)=hAPP(hAPP(c_Relation_Orel__comp(X5843,X5843,X5843),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5843,X5843),tc_HOL_Obool),X5842),X5840)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5843,X5843),tc_HOL_Obool),X5841),X5840)), inference(variable_rename,[status(thm)],[fact_rel__pow__add])). 4.46/4.72 fof(c_0_9697, plain, ![X2293, X2294, X2295, X2296]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2296,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2295,tc_fun(tc_fun(X2296,tc_HOL_Obool),tc_HOL_Obool)),X2294),hAPP(hAPP(c_COMBB(tc_fun(X2296,tc_HOL_Obool),tc_fun(tc_fun(X2296,tc_HOL_Obool),tc_HOL_Obool),X2295),c_Set_OPow(X2296)),X2293))),hAPP(c_Set_OPow(X2296),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2295,tc_fun(X2296,tc_HOL_Obool)),X2294),X2293)))), inference(variable_rename,[status(thm)],[fact_UN__Pow__subset])). 4.46/4.72 fof(c_0_9698, plain, ![X3094]:hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X3094),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)), inference(variable_rename,[status(thm)],[fact_wmin__emptyI])). 4.46/4.72 fof(c_0_9699, plain, ![X7785, X7786, X7787, X7788, X7789]:c_Enum_Oproduct(X7789,X7788,hAPP(hAPP(c_List_Olist_OCons(X7789),X7787),X7786),X7785)=hAPP(hAPP(c_List_Oappend(tc_prod(X7789,X7788)),hAPP(hAPP(c_List_Omap(X7788,tc_prod(X7789,X7788)),hAPP(c_Product__Type_OPair(X7789,X7788),X7787)),X7785)),c_Enum_Oproduct(X7789,X7788,X7786,X7785)), inference(variable_rename,[status(thm)],[fact_product_Osimps_I2_J])). 4.46/4.72 cnf(c_0_9700, plain, (hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1)))),c_Orderings_Oord__class_Oless(tc_Int_Oint))))=c_Int_Oint__ge__less__than2(X1)), inference(split_conjunct,[status(thm)],[c_0_5779])). 4.46/4.72 fof(c_0_9701, plain, ![X8067]:c_Finite__Set_Ofun__left__comm__idem(X8067,tc_fun(X8067,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X8067,tc_HOL_Obool),tc_fun(tc_fun(X8067,tc_HOL_Obool),tc_fun(X8067,tc_HOL_Obool)),X8067),hAPP(c_COMBC(tc_fun(X8067,tc_HOL_Obool),tc_fun(X8067,tc_HOL_Obool),tc_fun(X8067,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X8067,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X8067,tc_fun(X8067,tc_HOL_Obool),tc_fun(X8067,tc_HOL_Obool)),c_Set_Oinsert(X8067)),c_Orderings_Obot__class_Obot(tc_fun(X8067,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_fun__left__comm__idem__remove])). 4.46/4.72 fof(c_0_9702, plain, ![X10151, X10152, X10153]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X10153,X10152),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10153,X10152),c_Orderings_Otop__class_Otop(tc_fun(X10153,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X10152,tc_HOL_Obool),X10153),X10151)))=hAPP(hAPP(c_Product__Type_OSigma(X10153,X10152),c_Orderings_Otop__class_Otop(tc_fun(X10153,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X10152,tc_HOL_Obool),X10153),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10152,tc_HOL_Obool)),X10151))), inference(variable_rename,[status(thm)],[fact_Compl__Times__UNIV1])). 4.46/4.72 fof(c_0_9703, plain, ![X619, X620, X621]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X621,X620),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X621,X620),X619),hAPP(c_COMBK(tc_fun(X620,tc_HOL_Obool),X621),c_Orderings_Otop__class_Otop(tc_fun(X620,tc_HOL_Obool)))))=hAPP(hAPP(c_Product__Type_OSigma(X621,X620),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X621,tc_HOL_Obool)),X619)),hAPP(c_COMBK(tc_fun(X620,tc_HOL_Obool),X621),c_Orderings_Otop__class_Otop(tc_fun(X620,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_Compl__Times__UNIV2])). 4.46/4.72 fof(c_0_9704, plain, ![X4740, X4741, X4742, X4743, X4744]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4744,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4744,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4743,X4744,X4742),X4741)),hAPP(c_Set_Oimage(X4743,X4744,X4742),X4740))),hAPP(c_Set_Oimage(X4743,X4744,X4742),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4743,tc_HOL_Obool)),X4741),X4740)))), inference(variable_rename,[status(thm)],[fact_image__diff__subset])). 4.46/4.72 fof(c_0_9705, plain, ![X5263, X5264, X5265, X5266, X5267]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5267,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5266,X5267,X5265),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5266,tc_HOL_Obool)),X5264),X5263))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5267,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5266,X5267,X5265),X5264)),hAPP(c_Set_Oimage(X5266,X5267,X5265),X5263)))), inference(variable_rename,[status(thm)],[fact_image__Int__subset])). 4.46/4.72 cnf(c_0_9706, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)),X3)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)), inference(split_conjunct,[status(thm)],[c_0_5780])). 4.46/4.72 cnf(c_0_9707, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))), inference(split_conjunct,[status(thm)],[c_0_5781]), ['final']). 4.46/4.72 fof(c_0_9708, plain, ![X12964, X12965, X12966, X12967]:hAPP(hAPP(c_List_Oappend(X12967),hAPP(hAPP(c_List_Odrop(X12967),X12966),X12965)),hAPP(hAPP(c_List_Odrop(X12967),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12966),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12967)),X12965))),X12964))=hAPP(hAPP(c_List_Odrop(X12967),X12966),hAPP(hAPP(c_List_Oappend(X12967),X12965),X12964)), inference(variable_rename,[status(thm)],[fact_drop__append])). 4.46/4.72 fof(c_0_9709, plain, ![X7273, X7274, X7275, X7276]:hAPP(hAPP(c_List_Oappend(X7276),hAPP(hAPP(c_List_Otake(X7276),X7275),X7274)),hAPP(hAPP(c_List_Otake(X7276),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7275),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7276)),X7274))),X7273))=hAPP(hAPP(c_List_Otake(X7276),X7275),hAPP(hAPP(c_List_Oappend(X7276),X7274),X7273)), inference(variable_rename,[status(thm)],[fact_take__append])). 4.46/4.72 fof(c_0_9710, plain, ![X9203, X9204, X9205, X9206, X9207]:c_Map_Odom(X9207,X9205,X9203)=c_Map_Odom(X9207,X9206,hAPP(hAPP(c_COMBS(X9207,tc_Option_Ooption(X9205),tc_Option_Ooption(X9206)),hAPP(hAPP(c_COMBB(tc_fun(X9205,X9206),tc_fun(tc_Option_Ooption(X9205),tc_Option_Ooption(X9206)),X9207),c_Option_Omap(X9205,X9206)),X9204)),X9203)), inference(variable_rename,[status(thm)],[fact_dom__option__map])). 4.46/4.72 fof(c_0_9711, plain, ![X9933, X9934, X9935]:c_Lazy__Sequence_Ohb__flat(X9935,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X9935))),X9934,X9933))=c_Lazy__Sequence_Oappend(tc_Option_Ooption(X9935),hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X9935)),tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X9935)),c_Lazy__Sequence_Ohit__bound(X9935),c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X9935)))),X9934),c_Lazy__Sequence_Ohb__flat(X9935,X9933)), inference(variable_rename,[status(thm)],[fact_hb__flat_Osimps_I2_J])). 4.46/4.72 fof(c_0_9712, plain, ![X10522, X10523]:c_Random_Opick(X10523,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X10523),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X10523,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10523,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X10523)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X10522))=c_Random_Opick(X10523,X10522), inference(variable_rename,[status(thm)],[fact_pick__drop__zero])). 4.46/4.72 fof(c_0_9713, plain, ![X2424, X2425]:c_Random_Oselect__weight(X2425,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X2425),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X2425,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2425,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X2425)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X2424))=c_Random_Oselect__weight(X2425,X2424), inference(variable_rename,[status(thm)],[fact_select__weigth__drop__zero])). 4.46/4.72 fof(c_0_9714, plain, ![X3944, X3945, X3946, X3947, X3948]:c_List_OtakeWhile(tc_prod(X3948,X3947),hAPP(c_Fun_Ocomp(X3948,tc_HOL_Obool,tc_prod(X3948,X3947),X3946),c_Product__Type_Ofst(X3948,X3947)),hAPP(hAPP(c_List_Ozip(X3948,X3947),X3945),X3944))=hAPP(hAPP(c_List_Ozip(X3948,X3947),c_List_OtakeWhile(X3948,X3946,X3945)),X3944), inference(variable_rename,[status(thm)],[fact_zip__takeWhile__fst])). 4.46/4.72 fof(c_0_9715, plain, ![X7345, X7346, X7347, X7348, X7349]:c_List_OtakeWhile(tc_prod(X7349,X7348),hAPP(c_Fun_Ocomp(X7348,tc_HOL_Obool,tc_prod(X7349,X7348),X7346),c_Product__Type_Osnd(X7349,X7348)),hAPP(hAPP(c_List_Ozip(X7349,X7348),X7347),X7345))=hAPP(hAPP(c_List_Ozip(X7349,X7348),X7347),c_List_OtakeWhile(X7348,X7346,X7345)), inference(variable_rename,[status(thm)],[fact_zip__takeWhile__snd])). 4.46/4.72 cnf(c_0_9716, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4))),hAPP(X5,hAPP(c_Product__Type_Osnd(X2,X3),X4)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Product__Type_Oprod_Oprod__size(X2,X3,X1,X5,X4)), inference(split_conjunct,[status(thm)],[c_0_5782])). 4.46/4.72 cnf(c_0_9717, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X4)),c_List_Olexord(X1,X5)))|hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=X4), inference(split_conjunct,[status(thm)],[c_0_5783])). 4.46/4.72 cnf(c_0_9718, plain, (hAPP(c_Set_OCollect(tc_Nat_Onat),X1)=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),X1),c_Int_Onat))))), inference(split_conjunct,[status(thm)],[c_0_5784])). 4.46/4.72 cnf(c_0_9719, plain, (hAPP(c_List_Oset(X1),hAPP(c_List_Ofilter(X1,X2),X3))=hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),hAPP(c_List_Oset(X1),X3)))),X2))), inference(split_conjunct,[status(thm)],[c_0_5785])). 4.46/4.72 cnf(c_0_9720, plain, (hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),hAPP(hAPP(c_List_Oappend(tc_Int_Oint),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X1),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5786, c_0_5787]), c_0_5788]), c_0_5788])). 4.46/4.72 cnf(c_0_9721, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))=hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(hAPP(c_List_Oappend(X2),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_5789]), ['final']). 4.46/4.72 fof(c_0_9722, plain, ![X1365, X1366, X1367, X1368, X1369]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1369,X1368),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1369,X1368),X1367),X1365)),hAPP(hAPP(c_Product__Type_OSigma(X1369,X1368),X1366),X1365))=hAPP(hAPP(c_Product__Type_OSigma(X1369,X1368),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1369,tc_HOL_Obool)),X1367),X1366)),X1365), inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib1])). 4.46/4.72 fof(c_0_9723, plain, ![X5655, X5656, X5657, X5658, X5659]:hAPP(hAPP(c_Product__Type_OSigma(X5659,X5658),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5659,tc_HOL_Obool)),X5657),X5656)),X5655)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5659,X5658),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5659,X5658),X5657),X5655)),hAPP(hAPP(c_Product__Type_OSigma(X5659,X5658),X5656),X5655)), inference(variable_rename,[status(thm)],[fact_Sigma__Diff__distrib1])). 4.46/4.72 fof(c_0_9724, plain, ![X12410, X12411, X12412, X12413, X12414]:hAPP(hAPP(c_Product__Type_OSigma(X12414,X12413),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12414,tc_HOL_Obool)),X12412),X12411)),X12410)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X12414,X12413),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X12414,X12413),X12412),X12410)),hAPP(hAPP(c_Product__Type_OSigma(X12414,X12413),X12411),X12410)), inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib1])). 4.46/4.72 fof(c_0_9725, plain, ![X16850, X16851, X16852, X16853]:hAPP(hAPP(c_List_Odrop(X16853),X16852),hAPP(hAPP(c_List_Olist_OCons(X16853),X16851),X16850))=c_Nat_Onat_Onat__case(tc_List_Olist(X16853),hAPP(hAPP(c_List_Olist_OCons(X16853),X16851),X16850),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X16853),tc_List_Olist(X16853)),c_List_Odrop(X16853)),X16850),X16852), inference(variable_rename,[status(thm)],[fact_drop__Cons])). 4.46/4.72 cnf(c_0_9726, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)))=c_Divides_Opdivmod(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5790])). 4.46/4.72 cnf(c_0_9727, plain, (c_Divides_Odivmod__int(X1,X2)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5791]), ['final']). 4.46/4.72 cnf(c_0_9728, plain, (hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X1))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))))), inference(split_conjunct,[status(thm)],[c_0_5792])). 4.46/4.72 cnf(c_0_9729, plain, (hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),X3)=hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5793, c_0_5670]), c_0_5671]), c_0_4531]), c_0_4531])). 4.46/4.72 cnf(c_0_9730, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool))),X4)),X5))=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=X2), inference(split_conjunct,[status(thm)],[c_0_5794])). 4.46/4.72 fof(c_0_9731, plain, ![X1391, X1392, X1393, X1394]:c_New__Random__Sequence_Oneg__map(X1394,X1393,X1392,X1391)=c_New__Random__Sequence_Oneg__bind(X1394,X1393,X1391,hAPP(c_Fun_Ocomp(X1393,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1393)))))),X1394,c_New__Random__Sequence_Oneg__single(X1393)),X1392)), inference(variable_rename,[status(thm)],[fact_neg__map__def])). 4.46/4.72 cnf(c_0_9732, plain, (hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),hAPP(c_COMBC(X2,X1,X2),X3)),X5),hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X4)))=hAPP(c_List_Ofoldl(X2,X1,X3,X5),X4)), inference(rw,[status(thm)],[c_0_5795, c_0_4713])). 4.46/4.72 cnf(c_0_9733, plain, (X1=hAPP(c_List_Orev(X2),hAPP(c_List_Orev(X2),X1))), inference(split_conjunct,[status(thm)],[c_0_5796]), ['final']). 4.46/4.72 fof(c_0_9734, plain, ![X14630, X14631, X14632, X14633, X14634, X14635]:c_Map_Omap__add(X14635,X14634,X14633,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X14635,tc_Option_Ooption(X14634)),X14632),X14631),hAPP(c_Option_Ooption_OSome(X14634),X14630)))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X14635,tc_Option_Ooption(X14634)),c_Map_Omap__add(X14635,X14634,X14633,X14632)),X14631),hAPP(c_Option_Ooption_OSome(X14634),X14630)), inference(variable_rename,[status(thm)],[fact_map__add__upd])). 4.46/4.72 fof(c_0_9735, plain, ![X11193, X11194, X11195, X11196]:hAPP(c_Product__Type_Oprod_Oprod__case(X11196,X11195,X11194),hAPP(hAPP(c_COMBB(tc_fun(X11195,tc_prod(X11196,X11195)),tc_fun(X11195,X11194),X11196),hAPP(c_COMBB(tc_prod(X11196,X11195),X11194,X11195),X11193)),c_Product__Type_OPair(X11196,X11195)))=X11193, inference(variable_rename,[status(thm)],[fact_split__eta])). 4.46/4.72 fof(c_0_9736, plain, ![X17002, X17003, X17004, X17005]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17005,tc_fun(X17004,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X17005,tc_HOL_Obool),X17003)),X17002)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X17005,tc_HOL_Obool),tc_fun(X17004,tc_HOL_Obool)),X17003),hAPP(hAPP(c_COMBC(tc_fun(X17005,tc_HOL_Obool),tc_fun(X17005,tc_fun(X17004,tc_HOL_Obool)),tc_fun(X17004,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17005,tc_fun(X17004,tc_HOL_Obool))),X17002)), inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I8_J])). 4.46/4.72 fof(c_0_9737, plain, ![X15832, X15833, X15834, X15835]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15835,tc_fun(X15834,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X15835,tc_HOL_Obool),X15833)),X15832)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X15835,tc_HOL_Obool),tc_fun(X15834,tc_HOL_Obool)),X15833),hAPP(hAPP(c_COMBC(tc_fun(X15835,tc_HOL_Obool),tc_fun(X15835,tc_fun(X15834,tc_HOL_Obool)),tc_fun(X15834,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15835,tc_fun(X15834,tc_HOL_Obool))),X15832)), inference(variable_rename,[status(thm)],[fact_UN__simps_I8_J])). 4.46/4.72 cnf(c_0_9738, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2),X3))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5797])). 4.46/4.72 fof(c_0_9739, plain, ![X6311, X6312, X6313, X6314, X6315]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6315,tc_HOL_Obool)),hAPP(c_List_Oset(X6315),hAPP(hAPP(c_List_Otake(X6315),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6314)),X6311)),X6312))),c_Map_Odom(X6315,X6314,X6313))=c_Map_Odom(X6315,X6314,c_Map_Omap__upds(X6315,X6314,X6313,X6312,X6311)), inference(variable_rename,[status(thm)],[fact_dom__map__upds])). 4.46/4.72 cnf(c_0_9740, plain, (c_FunDef_Opair__leq=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[fact_pair__leq__def])). 4.46/4.72 cnf(c_0_9741, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_Ovimage(X2,X4,X5)),X6))=hAPP(c_Set_Ovimage(X2,X4,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6))), inference(split_conjunct,[status(thm)],[c_0_5798])). 4.46/4.72 cnf(c_0_9742, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_Ovimage(X2,X4,X5)),X6))=hAPP(c_Set_Ovimage(X2,X4,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6))), inference(split_conjunct,[status(thm)],[c_0_5799])). 4.46/4.72 fof(c_0_9743, plain, ![X7671, X7672, X7673, X7674, X7675, X7676]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7673,tc_fun(X7675,tc_HOL_Obool)),X7672),hAPP(hAPP(c_COMBB(tc_fun(X7676,tc_HOL_Obool),tc_fun(X7675,tc_HOL_Obool),X7673),c_Relation_OImage(X7676,X7675,X7674)),X7671))=hAPP(c_Relation_OImage(X7676,X7675,X7674),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7673,tc_fun(X7676,tc_HOL_Obool)),X7672),X7671)), inference(variable_rename,[status(thm)],[fact_Image__UN])). 4.46/4.72 cnf(c_0_9744, plain, (hAPP(c_List_Orotate(X1,X2),X3)=hAPP(c_List_Orotate(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3)), inference(split_conjunct,[status(thm)],[c_0_5800])). 4.46/4.72 fof(c_0_9745, plain, ![X6967, X6968, X6969, X6970]:c_New__Random__Sequence_Opos__map(X6970,X6969,X6968,X6967)=c_New__Random__Sequence_Opos__bind(X6970,X6969,X6967,hAPP(c_Fun_Ocomp(X6969,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X6969))))),X6970,c_New__Random__Sequence_Opos__single(X6969)),X6968)), inference(variable_rename,[status(thm)],[fact_pos__map__def])). 4.46/4.72 cnf(c_0_9746, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OField(X1),X4))=hAPP(c_Relation_OField(X1),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_5801])). 4.46/4.72 fof(c_0_9747, plain, ![X10697, X10698, X10699]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10699,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10699,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X10699,tc_HOL_Obool),tc_HOL_Obool)),X10698),X10697))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10699,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10699,tc_HOL_Obool),X10698)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10699,tc_HOL_Obool),X10697)))), inference(variable_rename,[status(thm)],[fact_Union__Int__subset])). 4.46/4.72 fof(c_0_9748, plain, ![X15416, X15417, X15418]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15418,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15418,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X15418,tc_HOL_Obool),X15417)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X15418,tc_HOL_Obool),X15416))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X15418,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X15418,tc_HOL_Obool),tc_HOL_Obool)),X15417),X15416)))), inference(variable_rename,[status(thm)],[fact_Inter__Un__subset])). 4.46/4.72 fof(c_0_9749, plain, ![X14680, X14681, X14682, X14683, X14684]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14683,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14684,tc_fun(X14683,tc_HOL_Obool)),X14682),X14680)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14684,tc_fun(X14683,tc_HOL_Obool)),X14681),X14680))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14684,tc_fun(X14683,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14684,tc_HOL_Obool)),X14682),X14681)),X14680), inference(variable_rename,[status(thm)],[fact_UN__Un])). 4.46/4.72 fof(c_0_9750, plain, ![X6849, X6850, X6851, X6852, X6853]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6853,tc_fun(X6852,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6853,tc_HOL_Obool)),X6851),X6850)),X6849)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6852,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6853,tc_fun(X6852,tc_HOL_Obool)),X6851),X6849)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6853,tc_fun(X6852,tc_HOL_Obool)),X6850),X6849)), inference(variable_rename,[status(thm)],[fact_INT__Un])). 4.46/4.72 cnf(c_0_9751, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2))), inference(rw,[status(thm)],[c_0_5802, c_0_5689])). 4.46/4.72 fof(c_0_9752, plain, ![X7913, X7914, X7915, X7916, X7917]:hAPP(hAPP(c_List_Oappend(X7917),X7916),hAPP(hAPP(c_List_Olist_OCons(X7917),X7913),X7914))=hAPP(hAPP(c_List_Olist__update(X7917,hAPP(hAPP(c_List_Oappend(X7917),X7916),hAPP(hAPP(c_List_Olist_OCons(X7917),X7915),X7914))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7917)),X7916)),X7913), inference(variable_rename,[status(thm)],[fact_list__update__length])). 4.46/4.72 fof(c_0_9753, plain, ![X3219, X3220]:hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),X3220)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3219),X3220)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X3220),X3219), inference(variable_rename,[status(thm)],[fact_image__add__int__atLeastLessThan])). 4.46/4.72 cnf(c_0_9754, plain, (hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))=hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5803])). 4.46/4.72 fof(c_0_9755, plain, ![X8811, X8812, X8813]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X8813,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X8813,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X8813),X8812)),hAPP(c_Set_OPow(X8813),X8811))),hAPP(c_Set_OPow(X8813),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8813,tc_HOL_Obool)),X8812),X8811)))), inference(variable_rename,[status(thm)],[fact_Un__Pow__subset])). 4.46/4.72 fof(c_0_9756, plain, ![X323, X324]:hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X324)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X323)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X324),X323), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J])). 4.46/4.72 fof(c_0_9757, plain, ![X9900, X9901, X9902, X9903, X9904]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9903,tc_HOL_Obool)),hAPP(c_Relation_OImage(X9904,X9903,X9902),X9900)),hAPP(c_Relation_OImage(X9904,X9903,X9901),X9900))=hAPP(c_Relation_OImage(X9904,X9903,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X9904,X9903),tc_HOL_Obool)),X9902),X9901)),X9900), inference(variable_rename,[status(thm)],[fact_Un__Image])). 4.46/4.72 cnf(c_0_9758, plain, (c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),X1)),X2)=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))), inference(split_conjunct,[status(thm)],[c_0_5804])). 4.46/4.72 cnf(c_0_9759, plain, (X4=hAPP(hAPP(c_List_Ozip(X2,X3),X5),X1)|X1!=hAPP(hAPP(c_List_Omap(tc_prod(X2,X3),X3),c_Product__Type_Osnd(X2,X3)),X4)|X5!=hAPP(hAPP(c_List_Omap(tc_prod(X2,X3),X2),c_Product__Type_Ofst(X2,X3)),X4)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)), inference(split_conjunct,[status(thm)],[c_0_5304])). 4.46/4.72 cnf(c_0_9760, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)), inference(split_conjunct,[status(thm)],[c_0_5805]), ['final']). 4.46/4.72 fof(c_0_9761, plain, ![X15052, X15053, X15054]:c_Fun_Oinj__on(tc_prod(X15054,X15053),tc_prod(X15053,X15054),hAPP(c_Product__Type_Oprod_Oprod__case(X15054,X15053,tc_prod(X15053,X15054)),hAPP(c_COMBC(X15053,X15054,tc_prod(X15053,X15054)),c_Product__Type_OPair(X15053,X15054))),X15052), inference(variable_rename,[status(thm)],[fact_swap__inj__on])). 4.46/4.72 fof(c_0_9762, plain, ![X15599, X15600, X15601, X15602]:hAPP(c_Fun_Ocomp(X15602,X15602,X15602,hAPP(hAPP(c_Nat_Ocompow(X15602,X15602),X15601),X15599)),hAPP(hAPP(c_Nat_Ocompow(X15602,X15602),X15600),X15599))=hAPP(hAPP(c_Nat_Ocompow(X15602,X15602),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15601),X15600)),X15599), inference(variable_rename,[status(thm)],[fact_funpow__add])). 4.46/4.72 fof(c_0_9763, plain, ![X7692, X7693, X7694, X7695, X7696]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7694,tc_fun(X7696,tc_HOL_Obool)),X7693),hAPP(hAPP(c_COMBB(tc_fun(X7696,tc_HOL_Obool),tc_fun(X7696,tc_HOL_Obool),X7694),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7696,tc_HOL_Obool)),X7695)),X7692))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7696,tc_HOL_Obool)),X7695),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7694,tc_fun(X7696,tc_HOL_Obool)),X7693),X7692)), inference(variable_rename,[status(thm)],[fact_Un__INT__distrib])). 4.46/4.72 fof(c_0_9764, plain, ![X8219, X8220, X8221, X8222, X8223]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8223,tc_HOL_Obool)),X8222),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8221,tc_fun(X8223,tc_HOL_Obool)),X8220),X8219))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8221,tc_fun(X8223,tc_HOL_Obool)),X8220),hAPP(hAPP(c_COMBB(tc_fun(X8223,tc_HOL_Obool),tc_fun(X8223,tc_HOL_Obool),X8221),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8223,tc_HOL_Obool)),X8222)),X8219)), inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I7_J])). 4.46/4.72 fof(c_0_9765, plain, ![X2790, X2791, X2792, X2793, X2794]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2794,tc_HOL_Obool)),X2793),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2792,tc_fun(X2794,tc_HOL_Obool)),X2791),X2790))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2792,tc_fun(X2794,tc_HOL_Obool)),X2791),hAPP(hAPP(c_COMBB(tc_fun(X2794,tc_HOL_Obool),tc_fun(X2794,tc_HOL_Obool),X2792),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2794,tc_HOL_Obool)),X2793)),X2790)), inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I5_J])). 4.46/4.72 cnf(c_0_9766, plain, (c_Lazy__Sequence_Ohb__bind(X1,X2,hAPP(X3,X4),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))),X5),X4))=hAPP(c_New__DSequence_Oneg__bind(X1,X2,X3,X5),X4)), inference(split_conjunct,[status(thm)],[c_0_5806])). 4.46/4.72 fof(c_0_9767, plain, ![X2215, X2216, X2217, X2218, X2219]:hAPP(c_Option_Omap(X2217,X2218),hAPP(c_Fun_Ocomp(X2219,X2218,X2217,X2216),X2215))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X2219),tc_Option_Ooption(X2218),tc_Option_Ooption(X2217),hAPP(c_Option_Omap(X2219,X2218),X2216)),hAPP(c_Option_Omap(X2217,X2219),X2215)), inference(variable_rename,[status(thm)],[fact_Option_Omap_Ocomp])). 4.46/4.72 fof(c_0_9768, plain, ![X5928, X5929, X5930, X5931, X5932]:hAPP(c_List_Omap(X5930,X5931),hAPP(c_Fun_Ocomp(X5932,X5931,X5930,X5929),X5928))=hAPP(c_Fun_Ocomp(tc_List_Olist(X5932),tc_List_Olist(X5931),tc_List_Olist(X5930),hAPP(c_List_Omap(X5932,X5931),X5929)),hAPP(c_List_Omap(X5930,X5932),X5928)), inference(variable_rename,[status(thm)],[fact_map__comp__map])). 4.46/4.72 cnf(c_0_9769, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))=c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),X2)),X1)), inference(split_conjunct,[status(thm)],[c_0_5807])). 4.46/4.72 fof(c_0_9770, plain, ![X15465, X15466, X15467, X15468]:hAPP(c_Relation_Oconverse(X15468,X15467),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15468,X15467),tc_HOL_Obool)),X15466),X15465))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15467,X15468),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X15468,X15467),X15466)),hAPP(c_Relation_Oconverse(X15468,X15467),X15465)), inference(variable_rename,[status(thm)],[fact_converse__Un])). 4.46/4.72 fof(c_0_9771, plain, ![X12707, X12708, X12709, X12710]:hAPP(c_Relation_Oconverse(X12710,X12709),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X12710,X12709),tc_HOL_Obool)),X12708),X12707))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X12709,X12710),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X12710,X12709),X12708)),hAPP(c_Relation_Oconverse(X12710,X12709),X12707)), inference(variable_rename,[status(thm)],[fact_converse__Int])). 4.46/4.72 cnf(c_0_9772, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X3)),X3)=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5808])). 4.46/4.72 cnf(c_0_9773, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X3)),X3)=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_5809]), ['final']). 4.46/4.72 fof(c_0_9774, plain, ![X4676, X4677, X4678]:c_List_Opartition(X4678,X4677,X4676)=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4678),tc_List_Olist(X4678)),hAPP(c_List_Ofilter(X4678,X4677),X4676)),hAPP(c_List_Ofilter(X4678,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X4678,c_fNot),X4677)),X4676)), inference(variable_rename,[status(thm)],[fact_partition__filter__conv])). 4.46/4.72 cnf(c_0_9775, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5))=hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_5810])). 4.46/4.72 fof(c_0_9776, plain, ![X6455, X6456, X6457, X6458, X6459, X6460]:hAPP(c_Set_Oimage(X6460,X6459,X6458),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6457,tc_fun(X6460,tc_HOL_Obool)),X6456),X6455))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6457,tc_fun(X6459,tc_HOL_Obool)),X6456),hAPP(hAPP(c_COMBB(tc_fun(X6460,tc_HOL_Obool),tc_fun(X6459,tc_HOL_Obool),X6457),c_Set_Oimage(X6460,X6459,X6458)),X6455)), inference(variable_rename,[status(thm)],[fact_image__UN])). 4.46/4.72 fof(c_0_9777, plain, ![X10586, X10587, X10588, X10589, X10590]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10589,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10590,X10589,X10588),X10587)),hAPP(c_Relation_OImage(X10590,X10589,X10588),X10586))=hAPP(c_Relation_OImage(X10590,X10589,X10588),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10590,tc_HOL_Obool)),X10587),X10586)), inference(variable_rename,[status(thm)],[fact_Image__Un])). 4.46/4.72 fof(c_0_9778, plain, ![X401, X402, X403, X404, X405]:c_Map_Omap__upds(X405,X404,X403,X402,X401)=c_Map_Omap__add(X405,X404,X403,hAPP(c_Map_Omap__of(X405,X404),hAPP(c_List_Orev(tc_prod(X405,X404)),hAPP(hAPP(c_List_Ozip(X405,X404),X402),X401)))), inference(variable_rename,[status(thm)],[fact_map__upds__def])). 4.46/4.72 cnf(c_0_9779, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5))=hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_5811])). 4.46/4.72 cnf(c_0_9780, plain, (hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5))), inference(split_conjunct,[status(thm)],[c_0_5812])). 4.46/4.72 fof(c_0_9781, plain, ![X2833, X2834, X2835, X2836, X2837]:hAPP(hAPP(c_List_Odrop(tc_prod(X2837,X2836)),X2835),hAPP(hAPP(c_List_Ozip(X2837,X2836),X2834),X2833))=hAPP(hAPP(c_List_Ozip(X2837,X2836),hAPP(hAPP(c_List_Odrop(X2837),X2835),X2834)),hAPP(hAPP(c_List_Odrop(X2836),X2835),X2833)), inference(variable_rename,[status(thm)],[fact_drop__zip])). 4.46/4.72 cnf(c_0_9782, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X1,X2))),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))), inference(split_conjunct,[status(thm)],[c_0_5813])). 4.46/4.72 cnf(c_0_9783, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2)))))), inference(split_conjunct,[status(thm)],[c_0_5814])). 4.46/4.72 fof(c_0_9784, plain, ![X6996, X6997, X6998, X6999]:hAPP(c_List_Oset(tc_prod(X6999,X6998)),c_Enum_Oproduct(X6999,X6998,X6997,X6996))=hAPP(hAPP(c_Product__Type_OSigma(X6999,X6998),hAPP(c_List_Oset(X6999),X6997)),hAPP(c_COMBK(tc_fun(X6998,tc_HOL_Obool),X6999),hAPP(c_List_Oset(X6998),X6996))), inference(variable_rename,[status(thm)],[fact_product__list__set])). 4.46/4.72 fof(c_0_9785, plain, ![X2122, X2123, X2124]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2124),X2123))),X2122)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2124)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2123)),X2122)), inference(variable_rename,[status(thm)],[fact_zadd__int__left])). 4.46/4.72 fof(c_0_9786, plain, ![X16902, X16903, X16904, X16905]:hAPP(c_Finite__Set_Ocard(tc_prod(X16905,X16904)),hAPP(hAPP(c_Product__Type_OSigma(X16905,X16904),X16903),hAPP(c_COMBK(tc_fun(X16904,tc_HOL_Obool),X16905),X16902)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X16905),X16903)),hAPP(c_Finite__Set_Ocard(X16904),X16902)), inference(variable_rename,[status(thm)],[fact_card__cartesian__product])). 4.46/4.72 fof(c_0_9787, plain, ![X10550, X10551, X10552]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X10552,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X10552),X10550)),hAPP(c_Set_Oimage(tc_fun(X10552,tc_HOL_Obool),tc_fun(X10552,tc_HOL_Obool),hAPP(c_Set_Oinsert(X10552),X10551)),hAPP(c_Set_OPow(X10552),X10550)))=hAPP(c_Set_OPow(X10552),hAPP(hAPP(c_Set_Oinsert(X10552),X10551),X10550)), inference(variable_rename,[status(thm)],[fact_Pow__insert])). 4.46/4.72 cnf(c_0_9788, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),c_List_Oreplicate(X1,X3,X4)),c_List_Oreplicate(X2,X5,X6))=c_List_Oreplicate(tc_prod(X1,X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X3),X5),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X6))), inference(split_conjunct,[status(thm)],[c_0_5815])). 4.46/4.72 fof(c_0_9789, plain, ![X4267, X4268]:hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4268),tc_List_Olist(X4268))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4268),tc_List_Olist(X4268)),c_List_Olist_ONil(X4268)),c_List_Olist_ONil(X4268))),c_List_Olistrel(X4268,X4267))), inference(variable_rename,[status(thm)],[fact_listrel_ONil])). 4.46/4.72 cnf(c_0_9790, plain, (c_Map_Odom(X2,X3,X1)=hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))|X1!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X2,tc_Option_Ooption(X3)),hAPP(c_COMBK(tc_Option_Ooption(X3),X2),c_Option_Ooption_ONone(X3))),X4),hAPP(c_Option_Ooption_OSome(X3),X5))), inference(split_conjunct,[status(thm)],[c_0_5816])). 4.46/4.72 cnf(c_0_9791, plain, (hAPP(c_List_Oset(X1),c_List_Oconcat(X1,X2))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)),c_List_Oset(X1))), inference(split_conjunct,[status(thm)],[c_0_5817])). 4.46/4.72 fof(c_0_9792, plain, ![X7538, X7539, X7540]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7540,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7540,tc_HOL_Obool),X7539)),X7538)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X7540,tc_HOL_Obool),tc_fun(X7540,tc_HOL_Obool)),X7539),hAPP(hAPP(c_COMBC(tc_fun(X7540,tc_HOL_Obool),tc_fun(X7540,tc_HOL_Obool),tc_fun(X7540,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7540,tc_HOL_Obool))),X7538)), inference(variable_rename,[status(thm)],[fact_Int__Union2])). 4.46/4.72 cnf(c_0_9793, plain, (hAPP(c_List_Ofilter(X3,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),hAPP(c_fequal,X1))),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))=hAPP(c_List_Ofilter(X3,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),hAPP(c_fequal,X1))),X4)|X1!=X2), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5818, c_0_5035]), c_0_5035])). 4.46/4.72 fof(c_0_9794, plain, ![X11926, X11927, X11928, X11929, X11930]:hAPP(c_Relation_Oconverse(X11930,X11929),hAPP(hAPP(c_Relation_Orel__comp(X11930,X11928,X11929),X11927),X11926))=hAPP(hAPP(c_Relation_Orel__comp(X11929,X11928,X11930),hAPP(c_Relation_Oconverse(X11928,X11929),X11926)),hAPP(c_Relation_Oconverse(X11930,X11928),X11927)), inference(variable_rename,[status(thm)],[fact_converse__rel__comp])). 4.46/4.72 cnf(c_0_9795, plain, (hAPP(c_List_Orotate(X1,hAPP(c_Nat_OSuc,X2)),X3)=hAPP(c_List_Orotate1(X1),hAPP(c_List_Orotate(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5819])). 4.46/4.72 fof(c_0_9796, plain, ![X10179, X10180, X10181, X10182, X10183]:hAPP(c_List_Ofilter(X10183,X10182),hAPP(hAPP(c_List_Omap(X10181,X10183),X10180),X10179))=hAPP(hAPP(c_List_Omap(X10181,X10183),X10180),hAPP(c_List_Ofilter(X10181,hAPP(c_Fun_Ocomp(X10183,tc_HOL_Obool,X10181,X10182),X10180)),X10179)), inference(variable_rename,[status(thm)],[fact_filter__map])). 4.46/4.72 fof(c_0_9797, plain, ![X13183, X13184]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X13184,X13184),tc_HOL_Obool)),c_Relation_OId__on(X13184,X13183)),hAPP(hAPP(c_Product__Type_OSigma(X13184,X13184),X13183),hAPP(c_COMBK(tc_fun(X13184,tc_HOL_Obool),X13184),X13183)))), inference(variable_rename,[status(thm)],[fact_Id__on__subset__Times])). 4.46/4.72 fof(c_0_9798, plain, ![X16824, X16825, X16826]:hBOOL(hAPP(hAPP(c_member(tc_prod(X16826,X16826)),hAPP(hAPP(c_Product__Type_OPair(X16826,X16826),X16825),X16825)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X16826,X16826),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16824))), inference(variable_rename,[status(thm)],[fact_rel__pow__0__I])). 4.46/4.72 cnf(c_0_9799, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),X2),X3)=hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Oconcat(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_5820])). 4.46/4.72 cnf(c_0_9800, plain, (hAPP(hAPP(c_Map_Omap__of(X3,X4),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X2),X5)),X6)),X1)=hAPP(c_Option_Ooption_OSome(X4),X5)|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5821])). 4.46/4.72 fof(c_0_9801, plain, ![X2585, X2586, X2587]:c_Transitive__Closure_Ortrancl(X2587,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2587,X2587),tc_HOL_Obool)),X2586),X2585))=c_Transitive__Closure_Ortrancl(X2587,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2587,X2587),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X2587,X2586)),c_Transitive__Closure_Ortrancl(X2587,X2585))), inference(variable_rename,[status(thm)],[fact_rtrancl__Un__rtrancl])). 4.46/4.72 fof(c_0_9802, plain, ![X6250, X6251, X6252, X6253]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6252,tc_HOL_Obool)),hAPP(c_Relation_ORange(X6253,X6252),X6251)),hAPP(c_Relation_ORange(X6253,X6252),X6250))=hAPP(c_Relation_ORange(X6253,X6252),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X6253,X6252),tc_HOL_Obool)),X6251),X6250)), inference(variable_rename,[status(thm)],[fact_Range__Un__eq])). 4.46/4.72 fof(c_0_9803, plain, ![X8923, X8924, X8925, X8926]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8926,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X8926,X8925),X8924)),hAPP(c_Relation_ODomain(X8926,X8925),X8923))=hAPP(c_Relation_ODomain(X8926,X8925),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X8926,X8925),tc_HOL_Obool)),X8924),X8923)), inference(variable_rename,[status(thm)],[fact_Domain__Un__eq])). 4.46/4.72 cnf(c_0_9804, plain, (hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc)))=c_Wellfounded_Opred__nat), inference(split_conjunct,[status(thm)],[fact_pred__nat__def])). 4.46/4.72 fof(c_0_9805, plain, ![X9439, X9440, X9441, X9442]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9441,tc_fun(X9442,tc_HOL_Obool))),c_Predicate_Oconversep(X9442,X9441,X9440)),c_Predicate_Oconversep(X9442,X9441,X9439))=c_Predicate_Oconversep(X9442,X9441,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9442,tc_fun(X9441,tc_HOL_Obool))),X9440),X9439)), inference(variable_rename,[status(thm)],[fact_converse__meet])). 4.46/4.72 fof(c_0_9806, plain, ![X9001, X9002, X9003, X9004]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9003,tc_fun(tc_fun(X9004,tc_HOL_Obool),tc_HOL_Obool)),X9002),hAPP(hAPP(c_COMBB(tc_fun(X9004,tc_HOL_Obool),tc_fun(tc_fun(X9004,tc_HOL_Obool),tc_HOL_Obool),X9003),c_Set_OPow(X9004)),X9001))=hAPP(c_Set_OPow(X9004),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9003,tc_fun(X9004,tc_HOL_Obool)),X9002),X9001)), inference(variable_rename,[status(thm)],[fact_Pow__INT__eq])). 4.46/4.72 fof(c_0_9807, plain, ![X14877, X14878, X14879, X14880]:c_Predicate_Oconversep(X14880,X14879,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14880,tc_fun(X14879,tc_HOL_Obool))),X14878),X14877))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14879,tc_fun(X14880,tc_HOL_Obool))),c_Predicate_Oconversep(X14880,X14879,X14878)),c_Predicate_Oconversep(X14880,X14879,X14877)), inference(variable_rename,[status(thm)],[fact_converse__join])). 4.46/4.72 cnf(c_0_9808, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Map_Odom(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3))))), inference(split_conjunct,[status(thm)],[c_0_5822])). 4.46/4.72 fof(c_0_9809, plain, ![X3184, X3185, X3186, X3187]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3186,tc_fun(X3187,tc_HOL_Obool)),X3185),hAPP(hAPP(c_COMBB(tc_fun(X3187,tc_HOL_Obool),tc_fun(X3187,tc_HOL_Obool),X3186),c_Groups_Ouminus__class_Ouminus(tc_fun(X3187,tc_HOL_Obool))),X3184))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3187,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3186,tc_fun(X3187,tc_HOL_Obool)),X3185),X3184)), inference(variable_rename,[status(thm)],[fact_Compl__UN])). 4.46/4.72 fof(c_0_9810, plain, ![X3983, X3984, X3985, X3986]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3986,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3985,tc_fun(X3986,tc_HOL_Obool)),X3984),X3983))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3985,tc_fun(X3986,tc_HOL_Obool)),X3984),hAPP(hAPP(c_COMBB(tc_fun(X3986,tc_HOL_Obool),tc_fun(X3986,tc_HOL_Obool),X3985),c_Groups_Ouminus__class_Ouminus(tc_fun(X3986,tc_HOL_Obool))),X3983)), inference(variable_rename,[status(thm)],[fact_Compl__INT])). 4.46/4.72 fof(c_0_9811, plain, ![X7160, X7161, X7162, X7163, X7164]:hAPP(hAPP(c_Set_Oinsert(X7163),X7161),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7164,tc_fun(X7163,tc_HOL_Obool)),X7162),X7160))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7164,tc_fun(X7163,tc_HOL_Obool)),X7162),hAPP(hAPP(c_COMBB(tc_fun(X7163,tc_HOL_Obool),tc_fun(X7163,tc_HOL_Obool),X7164),hAPP(c_Set_Oinsert(X7163),X7161)),X7160)), inference(variable_rename,[status(thm)],[fact_INT__simps_I5_J])). 4.46/4.72 fof(c_0_9812, plain, ![X15338, X15339]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X15339),tc_List_Olist(X15339)),tc_HOL_Obool)),c_List_Olistrel1(X15339,c_Transitive__Closure_Ortrancl(X15339,X15338))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X15339),c_List_Olistrel1(X15339,X15338)))), inference(variable_rename,[status(thm)],[fact_listrel1__rtrancl__subset__rtrancl__listrel1])). 4.46/4.72 fof(c_0_9813, plain, ![X9326, X9327, X9328, X9329, X9330]:hAPP(c_Relation_ORange(X9330,X9329),hAPP(hAPP(c_Set_Oinsert(tc_prod(X9330,X9329)),hAPP(hAPP(c_Product__Type_OPair(X9330,X9329),X9328),X9327)),X9326))=hAPP(hAPP(c_Set_Oinsert(X9329),X9327),hAPP(c_Relation_ORange(X9330,X9329),X9326)), inference(variable_rename,[status(thm)],[fact_Range__insert])). 4.46/4.72 cnf(c_0_9814, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5823])). 4.46/4.72 cnf(c_0_9815, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5824, c_0_4800]), c_0_5825]), ['final']). 4.46/4.72 fof(c_0_9816, plain, ![X17118, X17119, X17120, X17121]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17121,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17121,tc_HOL_Obool)),X17120),X17118)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17121,tc_HOL_Obool)),X17119),X17118))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17121,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17121,tc_HOL_Obool)),X17120),X17119)),X17118), inference(variable_rename,[status(thm)],[fact_Un__Diff])). 4.46/4.72 fof(c_0_9817, plain, ![X817, X818, X819, X820, X821]:hAPP(c_Relation_ODomain(X821,X820),hAPP(hAPP(c_Set_Oinsert(tc_prod(X821,X820)),hAPP(hAPP(c_Product__Type_OPair(X821,X820),X819),X818)),X817))=hAPP(hAPP(c_Set_Oinsert(X821),X819),hAPP(c_Relation_ODomain(X821,X820),X817)), inference(variable_rename,[status(thm)],[fact_Domain__insert])). 4.46/4.72 fof(c_0_9818, plain, ![X2945, X2946, X2947, X2948]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2948,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2948,tc_HOL_Obool)),X2947),X2945)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2948,tc_HOL_Obool)),X2946),X2945))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2948,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2948,tc_HOL_Obool)),X2947),X2946)),X2945), inference(variable_rename,[status(thm)],[fact_Un__Int__distrib2])). 4.46/4.72 fof(c_0_9819, plain, ![X10453, X10454, X10455, X10456]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10456,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10456,tc_HOL_Obool)),X10455),X10454)),X10453)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10456,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10456,tc_HOL_Obool)),X10455),X10453)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10456,tc_HOL_Obool)),X10454),X10453)), inference(variable_rename,[status(thm)],[fact_Int__Un__distrib2])). 4.46/4.72 cnf(c_0_9820, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5826])). 4.46/4.72 fof(c_0_9821, plain, ![X9135, X9136, X9137, X9138]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9138,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9138,tc_HOL_Obool)),X9137),X9136)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9138,tc_HOL_Obool)),X9137),X9135))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9138,tc_HOL_Obool)),X9137),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9138,tc_HOL_Obool)),X9136),X9135)), inference(variable_rename,[status(thm)],[fact_Diff__Int])). 4.46/4.72 fof(c_0_9822, plain, ![X3075, X3076, X3077, X3078]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3078,tc_HOL_Obool)),X3077),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3078,tc_HOL_Obool)),X3076),X3075))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3078,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3078,tc_HOL_Obool)),X3077),X3076)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3078,tc_HOL_Obool)),X3077),X3075)), inference(variable_rename,[status(thm)],[fact_Un__Int__distrib])). 4.46/4.72 fof(c_0_9823, plain, ![X9561, X9562, X9563, X9564]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9564,tc_HOL_Obool)),X9563),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9564,tc_HOL_Obool)),X9562),X9561))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9564,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9564,tc_HOL_Obool)),X9563),X9562)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9564,tc_HOL_Obool)),X9563),X9561)), inference(variable_rename,[status(thm)],[fact_Int__Un__distrib])). 4.46/4.72 fof(c_0_9824, plain, ![X1616, X1617, X1618, X1619, X1620]:c_List_OtakeWhile(X1620,X1619,hAPP(hAPP(c_List_Omap(X1618,X1620),X1617),X1616))=hAPP(hAPP(c_List_Omap(X1618,X1620),X1617),c_List_OtakeWhile(X1618,hAPP(c_Fun_Ocomp(X1620,tc_HOL_Obool,X1618,X1619),X1617),X1616)), inference(variable_rename,[status(thm)],[fact_takeWhile__map])). 4.46/4.72 cnf(c_0_9825, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),X3))=hAPP(c_Relation_ODomain(X1,X2),hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3)))), inference(split_conjunct,[status(thm)],[c_0_5827])). 4.46/4.72 fof(c_0_9826, plain, ![X4681, X4682, X4683, X4684]:hAPP(hAPP(c_List_Olist_OCons(X4684),X4682),hAPP(hAPP(c_List_Oappend(X4684),c_List_Oreplicate(X4684,X4683,X4682)),X4681))=hAPP(hAPP(c_List_Oappend(X4684),c_List_Oreplicate(X4684,X4683,X4682)),hAPP(hAPP(c_List_Olist_OCons(X4684),X4682),X4681)), inference(variable_rename,[status(thm)],[fact_replicate__app__Cons__same])). 4.46/4.72 fof(c_0_9827, plain, ![X10310, X10311, X10312]:hAPP(c_List_Orev(X10312),hAPP(hAPP(c_List_Odrop(X10312),X10311),X10310))=hAPP(hAPP(c_List_Otake(X10312),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10312)),X10310)),X10311)),hAPP(c_List_Orev(X10312),X10310)), inference(variable_rename,[status(thm)],[fact_rev__drop])). 4.46/4.72 fof(c_0_9828, plain, ![X17380, X17381, X17382]:hAPP(c_List_Orev(X17382),hAPP(hAPP(c_List_Otake(X17382),X17381),X17380))=hAPP(hAPP(c_List_Odrop(X17382),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17382)),X17380)),X17381)),hAPP(c_List_Orev(X17382),X17380)), inference(variable_rename,[status(thm)],[fact_rev__take])). 4.46/4.72 fof(c_0_9829, plain, ![X12151, X12152, X12153, X12154, X12155]:c_List_Osplice(X12155,hAPP(hAPP(c_List_Olist_OCons(X12155),X12154),X12153),hAPP(hAPP(c_List_Olist_OCons(X12155),X12152),X12151))=hAPP(hAPP(c_List_Olist_OCons(X12155),X12154),hAPP(hAPP(c_List_Olist_OCons(X12155),X12152),c_List_Osplice(X12155,X12153,X12151))), inference(variable_rename,[status(thm)],[fact_splice_Osimps_I3_J])). 4.46/4.72 fof(c_0_9830, plain, ![X6027, X6028, X6029, X6030]:hAPP(hAPP(c_List_Onth(X6030),X6028),X6027)=hAPP(hAPP(c_List_Onth(X6030),hAPP(hAPP(c_List_Oappend(X6030),X6029),X6028)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6030)),X6029)),X6027)), inference(variable_rename,[status(thm)],[fact_nth__append__length__plus])). 4.46/4.72 fof(c_0_9831, plain, ![X7703, X7704, X7705, X7706, X7707]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7707,tc_Option_Ooption(X7706)),c_Map_Orestrict__map(X7707,X7706,X7705,X7703)),X7704),hAPP(X7705,X7704))=c_Map_Orestrict__map(X7707,X7706,X7705,hAPP(hAPP(c_Set_Oinsert(X7707),X7704),X7703)), inference(variable_rename,[status(thm)],[fact_restrict__map__insert])). 4.46/4.72 fof(c_0_9832, plain, ![X6816, X6817, X6818, X6819]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6819,tc_HOL_Obool)),hAPP(c_List_Oset(X6819),hAPP(hAPP(c_List_Olist__update(X6819,X6818),X6817),X6816))),hAPP(hAPP(c_Set_Oinsert(X6819),X6816),hAPP(c_List_Oset(X6819),X6818)))), inference(variable_rename,[status(thm)],[fact_set__update__subset__insert])). 4.46/4.72 fof(c_0_9833, plain, ![X5481, X5482, X5483, X5484]:c_Fun_Ocomp(X5483,X5483,X5484,hAPP(hAPP(c_Nat_Ocompow(X5483,X5483),X5482),X5481))=hAPP(hAPP(c_Nat_Ocompow(tc_fun(X5484,X5483),tc_fun(X5484,X5483)),X5482),c_Fun_Ocomp(X5483,X5483,X5484,X5481)), inference(variable_rename,[status(thm)],[fact_comp__funpow])). 4.46/4.72 fof(c_0_9834, plain, ![X2262, X2263, X2264, X2265, X2266, X2267, X2268, X2269]:hAPP(c_Product__Type_Omap__pair(X2269,X2268,X2267,X2266,X2265,X2264),hAPP(hAPP(c_Product__Type_OPair(X2269,X2267),X2263),X2262))=hAPP(hAPP(c_Product__Type_OPair(X2268,X2266),hAPP(X2265,X2263)),hAPP(X2264,X2262)), inference(variable_rename,[status(thm)],[fact_map__pair__simp])). 4.46/4.72 cnf(c_0_9835, hypothesis, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),v_F),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))))), inference(split_conjunct,[status(thm)],[conj_4])). 4.46/4.72 cnf(c_0_9836, plain, (X1=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5828])). 4.46/4.72 cnf(c_0_9837, hypothesis, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)),v_F)), inference(split_conjunct,[status(thm)],[conj_6])). 4.46/4.72 cnf(c_0_9838, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),c_Set_Ovimage(X2,X1,X4))=hAPP(c_Set_Ovimage(X2,X1,X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))), inference(split_conjunct,[status(thm)],[c_0_5829])). 4.46/4.72 fof(c_0_9839, plain, ![X17067, X17068]:c_HOL_OThe(X17068,hAPP(hAPP(c_COMBB(tc_fun(X17068,tc_HOL_Obool),tc_HOL_Obool,X17068),hAPP(c_fequal,X17067)),hAPP(hAPP(c_COMBC(X17068,tc_fun(X17068,tc_HOL_Obool),tc_fun(X17068,tc_HOL_Obool)),c_Set_Oinsert(X17068)),c_Orderings_Obot__class_Obot(tc_fun(X17068,tc_HOL_Obool)))))=c_Set_Othe__elem(X17068,X17067), inference(variable_rename,[status(thm)],[fact_the__elem__def])). 4.46/4.72 cnf(c_0_9840, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),c_List_OtakeWhile(X2,X3,X1)),c_List_OdropWhile(X2,X3,X1))), inference(split_conjunct,[status(thm)],[c_0_5830])). 4.46/4.72 cnf(c_0_9841, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),hAPP(c_List_Onth(X1),X2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))=X2), inference(split_conjunct,[status(thm)],[c_0_5831])). 4.46/4.72 fof(c_0_9842, plain, ![X13497, X13498, X13499, X13500, X13501, X13502]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13502,X13501),X13500),X13499),X13497)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13502,X13501),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13502,X13501),X13500),X13499),X13498)),X13499),X13497), inference(variable_rename,[status(thm)],[fact_fun__upd__upd])). 4.46/4.72 fof(c_0_9843, plain, ![X14398, X14399, X14400, X14401]:hAPP(hAPP(c_List_Odrop(X14401),X14399),hAPP(hAPP(c_List_Otake(X14401),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14400),X14399)),X14398))=hAPP(hAPP(c_List_Otake(X14401),X14400),hAPP(hAPP(c_List_Odrop(X14401),X14399),X14398)), inference(variable_rename,[status(thm)],[fact_take__drop])). 4.46/4.72 cnf(c_0_9844, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1),X3)),X2)), inference(split_conjunct,[status(thm)],[c_0_5832])). 4.46/4.72 fof(c_0_9845, plain, ![X6608, X6609, X6610]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6610),X6608)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6609),X6608))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6610),X6609)),X6608), inference(variable_rename,[status(thm)],[fact_diff__mult__distrib])). 4.46/4.72 fof(c_0_9846, plain, ![X776, X777, X778]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X778),X776)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X777),X776))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X778),X777)),X776), inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib])). 4.46/4.72 fof(c_0_9847, plain, ![X3531, X3532, X3533]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3533),X3532)),X3531)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3533),X3531)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3532),X3531)), inference(variable_rename,[status(thm)],[fact_add__mult__distrib])). 4.46/4.72 fof(c_0_9848, plain, ![X16418, X16419, X16420]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16420),X16419)),X16418)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16420),X16418)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16419),X16418)), inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib])). 4.46/4.72 cnf(c_0_9849, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X3,X4))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Nitpick_Opair__box_Opair__box__size(X5,X6,X1,X3,c_Nitpick_Opair__box_OPairBox(X5,X6,X2,X4))), inference(split_conjunct,[status(thm)],[c_0_5833])). 4.46/4.72 fof(c_0_9850, plain, ![X5320, X5321, X5322, X5323]:hAPP(hAPP(c_List_Odrop(X5323),X5322),hAPP(hAPP(c_List_Otake(X5323),X5321),X5320))=hAPP(hAPP(c_List_Otake(X5323),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5321),X5322)),hAPP(hAPP(c_List_Odrop(X5323),X5322),X5320)), inference(variable_rename,[status(thm)],[fact_drop__take])). 4.46/4.72 fof(c_0_9851, plain, ![X13650, X13651, X13652]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13652),X13651)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13652),X13650))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13652),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X13651),X13650)), inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib2])). 4.46/4.72 cnf(c_0_9852, plain, (hAPP(c_Set_Oimage(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3)),hAPP(c_Set_OPow(X1),X4))=hAPP(c_Set_OPow(X2),X5)|hAPP(c_Set_Oimage(X1,X2,X3),X4)!=X5), inference(split_conjunct,[status(thm)],[c_0_5834])). 4.46/4.72 fof(c_0_9853, plain, ![X2679, X2680, X2681]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2680),X2679))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2681),X2680)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2681),X2679)), inference(variable_rename,[status(thm)],[fact_add__mult__distrib2])). 4.46/4.72 fof(c_0_9854, plain, ![X9537, X9538, X9539]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9539),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9538),X9537))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9539),X9538)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9539),X9537)), inference(variable_rename,[status(thm)],[fact_diff__mult__distrib2])). 4.46/4.72 fof(c_0_9855, plain, ![X13257, X13258, X13259]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X13259),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13258),X13257))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X13259),X13258)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X13259),X13257)), inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib])). 4.46/4.72 fof(c_0_9856, plain, ![X2990, X2991, X2992, X2993, X2994]:c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X2993),hAPP(hAPP(c_Option_Omap(X2994,X2993),X2992),X2991),c_Lazy__Sequence_Ohb__map(X2994,X2993,X2992,X2990))=c_Lazy__Sequence_Ohb__map(X2994,X2993,X2992,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X2994),X2991,X2990)), inference(variable_rename,[status(thm)],[fact_hb__map_Osimps_I2_J])). 4.46/4.72 cnf(c_0_9857, plain, (hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)=hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5835])). 4.46/4.72 cnf(c_0_9858, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)=c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_5836])). 4.46/4.72 cnf(c_0_9859, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X1,tc_Nat_Onat),X2),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))=c_List_Olist_Olist__size(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_5837])). 4.46/4.72 cnf(c_0_9860, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),hAPP(c_COMBK(X1,tc_Nat_Onat),X2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))=c_List_Oreplicate(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_5838])). 4.46/4.72 fof(c_0_9861, plain, ![X5459, X5460, X5461, X5462]:hAPP(c_Map_Omap__of(X5462,X5461),hAPP(hAPP(c_List_Oappend(tc_prod(X5462,X5461)),X5460),X5459))=c_Map_Omap__add(X5462,X5461,hAPP(c_Map_Omap__of(X5462,X5461),X5459),hAPP(c_Map_Omap__of(X5462,X5461),X5460)), inference(variable_rename,[status(thm)],[fact_map__of__append])). 4.46/4.72 cnf(c_0_9862, plain, (c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1)))), inference(split_conjunct,[status(thm)],[c_0_5839])). 4.46/4.72 cnf(c_0_9863, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5840])). 4.46/4.72 cnf(c_0_9864, plain, (c_Nat__Transfer_Onat__set(hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X1))), inference(rw,[status(thm)],[c_0_5841, c_0_4531])). 4.46/4.72 fof(c_0_9865, plain, ![X5490, X5491]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5491),tc_List_Olist(X5491)),tc_HOL_Obool)),c_List_Olistrel(X5491,X5490)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5491),c_List_Olistrel1(X5491,X5490)))), inference(variable_rename,[status(thm)],[fact_listrel__subset__rtrancl__listrel1])). 4.46/4.72 fof(c_0_9866, plain, ![X2468, X2469, X2470, X2471, X2472]:hAPP(c_Lazy__Sequence_Obind(X2472,X2471,hAPP(X2470,X2468)),hAPP(hAPP(c_COMBC(X2472,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2471)),X2469),X2468))=hAPP(c_New__DSequence_Opos__bind(X2472,X2471,X2470,X2469),X2468), inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__bind__def])). 4.46/4.72 fof(c_0_9867, plain, ![X3821, X3822]:hAPP(c_List_Ofoldl(tc_List_Olist(X3822),X3822,hAPP(c_COMBC(X3822,tc_List_Olist(X3822),tc_List_Olist(X3822)),c_List_Olist_OCons(X3822)),c_List_Olist_ONil(X3822)),X3821)=hAPP(c_List_Orev(X3822),X3821), inference(variable_rename,[status(thm)],[fact_rev__foldl__cons])). 4.46/4.72 cnf(c_0_9868, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)=c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_5842])). 4.46/4.72 fof(c_0_9869, plain, ![X3131, X3132, X3133, X3134]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3134,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3134,tc_HOL_Obool)),X3133),X3131)),hAPP(hAPP(c_Set_Oinsert(X3134),X3132),c_Orderings_Obot__class_Obot(tc_fun(X3134,tc_HOL_Obool))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3134,tc_HOL_Obool)),X3133),hAPP(hAPP(c_Set_Oinsert(X3134),X3132),X3131)), inference(variable_rename,[status(thm)],[fact_Diff__insert])). 4.46/4.72 fof(c_0_9870, plain, ![X10486, X10487, X10488]:hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10488,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X10488),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X10487)),X10486)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10488,tc_Nat_Onat),X10487),X10486)), inference(variable_rename,[status(thm)],[fact_int__setprod])). 4.46/4.72 fof(c_0_9871, plain, ![X9458, X9459, X9460]:hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9460,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X9460),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X9459)),X9458)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9460,tc_Nat_Onat),X9459),X9458)), inference(variable_rename,[status(thm)],[fact_int__setsum])). 4.46/4.72 fof(c_0_9872, plain, ![X13204, X13205, X13206, X13207, X13208]:hAPP(hAPP(c_List_Olist_OCons(X13208),X13207),hAPP(hAPP(c_List_Olist__update(X13208,X13206),X13205),X13204))=hAPP(hAPP(c_List_Olist__update(X13208,hAPP(hAPP(c_List_Olist_OCons(X13208),X13207),X13206)),hAPP(c_Nat_OSuc,X13205)),X13204), inference(variable_rename,[status(thm)],[fact_list__update__code_I3_J])). 4.46/4.72 fof(c_0_9873, plain, ![X17254, X17255, X17256, X17257, X17258, X17259]:hAPP(c_List_Ofoldl(X17259,X17258,X17257,X17256),hAPP(hAPP(c_List_Oappend(X17258),X17255),X17254))=hAPP(c_List_Ofoldl(X17259,X17258,X17257,hAPP(c_List_Ofoldl(X17259,X17258,X17257,X17256),X17255)),X17254), inference(variable_rename,[status(thm)],[fact_foldl__append])). 4.46/4.72 cnf(c_0_9874, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),hAPP(c_Nat_OSuc,X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_5843])). 4.46/4.72 cnf(c_0_9875, plain, (c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4)),X5))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=X2), inference(split_conjunct,[status(thm)],[c_0_5844])). 4.46/4.72 fof(c_0_9876, plain, ![X9689, X9690]:hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X9690,X9689),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X9690),X9689)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X9690,X9689)))), inference(variable_rename,[status(thm)],[fact_divmod__nat__rel])). 4.46/4.72 fof(c_0_9877, plain, ![X10380, X10381, X10382]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10382,tc_HOL_Obool)),hAPP(c_Relation_OField(X10382),X10381)),hAPP(c_Relation_OField(X10382),X10380))=hAPP(c_Relation_OField(X10382),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10382,X10382),tc_HOL_Obool)),X10381),X10380)), inference(variable_rename,[status(thm)],[fact_Field__Un])). 4.46/4.72 fof(c_0_9878, plain, ![X9834, X9835, X9836, X9837]:hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X9837,tc_Option_Ooption(X9836)),hAPP(c_COMBK(tc_Option_Ooption(X9836),X9837),c_Option_Ooption_ONone(X9836))),X9835),c_Option_Ooption_ONone(X9836)),X9834)=c_Option_Ooption_ONone(X9836), inference(variable_rename,[status(thm)],[fact_empty__upd__none])). 4.46/4.72 cnf(c_0_9879, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5845, c_0_4517]), c_0_4517])). 4.46/4.72 fof(c_0_9880, plain, ![X15352, X15353, X15354, X15355]:hAPP(hAPP(c_Nat_Ocompow(X15355,X15355),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15353),X15354)),X15352)=hAPP(hAPP(c_Nat_Ocompow(X15355,X15355),X15354),hAPP(hAPP(c_Nat_Ocompow(X15355,X15355),X15353),X15352)), inference(variable_rename,[status(thm)],[fact_funpow__mult])). 4.46/4.72 cnf(c_0_9881, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Osplice(X1,X2,X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))), inference(split_conjunct,[status(thm)],[c_0_5846])). 4.46/4.72 fof(c_0_9882, plain, ![X3488, X3489, X3490, X3491]:hAPP(hAPP(c_List_Oappend(X3491),hAPP(c_List_Ofilter(X3491,X3490),X3489)),hAPP(c_List_Ofilter(X3491,X3490),X3488))=hAPP(c_List_Ofilter(X3491,X3490),hAPP(hAPP(c_List_Oappend(X3491),X3489),X3488)), inference(variable_rename,[status(thm)],[fact_filter__append])). 4.46/4.72 cnf(c_0_9883, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1)))), inference(split_conjunct,[status(thm)],[c_0_5847])). 4.46/4.72 fof(c_0_9884, plain, ![X3321, X3322, X3323]:hAPP(c_Option_Omap(X3323,X3322),X3321)=c_Option_Ooption_Ooption__case(tc_Option_Ooption(X3322),X3323,c_Option_Ooption_ONone(X3322),hAPP(hAPP(c_COMBB(X3322,tc_Option_Ooption(X3322),X3323),c_Option_Ooption_OSome(X3322)),X3321)), inference(variable_rename,[status(thm)],[fact_Option_Omap__def])). 4.46/4.72 cnf(c_0_9885, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Relation_OId(X1))), inference(split_conjunct,[status(thm)],[c_0_5848])). 4.46/4.72 cnf(c_0_9886, plain, (hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X1),c_List_Oupt(X2,X3))=c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),X3)), inference(split_conjunct,[status(thm)],[c_0_5849])). 4.46/4.72 cnf(c_0_9887, plain, (hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|hAPP(c_Nat_OSuc,X3)=hAPP(c_Finite__Set_Ocard(X1),X5)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=X2|hAPP(c_Finite__Set_Ocard(X1),X2)!=X3|hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)!=X5), inference(split_conjunct,[status(thm)],[c_0_5438])). 4.46/4.72 cnf(c_0_9888, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5850]), ['final']). 4.46/4.72 cnf(c_0_9889, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5851]), ['final']). 4.46/4.72 fof(c_0_9890, plain, ![X12655, X12656, X12657]:hAPP(c_List_Otl(X12657),hAPP(hAPP(c_List_Otake(X12657),X12656),X12655))=hAPP(hAPP(c_List_Otake(X12657),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12656),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X12657),X12655)), inference(variable_rename,[status(thm)],[fact_tl__take])). 4.46/4.72 fof(c_0_9891, plain, ![X1987, X1988]:hAPP(c_Set_OPow(X1988),hAPP(c_List_Oset(X1988),X1987))=hAPP(c_Set_Oimage(tc_List_Olist(X1988),tc_fun(X1988,tc_HOL_Obool),c_List_Oset(X1988)),hAPP(c_List_Oset(tc_List_Olist(X1988)),c_Enum_Osublists(X1988,X1987))), inference(variable_rename,[status(thm)],[fact_sublists__powset])). 4.46/4.72 fof(c_0_9892, plain, ![X17455, X17456, X17457]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17457),X17455),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17456),X17455))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17457,X17456)),X17455), inference(variable_rename,[status(thm)],[fact_mod__mult__distrib])). 4.46/4.72 fof(c_0_9893, plain, ![X13567, X13568, X13569]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13569),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X13568,X13567))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13569),X13568),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13569),X13567)), inference(variable_rename,[status(thm)],[fact_mod__mult__distrib2])). 4.46/4.72 fof(c_0_9894, plain, ![X6605, X6606, X6607]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X6605),X6606)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6607),X6606)),X6605)),X6606), inference(variable_rename,[status(thm)],[fact_mod__mult__self4])). 4.46/4.72 fof(c_0_9895, plain, ![X13833, X13834, X13835, X13836]:X13834=hAPP(hAPP(c_List_Onth(X13836),hAPP(hAPP(c_List_Oappend(X13836),X13835),hAPP(hAPP(c_List_Olist_OCons(X13836),X13834),X13833))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13836)),X13835)), inference(variable_rename,[status(thm)],[fact_nth__append__length])). 4.46/4.72 fof(c_0_9896, plain, ![X7011, X7012, X7013]:c_Random_Oselect__weight(X7013,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X7013)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X7013),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X7012)),X7011))=c_Random_Oselect__weight(X7013,X7011), inference(variable_rename,[status(thm)],[fact_select__weight__cons__zero])). 4.46/4.72 fof(c_0_9897, plain, ![X15972]:c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X15972),tc_HOL_Obool))=hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(X15972)),c_Option_Ooption_ONone(X15972)),hAPP(c_Set_Oimage(X15972,tc_Option_Ooption(X15972),c_Option_Ooption_OSome(X15972)),c_Orderings_Otop__class_Otop(tc_fun(X15972,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_UNIV__option__conv])). 4.46/4.72 fof(c_0_9898, plain, ![X9268, X9269]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X9269),tc_List_Olist(X9269)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X9269,X9268))=c_List_Olex(X9269,X9268), inference(variable_rename,[status(thm)],[fact_lex__def])). 4.46/4.72 cnf(c_0_9899, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orotate(X1,X2),X3))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)), inference(split_conjunct,[status(thm)],[c_0_5852])). 4.46/4.72 fof(c_0_9900, plain, ![X5922, X5923, X5924]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5924)),hAPP(c_List_Ofilter(X5924,X5923),X5922))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5924)),X5922))), inference(variable_rename,[status(thm)],[fact_length__filter__le])). 4.46/4.72 cnf(c_0_9901, plain, (c_Option_Ooption_ONone(X1)=c_Map_Omap__comp(X2,X1,X3,hAPP(c_COMBK(tc_Option_Ooption(X1),X2),c_Option_Ooption_ONone(X1)),X4,X5)), inference(split_conjunct,[status(thm)],[c_0_5853])). 4.46/4.72 fof(c_0_9902, plain, ![X17291, X17292]:c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X17292,X17291),tc_HOL_Obool))=hAPP(hAPP(c_Product__Type_OSigma(X17292,X17291),c_Orderings_Otop__class_Otop(tc_fun(X17292,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X17291,tc_HOL_Obool),X17292),c_Orderings_Otop__class_Otop(tc_fun(X17291,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_UNIV__Times__UNIV])). 4.46/4.72 cnf(c_0_9903, plain, (c_List_Olist_ONil(X1)=c_List_Oconcat(X1,c_List_Oreplicate(tc_List_Olist(X1),X2,c_List_Olist_ONil(X1)))), inference(split_conjunct,[status(thm)],[c_0_5854])). 4.46/4.72 fof(c_0_9904, plain, ![X10446, X10447, X10448]:hAPP(c_Lazy__Sequence_Oyield(X10448),c_Lazy__Sequence_Olazy__sequence_OInsert(X10448,X10447,X10446))=hAPP(c_Option_Ooption_OSome(tc_prod(X10448,tc_Lazy__Sequence_Olazy__sequence(X10448))),hAPP(hAPP(c_Product__Type_OPair(X10448,tc_Lazy__Sequence_Olazy__sequence(X10448)),X10447),X10446)), inference(variable_rename,[status(thm)],[fact__01])). 4.46/4.72 cnf(c_0_9905, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))=X2), inference(split_conjunct,[status(thm)],[c_0_5855])). 4.46/4.72 cnf(c_0_9906, plain, (hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))), inference(split_conjunct,[status(thm)],[c_0_5856])). 4.46/4.72 cnf(c_0_9907, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))), inference(split_conjunct,[status(thm)],[c_0_5857])). 4.46/4.72 cnf(c_0_9908, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Ovimage(X1,X3,X4),hAPP(hAPP(c_Set_Oinsert(X3),hAPP(X4,X2)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))))), inference(er,[status(thm)],[c_0_5858])). 4.46/4.72 cnf(c_0_9909, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_Set_Ovimage(X2,X1,X3),X4))),X4))), inference(split_conjunct,[status(thm)],[c_0_5859])). 4.46/4.72 cnf(c_0_9910, plain, (hAPP(c_Set_Ovimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5860])). 4.46/4.72 cnf(c_0_9911, plain, (X1=hAPP(c_Set_Ovimage(X2,X2,c_Fun_Oid(X2)),X1)), inference(split_conjunct,[status(thm)],[c_0_5861])). 4.46/4.72 cnf(c_0_9912, plain, (X1=hAPP(c_Set_Ovimage(X2,X2,c_COMBI(X2)),X1)), inference(split_conjunct,[status(thm)],[c_0_5862])). 4.46/4.72 cnf(c_0_9913, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5863])). 4.46/4.72 fof(c_0_9914, plain, ![X14547, X14548, X14549]:hAPP(hAPP(c_Nat_Ocompow(X14549,X14549),hAPP(c_Nat_OSuc,X14548)),X14547)=hAPP(c_Fun_Ocomp(X14549,X14549,X14549,X14547),hAPP(hAPP(c_Nat_Ocompow(X14549,X14549),X14548),X14547)), inference(variable_rename,[status(thm)],[fact_funpow_Osimps_I2_J])). 4.46/4.72 fof(c_0_9915, plain, ![X11292, X11293, X11294, X11295]:hAPP(hAPP(c_Set_Oinsert(X11295),X11294),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11295,tc_HOL_Obool)),X11293),X11292))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11295,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X11295),X11294),X11293)),hAPP(hAPP(c_Set_Oinsert(X11295),X11294),X11292)), inference(variable_rename,[status(thm)],[fact_insert__inter__insert])). 4.46/4.72 fof(c_0_9916, plain, ![X5381, X5382, X5383]:hAPP(c_List_Ofilter(X5383,hAPP(c_fequal,X5382)),X5381)=c_List_Oreplicate(X5383,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5383)),hAPP(c_List_Ofilter(X5383,hAPP(c_fequal,X5382)),X5381)),X5382), inference(variable_rename,[status(thm)],[fact_replicate__length__filter])). 4.46/4.72 fof(c_0_9917, plain, ![X6023, X6024, X6025, X6026]:hAPP(hAPP(c_List_Otake(X6026),hAPP(c_Nat_OSuc,X6025)),hAPP(hAPP(c_List_Olist_OCons(X6026),X6024),X6023))=hAPP(hAPP(c_List_Olist_OCons(X6026),X6024),hAPP(hAPP(c_List_Otake(X6026),X6025),X6023)), inference(variable_rename,[status(thm)],[fact_take__Suc__Cons])). 4.46/4.72 fof(c_0_9918, plain, ![X5089, X5090, X5091]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X5091)),hAPP(c_Set_Oimage(X5090,tc_Option_Ooption(X5091),hAPP(c_Map_Omap__of(X5090,X5091),X5089)),c_Orderings_Otop__class_Otop(tc_fun(X5090,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_finite__range__map__of])). 4.46/4.72 fof(c_0_9919, plain, ![X17288, X17289, X17290]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17290)),c_List_OtakeWhile(X17290,X17289,X17288))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17290)),X17288))), inference(variable_rename,[status(thm)],[fact_length__takeWhile__le])). 4.46/4.72 fof(c_0_9920, plain, ![X15011, X15012, X15013]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X15013,X15012)),X15011),X15012)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X15013),X15011),X15012), inference(variable_rename,[status(thm)],[fact_zpower__zmod])). 4.46/4.72 fof(c_0_9921, plain, ![X9500, X9501, X9502]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9502),X9500),X9501)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X9502,X9501)),X9500),X9501), inference(variable_rename,[status(thm)],[fact_zdiff__zmod__left])). 4.46/4.72 fof(c_0_9922, plain, ![X17500, X17501, X17502]:c_List_Olistsp(X17502,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17502,tc_HOL_Obool)),X17501),X17500))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X17502),tc_HOL_Obool)),c_List_Olistsp(X17502,X17501)),c_List_Olistsp(X17502,X17500)), inference(variable_rename,[status(thm)],[fact_listsp__inf__eq])). 4.46/4.72 cnf(c_0_9923, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5864])). 4.46/4.72 cnf(c_0_9924, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5865]), ['final']). 4.46/4.72 fof(c_0_9925, plain, ![X7578, X7579, X7580, X7581]:hAPP(hAPP(c_List_Oappend(X7581),c_List_Oreplicate(X7581,X7580,X7578)),c_List_Oreplicate(X7581,X7579,X7578))=c_List_Oreplicate(X7581,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7580),X7579),X7578), inference(variable_rename,[status(thm)],[fact_replicate__add])). 4.46/4.72 cnf(c_0_9926, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))), inference(split_conjunct,[status(thm)],[c_0_5866])). 4.46/4.72 cnf(c_0_9927, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5867]), ['final']). 4.46/4.72 fof(c_0_9928, plain, ![X16141, X16142, X16143]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16143),X16142),X16141)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16143),c_Divides_Odiv__class_Omod(tc_Int_Oint,X16142,X16141)),X16141), inference(variable_rename,[status(thm)],[fact_zmod__zmult1__eq])). 4.46/4.72 fof(c_0_9929, plain, ![X11565, X11566, X11567]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X11567),X11566),X11565)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X11567),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11566,X11565)),X11565), inference(variable_rename,[status(thm)],[fact_zdiff__zmod__right])). 4.46/4.72 fof(c_0_9930, plain, ![X13591, X13592, X13593]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13593),X13591)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13593),X13592)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13591),X13592)), inference(variable_rename,[status(thm)],[fact_diff__cancel2])). 4.46/4.72 fof(c_0_9931, plain, ![X2761, X2762, X2763]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2762),X2761)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2763),X2762)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2763),X2761)), inference(variable_rename,[status(thm)],[fact_diff__cancel])). 4.46/4.72 cnf(c_0_9932, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_5868])). 4.46/4.72 cnf(c_0_9933, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)), inference(split_conjunct,[status(thm)],[c_0_5869]), ['final']). 4.46/4.72 cnf(c_0_9934, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))))=hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5870])). 4.46/4.72 cnf(c_0_9935, plain, (c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Set_Oinsert(X3),X4)),X5))|X1!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5871])). 4.46/4.72 fof(c_0_9936, plain, ![X6470, X6471, X6472]:hAPP(c_Set_OPow(X6472),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6472,tc_HOL_Obool)),X6471),X6470))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X6472,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X6472),X6471)),hAPP(c_Set_OPow(X6472),X6470)), inference(variable_rename,[status(thm)],[fact_Pow__Int__eq])). 4.46/4.72 fof(c_0_9937, plain, ![X3180, X3181, X3182, X3183]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3183,tc_HOL_Obool)),c_Map_Odom(X3183,X3182,X3180)),c_Map_Odom(X3183,X3182,X3181))=c_Map_Odom(X3183,X3182,c_Map_Omap__add(X3183,X3182,X3181,X3180)), inference(variable_rename,[status(thm)],[fact_dom__map__add])). 4.46/4.72 fof(c_0_9938, plain, ![X14217, X14218, X14219]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X14219,X14218,X14218),hAPP(c_COMBK(tc_fun(X14218,X14218),X14219),c_COMBI(X14218))),X14217)=hAPP(c_Product__Type_Osnd(X14219,X14218),X14217), inference(variable_rename,[status(thm)],[fact_snd__def])). 4.46/4.72 cnf(c_0_9939, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X5)))|hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))!=X5), inference(split_conjunct,[status(thm)],[c_0_5872])). 4.46/4.72 cnf(c_0_9940, plain, (hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X1)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5873])). 4.46/4.72 fof(c_0_9941, plain, ![X11272, X11273]:c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X11273),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X11273))),c_List_Otranspose(X11273,X11272)))), inference(variable_rename,[status(thm)],[fact_sorted__transpose])). 4.46/4.72 cnf(c_0_9942, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)),X1)))|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_5498])). 4.46/4.72 fof(c_0_9943, plain, ![X9873, X9874, X9875]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9875,tc_HOL_Obool)),hAPP(c_List_Oset(X9875),hAPP(hAPP(c_List_Odrop(X9875),X9874),X9873))),hAPP(c_List_Oset(X9875),X9873))), inference(variable_rename,[status(thm)],[fact_set__drop__subset])). 4.46/4.72 cnf(c_0_9944, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_Enum_Osublists(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5874])). 4.46/4.72 fof(c_0_9945, plain, ![X593, X594, X595]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X595,tc_HOL_Obool)),hAPP(c_List_Oset(X595),hAPP(hAPP(c_List_Otake(X595),X594),X593))),hAPP(c_List_Oset(X595),X593))), inference(variable_rename,[status(thm)],[fact_set__take__subset])). 4.46/4.72 cnf(c_0_9946, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),X2))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5875])). 4.46/4.72 cnf(c_0_9947, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_5876]), ['final']). 4.46/4.72 cnf(c_0_9948, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),X2))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5877])). 4.46/4.72 cnf(c_0_9949, plain, (c_Relation_Oirrefl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1)))), inference(split_conjunct,[status(thm)],[c_0_5878])). 4.46/4.72 fof(c_0_9950, plain, ![X6447, X6448]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X6448,X6447)=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6448),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6447))), inference(variable_rename,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I2_J])). 4.46/4.72 fof(c_0_9951, plain, ![X5415, X5416, X5417, X5418, X5419, X5420, X5421]:hAPP(c_Product__Type_Ofst(X5421,X5420),hAPP(c_Product__Type_Omap__pair(X5419,X5421,X5418,X5420,X5417,X5416),X5415))=hAPP(X5417,hAPP(c_Product__Type_Ofst(X5419,X5418),X5415)), inference(variable_rename,[status(thm)],[fact_fst__map__pair])). 4.46/4.72 fof(c_0_9952, plain, ![X5959, X5960, X5961, X5962, X5963, X5964, X5965]:hAPP(c_Product__Type_Osnd(X5965,X5964),hAPP(c_Product__Type_Omap__pair(X5963,X5965,X5962,X5964,X5961,X5960),X5959))=hAPP(X5960,hAPP(c_Product__Type_Osnd(X5963,X5962),X5959)), inference(variable_rename,[status(thm)],[fact_snd__prod__fun])). 4.46/4.72 fof(c_0_9953, plain, ![X5374, X5375, X5376]:hAPP(c_Product__Type_Osnd(tc_List_Olist(X5376),tc_List_Olist(X5376)),c_List_Opartition(X5376,X5375,X5374))=hAPP(c_List_Ofilter(X5376,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X5376,c_fNot),X5375)),X5374), inference(variable_rename,[status(thm)],[fact_partition__filter2])). 4.46/4.72 fof(c_0_9954, plain, ![X14678, X14679]:hAPP(hAPP(c_List_Otake(X14679),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14679)),X14678)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X14678)=c_List_Obutlast(X14679,X14678), inference(variable_rename,[status(thm)],[fact_butlast__conv__take])). 4.46/4.72 cnf(c_0_9955, plain, (hAPP(c_Relation_ORange(X1,X1),X2)=hAPP(c_Relation_ORange(X1,X1),c_Transitive__Closure_Otrancl(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5879])). 4.46/4.72 cnf(c_0_9956, plain, (hAPP(c_Relation_ODomain(X1,X1),X2)=hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Otrancl(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5880])). 4.46/4.72 fof(c_0_9957, plain, ![X16365, X16366, X16367]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16367,tc_HOL_Obool)),hAPP(c_List_Oset(X16367),c_List_Osublist(X16367,X16366,X16365))),hAPP(c_List_Oset(X16367),X16366))), inference(variable_rename,[status(thm)],[fact_set__sublist__subset])). 4.46/4.72 fof(c_0_9958, plain, ![X9540, X9541, X9542]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9542,tc_HOL_Obool)),hAPP(c_List_Oset(X9542),c_List_Oremove1(X9542,X9541,X9540))),hAPP(c_List_Oset(X9542),X9540))), inference(variable_rename,[status(thm)],[fact_set__remove1__subset])). 4.46/4.72 fof(c_0_9959, plain, ![X17219, X17220, X17221]:hBOOL(hAPP(hAPP(c_member(tc_prod(X17221,X17221)),hAPP(hAPP(c_Product__Type_OPair(X17221,X17221),X17220),X17220)),c_Transitive__Closure_Ortrancl(X17221,X17219))), inference(variable_rename,[status(thm)],[fact_rtrancl_Ortrancl__refl])). 4.46/4.72 fof(c_0_9960, plain, ![X17435, X17436]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X17436)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17435))), inference(variable_rename,[status(thm)],[fact_negative__zless])). 4.46/4.72 cnf(c_0_9961, plain, (hAPP(c_List_Oset(X1),X2)=hAPP(c_List_Oset(X1),hAPP(c_List_Orotate(X1,X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5881])). 4.46/4.72 fof(c_0_9962, plain, ![X2560]:c_Fun_Oinj__on(X2560,tc_fun(X2560,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2560,tc_fun(X2560,tc_HOL_Obool),tc_fun(X2560,tc_HOL_Obool)),c_Set_Oinsert(X2560)),c_Orderings_Obot__class_Obot(tc_fun(X2560,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X2560,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_inj__singleton])). 4.46/4.72 fof(c_0_9963, plain, ![X8826, X8827, X8828, X8829]:c_List_Oremdups(X8829,hAPP(hAPP(c_List_Omap(X8828,X8829),X8827),X8826))=c_List_Oremdups(X8829,hAPP(hAPP(c_List_Omap(X8828,X8829),X8827),c_List_Oremdups(X8828,X8826))), inference(variable_rename,[status(thm)],[fact_remdups__map__remdups])). 4.46/4.72 fof(c_0_9964, plain, ![X13239, X13240]:c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13240),X13239))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13240),hAPP(c_Nat_OSuc,X13239)), inference(variable_rename,[status(thm)],[fact_diff__Suc])). 4.46/4.72 fof(c_0_9965, plain, ![X413, X414]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X414,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X414,X414),X413)),hAPP(c_Relation_ORange(X414,X414),X413))=hAPP(c_Relation_OField(X414),X413), inference(variable_rename,[status(thm)],[fact_Field__def])). 4.46/4.72 cnf(c_0_9966, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))|X1!=hAPP(c_Set_Oimage(tc_Nat_Onat,X2,X3),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X4)))), inference(split_conjunct,[status(thm)],[c_0_5261])). 4.46/4.72 fof(c_0_9967, plain, ![X12036, X12037, X12038, X12039, X12040, X12041, X12042]:hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X12042,X12041,X12040,X12039),X12038),X12037),X12036)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X12041,X12040,X12039),X12037),hAPP(X12038,X12036)), inference(variable_rename,[status(thm)],[fact_scomp__apply])). 4.46/4.72 cnf(c_0_9968, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1)))=hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))), inference(split_conjunct,[status(thm)],[c_0_5882])). 4.46/4.72 cnf(c_0_9969, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)), inference(rw,[status(thm)],[c_0_5883, c_0_5884]), ['final']). 4.46/4.72 fof(c_0_9970, plain, ![X10015, X10016, X10017, X10018, X10019]:hAPP(hAPP(c_List_Olist__update(X10019,X10018),X10017),X10015)=hAPP(hAPP(c_List_Olist__update(X10019,hAPP(hAPP(c_List_Olist__update(X10019,X10018),X10017),X10016)),X10017),X10015), inference(variable_rename,[status(thm)],[fact_list__update__overwrite])). 4.46/4.72 fof(c_0_9971, plain, ![X12421, X12422, X12423, X12424, X12425]:c_Predicate_Opred__comp(X12424,X12423,X12425,c_Predicate_Oconversep(X12423,X12424,X12421),c_Predicate_Oconversep(X12425,X12423,X12422))=c_Predicate_Oconversep(X12425,X12424,c_Predicate_Opred__comp(X12425,X12423,X12424,X12422,X12421)), inference(variable_rename,[status(thm)],[fact_converse__pred__comp])). 4.46/4.72 cnf(c_0_9972, plain, (c_List_Obutlast(X2,hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4))=c_List_Obutlast(X2,X3)|X1!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5885])). 4.46/4.72 fof(c_0_9973, plain, ![X15162, X15163, X15164, X15165]:hAPP(X15165,hAPP(hAPP(hAPP(c_Nat_Ocompow(X15164,X15164),X15163),X15165),X15162))=hAPP(hAPP(hAPP(c_Nat_Ocompow(X15164,X15164),X15163),X15165),hAPP(X15165,X15162)), inference(variable_rename,[status(thm)],[fact_funpow__swap1])). 4.46/4.72 fof(c_0_9974, plain, ![X16217, X16218, X16219, X16220]:hAPP(hAPP(c_List_Oappend(X16220),hAPP(hAPP(c_List_Oappend(X16220),X16219),X16218)),X16217)=hAPP(hAPP(c_List_Oappend(X16220),X16219),hAPP(hAPP(c_List_Oappend(X16220),X16218),X16217)), inference(variable_rename,[status(thm)],[fact_append__assoc])). 4.46/4.72 fof(c_0_9975, plain, ![X6581, X6582, X6583, X6584]:hAPP(hAPP(c_List_Olist_OCons(X6584),X6583),hAPP(hAPP(c_List_Oappend(X6584),X6582),X6581))=hAPP(hAPP(c_List_Oappend(X6584),hAPP(hAPP(c_List_Olist_OCons(X6584),X6583),X6582)),X6581), inference(variable_rename,[status(thm)],[fact_append__Cons])). 4.46/4.72 fof(c_0_9976, plain, ![X2744, X2745, X2746, X2747]:hAPP(hAPP(c_List_Odrop(X2747),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2746),X2745)),X2744)=hAPP(hAPP(c_List_Odrop(X2747),X2746),hAPP(hAPP(c_List_Odrop(X2747),X2745),X2744)), inference(variable_rename,[status(thm)],[fact_drop__drop])). 4.46/4.72 cnf(c_0_9977, plain, (hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Otake(X1),X3),X4))=hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X2),X3)),X4)), inference(split_conjunct,[status(thm)],[c_0_5886])). 4.46/4.72 fof(c_0_9978, plain, ![X9478, X9479]:hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X9479),X9478)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X9479,X9478))=c_Code__Numeral_Odiv__mod__code__numeral(X9479,X9478), inference(variable_rename,[status(thm)],[fact_div__mod__code__numeral__def])). 4.46/4.72 fof(c_0_9979, plain, ![X16094, X16095, X16096]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16096),X16095)),X16094)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16095),X16094)), inference(variable_rename,[status(thm)],[fact_nat__mult__assoc])). 4.46/4.72 fof(c_0_9980, plain, ![X1023, X1024, X1025]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1025),X1024)),X1023)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1025),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1024),X1023)), inference(variable_rename,[status(thm)],[fact_zmult__assoc])). 4.46/4.72 fof(c_0_9981, plain, ![X15034, X15035, X15036]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X15036),X15035)),X15034)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X15036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15035),X15034)), inference(variable_rename,[status(thm)],[fact_zpower__zpower])). 4.46/4.72 fof(c_0_9982, plain, ![X7335, X7336, X7337]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X7337),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7336),X7335))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X7337),X7336)),X7335), inference(variable_rename,[status(thm)],[fact_div__mult2__eq])). 4.46/4.72 fof(c_0_9983, plain, ![X13823, X13824, X13825]:hAPP(c_List_Orev(X13825),hAPP(hAPP(c_List_Oappend(X13825),X13824),X13823))=hAPP(hAPP(c_List_Oappend(X13825),hAPP(c_List_Orev(X13825),X13823)),hAPP(c_List_Orev(X13825),X13824)), inference(variable_rename,[status(thm)],[fact_rev__append])). 4.46/4.72 fof(c_0_9984, plain, ![X6005, X6006]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6006)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6005))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X6006),X6005)), inference(variable_rename,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I1_J])). 4.46/4.72 fof(c_0_9985, plain, ![X5788, X5789]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5789),X5788))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5789)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5788)), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J])). 4.46/4.72 fof(c_0_9986, plain, ![X10133, X10134]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10134),X10133))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10134)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10133)), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J])). 4.46/4.72 fof(c_0_9987, plain, ![X7949, X7950]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7950,tc_fun(X7950,tc_HOL_Obool)),X7949),hAPP(hAPP(c_COMBC(X7950,tc_fun(X7950,tc_HOL_Obool),tc_fun(X7950,tc_HOL_Obool)),c_Set_Oinsert(X7950)),c_Orderings_Obot__class_Obot(tc_fun(X7950,tc_HOL_Obool))))=X7949, inference(variable_rename,[status(thm)],[fact_UN__singleton])). 4.46/4.72 fof(c_0_9988, plain, ![X17467, X17468]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X17468),hAPP(c_List_Oset(X17468),X17467))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17468)),X17467))), inference(variable_rename,[status(thm)],[fact_card__length])). 4.46/4.72 cnf(c_0_9989, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),X2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5887])). 4.46/4.72 cnf(c_0_9990, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X1)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))=hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))), inference(split_conjunct,[status(thm)],[c_0_5888])). 4.46/4.72 cnf(c_0_9991, plain, (hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))=hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_5889]), ['final']). 4.46/4.72 fof(c_0_9992, plain, ![X2326, X2327, X2328]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2326,X2327)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2328),X2327)),X2326),X2327), inference(variable_rename,[status(thm)],[fact_mod__mult__self3])). 4.46/4.72 fof(c_0_9993, plain, ![X8113, X8114, X8115]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8115,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8115,tc_HOL_Obool)),X8114),X8113)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8115,tc_HOL_Obool)),X8114),X8113))=X8114, inference(variable_rename,[status(thm)],[fact_Un__Diff__Int])). 4.46/4.72 fof(c_0_9994, plain, ![X1249, X1250, X1251, X1252, X1253, X1254]:hAPP(hAPP(X1251,X1250),X1249)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1254,X1253,X1252),X1251),hAPP(hAPP(c_Product__Type_OPair(X1254,X1253),X1250),X1249)), inference(variable_rename,[status(thm)],[fact_split__conv])). 4.46/4.72 cnf(c_0_9995, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1))))), inference(rw,[status(thm)],[c_0_5890, c_0_5562])). 4.46/4.72 fof(c_0_9996, plain, ![X12771, X12772, X12773, X12774, X12775]:c_Map_Orestrict__map(X12775,X12774,c_Map_Orestrict__map(X12775,X12774,X12773,X12772),X12771)=c_Map_Orestrict__map(X12775,X12774,X12773,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12775,tc_HOL_Obool)),X12772),X12771)), inference(variable_rename,[status(thm)],[fact_restrict__restrict])). 4.46/4.72 fof(c_0_9997, plain, ![X4129, X4130, X4131, X4132]:hAPP(hAPP(c_List_Olist_OCons(X4132),X4129),X4130)=hAPP(hAPP(c_List_Olist__update(X4132,hAPP(hAPP(c_List_Olist_OCons(X4132),X4131),X4130)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4129), inference(variable_rename,[status(thm)],[fact_list__update__code_I2_J])). 4.46/4.72 cnf(c_0_9998, plain, (c_Relation_OId(X1)=hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId(X1))), inference(split_conjunct,[status(thm)],[c_0_5891])). 4.46/4.72 cnf(c_0_9999, plain, (X1=hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4)|hAPP(hAPP(c_List_Oappend(X2),X3),X1)!=X4), inference(split_conjunct,[status(thm)],[c_0_5411])). 4.46/4.72 cnf(c_0_10000, plain, (hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5892, c_0_5893]), c_0_5120])). 4.46/4.72 cnf(c_0_10001, plain, (hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5894, c_0_4760]), c_0_5120]), ['final']). 4.46/4.72 fof(c_0_10002, plain, ![X15570, X15571, X15572]:c_List_OtakeWhile(X15572,X15571,X15570)=hAPP(hAPP(c_List_Otake(X15572),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15572)),c_List_OtakeWhile(X15572,X15571,X15570))),X15570), inference(variable_rename,[status(thm)],[fact_takeWhile__eq__take])). 4.46/4.72 fof(c_0_10003, plain, ![X5060, X5061, X5062, X5063, X5064, X5065]:c_Hoare__Mirabelle_Otriple_Otriple__case(X5065,X5064,X5063,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5065),X5062),X5061),X5060))=hAPP(hAPP(hAPP(X5063,X5062),X5061),X5060), inference(variable_rename,[status(thm)],[fact_triple_Osimps_I2_J])). 4.46/4.72 fof(c_0_10004, plain, ![X16527, X16528, X16529, X16530, X16531, X16532]:hAPP(hAPP(hAPP(X16530,X16529),X16528),X16527)=c_Hoare__Mirabelle_Otriple_Otriple__rec(X16532,X16531,X16530,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16532),X16529),X16528),X16527)), inference(variable_rename,[status(thm)],[fact_triple_Orecs])). 4.46/4.72 fof(c_0_10005, plain, ![X6485, X6486, X6487]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X6487))),c_Enum_On__lists(X6487,X6486,X6485))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6487)),X6485)),X6486), inference(variable_rename,[status(thm)],[fact_length__n__lists])). 4.46/4.72 cnf(c_0_10006, plain, (c_Nitpick_Onorm__frac(X2,X1)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X1), inference(split_conjunct,[status(thm)],[c_0_5477])). 4.46/4.72 cnf(c_0_10007, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5895, c_0_4436]), c_0_4436]), ['final']). 4.46/4.72 fof(c_0_10008, plain, ![X15895]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15895),X15895)))), inference(variable_rename,[status(thm)],[fact_le__cube])). 4.46/4.72 cnf(c_0_10009, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_5896])). 4.46/4.72 cnf(c_0_10010, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_5897])). 4.46/4.72 fof(c_0_10011, plain, ![X6164, X6165, X6166]:hAPP(c_List_Otl(X6166),hAPP(hAPP(c_List_Otake(X6166),hAPP(c_Nat_OSuc,X6165)),X6164))=hAPP(hAPP(c_List_Otake(X6166),X6165),hAPP(c_List_Otl(X6166),X6164)), inference(variable_rename,[status(thm)],[fact_take__tl])). 4.46/4.72 fof(c_0_10012, plain, ![X15900, X15901, X15902]:hAPP(hAPP(c_List_Olist_OCons(X15902),X15901),c_List_Olist_ONil(X15902))=hAPP(hAPP(c_List_Otake(X15902),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X15902),X15901),X15900)), inference(variable_rename,[status(thm)],[fact_take__1__Cons])). 4.46/4.72 fof(c_0_10013, plain, ![X5168, X5169, X5170]:hAPP(hAPP(c_Set_Oinsert(X5170),X5169),X5168)=hAPP(hAPP(c_Set_Oinsert(X5170),X5169),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5170,tc_HOL_Obool)),X5168),hAPP(hAPP(c_Set_Oinsert(X5170),X5169),c_Orderings_Obot__class_Obot(tc_fun(X5170,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_insert__Diff__single])). 4.46/4.72 cnf(c_0_10014, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)=X2|hAPP(hAPP(c_List_Oappend(X1),X2),X4)!=X3), inference(split_conjunct,[status(thm)],[c_0_5411])). 4.46/4.72 cnf(c_0_10015, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X1))))), inference(split_conjunct,[status(thm)],[c_0_5898])). 4.46/4.72 cnf(c_0_10016, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X1))))), inference(split_conjunct,[status(thm)],[c_0_5899])). 4.46/4.72 fof(c_0_10017, plain, ![X15896]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X15896)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[fact_negative__zless__0])). 4.46/4.72 fof(c_0_10018, plain, ![X2465, X2466]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2466))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2465))), inference(variable_rename,[status(thm)],[fact_negative__zle])). 4.46/4.72 fof(c_0_10019, plain, ![X6558, X6559]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X6559)),X6558))), inference(variable_rename,[status(thm)],[fact_zero__le__zpower__abs])). 4.46/4.72 cnf(c_0_10020, plain, (c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))), inference(rw,[status(thm)],[c_0_5900, c_0_4471])). 4.46/4.72 fof(c_0_10021, plain, ![X3793, X3794]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X3794,X3793)),X3793)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3794),X3793), inference(variable_rename,[status(thm)],[fact_zminus__zmod])). 4.46/4.72 fof(c_0_10022, plain, ![X15100, X15101, X15102, X15103]:hAPP(hAPP(c_List_Onth(X15103),X15101),X15100)=hAPP(hAPP(c_List_Onth(X15103),hAPP(hAPP(c_List_Olist_OCons(X15103),X15102),X15101)),hAPP(c_Nat_OSuc,X15100)), inference(variable_rename,[status(thm)],[fact_nth__Cons__Suc])). 4.46/4.72 cnf(c_0_10023, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X2)=c_List_Olist_ONil(X1)|c_List_Olist_ONil(X1)!=X2), inference(rw,[status(thm)],[c_0_5901, c_0_5902])). 4.46/4.72 cnf(c_0_10024, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))=hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_5903])). 4.46/4.72 cnf(c_0_10025, plain, (hAPP(c_List_Orev(X1),X3)=hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))|hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))!=X3), inference(split_conjunct,[status(thm)],[c_0_5904])). 4.46/4.72 fof(c_0_10026, plain, ![X5630, X5631, X5632, X5633]:hAPP(hAPP(c_List_Odrop(X5633),hAPP(c_Nat_OSuc,X5632)),hAPP(hAPP(c_List_Olist_OCons(X5633),X5631),X5630))=hAPP(hAPP(c_List_Odrop(X5633),X5632),X5630), inference(variable_rename,[status(thm)],[fact_drop__Suc__Cons])). 4.46/4.72 cnf(c_0_10027, plain, (hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X1,X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5905])). 4.46/4.72 fof(c_0_10028, plain, ![X2483, X2484, X2485, X2486, X2487, X2488]:c_Product__Type_Oprod_Oprod__rec(X2488,X2487,X2486,X2485,hAPP(hAPP(c_Product__Type_OPair(X2488,X2487),X2484),X2483))=hAPP(hAPP(X2485,X2484),X2483), inference(variable_rename,[status(thm)],[fact_prod_Orecs])). 4.46/4.72 fof(c_0_10029, plain, ![X1935, X1936, X1937]:X1935=hAPP(hAPP(c_List_Oappend(X1937),hAPP(hAPP(c_List_Otake(X1937),X1936),X1935)),hAPP(hAPP(c_List_Odrop(X1937),X1936),X1935)), inference(variable_rename,[status(thm)],[fact_append__take__drop__id])). 4.46/4.72 fof(c_0_10030, plain, ![X6971, X6972, X6973]:hAPP(hAPP(c_Product__Type_OPair(X6972,X6971),hAPP(c_Product__Type_Ofst(X6972,X6971),X6973)),hAPP(c_Product__Type_Osnd(X6972,X6971),X6973))=X6973, inference(variable_rename,[status(thm)],[fact_surjective__pairing])). 4.46/4.72 fof(c_0_10031, plain, ![X4589, X4590, X4591, X4592, X4593, X4594]:c_Map_Omap__upds(X4594,X4593,c_Map_Omap__add(X4594,X4593,X4592,X4591),X4590,X4589)=c_Map_Omap__add(X4594,X4593,X4592,c_Map_Omap__upds(X4594,X4593,X4591,X4590,X4589)), inference(variable_rename,[status(thm)],[fact_map__add__upds])). 4.46/4.72 cnf(c_0_10032, plain, (hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(X3),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5))|X1!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5906])). 4.46/4.72 fof(c_0_10033, plain, ![X8716, X8717, X8718, X8719]:hAPP(hAPP(c_List_Onth(X8719),hAPP(hAPP(c_List_Olist_OCons(X8719),X8718),X8717)),X8716)=c_Nat_Onat_Onat__case(X8719,X8718,hAPP(c_List_Onth(X8719),X8717),X8716), inference(variable_rename,[status(thm)],[fact_nth_Osimps])). 4.46/4.72 cnf(c_0_10034, plain, (hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5907])). 4.46/4.72 fof(c_0_10035, plain, ![X11909, X11910, X11911, X11912]:hAPP(c_Map_Orestrict__map(X11912,X11911,hAPP(c_COMBK(tc_Option_Ooption(X11911),X11912),c_Option_Ooption_ONone(X11911)),X11910),X11909)=c_Option_Ooption_ONone(X11911), inference(variable_rename,[status(thm)],[fact_restrict__map__empty])). 4.46/4.72 fof(c_0_10036, plain, ![X8395, X8396, X8397]:c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8397,X8396),tc_HOL_Obool))=hAPP(hAPP(c_Product__Type_OSigma(X8397,X8396),X8395),hAPP(c_COMBK(tc_fun(X8396,tc_HOL_Obool),X8397),c_Orderings_Obot__class_Obot(tc_fun(X8396,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_Sigma__empty2])). 4.46/4.72 cnf(c_0_10037, plain, (c_List_Oreplicate(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X2),X3),X4)=hAPP(hAPP(c_List_Otake(X1),X2),c_List_Oreplicate(X1,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_5908])). 4.46/4.72 fof(c_0_10038, plain, ![X7277, X7278, X7279, X7280]:hAPP(hAPP(c_List_Odrop(X7280),X7279),c_List_Oreplicate(X7280,X7278,X7277))=c_List_Oreplicate(X7280,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7278),X7279),X7277), inference(variable_rename,[status(thm)],[fact_drop__replicate])). 4.46/4.72 fof(c_0_10039, plain, ![X17574, X17575]:c_Divides_Odiv__class_Omod(tc_Int_Oint,X17575,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X17574))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X17575),X17574)), inference(variable_rename,[status(thm)],[fact_zmod__zminus2])). 4.46/4.72 fof(c_0_10040, plain, ![X9569, X9570]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9570)),X9569)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9570)),hAPP(c_List_Otl(X9570),X9569)), inference(variable_rename,[status(thm)],[fact_length__tl])). 4.46/4.72 cnf(c_0_10041, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X1,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_5909])). 4.46/4.72 cnf(c_0_10042, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X2)))!=X3), inference(split_conjunct,[status(thm)],[c_0_5910])). 4.46/4.72 fof(c_0_10043, plain, ![X2006, X2007]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2007),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2006))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2007,X2006)), inference(variable_rename,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I2_J])). 4.46/4.72 fof(c_0_10044, plain, ![X3791, X3792]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X3792,X3791))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3792),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3791)), inference(variable_rename,[status(thm)],[fact_zmod__zminus__zminus])). 4.46/4.72 fof(c_0_10045, plain, ![X12953, X12954, X12955, X12956, X12957]:hAPP(hAPP(c_Product__Type_Oscomp(X12957,X12956,X12957,X12955),hAPP(c_Product__Type_OPair(X12956,X12957),X12954)),X12953)=hAPP(X12953,X12954), inference(variable_rename,[status(thm)],[fact_Pair__scomp])). 4.46/4.72 cnf(c_0_10046, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X2),c_Relation_OId(X1)),X3)=X3), inference(split_conjunct,[status(thm)],[c_0_5911])). 4.46/4.72 fof(c_0_10047, plain, ![X15298, X15299, X15300, X15301]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15301,tc_HOL_Obool)),c_Map_Odom(X15301,X15300,X15299)),X15298)=c_Map_Odom(X15301,X15300,c_Map_Orestrict__map(X15301,X15300,X15299,X15298)), inference(variable_rename,[status(thm)],[fact_dom__restrict])). 4.46/4.72 cnf(c_0_10048, plain, (hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))=c_List_Olistset(X1,c_List_Olist_ONil(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5912])). 4.46/4.72 fof(c_0_10049, plain, ![X16037, X16038, X16039, X16040, X16041, X16042]:hAPP(c_List_Olist_Olist__case(X16042,X16041,X16040,X16039),hAPP(hAPP(c_List_Olist_OCons(X16041),X16038),X16037))=hAPP(hAPP(X16039,X16038),X16037), inference(variable_rename,[status(thm)],[fact_list_Osimps_I5_J])). 4.46/4.72 cnf(c_0_10050, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X2),X3),c_Relation_OId(X2))=X3), inference(split_conjunct,[status(thm)],[c_0_5913])). 4.46/4.72 cnf(c_0_10051, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)=hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))))), inference(rw,[status(thm)],[c_0_5914, c_0_4517])). 4.46/4.72 fof(c_0_10052, plain, ![X10694, X10695, X10696]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10696,tc_HOL_Obool)),X10695),X10694)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10696,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10696,tc_HOL_Obool)),X10695),X10694)),X10694), inference(variable_rename,[status(thm)],[fact_Diff__idemp])). 4.46/4.72 fof(c_0_10053, plain, ![X5188, X5189, X5190]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5190,tc_HOL_Obool)),X5189),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5190,tc_HOL_Obool)),X5188),X5189))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5190,tc_HOL_Obool)),X5189),X5188), inference(variable_rename,[status(thm)],[fact_Un__Diff__cancel])). 4.46/4.72 fof(c_0_10054, plain, ![X11114, X11115, X11116]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11116,tc_HOL_Obool)),X11115),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11116,tc_HOL_Obool)),X11115),X11114))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11116,tc_HOL_Obool)),X11115),X11114), inference(variable_rename,[status(thm)],[fact_Int__left__absorb])). 4.46/4.72 fof(c_0_10055, plain, ![X14892, X14893, X14894]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14894,tc_HOL_Obool)),X14893),X14892)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14894,tc_HOL_Obool)),X14893),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14894,tc_HOL_Obool)),X14893),X14892)), inference(variable_rename,[status(thm)],[fact_Un__left__absorb])). 4.46/4.72 fof(c_0_10056, plain, ![X1275, X1276, X1277, X1278]:hAPP(hAPP(c_Relation_Orel__comp(X1278,X1277,X1276),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1278,X1277),tc_HOL_Obool))),X1275)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1278,X1276),tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_rel__comp__empty1])). 4.46/4.72 cnf(c_0_10057, plain, (hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X1,X2))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5915])). 4.46/4.72 fof(c_0_10058, plain, ![X12750, X12751, X12752, X12753]:c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X12753,X12751),tc_HOL_Obool))=hAPP(hAPP(c_Relation_Orel__comp(X12753,X12752,X12751),X12750),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X12752,X12751),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_rel__comp__empty2])). 4.46/4.72 fof(c_0_10059, plain, ![X16524, X16525, X16526]:c_Orderings_Otop__class_Otop(tc_fun(X16526,tc_HOL_Obool))=c_Map_Odom(X16526,X16525,hAPP(hAPP(c_COMBB(X16525,tc_Option_Ooption(X16525),X16526),c_Option_Ooption_OSome(X16525)),X16524)), inference(variable_rename,[status(thm)],[fact_dom__const])). 4.46/4.72 cnf(c_0_10060, plain, (c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Otrancl(X1,X2))=c_Transitive__Closure_Ortrancl(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5916])). 4.46/4.72 fof(c_0_10061, plain, ![X9153, X9154]:hAPP(hAPP(c_Relation_Orel__comp(X9154,X9154,X9154),c_Transitive__Closure_Ortrancl(X9154,X9153)),c_Transitive__Closure_Ortrancl(X9154,X9153))=c_Transitive__Closure_Ortrancl(X9154,X9153), inference(variable_rename,[status(thm)],[fact_rtrancl__idemp__self__comp])). 4.46/4.72 fof(c_0_10062, plain, ![X17193, X17194]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17194),X17193))=c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17194),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17193)), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J])). 4.46/4.72 cnf(c_0_10063, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X1),X4))=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=X2), inference(split_conjunct,[status(thm)],[c_0_5917])). 4.46/4.72 cnf(c_0_10064, plain, (c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat))))), inference(split_conjunct,[status(thm)],[fact_wf__less])). 4.46/4.72 cnf(c_0_10065, plain, (X3=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X2),X5)),X3)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=X2), inference(split_conjunct,[status(thm)],[c_0_5918])). 4.46/4.72 fof(c_0_10066, plain, ![X4302, X4303]:hAPP(c_Finite__Set_Ocard(X4303),X4302)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4303,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X4303),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4302), inference(variable_rename,[status(thm)],[fact_card__eq__setsum])). 4.46/4.72 fof(c_0_10067, plain, ![X3470, X3471]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3471)),X3470)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3471)),c_List_Obutlast(X3471,X3470)), inference(variable_rename,[status(thm)],[fact_length__butlast])). 4.46/4.72 fof(c_0_10068, plain, ![X1535, X1536]:c_Smallcheck_Osmall_H(X1536,hAPP(c_Code__Numeral_Oint__of,X1535),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X1535)))=hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),X1536),X1535), inference(variable_rename,[status(thm)],[fact_small__int__def])). 4.46/4.72 cnf(c_0_10069, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X2),X5))=X4|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=X2), inference(split_conjunct,[status(thm)],[c_0_5919])). 4.46/4.72 cnf(c_0_10070, plain, (X3=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X4,tc_HOL_Obool)),X1),X5))|X1!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5920])). 4.46/4.72 fof(c_0_10071, plain, ![X7370, X7371]:c_List_Olistrel1(X7371,hAPP(c_Relation_Oconverse(X7371,X7371),X7370))=hAPP(c_Relation_Oconverse(tc_List_Olist(X7371),tc_List_Olist(X7371)),c_List_Olistrel1(X7371,X7370)), inference(variable_rename,[status(thm)],[fact_listrel1__converse])). 4.46/4.72 fof(c_0_10072, plain, ![X11126, X11127, X11128, X11129, X11130]:c_Map_Omap__add(X11130,X11129,c_Map_Omap__add(X11130,X11129,X11128,X11127),X11126)=c_Map_Omap__add(X11130,X11129,X11128,c_Map_Omap__add(X11130,X11129,X11127,X11126)), inference(variable_rename,[status(thm)],[fact_map__add__assoc])). 4.46/4.72 fof(c_0_10073, plain, ![X1920, X1921, X1922, X1923]:hAPP(hAPP(c_Product__Type_Oscomp(X1923,X1922,X1921,tc_prod(X1922,X1921)),X1920),c_Product__Type_OPair(X1922,X1921))=X1920, inference(variable_rename,[status(thm)],[fact_scomp__Pair])). 4.46/4.72 fof(c_0_10074, plain, ![X2520, X2521]:hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2521,X2520))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2521),hAPP(c_Nat_OSuc,X2520)), inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastAtMost])). 4.46/4.72 fof(c_0_10075, plain, ![X5171, X5172, X5173, X5174, X5175]:c_List_Oreplicate(X5174,X5172,hAPP(X5173,X5171))=hAPP(hAPP(c_List_Omap(X5175,X5174),X5173),c_List_Oreplicate(X5175,X5172,X5171)), inference(variable_rename,[status(thm)],[fact_map__replicate])). 4.46/4.72 cnf(c_0_10076, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5921])). 4.46/4.72 cnf(c_0_10077, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X1,X4),tc_HOL_Obool))=c_Sum__Type_OPlus(X1,X4,X2,X3)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=X2|X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5922])). 4.46/4.72 cnf(c_0_10078, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),X2)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))), inference(split_conjunct,[status(thm)],[c_0_5923])). 4.46/4.72 cnf(c_0_10079, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_Divides_Odivmod__nat(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5924])). 4.46/4.72 cnf(c_0_10080, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X1),X2)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))), inference(split_conjunct,[status(thm)],[c_0_5925])). 4.46/4.72 cnf(c_0_10081, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X1),X2)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))), inference(split_conjunct,[status(thm)],[c_0_5926])). 4.46/4.72 cnf(c_0_10082, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),X2)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))), inference(split_conjunct,[status(thm)],[c_0_5927])). 4.46/4.72 fof(c_0_10083, plain, ![X11439, X11440, X11441, X11442]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11442)),X11441)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11442)),hAPP(hAPP(c_List_Olist__update(X11442,X11441),X11440),X11439)), inference(variable_rename,[status(thm)],[fact_length__list__update])). 4.46/4.72 cnf(c_0_10084, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OSKIP),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5928])). 4.46/4.72 fof(c_0_10085, plain, ![X5126, X5127, X5128, X5129]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5128,tc_fun(X5129,tc_HOL_Obool)),X5126),X5127)=c_Complete__Lattice_OInf__class_OInf(tc_fun(X5129,tc_HOL_Obool),hAPP(c_Set_Oimage(X5128,tc_fun(X5129,tc_HOL_Obool),X5127),X5126)), inference(variable_rename,[status(thm)],[fact_Inter__image__eq])). 4.46/4.72 cnf(c_0_10086, plain, (c_Option_Ooption_Ooption__size(X1,X2,hAPP(c_Option_Ooption_OSome(X1),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5929])). 4.46/4.72 fof(c_0_10087, plain, ![X5595, X5596]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5596),X5595))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X5596)),X5595), inference(variable_rename,[status(thm)],[fact_zmult__zminus])). 4.46/4.72 fof(c_0_10088, plain, ![X6933, X6934]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X6934),X6933))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6934)),X6933), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J])). 4.46/4.72 cnf(c_0_10089, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X3))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))!=X3), inference(split_conjunct,[status(thm)],[c_0_5930])). 4.46/4.72 fof(c_0_10090, plain, ![X1336, X1337, X1338]:hAPP(c_Product__Type_Ofst(tc_List_Olist(X1338),tc_List_Olist(X1338)),c_List_Opartition(X1338,X1337,X1336))=hAPP(c_List_Ofilter(X1338,X1337),X1336), inference(variable_rename,[status(thm)],[fact_partition__filter1])). 4.46/4.72 fof(c_0_10091, plain, ![X16400, X16401]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16401),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X16400))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X16401)),X16400), inference(variable_rename,[status(thm)],[fact_zdiv__zminus2])). 4.46/4.72 fof(c_0_10092, plain, ![X5825, X5826]:c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X5826),X5825), inference(variable_rename,[status(thm)],[fact_inj__on__add__nat])). 4.46/4.72 fof(c_0_10093, plain, ![X713]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X713))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[fact_negative__zle__0])). 4.46/4.72 fof(c_0_10094, plain, ![X385, X386]:c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X386,X385),tc_HOL_Obool))=c_Sum__Type_OPlus(X386,X385,c_Orderings_Otop__class_Otop(tc_fun(X386,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X385,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_UNIV__Plus__UNIV])). 4.46/4.72 cnf(c_0_10095, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X1,X2,X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5931])). 4.46/4.72 fof(c_0_10096, plain, ![X15283, X15284]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X15284,tc_HOL_Obool),tc_HOL_Obool)),X15283),hAPP(c_Set_OPow(X15284),c_Complete__Lattice_OSup__class_OSup(tc_fun(X15284,tc_HOL_Obool),X15283)))), inference(variable_rename,[status(thm)],[fact_subset__Pow__Union])). 4.46/4.72 cnf(c_0_10097, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5932])). 4.46/4.72 cnf(c_0_10098, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5933])). 4.46/4.72 cnf(c_0_10099, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2))=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5934])). 4.46/4.72 cnf(c_0_10100, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2))=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5935])). 4.46/4.72 cnf(c_0_10101, plain, (hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))=c_List_Olists(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5936])). 4.46/4.72 fof(c_0_10102, plain, ![X16029, X16030, X16031]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16031,tc_fun(X16030,tc_HOL_Obool)),X16029),hAPP(c_COMBK(tc_fun(X16030,tc_HOL_Obool),X16031),c_Orderings_Obot__class_Obot(tc_fun(X16030,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X16030,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_UN__empty2])). 4.46/4.72 fof(c_0_10103, plain, ![X13360, X13361]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X13361),X13360)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X13361,X13360)),X13360), inference(variable_rename,[status(thm)],[fact_mod__Suc__eq__Suc__mod])). 4.46/4.72 cnf(c_0_10104, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1))))), inference(rw,[status(thm)],[c_0_5937, c_0_5562])). 4.46/4.72 fof(c_0_10105, plain, ![X11346, X11347]:c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,X11347,X11346)=c_Smallcheck_Ofull__small_H(X11347,hAPP(c_Code__Numeral_Oint__of,X11346),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X11346))), inference(variable_rename,[status(thm)],[fact_full__small__int__def])). 4.46/4.72 fof(c_0_10106, plain, ![X15498, X15499]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X15499),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15498),c_Groups_Oone__class_Oone(tc_Int_Oint)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X15499,X15498), inference(variable_rename,[status(thm)],[fact_atLeastLessThanPlusOne__atLeastAtMost__int])). 4.46/4.72 fof(c_0_10107, plain, ![X4477, X4478, X4479]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4479,X4478,X4479),c_COMBK(X4479,X4478)),X4477)=hAPP(c_Product__Type_Ofst(X4479,X4478),X4477), inference(variable_rename,[status(thm)],[fact_fst__def])). 4.46/4.72 cnf(c_0_10108, plain, (c_HOL_OThe(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))=X2), inference(split_conjunct,[status(thm)],[c_0_5938])). 4.46/4.72 cnf(c_0_10109, plain, (c_Hilbert__Choice_OEps(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))=X2), inference(split_conjunct,[status(thm)],[c_0_5939])). 4.46/4.72 fof(c_0_10110, plain, ![X8187, X8188, X8189, X8190, X8191, X8192]:c_Nitpick_Opair__box_Opair__box__case(X8192,X8191,X8190,X8189,c_Nitpick_Opair__box_OPairBox(X8192,X8191,X8188,X8187))=hAPP(hAPP(X8189,X8188),X8187), inference(variable_rename,[status(thm)],[fact_pair__box_Osimps_I2_J])). 4.46/4.72 fof(c_0_10111, plain, ![X1458, X1459, X1460, X1461, X1462, X1463]:c_Nitpick_Opair__box_Opair__box__rec(X1463,X1462,X1461,X1460,c_Nitpick_Opair__box_OPairBox(X1463,X1462,X1459,X1458))=hAPP(hAPP(X1460,X1459),X1458), inference(variable_rename,[status(thm)],[fact_pair__box_Orecs])). 4.46/4.72 cnf(c_0_10112, plain, (hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X4,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X2))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5940])). 4.46/4.72 cnf(c_0_10113, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),c_Divides_Odivmod__nat(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_5941])). 4.46/4.72 fof(c_0_10114, plain, ![X5010, X5011, X5012]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5012,tc_HOL_Obool)),X5011),X5010)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5012,tc_HOL_Obool)),X5011),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5012,tc_HOL_Obool)),X5010)), inference(variable_rename,[status(thm)],[fact_Diff__Compl])). 4.46/4.72 fof(c_0_10115, plain, ![X11150, X11151, X11152]:hAPP(c_List_Oset(X11152),c_List_Oreplicate(X11152,hAPP(c_Nat_OSuc,X11151),X11150))=hAPP(hAPP(c_Set_Oinsert(X11152),X11150),c_Orderings_Obot__class_Obot(tc_fun(X11152,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_set__replicate__Suc])). 4.46/4.72 cnf(c_0_10116, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)))|X1!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_5942])). 4.46/4.72 fof(c_0_10117, plain, ![X10748, X10749, X10750, X10751]:hAPP(hAPP(c_Option_Omap(X10751,X10750),X10749),hAPP(c_Option_Ooption_OSome(X10751),X10748))=hAPP(c_Option_Ooption_OSome(X10750),hAPP(X10749,X10748)), inference(variable_rename,[status(thm)],[fact_option__map__Some])). 4.46/4.72 fof(c_0_10118, plain, ![X7052, X7053]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7053),X7052)),hAPP(c_Nat_OSuc,X7053))), inference(variable_rename,[status(thm)],[fact_diff__less__Suc])). 4.46/4.72 fof(c_0_10119, plain, ![X9036, X9037]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9037),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9036),X9037)))), inference(variable_rename,[status(thm)],[fact_less__add__Suc2])). 4.46/4.72 fof(c_0_10120, plain, ![X17386, X17387, X17388, X17389]:c_Hoare__Mirabelle_Otriple__valid(X17389,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17389),X17388),hAPP(c_Com_Ocom_OBODY,X17387)),X17386)), inference(variable_rename,[status(thm)],[fact_Body__triple__valid__0])). 4.46/4.72 fof(c_0_10121, plain, ![X3120]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X3120))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3120)), inference(variable_rename,[status(thm)],[fact_int__Suc])). 4.46/4.72 cnf(c_0_10122, plain, (X1=hAPP(c_Relation_OImage(X2,X2,c_Relation_OId(X2)),X1)), inference(split_conjunct,[status(thm)],[c_0_5943])). 4.46/4.72 cnf(c_0_10123, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3))|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))!=X3), inference(split_conjunct,[status(thm)],[c_0_5944])). 4.46/4.72 fof(c_0_10124, plain, ![X16994, X16995, X16996]:c_List_Oreplicate(X16996,hAPP(c_Nat_OSuc,X16995),X16994)=hAPP(hAPP(c_List_Olist_OCons(X16996),X16994),c_List_Oreplicate(X16996,X16995,X16994)), inference(variable_rename,[status(thm)],[fact_replicate__Suc])). 4.46/4.72 fof(c_0_10125, plain, ![X9433, X9434, X9435, X9436]:hAPP(c_New__DSequence_Oneg__union(X9436,X9435,X9434),X9433)=c_Lazy__Sequence_Oappend(tc_Option_Ooption(X9436),hAPP(X9435,X9433),hAPP(X9434,X9433)), inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__union__def])). 4.46/4.72 fof(c_0_10126, plain, ![X3584, X3585, X3586]:c_List_Obutlast(X3586,hAPP(hAPP(c_List_Odrop(X3586),X3585),X3584))=hAPP(hAPP(c_List_Odrop(X3586),X3585),c_List_Obutlast(X3586,X3584)), inference(variable_rename,[status(thm)],[fact_drop__butlast])). 4.46/4.72 fof(c_0_10127, plain, ![X7449, X7450, X7451, X7452, X7453]:c_HOL_OThe(X7452,c_Finite__Set_Ofold__graph(X7453,X7452,X7451,X7450,X7449))=hAPP(hAPP(c_Finite__Set_Ofold(X7453,X7452,X7451),X7450),X7449), inference(variable_rename,[status(thm)],[fact_fold__def])). 4.46/4.72 cnf(c_0_10128, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1))=hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))), inference(split_conjunct,[status(thm)],[c_0_5945])). 4.46/4.72 fof(c_0_10129, plain, ![X12462, X12463, X12464]:hAPP(c_Relation_OImage(X12464,X12464,c_Relation_OId__on(X12464,X12463)),X12462)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12464,tc_HOL_Obool)),X12463),X12462), inference(variable_rename,[status(thm)],[fact_Image__Id__on])). 4.46/4.72 fof(c_0_10130, plain, ![X14020, X14021]:X14020=c_Predicate_Opred__comp(X14021,X14021,X14021,c_fequal,c_Predicate_Opred__comp(X14021,X14021,X14021,X14020,c_fequal)), inference(variable_rename,[status(thm)],[fact_eq__comp__r])). 4.46/4.72 fof(c_0_10131, plain, ![X616, X617, X618]:c_List_Olistset(X618,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X618,tc_HOL_Obool)),X617),X616))=c_List_Oset__Cons(X618,X617,c_List_Olistset(X618,X616)), inference(variable_rename,[status(thm)],[fact_listset_Osimps_I2_J])). 4.46/4.72 cnf(c_0_10132, plain, (hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_5946])). 4.46/4.72 cnf(c_0_10133, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_5947])). 4.46/4.72 fof(c_0_10134, plain, ![X12302, X12303, X12304, X12305, X12306, X12307]:hAPP(hAPP(X12304,X12302),X12303)=hAPP(hAPP(hAPP(c_COMBC(X12307,X12306,X12305),X12304),X12303),X12302), inference(variable_rename,[status(thm)],[help_c__COMBC__1])). 4.46/4.72 cnf(c_0_10135, plain, (hAPP(X1,X2)=c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X4,X1,hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X2))))), inference(rw,[status(thm)],[c_0_5948, c_0_5562])). 4.46/4.72 fof(c_0_10136, plain, ![X766, X767, X768]:c_Map_Omap__add(X768,X767,hAPP(c_COMBK(tc_Option_Ooption(X767),X768),c_Option_Ooption_ONone(X767)),X766)=X766, inference(variable_rename,[status(thm)],[fact_empty__map__add])). 4.46/4.72 cnf(c_0_10137, plain, (c_List_Olast(X1,X2)=X3|hAPP(hAPP(c_List_Oappend(X1),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))!=X2), inference(split_conjunct,[status(thm)],[c_0_5469])). 4.46/4.72 cnf(c_0_10138, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))=X1), inference(rw,[status(thm)],[c_0_5949, c_0_5562])). 4.46/4.72 fof(c_0_10139, plain, ![X934, X935, X936]:X934=c_Map_Omap__add(X936,X935,X934,hAPP(c_COMBK(tc_Option_Ooption(X935),X936),c_Option_Ooption_ONone(X935))), inference(variable_rename,[status(thm)],[fact_map__add__empty])). 4.46/4.72 cnf(c_0_10140, plain, (hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X1),hAPP(c_Code__Numeral_Onat__of,X2)))=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5950])). 4.46/4.72 cnf(c_0_10141, plain, (X1=c_List_Obutlast(X2,X3)|hAPP(hAPP(c_List_Oappend(X2),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X4),c_List_Olist_ONil(X2)))!=X3), inference(split_conjunct,[status(thm)],[c_0_5469])). 4.46/4.72 fof(c_0_10142, plain, ![X972, X973, X974]:hAPP(hAPP(c_Set_Oinsert(X974),X973),hAPP(c_List_Oset(X974),X972))=hAPP(c_List_Oset(X974),c_List_Oinsert(X974,X973,X972)), inference(variable_rename,[status(thm)],[fact_List_Oset__insert])). 4.46/4.72 fof(c_0_10143, plain, ![X1420, X1421]:c_Map_Oran(X1421,X1420,hAPP(c_COMBK(tc_Option_Ooption(X1420),X1421),c_Option_Ooption_ONone(X1420)))=c_Orderings_Obot__class_Obot(tc_fun(X1420,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_ran__empty])). 4.46/4.72 fof(c_0_10144, plain, ![X8061, X8062]:c_List_Otranspose(X8062,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X8062)),c_List_Olist_ONil(X8062)),X8061))=c_List_Otranspose(X8062,X8061), inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I2_J])). 4.46/4.72 fof(c_0_10145, plain, ![X17269, X17270, X17271]:hAPP(c_Relation_ORange(X17271,X17270),hAPP(c_Relation_Oconverse(X17270,X17271),X17269))=hAPP(c_Relation_ODomain(X17270,X17271),X17269), inference(variable_rename,[status(thm)],[fact_Range__converse])). 4.46/4.72 cnf(c_0_10146, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)!=X1|X2!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)), inference(split_conjunct,[status(thm)],[c_0_5535])). 4.46/4.72 cnf(c_0_10147, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X1)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_5951]), ['final']). 4.46/4.72 cnf(c_0_10148, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))=c_Divides_Opdivmod(X2,X1)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X1), inference(split_conjunct,[status(thm)],[c_0_5952])). 4.46/4.72 fof(c_0_10149, plain, ![X710, X711, X712]:hAPP(c_Relation_ORange(X711,X712),X710)=hAPP(c_Relation_ODomain(X712,X711),hAPP(c_Relation_Oconverse(X711,X712),X710)), inference(variable_rename,[status(thm)],[fact_Domain__converse])). 4.46/4.72 fof(c_0_10150, plain, ![X10729, X10730]:c_Product__Type_Omap__pair(X10730,X10730,X10729,X10729,c_COMBI(X10730),c_COMBI(X10729))=c_Fun_Oid(tc_prod(X10730,X10729)), inference(variable_rename,[status(thm)],[fact_map__pair_Oidentity])). 4.46/4.72 fof(c_0_10151, plain, ![X1654, X1655]:c_Fun_Oid(tc_prod(X1655,X1654))=c_Product__Type_Omap__pair(X1655,X1655,X1654,X1654,c_Fun_Oid(X1655),c_Fun_Oid(X1654)), inference(variable_rename,[status(thm)],[fact_map__pair_Oid])). 4.46/4.72 fof(c_0_10152, plain, ![X6438, X6439, X6440, X6441, X6442, X6443]:hAPP(hAPP(X6440,X6439),X6438)=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X6443,X6442,X6441,X6440,c_Lazy__Sequence_Olazy__sequence_OInsert(X6442,X6439,X6438)), inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I5_J])). 4.46/4.72 fof(c_0_10153, plain, ![X3188, X3189]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X3189,tc_HOL_Obool),tc_fun(X3189,tc_HOL_Obool)),X3188),c_COMBI(tc_fun(X3189,tc_HOL_Obool)))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X3189,tc_HOL_Obool),X3188), inference(variable_rename,[status(thm)],[fact_Inter__def])). 4.46/4.72 fof(c_0_10154, plain, ![X17497, X17498]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X17498,tc_HOL_Obool),tc_fun(X17498,tc_HOL_Obool)),X17497),c_COMBI(tc_fun(X17498,tc_HOL_Obool)))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X17498,tc_HOL_Obool),X17497), inference(variable_rename,[status(thm)],[fact_Union__def])). 4.46/4.72 cnf(c_0_10155, plain, (hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2))), inference(split_conjunct,[status(thm)],[c_0_5953])). 4.46/4.72 cnf(c_0_10156, plain, (c_Code__Numeral_Osubtract__code__numeral=c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[fact_subtract__code__numeral__def]), ['final']). 4.46/4.72 fof(c_0_10157, plain, ![X15546, X15547, X15548, X15549]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X15549,X15548)),c_Nitpick_Opair__box_OPairBox(X15549,X15548,X15547,X15546)), inference(variable_rename,[status(thm)],[fact_pair__box_Osize_I2_J])). 4.46/4.72 fof(c_0_10158, plain, ![X2156, X2157, X2158]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2158,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2158,tc_HOL_Obool)),X2157),X2156)),X2157)), inference(variable_rename,[status(thm)],[fact_Diff__subset])). 4.46/4.72 fof(c_0_10159, plain, ![X12059, X12060, X12061]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12061,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12061,tc_HOL_Obool)),X12060),X12059)),X12060)), inference(variable_rename,[status(thm)],[fact_Int__lower1])). 4.46/4.72 fof(c_0_10160, plain, ![X7795, X7796, X7797, X7798, X7799]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Hoare__Mirabelle_Otriple_Otriple__size(X7799,X7798,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7799),X7797),X7796),X7795)), inference(variable_rename,[status(thm)],[fact_triple_Osize_I1_J])). 4.46/4.72 fof(c_0_10161, plain, ![X956]:hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X956))=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X956), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J])). 4.46/4.72 cnf(c_0_10162, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)), inference(rw,[status(thm)],[c_0_5954, c_0_5955])). 4.46/4.72 cnf(c_0_10163, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1)), inference(split_conjunct,[status(thm)],[c_0_5956]), ['final']). 4.46/4.72 fof(c_0_10164, plain, ![X11445, X11446, X11447]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11447,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11447,tc_HOL_Obool)),X11446),X11445)),X11445)), inference(variable_rename,[status(thm)],[fact_Int__lower2])). 4.46/4.72 fof(c_0_10165, plain, ![X4237, X4238, X4239]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4239,tc_HOL_Obool)),X4238),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4239,tc_HOL_Obool)),X4238),X4237))), inference(variable_rename,[status(thm)],[fact_Un__upper1])). 4.46/4.72 fof(c_0_10166, plain, ![X15718, X15719, X15720]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15720,tc_HOL_Obool)),X15719),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15720,tc_HOL_Obool)),X15718),X15719))), inference(variable_rename,[status(thm)],[fact_Un__upper2])). 4.46/4.72 fof(c_0_10167, plain, ![X3330, X3331, X3332, X3333]:hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(X3333)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3333),X3332),X3331),X3330))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_triple_Osize_I2_J])). 4.46/4.72 fof(c_0_10168, plain, ![X13852, X13853, X13854]:hAPP(c_List_Ofilter(X13854,X13853),c_List_Oremdups(X13854,X13852))=c_List_Oremdups(X13854,hAPP(c_List_Ofilter(X13854,X13853),X13852)), inference(variable_rename,[status(thm)],[fact_remdups__filter])). 4.46/4.72 fof(c_0_10169, plain, ![X15783, X15784]:hAPP(c_Relation_Oconverse(X15784,X15784),c_Transitive__Closure_Ortrancl(X15784,X15783))=c_Transitive__Closure_Ortrancl(X15784,hAPP(c_Relation_Oconverse(X15784,X15784),X15783)), inference(variable_rename,[status(thm)],[fact_rtrancl__converse])). 4.46/4.72 cnf(c_0_10170, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_5957, c_0_4760])). 4.46/4.72 cnf(c_0_10171, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X1))), inference(split_conjunct,[status(thm)],[c_0_5958])). 4.46/4.72 cnf(c_0_10172, plain, (hAPP(c_Product__Type_OPair(X2,X3),X4)=hAPP(c_Random_Oiterate(X2,X3,X1,X5),X4)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X1), inference(split_conjunct,[status(thm)],[c_0_5959])). 4.46/4.72 fof(c_0_10173, plain, ![X6145, X6146, X6147, X6148, X6149]:hAPP(c_Option_Ooption_Ooption__case(X6149,X6148,X6147,X6146),hAPP(c_Option_Ooption_OSome(X6148),X6145))=hAPP(X6146,X6145), inference(variable_rename,[status(thm)],[fact_option_Osimps_I5_J])). 4.46/4.72 cnf(c_0_10174, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_5565])). 4.46/4.72 fof(c_0_10175, plain, ![X2404, X2405, X2406]:hAPP(hAPP(c_List_Onth(X2406),hAPP(hAPP(c_List_Olist_OCons(X2406),X2405),X2404)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2405, inference(variable_rename,[status(thm)],[fact_nth__Cons__0])). 4.46/4.72 fof(c_0_10176, plain, ![X6658, X6659, X6660]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6660,tc_HOL_Obool)),X6659),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6660,tc_HOL_Obool)),X6658),X6659))=c_Orderings_Obot__class_Obot(tc_fun(X6660,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Diff__disjoint])). 4.46/4.72 cnf(c_0_10177, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X1,X2,X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5960])). 4.46/4.72 fof(c_0_10178, plain, ![X1478, X1479]:c_Orderings_Obot__class_Obot(tc_fun(X1479,tc_HOL_Obool))=c_Map_Odom(X1479,X1478,hAPP(c_COMBK(tc_Option_Ooption(X1478),X1479),c_Option_Ooption_ONone(X1478))), inference(variable_rename,[status(thm)],[fact_dom__empty])). 4.46/4.72 fof(c_0_10179, plain, ![X3673, X3674, X3675]:hAPP(hAPP(c_List_Olist__update(X3675,X3674),X3673),hAPP(hAPP(c_List_Onth(X3675),X3674),X3673))=X3674, inference(variable_rename,[status(thm)],[fact_list__update__id])). 4.46/4.72 fof(c_0_10180, plain, ![X7598, X7599, X7600]:X7598=hAPP(hAPP(c_List_Odrop(X7600),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X7600),X7599),X7598)), inference(variable_rename,[status(thm)],[fact_drop__1__Cons])). 4.46/4.72 fof(c_0_10181, plain, ![X7486]:hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X7486)),c_Int_OInteg)), inference(variable_rename,[status(thm)],[fact_Rep__Integ])). 4.46/4.72 cnf(c_0_10182, plain, (c_Wellfounded_OwfP(X1,hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse)))), inference(split_conjunct,[status(thm)],[c_0_5961])). 4.46/4.72 cnf(c_0_10183, plain, (hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(rw,[status(thm)],[c_0_5962, c_0_4531]), ['final']). 4.46/4.72 fof(c_0_10184, plain, ![X14895, X14896, X14897, X14898, X14899, X14900]:hAPP(X14897,hAPP(X14896,X14895))=hAPP(hAPP(hAPP(c_COMBB(X14900,X14899,X14898),X14897),X14896),X14895), inference(variable_rename,[status(thm)],[help_c__COMBB__1])). 4.46/4.72 cnf(c_0_10185, plain, (hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_5963])). 4.46/4.72 fof(c_0_10186, plain, ![X8385, X8386, X8387, X8388]:c_Lazy__Sequence_Oappend(X8388,c_Lazy__Sequence_Olazy__sequence_OInsert(X8388,X8387,X8386),X8385)=c_Lazy__Sequence_Olazy__sequence_OInsert(X8388,X8387,c_Lazy__Sequence_Oappend(X8388,X8386,X8385)), inference(variable_rename,[status(thm)],[fact__03])). 4.46/4.72 fof(c_0_10187, plain, ![X4788, X4789]:c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X4789,X4788)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4789),c_Groups_Oone__class_Oone(tc_Int_Oint))),X4788), inference(variable_rename,[status(thm)],[fact_atLeastPlusOneLessThan__greaterThanLessThan__int])). 4.46/4.72 fof(c_0_10188, plain, ![X11429, X11430]:hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X11430)),c_List_Olist_ONil(X11430)),c_List_Olists(X11430,X11429))), inference(variable_rename,[status(thm)],[fact_lists_ONil])). 4.46/4.72 fof(c_0_10189, plain, ![X2897, X2898, X2899]:c_Option_Ooption_ONone(X2898)=hAPP(hAPP(c_Map_Omap__of(X2899,X2898),c_List_Olist_ONil(tc_prod(X2899,X2898))),X2897), inference(variable_rename,[status(thm)],[fact_map__of__Cons__code_I1_J])). 4.46/4.72 fof(c_0_10190, plain, ![X2593, X2594]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2594),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2594),X2593)), inference(variable_rename,[status(thm)],[fact_diff__add__0])). 4.46/4.72 fof(c_0_10191, plain, ![X16283, X16284]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16283),X16284)=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X16284),X16283)), inference(variable_rename,[status(thm)],[fact_card__atLeastLessThan])). 4.46/4.72 cnf(c_0_10192, plain, (c_List_Olist_ONil(X2)=c_List_Obutlast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1))|X1!=c_List_Olist_ONil(X2)), inference(split_conjunct,[status(thm)],[c_0_5964])). 4.46/4.72 fof(c_0_10193, plain, ![X9592, X9593, X9594, X9595]:hBOOL(hAPP(c_Finite__Set_Ofold__graph(X9595,X9594,X9593,X9592,c_Orderings_Obot__class_Obot(tc_fun(X9595,tc_HOL_Obool))),X9592)), inference(variable_rename,[status(thm)],[fact_fold__graph_OemptyI])). 4.46/4.72 fof(c_0_10194, plain, ![X16899]:(hAPP(c_Int_OAbs__Integ,esk501_1(X16899))=X16899&hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk501_1(X16899)),c_Int_OInteg))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Abs__Integ__cases])])])])). 4.46/4.72 fof(c_0_10195, plain, ![X12441, X12442]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X12442),X12441)),X12442)), inference(variable_rename,[status(thm)],[fact_div__le__dividend])). 4.46/4.72 fof(c_0_10196, plain, ![X15544, X15545]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15545),X15544)),X15545)), inference(variable_rename,[status(thm)],[fact_diff__le__self])). 4.46/4.72 fof(c_0_10197, plain, ![X843]:hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X843))))), inference(variable_rename,[status(thm)],[fact_neg__zminus__int])). 4.46/4.72 fof(c_0_10198, plain, ![X5372]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5372),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5372),X5372))), inference(variable_rename,[status(thm)],[fact_le__square])). 4.46/4.72 fof(c_0_10199, plain, ![X7541, X7542]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7542),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7542),X7541))), inference(variable_rename,[status(thm)],[fact_le__add1])). 4.46/4.72 cnf(c_0_10200, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Divides_Odivmod__int(X1,X2)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X1), inference(split_conjunct,[status(thm)],[c_0_4492])). 4.46/4.72 fof(c_0_10201, plain, ![X15199, X15200, X15201, X15202, X15203]:c_Option_Ooption_Ooption__rec(X15203,X15202,X15201,X15200,hAPP(c_Option_Ooption_OSome(X15202),X15199))=hAPP(X15200,X15199), inference(variable_rename,[status(thm)],[fact_option_Orecs_I2_J])). 4.46/4.72 fof(c_0_10202, plain, ![X12289, X12290]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12290),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12289),X12290))), inference(variable_rename,[status(thm)],[fact_le__add2])). 4.46/4.72 fof(c_0_10203, plain, ![X2008, X2009, X2010, X2011, X2012]:hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X2012),X2011),X2010),X2009),X2008)=c_New__DSequence_Oneg__single(X2012,X2011), inference(variable_rename,[status(thm)],[fact_neg__single__def])). 4.46/4.72 fof(c_0_10204, plain, ![X13627, X13628, X13629, X13630, X13631]:c_New__DSequence_Opos__single(X13631,X13630)=hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X13631),X13630),X13629),X13628),X13627), inference(variable_rename,[status(thm)],[fact_pos__single__def])). 4.46/4.72 cnf(c_0_10205, plain, (X3=c_List_Oremove1(X4,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X3))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5965])). 4.46/4.72 fof(c_0_10206, plain, ![X1674, X1675]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1675)),hAPP(c_List_Orotate1(X1675),X1674))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1675)),X1674), inference(variable_rename,[status(thm)],[fact_length__rotate1])). 4.46/4.72 fof(c_0_10207, plain, ![X4966, X4967]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4967)),X4966)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4967)),hAPP(c_List_Orev(X4967),X4966)), inference(variable_rename,[status(thm)],[fact_length__rev])). 4.46/4.72 fof(c_0_10208, plain, ![X1091, X1092, X1093, X1094, X1095]:X1091=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1095,X1094,X1093),X1092),X1091),c_Orderings_Obot__class_Obot(tc_fun(X1094,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_fold__image__empty])). 4.46/4.72 cnf(c_0_10209, plain, (c_Relation_Osingle__valued(X1,X1,c_Relation_OId(X1))), inference(split_conjunct,[status(thm)],[c_0_5966])). 4.46/4.72 cnf(c_0_10210, plain, (hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1))), inference(split_conjunct,[status(thm)],[c_0_5967])). 4.46/4.72 fof(c_0_10211, plain, ![X7027]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7027))), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J])). 4.46/4.72 cnf(c_0_10212, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=X3), inference(split_conjunct,[status(thm)],[c_0_5968])). 4.46/4.72 cnf(c_0_10213, plain, (hAPP(hAPP(c_List_Otake(X1),X2),X3)=c_List_Osublist(X1,X3,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X2))), inference(split_conjunct,[status(thm)],[c_0_5969])). 4.46/4.72 fof(c_0_10214, plain, ![X13343, X13344]:c_Orderings_Otop__class_Otop(tc_fun(X13344,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13344,tc_HOL_Obool)),X13343),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X13344,tc_HOL_Obool)),X13343)), inference(variable_rename,[status(thm)],[fact_Compl__partition])). 4.46/4.72 cnf(c_0_10215, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)|X1!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_5970])). 4.46/4.72 fof(c_0_10216, plain, ![X597, X598]:hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X598,X597))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X598),X597), inference(variable_rename,[status(thm)],[fact_div__int__def])). 4.46/4.72 cnf(c_0_10217, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_5971])). 4.46/4.72 cnf(c_0_10218, plain, (c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))=c_Divides_OnegateSnd), inference(split_conjunct,[status(thm)],[fact_negateSnd__def])). 4.46/4.72 cnf(c_0_10219, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X1!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5534])). 4.46/4.72 cnf(c_0_10220, plain, (c_Wellfounded_Oless__than=c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)), inference(split_conjunct,[status(thm)],[fact_less__than__def])). 4.46/4.72 fof(c_0_10221, plain, ![X2286, X2287, X2288]:hAPP(hAPP(c_List_Ozip(X2288,X2287),c_List_Olist_ONil(X2288)),X2286)=c_List_Olist_ONil(tc_prod(X2288,X2287)), inference(variable_rename,[status(thm)],[fact_zip__Nil])). 4.46/4.72 fof(c_0_10222, plain, ![X3892, X3893, X3894, X3895, X3896]:X3892=hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3896,X3895),X3894),X3893),X3892),X3893), inference(variable_rename,[status(thm)],[fact_fun__upd__same])). 4.46/4.72 fof(c_0_10223, plain, ![X2436, X2437]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2437),X2436)),X2437)=X2436, inference(variable_rename,[status(thm)],[fact_diff__add__inverse])). 4.46/4.72 fof(c_0_10224, plain, ![X12240, X12241]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12241),X12240)),X12240)=X12241, inference(variable_rename,[status(thm)],[fact_diff__add__inverse2])). 4.46/4.72 fof(c_0_10225, plain, ![X4447, X4448, X4449, X4450]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4450,X4449),X4448),X4447),hAPP(X4448,X4447))=X4448, inference(variable_rename,[status(thm)],[fact_fun__upd__triv])). 4.46/4.72 fof(c_0_10226, plain, ![X4115, X4116, X4117]:c_List_Olist_ONil(tc_prod(X4117,X4116))=hAPP(hAPP(c_List_Ozip(X4117,X4116),X4115),c_List_Olist_ONil(X4116)), inference(variable_rename,[status(thm)],[fact_zip_Osimps_I1_J])). 4.46/4.72 cnf(c_0_10227, plain, (c_List_Olast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1))=X3|X1!=c_List_Olist_ONil(X2)), inference(split_conjunct,[status(thm)],[c_0_5972])). 4.46/4.72 cnf(c_0_10228, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_5973])). 4.46/4.72 fof(c_0_10229, plain, ![X9951, X9952]:hBOOL(hAPP(hAPP(c_member(tc_fun(X9952,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X9952,tc_HOL_Obool))),hAPP(c_Set_OPow(X9952),X9951))), inference(variable_rename,[status(thm)],[fact_Pow__bottom])). 4.46/4.72 fof(c_0_10230, plain, ![X1476, X1477]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1477,X1476)),X1477)), inference(variable_rename,[status(thm)],[fact_mod__less__eq__dividend])). 4.46/4.72 fof(c_0_10231, plain, ![X3616, X3617]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3617,tc_HOL_Obool)),X3616)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3617,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3617,tc_HOL_Obool))),X3616), inference(variable_rename,[status(thm)],[fact_Compl__eq__Diff__UNIV])). 4.46/4.72 cnf(c_0_10232, plain, (c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue))), inference(split_conjunct,[status(thm)],[fact_transfer__morphism__int__nat])). 4.46/4.72 cnf(c_0_10233, plain, (hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue)=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))), inference(rw,[status(thm)],[c_0_5974, c_0_4531]), ['final']). 4.46/4.72 fof(c_0_10234, plain, ![X8611, X8612]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8612,X8611)),X8611)=c_Groups_Ozero__class_Ozero(tc_Int_Oint), inference(variable_rename,[status(thm)],[fact_zmod__zdiv__trivial])). 4.46/4.72 cnf(c_0_10235, plain, (hAPP(c_New__DSequence_Oneg__decr__bind(X2,X3,X4,X5),X1)=c_Lazy__Sequence_Ohit__bound(X3)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X1), inference(split_conjunct,[status(thm)],[c_0_5109])). 4.46/4.72 fof(c_0_10236, plain, ![X1159, X1160, X1161]:hAPP(hAPP(c_Set_Oinsert(X1161),X1160),X1159)=hAPP(hAPP(c_Set_Oinsert(X1161),X1160),hAPP(hAPP(c_Set_Oinsert(X1161),X1160),X1159)), inference(variable_rename,[status(thm)],[fact_insert__absorb2])). 4.46/4.72 cnf(c_0_10237, plain, (c_Lazy__Sequence_Oempty(X2)=hAPP(c_New__DSequence_Opos__decr__bind(X3,X2,X4,X5),X1)|X1!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[c_0_5975])). 4.46/4.72 cnf(c_0_10238, plain, (hAPP(c_Set_OPow(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5976])). 4.46/4.72 cnf(c_0_10239, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X1)=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(rw,[status(thm)],[c_0_5977, c_0_5884])). 4.46/4.72 fof(c_0_10240, plain, ![X14931, X14932, X14933]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14933,tc_HOL_Obool)),X14932),hAPP(hAPP(c_Set_Oinsert(X14933),X14931),X14932))), inference(variable_rename,[status(thm)],[fact_subset__insertI])). 4.46/4.72 fof(c_0_10241, plain, ![X5212, X5213]:hAPP(c_Relation_OField(X5213),X5212)=hAPP(c_Relation_OField(X5213),hAPP(c_Relation_Oconverse(X5213,X5213),X5212)), inference(variable_rename,[status(thm)],[fact_Field__converse])). 4.46/4.72 fof(c_0_10242, plain, ![X1918]:hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1918), inference(variable_rename,[status(thm)],[fact_posDivAlg__0])). 4.46/4.72 fof(c_0_10243, plain, ![X10472, X10473, X10474, X10475]:c_Option_Ooption_ONone(X10474)=hAPP(c_Map_Orestrict__map(X10475,X10474,X10473,c_Orderings_Obot__class_Obot(tc_fun(X10475,tc_HOL_Obool))),X10472), inference(variable_rename,[status(thm)],[fact_restrict__map__to__empty])). 4.46/4.72 fof(c_0_10244, plain, ![X2866, X2867, X2868]:c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2868,X2867),tc_HOL_Obool))=hAPP(hAPP(c_Product__Type_OSigma(X2868,X2867),c_Orderings_Obot__class_Obot(tc_fun(X2868,tc_HOL_Obool))),X2866), inference(variable_rename,[status(thm)],[fact_Sigma__empty1])). 4.46/4.72 fof(c_0_10245, plain, ![X14121, X14122]:X14121=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X14122,X14122),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X14121), inference(variable_rename,[status(thm)],[fact_rel__pow__1])). 4.46/4.72 fof(c_0_10246, plain, ![X5470, X5471, X5472]:c_List_Oinsert(X5472,X5471,c_List_Oremdups(X5472,X5470))=c_List_Oremdups(X5472,c_List_Oinsert(X5472,X5471,X5470)), inference(variable_rename,[status(thm)],[fact_insert__remdups])). 4.46/4.72 fof(c_0_10247, plain, ![X6364, X6365, X6366]:hAPP(c_List_Orev(X6366),c_List_Oreplicate(X6366,X6365,X6364))=c_List_Oreplicate(X6366,X6365,X6364), inference(variable_rename,[status(thm)],[fact_rev__replicate])). 4.46/4.72 fof(c_0_10248, plain, ![X370, X371]:hBOOL(hAPP(hAPP(c_member(tc_fun(X371,tc_HOL_Obool)),X370),hAPP(c_Set_OPow(X371),X370))), inference(variable_rename,[status(thm)],[fact_Pow__top])). 4.46/4.72 fof(c_0_10249, plain, ![X4386, X4387, X4388]:hBOOL(hAPP(hAPP(c_member(X4388),X4387),hAPP(hAPP(c_Set_Oinsert(X4388),X4387),X4386))), inference(variable_rename,[status(thm)],[fact_insertI1])). 4.46/4.72 fof(c_0_10250, plain, ![X993, X994]:c_Divides_Odiv__class_Omod(tc_Int_Oint,X994,X993)=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X994,X993)), inference(variable_rename,[status(thm)],[fact_mod__int__def])). 4.46/4.72 fof(c_0_10251, plain, ![X10846, X10847, X10848]:c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(X10847))=c_Lazy__Sequence_Ohb__map(X10848,X10847,X10846,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(X10848))), inference(variable_rename,[status(thm)],[fact_hb__map_Osimps_I1_J])). 4.46/4.72 fof(c_0_10252, plain, ![X8514, X8515]:hAPP(hAPP(c_Set_Oinsert(X8515),X8514),c_Orderings_Obot__class_Obot(tc_fun(X8515,tc_HOL_Obool)))=c_Option_Oset(X8515,hAPP(c_Option_Ooption_OSome(X8515),X8514)), inference(variable_rename,[status(thm)],[fact_Option_Oset_Osimps_I2_J])). 4.46/4.72 fof(c_0_10253, plain, ![X3809, X3810]:c_List_Oinsert(X3810,X3809,c_List_Olist_ONil(X3810))=hAPP(hAPP(c_List_Olist_OCons(X3810),X3809),c_List_Olist_ONil(X3810)), inference(variable_rename,[status(thm)],[fact_insert__Nil])). 4.46/4.72 cnf(c_0_10254, plain, (c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5978])). 4.46/4.72 fof(c_0_10255, plain, ![X632, X633, X634, X635]:c_Nitpick_Ofold__graph_H(X635,X634,X633,X632,c_Orderings_Obot__class_Obot(tc_fun(X635,tc_HOL_Obool)),X632), inference(variable_rename,[status(thm)],[fact_fold__graph_H_Ointros_I1_J])). 4.46/4.72 fof(c_0_10256, plain, ![X9759, X9760, X9761]:hAPP(c_Finite__Set_Ofold1(X9761,X9760),hAPP(hAPP(c_Set_Oinsert(X9761),X9759),c_Orderings_Obot__class_Obot(tc_fun(X9761,tc_HOL_Obool))))=X9759, inference(variable_rename,[status(thm)],[fact_fold1__singleton])). 4.46/4.72 fof(c_0_10257, plain, ![X7151]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X7151))), inference(variable_rename,[status(thm)],[fact_zero__less__Suc])). 4.46/4.72 cnf(c_0_10258, plain, (hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_5979])). 4.46/4.72 cnf(c_0_10259, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),X2)=X2|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X1), inference(rw,[status(thm)],[c_0_5980, c_0_5317])). 4.46/4.72 fof(c_0_10260, plain, ![X14025, X14026, X14027, X14028]:X14027=hAPP(hAPP(c_Power_Opower_Opower(X14028,X14027,X14026),X14025),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__0])). 4.46/4.72 cnf(c_0_10261, plain, (hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5981])). 4.46/4.72 fof(c_0_10262, plain, ![X11913, X11914, X11915]:X11913=hAPP(c_Relation_Oconverse(X11915,X11914),hAPP(c_Relation_Oconverse(X11914,X11915),X11913)), inference(variable_rename,[status(thm)],[fact_converse__converse])). 4.46/4.72 fof(c_0_10263, plain, ![X14569, X14570, X14571]:c_HOL_OThe(X14571,c_Finite__Set_Ofold1Set(X14571,X14570,X14569))=hAPP(c_Finite__Set_Ofold1(X14571,X14570),X14569), inference(variable_rename,[status(thm)],[fact_fold1__def])). 4.46/4.72 fof(c_0_10264, plain, ![X6555, X6556]:hAPP(c_Relation_ORange(X6556,X6556),c_Transitive__Closure_Ortrancl(X6556,X6555))=c_Orderings_Otop__class_Otop(tc_fun(X6556,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Range__rtrancl])). 4.46/4.72 fof(c_0_10265, plain, ![X14410, X14411]:c_Orderings_Otop__class_Otop(tc_fun(X14411,tc_HOL_Obool))=hAPP(c_Relation_ODomain(X14411,X14411),c_Transitive__Closure_Ortrancl(X14411,X14410)), inference(variable_rename,[status(thm)],[fact_Domain__rtrancl])). 4.46/4.72 fof(c_0_10266, plain, ![X4121, X4122]:c_Relation_OId__on(X4122,X4121)=hAPP(c_Relation_Oconverse(X4122,X4122),c_Relation_OId__on(X4122,X4121)), inference(variable_rename,[status(thm)],[fact_converse__Id__on])). 4.46/4.72 cnf(c_0_10267, plain, (c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[fact_type__definition__code__numeral])). 4.46/4.72 fof(c_0_10268, plain, ![X13748, X13749]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X13749),X13748))), inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan])). 4.46/4.72 fof(c_0_10269, plain, ![X8644, X8645]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X8645),X8644))), inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan__int])). 4.46/4.72 cnf(c_0_10270, plain, (c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5982])). 4.46/4.72 fof(c_0_10271, plain, ![X14212, X14213]:c_Relation_Orefl__on(X14213,c_Orderings_Otop__class_Otop(tc_fun(X14213,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X14213,X14212)), inference(variable_rename,[status(thm)],[fact_refl__rtrancl])). 4.46/4.72 fof(c_0_10272, plain, ![X8335, X8336]:c_List_Olistrel(X8336,c_Transitive__Closure_Ortrancl(X8336,X8335))=c_Transitive__Closure_Ortrancl(tc_List_Olist(X8336),c_List_Olistrel1(X8336,X8335)), inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__eq__rtrancl__listrel1])). 4.46/4.72 fof(c_0_10273, plain, ![X8005, X8006, X8007]:c_List_Olist_ONil(X8007)=hAPP(hAPP(c_List_Olist__update(X8007,c_List_Olist_ONil(X8007)),X8006),X8005), inference(variable_rename,[status(thm)],[fact_list__update__code_I1_J])). 4.46/4.72 fof(c_0_10274, plain, ![X15478, X15479, X15480]:c_Orderings_Otop__class_Otop(tc_fun(X15479,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X15480,tc_fun(X15479,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X15480,tc_HOL_Obool))),X15478), inference(variable_rename,[status(thm)],[fact_INT__empty])). 4.46/4.72 fof(c_0_10275, plain, ![X7355, X7356, X7357, X7358]:X7355=hAPP(hAPP(c_Finite__Set_Ofold(X7358,X7357,X7356),X7355),c_Orderings_Obot__class_Obot(tc_fun(X7358,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_fold__empty])). 4.46/4.72 fof(c_0_10276, plain, ![X8673, X8674]:hAPP(hAPP(c_Nat_Ocompow(X8674,X8674),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8673)=c_Fun_Oid(X8674), inference(variable_rename,[status(thm)],[fact_funpow_Osimps_I1_J])). 4.46/4.72 fof(c_0_10277, plain, ![X7201, X7202, X7203]:c_Enum_Oproduct(X7203,X7202,c_List_Olist_ONil(X7203),X7201)=c_List_Olist_ONil(tc_prod(X7203,X7202)), inference(variable_rename,[status(thm)],[fact_product_Osimps_I1_J])). 4.46/4.72 fof(c_0_10278, plain, ![X1770, X1771, X1772]:hAPP(hAPP(c_Option_Omap(X1772,X1771),X1770),c_Option_Ooption_ONone(X1772))=c_Option_Ooption_ONone(X1771), inference(variable_rename,[status(thm)],[fact_option__map__None])). 4.46/4.72 fof(c_0_10279, plain, ![X11405, X11406, X11407]:c_Nitpick_OAbs__Frac(X11407,c_Nitpick_Onorm__frac(X11406,X11405))=hAPP(hAPP(c_Nitpick_Ofrac(X11407),X11406),X11405), inference(variable_rename,[status(thm)],[fact_Nitpick_Ofrac__def])). 4.46/4.72 fof(c_0_10280, plain, ![X14205, X14206]:hAPP(c_List_Oset(X14206),hAPP(c_List_Orotate1(X14206),X14205))=hAPP(c_List_Oset(X14206),X14205), inference(variable_rename,[status(thm)],[fact_set__rotate1])). 4.46/4.72 fof(c_0_10281, plain, ![X4522, X4523]:hAPP(c_List_Oset(X4523),X4522)=hAPP(c_List_Oset(X4523),hAPP(c_List_Orev(X4523),X4522)), inference(variable_rename,[status(thm)],[fact_set__rev])). 4.46/4.72 fof(c_0_10282, plain, ![X9891, X9892]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X9892)),hAPP(c_Option_Ooption_OSome(X9892),X9891)), inference(variable_rename,[status(thm)],[fact_option_Osize_I4_J])). 4.46/4.72 fof(c_0_10283, plain, ![X2133, X2134]:c_Orderings_Otop__class_Otop(tc_fun(X2134,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2134,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2134,tc_HOL_Obool))),X2133), inference(variable_rename,[status(thm)],[fact_Un__UNIV__left])). 4.46/4.72 fof(c_0_10284, plain, ![X17426, X17427]:c_Orderings_Otop__class_Otop(tc_fun(X17427,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17427,tc_HOL_Obool)),X17426),c_Orderings_Otop__class_Otop(tc_fun(X17427,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Un__UNIV__right])). 4.46/4.72 fof(c_0_10285, plain, ![X9265, X9266]:c_Fun_Oinj__on(tc_List_Olist(X9266),tc_List_Olist(X9266),c_List_Orev(X9266),X9265), inference(variable_rename,[status(thm)],[fact_inj__on__rev])). 4.46/4.72 fof(c_0_10286, plain, ![X13667]:hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X13667))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X13667), inference(variable_rename,[status(thm)],[fact_abs__int__eq])). 4.46/4.72 fof(c_0_10287, plain, ![X14952, X14953, X14954]:X14952=hAPP(c_Fun_Ocomp(X14954,X14954,X14953,c_Fun_Oid(X14954)),X14952), inference(variable_rename,[status(thm)],[fact_id__o])). 4.46/4.72 fof(c_0_10288, plain, ![X13976, X13977, X13978, X13979]:hAPP(c_List_Olist_Olist__case(X13979,X13978,X13977,X13976),c_List_Olist_ONil(X13978))=X13977, inference(variable_rename,[status(thm)],[fact_list_Osimps_I4_J])). 4.46/4.72 fof(c_0_10289, plain, ![X14045, X14046, X14047]:hAPP(c_Fun_Ocomp(X14047,X14046,X14047,X14045),c_Fun_Oid(X14047))=X14045, inference(variable_rename,[status(thm)],[fact_o__id])). 4.46/4.72 fof(c_0_10290, plain, ![X17040, X17041, X17042, X17043]:c_Fun_Ooverride__on(X17043,X17042,X17041,X17040,c_Orderings_Obot__class_Obot(tc_fun(X17043,tc_HOL_Obool)))=X17041, inference(variable_rename,[status(thm)],[fact_override__on__emptyset])). 4.46/4.72 fof(c_0_10291, plain, ![X3430, X3431, X3432, X3433]:X3431=hAPP(c_Option_Ooption_Ooption__case(X3433,X3432,X3431,X3430),c_Option_Ooption_ONone(X3432)), inference(variable_rename,[status(thm)],[fact_option_Osimps_I4_J])). 4.46/4.72 fof(c_0_10292, plain, ![X2234, X2235, X2236, X2237]:X2234=hAPP(c_List_Ofoldl(X2237,X2236,X2235,X2234),c_List_Olist_ONil(X2236)), inference(variable_rename,[status(thm)],[fact_foldl__Nil])). 4.46/4.72 cnf(c_0_10293, plain, (hAPP(c_Relation_ORange(X1,X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))!=X3), inference(split_conjunct,[status(thm)],[c_0_5983])). 4.46/4.72 fof(c_0_10294, plain, ![X7075, X7076, X7077, X7078]:c_Nat_Onat_Onat__case(X7078,X7077,X7076,hAPP(c_Nat_OSuc,X7075))=hAPP(X7076,X7075), inference(variable_rename,[status(thm)],[fact_nat__case__Suc])). 4.46/4.72 cnf(c_0_10295, plain, (hAPP(c_Relation_ODomain(X2,X3),X1)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|X1!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5984])). 4.46/4.72 fof(c_0_10296, plain, ![X14287, X14288, X14289]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14289)),c_List_Oreplicate(X14289,X14288,X14287))=X14288, inference(variable_rename,[status(thm)],[fact_length__replicate])). 4.46/4.72 fof(c_0_10297, plain, ![X7169, X7170, X7171]:hAPP(c_List_Ohd(X7171),hAPP(hAPP(c_List_Olist_OCons(X7171),X7170),X7169))=X7170, inference(variable_rename,[status(thm)],[fact_hd_Osimps])). 4.46/4.72 fof(c_0_10298, plain, ![X13788, X13789, X13790]:hAPP(c_List_Otl(X13790),hAPP(hAPP(c_List_Olist_OCons(X13790),X13789),X13788))=X13788, inference(variable_rename,[status(thm)],[fact_tl_Osimps_I2_J])). 4.46/4.72 fof(c_0_10299, plain, ![X1339]:X1339=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1339)),c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_diff__Suc__1])). 4.46/4.72 fof(c_0_10300, plain, ![X13209, X13210]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13210,tc_HOL_Obool)),X13209),c_Orderings_Otop__class_Otop(tc_fun(X13210,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_subset__UNIV])). 4.46/4.72 fof(c_0_10301, plain, ![X4320]:c_Relation_Orefl__on(X4320,c_Orderings_Obot__class_Obot(tc_fun(X4320,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4320,X4320),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_refl__on__empty])). 4.46/4.72 cnf(c_0_10302, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=X1), inference(split_conjunct,[status(thm)],[c_0_5985])). 4.46/4.72 fof(c_0_10303, plain, ![X14273, X14274]:c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X14274,X14273)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X14274)),X14273), inference(variable_rename,[status(thm)],[fact_atLeastSucLessThan__greaterThanLessThan])). 4.46/4.72 cnf(c_0_10304, plain, (c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral)=hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat)), inference(split_conjunct,[status(thm)],[fact_number__of__code__numeral__def])). 4.46/4.72 fof(c_0_10305, plain, ![X16097, X16098]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X16098,X16097))), inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost])). 4.46/4.72 cnf(c_0_10306, plain, (c_List_Olist__all2(X2,X3,X4,X1,c_List_Olist_ONil(X3))|X1!=c_List_Olist_ONil(X2)), inference(split_conjunct,[status(thm)],[c_0_5986])). 4.46/4.72 fof(c_0_10307, plain, ![X4888, X4889]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4889,tc_HOL_Obool)),X4888),c_Orderings_Otop__class_Otop(tc_fun(X4889,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X4889,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Diff__UNIV])). 4.46/4.72 fof(c_0_10308, plain, ![X13657, X13658]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X13658,X13657))), inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost__int])). 4.46/4.72 fof(c_0_10309, plain, ![X5398, X5399]:hBOOL(hAPP(hAPP(c_member(X5399),X5398),c_Orderings_Otop__class_Otop(tc_fun(X5399,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_UNIV__I])). 4.46/4.72 cnf(c_0_10310, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_5987])). 4.46/4.72 cnf(c_0_10311, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_5988])). 4.46/4.72 fof(c_0_10312, plain, ![X13865, X13866]:hAPP(c_List_Oset(X13866),X13865)=hAPP(c_List_Oset(X13866),c_List_Oremdups(X13866,X13865)), inference(variable_rename,[status(thm)],[fact_set__remdups])). 4.46/4.72 cnf(c_0_10313, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_5989])). 4.46/4.72 fof(c_0_10314, plain, ![X15055]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15055),hAPP(c_Nat_OSuc,X15055))), inference(variable_rename,[status(thm)],[fact_lessI])). 4.46/4.72 fof(c_0_10315, plain, ![X10910, X10911, X10912, X10913]:c_Option_Ooption_Ooption__rec(X10913,X10912,X10911,X10910,c_Option_Ooption_ONone(X10912))=X10911, inference(variable_rename,[status(thm)],[fact_option_Orecs_I1_J])). 4.46/4.72 fof(c_0_10316, plain, ![X2976, X2977, X2978, X2979]:c_Map_Omap__upds(X2979,X2978,X2977,X2976,c_List_Olist_ONil(X2978))=X2977, inference(variable_rename,[status(thm)],[fact_map__upds__Nil2])). 4.46/4.72 fof(c_0_10317, plain, ![X7988, X7989, X7990, X7991]:X7989=c_Map_Omap__upds(X7991,X7990,X7989,c_List_Olist_ONil(X7991),X7988), inference(variable_rename,[status(thm)],[fact_map__upds__Nil1])). 4.46/4.72 cnf(c_0_10318, plain, (hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X4),X1))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5990])). 4.46/4.72 fof(c_0_10319, plain, ![X15785, X15786, X15787]:X15785=c_Predicate_Oconversep(X15787,X15786,c_Predicate_Oconversep(X15786,X15787,X15785)), inference(variable_rename,[status(thm)],[fact_conversep__conversep])). 4.46/4.72 fof(c_0_10320, plain, ![X3036]:c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X3036),tc_HOL_Obool))=c_List_Olists(X3036,c_Orderings_Otop__class_Otop(tc_fun(X3036,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_lists__UNIV])). 4.46/4.72 fof(c_0_10321, plain, ![X2467]:c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X2467)=c_Lazy__Sequence_Osmall__lazy_H(X2467,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2467)), inference(variable_rename,[status(thm)],[fact_small__lazy__int__def])). 4.46/4.72 fof(c_0_10322, plain, ![X1684]:hAPP(c_Option_Omap(X1684,X1684),c_COMBI(X1684))=c_Fun_Oid(tc_Option_Ooption(X1684)), inference(variable_rename,[status(thm)],[fact_Option_Omap_Oidentity])). 4.46/4.72 fof(c_0_10323, plain, ![X11954]:hAPP(c_List_Omap(X11954,X11954),c_Fun_Oid(X11954))=c_Fun_Oid(tc_List_Olist(X11954)), inference(variable_rename,[status(thm)],[fact_List_Omap_Oid])). 4.46/4.72 fof(c_0_10324, plain, ![X3344]:c_Fun_Oid(tc_Option_Ooption(X3344))=hAPP(c_Option_Omap(X3344,X3344),c_Fun_Oid(X3344)), inference(variable_rename,[status(thm)],[fact_Option_Omap_Oid])). 4.46/4.72 fof(c_0_10325, plain, ![X11973, X11974]:X11973=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11974,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X11974,tc_HOL_Obool))),X11973), inference(variable_rename,[status(thm)],[fact_Int__UNIV__left])). 4.46/4.72 fof(c_0_10326, plain, ![X1232, X1233]:X1232=c_Set_Othe__elem(X1233,hAPP(hAPP(c_Set_Oinsert(X1233),X1232),c_Orderings_Obot__class_Obot(tc_fun(X1233,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_the__elem__eq])). 4.46/4.72 fof(c_0_10327, plain, ![X688]:hAPP(c_Relation_OField(X688),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X688,X688),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X688,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Field__empty])). 4.46/4.72 fof(c_0_10328, plain, ![X14161, X14162, X14163]:hAPP(c_Relation_OImage(X14163,X14162,X14161),c_Orderings_Obot__class_Obot(tc_fun(X14163,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X14162,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Image__empty])). 4.46/4.72 fof(c_0_10329, plain, ![X998]:c_Fun_Oid(tc_List_Olist(X998))=hAPP(c_List_Omap(X998,X998),c_COMBI(X998)), inference(variable_rename,[status(thm)],[fact_List_Omap_Oidentity])). 4.46/4.72 fof(c_0_10330, plain, ![X5755, X5756, X5757]:c_List_Omap__filter(X5757,X5756,X5755,c_List_Olist_ONil(X5757))=c_List_Olist_ONil(X5756), inference(variable_rename,[status(thm)],[fact_map__filter__simps_I2_J])). 4.46/4.72 fof(c_0_10331, plain, ![X3862, X3863, X3864]:c_List_Olist_ONil(X3863)=c_List_Omaps(X3864,X3863,X3862,c_List_Olist_ONil(X3864)), inference(variable_rename,[status(thm)],[fact_maps__simps_I2_J])). 4.46/4.72 fof(c_0_10332, plain, ![X9575]:c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X9575)), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J])). 4.46/4.72 fof(c_0_10333, plain, ![X9263, X9264]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9264,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9264,tc_HOL_Obool)),X9263))=X9263, inference(variable_rename,[status(thm)],[fact_double__complement])). 4.46/4.72 fof(c_0_10334, plain, ![X10230, X10231]:X10230=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10231,tc_HOL_Obool)),X10230),c_Orderings_Otop__class_Otop(tc_fun(X10231,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Int__UNIV__right])). 4.46/4.72 fof(c_0_10335, plain, ![X10430, X10431]:c_List_Olist_ONil(X10431)=hAPP(hAPP(c_List_Otake(X10431),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10430), inference(variable_rename,[status(thm)],[fact_take__0])). 4.46/4.72 fof(c_0_10336, plain, ![X11857, X11858]:c_List_Olist_ONil(X11858)=hAPP(hAPP(c_List_Odrop(X11858),X11857),c_List_Olist_ONil(X11858)), inference(variable_rename,[status(thm)],[fact_drop__Nil])). 4.46/4.72 fof(c_0_10337, plain, ![X3826, X3827]:c_List_Olist_ONil(X3827)=hAPP(hAPP(c_List_Otake(X3827),X3826),c_List_Olist_ONil(X3827)), inference(variable_rename,[status(thm)],[fact_take__Nil])). 4.46/4.72 cnf(c_0_10338, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_5991])). 4.46/4.72 fof(c_0_10339, plain, ![X12117]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12117)=hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X12117)), inference(variable_rename,[status(thm)],[fact_nat__of__number])). 4.46/4.72 cnf(c_0_10340, plain, (X1=hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))), inference(split_conjunct,[status(thm)],[c_0_5992])). 4.46/4.72 fof(c_0_10341, plain, ![X9134]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9134), inference(variable_rename,[status(thm)],[fact_diff__0__eq__0])). 4.46/4.72 fof(c_0_10342, plain, ![X4192]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4192), inference(variable_rename,[status(thm)],[fact_zdiv__zero])). 4.46/4.72 cnf(c_0_10343, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_5993])). 4.46/4.72 fof(c_0_10344, plain, ![X910]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X910),c_Groups_Ozero__class_Ozero(tc_Int_Oint))&c_Divides_Odiv__class_Omod(tc_Int_Oint,X910,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=X910), inference(variable_rename,[status(thm)],[fact_DIVISION__BY__ZERO])). 4.46/4.72 fof(c_0_10345, plain, ![X2769, X2770, X2771]:hAPP(c_Nat_Onat_Onat__rec(X2771,X2770,X2769),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2770, inference(variable_rename,[status(thm)],[fact_nat__rec__0])). 4.46/4.72 fof(c_0_10346, plain, ![X13137, X13138]:c_Fun_Oinj__on(X13138,tc_Option_Ooption(X13138),c_Option_Ooption_OSome(X13138),X13137), inference(variable_rename,[status(thm)],[fact_inj__Some])). 4.46/4.72 fof(c_0_10347, plain, ![X1586, X1587]:hAPP(c_Relation_ORange(X1587,X1587),c_Relation_OId__on(X1587,X1586))=X1586, inference(variable_rename,[status(thm)],[fact_Range__Id__on])). 4.46/4.72 fof(c_0_10348, plain, ![X7389, X7390]:X7389=hAPP(c_Relation_ODomain(X7390,X7390),c_Relation_OId__on(X7390,X7389)), inference(variable_rename,[status(thm)],[fact_Domain__Id__on])). 4.46/4.72 fof(c_0_10349, plain, ![X5898, X5899]:c_List_Olistrelp(X5899,X5898,c_List_Olist_ONil(X5899),c_List_Olist_ONil(X5899)), inference(variable_rename,[status(thm)],[fact_listrelp_ONil])). 4.46/4.72 fof(c_0_10350, plain, ![X884, X885]:c_List_Oremdups(X885,c_List_Oremdups(X885,X884))=c_List_Oremdups(X885,X884), inference(variable_rename,[status(thm)],[fact_remdups__remdups])). 4.46/4.72 fof(c_0_10351, plain, ![X7858, X7859]:c_Transitive__Closure_Ortrancl(X7859,X7858)=c_Transitive__Closure_Ortrancl(X7859,c_Transitive__Closure_Ortrancl(X7859,X7858)), inference(variable_rename,[status(thm)],[fact_rtrancl__idemp])). 4.46/4.72 fof(c_0_10352, plain, ![X4338]:c_List_Olist_ONil(tc_List_Olist(X4338))=c_List_Otranspose(X4338,c_List_Olist_ONil(tc_List_Olist(X4338))), inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I1_J])). 4.46/4.72 fof(c_0_10353, plain, ![X6183, X6184]:hBOOL(hAPP(c_List_Olistsp(X6184,X6183),c_List_Olist_ONil(X6184))), inference(variable_rename,[status(thm)],[fact_listsp_ONil])). 4.46/4.72 fof(c_0_10354, plain, ![X9814, X9815]:hBOOL(hAPP(c_List_Odistinct(X9815),c_List_Oremdups(X9815,X9814))), inference(variable_rename,[status(thm)],[fact_distinct__remdups])). 4.46/4.72 fof(c_0_10355, plain, ![X2692, X2693]:hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X2693,X2692))), inference(variable_rename,[status(thm)],[fact_distinct__upto])). 4.46/4.72 fof(c_0_10356, plain, ![X3517]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X3517,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X3517,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X3517,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Union__UNIV])). 4.46/4.72 fof(c_0_10357, plain, ![X17183, X17184, X17185]:hAPP(c_New__DSequence_Opos__single(X17185,X17184),X17183)=hAPP(c_Lazy__Sequence_Osingle(X17185),X17184), inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__single__def])). 4.46/4.72 fof(c_0_10358, plain, ![X16642, X16643]:hAPP(c_List_Ofilter(X16643,X16642),c_List_Olist_ONil(X16643))=c_List_Olist_ONil(X16643), inference(variable_rename,[status(thm)],[fact_filter_Osimps_I1_J])). 4.46/4.72 fof(c_0_10359, plain, ![X10071]:hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X10071)),c_Option_Ooption_ONone(X10071))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_option_Osize_I3_J])). 4.46/4.72 fof(c_0_10360, plain, ![X9806, X9807]:X9806=c_Complete__Lattice_OSup__class_OSup(tc_fun(X9807,tc_HOL_Obool),hAPP(c_Set_OPow(X9807),X9806)), inference(variable_rename,[status(thm)],[fact_Union__Pow__eq])). 4.46/4.72 fof(c_0_10361, plain, ![X16068]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16068)),c_List_Olist_ONil(X16068))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_list_Osize_I3_J])). 4.46/4.72 fof(c_0_10362, plain, ![X6509]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X6509)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X6509)), inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I3_J])). 4.46/4.72 fof(c_0_10363, plain, ![X14168]:hAPP(c_Set_OPow(X14168),c_Orderings_Otop__class_Otop(tc_fun(X14168,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X14168,tc_HOL_Obool),tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Pow__UNIV])). 4.46/4.72 fof(c_0_10364, plain, ![X10215, X10216, X10217]:c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X10217,X10216,X10215,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=X10216, inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I4_J])). 4.46/4.72 fof(c_0_10365, plain, ![X10409, X10410, X10411]:c_Nat_Onat_Onat__case(X10411,X10410,X10409,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X10410, inference(variable_rename,[status(thm)],[fact_nat__case__0])). 4.46/4.72 fof(c_0_10366, plain, ![X14349, X14350]:hAPP(c_Set_Oimage(X14350,X14350,c_COMBI(X14350)),X14349)=X14349, inference(variable_rename,[status(thm)],[fact_image__ident])). 4.46/4.72 fof(c_0_10367, plain, ![X783, X784]:hAPP(c_Set_Oimage(X784,X784,c_Fun_Oid(X784)),X783)=X783, inference(variable_rename,[status(thm)],[fact_image__id])). 4.46/4.72 fof(c_0_10368, plain, ![X1124, X1125]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1125,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1125,tc_HOL_Obool))),X1124)), inference(variable_rename,[status(thm)],[fact_empty__subsetI])). 4.46/4.72 fof(c_0_10369, plain, ![X2473, X2474, X2475, X2476]:X2474=hAPP(hAPP(c_COMBK(X2476,X2475),X2474),X2473), inference(variable_rename,[status(thm)],[help_c__COMBK__1])). 4.46/4.72 fof(c_0_10370, plain, ![X8354, X8355]:hAPP(hAPP(c_List_Oappend(X8355),c_List_Olist_ONil(X8355)),X8354)=X8354, inference(variable_rename,[status(thm)],[fact_append__Nil])). 4.46/4.72 fof(c_0_10371, plain, ![X11020, X11021]:hAPP(hAPP(c_List_Odrop(X11021),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X11020)=X11020, inference(variable_rename,[status(thm)],[fact_drop__0])). 4.46/4.72 cnf(c_0_10372, plain, (c_List_Olist__all2(X3,X3,c_fequal,X1,X2)|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5994])). 4.46/4.72 fof(c_0_10373, plain, ![X17158, X17159]:c_List_Osublist(X17159,X17158,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=c_List_Olist_ONil(X17159), inference(variable_rename,[status(thm)],[fact_sublist__empty])). 4.46/4.72 fof(c_0_10374, plain, ![X9949, X9950]:X9949=hAPP(hAPP(c_List_Oappend(X9950),X9949),c_List_Olist_ONil(X9950)), inference(variable_rename,[status(thm)],[fact_append__Nil2])). 4.46/4.72 fof(c_0_10375, plain, ![X6800, X6801]:c_Orderings_Obot__class_Obot(tc_fun(X6801,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6801,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X6801,tc_HOL_Obool))),X6800), inference(variable_rename,[status(thm)],[fact_empty__Diff])). 4.46/4.72 fof(c_0_10376, plain, ![X7208, X7209]:X7208=hAPP(c_Option_Othe(X7209),hAPP(c_Option_Ooption_OSome(X7209),X7208)), inference(variable_rename,[status(thm)],[fact_the_Osimps])). 4.46/4.72 fof(c_0_10377, plain, ![X8296, X8297]:c_Orderings_Obot__class_Obot(tc_fun(X8297,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8297,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X8297,tc_HOL_Obool))),X8296), inference(variable_rename,[status(thm)],[fact_Int__empty__left])). 4.46/4.72 fof(c_0_10378, plain, ![X15302, X15303]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15303,tc_HOL_Obool)),X15302),c_Orderings_Obot__class_Obot(tc_fun(X15303,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X15303,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Int__empty__right])). 4.46/4.72 fof(c_0_10379, plain, ![X14112]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X14112)=X14112, inference(variable_rename,[status(thm)],[fact_nat__mult__1])). 4.46/4.72 fof(c_0_10380, plain, ![X4725]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X4725)=X4725, inference(variable_rename,[status(thm)],[fact_zmult__1])). 4.46/4.72 fof(c_0_10381, plain, ![X11937]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X11937)=X11937, inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0])). 4.46/4.72 fof(c_0_10382, plain, ![X5685, X5686]:c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5686,tc_HOL_Obool),tc_HOL_Obool))=hAPP(hAPP(c_Equiv__Relations_Oquotient(X5686),c_Orderings_Obot__class_Obot(tc_fun(X5686,tc_HOL_Obool))),X5685), inference(variable_rename,[status(thm)],[fact_quotient__empty])). 4.46/4.72 cnf(c_0_10383, plain, (X1=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)), inference(split_conjunct,[status(thm)],[c_0_5995])). 4.46/4.72 fof(c_0_10384, plain, ![X9182]:c_Relation_OId__on(X9182,c_Orderings_Obot__class_Obot(tc_fun(X9182,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X9182,X9182),tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Id__on__empty])). 4.46/4.72 fof(c_0_10385, plain, ![X7907]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7907),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X7907, inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0])). 4.46/4.72 cnf(c_0_10386, plain, (X1=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5996])). 4.46/4.72 fof(c_0_10387, plain, ![X6240, X6241]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6241,tc_HOL_Obool)),X6240),X6240)), inference(variable_rename,[status(thm)],[fact_subset__refl])). 4.46/4.72 fof(c_0_10388, plain, ![X11324]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X11324,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X11324,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X11324,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Inter__UNIV])). 4.46/4.72 fof(c_0_10389, plain, ![X2838]:X2838=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2838),c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_nat__mult__1__right])). 4.46/4.72 fof(c_0_10390, plain, ![X11061]:X11061=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11061),c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(variable_rename,[status(thm)],[fact_zmult__1__right])). 4.46/4.72 fof(c_0_10391, plain, ![X8605, X8606, X8607]:c_Fun_Oinj__on(X8607,X8606,X8605,c_Orderings_Obot__class_Obot(tc_fun(X8607,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_inj__on__empty])). 4.46/4.72 fof(c_0_10392, plain, ![X8710, X8711, X8712]:hAPP(c_Set_Oimage(X8712,X8711,X8710),c_Orderings_Obot__class_Obot(tc_fun(X8712,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X8711,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_image__empty])). 4.46/4.72 fof(c_0_10393, plain, ![X1664, X1665]:X1664=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1665,tc_HOL_Obool)),X1664),c_Orderings_Obot__class_Obot(tc_fun(X1665,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Diff__empty])). 4.46/4.72 fof(c_0_10394, plain, ![X7485]:X7485=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X7485)), inference(variable_rename,[status(thm)],[fact_zminus__zminus])). 4.46/4.72 fof(c_0_10395, plain, ![X3393, X3394, X3395]:c_Lazy__Sequence_Ohb__single(X3395,X3394)=hAPP(c_New__DSequence_Oneg__single(X3395,X3394),X3393), inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__single__def])). 4.46/4.72 fof(c_0_10396, plain, ![X6712]:c_Wellfounded_Owf(X6712,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X6712,X6712),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_wf__empty])). 4.46/4.72 fof(c_0_10397, plain, ![X13456]:c_Orderings_Obot__class_Obot(tc_fun(X13456,tc_HOL_Obool))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X13456,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X13456,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq])). 4.46/4.72 fof(c_0_10398, plain, ![X4370, X4371]:c_Fun_Oinj__on(X4371,X4371,c_COMBI(X4371),X4370), inference(variable_rename,[status(thm)],[fact_inj__on__id2])). 4.46/4.72 fof(c_0_10399, plain, ![X10465, X10466]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10466,tc_HOL_Obool)),X10465),X10465)=c_Orderings_Obot__class_Obot(tc_fun(X10466,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Diff__cancel])). 4.46/4.72 fof(c_0_10400, plain, ![X1787]:hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1787),X1787)), inference(variable_rename,[status(thm)],[fact_eq__int__refl])). 4.46/4.72 fof(c_0_10401, plain, ![X15220, X15221]:c_Fun_Oinj__on(X15221,X15221,c_Fun_Oid(X15221),X15220), inference(variable_rename,[status(thm)],[fact_inj__on__id])). 4.46/4.72 fof(c_0_10402, plain, ![X15627, X15628]:c_Relation_Osingle__valued(X15628,X15628,c_Relation_OId__on(X15628,X15627)), inference(variable_rename,[status(thm)],[fact_single__valued__Id__on])). 4.46/4.72 fof(c_0_10403, plain, ![X2251, X2252]:c_Relation_Orefl__on(X2252,X2251,c_Relation_OId__on(X2252,X2251)), inference(variable_rename,[status(thm)],[fact_refl__on__Id__on])). 4.46/4.72 fof(c_0_10404, plain, ![X16901]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16901),X16901)), inference(variable_rename,[status(thm)],[fact_le__refl])). 4.46/4.72 fof(c_0_10405, plain, ![X4218]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4218),X4218)), inference(variable_rename,[status(thm)],[fact_zle__refl])). 4.46/4.72 fof(c_0_10406, plain, ![X6878, X6879]:c_List_OtakeWhile(X6879,X6878,c_List_Olist_ONil(X6879))=c_List_Olist_ONil(X6879), inference(variable_rename,[status(thm)],[fact_takeWhile_Osimps_I1_J])). 4.46/4.72 fof(c_0_10407, plain, ![X9484, X9485]:c_List_Olist_ONil(X9485)=c_List_Osublist(X9485,c_List_Olist_ONil(X9485),X9484), inference(variable_rename,[status(thm)],[fact_sublist__nil])). 4.46/4.72 cnf(c_0_10408, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls))), inference(split_conjunct,[status(thm)],[fact_rel__simps_I6_J])). 4.46/4.72 cnf(c_0_10409, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls))), inference(split_conjunct,[status(thm)],[fact_rel__simps_I23_J])). 4.46/4.72 fof(c_0_10410, plain, ![X4986, X4987]:c_List_Olist_ONil(X4987)=c_List_Oremove1(X4987,X4986,c_List_Olist_ONil(X4987)), inference(variable_rename,[status(thm)],[fact_remove1_Osimps_I1_J])). 4.46/4.72 fof(c_0_10411, plain, ![X3435, X3436]:c_Option_Ooption_Ooption__size(X3436,X3435,c_Option_Ooption_ONone(X3436))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_option_Osize_I1_J])). 4.46/4.72 cnf(c_0_10412, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)))), inference(split_conjunct,[status(thm)],[fact_neg__number__of__Min])). 4.46/4.72 fof(c_0_10413, plain, ![X6139, X6140]:c_List_Olist_Olist__size(X6140,X6139,c_List_Olist_ONil(X6140))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_list_Osize_I1_J])). 4.46/4.72 fof(c_0_10414, plain, ![X2095, X2096]:c_List_Olist_ONil(X2096)=c_List_Oreplicate(X2096,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2095), inference(variable_rename,[status(thm)],[fact_replicate__0])). 4.46/4.72 fof(c_0_10415, plain, ![X14120]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14120), inference(variable_rename,[status(thm)],[fact_zmod__zero])). 4.46/4.72 fof(c_0_10416, plain, ![X13115]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13115),X13115)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_diff__self__eq__0])). 4.46/4.72 fof(c_0_10417, plain, ![X6144]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X6144,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X6144,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X6144,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Inter__empty])). 4.46/4.72 cnf(c_0_10418, plain, (hBOOL(hAPP(hAPP(c_fequal,X1),X2))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5997])). 4.46/4.72 fof(c_0_10419, plain, ![X15727]:c_Orderings_Otop__class_Otop(tc_fun(X15727,tc_HOL_Obool))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X15727,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X15727,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Compl__empty__eq])). 4.46/4.72 fof(c_0_10420, plain, ![X8464, X8465]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8465,tc_HOL_Obool)),X8464),X8464)=X8464, inference(variable_rename,[status(thm)],[fact_Un__absorb])). 4.46/4.72 fof(c_0_10421, plain, ![X15152, X15153]:X15152=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15153,tc_HOL_Obool)),X15152),X15152), inference(variable_rename,[status(thm)],[fact_Int__absorb])). 4.46/4.72 fof(c_0_10422, plain, ![X2345]:hBOOL(hAPP(c_List_Odistinct(X2345),c_List_Olist_ONil(X2345))), inference(variable_rename,[status(thm)],[fact_distinct_Osimps_I1_J])). 4.46/4.72 fof(c_0_10423, plain, ![X6277]:hAPP(c_List_Orev(X6277),c_List_Olist_ONil(X6277))=c_List_Olist_ONil(X6277), inference(variable_rename,[status(thm)],[fact_rev_Osimps_I1_J])). 4.46/4.72 fof(c_0_10424, plain, ![X4562]:c_List_Olist_ONil(X4562)=hAPP(c_List_Otl(X4562),c_List_Olist_ONil(X4562)), inference(variable_rename,[status(thm)],[fact_tl_Osimps_I1_J])). 4.46/4.72 fof(c_0_10425, plain, ![X5139]:c_Orderings_Obot__class_Obot(tc_fun(X5139,tc_HOL_Obool))=hAPP(c_List_Oset(X5139),c_List_Olist_ONil(X5139)), inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I1_J])). 4.46/4.72 fof(c_0_10426, plain, ![X9691, X9692]:X9691=c_Lazy__Sequence_Oappend(X9692,c_Lazy__Sequence_Olazy__sequence_OEmpty(X9692),X9691), inference(variable_rename,[status(thm)],[fact__04])). 4.46/4.72 fof(c_0_10427, plain, ![X4924, X4925]:X4924=c_List_Osplice(X4925,c_List_Olist_ONil(X4925),X4924), inference(variable_rename,[status(thm)],[fact_splice_Osimps_I1_J])). 4.46/4.72 fof(c_0_10428, plain, ![X4391, X4392]:X4391=c_List_Osplice(X4392,X4391,c_List_Olist_ONil(X4392)), inference(variable_rename,[status(thm)],[fact_splice__Nil2])). 4.46/4.72 fof(c_0_10429, plain, ![X3434]:c_Option_Oset(X3434,c_Option_Ooption_ONone(X3434))=c_Orderings_Obot__class_Obot(tc_fun(X3434,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Option_Oset_Osimps_I1_J])). 4.46/4.72 cnf(c_0_10430, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OPls)=X1), inference(split_conjunct,[status(thm)],[c_0_5998])). 4.46/4.72 cnf(c_0_10431, plain, (c_Int_OPls=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X1)), inference(split_conjunct,[status(thm)],[c_0_5999])). 4.46/4.72 fof(c_0_10432, plain, ![X12803]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X12803,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X12803,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X12803,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Union__empty])). 4.46/4.72 cnf(c_0_10433, plain, (c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X1), inference(split_conjunct,[status(thm)],[c_0_5515])). 4.46/4.72 fof(c_0_10434, plain, ![X10408]:hBOOL(hAPP(c_Finite__Set_Ofinite(X10408),c_Orderings_Obot__class_Obot(tc_fun(X10408,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_finite_Oequations_I1_J])). 4.46/4.72 fof(c_0_10435, plain, ![X12535]:c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X12535), inference(variable_rename,[status(thm)],[fact_inj__Suc])). 4.46/4.72 fof(c_0_10436, plain, ![X8641]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X8641,X8641), inference(variable_rename,[status(thm)],[fact_zmod__self])). 4.46/4.72 fof(c_0_10437, plain, ![X14607, X14608]:hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X14608,tc_HOL_Obool)),X14607)), inference(variable_rename,[status(thm)],[fact_top1I])). 4.46/4.72 fof(c_0_10438, plain, ![X15058, X15059]:c_Relation_Ototal__on(X15059,c_Orderings_Obot__class_Obot(tc_fun(X15059,tc_HOL_Obool)),X15058), inference(variable_rename,[status(thm)],[fact_total__on__empty])). 4.46/4.72 fof(c_0_10439, plain, ![X7629]:c_Finite__Set_Ofun__left__comm__idem(X7629,tc_fun(X7629,tc_HOL_Obool),c_Set_Oinsert(X7629)), inference(variable_rename,[status(thm)],[fact_fun__left__comm__idem__insert])). 4.46/4.72 fof(c_0_10440, plain, ![X4540, X4541]:c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X4541,X4540)), inference(variable_rename,[status(thm)],[fact_sorted__upto])). 4.46/4.72 fof(c_0_10441, plain, ![X10281, X10282]:c_List_Olist__all(X10282,X10281,c_List_Olist_ONil(X10282)), inference(variable_rename,[status(thm)],[fact_list__all__simps_I2_J])). 4.46/4.72 fof(c_0_10442, plain, ![X1474, X1475]:c_Wellfounded_Owf(X1475,c_List_Omeasures(X1475,X1474)), inference(variable_rename,[status(thm)],[fact_wf__measures])). 4.46/4.72 fof(c_0_10443, plain, ![X9596]:c_Wellfounded_Owf(tc_fun(X9596,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X9596)), inference(variable_rename,[status(thm)],[fact_wf__finite__psubset])). 4.46/4.72 fof(c_0_10444, plain, ![X15454]:c_List_Olist_ONil(X15454)=c_List_Obutlast(X15454,c_List_Olist_ONil(X15454)), inference(variable_rename,[status(thm)],[fact_butlast_Osimps_I1_J])). 4.46/4.72 fof(c_0_10445, plain, ![X2519]:c_List_Olist_ONil(X2519)=c_List_Oremdups(X2519,c_List_Olist_ONil(X2519)), inference(variable_rename,[status(thm)],[fact_remdups_Osimps_I1_J])). 4.46/4.72 fof(c_0_10446, plain, ![X12084, X12085]:c_Hilbert__Choice_OEps(X12085,hAPP(c_fequal,X12084))=X12084, inference(variable_rename,[status(thm)],[fact_some__sym__eq__trivial])). 4.46/4.72 cnf(c_0_10447, plain, (hAPP(c_Code__Numeral_Oint__of,X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X1), inference(split_conjunct,[status(thm)],[c_0_4503])). 4.46/4.72 fof(c_0_10448, plain, ![X6655, X6656]:X6655=c_HOL_OThe(X6656,hAPP(c_fequal,X6655)), inference(variable_rename,[status(thm)],[fact_the__sym__eq__trivial])). 4.46/4.72 cnf(c_0_10449, plain, (c_Nitpick_Onat__gcd(X2,X1)=X2|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_6000])). 4.46/4.72 cnf(c_0_10450, plain, (c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=c_Random_Oinc__shift(X2,X1)|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_6001])). 4.46/4.72 fof(c_0_10451, plain, ![X5876]:c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5876)), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J])). 4.46/4.72 fof(c_0_10452, plain, ![X12053, X12054]:hAPP(c_New__DSequence_Opos__empty(X12054),X12053)=c_Lazy__Sequence_Oempty(X12054), inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__empty__def])). 4.46/4.72 cnf(c_0_10453, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls)=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[fact_zero__code__numeral__code])). 4.46/4.72 cnf(c_0_10454, plain, (hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[fact_one__code__numeral__def])). 4.46/4.72 fof(c_0_10455, plain, ![X8023]:c_Predicate_Oconversep(X8023,X8023,c_fequal)=c_fequal, inference(variable_rename,[status(thm)],[fact_conversep__eq])). 4.46/4.72 fof(c_0_10456, plain, ![X10485]:X10485=hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X10485)), inference(variable_rename,[status(thm)],[fact_Rep__Integ__inverse])). 4.46/4.72 cnf(c_0_10457, plain, (X1=hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X1))), inference(split_conjunct,[status(thm)],[c_0_6002])). 4.46/4.72 cnf(c_0_10458, plain, (X1=hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X1))), inference(split_conjunct,[status(thm)],[c_0_6003])). 4.46/4.72 fof(c_0_10459, plain, ![X2198]:hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,X2198))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_com_Osize_I15_J])). 4.46/4.72 fof(c_0_10460, plain, ![X8507, X8508]:class_HOL_Oequal(tc_Nitpick_Opair__box(X8508,X8507)), inference(variable_rename,[status(thm)],[arity_Nitpick__Opair____box__HOL_Oequal])). 4.46/4.72 fof(c_0_10461, plain, ![X10685, X10686]:class_HOL_Oequal(tc_sum(X10686,X10685)), inference(variable_rename,[status(thm)],[arity_sum__HOL_Oequal])). 4.46/4.72 fof(c_0_10462, plain, ![X15775, X15776]:class_HOL_Oequal(tc_prod(X15776,X15775)), inference(variable_rename,[status(thm)],[arity_prod__HOL_Oequal])). 4.46/4.72 fof(c_0_10463, plain, ![X9619, X9620]:class_Nat_Osize(tc_Nitpick_Opair__box(X9620,X9619)), inference(variable_rename,[status(thm)],[arity_Nitpick__Opair____box__Nat_Osize])). 4.46/4.72 fof(c_0_10464, plain, ![X15333, X15334]:class_Nat_Osize(tc_sum(X15334,X15333)), inference(variable_rename,[status(thm)],[arity_sum__Nat_Osize])). 4.46/4.72 fof(c_0_10465, plain, ![X11867, X11868]:class_Nat_Osize(tc_prod(X11868,X11867)), inference(variable_rename,[status(thm)],[arity_prod__Nat_Osize])). 4.46/4.72 fof(c_0_10466, plain, ![X9549, X9550]:c_Hoare__Mirabelle_Ohoare__derivs(X9550,X9549,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X9550),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_hoare__derivs_Oequations_I1_J])). 4.46/4.72 fof(c_0_10467, plain, ![X1553]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,X1553)), inference(variable_rename,[status(thm)],[fact_com_Osize_I7_J])). 4.46/4.72 fof(c_0_10468, plain, ![X15754]:c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X15754)), inference(variable_rename,[status(thm)],[fact_wf__int__ge__less__than2])). 4.46/4.72 fof(c_0_10469, plain, ![X1442]:c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X1442)), inference(variable_rename,[status(thm)],[fact_wf__int__ge__less__than])). 4.46/4.72 fof(c_0_10470, plain, ![X4823, X4824]:hAPP(c_COMBI(X4824),X4823)=X4823, inference(variable_rename,[status(thm)],[help_c__COMBI__1])). 4.46/4.72 fof(c_0_10471, plain, ![X3152, X3153]:X3152=hAPP(c_Fun_Oid(X3153),X3152), inference(variable_rename,[status(thm)],[fact_id__apply])). 4.46/4.72 fof(c_0_10472, plain, ![X9358]:X9358=hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X9358), inference(variable_rename,[status(thm)],[fact_nat__size])). 4.46/4.72 fof(c_0_10473, plain, ![X1468]:c_Equiv__Relations_Oequivp(X1468,c_fequal), inference(variable_rename,[status(thm)],[fact_identity__equivp])). 4.46/4.72 fof(c_0_10474, plain, ![X5340]:class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X5340)), inference(variable_rename,[status(thm)],[arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal])). 4.46/4.72 fof(c_0_10475, plain, ![X12330]:class_HOL_Oequal(tc_Option_Ooption(X12330)), inference(variable_rename,[status(thm)],[arity_Option__Ooption__HOL_Oequal])). 4.46/4.72 fof(c_0_10476, plain, ![X6345]:class_HOL_Oequal(tc_List_Olist(X6345)), inference(variable_rename,[status(thm)],[arity_List__Olist__HOL_Oequal])). 4.46/4.72 fof(c_0_10477, plain, ![X4780]:class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X4780)), inference(variable_rename,[status(thm)],[arity_Lazy____Sequence__Olazy____sequence__Nat_Osize])). 4.46/4.72 fof(c_0_10478, plain, ![X3921]:class_Nat_Osize(tc_Option_Ooption(X3921)), inference(variable_rename,[status(thm)],[arity_Option__Ooption__Nat_Osize])). 4.46/4.72 fof(c_0_10479, plain, ![X8577]:class_Nat_Osize(tc_List_Olist(X8577)), inference(variable_rename,[status(thm)],[arity_List__Olist__Nat_Osize])). 4.46/4.72 fof(c_0_10480, plain, ![X14742]:class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(X14742)), inference(variable_rename,[status(thm)],[arity_Hoare____Mirabelle__Otriple__HOL_Oequal])). 4.46/4.72 fof(c_0_10481, plain, ![X10168]:class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X10168)), inference(variable_rename,[status(thm)],[arity_Hoare____Mirabelle__Otriple__Nat_Osize])). 4.46/4.72 cnf(c_0_10482, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_Fun_Oid(X1)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X3))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),tc_fun(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X1),c_COMBS(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X2,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,X1)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,X1),tc_fun(X3,tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_fun(X3,X1)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X3,X1),tc_fun(X3,tc_HOL_Obool),X2)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X3,X1),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X3)),c_fequal))),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,X1),tc_fun(X3,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,X1),tc_fun(tc_fun(X3,X1),tc_fun(X3,X1)),X2),c_COMBB(X1,X1,X3)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4))),X5)))))),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X6))),X7)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),X5),X7))|~class_Rings_Osemiring__0(X1)|~c_Fun_Oinj__on(tc_prod(X2,X3),X1,hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,X1),tc_fun(X3,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,X1),tc_fun(tc_fun(X3,X1),tc_fun(X3,X1)),X2),c_COMBB(X1,X1,X3)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4))),X5)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X6),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X7)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6004, c_0_4945]), c_0_4945]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10483, plain, (hAPP(c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1))))=c_Divides_Odivmod__int(X2,X1)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2), inference(rw,[status(thm)],[c_0_6005, c_0_5670]), ['final']). 4.46/4.72 cnf(c_0_10484, plain, (hAPP(c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,X2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1))))=c_Divides_Odivmod__int(X2,X1)|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_6006, c_0_5670]), ['final']). 4.46/4.72 cnf(c_0_10485, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Orderings_Oord__class_Omax(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2))),X3)))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6007, c_0_4945]), c_0_4945]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10486, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Orderings_Oord__class_Omin(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2))),X3)))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6008, c_0_4945]), c_0_4945]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10487, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2))),X3)))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Odistrib__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6009, c_0_4945]), c_0_4945]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10488, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2))),X3)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Odistrib__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6010, c_0_4945]), c_0_4945]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10489, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X1,X1)),tc_fun(tc_Int_Oint,X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),X1),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X1,X1)),tc_fun(tc_Int_Oint,X1)),tc_Int_Oint),c_COMBB(tc_fun(X1,X1),X1,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_fun(X1,X1),X1),tc_Int_Oint),c_HOL_OLet(X1,X1)),c_Int_Oring__1__class_Oof__int(X1)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X1,X1),tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,X1)),tc_fun(tc_fun(X1,X1),tc_fun(X1,X1)),tc_Int_Oint),c_COMBS(X1,X1,X1)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X1,X1),tc_fun(X1,tc_fun(X1,X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,X1)),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_fun(X1,X1))),tc_Int_Oint),c_COMBB(X1,tc_fun(X1,X1),X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_COMBI(X1))))),hAPP(hAPP(c_COMBC(X1,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X1),c_Groups_Oplus__class_Oplus(X1)),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_COMBI(X1)))),c_Groups_Oone__class_Oone(X1))))),c_Divides_Odivmod__int(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))=hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6011, c_0_5670]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), ['final']). 4.46/4.72 cnf(c_0_10490, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X2)),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6012, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10491, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X2)),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6014, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10492, plain, (hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X1,X5,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X1),c_COMBC(X5,tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X1,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X5),tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X1,X5)))),c_Product__Type_OPair(X1,X5)))),X6),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X5),c_COMBC(X2,tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X5,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X2),tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X5,X2)))),c_Product__Type_OPair(X5,X2)))),X7)),X3),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Relation_Orel__comp(X1,X5,X2),X6),X7)))), inference(split_conjunct,[status(thm)],[c_0_6015]), ['final']). 4.46/4.72 cnf(c_0_10493, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X6)),X3),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X5),X6)))), inference(split_conjunct,[status(thm)],[c_0_6016]), ['final']). 4.46/4.72 cnf(c_0_10494, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X6)),X3),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X5),X6)))), inference(split_conjunct,[status(thm)],[c_0_6017]), ['final']). 4.46/4.72 cnf(c_0_10495, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X2),X3),tc_prod(X2,X3),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),X3),c_List_Olist_ONil(X2)),X4),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,tc_prod(tc_List_Olist(X2),X3)),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_prod(tc_List_Olist(X2),X3)),tc_fun(X3,tc_prod(tc_List_Olist(X2),X3))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X2),X3),tc_prod(tc_List_Olist(X2),X3)),tc_fun(tc_fun(X3,tc_prod(tc_List_Olist(X2),X3)),tc_fun(X3,tc_prod(tc_List_Olist(X2),X3))),X2),c_COMBB(tc_prod(tc_List_Olist(X2),X3),tc_prod(tc_List_Olist(X2),X3),X3)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X2),tc_fun(X3,tc_prod(tc_List_Olist(X2),X3))),tc_fun(tc_prod(tc_List_Olist(X2),X3),tc_prod(tc_List_Olist(X2),X3)),X2),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X2),X3,tc_prod(tc_List_Olist(X2),X3))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X2),tc_List_Olist(X2)),tc_fun(tc_List_Olist(X2),tc_fun(X3,tc_prod(tc_List_Olist(X2),X3))),X2),hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(X3,tc_prod(tc_List_Olist(X2),X3)),tc_List_Olist(X2)),c_Product__Type_OPair(tc_List_Olist(X2),X3))),c_List_Olist_OCons(X2))))),hAPP(c_Lazy__Sequence_Oanamorph(X3,X2,X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(X5,X4))=hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X3,X2,X5),X1),X4)), inference(split_conjunct,[status(thm)],[c_0_5653]), ['final']). 4.46/4.72 cnf(c_0_10496, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_6018]), ['final']). 4.46/4.72 cnf(c_0_10497, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6019, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), c_0_5134]), c_0_4760]), ['final']). 4.46/4.72 cnf(c_0_10498, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBS(X1,tc_fun(X3,tc_HOL_Obool),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,X2),tc_fun(tc_fun(X3,tc_HOL_Obool),X2),X1),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2)),hAPP(c_COMBC(X3,X1,X2),X4))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),c_Set_OCollect(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),X5))),hAPP(c_COMBC(X3,X1,tc_HOL_Obool),X6))))),X7)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2),hAPP(hAPP(c_COMBS(X3,tc_fun(X1,tc_HOL_Obool),X2),hAPP(hAPP(c_COMBB(tc_fun(X1,X2),tc_fun(tc_fun(X1,tc_HOL_Obool),X2),X3),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2)),X4)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),c_Set_OCollect(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X7))),X6)))),X5)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X7))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6020, c_0_4945]), c_0_4945]), ['final']). 4.46/4.72 cnf(c_0_10499, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))=hAPP(c_Code__Numeral_Oint__of,X1)|c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6021, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4760]), ['final']). 4.46/4.72 cnf(c_0_10500, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6022, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), ['final']). 4.46/4.72 cnf(c_0_10501, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_Set_Oimage(X3,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(X3,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(X3,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),X3),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X4)),X5)),X6)),X7))|c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(X8,esk123_9(X6,X4,X9,X5,X8,X2,X1,X7,X3))),hAPP(X5,esk123_9(X6,X4,X9,X5,X8,X2,X1,X7,X3))),hAPP(X9,esk123_9(X6,X4,X9,X5,X8,X2,X1,X7,X3)))))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_Set_Oimage(X3,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(X3,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(X3,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),X3),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X8)),X5)),X9)),X7))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X7))), inference(rw,[status(thm)],[c_0_6023, c_0_5580]), ['final']). 4.46/4.72 cnf(c_0_10502, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))=hAPP(c_Code__Numeral_Oint__of,X1)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6024, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), ['final']). 4.46/4.72 cnf(c_0_10503, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6025, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), ['final']). 4.46/4.72 cnf(c_0_10504, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)), inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6026, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013])])]), ['final']). 4.46/4.72 cnf(c_0_10505, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6027, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), c_0_4609]), c_0_4609]), c_0_5134]), c_0_4760]), c_0_4760]), c_0_4609]), c_0_4500]), c_0_4760]), c_0_5765]), c_0_4609]), c_0_4609]), ['final']). 4.46/4.72 cnf(c_0_10506, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6028, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), ['final']). 4.46/4.72 cnf(c_0_10507, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6029, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10508, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2))))),X6)),X3),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X6)))), inference(split_conjunct,[status(thm)],[c_0_6030]), ['final']). 4.46/4.72 cnf(c_0_10509, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2))))),X6)),X3),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X6)))), inference(split_conjunct,[status(thm)],[c_0_6031]), ['final']). 4.46/4.72 cnf(c_0_10510, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1)), inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6032, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013])])]), ['final']). 4.46/4.72 cnf(c_0_10511, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))|~class_Rings_Olinordered__idom(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6033, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10512, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6034, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10513, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6035, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), c_0_4609]), c_0_4609]), c_0_4760]), c_0_4760]), c_0_4609]), c_0_4500]), c_0_4760]), c_0_5765]), c_0_4609]), c_0_4609]), ['final']). 4.46/4.72 cnf(c_0_10514, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_Set_Oimage(X3,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(X3,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(X3,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),X3),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X4)),X5)),X6)),X7))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_Set_Oimage(X3,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(X3,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(X3,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),X3),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X8)),X5)),X9)),X7))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(X4,esk123_9(X6,X4,X9,X5,X8,X2,X1,X7,X3))),hAPP(X5,esk123_9(X6,X4,X9,X5,X8,X2,X1,X7,X3))),hAPP(X6,esk123_9(X6,X4,X9,X5,X8,X2,X1,X7,X3)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X7))), inference(rw,[status(thm)],[c_0_6036, c_0_5580]), ['final']). 4.46/4.72 cnf(c_0_10515, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X5)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olistrel(X1,X5)))), inference(split_conjunct,[status(thm)],[c_0_6037]), ['final']). 4.46/4.72 cnf(c_0_10516, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4)),c_fequal),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))))), inference(rw,[status(thm)],[c_0_6038, c_0_5689]), ['final']). 4.46/4.72 cnf(c_0_10517, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_Nat_Onat,X1),c_Finite__Set_Ocard(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X3))),X4)))),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X6),X3)|hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X4),esk140_6(X6,X4,X3,X2,X5,X1))))!=hAPP(X6,esk140_6(X6,X4,X3,X2,X5,X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6039, c_0_4945]), c_0_4945]), c_0_5320]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10518, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X1),X2))))),X3)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6040, c_0_4945]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10519, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X1),X2))))),X3)))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6041, c_0_4945]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10520, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)),X5),X6))), inference(split_conjunct,[status(thm)],[c_0_6016]), ['final']). 4.46/4.72 cnf(c_0_10521, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)),X5),X6))), inference(split_conjunct,[status(thm)],[c_0_6017]), ['final']). 4.46/4.72 cnf(c_0_10522, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X6),X7)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),X5)))|~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X1,X2,X3,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X2,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X2,X3)))),c_Product__Type_OPair(X2,X3)))),X5)),X6),X7))), inference(split_conjunct,[status(thm)],[c_0_6015]), ['final']). 4.46/4.72 cnf(c_0_10523, plain, (c_Lazy__Sequence_Oappend(tc_List_Olist(X1),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(X1,tc_List_Olist(X1)),tc_List_Olist(X1),c_Lazy__Sequence_Oproduct(X1,tc_List_Olist(X1),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_List_Olist(X1),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1))),X1),hAPP(c_COMBB(tc_List_Olist(X1),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1)),tc_List_Olist(X1)),c_Lazy__Sequence_Osingle(tc_List_Olist(X1)))),c_List_Olist_OCons(X1))))),c_Lazy__Sequence_Oempty(tc_List_Olist(X1))))=c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X1),X2)|~class_Lazy__Sequence_Osmall__lazy(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6042, c_0_5134]), c_0_5134]), ['final']). 4.46/4.72 cnf(c_0_10524, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_Nat_Onat,X1),c_Finite__Set_Ocard(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X3))),X4)))),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),hAPP(c_Finite__Set_Ocard(X2),X3))|hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X4),esk280_6(X6,X4,X3,X2,X5,X1))))!=X6|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6043, c_0_4945]), c_0_4945]), c_0_5320]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10525, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2))))),X3)))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Lattices_Odistrib__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6044, c_0_4945]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10526, plain, (c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X1),X2))))),X3)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Big__Operators_Olinorder__class_OMin(X1,X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Groups_Olinordered__ab__semigroup__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6045, c_0_4945]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10527, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2))))),X3)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Lattices_Odistrib__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6046, c_0_4945]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10528, plain, (hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X2,X1,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBC(X1,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X2,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X1),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X2,X1)))),c_Product__Type_OPair(X2,X1)))),X5)),X3),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_Relation_Oconverse(X2,X1),X5)))), inference(split_conjunct,[status(thm)],[c_0_6047]), ['final']). 4.46/4.72 cnf(c_0_10529, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)))|~class_Groups_Omonoid__mult(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6048, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10530, plain, (hBOOL(hAPP(hAPP(X1,esk409_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk410_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk410_3(X1,X2,X3)),esk409_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk410_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6049, c_0_4760]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), ['final']). 4.46/4.72 cnf(c_0_10531, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)))), inference(split_conjunct,[status(thm)],[c_0_6018]), ['final']). 4.46/4.72 cnf(c_0_10532, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6050, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10533, plain, (c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X1),X2))))),X3)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Big__Operators_Olinorder__class_OMax(X1,X3))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Groups_Olinordered__ab__semigroup__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6051, c_0_4945]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10534, plain, (c_Wellfounded_Omax__extp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4),X2,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Omax__ext(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_6052]), ['final']). 4.46/4.72 cnf(c_0_10535, plain, (c_List_Otranspose(X1,X2)=c_List_Olist_ONil(tc_List_Olist(X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk474_3(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_6053]), c_0_4868]), c_0_6054]), c_0_6055]), ['final']). 4.46/4.72 cnf(c_0_10536, plain, (c_List_Olistrelp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4),X2,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_6056]), ['final']). 4.46/4.72 cnf(c_0_10537, plain, (c_List_Olist_ONil(tc_List_Olist(X2))=X3|hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))=c_List_Otranspose(X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk474_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6057, c_0_4517]), c_0_4517]), ['final']). 4.46/4.72 cnf(c_0_10538, plain, (hBOOL(hAPP(hAPP(X1,esk229_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk230_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk229_3(X1,X2,X3)),esk230_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk230_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6058, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), ['final']). 4.46/4.72 cnf(c_0_10539, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))|~class_Groups_Omonoid__mult(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6059, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10540, plain, (c_List_Olist_ONil(tc_List_Olist(X1))=X2|hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X1)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_Nat_Onat,X1),tc_Nat_Onat),c_List_Onth(X1)),hAPP(c_List_Onth(tc_List_Olist(X1)),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))=c_List_Otranspose(X1,X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),esk474_3(X3,X1,X2)))!=X3), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6060, c_0_4517]), c_0_4517]), ['final']). 4.46/4.72 cnf(c_0_10541, plain, (hBOOL(hAPP(c_Predicate_ORangeP(X3,X1,hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),c_COMBC(X1,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X3,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_prod(X3,X1),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X3,X1)))),c_Product__Type_OPair(X3,X1)))),X4)),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ORange(X3,X1),X4)))), inference(split_conjunct,[status(thm)],[c_0_6061]), ['final']). 4.46/4.72 cnf(c_0_10542, plain, (hBOOL(hAPP(c_Predicate_ODomainP(X1,X3,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBC(X3,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X1,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X3),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X1,X3)))),c_Product__Type_OPair(X1,X3)))),X4)),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ODomain(X1,X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_6062]), ['final']). 4.46/4.72 cnf(c_0_10543, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6063, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10544, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6064, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10545, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6065, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10546, plain, (c_List_Otranspose(X1,X2)=c_List_Olist_ONil(tc_List_Olist(X1))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),esk474_3(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_6066]), c_0_4868]), c_0_6054]), c_0_6055]), ['final']). 4.46/4.72 cnf(c_0_10547, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X3)),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_6067]), ['final']). 4.46/4.72 cnf(c_0_10548, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_Nat_Onat,X1),c_Finite__Set_Ocard(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X3))),X4)))),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),hAPP(c_Finite__Set_Ocard(X2),X3))|hBOOL(hAPP(hAPP(c_member(X2),esk280_6(X6,X4,X3,X2,X5,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(rw,[status(thm)],[c_0_6068, c_0_4945]), ['final']). 4.46/4.72 cnf(c_0_10549, plain, (X4=X3|hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)!=hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)), inference(split_conjunct,[status(thm)],[c_0_6069]), ['final']). 4.46/4.72 cnf(c_0_10550, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X4))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(X1,X1,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X1),X3)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X1)),c_Nat_Osemiring__1__class_Oof__nat(X1))),X4))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))|~class_Rings_Ocomm__semiring__1(X1)), inference(rw,[status(thm)],[c_0_6070, c_0_6071]), ['final']). 4.46/4.72 cnf(c_0_10551, plain, (c_Equiv__Relations_Oequivp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2))|~c_Equiv__Relations_Oequiv(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)), inference(split_conjunct,[status(thm)],[c_0_6072]), ['final']). 4.46/4.72 cnf(c_0_10552, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBS(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),X3)),X4)),X5)),X6)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X6),X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X6),X3)))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6073, c_0_4531]), c_0_4531]), c_0_6074]), ['final']). 4.46/4.72 cnf(c_0_10553, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_Nat_Onat,X1),c_Finite__Set_Ocard(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X3))),X4)))),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X6),X3)|hBOOL(hAPP(hAPP(c_member(X2),esk140_6(X6,X4,X3,X2,X5,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(rw,[status(thm)],[c_0_6075, c_0_4945]), ['final']). 4.46/4.72 cnf(c_0_10554, plain, (c_Wellfounded_OwfP(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_6076]), ['final']). 4.46/4.72 cnf(c_0_10555, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk194_6(X2,X3,X4,X5,X1,X6)),X5))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBS(X1,tc_fun(X4,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBC(X1,X6,tc_fun(tc_fun(X4,tc_HOL_Obool),X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,X6),tc_fun(X6,tc_fun(tc_fun(X4,tc_HOL_Obool),X6)),X1),c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6))),X2)),c_Groups_Oone__class_Oone(X6))),X3)),c_Groups_Oone__class_Oone(X6)),X5)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,tc_prod(X1,X4),c_Groups_Otimes__class_Otimes(X6)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X4,X6),X2)),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X5),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~class_Groups_Ocomm__monoid__mult(X6)), inference(split_conjunct,[status(thm)],[c_0_6077]), ['final']). 4.46/4.72 cnf(c_0_10556, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))!=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6078, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10557, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,X1),tc_fun(tc_fun(X3,tc_HOL_Obool),X1),X2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,X1),tc_fun(X3,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,X1),tc_fun(tc_fun(X3,X1),tc_fun(X3,X1)),X2),c_COMBB(X1,X1,X3)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4))),X5))),X6)),X7)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X7)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),X5),X6))|~class_Rings_Osemiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_6079]), ['final']). 4.46/4.72 cnf(c_0_10558, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X5),X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X4)))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X2,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X2,X3)))),c_Product__Type_OPair(X2,X3))))),X4)),X5),X6))), inference(split_conjunct,[status(thm)],[c_0_6030]), ['final']). 4.46/4.72 cnf(c_0_10559, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),X2,X1),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2),X4)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),c_Set_OCollect(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),X5))),hAPP(c_COMBC(X3,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,tc_HOL_Obool),X3),c_fequal),X6)))))),hAPP(c_Set_Oimage(X3,X1,X6),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2),X4),X5)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5))), inference(rw,[status(thm)],[c_0_6080, c_0_4945]), ['final']). 4.46/4.72 cnf(c_0_10560, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)))|~class_Rings_Ocomm__semiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6081, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10561, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6082, c_0_5580]), c_0_5580]), ['final']). 4.46/4.72 cnf(c_0_10562, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X5),X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X4)))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X2,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X2,X3)))),c_Product__Type_OPair(X2,X3))))),X4)),X5),X6))), inference(split_conjunct,[status(thm)],[c_0_6031]), ['final']). 4.46/4.72 cnf(c_0_10563, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X3),X4)),X2)),c_FunDef_Omax__weak))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X3),X1)),c_FunDef_Opair__leq))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X4),X2)),c_FunDef_Omax__weak))), inference(split_conjunct,[status(thm)],[c_0_6083]), ['final']). 4.46/4.72 cnf(c_0_10564, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X3),X4)),X2)),c_FunDef_Omax__strict))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X3),X1)),c_FunDef_Opair__less))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X4),X2)),c_FunDef_Omax__strict))), inference(split_conjunct,[status(thm)],[c_0_6084]), ['final']). 4.46/4.72 cnf(c_0_10565, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X3),X4))),c_FunDef_Omin__strict))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X3)),c_FunDef_Opair__less))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),X4)),c_FunDef_Omin__strict))), inference(split_conjunct,[status(thm)],[c_0_6085]), ['final']). 4.46/4.72 cnf(c_0_10566, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6086, c_0_5580]), c_0_5580]), ['final']). 4.46/4.72 cnf(c_0_10567, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBS(X5,tc_fun(X1,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBC(X5,X6,tc_fun(tc_fun(X1,tc_HOL_Obool),X6)),hAPP(hAPP(c_COMBB(tc_fun(X1,X6),tc_fun(X6,tc_fun(tc_fun(X1,tc_HOL_Obool),X6)),X5),c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6))),X3)),c_Groups_Oone__class_Oone(X6))),X2)),c_Groups_Oone__class_Oone(X6)),X4)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,tc_prod(X5,X1),c_Groups_Otimes__class_Otimes(X6)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X1,X6),X3)),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X4),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk194_6(X3,X2,X1,X4,X5,X6))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Ocomm__monoid__mult(X6)), inference(split_conjunct,[status(thm)],[c_0_6077]), ['final']). 4.46/4.72 cnf(c_0_10568, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk56_11(X2,X3,X4,X5,X6,X7,X8,X1,X9,X10,X11)),X8))|hBOOL(hAPP(hAPP(c_member(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,tc_fun(X6,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X6,tc_HOL_Obool)),tc_fun(X6,tc_HOL_Obool),X11),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X6,tc_HOL_Obool)),X3)),X5))),X2))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X8),X7)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X11,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X11),X10),X9)))|~c_Equiv__Relations_Ocongruent2(X11,X1,tc_fun(X6,tc_HOL_Obool),X9,X7,X5)|~c_Equiv__Relations_Oequiv(X1,X8,X7)|~c_Equiv__Relations_Oequiv(X11,X10,X9)), inference(split_conjunct,[status(thm)],[c_0_6087]), ['final']). 4.46/4.72 cnf(c_0_10569, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X3),X4))),c_FunDef_Omin__weak))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X3)),c_FunDef_Opair__leq))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),X4)),c_FunDef_Omin__weak))), inference(split_conjunct,[status(thm)],[c_0_6088]), ['final']). 4.46/4.72 cnf(c_0_10570, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)))|~class_Rings_Osemiring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6089, c_0_5120]), c_0_5120]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), c_0_5120]), ['final']). 4.46/4.72 cnf(c_0_10571, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X1),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X2)),c_fequal)),X3)))),X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6090, c_0_4531]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10572, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OnegDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)))=c_Divides_OnegDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6091, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), ['final']). 4.46/4.72 cnf(c_0_10573, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk55_11(X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X1)),X11))|hBOOL(hAPP(hAPP(c_member(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X6,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X9,tc_fun(X6,tc_HOL_Obool)),tc_fun(X6,tc_HOL_Obool),X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,tc_fun(X6,tc_HOL_Obool)),X3)),X5))),X2))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X9,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X9),X8),X7)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X11),X10)))|~c_Equiv__Relations_Ocongruent2(X1,X9,tc_fun(X6,tc_HOL_Obool),X10,X7,X5)|~c_Equiv__Relations_Oequiv(X9,X8,X7)|~c_Equiv__Relations_Oequiv(X1,X11,X10)), inference(split_conjunct,[status(thm)],[c_0_6087]), ['final']). 4.46/4.72 cnf(c_0_10574, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),c_fequal),X3),X4))), inference(rw,[status(thm)],[c_0_6092, c_0_5689]), ['final']). 4.46/4.72 cnf(c_0_10575, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11,tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X11),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X1,tc_HOL_Obool)),X4)),X2))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(X2,esk55_11(X3,X4,X5,X2,X1,X6,X7,X8,X9,X10,X11)),esk56_11(X3,X4,X5,X2,X1,X6,X7,X8,X9,X10,X11))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X8,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X8),X7),X6)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X11,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X11),X10),X9)))|~c_Equiv__Relations_Ocongruent2(X11,X8,tc_fun(X1,tc_HOL_Obool),X9,X6,X2)|~c_Equiv__Relations_Oequiv(X8,X7,X6)|~c_Equiv__Relations_Oequiv(X11,X10,X9)), inference(split_conjunct,[status(thm)],[c_0_6087]), ['final']). 4.46/4.72 cnf(c_0_10576, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OnegDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)))=c_Divides_OnegDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6093, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), ['final']). 4.46/4.72 cnf(c_0_10577, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X1),c_Nat_OSuc)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2)))=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2))))|hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6094, c_0_6095]), c_0_5320]), c_0_4531]), c_0_4945]), c_0_5320]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10578, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_Option_Ooption(X2),tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),hAPP(c_Map_Omap__of(X1,X2),X3)))),c_Option_Ooption_OSome(X2)))=hAPP(c_List_Oset(tc_prod(X1,X2)),X3)|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))), inference(rw,[status(thm)],[c_0_6096, c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10579, plain, (hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X1),c_Nat_OSuc)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2))))=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2))))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6097, c_0_6095]), c_0_5320]), c_0_4531]), c_0_4945]), c_0_5320]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10580, plain, (c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X4,hAPP(X3,esk456_4(X1,X3,X4,X2)))),hAPP(X4,esk456_4(X1,X3,X4,X2))))), inference(rw,[status(thm)],[c_0_6098, c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10581, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Ocomm__semiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6099, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10582, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6100, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10583, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olistrel(X1,X2)))|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),esk46_4(X2,X3,X4,X1)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)), inference(split_conjunct,[status(thm)],[c_0_6037]), ['final']). 4.46/4.72 cnf(c_0_10584, plain, (hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(X1,X2)),X3),X4)=hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(X1),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X1),c_Smallcheck_Osmall__class_Osmall(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),X2),X3)),c_Product__Type_OPair(X1,X2)))),X4)),X4)|~class_Smallcheck_Osmall(X1)|~class_Smallcheck_Osmall(X2)), inference(split_conjunct,[status(thm)],[c_0_6101]), ['final']). 4.46/4.72 cnf(c_0_10585, plain, (hAPP(hAPP(X8,X9),X10)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X9),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool),X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X6),hAPP(hAPP(c_Set_Oinsert(X4),X10),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),X8))|~c_Equiv__Relations_Oequiv(X1,X2,X3)|~c_Equiv__Relations_Oequiv(X4,X5,X6)|~c_Equiv__Relations_Ocongruent2(X1,X4,tc_fun(X7,tc_HOL_Obool),X3,X6,X8)|~hBOOL(hAPP(hAPP(c_member(X1),X9),X2))|~hBOOL(hAPP(hAPP(c_member(X4),X10),X5))), inference(split_conjunct,[status(thm)],[c_0_6102]), ['final']). 4.46/4.72 cnf(c_0_10586, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(X3,X4)),hAPP(c_Com_Ocom_OBODY,X4)),hAPP(X5,X4))))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),c_Com_Ocom_OBODY)),X5)),X6)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X5)),X6))|~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X4),X6))), inference(rw,[status(thm)],[c_0_6103, c_0_5580]), ['final']). 4.46/4.72 cnf(c_0_10587, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olists(X1,X2)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6104, c_0_6105]), c_0_5320]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10588, plain, (c_Hoare__Mirabelle_Ohoare__valids(X1,X2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),c_Com_Ocom_OBODY)),X4)),X5))|~c_Hoare__Mirabelle_Ohoare__valids(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),c_Com_Ocom_OBODY)),X4)),X5)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_6106]), ['final']). 4.46/4.72 cnf(c_0_10589, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk460_6(X2,X3,X4,X5,X1,X6)),X5))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X1,X4),X6),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X4,X6),X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X5),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),hAPP(hAPP(c_COMBS(X1,tc_fun(X4,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBB(tc_fun(X4,X6),tc_fun(tc_fun(X4,tc_HOL_Obool),X6),X1),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X6)),X2)),X3)),X5)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~class_Groups_Ocomm__monoid__add(X6)), inference(split_conjunct,[status(thm)],[c_0_6107]), ['final']). 4.46/4.72 cnf(c_0_10590, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),esk223_4(X1,X2,X3,X4)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk224_4(X1,X2,X3,X4)),esk225_4(X1,X2,X3,X4)))))|hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))), inference(split_conjunct,[status(thm)],[c_0_4913]), ['final']). 4.46/4.72 cnf(c_0_10591, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)))),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6108, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10592, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olists(X1,X2)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6109, c_0_6105]), c_0_5320]), c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10593, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6110, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10594, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6111, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10595, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OposDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)))=c_Divides_OposDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6112, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), ['final']). 4.46/4.72 cnf(c_0_10596, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),c_Com_Ocom_OBODY)),X4)),X5))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),c_Com_Ocom_OBODY)),X4)),X5)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_6113]), ['final']). 4.46/4.72 cnf(c_0_10597, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OposDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)))=c_Divides_OposDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6114, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), ['final']). 4.46/4.72 cnf(c_0_10598, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))), inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6115, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013])])]), ['final']). 4.46/4.72 cnf(c_0_10599, plain, (hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_fun(X1,X2)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,X2),tc_List_Olist(X2)),c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_fun(X1,tc_Option_Ooption(X2)),tc_List_Olist(X2)),c_Map_Omap__of(X1,X2)),hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1))))),c_Enum_On__lists(X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1)),c_Enum_Oenum__class_Oenum(X2)))=c_Enum_Oenum__class_Oenum(tc_fun(X1,X2))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_6116]), ['final']). 4.46/4.72 cnf(c_0_10600, plain, (c_Enum_Oall__n__lists(X2,hAPP(hAPP(c_COMBB(tc_fun(X1,X2),tc_HOL_Obool,tc_List_Olist(X2)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,X2),tc_List_Olist(X2)),c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_fun(X1,tc_Option_Ooption(X2)),tc_List_Olist(X2)),c_Map_Omap__of(X1,X2)),hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1)))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X1,X2)),X3))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_6117]), ['final']). 4.46/4.72 cnf(c_0_10601, plain, (c_Enum_Oex__n__lists(X2,hAPP(hAPP(c_COMBB(tc_fun(X1,X2),tc_HOL_Obool,tc_List_Olist(X2)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,X2),tc_List_Olist(X2)),c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_fun(X1,tc_Option_Ooption(X2)),tc_List_Olist(X2)),c_Map_Omap__of(X1,X2)),hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1)))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X1,X2)),X3))|~class_Enum_Oenum(X2)|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_6118]), ['final']). 4.46/4.72 cnf(c_0_10602, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6119, c_0_5644]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10603, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X1,X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X1,X3)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))),c_Wellfounded_Omin__ext(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2))), inference(rw,[status(thm)],[c_0_6120, c_0_5580]), ['final']). 4.46/4.72 cnf(c_0_10604, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X1,X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X1,X3)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))),c_Wellfounded_Omax__ext(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2))), inference(rw,[status(thm)],[c_0_6121, c_0_5580]), ['final']). 4.46/4.72 cnf(c_0_10605, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)))))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X3)))), inference(rw,[status(thm)],[c_0_6122, c_0_6123]), ['final']). 4.46/4.72 cnf(c_0_10606, plain, (hBOOL(hAPP(hAPP(hAPP(X1,esk223_4(X1,X2,X3,X4)),esk224_4(X1,X2,X3,X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),esk225_4(X1,X2,X3,X4))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk224_4(X1,X2,X3,X4)),esk225_4(X1,X2,X3,X4)))|hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))|hAPP(esk223_4(X1,X2,X3,X4),esk225_4(X1,X2,X3,X4))!=c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))), inference(rw,[status(thm)],[c_0_6124, c_0_4760]), ['final']). 4.46/4.72 cnf(c_0_10607, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6125, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10608, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))), inference(split_conjunct,[status(thm)],[c_0_6126]), ['final']). 4.46/4.72 cnf(c_0_10609, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(c_List_Orev(X1),c_List_OtakeWhile(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)))=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_List_Orev(X1),X3)))),hAPP(c_List_Orev(X1),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6127, c_0_5670]), c_0_5671]), c_0_5670]), c_0_5671]), ['final']). 4.46/4.72 cnf(c_0_10610, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk59_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X1,c_Groups_Otimes__class_Otimes(X5)),X2),c_Groups_Oone__class_Oone(X5)),X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X1,c_Groups_Otimes__class_Otimes(X5)),X2),c_Groups_Oone__class_Oone(X5)),X3))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X1,c_Groups_Otimes__class_Otimes(X5)),X2),c_Groups_Oone__class_Oone(X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Ocomm__monoid__mult(X5)), inference(split_conjunct,[status(thm)],[c_0_6128]), ['final']). 4.46/4.72 cnf(c_0_10611, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X4)),c_Wellfounded_Omax__ext(X1,X2)))|~c_Wellfounded_Omax__extp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2),X3,X4)), inference(split_conjunct,[status(thm)],[c_0_6052]), ['final']). 4.46/4.72 cnf(c_0_10612, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6129, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10613, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6130, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10614, plain, (c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),X3))))|hBOOL(hAPP(X2,esk456_4(X1,X3,X4,X2)))), inference(rw,[status(thm)],[c_0_6131, c_0_4531]), ['final']). 4.46/4.72 cnf(c_0_10615, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X2))=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X2)|~c_Fun_Oinj__on(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X1),c_Equiv__Relations_Oquotient(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X2),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_6132]), ['final']). 4.46/4.72 cnf(c_0_10616, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))|~class_Fields_Olinordered__field__inverse__zero(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6133, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), ['final']). 4.46/4.72 cnf(c_0_10617, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6134, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10618, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk267_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Fields_Ofield(X5)), inference(split_conjunct,[status(thm)],[c_0_6135]), ['final']). 4.46/4.72 cnf(c_0_10619, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X3),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X7)),X3)))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X7),X3))))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X3),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X5),X7)))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X3),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X4),X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))), inference(rw,[status(thm)],[c_0_6136, c_0_5643]), ['final']). 4.46/4.72 cnf(c_0_10620, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),X7)),X1)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),X7),X1))))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X3,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5),X7)))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X6)))), inference(rw,[status(thm)],[c_0_6137, c_0_4784]), ['final']). 4.46/4.72 cnf(c_0_10621, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6138, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10622, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)))=hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6139, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10623, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X4),c_Groups_Oone__class_Oone(X1)),X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X3))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4)),X5)),c_Groups_Oone__class_Oone(X1)),X3)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6140]), ['final']). 4.46/4.72 cnf(c_0_10624, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X5,X1),X6),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X1,X6),X3)),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X4),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X6),hAPP(hAPP(c_COMBS(X5,tc_fun(X1,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBB(tc_fun(X1,X6),tc_fun(tc_fun(X1,tc_HOL_Obool),X6),X5),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6)),X3)),X2)),X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk460_6(X3,X2,X1,X4,X5,X6))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Ocomm__monoid__add(X6)), inference(split_conjunct,[status(thm)],[c_0_6107]), ['final']). 4.46/4.72 cnf(c_0_10625, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)),X5)),X6)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(X4,X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X6)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X6))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6))), inference(rw,[status(thm)],[c_0_6141, c_0_5670]), ['final']). 4.46/4.72 cnf(c_0_10626, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6142, c_0_4912]), c_0_4609]), c_0_4436]), ['final']). 4.46/4.72 cnf(c_0_10627, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6143, c_0_4760]), c_0_4609]), c_0_4500]), c_0_4760]), c_0_5765]), c_0_4609]), c_0_4609]), c_0_4609]), c_0_4609]), ['final']). 4.46/4.72 cnf(c_0_10628, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6144, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10629, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6145, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10630, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6146, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10631, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X5)),hAPP(c_Relation_Oconverse(X1,X2),X3)))|~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_6047]), ['final']). 4.46/4.72 cnf(c_0_10632, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X1)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(X2,X3)),hAPP(X2,hAPP(c_Nat_OSuc,X4)))|~class_Groups_Oab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))), inference(rw,[status(thm)],[c_0_6147, c_0_5644]), ['final']). 4.46/4.72 cnf(c_0_10633, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olistrel(X1,X2)))|~c_List_Olistrelp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2),X3,X4)), inference(split_conjunct,[status(thm)],[c_0_6056]), ['final']). 4.46/4.72 cnf(c_0_10634, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X2,X3),X1),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X1),X4)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X5),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X6)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,X1),tc_fun(tc_fun(X3,tc_HOL_Obool),X1),X2),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X1)),X4)),X6)),X5)|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_6148]), ['final']). 4.46/4.72 cnf(c_0_10635, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X2,X3),X1),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X1),X4)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X5),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X6)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,X1),tc_fun(tc_fun(X3,tc_HOL_Obool),X1),X2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1)),X4)),X6)),X5)|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6149]), ['final']). 4.46/4.72 cnf(c_0_10636, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X2)))))|hAPP(c_Nat_OSuc,X2)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6150, c_0_4609]), c_0_5671]), c_0_5671]), c_0_6151]), c_0_5320]), c_0_6074]), ['final']). 4.46/4.72 cnf(c_0_10637, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6152, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.72 cnf(c_0_10638, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk465_6(X2,X3,X4,X5,X1,X6)),X5))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X1,X4),X6),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X4,X6),X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X5),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X6),hAPP(hAPP(c_COMBS(X1,tc_fun(X4,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBB(tc_fun(X4,X6),tc_fun(tc_fun(X4,tc_HOL_Obool),X6),X1),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X6)),X2)),X3)),X5)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~class_Groups_Ocomm__monoid__mult(X6)), inference(split_conjunct,[status(thm)],[c_0_6153]), ['final']). 4.46/4.72 cnf(c_0_10639, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk419_5(X5,X4,X3,X2,X1)),esk419_5(X5,X4,X3,X2,X1))),X5))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olexord(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_List_Oappend(X1),X2),X4))),c_List_Olexord(X1,X5)))), inference(split_conjunct,[status(thm)],[c_0_6154]), ['final']). 4.46/4.72 cnf(c_0_10640, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X6),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X6),X3),X7)),hAPP(hAPP(c_Product__Type_OSigma(X1,X6),X4),hAPP(c_COMBK(tc_fun(X6,tc_HOL_Obool),X1),X8))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X6),tc_HOL_Obool)),X7),hAPP(hAPP(c_Product__Type_OSigma(X2,X6),X5),hAPP(c_COMBK(tc_fun(X6,tc_HOL_Obool),X2),X8))))), inference(split_conjunct,[status(thm)],[c_0_6155]), ['final']). 4.46/4.73 cnf(c_0_10641, plain, (hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,X1))=hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2)),c_Int_Ointrel))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6156, c_0_5580]), c_0_5580]), ['final']). 4.46/4.73 cnf(c_0_10642, plain, (hBOOL(hAPP(hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)),X3))|~c_Relation_Orefl__on(X1,X2,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6157, c_0_4945]), c_0_4945]), c_0_4961]), ['final']). 4.46/4.73 cnf(c_0_10643, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X4)),X2))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X4),X2))))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))), inference(split_conjunct,[status(thm)],[c_0_6158]), ['final']). 4.46/4.73 cnf(c_0_10644, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),X3)),X4)),c_Groups_Ozero__class_Ozero(X2))),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),X3))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(rw,[status(thm)],[c_0_6159, c_0_4945]), ['final']). 4.46/4.73 cnf(c_0_10645, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)),X5)),X6)=hAPP(hAPP(c_Power_Opower__class_Opower(X2),X5),hAPP(c_Finite__Set_Ocard(X1),X6))|hBOOL(hAPP(hAPP(c_member(X1),X3),X6))|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6))), inference(rw,[status(thm)],[c_0_6160, c_0_5670]), ['final']). 4.46/4.73 cnf(c_0_10646, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(X2,esk267_5(X2,X3,X4,X5,X1))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X1),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X1),X2),X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_6135]), ['final']). 4.46/4.73 cnf(c_0_10647, plain, (hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),X3)=hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,X1),c_List_Onth(X1)),X3)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_List_Otranspose(X1,X2)))|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)))), inference(split_conjunct,[status(thm)],[c_0_6161]), ['final']). 4.46/4.73 cnf(c_0_10648, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X2)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),c_Transitive__Closure_Ortrancl(X1,X2)))|~c_Relation_Osingle__valued(X1,X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),c_Transitive__Closure_Ortrancl(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_6162]), ['final']). 4.46/4.73 cnf(c_0_10649, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),c_Hilbert__Choice_OEps(tc_List_Olist(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X2),tc_HOL_Obool)),c_List_Odistinct(X2)),hAPP(hAPP(c_COMBC(tc_List_Olist(X2),tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X2)),c_fequal),c_List_Oset(X2))),X4)))))=c_Nitpick_Osetsum_H(X2,X1,X3,X4)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6163, c_0_5320]), c_0_6164]), ['final']). 4.46/4.73 cnf(c_0_10650, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6165, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.73 cnf(c_0_10651, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4)),X2))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X2))))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_6166]), ['final']). 4.46/4.73 cnf(c_0_10652, plain, (hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Relation_ODomain(X1,X2),X3)))|~hBOOL(hAPP(c_Predicate_ODomainP(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_6062]), ['final']). 4.46/4.73 cnf(c_0_10653, plain, (hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_ORange(X1,X2),X3)))|~hBOOL(hAPP(c_Predicate_ORangeP(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_6061]), ['final']). 4.46/4.73 cnf(c_0_10654, plain, (hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),X2)))|hAPP(c_Map_Omap__of(X1,X3),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X5))=hAPP(c_Map_Omap__of(X1,X3),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),hAPP(c_Map_Omap__of(X1,X3),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X5))),X6),hAPP(c_Option_Ooption_OSome(X3),X7))!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),hAPP(c_Map_Omap__of(X1,X3),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4))),X6),hAPP(c_Option_Ooption_OSome(X3),X8))), inference(split_conjunct,[status(thm)],[c_0_6167]), ['final']). 4.46/4.73 cnf(c_0_10655, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1)),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X3,esk40_3(X2,X1,X3))),hAPP(X1,esk40_3(X2,X1,X3))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6168, c_0_6071]), c_0_6071]), c_0_6071]), ['final']). 4.46/4.73 cnf(c_0_10656, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6169, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013])]), ['final']). 4.46/4.73 cnf(c_0_10657, plain, (hAPP(c_Option_Ooption_OSome(X4),X7)=hAPP(hAPP(c_Map_Omap__of(X2,X4),hAPP(hAPP(c_List_Omap(tc_prod(X1,X4),tc_prod(X2,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X4,tc_prod(X2,X4)),hAPP(hAPP(c_COMBB(X2,tc_fun(X4,tc_prod(X2,X4)),X1),c_Product__Type_OPair(X2,X4)),X3))),X5)),hAPP(X3,X6))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|hAPP(hAPP(c_Map_Omap__of(X1,X4),X5),X6)!=hAPP(c_Option_Ooption_OSome(X4),X7)), inference(split_conjunct,[status(thm)],[c_0_6170]), ['final']). 4.46/4.73 cnf(c_0_10658, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),c_List_Otranspose(X1,X2)),X3)),X4)=hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),X4)),X3)|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X2))))), inference(split_conjunct,[status(thm)],[c_0_6171]), ['final']). 4.46/4.73 cnf(c_0_10659, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_6067]), ['final']). 4.46/4.73 cnf(c_0_10660, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),esk189_4(X4,X3,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X3),esk189_4(X4,X3,X2,X1)))),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_4971]), ['final']). 4.46/4.73 cnf(c_0_10661, plain, (c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),c_Set_OCollect(X1)),hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1)))))=c_Complete__Lattice_OInf__class_OInf(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(rw,[status(thm)],[c_0_6172, c_0_6173]), ['final']). 4.46/4.73 cnf(c_0_10662, plain, (c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),c_Set_OCollect(X1)),hAPP(c_COMBC(X1,X1,tc_HOL_Obool),hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1))))))=c_Complete__Lattice_OSup__class_OSup(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(rw,[status(thm)],[c_0_6174, c_0_6173]), ['final']). 4.46/4.73 cnf(c_0_10663, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,X1),tc_fun(tc_fun(X3,tc_HOL_Obool),X1),X2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1)),hAPP(c_COMBC(X3,X2,X1),X4))),X5)),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),hAPP(hAPP(c_COMBC(X3,tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_fun(tc_fun(X2,tc_HOL_Obool),X1),X3),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1)),X4)),X6)),X5)|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6175]), ['final']). 4.46/4.73 cnf(c_0_10664, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2)),c_Int_Onat)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6176, c_0_4609]), c_0_5671]), c_0_5671]), c_0_6151]), c_0_5320]), c_0_6074]), ['final']). 4.46/4.73 cnf(c_0_10665, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2)),c_Int_Onat)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6177, c_0_4609]), c_0_5671]), c_0_5671]), c_0_6151]), c_0_5320]), c_0_6074]), c_0_6178]), ['final']). 4.46/4.73 cnf(c_0_10666, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X4))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2))))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6179, c_0_5580]), c_0_5580]), ['final']). 4.46/4.73 cnf(c_0_10667, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X4))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2))))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6180, c_0_5580]), c_0_5580]), ['final']). 4.46/4.73 cnf(c_0_10668, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Nitpick_Onorm__frac(X2,X1)=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X2),X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5477]), ['final']). 4.46/4.73 cnf(c_0_10669, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X2)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6181, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), ['final']). 4.46/4.73 cnf(c_0_10670, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6182, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), ['final']). 4.46/4.73 cnf(c_0_10671, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Groups_Omonoid__mult(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6183, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.73 cnf(c_0_10672, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6184, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.73 cnf(c_0_10673, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),X2)|~class_Groups_Omonoid__mult(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6185, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_6186]), ['final']). 4.46/4.73 cnf(c_0_10674, plain, (c_Relation_Orefl__on(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk73_3(X3,X2,X1)),esk73_3(X3,X2,X1))),X3))|~hBOOL(hAPP(hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)),esk74_3(X3,X2,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6187, c_0_4945]), c_0_4945]), c_0_4961]), ['final']). 4.46/4.73 cnf(c_0_10675, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X5,X1),X6),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X1,X6),X3)),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X4),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X6),hAPP(hAPP(c_COMBS(X5,tc_fun(X1,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBB(tc_fun(X1,X6),tc_fun(tc_fun(X1,tc_HOL_Obool),X6),X5),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X6)),X3)),X2)),X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk465_6(X3,X2,X1,X4,X5,X6))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Ocomm__monoid__mult(X6)), inference(split_conjunct,[status(thm)],[c_0_6153]), ['final']). 4.46/4.73 cnf(c_0_10676, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),c_Map_Omap__upds(X1,X3,X5,X2,X4)),X6),hAPP(c_Option_Ooption_OSome(X3),hAPP(hAPP(c_List_Onth(X3),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))=c_Map_Omap__upds(X1,X3,X5,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X6),c_List_Olist_ONil(X1))),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)))), inference(split_conjunct,[status(thm)],[c_0_6188]), ['final']). 4.46/4.73 cnf(c_0_10677, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X6)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))), inference(split_conjunct,[status(thm)],[c_0_6189]), ['final']). 4.46/4.73 cnf(c_0_10678, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBC(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X4)),X5)),X6))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X4)|hBOOL(hAPP(hAPP(c_member(X1),X5),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6190, c_0_4945]), c_0_4891]), ['final']). 4.46/4.73 cnf(c_0_10679, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Oplus__class_Oplus(X1)),X3)),X4)),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X4),X5)))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6191]), ['final']). 4.46/4.73 cnf(c_0_10680, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk31_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Ocomm__monoid__mult(X5)), inference(split_conjunct,[status(thm)],[c_0_6192]), ['final']). 4.46/4.73 cnf(c_0_10681, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk118_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Ocomm__monoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6193]), ['final']). 4.46/4.73 cnf(c_0_10682, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk124_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Ocomm__monoid__mult(X5)), inference(split_conjunct,[status(thm)],[c_0_6194]), ['final']). 4.46/4.73 cnf(c_0_10683, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk426_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Ocomm__monoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6195]), ['final']). 4.46/4.73 cnf(c_0_10684, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X5),X4)))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Ominus__class_Ominus(X1)),X3)),X5)),X4))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6196]), ['final']). 4.46/4.73 cnf(c_0_10685, plain, (hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X1),c_Groups_Otimes__class_Otimes(X1)),hAPP(c_Groups_Otimes__class_Otimes(X1),X2))),c_COMBI(X1)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X3))))|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6197, c_0_4760]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_10686, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBC(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X4)),X5)),X6))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X1),X6),X3))|hBOOL(hAPP(hAPP(c_member(X1),X5),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6198, c_0_4945]), c_0_4891]), ['final']). 4.46/4.73 cnf(c_0_10687, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)))|~c_FunDef_Oreduction__pair(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_6199]), ['final']). 4.46/4.73 cnf(c_0_10688, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel(X1,X2)),c_Nitpick_Oprod(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olists(X1,X3),c_List_Olists(X1,X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))), inference(rw,[status(thm)],[c_0_6200, c_0_6201]), ['final']). 4.46/4.73 cnf(c_0_10689, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|c_Groups_Ozero__class_Ozero(X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X3,X3),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,X3),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X3)),X4)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X3,tc_Nat_Onat),X4),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))|~class_Groups_Oab__group__add(X3)), inference(split_conjunct,[status(thm)],[c_0_4931]), ['final']). 4.46/4.73 cnf(c_0_10690, plain, (X2=X3|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)|hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)!=hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),esk502_3(X3,X2,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6202, c_0_4736]), c_0_4736]), ['final']). 4.46/4.73 cnf(c_0_10691, plain, (X2=X3|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)|hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)!=hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),esk18_3(X2,X3,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6203, c_0_4736]), c_0_4736]), ['final']). 4.46/4.73 cnf(c_0_10692, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk484_5(X2,X3,X4,X5,X1)),esk485_5(X2,X3,X4,X5,X1))),X2))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2))))), inference(split_conjunct,[status(thm)],[c_0_6204]), ['final']). 4.46/4.73 cnf(c_0_10693, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk479_5(X2,X3,X4,X5,X1)),esk478_5(X2,X3,X4,X5,X1))),X2))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2))))), inference(split_conjunct,[status(thm)],[c_0_6205]), ['final']). 4.46/4.73 cnf(c_0_10694, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2)),c_Int_Ointrel))|hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,X1))!=hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6206, c_0_5580]), c_0_5580]), ['final']). 4.46/4.73 cnf(c_0_10695, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)),c_Groups_Oone__class_Oone(X2))),X5)=c_Groups_Oone__class_Oone(X2)|hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~class_Groups_Ocomm__monoid__mult(X2)), inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_6207, c_0_5670]), c_0_6208]), ['final']). 4.46/4.73 cnf(c_0_10696, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)),c_Groups_Ozero__class_Ozero(X2))),X5)=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~class_Groups_Ocomm__monoid__add(X2)), inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_6209, c_0_5670]), c_0_6210]), ['final']). 4.46/4.73 cnf(c_0_10697, plain, (c_Equiv__Relations_Oequiv(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)|~c_Equiv__Relations_Oequivp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2))), inference(split_conjunct,[status(thm)],[c_0_6072]), ['final']). 4.46/4.73 cnf(c_0_10698, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6211, c_0_5266]), c_0_5266]), c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_10699, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1))),c_COMBI(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6212, c_0_4760]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_10700, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk473_8(X2,X3,X4,X1,X5,X6,X7,X8)),X4))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X7,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X1),c_Set_Oimage(X8,X7,X6)),X3))=hAPP(c_Set_Oimage(X8,X7,X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X8,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~c_Fun_Oinj__on(X8,X7,X6,X5)), inference(split_conjunct,[status(thm)],[c_0_6213]), ['final']). 4.46/4.73 cnf(c_0_10701, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6214, c_0_4760]), c_0_4609]), c_0_4500]), c_0_4760]), c_0_5765]), c_0_4609]), c_0_4609]), c_0_4609]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_10702, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X6))),hAPP(hAPP(c_List_Oappend(X1),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X7)))),c_List_Olexord(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_6215]), ['final']). 4.46/4.73 cnf(c_0_10703, plain, (X1=hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3)|hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),hAPP(hAPP(c_List_Onth(X2),X1),esk189_4(X4,X3,X1,X2))),hAPP(hAPP(c_List_Onth(X2),X3),esk189_4(X4,X3,X1,X2)))),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X1),X3)),c_List_Olexord(X2,X4)))), inference(split_conjunct,[status(thm)],[c_0_4971]), ['final']). 4.46/4.73 cnf(c_0_10704, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk189_4(X1,X2,X3,X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X2))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X3),X2)),c_List_Olexord(X4,X1)))), inference(rw,[status(thm)],[c_0_6216, c_0_4986]), ['final']). 4.46/4.73 cnf(c_0_10705, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6217, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), ['final']). 4.46/4.73 cnf(c_0_10706, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6218, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013])]), ['final']). 4.46/4.73 cnf(c_0_10707, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6219, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013])]), ['final']). 4.46/4.73 cnf(c_0_10708, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBC(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X4)),X5)),X6))=X4|hBOOL(hAPP(hAPP(c_member(X1),X6),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6220, c_0_4945]), c_0_4891]), ['final']). 4.46/4.73 cnf(c_0_10709, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X5),c_List_Olist_ONil(X1)))),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X6),c_List_Olist_ONil(X1))))),c_List_Olistrel1(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_6221]), ['final']). 4.46/4.73 cnf(c_0_10710, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk478_5(X2,X3,X4,X5,X1)),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2))))), inference(split_conjunct,[status(thm)],[c_0_6205]), ['final']). 4.46/4.73 cnf(c_0_10711, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk484_5(X3,X4,X5,X2,X1))),c_Transitive__Closure_Ortrancl(X1,X4)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X3))))), inference(split_conjunct,[status(thm)],[c_0_6204]), ['final']). 4.46/4.73 cnf(c_0_10712, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))|hAPP(hAPP(c_List_Otake(X1),X5),X2)!=hAPP(hAPP(c_List_Otake(X1),X5),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),X5)),hAPP(hAPP(c_List_Onth(X1),X3),X5))),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))), inference(rw,[status(thm)],[c_0_6222, c_0_4986]), ['final']). 4.46/4.73 cnf(c_0_10713, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__upds(X1,X2,X3,X4,X5)),X6),hAPP(c_Option_Ooption_OSome(X2),X7))=c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X6),X4),hAPP(hAPP(c_List_Olist_OCons(X2),X7),X5))|hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)),X4))))), inference(rw,[status(thm)],[c_0_6223, c_0_6224]), ['final']). 4.46/4.73 cnf(c_0_10714, plain, (hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),X2),hAPP(hAPP(c_COMBC(tc_List_Olist(X2),tc_Nat_Onat,X2),c_List_Onth(X2)),X1)),hAPP(c_List_Ofilter(tc_List_Olist(X2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X2)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1)),c_Nat_Osize__class_Osize(tc_List_Olist(X2)))),X3))=hAPP(hAPP(c_List_Onth(tc_List_Olist(X2)),c_List_Otranspose(X2,X3)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),c_List_Otranspose(X2,X3))))), inference(split_conjunct,[status(thm)],[c_0_6225]), ['final']). 4.46/4.73 cnf(c_0_10715, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)),c_Groups_Oone__class_Oone(X2))),X5)=hAPP(X4,X3)|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(rw,[status(thm)],[c_0_6226, c_0_5670]), ['final']). 4.46/4.73 cnf(c_0_10716, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)),c_Groups_Ozero__class_Ozero(X2))),X5)=hAPP(X4,X3)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(rw,[status(thm)],[c_0_6227, c_0_5670]), ['final']). 4.46/4.73 cnf(c_0_10717, plain, (hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)))),X3))=c_List_OtakeWhile(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_List_Orev(X1),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6228, c_0_5670]), c_0_5671]), c_0_6229]), c_0_5670]), c_0_5671]), ['final']). 4.46/4.73 cnf(c_0_10718, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk505_7(X2,X3,X4,X5,X6,X7,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)))|hAPP(hAPP(X7,hAPP(X4,X3)),hAPP(X4,X2))=hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~c_Finite__Set_Ofolding__image__simple(X8,X1,X7,X6,X5,X4)), inference(split_conjunct,[status(thm)],[c_0_6230]), ['final']). 4.46/4.73 cnf(c_0_10719, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X3),tc_prod(X7,X3))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X3),tc_prod(X7,X3)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X2),X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X2),X5))),c_Recdef_Osame__fst(X7,X3,X1,X6)))|~hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),hAPP(X6,X2)))), inference(split_conjunct,[status(thm)],[c_0_6231]), ['final']). 4.46/4.73 cnf(c_0_10720, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X5,c_Groups_Otimes__class_Otimes(X1)),X2),c_Groups_Oone__class_Oone(X1)),X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X5,c_Groups_Otimes__class_Otimes(X1)),X2),c_Groups_Oone__class_Oone(X1)),X3))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X5,c_Groups_Otimes__class_Otimes(X1)),X2),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X3))|c_Groups_Oone__class_Oone(X1)!=hAPP(X2,esk59_5(X2,X3,X4,X5,X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_6128]), ['final']). 4.46/4.73 cnf(c_0_10721, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X6)),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X6),X4)))), inference(split_conjunct,[status(thm)],[c_0_6232]), ['final']). 4.46/4.73 cnf(c_0_10722, plain, (hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Otimes__class_Otimes(X1)),c_COMBI(X1)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),c_Int_OMin)))))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6233, c_0_4784]), c_0_4784]), c_0_4784]), ['final']). 4.46/4.73 cnf(c_0_10723, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X4))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_6234]), ['final']). 4.46/4.73 cnf(c_0_10724, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X2)|hBOOL(hAPP(X1,esk345_2(X1,X2)))|hBOOL(hAPP(X2,esk345_2(X1,X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6235, c_0_4531]), c_0_5320]), c_0_5320]), c_0_4531]), ['final']). 4.46/4.73 cnf(c_0_10725, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X5))),X4))))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5))), inference(split_conjunct,[status(thm)],[c_0_6236]), ['final']). 4.46/4.73 cnf(c_0_10726, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBC(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X4)),X5)),X6))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6237, c_0_4945]), c_0_4891]), ['final']). 4.46/4.73 cnf(c_0_10727, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk84_4(X2,X3,X1,X4)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2)),X3)|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk82_4(X2,X3,X1,X4)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))|~class_Groups_Ocomm__monoid__add(X4)), inference(split_conjunct,[status(thm)],[c_0_6238]), ['final']). 4.46/4.73 cnf(c_0_10728, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Osemiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6239, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.73 cnf(c_0_10729, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X6)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X6)),X5))), inference(split_conjunct,[status(thm)],[c_0_6240]), ['final']). 4.46/4.73 cnf(c_0_10730, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_OwfP(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2))), inference(split_conjunct,[status(thm)],[c_0_6076]), ['final']). 4.46/4.73 cnf(c_0_10731, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olistrel(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X6)),c_List_Olistrel(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_6241]), ['final']). 4.46/4.73 cnf(c_0_10732, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),X3))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_List_Otranspose(X1,X2)))|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)))), inference(split_conjunct,[status(thm)],[c_0_6242]), ['final']). 4.46/4.73 cnf(c_0_10733, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Osemiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6243, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.73 cnf(c_0_10734, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(X5,hAPP(hAPP(c_List_Ozip(X3,X1),X4),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6244, c_0_4986]), c_0_6245]), c_0_4986]), c_0_6245]), ['final']). 4.46/4.73 cnf(c_0_10735, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk83_4(X2,X3,X1,X4)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2)),X3)|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk82_4(X2,X3,X1,X4)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))|~class_Groups_Ocomm__monoid__add(X4)), inference(split_conjunct,[status(thm)],[c_0_6238]), ['final']). 4.46/4.73 cnf(c_0_10736, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X5))),X4))))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))), inference(split_conjunct,[status(thm)],[c_0_6246]), ['final']). 4.46/4.73 cnf(c_0_10737, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6247, c_0_5120]), c_0_5120]), ['final']). 4.46/4.73 cnf(c_0_10738, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X5))),c_Wellfounded_Olex__prod(X1,X2,X6,X7)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),X5)),X7))), inference(er,[status(thm)],[c_0_6248]), ['final']). 4.46/4.73 cnf(c_0_10739, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6249, c_0_5266]), c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_10740, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6250, c_0_5266]), c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_10741, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X2),X1)),c_List_Olexord(X4,X3)))|X2=X1|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X1),X2)),c_List_Olexord(X4,X3)))|esk511_4(X1,X2,X3,X4)!=esk510_4(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_6251]), ['final']). 4.46/4.73 cnf(c_0_10742, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X6))),c_Wellfounded_Omax__ext(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Omax__ext(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X5),X6)),c_Wellfounded_Omax__ext(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_6252]), ['final']). 4.46/4.73 cnf(c_0_10743, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X2),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X1,X2),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X2,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X4))),X4)),X5))|~c_Equiv__Relations_Ocongruent(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X5),X3))), inference(split_conjunct,[status(thm)],[c_0_6253]), ['final']). 4.46/4.73 cnf(c_0_10744, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk507_8(X2,X3,X4,X5,X6,X7,X8,X1)),hAPP(c_List_Oset(X1),X8)))|hAPP(c_List_Ofoldl(X7,X1,hAPP(c_COMBC(X1,X7,X7),X5),hAPP(X4,X2)),X8)=hAPP(X4,hAPP(c_List_Ofoldl(X6,X1,hAPP(c_COMBC(X1,X6,X6),X3),X2),X8))), inference(split_conjunct,[status(thm)],[c_0_6254]), ['final']). 4.46/4.73 cnf(c_0_10745, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk189_4(X4,X3,X2,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))), inference(rw,[status(thm)],[c_0_6255, c_0_4986]), ['final']). 4.46/4.73 cnf(c_0_10746, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))), inference(split_conjunct,[status(thm)],[c_0_6256]), ['final']). 4.46/4.73 cnf(c_0_10747, plain, (X2=X3|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk502_3(X3,X2,X1)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)|hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)!=hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6257, c_0_4736]), c_0_4736]), ['final']). 4.46/4.73 cnf(c_0_10748, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X4))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X5))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6258]), ['final']). 4.46/4.73 cnf(c_0_10749, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk287_4(X3,X4,X2,X1))),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),esk287_4(X3,X4,X2,X1)))),X3)))), inference(rw,[status(thm)],[c_0_6259, c_0_5100]), ['final']). 4.46/4.73 cnf(c_0_10750, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk358_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Oordered__ab__semigroup__add(X5)|~class_Groups_Ocomm__monoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6260]), ['final']). 4.46/4.73 cnf(c_0_10751, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)))|hBOOL(hAPP(hAPP(X3,esk381_6(X3,X5,X4,X6,X2,X1)),esk382_6(X3,X5,X4,X6,X2,X1)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X6),X4),X5)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6261, c_0_5580]), c_0_5580]), ['final']). 4.46/4.73 cnf(c_0_10752, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)))|hBOOL(hAPP(hAPP(X6,esk21_6(X5,X6,X4,X3,X2,X1)),esk22_6(X5,X6,X4,X3,X2,X1)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X6)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6262, c_0_5580]), c_0_5580]), ['final']). 4.46/4.73 cnf(c_0_10753, plain, (X2=X3|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk18_3(X2,X3,X1)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)|hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)!=hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6263, c_0_4736]), c_0_4736]), ['final']). 4.46/4.73 cnf(c_0_10754, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X5),tc_prod(X1,X5))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X5),tc_prod(X1,X5)),hAPP(hAPP(c_Product__Type_OPair(X1,X5),X2),X6)),hAPP(hAPP(c_Product__Type_OPair(X1,X5),X3),X7))),c_Wellfounded_Olex__prod(X1,X5,X4,X8)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_4988]), ['final']). 4.46/4.73 cnf(c_0_10755, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6264, c_0_5266]), c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_10756, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6265, c_0_5266]), c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_10757, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))|~class_Groups_Oab__group__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))), inference(split_conjunct,[status(thm)],[c_0_6266]), ['final']). 4.46/4.73 cnf(c_0_10758, plain, (c_Equiv__Relations_Ocongruent(X1,tc_fun(X7,tc_HOL_Obool),X3,hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool),X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X6),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),X8))|~c_Equiv__Relations_Oequiv(X1,X2,X3)|~c_Equiv__Relations_Oequiv(X4,X5,X6)|~c_Equiv__Relations_Ocongruent2(X1,X4,tc_fun(X7,tc_HOL_Obool),X3,X6,X8)|~hBOOL(hAPP(hAPP(c_member(X4),X9),X5))), inference(split_conjunct,[status(thm)],[c_0_6267]), ['final']). 4.46/4.73 cnf(c_0_10759, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X1)),X2)|hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),esk82_4(X1,X2,X3,X4)),X2))|hAPP(X1,esk85_4(X1,X2,X3,X4))!=c_Groups_Ozero__class_Ozero(X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3,tc_HOL_Obool)),X2))|~class_Groups_Ocomm__monoid__add(X4)), inference(split_conjunct,[status(thm)],[c_0_6238]), ['final']). 4.46/4.73 cnf(c_0_10760, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X3))),X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X4),esk201_4(X4,X1,X3,X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6268, c_0_4531]), c_0_4531]), c_0_4531]), ['final']). 4.46/4.73 cnf(c_0_10761, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(c_fequal,X3))),X4)),c_Groups_Ozero__class_Ozero(X2))),X5)=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~class_Groups_Ocomm__monoid__add(X2)), inference(csr,[status(thm)],[c_0_6269, c_0_6210]), ['final']). 4.46/4.73 cnf(c_0_10762, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk85_4(X2,X3,X1,X4)),esk84_4(X2,X3,X1,X4)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2)),X3)|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk82_4(X2,X3,X1,X4)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))|~class_Groups_Ocomm__monoid__add(X4)), inference(split_conjunct,[status(thm)],[c_0_6238]), ['final']). 4.46/4.73 cnf(c_0_10763, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk85_4(X2,X3,X1,X4)),esk83_4(X2,X3,X1,X4)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2)),X3)|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk82_4(X2,X3,X1,X4)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))|~class_Groups_Ocomm__monoid__add(X4)), inference(split_conjunct,[status(thm)],[c_0_6238]), ['final']). 4.46/4.73 cnf(c_0_10764, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk25_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk26_5(X2,X3,X4,X5,X1)),X2)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6270]), ['final']). 4.46/4.73 cnf(c_0_10765, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk390_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk391_5(X3,X4,X5,X2,X1)),X3)))|X4=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_6271]), ['final']). 4.46/4.73 cnf(c_0_10766, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X4,X3))),X3)),X5)=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X4,hAPP(hAPP(c_List_Oappend(X1),X3),X5)))),hAPP(hAPP(c_List_Oappend(X1),X3),X5))|hBOOL(hAPP(X4,X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6272, c_0_4916]), c_0_4916]), ['final']). 4.46/4.73 cnf(c_0_10767, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X4))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X5))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6273]), ['final']). 4.46/4.73 cnf(c_0_10768, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)))),c_List_Olistrel1(X1,X6)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X6))), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6274])]), ['final']). 4.46/4.73 cnf(c_0_10769, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(c_fequal,X3))),X4)),c_Groups_Oone__class_Oone(X2))),X5)=c_Groups_Oone__class_Oone(X2)|hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~class_Groups_Ocomm__monoid__mult(X2)), inference(csr,[status(thm)],[c_0_6275, c_0_6208]), ['final']). 4.46/4.73 cnf(c_0_10770, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk345_2(X1,X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6276, c_0_4531]), c_0_5320]), c_0_5320]), c_0_4531]), ['final']). 4.46/4.73 cnf(c_0_10771, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6277]), ['final']). 4.46/4.73 cnf(c_0_10772, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X2)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6278, c_0_4609]), c_0_5671]), c_0_6151]), ['final']). 4.46/4.73 cnf(c_0_10773, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X5))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5)),X6)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X4))), inference(split_conjunct,[status(thm)],[c_0_6279]), ['final']). 4.46/4.73 cnf(c_0_10774, plain, (hAPP(c_List_Ofoldl(X2,X8,hAPP(c_COMBC(X8,X2,X2),X6),hAPP(X3,X5)),X7)=hAPP(X3,hAPP(c_List_Ofoldl(X1,X8,hAPP(c_COMBC(X8,X1,X1),X4),X5),X7))|hAPP(c_Fun_Ocomp(X1,X2,X1,X3),hAPP(X4,esk507_8(X5,X4,X3,X6,X1,X2,X7,X8)))!=hAPP(c_Fun_Ocomp(X2,X2,X1,hAPP(X6,esk507_8(X5,X4,X3,X6,X1,X2,X7,X8))),X3)), inference(split_conjunct,[status(thm)],[c_0_6254]), ['final']). 4.46/4.73 cnf(c_0_10775, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk46_4(X2,X3,X4,X1)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X4),X3))))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olistrel(X1,X2)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)), inference(split_conjunct,[status(thm)],[c_0_6037]), ['final']). 4.46/4.73 cnf(c_0_10776, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X2),X3)))),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X2),X3))))=c_Nitpick_Oof__frac(X2,X1,X3)|~class_Rings_Oinverse(X1)|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6280, c_0_6281]), c_0_6281]), ['final']). 4.46/4.73 cnf(c_0_10777, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X2)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6282, c_0_4609]), c_0_5671]), c_0_6151]), ['final']). 4.46/4.73 cnf(c_0_10778, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk1_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk3_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(rw,[status(thm)],[c_0_6283, c_0_4736]), ['final']). 4.46/4.73 cnf(c_0_10779, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2)),c_List_Olexord(X1,X4)))|X3=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk511_4(X2,X3,X4,X1)),esk510_4(X2,X3,X4,X1))),X4))), inference(split_conjunct,[status(thm)],[c_0_6251]), ['final']). 4.46/4.73 cnf(c_0_10780, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2)),c_List_Olexord(X1,X4)))|X3=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk510_4(X2,X3,X4,X1)),esk511_4(X2,X3,X4,X1))),X4))), inference(split_conjunct,[status(thm)],[c_0_6251]), ['final']). 4.46/4.73 cnf(c_0_10781, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6284, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.73 cnf(c_0_10782, plain, (X1=hAPP(hAPP(X2,X3),X4)|c_Nitpick_Ofold__graph_H(X5,X6,X2,X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X7),hAPP(hAPP(c_Set_Oinsert(X5),esk333_7(X4,X3,X7,X1,X2,X6,X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),esk334_7(X4,X3,X7,X1,X2,X6,X5))|~c_Nitpick_Ofold__graph_H(X5,X6,X2,X1,X7,hAPP(hAPP(X2,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_6285]), ['final']). 4.46/4.73 cnf(c_0_10783, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk1_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk2_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(rw,[status(thm)],[c_0_6286, c_0_4736]), ['final']). 4.46/4.73 cnf(c_0_10784, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OCond(X4,X5,X6)),X7)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X4))),X6),X7)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,X4)),X5),X7)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6287, c_0_5580]), c_0_5580]), c_0_5580]), ['final']). 4.46/4.73 cnf(c_0_10785, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4))),c_FunDef_Opair__leq))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_6288]), ['final']). 4.46/4.73 cnf(c_0_10786, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4))),c_FunDef_Opair__less))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_6289]), ['final']). 4.46/4.73 cnf(c_0_10787, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk471_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Oordered__comm__monoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6290]), ['final']). 4.46/4.73 cnf(c_0_10788, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk25_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk26_5(X2,X3,X4,X5,X1)),X2)))|X4=X5|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6270]), ['final']). 4.46/4.73 cnf(c_0_10789, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk390_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk391_5(X3,X4,X5,X2,X1)),X3)))|X2=X5|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_6271]), ['final']). 4.46/4.73 cnf(c_0_10790, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|hAPP(hAPP(c_List_Otake(X1),esk189_4(X4,X3,X2,X1)),X2)=hAPP(hAPP(c_List_Otake(X1),esk189_4(X4,X3,X2,X1)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_4971]), ['final']). 4.46/4.73 cnf(c_0_10791, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Nitpick_Ofold__graph_H(X1,X3,X4,X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),esk333_7(X6,X7,X2,X5,X4,X3,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),esk334_7(X6,X7,X2,X5,X4,X3,X1))|~c_Nitpick_Ofold__graph_H(X1,X3,X4,X5,X2,hAPP(hAPP(X4,X7),X6))), inference(split_conjunct,[status(thm)],[c_0_6285]), ['final']). 4.46/4.73 cnf(c_0_10792, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),X2)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6291, c_0_6292]), c_0_6292]), ['final']). 4.46/4.73 cnf(c_0_10793, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Hilbert__Choice_OEps(tc_List_Olist(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Odistinct(X1)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_List_Oset(X1))),X2))))=c_Nitpick_Ocard_H(X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6293, c_0_5320]), c_0_6164]), ['final']). 4.46/4.73 cnf(c_0_10794, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))), inference(split_conjunct,[status(thm)],[c_0_6294]), ['final']). 4.46/4.73 cnf(c_0_10795, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))), inference(split_conjunct,[status(thm)],[c_0_6295]), ['final']). 4.46/4.73 cnf(c_0_10796, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olex(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X6)), inference(split_conjunct,[status(thm)],[c_0_5016]), ['final']). 4.46/4.73 cnf(c_0_10797, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X6)),c_List_Olex(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olex(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_5016]), ['final']). 4.46/4.73 cnf(c_0_10798, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X6)),c_List_Olistrel1(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olistrel1(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_6296]), ['final']). 4.46/4.73 cnf(c_0_10799, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk481_4(X1,X2,X3,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X3),X2)),c_List_Olistrel(X4,X1)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X2)), inference(split_conjunct,[status(thm)],[c_0_6297]), ['final']). 4.46/4.73 cnf(c_0_10800, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X5))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5)),X6)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5)),X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X1))), inference(split_conjunct,[status(thm)],[c_0_6298]), ['final']). 4.46/4.73 cnf(c_0_10801, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X8,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X5),c_Set_Oimage(X1,X8,X7)),X2))=hAPP(c_Set_Oimage(X1,X8,X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk473_8(X3,X2,X4,X5,X6,X7,X8,X1))),X6))|~hBOOL(hAPP(hAPP(c_member(X5),X3),X4))|~c_Fun_Oinj__on(X1,X8,X7,X6)), inference(split_conjunct,[status(thm)],[c_0_6213]), ['final']). 4.46/4.73 cnf(c_0_10802, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X3)))))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[c_0_6299, c_0_5580]), ['final']). 4.46/4.73 cnf(c_0_10803, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olexord(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_5014]), ['final']). 4.46/4.73 cnf(c_0_10804, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(hAPP(c_List_Onth(X2),X4),X1))),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X3),X4)),c_List_Olistrel(X2,X5)))), inference(split_conjunct,[status(thm)],[c_0_6297]), ['final']). 4.46/4.73 cnf(c_0_10805, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))),c_List_Olexord(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olexord(X1,X5)))), inference(er,[status(thm)],[c_0_6300]), ['final']). 4.46/4.73 cnf(c_0_10806, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6301]), ['final']). 4.46/4.73 cnf(c_0_10807, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Rings_Oinverse__class_Odivide(X1)),X4)),X5)),X3)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3))|~class_Fields_Ofield__inverse__zero(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6302]), ['final']). 4.46/4.73 cnf(c_0_10808, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X5),X3)),c_Wellfounded_Omax__ext(X1,X4)))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk173_4(X4,X3,X5,X1)),X2)),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_6303]), ['final']). 4.46/4.73 cnf(c_0_10809, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk238_4(X2,X3,X4,X1)),X5)),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_5587]), ['final']). 4.46/4.73 cnf(c_0_10810, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_List_Oappend(X1),X2),X4))),c_List_Olistrel1(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olistrel1(X1,X5)))), inference(er,[status(thm)],[c_0_6304]), ['final']). 4.46/4.73 cnf(c_0_10811, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6305]), ['final']). 4.46/4.73 cnf(c_0_10812, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X1)),X2)|hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),esk82_4(X1,X2,X3,X4)),X2))|esk83_4(X1,X2,X3,X4)!=esk84_4(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3,tc_HOL_Obool)),X2))|~class_Groups_Ocomm__monoid__add(X4)), inference(split_conjunct,[status(thm)],[c_0_6238]), ['final']). 4.46/4.73 cnf(c_0_10813, plain, (hAPP(X4,X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),hAPP(hAPP(c_COMBC(X1,X5,X5),hAPP(hAPP(c_COMBS(X1,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X1),c_If(X5)),hAPP(c_fequal,X2))),X4)),c_Groups_Oone__class_Oone(X5))),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Ocomm__monoid__mult(X5)), inference(split_conjunct,[status(thm)],[c_0_5000]), ['final']). 4.46/4.73 cnf(c_0_10814, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_List_Oappend(X1),X4),X3))),c_List_Olistrel1(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel1(X1,X5)))), inference(er,[status(thm)],[c_0_6306]), ['final']). 4.46/4.73 cnf(c_0_10815, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))),c_List_Olex(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olex(X1,X5)))), inference(er,[status(thm)],[c_0_6307]), ['final']). 4.46/4.73 cnf(c_0_10816, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk275_8(X3,X4,X5,X2,X1,X6,X7,X8)),esk276_8(X3,X4,X5,X2,X1,X6,X7,X8))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X7)),X6),hAPP(c_Set_Oimage(tc_prod(X1,X2),tc_prod(X8,X7),c_Product__Type_Omap__pair(X1,X8,X2,X7,X5,X4)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6308]), ['final']). 4.46/4.73 cnf(c_0_10817, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X5))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X5)))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),hAPP(c_Nat_OSuc,X4)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6309, c_0_5644]), c_0_5644]), ['final']). 4.46/4.73 cnf(c_0_10818, plain, (hAPP(X4,X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),hAPP(hAPP(c_COMBC(X1,X5,X5),hAPP(hAPP(c_COMBS(X1,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X1),c_If(X5)),hAPP(c_fequal,X2))),X4)),c_Groups_Ozero__class_Ozero(X5))),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Ocomm__monoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_4997]), ['final']). 4.46/4.73 cnf(c_0_10819, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk84_4(X2,X3,X1,X4)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2)),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk82_4(X2,X3,X1,X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))|~class_Groups_Ocomm__monoid__add(X4)), inference(split_conjunct,[status(thm)],[c_0_6238]), ['final']). 4.46/4.73 cnf(c_0_10820, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk83_4(X2,X3,X1,X4)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2)),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk82_4(X2,X3,X1,X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))|~class_Groups_Ocomm__monoid__add(X4)), inference(split_conjunct,[status(thm)],[c_0_6238]), ['final']). 4.46/4.73 cnf(c_0_10821, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk122_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X4),X1),c_Product__Type_Ofst(X1,X4)),X3))))|hAPP(c_Map_Omap__of(X1,X4),X2)=hAPP(c_Map_Omap__of(X1,X4),X3)|hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X4),X1),c_Product__Type_Ofst(X1,X4)),X2))!=hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X4),X1),c_Product__Type_Ofst(X1,X4)),X3))), inference(split_conjunct,[status(thm)],[c_0_6310]), ['final']). 4.46/4.73 cnf(c_0_10822, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))),c_List_Olistrel1(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),X4)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))), inference(er,[status(thm)],[c_0_6311]), ['final']). 4.46/4.73 cnf(c_0_10823, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk373_5(X2,X3,X4,X1,X5)),hAPP(c_List_Oset(X1),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X1,X5),X3),X4))),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X1,X5),X2),X4))))|~class_Groups_Oordered__ab__semigroup__add(X5)|~class_Groups_Omonoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6312]), ['final']). 4.46/4.73 cnf(c_0_10824, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X5)))))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_6313]), ['final']). 4.46/4.73 cnf(c_0_10825, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X2)|~hBOOL(hAPP(X2,esk345_2(X1,X2)))|~hBOOL(hAPP(X1,esk345_2(X1,X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6314, c_0_4531]), c_0_5320]), c_0_5320]), c_0_4531]), ['final']). 4.46/4.73 cnf(c_0_10826, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))), inference(rw,[status(thm)],[c_0_6315, c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_10827, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Product__Type_Ofst(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X1,X2),X3))),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),X1),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X1)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X1)),X2))))), inference(split_conjunct,[status(thm)],[c_0_6316]), ['final']). 4.46/4.73 cnf(c_0_10828, plain, (hAPP(c_Fun_Ocomp(X2,X2,X7,hAPP(X4,X6)),hAPP(c_Fun_Ocomp(X2,X2,X7,hAPP(X4,X5)),X8))=hAPP(c_Fun_Ocomp(X2,X2,X7,hAPP(X4,X5)),hAPP(c_Fun_Ocomp(X2,X2,X7,hAPP(X4,X6)),X8))|~c_Finite__Set_Ofolding(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6))), inference(split_conjunct,[status(thm)],[c_0_6317]), ['final']). 4.46/4.73 cnf(c_0_10829, plain, (hAPP(X1,esk174_7(X2,X3,X1,X4,X5,X6,X7))=hAPP(X1,esk175_7(X2,X3,X1,X4,X5,X6,X7))|X3=X2|~hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X6),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X6),X5)))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X2),X1)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),X1)|~c_Equiv__Relations_Ocongruent(X7,tc_fun(X4,tc_HOL_Obool),X5,X1)|~c_Equiv__Relations_Oequiv(X7,X6,X5)), inference(split_conjunct,[status(thm)],[c_0_6318]), ['final']). 4.46/4.73 cnf(c_0_10830, plain, (hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)|~c_Equiv__Relations_Oequiv(X1,X5,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X3))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_6319, c_0_6320]), c_0_6321]), ['final']). 4.46/4.73 cnf(c_0_10831, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk73_3(X3,X2,X1)),X2))|~hBOOL(hAPP(hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)),esk74_3(X3,X2,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6322, c_0_4945]), c_0_4945]), c_0_4961]), ['final']). 4.46/4.73 cnf(c_0_10832, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X4))),c_Int_Ointrel))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_6323]), ['final']). 4.46/4.73 cnf(c_0_10833, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X5),X2)),hAPP(hAPP(c_List_Oappend(X1),X5),X3))),c_List_Olexord(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_6324]), ['final']). 4.46/4.73 cnf(c_0_10834, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3))),c_List_Olistrel1(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_6325]), ['final']). 4.46/4.73 cnf(c_0_10835, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X7)),X8))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X1),tc_prod(X5,X1))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X1),tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X6),X2)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X7),X3))),c_Wellfounded_Olex__prod(X5,X1,X8,X4)))), inference(split_conjunct,[status(thm)],[c_0_4988]), ['final']). 4.46/4.73 cnf(c_0_10836, plain, (hAPP(X1,esk159_6(X2,X3,X1,X4,X5,X6))=hAPP(X1,esk158_6(X2,X3,X1,X4,X5,X6))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X6),X3),hAPP(c_Set_Oimage(X5,X2,X1),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X6),hAPP(c_Fun_Ocomp(X2,X6,X5,X3),X1)),X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Ocomm__monoid__add(X6)), inference(split_conjunct,[status(thm)],[c_0_6326]), ['final']). 4.46/4.73 cnf(c_0_10837, plain, (X1=hAPP(c_Groups_Ouminus__class_Ouminus(X2),c_Groups_Oone__class_Oone(X2))|X1=c_Groups_Oone__class_Oone(X2)|hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))!=c_Groups_Oone__class_Oone(X2)|~class_Rings_Oring__1__no__zero__divisors(X2)), inference(rw,[status(thm)],[c_0_6327, c_0_6013]), ['final']). 4.46/4.73 cnf(c_0_10838, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))), inference(rw,[status(thm)],[c_0_6328, c_0_6013]), ['final']). 4.46/4.73 cnf(c_0_10839, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))), inference(rw,[status(thm)],[c_0_6329, c_0_6013]), ['final']). 4.46/4.73 cnf(c_0_10840, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(X1)))), inference(rw,[status(thm)],[c_0_6330, c_0_6013]), ['final']). 4.46/4.73 cnf(c_0_10841, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~c_Equiv__Relations_Oequiv(X1,X5,X4)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X6),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X5),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X6))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X6))), inference(er,[status(thm)],[c_0_6331]), ['final']). 4.46/4.73 cnf(c_0_10842, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk159_6(X2,X3,X4,X5,X1,X6)),X5))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X6),X3),hAPP(c_Set_Oimage(X1,X2,X4),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),hAPP(c_Fun_Ocomp(X2,X6,X1,X3),X4)),X5)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~class_Groups_Ocomm__monoid__add(X6)), inference(split_conjunct,[status(thm)],[c_0_6326]), ['final']). 4.46/4.73 cnf(c_0_10843, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk158_6(X2,X3,X4,X5,X1,X6)),X5))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X6),X3),hAPP(c_Set_Oimage(X1,X2,X4),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),hAPP(c_Fun_Ocomp(X2,X6,X1,X3),X4)),X5)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~class_Groups_Ocomm__monoid__add(X6)), inference(split_conjunct,[status(thm)],[c_0_6326]), ['final']). 4.46/4.73 cnf(c_0_10844, plain, (c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X2,X1))=hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X1))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(rw,[status(thm)],[c_0_6332, c_0_6292]), ['final']). 4.46/4.73 cnf(c_0_10845, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X3))),X4))))|hBOOL(hAPP(X3,esk201_4(X4,X1,X3,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6333, c_0_4531]), c_0_4531]), ['final']). 4.46/4.73 cnf(c_0_10846, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),X3))|hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)!=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X5))|~c_Equiv__Relations_Oequiv(X1,X5,X3)), inference(split_conjunct,[status(thm)],[c_0_5020]), ['final']). 4.46/4.73 cnf(c_0_10847, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))), inference(rw,[status(thm)],[c_0_6334, c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_10848, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X1),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X6,X1),X5),X2)),hAPP(hAPP(c_Product__Type_OSigma(X6,X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk218_6(X3,X2,X1,X4,X5,X6))),hAPP(X3,esk218_6(X3,X2,X1,X4,X5,X6))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool)),X5),X4))), inference(split_conjunct,[status(thm)],[c_0_6335]), ['final']). 4.46/4.73 cnf(c_0_10849, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))|X3=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X5),c_List_Olist_ONil(X1)))),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X6),c_List_Olist_ONil(X1))))),c_List_Olistrel1(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_6221]), ['final']). 4.46/4.73 cnf(c_0_10850, plain, (X4=X5|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),X3))|~c_Relation_Ototal__on(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X2))), inference(split_conjunct,[status(thm)],[c_0_6336]), ['final']). 4.46/4.73 cnf(c_0_10851, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk470_7(X2,X3,X4,X5,X6,X7,X1)),X7))|hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X3),X4)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))|~c_Equiv__Relations_Ocongruent(X1,tc_fun(X5,tc_HOL_Obool),X6,X4)|~c_Equiv__Relations_Oequiv(X1,X7,X6)), inference(split_conjunct,[status(thm)],[c_0_6337]), ['final']). 4.46/4.73 cnf(c_0_10852, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4))|~c_FunDef_Oreduction__pair(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)))|~c_Wellfounded_Owf(X1,X4)), inference(split_conjunct,[status(thm)],[c_0_6338]), ['final']). 4.46/4.73 cnf(c_0_10853, plain, (X1=hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3)|hAPP(hAPP(c_List_Otake(X2),esk189_4(X4,X3,X1,X2)),X1)=hAPP(hAPP(c_List_Otake(X2),esk189_4(X4,X3,X1,X2)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X1),X3)),c_List_Olexord(X2,X4)))), inference(split_conjunct,[status(thm)],[c_0_4971]), ['final']). 4.46/4.73 cnf(c_0_10854, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Fields_Olinordered__field__inverse__zero(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6339, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), ['final']). 4.46/4.73 cnf(c_0_10855, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X7)),hAPP(hAPP(c_Product__Type_OPair(X6,X7),hAPP(X8,X3)),hAPP(X9,X4))),hAPP(c_Set_Oimage(tc_prod(X1,X2),tc_prod(X6,X7),c_Product__Type_Omap__pair(X1,X6,X2,X7,X8,X9)),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_6340]), ['final']). 4.46/4.73 cnf(c_0_10856, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3))),c_List_Olex(X1,X6)))), inference(csr,[status(thm)],[c_0_6341, c_0_6342]), ['final']). 4.46/4.73 cnf(c_0_10857, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X2)),X2),X1))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X2))), inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6343, c_0_5100]), c_0_6344])])]), ['final']). 4.46/4.73 cnf(c_0_10858, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X3),X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X5))),X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))|~hBOOL(hAPP(X5,X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6345, c_0_4531]), c_0_4531]), c_0_4531]), ['final']). 4.46/4.73 cnf(c_0_10859, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5)))|hBOOL(hAPP(hAPP(c_member(X1),esk254_5(X5,X3,X4,X2,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6346, c_0_4531]), c_0_4531]), ['final']). 4.46/4.73 cnf(c_0_10860, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,hAPP(X2,X3)))),hAPP(hAPP(c_List_Omap(X4,X1),X2),X5))=hAPP(hAPP(c_List_Omap(X4,X1),X2),hAPP(c_List_Ofilter(X4,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_fequal,X3))),X5))|~c_Fun_Oinj__on(X4,X1,X2,hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(c_List_Oset(X4),X5)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6347, c_0_5671]), c_0_5671]), ['final']). 4.46/4.73 cnf(c_0_10861, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X1,tc_HOL_Obool),X1,hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X2),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(rw,[status(thm)],[c_0_6348, c_0_6349]), ['final']). 4.46/4.73 cnf(c_0_10862, plain, (hAPP(c_Fun_Ocomp(X2,X2,X6,hAPP(X4,X5)),hAPP(c_Fun_Ocomp(X2,X2,X6,hAPP(X3,X7)),X8))=hAPP(c_Fun_Ocomp(X2,X2,X6,hAPP(X3,X7)),hAPP(c_Fun_Ocomp(X2,X2,X6,hAPP(X4,X5)),X8))|~c_Finite__Set_Ofolding(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_6350]), ['final']). 4.46/4.73 cnf(c_0_10863, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk218_6(X2,X3,X4,X5,X6,X1)),X6))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X4),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X6),X3)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X5),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X5))), inference(split_conjunct,[status(thm)],[c_0_6335]), ['final']). 4.46/4.73 cnf(c_0_10864, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4))=hAPP(hAPP(c_List_Oappend(X1),X3),X4)|hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)),hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4))!=X4|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)!=X2|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)!=X3), inference(er,[status(thm)],[c_0_6351]), ['final']). 4.46/4.73 cnf(c_0_10865, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),esk129_7(X6,X7,X5,X4,X3,X2,X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X5))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X7))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_6352]), ['final']). 4.46/4.73 cnf(c_0_10866, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X3)|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk108_4(X2,X4,X3,X1))),X3)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),esk108_4(X2,X4,X3,X1)))),X2)), inference(rw,[status(thm)],[c_0_6353, c_0_5100]), ['final']). 4.46/4.73 cnf(c_0_10867, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))), inference(rw,[status(thm)],[c_0_6354, c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_10868, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),X5))|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_6355]), ['final']). 4.46/4.73 cnf(c_0_10869, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk85_4(X2,X3,X1,X4)),esk84_4(X2,X3,X1,X4)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2)),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk82_4(X2,X3,X1,X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))|~class_Groups_Ocomm__monoid__add(X4)), inference(split_conjunct,[status(thm)],[c_0_6238]), ['final']). 4.46/4.73 cnf(c_0_10870, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk85_4(X2,X3,X1,X4)),esk83_4(X2,X3,X1,X4)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X2)),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk82_4(X2,X3,X1,X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X3))|~class_Groups_Ocomm__monoid__add(X4)), inference(split_conjunct,[status(thm)],[c_0_6238]), ['final']). 4.46/4.73 cnf(c_0_10871, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X6)),hAPP(hAPP(c_Product__Type_OPair(X1,X6),X3),X7)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X6),X5),X8)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X6)),hAPP(hAPP(c_Product__Type_OPair(X2,X6),X4),X7)),X8))), inference(split_conjunct,[status(thm)],[c_0_6356]), ['final']). 4.46/4.73 cnf(c_0_10872, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Oplus__class_Oplus(X1)),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X5))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6357]), ['final']). 4.46/4.73 cnf(c_0_10873, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6358, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), ['final']). 4.46/4.73 cnf(c_0_10874, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6359, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), ['final']). 4.46/4.73 cnf(c_0_10875, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Ominus__class_Ominus(X1)),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X5))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6360]), ['final']). 4.46/4.73 cnf(c_0_10876, plain, (hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),hAPP(c_Fun_Othe__inv__into(X2,X5,hAPP(c_Set_Oimage(X1,X2,X4),X3),X6),X7))=hAPP(c_Fun_Othe__inv__into(X1,X5,X3,hAPP(c_Fun_Ocomp(X2,X5,X1,X6),X4)),X7)|~c_Fun_Oinj__on(X2,X5,X6,hAPP(c_Set_Oimage(X1,X2,X4),X3))|~c_Fun_Oinj__on(X1,X2,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X5),X7),hAPP(c_Set_Oimage(X2,X5,X6),hAPP(c_Set_Oimage(X1,X2,X4),X3))))), inference(rw,[status(thm)],[c_0_6361, c_0_6281]), ['final']). 4.46/4.73 cnf(c_0_10877, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X4))),X3))|~class_Rings_Olinordered__semiring__1__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X6))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),X6)!=c_Groups_Oone__class_Oone(X1)), inference(split_conjunct,[status(thm)],[c_0_6362]), ['final']). 4.46/4.73 cnf(c_0_10878, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X4))),X3))|~class_Rings_Olinordered__semiring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X6))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),X6)!=c_Groups_Oone__class_Oone(X1)), inference(split_conjunct,[status(thm)],[c_0_6363]), ['final']). 4.46/4.73 cnf(c_0_10879, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6364, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), ['final']). 4.46/4.73 cnf(c_0_10880, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk173_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2)))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_6303]), ['final']). 4.46/4.73 cnf(c_0_10881, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk238_4(X2,X3,X4,X1)),X4))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_5587]), ['final']). 4.46/4.73 cnf(c_0_10882, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6365]), ['final']). 4.46/4.73 cnf(c_0_10883, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X5,X1),X2),X4))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X5,X1),X3),X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk373_5(X3,X2,X4,X5,X1))),hAPP(X3,esk373_5(X3,X2,X4,X5,X1))))|~class_Groups_Oordered__ab__semigroup__add(X1)|~class_Groups_Omonoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6312]), ['final']). 4.46/4.73 cnf(c_0_10884, plain, (hBOOL(hAPP(hAPP(X1,esk246_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),esk247_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk246_3(X1,X2,X3)),esk247_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(rw,[status(thm)],[c_0_6366, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_10885, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),c_Big__Operators_Olinorder__class_OMin(X1,X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6367]), ['final']). 4.46/4.73 cnf(c_0_10886, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X3)),X4)),X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6368]), ['final']). 4.46/4.73 cnf(c_0_10887, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X4)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6369]), ['final']). 4.46/4.73 cnf(c_0_10888, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X4),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X1),X5))),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X1),X5))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X6),X5))), inference(split_conjunct,[status(thm)],[c_0_6370]), ['final']). 4.46/4.73 cnf(c_0_10889, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X4)),hAPP(hAPP(c_Set_Oinsert(X1),c_HOL_OThe(X1,hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X4)),X3))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X1,X2,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(rw,[status(thm)],[c_0_6371, c_0_4891]), ['final']). 4.46/4.73 cnf(c_0_10890, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk183_5(X2,X3,X4,X1,X5)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X4|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Oordered__cancel__ab__semigroup__add(X5)|~class_Groups_Ocomm__monoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6372]), ['final']). 4.46/4.73 cnf(c_0_10891, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk425_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X3)),X2)))), inference(split_conjunct,[status(thm)],[c_0_6373]), ['final']). 4.46/4.73 cnf(c_0_10892, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk128_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X3)),X2)))), inference(split_conjunct,[status(thm)],[c_0_6374]), ['final']). 4.46/4.73 cnf(c_0_10893, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk32_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6375]), ['final']). 4.46/4.73 cnf(c_0_10894, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X1)),X2)|hAPP(X1,esk85_4(X1,X2,X3,X4))!=c_Groups_Ozero__class_Ozero(X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),esk82_4(X1,X2,X3,X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3,tc_HOL_Obool)),X2))|~class_Groups_Ocomm__monoid__add(X4)), inference(split_conjunct,[status(thm)],[c_0_6238]), ['final']). 4.46/4.73 cnf(c_0_10895, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X5))),c_List_Olistrel1(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_6376]), ['final']). 4.46/4.73 cnf(c_0_10896, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6377]), ['final']). 4.46/4.73 cnf(c_0_10897, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),X4))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X2,X3),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3))), inference(split_conjunct,[status(thm)],[c_0_6378]), ['final']). 4.46/4.73 cnf(c_0_10898, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X1)),c_FunDef_Omax__strict))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_6379]), ['final']). 4.46/4.73 cnf(c_0_10899, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),X2))))|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6380, c_0_6381]), c_0_6382]), ['final']). 4.46/4.73 cnf(c_0_10900, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))),hAPP(c_Finite__Set_Ocard(X1),X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(rw,[status(thm)],[c_0_6383, c_0_6384]), ['final']). 4.46/4.73 cnf(c_0_10901, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olexord(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_5014]), ['final']). 4.46/4.73 cnf(c_0_10902, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)),X4)=hAPP(hAPP(c_List_Onth(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3)))))), inference(rw,[status(thm)],[c_0_6385, c_0_6386]), ['final']). 4.46/4.73 cnf(c_0_10903, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X4,c_Groups_Otimes__class_Otimes(X1)),X6),X7),hAPP(c_Set_Oimage(X2,X4,X5),X3))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(c_Fun_Ocomp(X4,X1,X2,X6),X5)),X7),X3)|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~c_Fun_Oinj__on(X2,X4,X5,X3)), inference(split_conjunct,[status(thm)],[c_0_6387]), ['final']). 4.46/4.73 cnf(c_0_10904, plain, (hBOOL(hAPP(hAPP(c_member(X2),hAPP(c_Random_Opick(X2,X3),X1)),hAPP(c_List_Oset(X2),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X2),X2),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X2)),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X2),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X2)),X3))))), inference(split_conjunct,[status(thm)],[c_0_6388]), ['final']). 4.46/4.73 cnf(c_0_10905, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X2,X1)),X3))|~c_Enum_Oall__n__lists(X1,hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_HOL_Obool,tc_List_Olist(X1)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Option_Ooption(X1)),tc_fun(X2,X1),tc_List_Olist(X1)),c_Fun_Ocomp(tc_Option_Ooption(X1),X1,X2,c_Option_Othe(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X2,X1)),tc_fun(X2,tc_Option_Ooption(X1)),tc_List_Olist(X1)),c_Map_Omap__of(X2,X1)),hAPP(c_List_Ozip(X2,X1),c_Enum_Oenum__class_Oenum(X2))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_Enum_Oenum__class_Oenum(X2)))|~class_Enum_Oenum(X2)|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_6117]), ['final']). 4.46/4.73 cnf(c_0_10906, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk401_6(X2,X3,X4,X5,X1,X6)),X5))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),X4),X2),X5)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),X3),X2),X5)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~class_Groups_Oab__semigroup__mult(X6)), inference(split_conjunct,[status(thm)],[c_0_6389]), ['final']). 4.46/4.73 cnf(c_0_10907, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),c_Big__Operators_Olinorder__class_OMax(X1,X3))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6390]), ['final']). 4.46/4.73 cnf(c_0_10908, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X6),X4),X5)))|~hBOOL(hAPP(hAPP(X6,esk381_6(X3,X5,X4,X6,X2,X1)),esk382_6(X3,X5,X4,X6,X2,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6391, c_0_5580]), c_0_5580]), ['final']). 4.46/4.73 cnf(c_0_10909, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X6)))|~hBOOL(hAPP(hAPP(X5,esk21_6(X5,X6,X4,X3,X2,X1)),esk22_6(X5,X6,X4,X3,X2,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6392, c_0_5580]), c_0_5580]), ['final']). 4.46/4.73 cnf(c_0_10910, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X2,X1)),X3))|~c_Enum_Oex__n__lists(X1,hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_HOL_Obool,tc_List_Olist(X1)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Option_Ooption(X1)),tc_fun(X2,X1),tc_List_Olist(X1)),c_Fun_Ocomp(tc_Option_Ooption(X1),X1,X2,c_Option_Othe(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X2,X1)),tc_fun(X2,tc_Option_Ooption(X1)),tc_List_Olist(X1)),c_Map_Omap__of(X2,X1)),hAPP(c_List_Ozip(X2,X1),c_Enum_Oenum__class_Oenum(X2))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_Enum_Oenum__class_Oenum(X2)))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_6118]), ['final']). 4.46/4.73 cnf(c_0_10911, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X1),X5))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,X5)))), inference(split_conjunct,[status(thm)],[c_0_6393]), ['final']). 4.46/4.73 cnf(c_0_10912, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),X3)),X2)),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6394, c_0_5266]), c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_10913, plain, (hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6395, c_0_4760]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_10914, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X2)))),hAPP(hAPP(c_List_Oappend(X1),X4),X2))=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X3,X2))),X2)|hBOOL(hAPP(hAPP(c_member(X1),esk304_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),X4)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6396, c_0_4916]), c_0_4916]), ['final']). 4.46/4.73 cnf(c_0_10915, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),esk127_5(X2,X3,X4,X5,X1)),X3)),c_List_Olistrel(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_6397]), ['final']). 4.46/4.73 cnf(c_0_10916, plain, (c_FunDef_Oreduction__pair(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)))), inference(split_conjunct,[status(thm)],[c_0_6199]), ['final']). 4.46/4.73 cnf(c_0_10917, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),esk308_5(X3,X4,X2,X5,X1))),c_List_Olistrel(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),X4)),c_List_Olistrel(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_6398]), ['final']). 4.46/4.73 cnf(c_0_10918, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X5,X2)),hAPP(X5,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X1,tc_Nat_Onat)),X5),X4))))), inference(split_conjunct,[status(thm)],[c_0_6399]), ['final']). 4.46/4.73 cnf(c_0_10919, plain, (hBOOL(hAPP(hAPP(c_member(X2),X4),X3))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X5,X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),X6),X3))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),X6),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6400]), ['final']). 4.46/4.73 cnf(c_0_10920, plain, (hAPP(c_Nat_OSuc,X1)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X1)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6401, c_0_4609]), c_0_5671]), c_0_5671]), c_0_6151]), c_0_5320]), c_0_6074]), ['final']). 4.46/4.73 cnf(c_0_10921, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1)),c_Int_Onat)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6402, c_0_4609]), c_0_5671]), c_0_5671]), c_0_6151]), c_0_5320]), c_0_6074]), ['final']). 4.46/4.73 cnf(c_0_10922, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1)),c_Int_Onat)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6403, c_0_6178]), c_0_4609]), c_0_5671]), c_0_5671]), c_0_6151]), c_0_5320]), c_0_6074]), ['final']). 4.46/4.73 cnf(c_0_10923, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6404]), ['final']). 4.46/4.73 cnf(c_0_10924, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk237_5(X3,X4,X5,X1,X2))),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X5),X4)),c_Wellfounded_Omax__ext(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_5587]), ['final']). 4.46/4.73 cnf(c_0_10925, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk462_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6405]), ['final']). 4.46/4.73 cnf(c_0_10926, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk316_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X4))), inference(rw,[status(thm)],[c_0_6406, c_0_5134]), ['final']). 4.46/4.73 cnf(c_0_10927, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))|hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~c_Equiv__Relations_Oequiv(X1,X5,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_6407]), ['final']). 4.46/4.73 cnf(c_0_10928, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4))),c_FunDef_Opair__leq))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6408]), ['final']). 4.46/4.73 cnf(c_0_10929, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk444_2(X1,X2)))))|hBOOL(hAPP(X1,esk446_2(X1,X2)))|hBOOL(hAPP(X1,esk443_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,X3))), inference(rw,[status(thm)],[c_0_6409, c_0_6410]), ['final']). 4.46/4.73 cnf(c_0_10930, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6411]), ['final']). 4.46/4.73 cnf(c_0_10931, plain, (hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6))=hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X6))),hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),X6)))|~c_Finite__Set_Ofolding(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6))), inference(split_conjunct,[status(thm)],[c_0_6412]), ['final']). 4.46/4.73 cnf(c_0_10932, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,hAPP(X2,X3)))),hAPP(hAPP(c_List_Omap(X4,X1),X2),X5))=hAPP(hAPP(c_List_Omap(X4,X1),X2),hAPP(c_List_Ofilter(X4,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_fequal,X3))),X5))|~c_Fun_Oinj__on(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6413, c_0_5671]), c_0_5671]), ['final']). 4.46/4.73 cnf(c_0_10933, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4))),c_FunDef_Opair__less))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6414]), ['final']). 4.46/4.73 cnf(c_0_10934, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X3,tc_HOL_Obool),X4),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4),X1)),X2)|esk83_4(X1,X2,X3,X4)!=esk84_4(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),esk82_4(X1,X2,X3,X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3,tc_HOL_Obool)),X2))|~class_Groups_Ocomm__monoid__add(X4)), inference(split_conjunct,[status(thm)],[c_0_6238]), ['final']). 4.46/4.73 cnf(c_0_10935, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),esk322_4(X3,X4,X2,X1))),esk321_4(X3,X4,X2,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel1(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_5018]), ['final']). 4.46/4.73 cnf(c_0_10936, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk3_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),esk1_2(X2,X1)))), inference(rw,[status(thm)],[c_0_6415, c_0_4736]), ['final']). 4.46/4.73 cnf(c_0_10937, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X2)),X2),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))), inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_6416, c_0_5100])]), ['final']). 4.46/4.73 cnf(c_0_10938, plain, (hAPP(hAPP(X3,hAPP(hAPP(X5,X7),X6)),hAPP(hAPP(X5,X8),X6))=hAPP(hAPP(X5,hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),X3),X7)),X8)),X6)|~c_Finite__Set_Ofolding__image(X1,X2,X3,X4,X5)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6))), inference(split_conjunct,[status(thm)],[c_0_6417]), ['final']). 4.46/4.73 cnf(c_0_10939, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk2_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),esk1_2(X2,X1)))), inference(rw,[status(thm)],[c_0_6418, c_0_4736]), ['final']). 4.46/4.73 cnf(c_0_10940, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X6),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5))|hAPP(X3,esk372_8(X6,X3,X5,X5,X4,X4,X1,X2))!=hAPP(X6,esk372_8(X6,X3,X5,X5,X4,X4,X1,X2))|~class_Orderings_Oord(X1)|~class_Groups_Ocomm__monoid__add(X2)), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6419])]), ['final']). 4.46/4.73 cnf(c_0_10941, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4))=hAPP(hAPP(c_List_Oappend(X1),X3),X4)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)!=X2), inference(er,[status(thm)],[c_0_6420]), ['final']). 4.46/4.73 cnf(c_0_10942, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_Enum_Oenum__class_Oenum__all(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2)))))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X1,X2)),X3))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_6421]), ['final']). 4.46/4.73 cnf(c_0_10943, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_Enum_Oenum__class_Oenum__ex(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2)))))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X1,X2)),X3))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_6422]), ['final']). 4.46/4.73 cnf(c_0_10944, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X1,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,tc_HOL_Obool),X1),c_fequal),X4)),hAPP(X4,esk274_4(X4,X3,X2,X1))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6423, c_0_4945]), c_0_5320]), c_0_4531]), ['final']). 4.46/4.73 cnf(c_0_10945, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk79_4(X1,X2,X3,X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(c_Nat_OSuc,esk78_4(X1,X2,X3,X4)))),hAPP(X2,esk78_4(X1,X2,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X4)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))), inference(rw,[status(thm)],[c_0_6424, c_0_5644]), ['final']). 4.46/4.73 cnf(c_0_10946, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk79_4(X2,X3,X4,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X3,hAPP(c_Nat_OSuc,esk78_4(X2,X3,X4,X1)))),hAPP(X3,esk78_4(X2,X3,X4,X1))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X4))), inference(rw,[status(thm)],[c_0_6425, c_0_5644]), ['final']). 4.46/4.73 cnf(c_0_10947, plain, (hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X6)),hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X7)),X8))=hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X7)),hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X6)),X8))|~c_Finite__Set_Ofolding(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_6426]), ['final']). 4.46/4.73 cnf(c_0_10948, plain, (X3=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk174_7(X2,X3,X4,X5,X6,X7,X1)),esk175_7(X2,X3,X4,X5,X6,X7,X1))),X6))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X2),X4)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X3),X4)|~c_Equiv__Relations_Ocongruent(X1,tc_fun(X5,tc_HOL_Obool),X6,X4)|~c_Equiv__Relations_Oequiv(X1,X7,X6)), inference(split_conjunct,[status(thm)],[c_0_6318]), ['final']). 4.46/4.73 cnf(c_0_10949, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)=X3|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X5),X3))|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_6427]), ['final']). 4.46/4.73 cnf(c_0_10950, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4))),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_6428]), ['final']). 4.46/4.73 cnf(c_0_10951, plain, (c_Map_Orestrict__map(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),X5),X6)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X6)),X4),X5)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X6))), inference(rw,[status(thm)],[c_0_6429, c_0_6430]), ['final']). 4.46/4.73 cnf(c_0_10952, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6431]), ['final']). 4.46/4.73 cnf(c_0_10953, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),esk481_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk481_4(X3,X4,X2,X1)))),X3))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)), inference(split_conjunct,[status(thm)],[c_0_6297]), ['final']). 4.46/4.73 cnf(c_0_10954, plain, (hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X1,hAPP(hAPP(c_List_Oappend(X4),X3),X2)))),hAPP(hAPP(c_List_Oappend(X4),X3),X2))=hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X1,X2))),X2)|~hBOOL(hAPP(X1,esk304_4(X2,X1,X3,X4)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6432, c_0_4916]), c_0_4916]), ['final']). 4.46/4.73 cnf(c_0_10955, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_6433]), ['final']). 4.46/4.73 cnf(c_0_10956, plain, (hAPP(c_Map_Omap__of(X1,X3),hAPP(hAPP(c_List_Omap(X1,tc_prod(X1,X3)),hAPP(hAPP(c_COMBS(X1,X3,tc_prod(X1,X3)),c_Product__Type_OPair(X1,X3)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X3),X3,X1),c_Option_Othe(X3)),X4))),X2))=X4|hAPP(c_List_Oset(X1),X2)!=c_Map_Odom(X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_6434]), ['final']). 4.46/4.73 cnf(c_0_10957, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)=X3|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X5),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_6435]), ['final']). 4.46/4.73 cnf(c_0_10958, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6436]), ['final']). 4.46/4.73 cnf(c_0_10959, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5)))|hBOOL(hAPP(X3,esk254_5(X5,X3,X4,X2,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6437, c_0_4531]), c_0_4531]), ['final']). 4.46/4.73 cnf(c_0_10960, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)),X4)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_6438]), ['final']). 4.46/4.73 cnf(c_0_10961, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)),X4)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_6439]), ['final']). 4.46/4.73 cnf(c_0_10962, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk175_7(X2,X3,X4,X5,X6,X7,X1)),X7))|X3=X2|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X2),X4)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X3),X4)|~c_Equiv__Relations_Ocongruent(X1,tc_fun(X5,tc_HOL_Obool),X6,X4)|~c_Equiv__Relations_Oequiv(X1,X7,X6)), inference(split_conjunct,[status(thm)],[c_0_6318]), ['final']). 4.46/4.73 cnf(c_0_10963, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk174_7(X2,X3,X4,X5,X6,X7,X1)),X7))|X3=X2|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X6)))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X2),X4)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X3),X4)|~c_Equiv__Relations_Ocongruent(X1,tc_fun(X5,tc_HOL_Obool),X6,X4)|~c_Equiv__Relations_Oequiv(X1,X7,X6)), inference(split_conjunct,[status(thm)],[c_0_6318]), ['final']). 4.46/4.73 cnf(c_0_10964, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X1),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X1),X2),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X3))|c_Groups_Oone__class_Oone(X1)!=hAPP(X2,esk31_5(X2,X3,X4,X5,X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_6192]), ['final']). 4.46/4.73 cnf(c_0_10965, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X3))|c_Groups_Ozero__class_Ozero(X1)!=hAPP(X2,esk118_5(X2,X3,X4,X5,X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6193]), ['final']). 4.46/4.73 cnf(c_0_10966, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk444_2(X1,X2)))))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk445_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|hBOOL(hAPP(X1,esk443_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,X3))), inference(rw,[status(thm)],[c_0_6440, c_0_6410]), ['final']). 4.46/4.73 cnf(c_0_10967, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)),X4)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_6441]), ['final']). 4.46/4.73 cnf(c_0_10968, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)),X4)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_6442]), ['final']). 4.46/4.73 cnf(c_0_10969, plain, (hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6443, c_0_4945]), c_0_4945]), ['final']). 4.46/4.73 cnf(c_0_10970, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk66_3(X3,X2,X1)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk64_3(X3,X2,X1)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))), inference(csr,[status(thm)],[c_0_6444, c_0_6445]), ['final']). 4.46/4.73 cnf(c_0_10971, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X2))|hAPP(X1,esk124_5(X1,X2,X3,X4,X5))!=c_Groups_Oone__class_Oone(X5)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))|~class_Groups_Ocomm__monoid__mult(X5)), inference(split_conjunct,[status(thm)],[c_0_6194]), ['final']). 4.46/4.73 cnf(c_0_10972, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X2))|hAPP(X1,esk426_5(X1,X2,X3,X4,X5))!=c_Groups_Ozero__class_Ozero(X5)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))|~class_Groups_Ocomm__monoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6195]), ['final']). 4.46/4.73 cnf(c_0_10973, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Oappend(X3),X5),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3)))),hAPP(hAPP(c_List_Oappend(X3),X6),hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_Olist_ONil(X3))))),c_List_Olistrel1(X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_6221]), ['final']). 4.46/4.73 cnf(c_0_10974, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),esk1_2(X1,X2)),hAPP(c_List_Oset(tc_List_Olist(X2)),X1)))|hBOOL(hAPP(c_List_Odistinct(X2),hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1)))|esk3_2(X1,X2)!=esk2_2(X1,X2)|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1))), inference(rw,[status(thm)],[c_0_6446, c_0_4736]), ['final']). 4.46/4.73 cnf(c_0_10975, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)))=hAPP(hAPP(c_List_Olist_OCons(X1),X4),hAPP(c_List_Ofilter(X1,X2),X5))|hBOOL(hAPP(hAPP(c_member(X1),esk530_6(hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)),X2,hAPP(c_List_Ofilter(X1,X2),X5),X4,X1,X3)),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4))), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6447])]), ['final']). 4.46/4.73 cnf(c_0_10976, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk65_3(X3,X2,X1)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk64_3(X3,X2,X1)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))), inference(csr,[status(thm)],[c_0_6448, c_0_6445]), ['final']). 4.46/4.73 cnf(c_0_10977, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~c_Equiv__Relations_Oequiv(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3))), inference(split_conjunct,[status(thm)],[c_0_6449]), ['final']). 4.46/4.73 cnf(c_0_10978, plain, (hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3))=hAPP(c_Finite__Set_Ocard(X1),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Fun_Oinj__on(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X1),c_Equiv__Relations_Oquotient(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_6450]), ['final']). 4.46/4.73 cnf(c_0_10979, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X3))),hAPP(X2,X4))),c_Transitive__Closure_Ortrancl(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,hAPP(c_Nat_OSuc,esk285_5(X3,X4,X5,X2,X1)))),hAPP(X2,esk285_5(X3,X4,X5,X2,X1)))),c_Transitive__Closure_Ortrancl(X1,X5)))), inference(split_conjunct,[status(thm)],[c_0_6451]), ['final']). 4.46/4.73 cnf(c_0_10980, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk390_5(X2,X3,X4,X5,X1)),X4)),X2))|X3=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6271]), ['final']). 4.46/4.73 cnf(c_0_10981, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk25_5(X3,X4,X5,X2,X1))),X3))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_6270]), ['final']). 4.46/4.73 cnf(c_0_10982, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),X6))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),hAPP(c_Set_Oimage(X1,X2,X3),X6))|~c_Fun_Oinj__on(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X4))), inference(split_conjunct,[status(thm)],[c_0_6452]), ['final']). 4.46/4.73 cnf(c_0_10983, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),X6))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),hAPP(c_Set_Oimage(X1,X2,X3),X6))|~c_Fun_Oinj__on(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X4))), inference(split_conjunct,[status(thm)],[c_0_6453]), ['final']). 4.46/4.73 cnf(c_0_10984, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),X3))|~c_Equiv__Relations_Oequiv(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_6454]), ['final']). 4.46/4.73 cnf(c_0_10985, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,X1),X1,X2),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X1),X5)),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X1),X5),hAPP(hAPP(c_COMBB(tc_fun(X2,X1),X1,X4),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3)),hAPP(c_COMBC(X2,X4,X1),X6)))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6455]), ['final']). 4.46/4.73 cnf(c_0_10986, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk463_4(X1,X2,X3,X4)),esk462_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6405]), ['final']). 4.46/4.73 cnf(c_0_10987, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk317_4(X1,X2,X3,X4)),esk316_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X4))), inference(rw,[status(thm)],[c_0_6456, c_0_5134]), ['final']). 4.46/4.73 cnf(c_0_10988, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,X1),X1,X2),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X1),X5)),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X1),X5),hAPP(hAPP(c_COMBB(tc_fun(X2,X1),X1,X4),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3)),hAPP(c_COMBC(X2,X4,X1),X6)))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6457]), ['final']). 4.46/4.73 cnf(c_0_10989, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4)),X5)),X6))|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_6458]), ['final']). 4.46/4.73 cnf(c_0_10990, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_6459]), ['final']). 4.46/4.73 cnf(c_0_10991, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4))), inference(split_conjunct,[status(thm)],[c_0_6460]), ['final']). 4.46/4.73 cnf(c_0_10992, plain, (hAPP(hAPP(c_List_Olist__update(X1,hAPP(c_List_Orev(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_OSuc,X3))),X4)=hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6461, c_0_6462]), c_0_5644]), ['final']). 4.46/4.73 cnf(c_0_10993, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4)),X5)),X6))|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_6463]), ['final']). 4.46/4.73 cnf(c_0_10994, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4)),X5)),X6)))|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_6464]), ['final']). 4.46/4.73 cnf(c_0_10995, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4)),X5)),X6)))|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_6465]), ['final']). 4.46/4.73 cnf(c_0_10996, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X1),hAPP(c_fequal,esk36_5(X5,X4,X2,X1,X3)))),X4),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X1),hAPP(X5,esk35_5(X5,X4,X2,X1,X3))))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6466, c_0_5580]), c_0_5670]), c_0_5580]), c_0_5580]), ['final']). 4.46/4.73 cnf(c_0_10997, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk295_5(X2,X3,X4,X1,X5)),hAPP(c_List_Oset(X1),X4)))|hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X1,X5),X2),hAPP(c_List_Ofilter(X1,X3),X4)))=hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X1,X5),X2),X4))|~class_Groups_Omonoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6467]), ['final']). 4.46/4.73 cnf(c_0_10998, plain, (hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))|~hBOOL(hAPP(hAPP(hAPP(X1,esk223_4(X1,X2,X3,X4)),esk224_4(X1,X2,X3,X4)),esk225_4(X1,X2,X3,X4)))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))), inference(split_conjunct,[status(thm)],[c_0_4913]), ['final']). 4.46/4.73 cnf(c_0_10999, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk126_5(X2,X3,X4,X5,X1)),X4)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_6397]), ['final']). 4.46/4.73 cnf(c_0_11000, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk307_5(X3,X4,X5,X2,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),X4)),c_List_Olistrel(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_6398]), ['final']). 4.46/4.73 cnf(c_0_11001, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk1_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),esk2_2(X2,X1))),hAPP(c_List_Oset(X1),esk3_2(X2,X1)))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(rw,[status(thm)],[c_0_6468, c_0_4736]), ['final']). 4.46/4.73 cnf(c_0_11002, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk86_4(X2,X3,X4,X1)),X4))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_Nat_Onat,X1),c_Finite__Set_Ocard(X3)),X2)),X4)=hAPP(c_Finite__Set_Ocard(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OSigma(X1,X3),X4),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_6469]), ['final']). 4.46/4.73 cnf(c_0_11003, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OSemi(X4,X5)),X6)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X7),X5),X6)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X7)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6470, c_0_5580]), c_0_5580]), c_0_5580]), ['final']). 4.46/4.73 cnf(c_0_11004, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk380_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Ocomm__monoid__mult(X5)), inference(split_conjunct,[status(thm)],[c_0_6471]), ['final']). 4.46/4.73 cnf(c_0_11005, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk181_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),X2),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Ocomm__monoid__mult(X5)), inference(split_conjunct,[status(thm)],[c_0_6472]), ['final']). 4.46/4.73 cnf(c_0_11006, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk447_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Ocomm__monoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6473]), ['final']). 4.46/4.73 cnf(c_0_11007, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6474, c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), ['final']). 4.46/4.73 cnf(c_0_11008, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(c_Set_Oimage(X1,X1,X2),X3))=hAPP(X2,hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X3))|~class_Lattices_Oab__semigroup__idem__mult(X1)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X2,esk437_3(X3,X2,X1))),hAPP(X2,esk438_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk437_3(X3,X2,X1)),esk438_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6475]), ['final']). 4.46/4.73 cnf(c_0_11009, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(X3,esk275_8(X4,X5,X3,X6,X7,X8,X2,X1))),hAPP(X5,esk276_8(X4,X5,X3,X6,X7,X8,X2,X1)))=X8|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),X8),hAPP(c_Set_Oimage(tc_prod(X7,X6),tc_prod(X1,X2),c_Product__Type_Omap__pair(X7,X1,X6,X2,X3,X5)),X4)))), inference(split_conjunct,[status(thm)],[c_0_6308]), ['final']). 4.46/4.73 cnf(c_0_11010, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk12_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(hAPP(c_member(X1),esk11_4(X2,X3,X4,X1)),X3))|hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_6476]), ['final']). 4.46/4.73 cnf(c_0_11011, plain, (hAPP(hAPP(c_Product__Type_OPair(X2,X4),hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(hAPP(c_List_Onth(X4),X5),X1))=hAPP(hAPP(c_List_Onth(tc_prod(X2,X4)),hAPP(hAPP(c_List_Ozip(X2,X4),X3),X5)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5)))), inference(split_conjunct,[status(thm)],[c_0_6477]), ['final']). 4.46/4.73 cnf(c_0_11012, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk146_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Ocomm__monoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6478]), ['final']). 4.46/4.73 cnf(c_0_11013, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk64_3(X3,X2,X1)),X2))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk65_3(X3,X2,X1)),esk66_3(X3,X2,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))), inference(csr,[status(thm)],[c_0_6479, c_0_6445]), ['final']). 4.46/4.73 cnf(c_0_11014, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6480]), ['final']). 4.46/4.73 cnf(c_0_11015, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1))),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_6481]), ['final']). 4.46/4.73 cnf(c_0_11016, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2)),c_List_Olex(X1,X4)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2)),c_List_Olexord(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_5030]), ['final']). 4.46/4.73 cnf(c_0_11017, plain, (X5=X6|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X6))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X6),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X4)))|~c_Equiv__Relations_Oequiv(X1,X7,X4)), inference(split_conjunct,[status(thm)],[c_0_5026]), ['final']). 4.46/4.73 cnf(c_0_11018, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Finite__Set_Ocard(X5),X4))),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk232_5(X3,X2,X4,X5,X1))),X3))|~class_Rings_Osemiring__1(X1)|~class_Groups_Oordered__ab__semigroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6482]), ['final']). 4.46/4.73 cnf(c_0_11019, plain, (hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~c_Equiv__Relations_Oequiv(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3))), inference(split_conjunct,[status(thm)],[c_0_6483]), ['final']). 4.46/4.73 cnf(c_0_11020, plain, (X4=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))|hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X2,tc_HOL_Obool)),X4),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X5),c_Relation_OImage(X2,X1,X3)),X6))|~c_Relation_Osingle__valued(X1,X2,hAPP(c_Relation_Oconverse(X2,X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6484]), ['final']). 4.46/4.73 cnf(c_0_11021, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5)|hAPP(hAPP(X2,hAPP(X3,X4)),hAPP(X3,X5))=hAPP(hAPP(X2,hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5))),hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5)))|~c_Finite__Set_Ofolding__one(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_6485]), ['final']). 4.46/4.73 cnf(c_0_11022, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Orestrict__map(X1,X4,X5,X3)),X2),c_Option_Ooption_ONone(X4))=c_Map_Orestrict__map(X1,X4,X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6486]), ['final']). 4.46/4.73 cnf(c_0_11023, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk290_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6487]), ['final']). 4.46/4.73 cnf(c_0_11024, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk349_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6488]), ['final']). 4.46/4.73 cnf(c_0_11025, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),X3),X2),X4)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),X1),X2),X4)|hAPP(X1,esk401_6(X2,X1,X3,X4,X5,X6))!=hAPP(X3,esk401_6(X2,X1,X3,X4,X5,X6))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Oab__semigroup__mult(X6)), inference(split_conjunct,[status(thm)],[c_0_6389]), ['final']). 4.46/4.73 cnf(c_0_11026, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk390_5(X2,X3,X4,X5,X1)),X4)),X2))|X5=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6271]), ['final']). 4.46/4.73 cnf(c_0_11027, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__upds(X1,X2,X3,X4,X5)),X6),hAPP(c_Option_Ooption_OSome(X2),X7))=c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X6),X4),hAPP(hAPP(c_List_Olist_OCons(X2),X7),X5))|hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),X4)))), inference(rw,[status(thm)],[c_0_6489, c_0_6224]), ['final']). 4.46/4.73 cnf(c_0_11028, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk66_3(X3,X2,X1)),X2))|hAPP(c_Finite__Set_Ocard(X1),esk64_3(X3,X2,X1))!=X3|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))), inference(csr,[status(thm)],[c_0_6490, c_0_6445]), ['final']). 4.46/4.73 cnf(c_0_11029, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk65_3(X3,X2,X1)),X2))|hAPP(c_Finite__Set_Ocard(X1),esk64_3(X3,X2,X1))!=X3|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))), inference(csr,[status(thm)],[c_0_6491, c_0_6445]), ['final']). 4.46/4.73 cnf(c_0_11030, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk508_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Lattices_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_6492]), ['final']). 4.46/4.73 cnf(c_0_11031, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk25_5(X3,X4,X5,X2,X1))),X3))|X5=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_6270]), ['final']). 4.46/4.73 cnf(c_0_11032, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk358_5(X2,X3,X4,X5,X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Oordered__ab__semigroup__add(X1)|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6260]), ['final']). 4.46/4.73 cnf(c_0_11033, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X6),X1),hAPP(c_Set_Oimage(X5,X3,X2),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X6),hAPP(c_Fun_Ocomp(X3,X6,X5,X1),X2)),X4)|hAPP(X1,hAPP(X2,esk158_6(X3,X1,X2,X4,X5,X6)))!=c_Groups_Ozero__class_Ozero(X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Ocomm__monoid__add(X6)), inference(split_conjunct,[status(thm)],[c_0_6326]), ['final']). 4.46/4.73 cnf(c_0_11034, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk42_4(X2,X3,X4,X1)),X3)),c_Transitive__Closure_Ortrancl(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))), inference(rw,[status(thm)],[c_0_6493, c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_11035, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk388_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6494]), ['final']). 4.46/4.73 cnf(c_0_11036, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X5),X3)),hAPP(X5,X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))|hAPP(X5,X2)=c_Groups_Ozero__class_Ozero(X4)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Fields_Ofield(X4)), inference(split_conjunct,[status(thm)],[c_0_6495]), ['final']). 4.46/4.73 cnf(c_0_11037, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6496, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11038, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6497, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11039, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk526_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2),X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_6498]), ['final']). 4.46/4.73 cnf(c_0_11040, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk427_4(X3,X4,X2,X1))),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3))))), inference(rw,[status(thm)],[c_0_6499, c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_11041, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6500, c_0_5266]), c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_11042, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X4|hBOOL(hAPP(hAPP(c_member(X1),hAPP(X3,X4)),X4))|~c_Finite__Set_Ofolding__one(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(X2,esk136_4(X4,X3,X2,X1)),esk137_4(X4,X3,X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk136_4(X4,X3,X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk137_4(X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_6501]), ['final']). 4.46/4.73 cnf(c_0_11043, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk32_5(X2,X3,X4,X5,X1)),X4)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X3)),X2)))), inference(split_conjunct,[status(thm)],[c_0_6375]), ['final']). 4.46/4.73 cnf(c_0_11044, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk366_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X2),X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6502]), ['final']). 4.46/4.73 cnf(c_0_11045, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X5),X3)),hAPP(X5,X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Oab__group__add(X4)), inference(split_conjunct,[status(thm)],[c_0_6503]), ['final']). 4.46/4.73 cnf(c_0_11046, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6504, c_0_4760]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), ['final']). 4.46/4.73 cnf(c_0_11047, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6505, c_0_4760]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), ['final']). 4.46/4.73 cnf(c_0_11048, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X3)),X4)),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))),X4)|~class_Rings_Osemiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_6506]), ['final']). 4.46/4.73 cnf(c_0_11049, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk425_5(X3,X4,X5,X2,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6373]), ['final']). 4.46/4.73 cnf(c_0_11050, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk128_5(X3,X4,X5,X2,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6374]), ['final']). 4.46/4.73 cnf(c_0_11051, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X1),X5))))|hAPP(X1,X2)!=hAPP(X1,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,X5)))), inference(split_conjunct,[status(thm)],[c_0_6399]), ['final']). 4.46/4.73 cnf(c_0_11052, plain, (c_Map_Omap__upds(X3,X1,c_Map_Orestrict__map(X3,X1,X6,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X5),hAPP(c_List_Oset(X3),X4))),X4,X2)=c_Map_Orestrict__map(X3,X1,c_Map_Omap__upds(X3,X1,X6,X4,X2),X5)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_List_Oset(X3),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_6507]), ['final']). 4.46/4.73 cnf(c_0_11053, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5146]), ['final']). 4.46/4.73 cnf(c_0_11054, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)),hAPP(X5,X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))|~class_Rings_Oring(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(hAPP(c_member(X2),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_6508]), ['final']). 4.46/4.73 cnf(c_0_11055, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5)), inference(split_conjunct,[status(thm)],[c_0_6509]), ['final']). 4.46/4.73 cnf(c_0_11056, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5)), inference(split_conjunct,[status(thm)],[c_0_5794]), ['final']). 4.46/4.73 cnf(c_0_11057, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_6510]), ['final']). 4.46/4.73 cnf(c_0_11058, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),esk378_3(X1,X2,X3))),esk379_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk378_3(X1,X2,X3)),esk379_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_6511, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11059, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X2),X1)),c_List_Olistrel1(X3,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X3),X6),X1))),c_List_Olistrel1(X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_6296]), ['final']). 4.46/4.73 cnf(c_0_11060, plain, (hAPP(X1,esk79_4(X2,X1,X3,X4))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X1,hAPP(c_Nat_OSuc,esk78_4(X2,X1,X3,X4)))),hAPP(X1,esk78_4(X2,X1,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))), inference(rw,[status(thm)],[c_0_6512, c_0_5644]), ['final']). 4.46/4.73 cnf(c_0_11061, plain, (c_Groups_Oone__class_Oone(X1)=X2|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Groups_Oone__class_Oone(X1)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(c_Power_Opower__class_Opower(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_6513]), ['final']). 4.46/4.73 cnf(c_0_11062, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X4)),X5)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool))),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_6514]), ['final']). 4.46/4.73 cnf(c_0_11063, plain, (hAPP(c_Set_Oimage(tc_prod(X2,X5),tc_prod(X1,X4),c_Product__Type_Omap__pair(X2,X1,X5,X4,X3,X6)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X2,X5),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X4),tc_HOL_Obool))|c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X2,X1,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))|c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X5,X4,X6),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_6515]), ['final']). 4.46/4.73 cnf(c_0_11064, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk471_5(X2,X3,X4,X5,X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Oordered__comm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6290]), ['final']). 4.46/4.73 cnf(c_0_11065, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk219_5(X2,X3,X4,X5,X1)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hBOOL(hAPP(X2,X7))|~hBOOL(hAPP(hAPP(c_member(X5),X6),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X7),hAPP(X3,X6)))), inference(split_conjunct,[status(thm)],[c_0_6516]), ['final']). 4.46/4.73 cnf(c_0_11066, plain, (hBOOL(hAPP(hAPP(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk38_3(X1,X2,X3))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk39_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk39_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6517]), ['final']). 4.46/4.73 cnf(c_0_11067, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4)))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_6518]), ['final']). 4.46/4.73 cnf(c_0_11068, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk168_5(X3,X4,X5,X2,X1)),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X4))))|c_List_Olist__all2(X1,X2,X3,X5,X4)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5)), inference(split_conjunct,[status(thm)],[c_0_6519]), ['final']). 4.46/4.73 cnf(c_0_11069, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk491_5(X3,X4,X5,X2,X1)),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X3))))|c_List_Olist__all2(X1,X2,X5,X4,X3)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_6520]), ['final']). 4.46/4.73 cnf(c_0_11070, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X2)),X2),X1))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))), inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6521, c_0_5100]), c_0_6344])])]), ['final']). 4.46/4.73 cnf(c_0_11071, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X3,tc_HOL_Obool),X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X3,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_Set_Oinsert(X3)),X4)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X2)=hAPP(c_Set_Oimage(X1,X3,X4),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6522]), ['final']). 4.46/4.73 cnf(c_0_11072, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1))), inference(er,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6523, c_0_5100]), c_0_6344])]), c_0_6524])]), ['final']). 4.46/4.73 cnf(c_0_11073, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6525, c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), ['final']). 4.46/4.73 cnf(c_0_11074, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X6),X2),hAPP(c_Set_Oimage(X5,X1,X3),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X6),hAPP(c_Fun_Ocomp(X1,X6,X5,X2),X3)),X4)|esk158_6(X1,X2,X3,X4,X5,X6)!=esk159_6(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Ocomm__monoid__add(X6)), inference(split_conjunct,[status(thm)],[c_0_6326]), ['final']). 4.46/4.73 cnf(c_0_11075, plain, (hAPP(c_Map_Omap__of(X1,X2),X4)=hAPP(c_Map_Omap__of(X1,X2),X3)|hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),esk122_4(X4,X3,X2,X1))!=hAPP(hAPP(c_Map_Omap__of(X1,X2),X4),esk122_4(X4,X3,X2,X1))|hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4))!=hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_6310]), ['final']). 4.46/4.73 cnf(c_0_11076, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),X4))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6526]), ['final']). 4.46/4.73 cnf(c_0_11077, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3)))|~class_Groups_Oab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_6527]), ['final']). 4.46/4.73 cnf(c_0_11078, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))=X1|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))), inference(split_conjunct,[status(thm)],[c_0_6528]), ['final']). 4.46/4.73 cnf(c_0_11079, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk444_2(X1,X2)))))|hBOOL(hAPP(X1,esk445_2(X1,X2)))|hBOOL(hAPP(X1,esk443_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,X3))), inference(rw,[status(thm)],[c_0_6529, c_0_6410]), ['final']). 4.46/4.73 cnf(c_0_11080, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X1)),c_FunDef_Omax__weak))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_6530]), ['final']). 4.46/4.73 cnf(c_0_11081, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6531, c_0_4760]), c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11082, plain, (hAPP(c_Map_Omap__of(X1,X2),X3)=hAPP(c_Map_Omap__of(X1,X2),X4)|hAPP(c_List_Oset(tc_prod(X1,X2)),X3)!=hAPP(c_List_Oset(tc_prod(X1,X2)),X4)|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4)))), inference(split_conjunct,[status(thm)],[c_0_6532]), ['final']). 4.46/4.73 cnf(c_0_11083, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X1,tc_HOL_Obool)),X4),X2)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk470_7(X3,X4,X2,X1,X5,X6,X7))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X6),X5)))|~c_Equiv__Relations_Ocongruent(X7,tc_fun(X1,tc_HOL_Obool),X5,X2)|~c_Equiv__Relations_Oequiv(X7,X6,X5)), inference(split_conjunct,[status(thm)],[c_0_6337]), ['final']). 4.46/4.73 cnf(c_0_11084, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)))=hAPP(hAPP(c_List_Olist_OCons(X1),X4),hAPP(c_List_Ofilter(X1,X2),X5))|hBOOL(hAPP(hAPP(c_member(X1),esk154_7(hAPP(c_List_Ofilter(X1,X2),X5),X4,hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)),X2,X1,X3,X5)),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4))), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6533])]), ['final']). 4.46/4.73 cnf(c_0_11085, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X4))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_6534]), ['final']). 4.46/4.73 cnf(c_0_11086, plain, (c_List_Olist__all2(X1,X5,hAPP(hAPP(c_COMBC(X1,tc_fun(X5,X2),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X5,X2),tc_fun(X5,tc_HOL_Obool)),X1),c_COMBB(X2,tc_HOL_Obool,X5)),X3)),X6),X4,X7)|~c_List_Olist__all2(X1,X2,X3,X4,hAPP(hAPP(c_List_Omap(X5,X2),X6),X7))), inference(split_conjunct,[status(thm)],[c_0_6535]), ['final']). 4.46/4.73 cnf(c_0_11087, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X3))|~c_Equiv__Relations_Oequiv(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))))), inference(split_conjunct,[status(thm)],[c_0_6536]), ['final']). 4.46/4.73 cnf(c_0_11088, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X6),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk372_8(X3,X6,X5,X5,X4,X4,X1,X2)),X5))|~class_Orderings_Oord(X1)|~class_Groups_Ocomm__monoid__add(X2)), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6537])]), ['final']). 4.46/4.73 cnf(c_0_11089, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X6),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),esk372_8(X3,X6,X5,X5,X4,X4,X1,X2)))|~class_Orderings_Oord(X1)|~class_Groups_Ocomm__monoid__add(X2)), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6538])]), ['final']). 4.46/4.73 cnf(c_0_11090, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X4))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_6539]), ['final']). 4.46/4.73 cnf(c_0_11091, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X2)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6540, c_0_4609]), c_0_5671]), c_0_6151]), ['final']). 4.46/4.73 cnf(c_0_11092, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X2)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6541, c_0_4609]), c_0_5671]), c_0_6151]), ['final']). 4.46/4.73 cnf(c_0_11093, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk291_4(X1,X2,X3,X4)),esk290_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6487]), ['final']). 4.46/4.73 cnf(c_0_11094, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk350_4(X2,X3,X4,X1)),esk349_4(X2,X3,X4,X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))), inference(split_conjunct,[status(thm)],[c_0_6488]), ['final']). 4.46/4.73 cnf(c_0_11095, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk256_3(X1,X2,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(c_Nat_OSuc,esk255_3(X1,X2,X3)))),hAPP(X2,esk255_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))), inference(rw,[status(thm)],[c_0_6542, c_0_5644]), ['final']). 4.46/4.73 cnf(c_0_11096, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6543, c_0_4517]), c_0_4517]), c_0_4517]), ['final']). 4.46/4.73 cnf(c_0_11097, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk232_5(X2,X3,X4,X1,X5)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(c_Finite__Set_Ocard(X1),X4))),X2)))|~class_Rings_Osemiring__1(X5)|~class_Groups_Oordered__ab__semigroup__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6482]), ['final']). 4.46/4.73 cnf(c_0_11098, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk72_3(X1,X2,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(c_Nat_OSuc,esk71_3(X1,X2,X3)))),hAPP(X2,esk71_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))), inference(rw,[status(thm)],[c_0_6544, c_0_5644]), ['final']). 4.46/4.73 cnf(c_0_11099, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(X2,c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(c_Set_Oimage(X1,X1,X2),X3))|~class_Orderings_Olinorder(X1)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk281_3(X3,X2,X1))),hAPP(X2,esk282_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk281_3(X3,X2,X1)),esk282_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6545]), ['final']). 4.46/4.73 cnf(c_0_11100, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(X2,c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))=c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(c_Set_Oimage(X1,X1,X2),X3))|~class_Orderings_Olinorder(X1)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk354_3(X3,X2,X1))),hAPP(X2,esk355_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk354_3(X3,X2,X1)),esk355_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6546]), ['final']). 4.46/4.73 cnf(c_0_11101, plain, (hAPP(hAPP(c_List_Ozip(X1,X3),hAPP(hAPP(c_List_Oappend(X1),X2),X6)),hAPP(hAPP(c_List_Oappend(X3),X4),X5))=hAPP(hAPP(c_List_Oappend(tc_prod(X1,X3)),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4)),hAPP(hAPP(c_List_Ozip(X1,X3),X6),X5))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X6)), inference(split_conjunct,[status(thm)],[c_0_6547]), ['final']). 4.46/4.73 cnf(c_0_11102, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk79_4(X2,X3,X4,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk78_4(X2,X3,X4,X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X4))), inference(split_conjunct,[status(thm)],[c_0_5066]), ['final']). 4.46/4.73 cnf(c_0_11103, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk79_4(X1,X2,X3,X4)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk78_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X4)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_5066]), ['final']). 4.46/4.73 cnf(c_0_11104, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(c_List_Ofilter(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X6)),X3)),X4)=hAPP(c_Option_Ooption_OSome(X2),X5)|hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),X4)!=hAPP(c_Option_Ooption_OSome(X2),X5)|~hBOOL(hAPP(hAPP(X6,X4),X5))), inference(split_conjunct,[status(thm)],[c_0_6548]), ['final']). 4.46/4.73 cnf(c_0_11105, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Ozip(X2,X3),X4),X5)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Otake(tc_prod(X2,X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X5))),hAPP(hAPP(c_List_Ozip(X2,X3),X4),X5))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6549, c_0_4986]), c_0_4986]), c_0_6550]), ['final']). 4.46/4.73 cnf(c_0_11106, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6551, c_0_4760]), c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11107, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X1),X2)),X3)),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_6552]), c_0_6553]), c_0_6554]), ['final']). 4.46/4.73 cnf(c_0_11108, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))|c_Map_Omap__add(X1,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),X5),X2),hAPP(c_Option_Ooption_OSome(X3),X6)),X4)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),c_Map_Omap__add(X1,X3,X5,X4)),X2),hAPP(c_Option_Ooption_OSome(X3),X6))), inference(split_conjunct,[status(thm)],[c_0_6555]), ['final']). 4.46/4.73 cnf(c_0_11109, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|X2!=hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_4971]), ['final']). 4.46/4.73 cnf(c_0_11110, plain, (X3=X4|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_Enum_Oenum__class_Oenum(X2))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_Enum_Oenum__class_Oenum(X2))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)|hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),X1,X2,c_Option_Othe(X1)),hAPP(c_Map_Omap__of(X2,X1),hAPP(hAPP(c_List_Ozip(X2,X1),c_Enum_Oenum__class_Oenum(X2)),X3)))!=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),X1,X2,c_Option_Othe(X1)),hAPP(c_Map_Omap__of(X2,X1),hAPP(hAPP(c_List_Ozip(X2,X1),c_Enum_Oenum__class_Oenum(X2)),X4)))), inference(split_conjunct,[status(thm)],[c_0_6556]), ['final']). 4.46/4.73 cnf(c_0_11111, plain, (X2=X3|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))), inference(rw,[status(thm)],[c_0_6557, c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_11112, plain, (hAPP(X2,X3)=hAPP(X2,X4)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X4),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X3),X6))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X3),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X4),X6))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6558]), ['final']). 4.46/4.73 cnf(c_0_11113, plain, (c_Hoare__Mirabelle_Ohoare__valids(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OWhile(X4,X5)),c_Hoare__Mirabelle_Opeek__and(X1,X3,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X4)))))|~c_Hoare__Mirabelle_Ohoare__valids(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,X4)),X5),X3)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6559, c_0_5580]), c_0_5580]), ['final']). 4.46/4.73 cnf(c_0_11114, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2)),X2))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk520_2(X2,X1)),esk521_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk520_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk521_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_6560]), ['final']). 4.46/4.73 cnf(c_0_11115, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4)=X5|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hAPP(hAPP(c_List_Oappend(X1),X2),X5)!=hAPP(hAPP(c_List_Oappend(X1),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_5038]), ['final']). 4.46/4.73 cnf(c_0_11116, plain, (c_List_OtakeWhile(tc_List_Olist(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X1))),X2)=c_List_Otranspose(X1,c_List_Otranspose(X1,X2))|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6561, c_0_5670]), c_0_5580]), c_0_5671]), ['final']). 4.46/4.73 cnf(c_0_11117, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OSup__fin(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6562]), ['final']). 4.46/4.73 cnf(c_0_11118, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OInf__fin(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6563]), ['final']). 4.46/4.73 cnf(c_0_11119, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Big__Operators_Olinorder__class_OMax(X1,X2)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6564]), ['final']). 4.46/4.73 cnf(c_0_11120, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olinorder__class_OMin(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6565]), ['final']). 4.46/4.73 cnf(c_0_11121, plain, (hAPP(hAPP(X3,X5),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),X4)|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))), inference(split_conjunct,[status(thm)],[c_0_6566]), ['final']). 4.46/4.73 cnf(c_0_11122, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X5),X3),X6)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X5),X4),X7)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X5),tc_HOL_Obool)),X6),X7))), inference(split_conjunct,[status(thm)],[c_0_6567]), ['final']). 4.46/4.73 cnf(c_0_11123, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6568]), ['final']). 4.46/4.73 cnf(c_0_11124, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))|hAPP(hAPP(c_List_Oappend(X2),X3),hAPP(hAPP(c_List_Olist__update(X2,X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))),X5))=hAPP(hAPP(c_List_Olist__update(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X4)),X1),X5)), inference(split_conjunct,[status(thm)],[c_0_6569]), ['final']). 4.46/4.73 cnf(c_0_11125, plain, (hAPP(hAPP(X6,hAPP(X5,X4)),hAPP(X5,X3))=hAPP(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X4),X3))|X1!=hAPP(X2,esk505_7(X3,X4,X5,X2,X1,X6,X7))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X4))|~c_Finite__Set_Ofolding__image__simple(X8,X7,X6,X1,X2,X5)), inference(split_conjunct,[status(thm)],[c_0_6230]), ['final']). 4.46/4.73 cnf(c_0_11126, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)))|hBOOL(hAPP(hAPP(X3,esk35_5(X5,X4,X2,X1,X3)),esk36_5(X5,X4,X2,X1,X3)))), inference(rw,[status(thm)],[c_0_6570, c_0_5580]), ['final']). 4.46/4.73 cnf(c_0_11127, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X2,X4)))|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X3),hAPP(hAPP(c_List_Olist_OCons(X5),X4),X6))=hAPP(hAPP(c_List_Olist_OCons(X5),X4),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X3),X6))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6571]), ['final']). 4.46/4.73 cnf(c_0_11128, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4))|~hBOOL(hAPP(X5,esk254_5(X5,X3,X4,X2,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6572, c_0_4531]), c_0_4531]), ['final']). 4.46/4.73 cnf(c_0_11129, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X4)),X2)),X3)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X1))), inference(split_conjunct,[status(thm)],[c_0_6438]), ['final']). 4.46/4.73 cnf(c_0_11130, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3,X5),tc_prod(X3,X5))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3,X5),tc_prod(X3,X5)),hAPP(hAPP(c_Product__Type_OPair(X3,X5),X1),X6)),hAPP(hAPP(c_Product__Type_OPair(X3,X5),X2),X7))),c_Wellfounded_Olex__prod(X3,X5,X4,X8)))), inference(split_conjunct,[status(thm)],[c_0_4988]), ['final']). 4.46/4.73 cnf(c_0_11131, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk180_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(hAPP(c_member(X1),esk179_4(X2,X3,X4,X1)),X3))|~hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_6573]), ['final']). 4.46/4.73 cnf(c_0_11132, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk326_6(X3,X4,X1,X5,X2,X6)),esk327_6(X3,X4,X1,X5,X2,X6))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X2)),X5),hAPP(hAPP(c_Relation_Orel__comp(X6,X1,X2),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_6574]), ['final']). 4.46/4.73 cnf(c_0_11133, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X4)),X2)),X3)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X1))), inference(split_conjunct,[status(thm)],[c_0_6439]), ['final']). 4.46/4.73 cnf(c_0_11134, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X1)),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X4))), inference(split_conjunct,[status(thm)],[c_0_6441]), ['final']). 4.46/4.73 cnf(c_0_11135, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X1)),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X4))), inference(split_conjunct,[status(thm)],[c_0_6442]), ['final']). 4.46/4.73 cnf(c_0_11136, plain, (hAPP(hAPP(X3,hAPP(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X7),X8))),hAPP(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X7),X8)))=hAPP(hAPP(X3,hAPP(X6,X7)),hAPP(X6,X8))|~c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X8))), inference(split_conjunct,[status(thm)],[c_0_6575]), ['final']). 4.46/4.73 cnf(c_0_11137, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk325_6(X3,X4,X2,X5,X6,X1)),esk326_6(X3,X4,X2,X5,X6,X1))),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X6)),X5),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X6),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_6574]), ['final']). 4.46/4.73 cnf(c_0_11138, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk143_2(X2,X1)),esk144_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk143_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk144_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_6576]), ['final']). 4.46/4.73 cnf(c_0_11139, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk522_2(X2,X1)),esk523_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk522_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk523_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_6577]), ['final']). 4.46/4.73 cnf(c_0_11140, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),esk498_3(X1,X2,X3)),esk499_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6578]), ['final']). 4.46/4.73 cnf(c_0_11141, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2)),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X3))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_6579]), ['final']). 4.46/4.73 cnf(c_0_11142, plain, (hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Otake(X2),X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Odrop(X2),X1),X3))),c_List_Olist_ONil(X2)))=hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_OSuc,X1)),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6580]), ['final']). 4.46/4.73 cnf(c_0_11143, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(hAPP(c_member(X2),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_6581]), ['final']). 4.46/4.73 cnf(c_0_11144, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk378_3(X1,X2,X3)),esk379_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_5086]), ['final']). 4.46/4.73 cnf(c_0_11145, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk246_3(X1,X2,X3)),esk247_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_5045]), ['final']). 4.46/4.73 cnf(c_0_11146, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk229_3(X1,X2,X3)),esk230_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_4519]), ['final']). 4.46/4.73 cnf(c_0_11147, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk409_3(X1,X2,X3)),esk410_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_4513]), ['final']). 4.46/4.73 cnf(c_0_11148, plain, (hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|hAPP(hAPP(X3,X5),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),hAPP(hAPP(c_Set_Oinsert(X1),X5),X4))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_6582]), ['final']). 4.46/4.73 cnf(c_0_11149, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(hAPP(c_member(X2),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_6583]), ['final']). 4.46/4.73 cnf(c_0_11150, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk38_3(X1,X2,X3)),esk39_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6517]), ['final']). 4.46/4.73 cnf(c_0_11151, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk427_4(X2,X3,X4,X1)),X3)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))), inference(rw,[status(thm)],[c_0_6584, c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_11152, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk42_4(X3,X4,X2,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3))))), inference(rw,[status(thm)],[c_0_6585, c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_11153, plain, (c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X6),X7))=c_Map_Omap__upds(X1,X2,X3,X5,X7)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X7)),X5))))), inference(rw,[status(thm)],[c_0_6586, c_0_6224]), ['final']). 4.46/4.73 cnf(c_0_11154, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk64_3(X3,X2,X1)),X2))|esk66_3(X3,X2,X1)!=esk65_3(X3,X2,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))), inference(csr,[status(thm)],[c_0_6587, c_0_6445]), ['final']). 4.46/4.73 cnf(c_0_11155, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X4)),hAPP(hAPP(c_Relation_Oinv__image(X1,X6),X5),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,X3)),hAPP(X2,X4))),X5))), inference(split_conjunct,[status(thm)],[c_0_6588]), ['final']). 4.46/4.73 cnf(c_0_11156, plain, (c_Relation_Orefl__on(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X3))|~c_Relation_Orefl__on(X1,hAPP(X2,esk209_5(X3,X2,X1,X4,X5)),hAPP(X3,esk209_5(X3,X2,X1,X4,X5)))), inference(split_conjunct,[status(thm)],[c_0_6589]), ['final']). 4.46/4.73 cnf(c_0_11157, plain, (c_Map_Oran(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3))=hAPP(c_Relation_ORange(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))), inference(rw,[status(thm)],[c_0_6590, c_0_6591]), ['final']). 4.46/4.73 cnf(c_0_11158, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(hAPP(c_Set_Oinsert(X1),hAPP(hAPP(c_List_Onth(X1),X2),X4)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X4),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6592]), ['final']). 4.46/4.73 cnf(c_0_11159, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X4))|~class_Groups_Oab__group__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_6593]), ['final']). 4.46/4.73 cnf(c_0_11160, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)))),X3))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(rw,[status(thm)],[c_0_6594, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11161, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)))),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(rw,[status(thm)],[c_0_6595, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11162, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|c_Lazy__Sequence_Ohb__flat(X3,c_Lazy__Sequence_Ohb__map(X2,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X3)),hAPP(hAPP(c_COMBC(X2,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X3))),X5),X1),hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))=hAPP(c_New__DSequence_Oneg__decr__bind(X2,X3,X4,X5),X1)), inference(rw,[status(thm)],[c_0_6596, c_0_6597]), ['final']). 4.46/4.73 cnf(c_0_11163, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk463_4(X1,X2,X3,X4)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6405]), ['final']). 4.46/4.73 cnf(c_0_11164, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk317_4(X4,X1,X3,X2)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[c_0_6598, c_0_5134]), ['final']). 4.46/4.73 cnf(c_0_11165, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X1))),hAPP(X4,hAPP(c_Nat_OSuc,X1)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1)))|~class_Groups_Ocomm__monoid__add(X3)), inference(split_conjunct,[status(thm)],[c_0_6599]), ['final']). 4.46/4.73 cnf(c_0_11166, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Groups_Oone__class_Oone(X1)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),c_Nat_Osemiring__1__class_Oof__nat(X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_6600]), ['final']). 4.46/4.73 cnf(c_0_11167, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X3))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(er,[status(thm)],[c_0_6601]), ['final']). 4.46/4.73 cnf(c_0_11168, plain, (hAPP(hAPP(c_List_Odrop(X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),c_List_OtakeWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)))),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))=hAPP(hAPP(c_List_Odrop(X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),c_List_OtakeWhile(X3,X1,X4))),X4)|~hBOOL(hAPP(X1,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6602, c_0_4916]), c_0_4916]), ['final']). 4.46/4.73 cnf(c_0_11169, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=esk499_3(X1,X2,X3)|hBOOL(hAPP(hAPP(X1,esk499_3(X1,X2,X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk498_3(X1,X2,X3),esk499_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6578]), ['final']). 4.46/4.73 cnf(c_0_11170, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X3)),X2)),X3)),X2))), inference(rw,[status(thm)],[c_0_6603, c_0_5689]), ['final']). 4.46/4.73 cnf(c_0_11171, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X2)),X3)),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X5)|~class_Rings_Oring(X1)), inference(er,[status(thm)],[c_0_6604]), ['final']). 4.46/4.73 cnf(c_0_11172, plain, (hAPP(hAPP(c_List_Oappend(X3),hAPP(hAPP(c_List_Otake(X3),X1),X4)),hAPP(hAPP(c_List_Otake(X3),X2),hAPP(hAPP(c_List_Odrop(X3),X1),X4)))=hAPP(hAPP(c_List_Otake(X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)))), inference(split_conjunct,[status(thm)],[c_0_6605]), ['final']). 4.46/4.73 cnf(c_0_11173, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk392_3(X2,X3,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)))|hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6606]), ['final']). 4.46/4.73 cnf(c_0_11174, plain, (X1=X2|hAPP(c_List_Oset(X3),X1)!=hAPP(c_List_Oset(X3),X2)|~c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X5),X2))|~c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X5),X1))|~c_Fun_Oinj__on(X3,X4,X5,hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Oappend(X3),X1),X2)))|~class_Orderings_Olinorder(X4)|~hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(X3,X4),X5),X2)))|~hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(X3,X4),X5),X1)))), inference(rw,[status(thm)],[c_0_6607, c_0_6608]), ['final']). 4.46/4.73 cnf(c_0_11175, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk197_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6609]), ['final']). 4.46/4.73 cnf(c_0_11176, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk104_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6610]), ['final']). 4.46/4.73 cnf(c_0_11177, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk106_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6611]), ['final']). 4.46/4.73 cnf(c_0_11178, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4))=hAPP(hAPP(c_List_Oappend(X1),X3),X4)|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)!=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))), inference(er,[status(thm)],[c_0_6612]), ['final']). 4.46/4.73 cnf(c_0_11179, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|hAPP(hAPP(X4,X3),hAPP(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=hAPP(X5,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Finite__Set_Ofolding__one(X1,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_6613]), ['final']). 4.46/4.73 cnf(c_0_11180, plain, (X5=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X4)),X2)),X3)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X1))), inference(split_conjunct,[status(thm)],[c_0_5097]), ['final']). 4.46/4.73 cnf(c_0_11181, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6614]), ['final']). 4.46/4.73 cnf(c_0_11182, plain, (X1=X2|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X2),X6)),X1),X7)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X1),X7)),X2),X6)), inference(split_conjunct,[status(thm)],[c_0_6615]), ['final']). 4.46/4.73 cnf(c_0_11183, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk450_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6616]), ['final']). 4.46/4.73 cnf(c_0_11184, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),esk314_4(X3,X1,X4,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk313_4(X3,X1,X4,X2)),esk315_4(X3,X1,X4,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X4),X1)),c_List_Olistrel1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_6617]), ['final']). 4.46/4.73 cnf(c_0_11185, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),esk314_4(X3,X4,X1,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk312_4(X3,X4,X1,X2)),esk315_4(X3,X4,X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X1),X4)),c_List_Olistrel1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_6617]), ['final']). 4.46/4.73 cnf(c_0_11186, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6618]), ['final']). 4.46/4.73 cnf(c_0_11187, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6619]), ['final']). 4.46/4.73 cnf(c_0_11188, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6620]), ['final']). 4.46/4.73 cnf(c_0_11189, plain, (hAPP(hAPP(X3,X5),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),hAPP(hAPP(c_Set_Oinsert(X1),X5),X4))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_6621]), ['final']). 4.46/4.73 cnf(c_0_11190, plain, (X4=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X5),X3),c_List_Oremove1(X2,X3,X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X4)))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X5),X4))|hAPP(c_List_Ohd(X2),hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),hAPP(c_fequal,hAPP(X5,X3))),X5)),X4))!=X3), inference(split_conjunct,[status(thm)],[c_0_6622]), ['final']). 4.46/4.73 cnf(c_0_11191, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2),X3)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(rw,[status(thm)],[c_0_6623, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11192, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6624, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_6625]), c_0_4436]), c_0_6626]), ['final']). 4.46/4.73 cnf(c_0_11193, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X2,tc_Option_Ooption(X1)),X3),X4),hAPP(c_Option_Ooption_OSome(X1),X5))),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_6627]), ['final']). 4.46/4.73 cnf(c_0_11194, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1))),X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_6628]), ['final']). 4.46/4.73 cnf(c_0_11195, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1))),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6629]), ['final']). 4.46/4.73 cnf(c_0_11196, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6630, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_6631]), ['final']). 4.46/4.73 cnf(c_0_11197, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X6),hAPP(c_List_Ofilter(X2,X5),X4))=hAPP(c_List_Ofilter(X2,X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X6),X4))|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))|~hBOOL(hAPP(X5,X6))), inference(split_conjunct,[status(thm)],[c_0_6632]), ['final']). 4.46/4.73 cnf(c_0_11198, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6633, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4912]), ['final']). 4.46/4.73 cnf(c_0_11199, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5)),X4)|~class_Rings_Osemiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_6634]), ['final']). 4.46/4.73 cnf(c_0_11200, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk538_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3)))=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk536_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3)))=X1|epred2_3(X3,X2,X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6635, c_0_4760]), c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11201, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X5),X3)|hAPP(X5,X2)=c_Groups_Ozero__class_Ozero(X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Fields_Ofield(X4)), inference(split_conjunct,[status(thm)],[c_0_6495]), ['final']). 4.46/4.73 cnf(c_0_11202, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OWhile(X4,X5)),c_Hoare__Mirabelle_Opeek__and(X1,X3,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X4)))))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,X4)),X5),X3)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6636, c_0_5580]), c_0_5580]), ['final']). 4.46/4.73 cnf(c_0_11203, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5)),X3)),X4)),X6))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_6458]), ['final']). 4.46/4.73 cnf(c_0_11204, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk28_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk27_3(X1,X2,X3)))=X1|hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(rw,[status(thm)],[c_0_6637, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11205, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk311_4(X1,X2,X3,X4)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))), inference(split_conjunct,[status(thm)],[c_0_6638]), ['final']). 4.46/4.73 cnf(c_0_11206, plain, (hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)=hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X1))),X1)|hBOOL(hAPP(X3,X4))|X1!=hAPP(hAPP(c_List_Oappend(X2),c_List_OtakeWhile(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5))), inference(rw,[status(thm)],[c_0_6639, c_0_4916]), ['final']). 4.46/4.73 cnf(c_0_11207, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk156_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk155_3(X1,X2,X3)))=X1|hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_6640, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11208, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))|~class_Int_Onumber(X1)|~class_Rings_Osemiring(X1)), inference(split_conjunct,[status(thm)],[c_0_6641]), ['final']). 4.46/4.73 cnf(c_0_11209, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5)),X3)),X4)),X6))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_6463]), ['final']). 4.46/4.73 cnf(c_0_11210, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X5),X2)),X3)),X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_6464]), ['final']). 4.46/4.73 cnf(c_0_11211, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X5),X2)),X3)),X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_6465]), ['final']). 4.46/4.73 cnf(c_0_11212, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_6642]), ['final']). 4.46/4.73 cnf(c_0_11213, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X3),hAPP(hAPP(c_Relation_Orel__comp(X2,X2,X2),X4),c_Transitive__Closure_Ortrancl(X2,X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X3),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),X1),X4)))), inference(rw,[status(thm)],[c_0_6643, c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_11214, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk221_5(X2,X3,X4,X5,X1)),hAPP(X3,esk220_5(X2,X3,X4,X5,X1))))|hBOOL(hAPP(X2,X6))|~hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_6516]), ['final']). 4.46/4.73 cnf(c_0_11215, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(X6,X2)),hAPP(X6,X3))),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Oinv__image(X4,X1),X5),X6)))), inference(split_conjunct,[status(thm)],[c_0_6588]), ['final']). 4.46/4.73 cnf(c_0_11216, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4))|~class_Rings_Oring(X1)|~class_Int_Onumber(X1)), inference(split_conjunct,[status(thm)],[c_0_6644]), ['final']). 4.46/4.73 cnf(c_0_11217, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X4,X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),hAPP(hAPP(c_Set_Oinsert(X2),X5),X3))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6645]), ['final']). 4.46/4.73 cnf(c_0_11218, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X4,X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),hAPP(hAPP(c_Set_Oinsert(X2),X5),X3))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6646]), ['final']). 4.46/4.73 cnf(c_0_11219, plain, (hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X6))=hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6))|~c_Finite__Set_Ofolding(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),X6)), inference(split_conjunct,[status(thm)],[c_0_6647]), ['final']). 4.46/4.73 cnf(c_0_11220, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X3),X4)))|c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X4|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk183_5(X3,X2,X4,X5,X1))),hAPP(X3,esk183_5(X3,X2,X4,X5,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6372]), ['final']). 4.46/4.73 cnf(c_0_11221, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk312_4(X2,X3,X4,X1)),esk313_4(X2,X3,X4,X1))),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olistrel1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_6617]), ['final']). 4.46/4.73 cnf(c_0_11222, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X5,X3)),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X5),c_List_Oremove1(X2,X3,X4))))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X5),X4))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_6648]), ['final']). 4.46/4.73 cnf(c_0_11223, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X4))),X3)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_6649, c_0_4912]), ['final']). 4.46/4.73 cnf(c_0_11224, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X2))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk65_3(X3,X2,X1)),esk66_3(X3,X2,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(c_Finite__Set_Ocard(X1),esk64_3(X3,X2,X1))!=X3|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))), inference(csr,[status(thm)],[c_0_6650, c_0_6445]), ['final']). 4.46/4.73 cnf(c_0_11225, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2))),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Olist_OCons(X1),X3),hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2))),X4))|X2=X3), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6651, c_0_5671]), c_0_5671]), ['final']). 4.46/4.73 cnf(c_0_11226, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),X2))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),esk440_2(X2,X1)),esk441_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk440_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk441_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_6652]), ['final']). 4.46/4.73 cnf(c_0_11227, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),X2))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),esk278_2(X2,X1)),esk279_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk278_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk279_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_6653]), ['final']). 4.46/4.73 cnf(c_0_11228, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk307_5(X2,X3,X4,X5,X1)),esk308_5(X2,X3,X4,X5,X1))=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)),X3)),c_List_Olistrel(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_6398]), ['final']). 4.46/4.73 cnf(c_0_11229, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Rings_Oinverse__class_Odivide(X1)),X3)),X4)),X5)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5)),X4)|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_6654]), ['final']). 4.46/4.73 cnf(c_0_11230, plain, (hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),hAPP(hAPP(c_Set_Oinsert(X1),X5),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X5),X6)),X4)|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_6655]), ['final']). 4.46/4.73 cnf(c_0_11231, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)=c_Int_OMin|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6656, c_0_6631]), c_0_4609]), c_0_6657]), c_0_4760]), c_0_4912]), c_0_6658]), c_0_6659]), c_0_4609]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_11232, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(X4,X3),hAPP(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=hAPP(X5,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Finite__Set_Ofolding__one(X1,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_6660]), ['final']). 4.46/4.73 cnf(c_0_11233, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3)),hAPP(X4,X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6661]), ['final']). 4.46/4.73 cnf(c_0_11234, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4,X1))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6662]), ['final']). 4.46/4.73 cnf(c_0_11235, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk126_5(X2,X3,X4,X5,X1)),esk127_5(X2,X3,X4,X5,X1))=X5|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_6397]), ['final']). 4.46/4.73 cnf(c_0_11236, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk263_3(X3,X2,X1)),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3))))), inference(rw,[status(thm)],[c_0_6663, c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_11237, plain, (X2=X3|hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X5),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X5))))), inference(split_conjunct,[status(thm)],[c_0_6664]), ['final']). 4.46/4.73 cnf(c_0_11238, plain, (c_Equiv__Relations_Ocongruent(X1,X2,X4,X3)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X2),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X1,X2),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X2,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X3))),X3)),esk500_4(X3,X4,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_6253]), ['final']). 4.46/4.73 cnf(c_0_11239, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))),hAPP(X2,X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))|~class_Groups_Ocomm__monoid__add(X1)), inference(rw,[status(thm)],[c_0_6665, c_0_5884]), ['final']). 4.46/4.73 cnf(c_0_11240, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6666, c_0_6631]), c_0_4609]), c_0_6657]), c_0_4760]), c_0_4912]), c_0_6658]), c_0_6667]), c_0_4609]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_11241, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))),c_Int_Ointrel))), inference(split_conjunct,[status(thm)],[c_0_6323]), ['final']). 4.46/4.73 cnf(c_0_11242, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),c_Transitive__Closure_Ortrancl(X5,X2)))|esk485_5(X1,X2,X3,X4,X5)!=esk484_5(X1,X2,X3,X4,X5)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X2),X1))))), inference(split_conjunct,[status(thm)],[c_0_6204]), ['final']). 4.46/4.73 cnf(c_0_11243, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),c_Transitive__Closure_Ortrancl(X5,X2)))|esk478_5(X1,X2,X3,X4,X5)!=esk479_5(X1,X2,X3,X4,X5)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X2),X1))))), inference(split_conjunct,[status(thm)],[c_0_6205]), ['final']). 4.46/4.73 cnf(c_0_11244, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X3,X1))), inference(rw,[status(thm)],[c_0_6668, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11245, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))),X3)|hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6669, c_0_4609]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_11246, plain, (X4=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X5),X2)),X3)),X6)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)|~class_Rings_Oring(X1)), inference(split_conjunct,[status(thm)],[c_0_5114]), ['final']). 4.46/4.73 cnf(c_0_11247, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X1),X5))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_6670]), ['final']). 4.46/4.73 cnf(c_0_11248, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))|c_Fun_Oinj__on(X4,X1,X2,hAPP(hAPP(c_Set_Oinsert(X4),X3),X5))|~c_Fun_Oinj__on(X4,X1,X2,X5)), inference(split_conjunct,[status(thm)],[c_0_6671]), ['final']). 4.46/4.73 cnf(c_0_11249, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X1))), inference(rw,[status(thm)],[c_0_6672, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11250, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk105_4(X1,X2,X3,X4)),esk104_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6610]), ['final']). 4.46/4.73 cnf(c_0_11251, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk198_4(X2,X3,X4,X1)),esk197_4(X2,X3,X4,X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X4)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))), inference(split_conjunct,[status(thm)],[c_0_6609]), ['final']). 4.46/4.73 cnf(c_0_11252, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk451_4(X1,X2,X3,X4)),esk450_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6616]), ['final']). 4.46/4.73 cnf(c_0_11253, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk107_4(X1,X2,X3,X4)),esk106_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6611]), ['final']). 4.46/4.73 cnf(c_0_11254, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X3,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X3,X2))=c_Smallcheck_Osmall_H(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_6673]), ['final']). 4.46/4.73 cnf(c_0_11255, plain, (X4=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X5|hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5))=hAPP(hAPP(X2,hAPP(X3,X4)),hAPP(X3,X5))|~c_Finite__Set_Ofolding__one(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_6674]), ['final']). 4.46/4.73 cnf(c_0_11256, plain, (hBOOL(hAPP(X1,esk480_3(X2,X1,X3)))|hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6675]), ['final']). 4.46/4.73 cnf(c_0_11257, plain, (hBOOL(hAPP(X1,esk442_3(X2,X1,X3)))|hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5144]), ['final']). 4.46/4.73 cnf(c_0_11258, plain, (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1))),X4)),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),X4)))), inference(split_conjunct,[status(thm)],[c_0_6676]), ['final']). 4.46/4.73 cnf(c_0_11259, plain, (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1))),X4)),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),X4)))), inference(split_conjunct,[status(thm)],[c_0_6677]), ['final']). 4.46/4.73 cnf(c_0_11260, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X3),X5))=hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~c_Relation_Osingle__valued(X1,X2,hAPP(c_Relation_Oconverse(X2,X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6678]), ['final']). 4.46/4.73 cnf(c_0_11261, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))), inference(split_conjunct,[status(thm)],[c_0_6679]), ['final']). 4.46/4.73 cnf(c_0_11262, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))), inference(split_conjunct,[status(thm)],[c_0_6680]), ['final']). 4.46/4.73 cnf(c_0_11263, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))), inference(split_conjunct,[status(thm)],[c_0_6681]), ['final']). 4.46/4.73 cnf(c_0_11264, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6682]), ['final']). 4.46/4.73 cnf(c_0_11265, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk494_6(X3,X4,X5,X2,X1,X6)),esk495_6(X3,X4,X5,X2,X1,X6))=X6|hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(X5,tc_HOL_Obool)),X3),X6)))), inference(split_conjunct,[status(thm)],[c_0_6683]), ['final']). 4.46/4.73 cnf(c_0_11266, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))), inference(split_conjunct,[status(thm)],[c_0_6684]), ['final']). 4.46/4.73 cnf(c_0_11267, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_6685]), ['final']). 4.46/4.73 cnf(c_0_11268, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_6686]), ['final']). 4.46/4.73 cnf(c_0_11269, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))|~class_Rings_Oordered__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))), inference(split_conjunct,[status(thm)],[c_0_6687]), ['final']). 4.46/4.73 cnf(c_0_11270, plain, (c_Wellfounded_Oacyclic(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk331_2(X2,X1)),esk331_2(X2,X1))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))), inference(rw,[status(thm)],[c_0_6688, c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_11271, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6689]), ['final']). 4.46/4.73 cnf(c_0_11272, plain, (hBOOL(hAPP(X4,X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X4),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_6690]), ['final']). 4.46/4.73 cnf(c_0_11273, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6691]), ['final']). 4.46/4.73 cnf(c_0_11274, plain, (c_Wellfounded_Oacyclic(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk110_2(X2,X1)),esk110_2(X2,X1))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))), inference(rw,[status(thm)],[c_0_6692, c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_11275, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))|~class_Rings_Oordered__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))), inference(split_conjunct,[status(thm)],[c_0_6693]), ['final']). 4.46/4.73 cnf(c_0_11276, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_6694]), ['final']). 4.46/4.73 cnf(c_0_11277, plain, (hAPP(X1,esk256_3(X2,X1,X3))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X1,hAPP(c_Nat_OSuc,esk255_3(X2,X1,X3)))),hAPP(X1,esk255_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))), inference(rw,[status(thm)],[c_0_6695, c_0_5644]), ['final']). 4.46/4.73 cnf(c_0_11278, plain, (hAPP(X1,esk72_3(X2,X1,X3))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X1,hAPP(c_Nat_OSuc,esk71_3(X2,X1,X3)))),hAPP(X1,esk71_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))), inference(rw,[status(thm)],[c_0_6696, c_0_5644]), ['final']). 4.46/4.73 cnf(c_0_11279, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3)),X4)),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X4))), inference(er,[status(thm)],[c_0_6697]), ['final']). 4.46/4.73 cnf(c_0_11280, plain, (c_HOL_OThe(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=c_Partial__Function_Oflat__lub(X1,X3,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))), inference(rw,[status(thm)],[c_0_6698, c_0_4945]), ['final']). 4.46/4.73 cnf(c_0_11281, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk156_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5128]), ['final']). 4.46/4.73 cnf(c_0_11282, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk28_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5126]), ['final']). 4.46/4.73 cnf(c_0_11283, plain, (c_Fun_Oinj__on(tc_prod(X1,X5),tc_prod(X2,X6),c_Product__Type_Omap__pair(X1,X2,X5,X6,X3,X7),hAPP(hAPP(c_Product__Type_OSigma(X1,X5),X4),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X1),X8)))|~c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Oinj__on(X5,X6,X7,X8)), inference(split_conjunct,[status(thm)],[c_0_6699]), ['final']). 4.46/4.73 cnf(c_0_11284, plain, (hAPP(c_Option_Ooption_OSome(X4),esk448_5(X2,X5,X4,X3,X1))=hAPP(hAPP(c_Map_Omap__of(X1,X4),hAPP(hAPP(c_List_Ozip(X1,X4),X3),X5)),X2)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)), inference(split_conjunct,[status(thm)],[c_0_6700]), ['final']). 4.46/4.73 cnf(c_0_11285, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omlex__prod(X4,X1,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),X5))), inference(split_conjunct,[status(thm)],[c_0_6701]), ['final']). 4.46/4.73 cnf(c_0_11286, plain, (hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),hAPP(c_Orderings_Oord__class_Oless(X1),X5)),X3)),X4)=c_List_OtakeWhile(X2,hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),hAPP(c_Orderings_Oord__class_Oless(X1),X5)),X3),X4)|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_6702]), ['final']). 4.46/4.73 cnf(c_0_11287, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_6703, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11288, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3)),X4)),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X3))), inference(er,[status(thm)],[c_0_6704]), ['final']). 4.46/4.73 cnf(c_0_11289, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X4,X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2)),X3)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6705]), ['final']). 4.46/4.73 cnf(c_0_11290, plain, (X3=hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Otake(X2),X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_OSuc,X1)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6706]), ['final']). 4.46/4.73 cnf(c_0_11291, plain, (c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X4))|~c_Fun_Oinj__on(X1,X2,X3,X4)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),X4))),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X5)))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~c_Fun_Oinj__on(X1,X2,X3,X5)), inference(split_conjunct,[status(thm)],[c_0_6707]), ['final']). 4.46/4.73 cnf(c_0_11292, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_6708, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11293, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4))))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),esk442_3(X3,X1,X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(X1,X2))), inference(rw,[status(thm)],[c_0_6709, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11294, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk480_3(X2,X1,X3)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6675]), ['final']). 4.46/4.73 cnf(c_0_11295, plain, (hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X6)),hAPP(X4,X5))=hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6))|~c_Finite__Set_Ofolding(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6))), inference(split_conjunct,[status(thm)],[c_0_6710]), ['final']). 4.46/4.73 cnf(c_0_11296, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3))), inference(er,[status(thm)],[c_0_6711]), ['final']). 4.46/4.73 cnf(c_0_11297, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))=hAPP(c_fequal,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))), inference(rw,[status(thm)],[c_0_6712, c_0_5580]), ['final']). 4.46/4.73 cnf(c_0_11298, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6713, c_0_4760]), c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11299, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk80_3(X2,X3,X1)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Int_Oint),X2),X3)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X1),c_Int_Onat),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_6714]), ['final']). 4.46/4.73 cnf(c_0_11300, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_Nat_Onat,X4),c_Finite__Set_Ocard(X1)),X2)),X3)=hAPP(c_Finite__Set_Ocard(tc_prod(X4,X1)),hAPP(hAPP(c_Product__Type_OSigma(X4,X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk86_4(X2,X1,X3,X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(split_conjunct,[status(thm)],[c_0_6469]), ['final']). 4.46/4.73 cnf(c_0_11301, plain, (c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,X5,hAPP(hAPP(X3,X8),X9))|~c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X7)|~hBOOL(hAPP(hAPP(c_member(X1),X6),X5))|hAPP(hAPP(X3,X8),X9)!=hAPP(hAPP(X3,X6),X7)), inference(split_conjunct,[status(thm)],[c_0_6285]), ['final']). 4.46/4.73 cnf(c_0_11302, plain, (hAPP(c_List_Oset(tc_prod(X1,X2)),X3)=hAPP(c_List_Oset(tc_prod(X1,X2)),X4)|hAPP(c_Map_Omap__of(X1,X2),X3)!=hAPP(c_Map_Omap__of(X1,X2),X4)|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4)))), inference(split_conjunct,[status(thm)],[c_0_6532]), ['final']). 4.46/4.73 cnf(c_0_11303, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X1,X2,X3)),X2))|~hBOOL(hAPP(X3,X1))), inference(rw,[status(thm)],[c_0_6715, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11304, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))), inference(er,[status(thm)],[c_0_6716]), ['final']). 4.46/4.73 cnf(c_0_11305, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6717, c_0_4760]), c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11306, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6718, c_0_4760]), c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11307, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X4)))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X2,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_6719]), ['final']). 4.46/4.73 cnf(c_0_11308, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk532_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X1))), inference(rw,[status(thm)],[c_0_6720, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11309, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))|~class_Int_Onumber(X1)|~class_Rings_Osemiring(X1)), inference(split_conjunct,[status(thm)],[c_0_6721]), ['final']). 4.46/4.73 cnf(c_0_11310, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),c_Map_Omap__add(X2,X1,X3,hAPP(c_Map_Omap__of(X2,X1),X4))),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_6722]), ['final']). 4.46/4.73 cnf(c_0_11311, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))=hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X2),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6723, c_0_4517]), c_0_4517]), ['final']). 4.46/4.73 cnf(c_0_11312, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)|~class_Rings_Osemiring(X1)), inference(split_conjunct,[status(thm)],[c_0_6724]), ['final']). 4.46/4.73 cnf(c_0_11313, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~c_Nitpick_Oless__frac(X1,X2,X3)), inference(rw,[status(thm)],[c_0_6725, c_0_6281]), ['final']). 4.46/4.73 cnf(c_0_11314, plain, (hAPP(hAPP(X6,X8),X10)=hAPP(hAPP(X6,X7),X9)|~c_Equiv__Relations_Ocongruent2(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X7),X8)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X9),X10)),X5))), inference(split_conjunct,[status(thm)],[c_0_6726]), ['final']). 4.46/4.73 cnf(c_0_11315, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk172_3(X1,X2,X3)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X2))))|X3=X2|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)), inference(split_conjunct,[status(thm)],[c_0_5407]), ['final']). 4.46/4.73 cnf(c_0_11316, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6727]), ['final']). 4.46/4.73 cnf(c_0_11317, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6728]), ['final']). 4.46/4.73 cnf(c_0_11318, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~c_Nitpick_Oless__eq__frac(X1,X2,X3)), inference(rw,[status(thm)],[c_0_6729, c_0_6281]), ['final']). 4.46/4.73 cnf(c_0_11319, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),X1)=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))), inference(er,[status(thm)],[c_0_6730]), ['final']). 4.46/4.73 cnf(c_0_11320, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X5),X4)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~c_Fun_Oinj__on(X2,X1,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_6707]), ['final']). 4.46/4.73 cnf(c_0_11321, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4)),X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)))|hAPP(hAPP(c_List_Oappend(X2),X4),X5)!=hAPP(hAPP(c_List_Oappend(X2),X3),X1)), inference(split_conjunct,[status(thm)],[c_0_5038]), ['final']). 4.46/4.73 cnf(c_0_11322, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6731]), ['final']). 4.46/4.73 cnf(c_0_11323, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6732]), ['final']). 4.46/4.73 cnf(c_0_11324, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),hAPP(c_List_Oset(X2),X3)),X4)=hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(X1)),X4)),c_Orderings_Otop__class_Otop(X1)),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6733]), ['final']). 4.46/4.73 cnf(c_0_11325, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_6734]), ['final']). 4.46/4.73 cnf(c_0_11326, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk388_4(X2,X3,X4,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6494]), ['final']). 4.46/4.73 cnf(c_0_11327, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk508_4(X2,X3,X4,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Lattices_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_6492]), ['final']). 4.46/4.73 cnf(c_0_11328, plain, (hAPP(c_List_Ofilter(X1,X3),X2)=c_List_OtakeWhile(X1,X3,X2)|hBOOL(hAPP(hAPP(c_member(X1),esk413_3(X2,X3,X1)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X3,X2))),X2))))), inference(rw,[status(thm)],[c_0_6735, c_0_4916]), ['final']). 4.46/4.73 cnf(c_0_11329, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))|~class_Int_Onumber(X1)|~class_Rings_Oring(X1)), inference(split_conjunct,[status(thm)],[c_0_6736]), ['final']). 4.46/4.73 cnf(c_0_11330, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6737]), ['final']). 4.46/4.73 cnf(c_0_11331, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6738]), ['final']). 4.46/4.73 cnf(c_0_11332, plain, (hAPP(X4,X5)=hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(X3,X6))|~c_Finite__Set_Ofolding(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X5))), inference(split_conjunct,[status(thm)],[c_0_6739]), ['final']). 4.46/4.73 cnf(c_0_11333, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5),X1))), inference(split_conjunct,[status(thm)],[c_0_6740]), ['final']). 4.46/4.73 cnf(c_0_11334, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6741]), ['final']). 4.46/4.73 cnf(c_0_11335, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk366_4(X3,X2,X4,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6502]), ['final']). 4.46/4.73 cnf(c_0_11336, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk526_4(X3,X2,X4,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_6498]), ['final']). 4.46/4.73 cnf(c_0_11337, plain, (X3=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),X4),hAPP(c_Option_Ooption_OSome(X2),esk457_4(X4,X3,X2,X1)))|c_Map_Odom(X1,X2,X3)!=hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5816]), ['final']). 4.46/4.73 cnf(c_0_11338, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))))|~hBOOL(hAPP(hAPP(c_member(X2),X6),X4))), inference(split_conjunct,[status(thm)],[c_0_6370]), ['final']). 4.46/4.73 cnf(c_0_11339, plain, (hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Otake(X2),X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_OSuc,X1)),X3)))=hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6742]), ['final']). 4.46/4.73 cnf(c_0_11340, plain, (hAPP(X5,X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X5)|~c_Equiv__Relations_Oequiv(X1,X2,X3)|~c_Equiv__Relations_Ocongruent(X1,tc_fun(X4,tc_HOL_Obool),X3,X5)|~hBOOL(hAPP(hAPP(c_member(X1),X6),X2))), inference(split_conjunct,[status(thm)],[c_0_6743]), ['final']). 4.46/4.73 cnf(c_0_11341, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|hAPP(c_Random_Oiterate(X2,X3,X1,X4),X5)=hAPP(hAPP(c_Product__Type_Oscomp(X3,X2,X3,tc_prod(X2,X3)),hAPP(X4,X5)),c_Random_Oiterate(X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X4))), inference(split_conjunct,[status(thm)],[c_0_5959]), ['final']). 4.46/4.73 cnf(c_0_11342, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk89_3(X2,X3,X1)),esk89_3(X2,X3,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olexord(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_6744]), ['final']). 4.46/4.73 cnf(c_0_11343, plain, (hAPP(X1,X2)=hAPP(X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X1),X5))))), inference(split_conjunct,[status(thm)],[c_0_6399]), ['final']). 4.46/4.73 cnf(c_0_11344, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk291_4(X1,X2,X3,X4)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6487]), ['final']). 4.46/4.73 cnf(c_0_11345, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk350_4(X1,X2,X3,X4)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6488]), ['final']). 4.46/4.73 cnf(c_0_11346, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X1,X2,X3)),X2))), inference(rw,[status(thm)],[c_0_6745, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11347, plain, (hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_OSuc,X1)),X3)=hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Otake(X2),X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),c_List_Olist_ONil(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6746]), ['final']). 4.46/4.73 cnf(c_0_11348, plain, (hAPP(c_Random_Opick(X1,hAPP(hAPP(c_List_Omap(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,X1)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X3))=hAPP(hAPP(c_List_Onth(X1),X2),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))), inference(rw,[status(thm)],[c_0_6747, c_0_5334]), ['final']). 4.46/4.73 cnf(c_0_11349, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk532_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_6748, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11350, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk475_3(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6749]), ['final']). 4.46/4.73 cnf(c_0_11351, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk13_3(X3,X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[c_0_6750, c_0_5134]), ['final']). 4.46/4.73 cnf(c_0_11352, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),hAPP(c_List_Oset(X2),X3)),X4)=hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__sup__class_Osup(X1)),X4)),c_Orderings_Obot__class_Obot(X1)),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6751]), ['final']). 4.46/4.73 cnf(c_0_11353, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X2),X6),hAPP(c_Set_Oimage(X1,X5,X7),X4))|hBOOL(hAPP(hAPP(c_member(X1),esk365_8(X6,X3,hAPP(c_Set_Oimage(X1,X5,X7),X4),X4,X7,X5,X1,X2)),X4))|~c_Fun_Oinj__on(X1,X5,X7,X4)|~class_Groups_Ocomm__monoid__mult(X2)), inference(er,[status(thm)],[c_0_6752]), ['final']). 4.46/4.73 cnf(c_0_11354, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_6753]), ['final']). 4.46/4.73 cnf(c_0_11355, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk503_3(X2,X3,X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6754]), ['final']). 4.46/4.73 cnf(c_0_11356, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk454_3(X2,X3,X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3)))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_6755]), ['final']). 4.46/4.73 cnf(c_0_11357, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk228_3(X2,X3,X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6756]), ['final']). 4.46/4.73 cnf(c_0_11358, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X2),X6),hAPP(c_Set_Oimage(X1,X5,X7),X4))|hBOOL(hAPP(hAPP(c_member(X1),esk270_8(X6,X3,hAPP(c_Set_Oimage(X1,X5,X7),X4),X4,X7,X5,X1,X2)),X4))|~c_Fun_Oinj__on(X1,X5,X7,X4)|~class_Groups_Ocomm__monoid__add(X2)), inference(er,[status(thm)],[c_0_6757]), ['final']). 4.46/4.73 cnf(c_0_11359, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6758, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), ['final']). 4.46/4.73 cnf(c_0_11360, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_6759]), ['final']). 4.46/4.73 cnf(c_0_11361, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6760, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), ['final']). 4.46/4.73 cnf(c_0_11362, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_List_Onth(X1),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))=hAPP(c_List_Ohd(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X2))), inference(rw,[status(thm)],[c_0_6761, c_0_5902]), ['final']). 4.46/4.73 cnf(c_0_11363, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))|c_List_OtakeWhile(X2,X4,X3)=hAPP(hAPP(c_List_Otake(X2),X1),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk62_4(X4,X3,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6762]), ['final']). 4.46/4.73 cnf(c_0_11364, plain, (hBOOL(hAPP(hAPP(c_member(X6),hAPP(hAPP(X7,X3),X4)),hAPP(c_Set_Oimage(tc_prod(X1,X2),X6,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X6),X7)),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_6763]), ['final']). 4.46/4.73 cnf(c_0_11365, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X6))),c_List_Olexord(X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_5014]), ['final']). 4.46/4.73 cnf(c_0_11366, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|X3=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olex(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_5016]), ['final']). 4.46/4.73 cnf(c_0_11367, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X4))|~c_Wellfounded_Oacyclic(X1,X4)), inference(split_conjunct,[status(thm)],[c_0_6764]), ['final']). 4.46/4.73 cnf(c_0_11368, plain, (hAPP(X6,X7)=hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X7),hAPP(hAPP(c_Set_Oinsert(X2),X8),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))|~c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))|~hBOOL(hAPP(hAPP(c_member(X2),X8),X7))), inference(split_conjunct,[status(thm)],[c_0_6765]), ['final']). 4.46/4.73 cnf(c_0_11369, plain, (hAPP(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X7),X8))=hAPP(hAPP(X3,hAPP(X6,X7)),hAPP(X6,X8))|~c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X8))|c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X7),X8)), inference(split_conjunct,[status(thm)],[c_0_6766]), ['final']). 4.46/4.73 cnf(c_0_11370, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X3,X1),hAPP(hAPP(c_COMBB(X1,X1,X3),hAPP(c_Groups_Otimes__class_Otimes(X1),X2)),X4)),X5))|~class_Rings_Osemiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_6767]), ['final']). 4.46/4.73 cnf(c_0_11371, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X2,hAPP(c_Relation_Oconverse(X2,X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X5)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_6768]), ['final']). 4.46/4.73 cnf(c_0_11372, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|c_Wellfounded_Owf(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X4))|~c_Wellfounded_Owf(X1,X4)), inference(split_conjunct,[status(thm)],[c_0_6769]), ['final']). 4.46/4.73 cnf(c_0_11373, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|X3=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olistrel1(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_6296]), ['final']). 4.46/4.73 cnf(c_0_11374, plain, (hBOOL(hAPP(X1,esk180_4(X1,X2,X3,X4)))|hBOOL(hAPP(hAPP(c_member(X4),esk179_4(X1,X2,X3,X4)),X2))|~hBOOL(hAPP(X1,X5))|~hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6573]), ['final']). 4.46/4.73 cnf(c_0_11375, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk180_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(X2,esk179_4(X2,X3,X4,X1)))|~hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_6573]), ['final']). 4.46/4.73 cnf(c_0_11376, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),X4)),hAPP(hAPP(c_List_Onth(X1),X2),X3)))|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Orev(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))), inference(split_conjunct,[status(thm)],[c_0_6770]), ['final']). 4.46/4.73 cnf(c_0_11377, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk339_6(X2,X3,X4,X5,X1,X6)),X6))|c_Fun_Oinj__on(X5,X4,X3,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X5,tc_HOL_Obool)),X6),X2))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X6), inference(split_conjunct,[status(thm)],[c_0_6771]), ['final']). 4.46/4.73 cnf(c_0_11378, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2)),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X3))|~class_Lattices_Oab__semigroup__idem__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6772]), ['final']). 4.46/4.73 cnf(c_0_11379, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk28_3(X1,X2,X3)),X3))|hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5126]), ['final']). 4.46/4.73 cnf(c_0_11380, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk156_3(X2,X3,X1)))|hBOOL(hAPP(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5128]), ['final']). 4.46/4.73 cnf(c_0_11381, plain, (c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6773]), ['final']). 4.46/4.73 cnf(c_0_11382, plain, (c_FunDef_Oreduction__pair(X1,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_6774]), ['final']). 4.46/4.73 cnf(c_0_11383, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),X2)),X2)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_6775]), ['final']). 4.46/4.73 cnf(c_0_11384, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk79_4(X1,X2,X3,X4)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk78_4(X1,X2,X3,X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X4)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_5066]), ['final']). 4.46/4.73 cnf(c_0_11385, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk527_4(X1,X2,X3,X4)),X4))|hAPP(hAPP(c_List_Otake(X3),X4),X2)=hAPP(hAPP(c_List_Otake(X3),X4),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2)))), inference(split_conjunct,[status(thm)],[c_0_6776]), ['final']). 4.46/4.73 cnf(c_0_11386, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk79_4(X2,X3,X4,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk78_4(X2,X3,X4,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X4))), inference(split_conjunct,[status(thm)],[c_0_5066]), ['final']). 4.46/4.73 cnf(c_0_11387, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)))=hAPP(hAPP(c_List_Olist_OCons(X1),X4),hAPP(c_List_Ofilter(X1,X2),X5))|hBOOL(hAPP(X2,esk530_6(hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)),X2,hAPP(c_List_Ofilter(X1,X2),X5),X4,X1,X3)))|~hBOOL(hAPP(X2,X4))), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6777])]), ['final']). 4.46/4.73 cnf(c_0_11388, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),X4))=hAPP(hAPP(X3,X6),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),X4))|~c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_6778]), ['final']). 4.46/4.73 cnf(c_0_11389, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X6),X5)),X4)|~c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_6779]), ['final']). 4.46/4.73 cnf(c_0_11390, plain, (hBOOL(hAPP(hAPP(c_member(X1),X6),X5))|hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X3,X6))=hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X1),X6),X5))|~c_Finite__Set_Ofolding(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_6780]), ['final']). 4.46/4.73 cnf(c_0_11391, plain, (hAPP(X1,esk79_4(X2,X1,X3,X4))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk78_4(X2,X1,X3,X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_5066]), ['final']). 4.46/4.73 cnf(c_0_11392, plain, (hAPP(X1,esk79_4(X2,X1,X3,X4))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk78_4(X2,X1,X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_5066]), ['final']). 4.46/4.73 cnf(c_0_11393, plain, (X1=c_List_Olist_ONil(X2)|hAPP(c_List_Ofoldl(X2,X2,hAPP(c_COMBC(X2,X2,X2),c_Orderings_Oord__class_Omax(X2)),X3),hAPP(c_List_Orev(X2),X1))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),hAPP(hAPP(c_List_Onth(X2),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3)|~class_Orderings_Olinorder(X2)|~c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Orev(X2),X1))), inference(rw,[status(thm)],[c_0_6781, c_0_4713]), ['final']). 4.46/4.73 cnf(c_0_11394, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X3,X1))), inference(rw,[status(thm)],[c_0_6782, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11395, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)))=hAPP(hAPP(c_List_Olist_OCons(X1),X4),hAPP(c_List_Ofilter(X1,X2),X5))|hBOOL(hAPP(X2,esk154_7(hAPP(c_List_Ofilter(X1,X2),X5),X4,hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)),X2,X1,X3,X5)))|~hBOOL(hAPP(X2,X4))), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6783])]), ['final']). 4.46/4.73 cnf(c_0_11396, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Oone__class_Oone(X1)))), inference(split_conjunct,[status(thm)],[c_0_6784]), ['final']). 4.46/4.73 cnf(c_0_11397, plain, (hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X1),X6),X5))=hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(X3,X6))|~c_Finite__Set_Ofolding(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_6785]), ['final']). 4.46/4.73 cnf(c_0_11398, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X2),X1),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X2)),X3)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X2)))), inference(split_conjunct,[status(thm)],[c_0_6786]), ['final']). 4.46/4.73 cnf(c_0_11399, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X3,X1))), inference(rw,[status(thm)],[c_0_6787, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11400, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),hAPP(c_List_Oset(X4),X5))))|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X1,X2),X3),X5)=c_List_Olinorder__class_Oinsort__insert__key(X4,X1,X2,X3,X5)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6788]), ['final']). 4.46/4.73 cnf(c_0_11401, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk237_5(X2,X3,X4,X1,X5)),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_5587]), ['final']). 4.46/4.73 cnf(c_0_11402, plain, (hBOOL(hAPP(hAPP(c_member(X1),X4),X5))|hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X6,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X7))|hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)!=hAPP(hAPP(c_Set_Oinsert(X1),X4),X5)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X6,X4,X5),X7))), inference(split_conjunct,[status(thm)],[c_0_6789]), ['final']). 4.46/4.73 cnf(c_0_11403, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X3))))=c_Groups_Oone__class_Oone(X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6790, c_0_4760]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_11404, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))=hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X4))|hAPP(c_Map_Omap__of(X1,X2),X3)!=hAPP(c_Map_Omap__of(X1,X2),X4)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6791, c_0_5275]), c_0_5275]), ['final']). 4.46/4.73 cnf(c_0_11405, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X4)),X3)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))|hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))|hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),X3)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_6792]), ['final']). 4.46/4.73 cnf(c_0_11406, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))!=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)|c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))!=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X4)), inference(split_conjunct,[status(thm)],[c_0_6793]), ['final']). 4.46/4.73 cnf(c_0_11407, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk209_5(X2,X3,X4,X5,X1)),X5))|c_Relation_Orefl__on(X4,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X5),X2))), inference(split_conjunct,[status(thm)],[c_0_6589]), ['final']). 4.46/4.73 cnf(c_0_11408, plain, (X1=hAPP(hAPP(X2,X3),X4)|hAPP(hAPP(X2,X3),X4)=hAPP(hAPP(X2,esk333_7(X4,X3,X5,X1,X2,X6,X7)),esk334_7(X4,X3,X5,X1,X2,X6,X7))|~c_Nitpick_Ofold__graph_H(X7,X6,X2,X1,X5,hAPP(hAPP(X2,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_6285]), ['final']). 4.46/4.73 cnf(c_0_11409, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),hAPP(hAPP(X3,X6),X7)))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X7))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X5))), inference(split_conjunct,[status(thm)],[c_0_6794]), ['final']). 4.46/4.73 cnf(c_0_11410, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk249_6(X4,X3,X5,X6,X2,X1)),esk250_6(X4,X3,X5,X6,X2,X1))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X5,tc_fun(X1,tc_HOL_Obool)),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_6795]), ['final']). 4.46/4.73 cnf(c_0_11411, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_6796, c_0_4436]), ['final']). 4.46/4.73 cnf(c_0_11412, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),X1)=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3))), inference(er,[status(thm)],[c_0_6797]), ['final']). 4.46/4.73 cnf(c_0_11413, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBC(X2,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,tc_HOL_Obool),X2),c_fequal),X3)),hAPP(X4,X5))),X5)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6798]), ['final']). 4.46/4.73 cnf(c_0_11414, plain, (hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(c_Set_Oimage(X1,X4,X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=hAPP(c_Set_Oimage(X1,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X4),X6),X2),X5)),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6799]), ['final']). 4.46/4.73 cnf(c_0_11415, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6800, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), ['final']). 4.46/4.73 cnf(c_0_11416, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5146]), ['final']). 4.46/4.73 cnf(c_0_11417, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_List_Orev(X1),X3)))|~class_Groups_Omonoid__add(X1)), inference(rw,[status(thm)],[c_0_6801, c_0_4713]), ['final']). 4.46/4.73 cnf(c_0_11418, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(X3,X4),X5)=hAPP(hAPP(X3,esk333_7(X5,X4,X2,X6,X3,X7,X1)),esk334_7(X5,X4,X2,X6,X3,X7,X1))|~c_Nitpick_Ofold__graph_H(X1,X7,X3,X6,X2,hAPP(hAPP(X3,X4),X5))), inference(split_conjunct,[status(thm)],[c_0_6285]), ['final']). 4.46/4.73 cnf(c_0_11419, plain, (hAPP(hAPP(c_List_Oappend(X1),esk341_5(X2,X3,X4,X5,X1)),X4)=X2|hAPP(hAPP(c_List_Oappend(X1),esk340_5(X2,X3,X4,X5,X1)),X2)=X4|hAPP(hAPP(c_List_Oappend(X1),X3),X2)!=hAPP(hAPP(c_List_Oappend(X1),X5),X4)), inference(split_conjunct,[status(thm)],[c_0_6802]), ['final']). 4.46/4.73 cnf(c_0_11420, plain, (hAPP(hAPP(c_List_Oappend(X1),esk341_5(X2,X3,X4,X5,X1)),X4)=X2|hAPP(hAPP(c_List_Oappend(X1),X5),esk340_5(X2,X3,X4,X5,X1))=X3|hAPP(hAPP(c_List_Oappend(X1),X3),X2)!=hAPP(hAPP(c_List_Oappend(X1),X5),X4)), inference(split_conjunct,[status(thm)],[c_0_6802]), ['final']). 4.46/4.73 cnf(c_0_11421, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X2),X3)))|hAPP(c_Random_Opick(X2,X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X2),X3)))=hAPP(c_Random_Opick(X2,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X2)),X3),X4)),X1)), inference(split_conjunct,[status(thm)],[c_0_6803]), ['final']). 4.46/4.73 cnf(c_0_11422, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6804, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), ['final']). 4.46/4.73 cnf(c_0_11423, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6805, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), ['final']). 4.46/4.73 cnf(c_0_11424, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),X3),esk341_5(X4,X3,X5,X1,X2))|hAPP(hAPP(c_List_Oappend(X2),esk340_5(X4,X3,X5,X1,X2)),X4)=X5|hAPP(hAPP(c_List_Oappend(X2),X3),X4)!=hAPP(hAPP(c_List_Oappend(X2),X1),X5)), inference(split_conjunct,[status(thm)],[c_0_6802]), ['final']). 4.46/4.73 cnf(c_0_11425, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),X3),esk341_5(X4,X3,X5,X1,X2))|hAPP(hAPP(c_List_Oappend(X2),X1),esk340_5(X4,X3,X5,X1,X2))=X3|hAPP(hAPP(c_List_Oappend(X2),X3),X4)!=hAPP(hAPP(c_List_Oappend(X2),X1),X5)), inference(split_conjunct,[status(thm)],[c_0_6802]), ['final']). 4.46/4.73 cnf(c_0_11426, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hAPP(hAPP(c_List_Oappend(X1),X2),X4)!=hAPP(hAPP(c_List_Oappend(X1),X3),X5)), inference(split_conjunct,[status(thm)],[c_0_5038]), ['final']). 4.46/4.73 cnf(c_0_11427, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))), inference(split_conjunct,[status(thm)],[c_0_6806]), ['final']). 4.46/4.73 cnf(c_0_11428, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_6807]), ['final']). 4.46/4.73 cnf(c_0_11429, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6808]), ['final']). 4.46/4.73 cnf(c_0_11430, plain, (c_Wellfounded_OwfP(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),X2))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Predicate_ODomainP(X1,X1,hAPP(X2,esk185_3(X3,X2,X1)))),c_Predicate_ORangeP(X1,X1,hAPP(X2,esk186_3(X3,X2,X1))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~c_Wellfounded_OwfP(X1,hAPP(X2,esk184_3(X3,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_6809]), ['final']). 4.46/4.73 cnf(c_0_11431, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X5|hAPP(X4,hAPP(X3,X5))=hAPP(X3,hAPP(c_Set_Oimage(X1,X1,X4),X5))|~c_Finite__Set_Ofolding__one__idem(X1,X2,X3)|hAPP(X4,hAPP(hAPP(X2,esk94_5(X5,X4,X3,X2,X1)),esk95_5(X5,X4,X3,X2,X1)))!=hAPP(hAPP(X2,hAPP(X4,esk94_5(X5,X4,X3,X2,X1))),hAPP(X4,esk95_5(X5,X4,X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_6810]), ['final']). 4.46/4.73 cnf(c_0_11432, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6811]), ['final']). 4.46/4.73 cnf(c_0_11433, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6812]), ['final']). 4.46/4.73 cnf(c_0_11434, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_6813, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11435, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X5),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Oab__group__add(X4)), inference(split_conjunct,[status(thm)],[c_0_6503]), ['final']). 4.46/4.73 cnf(c_0_11436, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk536_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3)))=X1|epred2_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk538_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_6814, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11437, plain, (hBOOL(hAPP(X1,esk446_2(X1,X2)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk444_2(X1,X2)))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,esk443_2(X1,X2)))|~hBOOL(hAPP(X1,X3))), inference(rw,[status(thm)],[c_0_6815, c_0_6410]), ['final']). 4.46/4.73 cnf(c_0_11438, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk7_4(X3,X4,X1,X2)),esk8_4(X3,X4,X1,X2))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),X4),hAPP(c_Relation_Oconverse(X1,X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_6816]), ['final']). 4.46/4.73 cnf(c_0_11439, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk233_4(X2,X3,X1,X4)),X3))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4,X1,c_Groups_Otimes__class_Otimes(X4)),X2),c_Groups_Oone__class_Oone(X4)),X3)=c_Groups_Oone__class_Oone(X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Ocomm__monoid__mult(X4)), inference(split_conjunct,[status(thm)],[c_0_6817]), ['final']). 4.46/4.73 cnf(c_0_11440, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk538_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3)))=X1|epred2_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk536_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_6818, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11441, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),hAPP(c_Set_Oimage(X4,X1,X5),X6))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X2),X7),X6)|hAPP(X7,esk365_8(X3,X7,hAPP(c_Set_Oimage(X4,X1,X5),X6),X6,X5,X1,X4,X2))!=hAPP(X3,hAPP(X5,esk365_8(X3,X7,hAPP(c_Set_Oimage(X4,X1,X5),X6),X6,X5,X1,X4,X2)))|~c_Fun_Oinj__on(X4,X1,X5,X6)|~class_Groups_Ocomm__monoid__mult(X2)), inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_6819, c_0_6281])]), ['final']). 4.46/4.73 cnf(c_0_11442, plain, (hAPP(X6,hAPP(hAPP(c_Set_Oinsert(X2),X8),X7))=hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X7),hAPP(hAPP(c_Set_Oinsert(X2),X8),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))|~c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))), inference(split_conjunct,[status(thm)],[c_0_6820]), ['final']). 4.46/4.73 cnf(c_0_11443, plain, (hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6))=hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X6))|~c_Finite__Set_Ofolding__idem(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6))), inference(split_conjunct,[status(thm)],[c_0_6821]), ['final']). 4.46/4.73 cnf(c_0_11444, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[c_0_6822, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11445, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(c_Fun_Ocomp(X3,X1,X2,X6),X4)),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),X6),hAPP(c_Set_Oimage(X2,X3,X4),X5))|~class_Groups_Ocomm__monoid__add(X1)|~c_Fun_Oinj__on(X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_6823]), ['final']). 4.46/4.73 cnf(c_0_11446, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk322_4(X1,X2,X3,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X3),X2)),c_List_Olistrel1(X4,X1)))), inference(split_conjunct,[status(thm)],[c_0_5018]), ['final']). 4.46/4.73 cnf(c_0_11447, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_6824, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11448, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),X1)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))), inference(rw,[status(thm)],[c_0_6825, c_0_4836]), ['final']). 4.46/4.73 cnf(c_0_11449, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X3),X6)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(X6,X2)))), inference(split_conjunct,[status(thm)],[c_0_6826]), ['final']). 4.46/4.73 cnf(c_0_11450, plain, (hAPP(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1))=hAPP(hAPP(c_List_Onth(X5),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),X4),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X2)))),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))), inference(rw,[status(thm)],[c_0_6827, c_0_4517]), ['final']). 4.46/4.73 cnf(c_0_11451, plain, (hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)=hAPP(hAPP(c_List_Odrop(X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),c_List_OtakeWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)))),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))|hBOOL(hAPP(X1,X2))), inference(rw,[status(thm)],[c_0_6828, c_0_4916]), ['final']). 4.46/4.73 cnf(c_0_11452, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X4),X5)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X5),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))), inference(rw,[status(thm)],[c_0_6829, c_0_6349]), ['final']). 4.46/4.73 cnf(c_0_11453, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X4),X5)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X5),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))), inference(rw,[status(thm)],[c_0_6830, c_0_6349]), ['final']). 4.46/4.73 cnf(c_0_11454, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X2,X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3),X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))), inference(rw,[status(thm)],[c_0_6831, c_0_5955]), ['final']). 4.46/4.73 cnf(c_0_11455, plain, (hAPP(c_Finite__Set_Ocard(X1),X4)=hAPP(c_Finite__Set_Ocard(X2),X5)|~c_Fun_Oinj__on(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),X5))|~c_Fun_Oinj__on(X2,X1,X6,X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X6),X5)),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))), inference(split_conjunct,[status(thm)],[c_0_6832]), ['final']). 4.46/4.73 cnf(c_0_11456, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|hAPP(c_Lazy__Sequence_Obind(X2,X3,hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X2,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X3)),X5),X1))=hAPP(c_New__DSequence_Opos__decr__bind(X2,X3,X4,X5),X1)), inference(split_conjunct,[status(thm)],[c_0_5975]), ['final']). 4.46/4.73 cnf(c_0_11457, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1)=X3|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3))), inference(er,[status(thm)],[c_0_6833]), ['final']). 4.46/4.73 cnf(c_0_11458, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))|hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_4650]), ['final']). 4.46/4.73 cnf(c_0_11459, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6834, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4912]), ['final']). 4.46/4.73 cnf(c_0_11460, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6835, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_6631]), ['final']). 4.46/4.73 cnf(c_0_11461, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_6836]), ['final']). 4.46/4.73 cnf(c_0_11462, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2))=c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_6837]), ['final']). 4.46/4.73 cnf(c_0_11463, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3))))), inference(split_conjunct,[status(thm)],[c_0_6838]), ['final']). 4.46/4.73 cnf(c_0_11464, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk43_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X1,X3,X4)),c_List_Olist_Olist__size(X1,X2,X4)))), inference(split_conjunct,[status(thm)],[c_0_6839]), ['final']). 4.46/4.73 cnf(c_0_11465, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6840]), ['final']). 4.46/4.73 cnf(c_0_11466, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X4),c_Wellfounded_Oless__than),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))), inference(rw,[status(thm)],[c_0_6841, c_0_6842]), ['final']). 4.46/4.73 cnf(c_0_11467, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)))),X3))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6843]), ['final']). 4.46/4.73 cnf(c_0_11468, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X1),X2),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X1),X4),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk518_5(X2,X4,X3,X3,X1)))|~class_Groups_Ocomm__monoid__add(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~c_Nat__Transfer_Onat__set(X3)), inference(er,[status(thm)],[c_0_6844]), ['final']). 4.46/4.73 cnf(c_0_11469, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X2),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X4),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk9_5(X2,X4,X3,X3,X1)))|~class_Groups_Ocomm__monoid__add(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~c_Nat__Transfer_Onat__set(X3)), inference(er,[status(thm)],[c_0_6845]), ['final']). 4.46/4.73 cnf(c_0_11470, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6846]), ['final']). 4.46/4.73 cnf(c_0_11471, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)))))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6847]), ['final']). 4.46/4.73 cnf(c_0_11472, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6848, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), ['final']). 4.46/4.73 cnf(c_0_11473, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6849, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), ['final']). 4.46/4.73 cnf(c_0_11474, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),X4)))|c_List_OtakeWhile(X2,X1,X3)=hAPP(hAPP(c_List_Otake(X2),X4),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk62_4(X1,X3,X2,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6762]), ['final']). 4.46/4.73 cnf(c_0_11475, plain, (hAPP(hAPP(c_List_Otake(X1),X4),X3)=hAPP(hAPP(c_List_Otake(X1),X4),X2)|hAPP(hAPP(c_List_Onth(X1),X2),esk527_4(X2,X3,X1,X4))!=hAPP(hAPP(c_List_Onth(X1),X3),esk527_4(X2,X3,X1,X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6776]), ['final']). 4.46/4.73 cnf(c_0_11476, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk445_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk444_2(X1,X2)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,esk443_2(X1,X2)))|~hBOOL(hAPP(X1,X3))), inference(rw,[status(thm)],[c_0_6850, c_0_6410]), ['final']). 4.46/4.73 cnf(c_0_11477, plain, (hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X3,X6))=hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X6)),hAPP(X4,X5))|~c_Finite__Set_Ofolding(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_6851]), ['final']). 4.46/4.73 cnf(c_0_11478, plain, (hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),c_List_Olist_ONil(tc_Nat_Onat)))=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[c_0_6852, c_0_5884]), ['final']). 4.46/4.73 cnf(c_0_11479, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6853, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), ['final']). 4.46/4.73 cnf(c_0_11480, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6854, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), ['final']). 4.46/4.73 cnf(c_0_11481, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))|hAPP(hAPP(c_List_Onth(X2),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))=hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Oappend(X2),X3),X4)),X1)), inference(split_conjunct,[status(thm)],[c_0_6855]), ['final']). 4.46/4.73 cnf(c_0_11482, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk389_4(X3,X1,X4,X2)),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),X4)),hAPP(c_Finite__Set_Ocard(X1),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))), inference(split_conjunct,[status(thm)],[c_0_6856]), ['final']). 4.46/4.73 cnf(c_0_11483, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X1,X2,X3)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,X1))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_11484, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk15_6(X2,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X4),X5),X4,X5,X1,X3)),X5))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(X4,X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X4),X5)))|~class_Groups_Oordered__ab__group__add(X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(er,[status(thm)],[c_0_6857]), ['final']). 4.46/4.73 cnf(c_0_11485, plain, (hAPP(hAPP(c_List_Olist__update(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X4)),X1),X5)=hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X5)),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6858]), ['final']). 4.46/4.73 cnf(c_0_11486, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4))), inference(split_conjunct,[status(thm)],[c_0_6859]), ['final']). 4.46/4.73 cnf(c_0_11487, plain, (hAPP(c_Product__Type_Omap__pair(X2,X2,X3,X6,c_Fun_Oid(X2),X1),X4)=hAPP(c_Product__Type_Omap__pair(X2,X2,X3,X6,c_Fun_Oid(X2),X5),X4)|hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4))!=hAPP(X5,hAPP(c_Product__Type_Osnd(X2,X3),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6860, c_0_4825]), c_0_4825]), ['final']). 4.46/4.73 cnf(c_0_11488, plain, (hAPP(c_Product__Type_Omap__pair(X2,X6,X3,X3,X1,c_Fun_Oid(X3)),X4)=hAPP(c_Product__Type_Omap__pair(X2,X6,X3,X3,X5,c_Fun_Oid(X3)),X4)|hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4))!=hAPP(X5,hAPP(c_Product__Type_Ofst(X2,X3),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6861, c_0_6862]), c_0_6862]), ['final']). 4.46/4.73 cnf(c_0_11489, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6863, c_0_6381]), c_0_6382]), ['final']). 4.46/4.73 cnf(c_0_11490, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Oone__class_Oone(X1)))), inference(split_conjunct,[status(thm)],[c_0_6864]), ['final']). 4.46/4.73 cnf(c_0_11491, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),c_Groups_Oone__class_Oone(X1)))), inference(split_conjunct,[status(thm)],[c_0_6865]), ['final']). 4.46/4.73 cnf(c_0_11492, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk272_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))|hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6866]), ['final']). 4.46/4.73 cnf(c_0_11493, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),X3)),c_Divides_Odiv__class_Omod(X1,X2,X3))),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_6867]), ['final']). 4.46/4.73 cnf(c_0_11494, plain, (hBOOL(hAPP(hAPP(c_member(X4),esk11_4(X1,X2,X3,X4)),X2))|hBOOL(hAPP(X1,X5))|~hBOOL(hAPP(X1,esk12_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6476]), ['final']). 4.46/4.73 cnf(c_0_11495, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk12_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(X2,esk11_4(X2,X3,X4,X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_6476]), ['final']). 4.46/4.73 cnf(c_0_11496, plain, (hAPP(hAPP(c_List_Olist__update(X1,X2),esk322_4(X3,X4,X2,X1)),esk321_4(X3,X4,X2,X1))=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel1(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_5018]), ['final']). 4.46/4.73 cnf(c_0_11497, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_6868]), ['final']). 4.46/4.73 cnf(c_0_11498, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk532_3(X1,X2,X3)))|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,X1))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_11499, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6869]), ['final']). 4.46/4.73 cnf(c_0_11500, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBS(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X3)),X4))))|~class_Orderings_Oorder(X2)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))), inference(rw,[status(thm)],[c_0_6870, c_0_5671]), ['final']). 4.46/4.73 cnf(c_0_11501, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X4))),c_Divides_Odiv__class_Omod(X1,X2,X4))),X3)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_6871]), ['final']). 4.46/4.73 cnf(c_0_11502, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3),X4))|~class_Groups_Ocomm__monoid__add(X1)), inference(rw,[status(thm)],[c_0_6872, c_0_5884]), ['final']). 4.46/4.73 cnf(c_0_11503, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X1),X2))),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6873]), ['final']). 4.46/4.73 cnf(c_0_11504, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6808]), ['final']). 4.46/4.73 cnf(c_0_11505, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6812]), ['final']). 4.46/4.73 cnf(c_0_11506, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6808]), ['final']). 4.46/4.73 cnf(c_0_11507, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6812]), ['final']). 4.46/4.73 cnf(c_0_11508, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),X2),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))|~class_Groups_Ocomm__monoid__add(X1)), inference(rw,[status(thm)],[c_0_6874, c_0_6875]), ['final']). 4.46/4.73 cnf(c_0_11509, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)))),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6876])]), ['final']). 4.46/4.73 cnf(c_0_11510, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5)|X4=X5|~c_Equiv__Relations_Oequiv(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_6877]), ['final']). 4.46/4.73 cnf(c_0_11511, plain, (hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X4),X5)),X6))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6878]), ['final']). 4.46/4.73 cnf(c_0_11512, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6846]), ['final']). 4.46/4.73 cnf(c_0_11513, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6840]), ['final']). 4.46/4.73 cnf(c_0_11514, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6808]), ['final']). 4.46/4.73 cnf(c_0_11515, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6812]), ['final']). 4.46/4.73 cnf(c_0_11516, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))), inference(er,[status(thm)],[c_0_6879]), ['final']). 4.46/4.73 cnf(c_0_11517, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,X1,tc_Nat_Onat),X3),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X1),X3),X2)|~class_Groups_Ocomm__monoid__add(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~c_Nat__Transfer_Onat__set(X2)), inference(split_conjunct,[status(thm)],[c_0_6880]), ['final']). 4.46/4.73 cnf(c_0_11518, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X3),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,X1,tc_Nat_Onat),X3),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2))|~class_Groups_Ocomm__monoid__add(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~c_Nat__Transfer_Onat__set(X2)), inference(split_conjunct,[status(thm)],[c_0_6881]), ['final']). 4.46/4.73 cnf(c_0_11519, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6882, c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), ['final']). 4.46/4.73 cnf(c_0_11520, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk538_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3)))=X1|epred2_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk536_3(X1,X2,X3)),X2))), inference(rw,[status(thm)],[c_0_6883, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11521, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk14_3(X1,X2,X3)),esk13_3(X1,X2,X3))=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)=X2|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(rw,[status(thm)],[c_0_6884, c_0_5134]), ['final']). 4.46/4.73 cnf(c_0_11522, plain, (X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk476_3(X2,X1,X3)),esk475_3(X2,X1,X3))|X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6749]), ['final']). 4.46/4.73 cnf(c_0_11523, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6846]), ['final']). 4.46/4.73 cnf(c_0_11524, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk536_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3)))=X1|epred2_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk538_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_6885, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11525, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1)=X3|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3))), inference(er,[status(thm)],[c_0_6886]), ['final']). 4.46/4.73 cnf(c_0_11526, plain, (hBOOL(hAPP(hAPP(c_member(X2),X8),X7))|hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,X7))=hAPP(X6,hAPP(hAPP(c_Set_Oinsert(X2),X8),X7))|~c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))), inference(split_conjunct,[status(thm)],[c_0_6887]), ['final']). 4.46/4.73 cnf(c_0_11527, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk164_5(X2,X3,X4,X1,X5)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X4),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_6888]), ['final']). 4.46/4.73 cnf(c_0_11528, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6840]), ['final']). 4.46/4.73 cnf(c_0_11529, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6840]), ['final']). 4.46/4.73 cnf(c_0_11530, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6846]), ['final']). 4.46/4.73 cnf(c_0_11531, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X4))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6889]), ['final']). 4.46/4.73 cnf(c_0_11532, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk138_5(X2,X3,X1,X4,X5)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X5,tc_HOL_Obool)),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6890]), ['final']). 4.46/4.73 cnf(c_0_11533, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),X1)=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))), inference(er,[status(thm)],[c_0_6891]), ['final']). 4.46/4.73 cnf(c_0_11534, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5))), inference(split_conjunct,[status(thm)],[c_0_6892]), ['final']). 4.46/4.73 cnf(c_0_11535, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X4))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6893]), ['final']). 4.46/4.73 cnf(c_0_11536, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,esk532_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_6894, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11537, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk435_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(er,[status(thm)],[c_0_6895]), ['final']). 4.46/4.73 cnf(c_0_11538, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_5844]), ['final']). 4.46/4.73 cnf(c_0_11539, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_6896]), ['final']). 4.46/4.73 cnf(c_0_11540, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Int_Onat)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2)|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6897, c_0_6898]), c_0_6899]), ['final']). 4.46/4.73 cnf(c_0_11541, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2)=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))|~c_Nat__Transfer_Onat__set(X1)|~c_Nat__Transfer_Onat__set(X2)), inference(split_conjunct,[status(thm)],[c_0_6900]), ['final']). 4.46/4.73 cnf(c_0_11542, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,esk534_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_6901, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11543, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),esk2_2(X2,X1))),hAPP(c_List_Oset(X1),esk3_2(X2,X1)))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),esk1_2(X2,X1)))), inference(rw,[status(thm)],[c_0_6902, c_0_4736]), ['final']). 4.46/4.73 cnf(c_0_11544, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk383_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OSigma(X1,X3),X4),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_6903]), ['final']). 4.46/4.73 cnf(c_0_11545, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)=c_List_Olist_ONil(X1)|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk357_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))), inference(rw,[status(thm)],[c_0_6904, c_0_4736]), ['final']). 4.46/4.73 cnf(c_0_11546, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk257_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(er,[status(thm)],[c_0_6905]), ['final']). 4.46/4.73 cnf(c_0_11547, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)=hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_6906]), ['final']). 4.46/4.73 cnf(c_0_11548, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)=c_List_Olist_ONil(X1)|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk195_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))), inference(rw,[status(thm)],[c_0_6907, c_0_4736]), ['final']). 4.46/4.73 cnf(c_0_11549, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),X4)),hAPP(hAPP(c_List_Onth(X1),X2),X3)))|~c_List_Olinorder__class_Osorted(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6908]), ['final']). 4.46/4.73 cnf(c_0_11550, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_5030]), ['final']). 4.46/4.73 cnf(c_0_11551, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X1,X2,X3)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_11552, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk483_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X4),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_6909]), ['final']). 4.46/4.73 cnf(c_0_11553, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X4),hAPP(hAPP(c_List_Ozip(X1,X4),X3),hAPP(hAPP(c_List_Omap(X1,X4),X5),X3))),X2)=hAPP(c_Option_Ooption_OSome(X4),hAPP(X5,X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_6910]), ['final']). 4.46/4.73 cnf(c_0_11554, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk265_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X4),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_6911]), ['final']). 4.46/4.73 cnf(c_0_11555, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X2))|hAPP(c_Finite__Set_Ocard(X1),esk64_3(X3,X2,X1))!=X3|esk66_3(X3,X2,X1)!=esk65_3(X3,X2,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))), inference(csr,[status(thm)],[c_0_6912, c_0_6445]), ['final']). 4.46/4.73 cnf(c_0_11556, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk198_4(X1,X2,X3,X4)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6609]), ['final']). 4.46/4.73 cnf(c_0_11557, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk105_4(X1,X2,X3,X4)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6610]), ['final']). 4.46/4.73 cnf(c_0_11558, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))=c_Groups_Oone__class_Oone(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6913, c_0_4760]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_11559, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X1),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_6914]), ['final']). 4.46/4.73 cnf(c_0_11560, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_6915]), ['final']). 4.46/4.73 cnf(c_0_11561, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_6916]), ['final']). 4.46/4.73 cnf(c_0_11562, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk451_4(X1,X2,X3,X4)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6616]), ['final']). 4.46/4.73 cnf(c_0_11563, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk107_4(X1,X2,X3,X4)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6611]), ['final']). 4.46/4.73 cnf(c_0_11564, plain, (X1=X2|X3=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X4),hAPP(hAPP(c_List_Olist_OCons(X5),X1),c_List_Olist_ONil(X5)))),hAPP(hAPP(c_List_Oappend(X5),X3),hAPP(hAPP(c_List_Olist_OCons(X5),X2),c_List_Olist_ONil(X5))))),c_List_Olistrel1(X5,X6)))), inference(split_conjunct,[status(thm)],[c_0_6221]), ['final']). 4.46/4.73 cnf(c_0_11565, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk63_5(X2,X3,X4,X1,X5)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5),X4),X3)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X5)), inference(split_conjunct,[status(thm)],[c_0_6917]), ['final']). 4.46/4.73 cnf(c_0_11566, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk416_4(X2,X3,X1,X4)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X2),X3)))|~class_Rings_Olinordered__semidom(X4)), inference(split_conjunct,[status(thm)],[c_0_6918]), ['final']). 4.46/4.73 cnf(c_0_11567, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)), inference(er,[status(thm)],[c_0_6919]), ['final']). 4.46/4.73 cnf(c_0_11568, plain, (hAPP(c_Set_Oimage(X2,X4,hAPP(c_Fun_Ocomp(X1,X4,X2,X5),X3)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))|c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X2,X1,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))|c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X1,X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_6920]), ['final']). 4.46/4.73 cnf(c_0_11569, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk433_3(X2,X3,X1)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X3),X2)))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_6921]), ['final']). 4.46/4.73 cnf(c_0_11570, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk432_3(X2,X3,X1)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X3),X2)))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_6921]), ['final']). 4.46/4.73 cnf(c_0_11571, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk344_4(X2,X3,X1,X4)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X2),X3)))|~class_Rings_Olinordered__semidom(X4)), inference(split_conjunct,[status(thm)],[c_0_6922]), ['final']). 4.46/4.73 cnf(c_0_11572, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk243_5(X2,X3,X1,X4,X5)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X5),X3),X2)))|~class_Complete__Lattice_Ocomplete__lattice(X5)), inference(split_conjunct,[status(thm)],[c_0_6923]), ['final']). 4.46/4.73 cnf(c_0_11573, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2))), inference(csr,[status(thm)],[c_0_6924, c_0_6925]), ['final']). 4.46/4.73 cnf(c_0_11574, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X5))), inference(csr,[status(thm)],[c_0_6926, c_0_6925]), ['final']). 4.46/4.73 cnf(c_0_11575, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6927]), ['final']). 4.46/4.73 cnf(c_0_11576, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6928]), ['final']). 4.46/4.73 cnf(c_0_11577, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X2,X3),X6)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))))), inference(split_conjunct,[status(thm)],[c_0_6929]), ['final']). 4.46/4.73 cnf(c_0_11578, plain, (hAPP(c_Option_Ooption_OSome(X2),X4)=hAPP(hAPP(c_Map_Omap__of(X1,X2),X5),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_List_Oset(tc_prod(X1,X2)),X5)))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X5)))), inference(split_conjunct,[status(thm)],[c_0_6930]), ['final']). 4.46/4.73 cnf(c_0_11579, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X1,X2)),X3))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_Enum_Oenum__class_Oenum__all(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2)))))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_6421]), ['final']). 4.46/4.73 cnf(c_0_11580, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X1,X2)),X3))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_Enum_Oenum__class_Oenum__ex(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2)))))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_6422]), ['final']). 4.46/4.73 cnf(c_0_11581, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_6931]), ['final']). 4.46/4.73 cnf(c_0_11582, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4))),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X4))))|c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X2,X1,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_6932]), ['final']). 4.46/4.73 cnf(c_0_11583, plain, (hAPP(hAPP(c_List_Onth(X2),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(c_Nat_OSuc,X1)))=hAPP(hAPP(c_List_Onth(X2),hAPP(c_List_Orev(X2),X3)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6933]), ['final']). 4.46/4.73 cnf(c_0_11584, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_6934]), ['final']). 4.46/4.73 cnf(c_0_11585, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk188_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk187_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_6935, c_0_5100]), ['final']). 4.46/4.73 cnf(c_0_11586, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X3),hAPP(hAPP(c_List_Olist_OCons(X5),X4),X6))=hAPP(hAPP(c_List_Olist_OCons(X5),X3),hAPP(hAPP(c_List_Olist_OCons(X5),X4),X6))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X2,X4)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6571]), ['final']). 4.46/4.73 cnf(c_0_11587, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X6,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(X5,X2),X7)))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X6,X3),X7))), inference(split_conjunct,[status(thm)],[c_0_6936]), ['final']). 4.46/4.73 cnf(c_0_11588, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),c_Orderings_Otop__class_Otop(X1)),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X4),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))), inference(rw,[status(thm)],[c_0_6937, c_0_6349]), ['final']). 4.46/4.73 cnf(c_0_11589, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X4),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_6938]), ['final']). 4.46/4.73 cnf(c_0_11590, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(esk4_2(X2,X1),hAPP(c_Nat_OSuc,X3))),hAPP(esk4_2(X2,X1),X3))),X2))|c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_6939]), ['final']). 4.46/4.73 cnf(c_0_11591, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_6940]), ['final']). 4.46/4.73 cnf(c_0_11592, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3),hAPP(c_Nat_OSuc,X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6941]), ['final']). 4.46/4.73 cnf(c_0_11593, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X4),X2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_6942]), ['final']). 4.46/4.73 cnf(c_0_11594, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X4),X2)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_6943]), ['final']). 4.46/4.73 cnf(c_0_11595, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X4),X2)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_6944]), ['final']). 4.46/4.73 cnf(c_0_11596, plain, (c_List_Olist__all2(X1,X3,X4,X6,hAPP(hAPP(c_List_Omap(X2,X3),X5),X7))|~c_List_Olist__all2(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X3),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X2,X3),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(X3,tc_HOL_Obool,X2)),X4)),X5),X6,X7)), inference(split_conjunct,[status(thm)],[c_0_6535]), ['final']). 4.46/4.73 cnf(c_0_11597, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_6945]), ['final']). 4.46/4.73 cnf(c_0_11598, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X2,X3),X5)),hAPP(c_Relation_OImage(X1,X2,X4),X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X6))), inference(split_conjunct,[status(thm)],[c_0_6946]), ['final']). 4.46/4.73 cnf(c_0_11599, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5)),X2),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6947, c_0_5580]), c_0_5580]), ['final']). 4.46/4.73 cnf(c_0_11600, plain, (hBOOL(hAPP(X4,X2))|hBOOL(hAPP(hAPP(c_member(X1),esk10_4(X4,X3,X5,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6476]), ['final']). 4.46/4.73 cnf(c_0_11601, plain, (hBOOL(hAPP(X4,X2))|hBOOL(hAPP(hAPP(c_member(X1),esk10_4(X4,X5,X3,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X5)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6476]), ['final']). 4.46/4.73 cnf(c_0_11602, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),esk506_7(X6,X5,X7,X4,X3,X2,X1)))|hBOOL(hAPP(hAPP(c_member(X1),X7),X5))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,hAPP(hAPP(c_Set_Oinsert(X1),X7),X5)),X6))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_6948]), ['final']). 4.46/4.73 cnf(c_0_11603, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))),hAPP(X2,X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))|~class_Groups_Ocomm__monoid__add(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6949, c_0_6071]), c_0_5884]), c_0_6071]), ['final']). 4.46/4.73 cnf(c_0_11604, plain, (hAPP(X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X7),X8))=hAPP(hAPP(X3,hAPP(X6,X7)),hAPP(X6,X8))|~c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X8))), inference(split_conjunct,[status(thm)],[c_0_6950]), ['final']). 4.46/4.73 cnf(c_0_11605, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X4))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_6951]), ['final']). 4.46/4.73 cnf(c_0_11606, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X4))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_6952]), ['final']). 4.46/4.73 cnf(c_0_11607, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X4))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_6953]), ['final']). 4.46/4.73 cnf(c_0_11608, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Olist__update(X1,X4),X8),X6),hAPP(hAPP(c_List_Olist__update(X2,X5),X8),X7))|~c_List_Olist__all2(X1,X2,X3,X4,X5)|~hBOOL(hAPP(hAPP(X3,X6),X7))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)))), inference(split_conjunct,[status(thm)],[c_0_6954]), ['final']). 4.46/4.73 cnf(c_0_11609, plain, (c_List_Olist__all2(X2,X4,X5,hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X7),hAPP(hAPP(c_List_Olist__update(X4,X6),X1),X8))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))|~c_List_Olist__all2(X2,X4,X5,X3,X6)|~hBOOL(hAPP(hAPP(X5,X7),X8))), inference(split_conjunct,[status(thm)],[c_0_6955]), ['final']). 4.46/4.73 cnf(c_0_11610, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(c_Set_Oimage(X4,X1,X5),X6))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X2),X7),X6)|hAPP(X3,hAPP(X5,esk270_8(X3,X7,hAPP(c_Set_Oimage(X4,X1,X5),X6),X6,X5,X1,X4,X2)))!=hAPP(X7,esk270_8(X3,X7,hAPP(c_Set_Oimage(X4,X1,X5),X6),X6,X5,X1,X4,X2))|~c_Fun_Oinj__on(X4,X1,X5,X6)|~class_Groups_Ocomm__monoid__add(X2)), inference(er,[status(thm)],[c_0_6956]), ['final']). 4.46/4.73 cnf(c_0_11611, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|c_Option_Ooption_ONone(X4)=hAPP(hAPP(c_Map_Omap__of(X1,X4),hAPP(hAPP(c_List_Ozip(X1,X4),X3),X5)),X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5)), inference(split_conjunct,[status(thm)],[c_0_6957]), ['final']). 4.46/4.73 cnf(c_0_11612, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X4))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4))))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_6958]), ['final']). 4.46/4.73 cnf(c_0_11613, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))|~class_Orderings_Oorder(X2)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBS(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X3)),X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))), inference(rw,[status(thm)],[c_0_6959, c_0_5671]), ['final']). 4.46/4.73 cnf(c_0_11614, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X2)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6960, c_0_4448]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_11615, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),c_List_OtakeWhile(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5))|hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)!=hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X1))),X1)), inference(rw,[status(thm)],[c_0_6961, c_0_4916]), ['final']). 4.46/4.73 cnf(c_0_11616, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),X4)=c_Option_Ooption_ONone(X2)|hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))))), inference(rw,[status(thm)],[c_0_6962, c_0_5275]), ['final']). 4.46/4.73 cnf(c_0_11617, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))=c_Divides_OposDivAlg(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_6963]), ['final']). 4.46/4.73 cnf(c_0_11618, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))),hAPP(X2,hAPP(c_Nat_OSuc,X3)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)))|~class_Groups_Ocomm__monoid__add(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6964, c_0_6965]), c_0_6965]), ['final']). 4.46/4.73 cnf(c_0_11619, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X3),c_Int_Onat),X1)),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Int_Oint),X1),X2)|~c_Nat__Transfer_Ois__nat(hAPP(X1,esk88_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_6966]), ['final']). 4.46/4.73 cnf(c_0_11620, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Int_Oint),X1),X2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X3),c_Int_Onat),X1)),X2))|~c_Nat__Transfer_Ois__nat(hAPP(X1,esk80_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_6714]), ['final']). 4.46/4.73 cnf(c_0_11621, plain, (hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X3)))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2))),X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_6676]), ['final']). 4.46/4.73 cnf(c_0_11622, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk420_5(X2,X3,X1,X4,X5)),X3))|hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X5,tc_HOL_Obool)),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6967]), ['final']). 4.46/4.73 cnf(c_0_11623, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(X2,c_Big__Operators_Olinorder__class_OMax(X1,X3))=c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_Set_Oimage(X1,X1,X2),X3))|~class_Orderings_Olinorder(X1)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk241_3(X3,X2,X1))),hAPP(X2,esk242_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk241_3(X3,X2,X1)),esk242_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6968]), ['final']). 4.46/4.73 cnf(c_0_11624, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(X2,c_Big__Operators_Olattice__class_OInf__fin(X1,X3))=c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_Set_Oimage(X1,X1,X2),X3))|~class_Lattices_Olattice(X1)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X2,esk323_3(X3,X2,X1))),hAPP(X2,esk324_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),esk323_3(X3,X2,X1)),esk324_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6969]), ['final']). 4.46/4.73 cnf(c_0_11625, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(X2,c_Big__Operators_Olattice__class_OSup__fin(X1,X3))=c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_Set_Oimage(X1,X1,X2),X3))|~class_Lattices_Olattice(X1)|hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),esk60_3(X3,X2,X1)),esk61_3(X3,X2,X1)))!=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X2,esk60_3(X3,X2,X1))),hAPP(X2,esk61_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6970]), ['final']). 4.46/4.73 cnf(c_0_11626, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(X2,c_Big__Operators_Olinorder__class_OMin(X1,X3))=c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_Set_Oimage(X1,X1,X2),X3))|~class_Orderings_Olinorder(X1)|hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk49_3(X3,X2,X1)),esk50_3(X3,X2,X1)))!=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk49_3(X3,X2,X1))),hAPP(X2,esk50_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6971]), ['final']). 4.46/4.73 cnf(c_0_11627, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_5456]), ['final']). 4.46/4.73 cnf(c_0_11628, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X2),X4),hAPP(c_Set_Oimage(X1,X3,X5),X6))|~c_Fun_Oinj__on(X1,X3,X5,X6)|~class_Groups_Ocomm__monoid__mult(X2)), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6972])]), ['final']). 4.46/4.73 cnf(c_0_11629, plain, (hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X3)))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2))),X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_6677]), ['final']). 4.46/4.73 cnf(c_0_11630, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2))))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6973, c_0_4945]), c_0_5320]), c_0_4531]), ['final']). 4.46/4.73 cnf(c_0_11631, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1))))|~class_Rings_Olinordered__ring__strict(X2)), inference(split_conjunct,[status(thm)],[c_0_5456]), ['final']). 4.46/4.73 cnf(c_0_11632, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),esk528_5(X1,X3,X4,X5,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X5),esk529_5(X1,X3,X4,X5,X2)))|hAPP(hAPP(c_List_Olist_OCons(X2),X5),X4)!=hAPP(c_List_Ofilter(X2,X3),X1)), inference(split_conjunct,[status(thm)],[c_0_5072]), ['final']). 4.46/4.73 cnf(c_0_11633, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),esk152_5(X3,X4,X1,X5,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),esk153_5(X3,X4,X1,X5,X2)))|hAPP(c_List_Ofilter(X2,X5),X1)!=hAPP(hAPP(c_List_Olist_OCons(X2),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_5090]), ['final']). 4.46/4.73 cnf(c_0_11634, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X1,X1),c_Groups_Ouminus__class_Ouminus(X1)),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)))|~class_Groups_Oab__group__add(X1)), inference(rw,[status(thm)],[c_0_6974, c_0_6975]), ['final']). 4.46/4.73 cnf(c_0_11635, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))=c_Divides_OnegDivAlg(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_6976]), ['final']). 4.46/4.73 cnf(c_0_11636, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X4,X5),X1),hAPP(c_List_Ofilter(X4,X2),X3)))=hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X4,X5),X1),X3))|hAPP(X1,esk295_5(X1,X2,X3,X4,X5))!=c_Groups_Ozero__class_Ozero(X5)|~class_Groups_Omonoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6467]), ['final']). 4.46/4.73 cnf(c_0_11637, plain, (X1=hAPP(hAPP(X2,X3),esk506_7(X1,X4,X3,X5,X2,X6,X7))|hBOOL(hAPP(hAPP(c_member(X7),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X6,X2,X5,hAPP(hAPP(c_Set_Oinsert(X7),X3),X4)),X1))|~c_Finite__Set_Ofun__left__comm(X7,X6,X2)), inference(split_conjunct,[status(thm)],[c_0_6948]), ['final']). 4.46/4.73 cnf(c_0_11638, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2))))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_6977]), ['final']). 4.46/4.73 cnf(c_0_11639, plain, (X4=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X5|hAPP(hAPP(X2,hAPP(X3,X4)),hAPP(X3,X5))=hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~c_Finite__Set_Ofolding__one__idem(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_6978]), ['final']). 4.46/4.73 cnf(c_0_11640, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6979]), ['final']). 4.46/4.73 cnf(c_0_11641, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6980, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11642, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,esk532_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X1))), inference(rw,[status(thm)],[c_0_6981, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11643, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,esk534_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X1))), inference(rw,[status(thm)],[c_0_6982, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11644, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X4,X5),X2),hAPP(c_List_Ofilter(X4,X1),X3)))=hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X4,X5),X2),X3))|~hBOOL(hAPP(X1,esk295_5(X2,X1,X3,X4,X5)))|~class_Groups_Omonoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6467]), ['final']). 4.46/4.73 cnf(c_0_11645, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X1),esk93_4(X2,X3,X1,X4)),X3))|hAPP(X2,X4)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6983, c_0_4836]), c_0_4836]), ['final']). 4.46/4.73 cnf(c_0_11646, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk532_3(X1,X2,X3)))|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_11647, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6984, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11648, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6985, c_0_4760]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), ['final']). 4.46/4.73 cnf(c_0_11649, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6808]), ['final']). 4.46/4.73 cnf(c_0_11650, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X2))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6812]), ['final']). 4.46/4.73 cnf(c_0_11651, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6808]), ['final']). 4.46/4.73 cnf(c_0_11652, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X2))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6812]), ['final']). 4.46/4.73 cnf(c_0_11653, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X3)|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6986, c_0_4609]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_11654, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6987, c_0_4760]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), ['final']). 4.46/4.73 cnf(c_0_11655, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X1),X2),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X3))|~class_Groups_Ocomm__monoid__add(X1)|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_6988]), ['final']). 4.46/4.73 cnf(c_0_11656, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X3))|~class_Groups_Ocomm__monoid__add(X1)|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_6989]), ['final']). 4.46/4.73 cnf(c_0_11657, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk538_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3)))=X1|epred2_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[c_0_6990, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11658, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6846]), ['final']). 4.46/4.73 cnf(c_0_11659, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6846]), ['final']). 4.46/4.73 cnf(c_0_11660, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6840]), ['final']). 4.46/4.73 cnf(c_0_11661, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6840]), ['final']). 4.46/4.73 cnf(c_0_11662, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk536_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3)))=X1|epred2_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_6991, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11663, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X6),X3)|~class_Divides_Osemiring__div(X1)|c_Divides_Odiv__class_Omod(X1,X2,X3)!=c_Divides_Odiv__class_Omod(X1,X4,X3)|c_Divides_Odiv__class_Omod(X1,X5,X3)!=c_Divides_Odiv__class_Omod(X1,X6,X3)), inference(split_conjunct,[status(thm)],[c_0_6992]), ['final']). 4.46/4.73 cnf(c_0_11664, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),c_Orderings_Obot__class_Obot(X1)),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X4),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))), inference(rw,[status(thm)],[c_0_6993, c_0_6349]), ['final']). 4.46/4.73 cnf(c_0_11665, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X3))),X2)=c_List_Osublist(X1,X2,X3)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(rw,[status(thm)],[c_0_6994, c_0_4945]), ['final']). 4.46/4.73 cnf(c_0_11666, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X4)),hAPP(c_Finite__Set_Ocard(X2),X5)))|~c_Fun_Oinj__on(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))), inference(split_conjunct,[status(thm)],[c_0_6995]), ['final']). 4.46/4.73 cnf(c_0_11667, plain, (hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X4),X5)=hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),hAPP(c_List_Oset(X1),X5))|~c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_6996]), ['final']). 4.46/4.73 cnf(c_0_11668, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk74_3(X2,X3,X1)),X2))|hBOOL(hAPP(hAPP(c_member(X1),esk73_3(X2,X3,X1)),X3))|c_Relation_Orefl__on(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_4937]), ['final']). 4.46/4.73 cnf(c_0_11669, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X2,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6997]), ['final']). 4.46/4.73 cnf(c_0_11670, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk436_4(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3),X3,X2)),esk435_4(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3),X3,X2))=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)=X2|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(er,[status(thm)],[c_0_6998]), ['final']). 4.46/4.73 cnf(c_0_11671, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_6999]), ['final']). 4.46/4.73 cnf(c_0_11672, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_7000]), ['final']). 4.46/4.73 cnf(c_0_11673, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),hAPP(c_Relation_Oconverse(X1,X2),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_7001]), ['final']). 4.46/4.73 cnf(c_0_11674, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel1(X1,X2)),c_List_Olistrel(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)), inference(split_conjunct,[status(thm)],[c_0_7002]), ['final']). 4.46/4.73 cnf(c_0_11675, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk258_4(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3),X3,X2)),esk257_4(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3),X3,X2))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)=X2|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(er,[status(thm)],[c_0_7003]), ['final']). 4.46/4.73 cnf(c_0_11676, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X2))))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_7004]), ['final']). 4.46/4.73 cnf(c_0_11677, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_7005]), ['final']). 4.46/4.73 cnf(c_0_11678, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_7006]), ['final']). 4.46/4.73 cnf(c_0_11679, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_7007]), ['final']). 4.46/4.73 cnf(c_0_11680, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk256_3(X1,X2,X3)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk255_3(X1,X2,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.46/4.73 cnf(c_0_11681, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk72_3(X1,X2,X3)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk71_3(X1,X2,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))), inference(split_conjunct,[status(thm)],[c_0_5095]), ['final']). 4.46/4.73 cnf(c_0_11682, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk428_3(X3,X2,X1)),esk429_3(X3,X2,X1))=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olexord(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_5783]), ['final']). 4.46/4.73 cnf(c_0_11683, plain, (X1=X2|hAPP(hAPP(c_List_Olist__update(X3,hAPP(hAPP(c_List_Olist__update(X3,X4),X2),X5)),X1),X6)=hAPP(hAPP(c_List_Olist__update(X3,hAPP(hAPP(c_List_Olist__update(X3,X4),X1),X6)),X2),X5)), inference(split_conjunct,[status(thm)],[c_0_7008]), ['final']). 4.46/4.73 cnf(c_0_11684, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X6),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5),X3)|~class_Divides_Osemiring__div(X1)|c_Divides_Odiv__class_Omod(X1,X2,X3)!=c_Divides_Odiv__class_Omod(X1,X4,X3)|c_Divides_Odiv__class_Omod(X1,X5,X3)!=c_Divides_Odiv__class_Omod(X1,X6,X3)), inference(split_conjunct,[status(thm)],[c_0_7009]), ['final']). 4.46/4.73 cnf(c_0_11685, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X3))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_7007]), ['final']). 4.46/4.73 cnf(c_0_11686, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_7010]), ['final']). 4.46/4.73 cnf(c_0_11687, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2))|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_7011]), ['final']). 4.46/4.73 cnf(c_0_11688, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X5),X2)),hAPP(c_List_Oset(tc_prod(X3,X1)),X4)))|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(hAPP(c_Map_Omap__of(X3,X1),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_7012]), ['final']). 4.46/4.73 cnf(c_0_11689, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Rings_Oordered__ring__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_7013]), ['final']). 4.46/4.73 cnf(c_0_11690, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Rings_Oordered__ring__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_7013]), ['final']). 4.46/4.73 cnf(c_0_11691, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2))|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_7014]), ['final']). 4.46/4.73 cnf(c_0_11692, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X6),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5),X3)|~class_Divides_Oring__div(X1)|c_Divides_Odiv__class_Omod(X1,X2,X3)!=c_Divides_Odiv__class_Omod(X1,X4,X3)|c_Divides_Odiv__class_Omod(X1,X5,X3)!=c_Divides_Odiv__class_Omod(X1,X6,X3)), inference(split_conjunct,[status(thm)],[c_0_7015]), ['final']). 4.46/4.73 cnf(c_0_11693, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk125_3(X2,X3,X1))),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_7016]), ['final']). 4.46/4.73 cnf(c_0_11694, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))), inference(split_conjunct,[status(thm)],[c_0_4650]), ['final']). 4.46/4.73 cnf(c_0_11695, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))),X2)|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7017]), ['final']). 4.46/4.73 cnf(c_0_11696, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Oordered__ring__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_7013]), ['final']). 4.46/4.73 cnf(c_0_11697, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Oordered__ring__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_7013]), ['final']). 4.46/4.73 cnf(c_0_11698, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk253_4(X2,X3,X1,X4)),hAPP(c_List_Oset(X1),X3)))|hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))), inference(split_conjunct,[status(thm)],[c_0_7018]), ['final']). 4.46/4.73 cnf(c_0_11699, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk434_3(X3,X2,X1)),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_7019]), ['final']). 4.46/4.73 cnf(c_0_11700, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))),X2)|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_7020]), ['final']). 4.46/4.73 cnf(c_0_11701, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5))=hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_7021]), ['final']). 4.46/4.73 cnf(c_0_11702, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_7022]), ['final']). 4.46/4.73 cnf(c_0_11703, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBS(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Oord__class_Oless__eq(X2)),X3)),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))|~class_Orderings_Oorder(X2)|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_7023]), ['final']). 4.46/4.73 cnf(c_0_11704, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Set_Oimage(X2,X4,hAPP(hAPP(c_COMBB(X1,X4,X2),X5),X3)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Oimage(X2,X1,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_7024]), ['final']). 4.46/4.73 cnf(c_0_11705, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))),X2)|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_7025]), ['final']). 4.46/4.73 cnf(c_0_11706, plain, (c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),X2)=hAPP(c_List_Ofoldl(tc_List_Olist(X1),X1,hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1))),c_List_Olist_ONil(X1)),X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7026]), ['final']). 4.46/4.73 cnf(c_0_11707, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7027]), ['final']). 4.46/4.73 cnf(c_0_11708, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X3))|~class_Fields_Ofield(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7028]), ['final']). 4.46/4.73 cnf(c_0_11709, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7029]), ['final']). 4.46/4.73 cnf(c_0_11710, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X4),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7030]), ['final']). 4.46/4.73 cnf(c_0_11711, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6808]), ['final']). 4.46/4.73 cnf(c_0_11712, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6812]), ['final']). 4.46/4.73 cnf(c_0_11713, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7031]), ['final']). 4.46/4.73 cnf(c_0_11714, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7032]), ['final']). 4.46/4.73 cnf(c_0_11715, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7033]), ['final']). 4.46/4.73 cnf(c_0_11716, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Odrop(X3),X2),X4))),hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Odrop(X3),X1),X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7034]), ['final']). 4.46/4.73 cnf(c_0_11717, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Otake(X3),X1),X4))),hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Otake(X3),X2),X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7035]), ['final']). 4.46/4.73 cnf(c_0_11718, plain, (c_List_OtakeWhile(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),c_List_Olast(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X2)=c_List_Obutlast(X1,X2)|X2=c_List_Olist_ONil(X1)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7036, c_0_5670]), c_0_5671]), ['final']). 4.46/4.73 cnf(c_0_11719, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X4),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7037]), ['final']). 4.46/4.73 cnf(c_0_11720, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X4),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7038]), ['final']). 4.46/4.73 cnf(c_0_11721, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk273_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2)))|hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6866]), ['final']). 4.46/4.73 cnf(c_0_11722, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6846]), ['final']). 4.46/4.73 cnf(c_0_11723, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|c_Option_Ooption_ONone(X4)=hAPP(hAPP(c_Map_Omap__of(X1,X4),hAPP(hAPP(c_List_Ozip(X1,X4),X3),hAPP(hAPP(c_List_Omap(X1,X4),X5),X3))),X2)), inference(split_conjunct,[status(thm)],[c_0_6910]), ['final']). 4.46/4.73 cnf(c_0_11724, plain, (c_List_Olist__all(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X3))),X4)|~c_List_Olist__ex1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~hBOOL(hAPP(X2,X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7039, c_0_5671]), c_0_7040]), c_0_4934]), ['final']). 4.46/4.73 cnf(c_0_11725, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk178_4(X2,X3,X4,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3))|~hBOOL(hAPP(X2,X5))), inference(split_conjunct,[status(thm)],[c_0_6573]), ['final']). 4.46/4.73 cnf(c_0_11726, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk178_4(X2,X3,X4,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))), inference(split_conjunct,[status(thm)],[c_0_6573]), ['final']). 4.46/4.73 cnf(c_0_11727, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X3)),X3)))|~c_Relation_Orefl__on(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7041]), ['final']). 4.46/4.73 cnf(c_0_11728, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6840]), ['final']). 4.46/4.73 cnf(c_0_11729, plain, (X1=hAPP(X2,esk256_3(X1,X2,X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk255_3(X1,X2,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.46/4.73 cnf(c_0_11730, plain, (X1=hAPP(X2,esk72_3(X1,X2,X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk71_3(X1,X2,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))), inference(split_conjunct,[status(thm)],[c_0_5095]), ['final']). 4.46/4.73 cnf(c_0_11731, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7042, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), ['final']). 4.46/4.73 cnf(c_0_11732, plain, (hBOOL(hAPP(hAPP(c_member(X2),X4),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7043]), ['final']). 4.46/4.73 cnf(c_0_11733, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7044, c_0_4836]), c_0_4836]), ['final']). 4.46/4.73 cnf(c_0_11734, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7045, c_0_4836]), c_0_4836]), ['final']). 4.46/4.73 cnf(c_0_11735, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2)|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7046]), ['final']). 4.46/4.73 cnf(c_0_11736, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7047, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), ['final']). 4.46/4.73 cnf(c_0_11737, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7048, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), ['final']). 4.46/4.73 cnf(c_0_11738, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7049, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), ['final']). 4.46/4.73 cnf(c_0_11739, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6808]), ['final']). 4.46/4.73 cnf(c_0_11740, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),hAPP(c_Groups_Otimes__class_Otimes(X1),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X5))|~class_Rings_Osemiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_7050]), ['final']). 4.46/4.73 cnf(c_0_11741, plain, (hBOOL(hAPP(hAPP(c_member(X2),X4),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7051]), ['final']). 4.46/4.73 cnf(c_0_11742, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))|c_List_OtakeWhile(X2,X4,X3)=hAPP(hAPP(c_List_Otake(X2),X1),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk62_4(X4,X3,X2,X1)),X1))), inference(split_conjunct,[status(thm)],[c_0_6762]), ['final']). 4.46/4.73 cnf(c_0_11743, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6812]), ['final']). 4.46/4.73 cnf(c_0_11744, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6846]), ['final']). 4.46/4.73 cnf(c_0_11745, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6840]), ['final']). 4.46/4.73 cnf(c_0_11746, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk188_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk187_3(X1,X2,X3)))=X2|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)))), inference(rw,[status(thm)],[c_0_7052, c_0_5100]), ['final']). 4.46/4.73 cnf(c_0_11747, plain, (X1=X2|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6,tc_Option_Ooption(X4)),X3),X2),hAPP(c_Option_Ooption_OSome(X4),X7)),X1)=hAPP(c_Option_Ooption_OSome(X4),X5)|hAPP(X3,X1)!=hAPP(c_Option_Ooption_OSome(X4),X5)), inference(split_conjunct,[status(thm)],[c_0_7053]), ['final']). 4.46/4.73 cnf(c_0_11748, plain, (hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_OSuc,X1)),X3))=hAPP(hAPP(c_List_Odrop(X2),X1),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_7054]), ['final']). 4.46/4.73 cnf(c_0_11749, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7055, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4436]), c_0_4436]), ['final']). 4.46/4.73 cnf(c_0_11750, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omlex__prod(X4,X1,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_7056]), ['final']). 4.46/4.73 cnf(c_0_11751, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X4)))|~hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),hAPP(c_Nat_OSuc,X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_7057]), ['final']). 4.46/4.73 cnf(c_0_11752, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7058, c_0_4500]), c_0_4760]), c_0_5765]), ['final']). 4.46/4.73 cnf(c_0_11753, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7059, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4436]), c_0_4436]), ['final']). 4.46/4.73 cnf(c_0_11754, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7060, c_0_4500]), c_0_4760]), c_0_5765]), ['final']). 4.46/4.73 cnf(c_0_11755, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7061, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4436]), c_0_4436]), ['final']). 4.46/4.73 cnf(c_0_11756, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk370_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk369_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[c_0_7062, c_0_5100]), ['final']). 4.46/4.73 cnf(c_0_11757, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk249_6(X3,X4,X2,X1,X5,X6)),esk250_6(X3,X4,X2,X1,X5,X6))=X3|~hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(X6,tc_HOL_Obool)),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_6795]), ['final']). 4.46/4.73 cnf(c_0_11758, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),esk228_3(X2,X3,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6756]), ['final']). 4.46/4.73 cnf(c_0_11759, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk503_3(X2,X3,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6754]), ['final']). 4.46/4.73 cnf(c_0_11760, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3)))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk454_3(X2,X3,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_6755]), ['final']). 4.46/4.73 cnf(c_0_11761, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X5))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7063]), ['final']). 4.46/4.73 cnf(c_0_11762, plain, (hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,X2),X5),X4)=hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4))|~c_Finite__Set_Ofolding__one(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_7064]), ['final']). 4.46/4.73 cnf(c_0_11763, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7065, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4609]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_11764, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7066, c_0_4436]), c_0_4500]), c_0_4760]), c_0_5765]), c_0_4436]), ['final']). 4.46/4.73 cnf(c_0_11765, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7067, c_0_4500]), c_0_4760]), c_0_5765]), ['final']). 4.46/4.73 cnf(c_0_11766, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7068, c_0_4436]), c_0_4500]), c_0_4760]), c_0_5765]), c_0_4436]), ['final']). 4.46/4.73 cnf(c_0_11767, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk458_5(X3,X4,X1,X5,X2)),X5)),X4))|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Relation_OImage(X1,X2,X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_7069]), ['final']). 4.46/4.73 cnf(c_0_11768, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk216_5(X3,X4,X1,X5,X2)),X5)),X4))|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Relation_OImage(X1,X2,X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_7070]), ['final']). 4.46/4.73 cnf(c_0_11769, plain, (c_Nitpick_Ofold__graph_H(X1,X4,X5,X6,X3,hAPP(hAPP(X5,X2),X7))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~c_Nitpick_Ofold__graph_H(X1,X4,X5,X6,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X7)), inference(split_conjunct,[status(thm)],[c_0_7071]), ['final']). 4.46/4.73 cnf(c_0_11770, plain, (c_Wellfounded_OwfP(X3,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_fun(X3,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))),X1))|hAPP(X1,esk185_3(X2,X1,X3))!=hAPP(X1,esk186_3(X2,X1,X3))|~c_Wellfounded_OwfP(X3,hAPP(X1,esk184_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_6809]), ['final']). 4.46/4.73 cnf(c_0_11771, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),c_Big__Operators_Olinorder__class_OMax(X1,X3))=c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7072]), ['final']). 4.46/4.73 cnf(c_0_11772, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7073, c_0_4500]), c_0_4760]), c_0_5765]), ['final']). 4.46/4.73 cnf(c_0_11773, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7074, c_0_4436]), c_0_4500]), c_0_4760]), c_0_5765]), c_0_4436]), ['final']). 4.46/4.73 cnf(c_0_11774, plain, (hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~c_Equiv__Relations_Oequiv(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_7075]), ['final']). 4.46/4.73 cnf(c_0_11775, plain, (hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X5)),hAPP(X3,X6))=hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X6)),hAPP(X3,X5))|~c_Finite__Set_Ofolding(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_7076]), ['final']). 4.46/4.73 cnf(c_0_11776, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk325_6(X3,X4,X5,X6,X2,X1)),esk327_6(X3,X4,X5,X6,X2,X1))=X6|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),X6),hAPP(hAPP(c_Relation_Orel__comp(X1,X5,X2),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_6574]), ['final']). 4.46/4.73 cnf(c_0_11777, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk384_5(X1,X2,X3,X4,X5)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X4)))|c_List_Olist__all2(X5,X3,X1,X4,X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2)), inference(split_conjunct,[status(thm)],[c_0_7077]), ['final']). 4.46/4.73 cnf(c_0_11778, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk293_5(X1,X2,X3,X4,X5)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X2)))|c_List_Olist__all2(X5,X4,X3,X2,X1)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X1)), inference(split_conjunct,[status(thm)],[c_0_7078]), ['final']). 4.46/4.73 cnf(c_0_11779, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,X1))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_11780, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))=c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7079]), ['final']). 4.46/4.73 cnf(c_0_11781, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_6661]), ['final']). 4.46/4.73 cnf(c_0_11782, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Nat_OSuc,esk91_3(X3,X2,X1)))))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_7057]), ['final']). 4.46/4.73 cnf(c_0_11783, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))), inference(split_conjunct,[status(thm)],[c_0_7080]), ['final']). 4.46/4.73 cnf(c_0_11784, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk538_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk536_3(X1,X2,X3)),X2))|epred2_3(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5124]), ['final']). 4.46/4.73 cnf(c_0_11785, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),X5)),X6))|~c_Fun_Oinj__on(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X6))), inference(split_conjunct,[status(thm)],[c_0_7081]), ['final']). 4.46/4.73 cnf(c_0_11786, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Owf(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_7082]), ['final']). 4.46/4.73 cnf(c_0_11787, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))), inference(rw,[status(thm)],[c_0_7083, c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_11788, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk220_5(X2,X3,X4,X1,X5)),X4))|hBOOL(hAPP(X2,X6))|~hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_6516]), ['final']). 4.46/4.73 cnf(c_0_11789, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk538_3(X2,X1,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk536_3(X2,X1,X3)))|epred2_3(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5124]), ['final']). 4.46/4.73 cnf(c_0_11790, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),c_Big__Operators_Olinorder__class_OMin(X1,X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7084]), ['final']). 4.46/4.73 cnf(c_0_11791, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7085]), ['final']). 4.46/4.73 cnf(c_0_11792, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Olinordered__comm__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))), inference(split_conjunct,[status(thm)],[c_0_7086]), ['final']). 4.46/4.73 cnf(c_0_11793, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7087]), ['final']). 4.46/4.73 cnf(c_0_11794, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_7088]), ['final']). 4.46/4.73 cnf(c_0_11795, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1)=X3|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))), inference(er,[status(thm)],[c_0_7089]), ['final']). 4.46/4.73 cnf(c_0_11796, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))), inference(split_conjunct,[status(thm)],[c_0_7090]), ['final']). 4.46/4.73 cnf(c_0_11797, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))), inference(split_conjunct,[status(thm)],[c_0_7091]), ['final']). 4.46/4.73 cnf(c_0_11798, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Rings_Oordered__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))), inference(split_conjunct,[status(thm)],[c_0_7092]), ['final']). 4.46/4.73 cnf(c_0_11799, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Oordered__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))), inference(split_conjunct,[status(thm)],[c_0_7093]), ['final']). 4.46/4.73 cnf(c_0_11800, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk476_3(X1,X2,X3)),X1))|X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6749]), ['final']). 4.46/4.73 cnf(c_0_11801, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk14_3(X3,X1,X2)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[c_0_7094, c_0_5134]), ['final']). 4.46/4.73 cnf(c_0_11802, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk538_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3)))=X1|epred2_3(X3,X2,X1)|~hBOOL(hAPP(X3,esk535_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_7095, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11803, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))=c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7096]), ['final']). 4.46/4.73 cnf(c_0_11804, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7097]), ['final']). 4.46/4.73 cnf(c_0_11805, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Oordered__comm__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))), inference(split_conjunct,[status(thm)],[c_0_7098]), ['final']). 4.46/4.73 cnf(c_0_11806, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7085]), ['final']). 4.46/4.73 cnf(c_0_11807, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk536_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3)))=X1|epred2_3(X3,X2,X1)|~hBOOL(hAPP(X3,esk537_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_7099, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11808, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6756]), ['final']). 4.46/4.73 cnf(c_0_11809, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_6755]), ['final']). 4.46/4.73 cnf(c_0_11810, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6754]), ['final']). 4.46/4.73 cnf(c_0_11811, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Groups_Otimes__class_Otimes(X1)),X3),X2)|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7100]), ['final']). 4.46/4.73 cnf(c_0_11812, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_7101]), ['final']). 4.46/4.73 cnf(c_0_11813, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_7102]), ['final']). 4.46/4.73 cnf(c_0_11814, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(hAPP(c_List_Omap(X1,X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X4),X5),X2),X6)),X3)=hAPP(hAPP(c_List_Omap(X1,X4),X5),X3)), inference(split_conjunct,[status(thm)],[c_0_7103]), ['final']). 4.46/4.73 cnf(c_0_11815, plain, (hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(c_Relation_OImage(X1,X4,X6),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),X6))), inference(split_conjunct,[status(thm)],[c_0_7104]), ['final']). 4.46/4.73 cnf(c_0_11816, plain, (hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X4)),hAPP(X3,X5))=hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X5)),hAPP(X3,X4))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7105]), ['final']). 4.46/4.73 cnf(c_0_11817, plain, (X1=hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))|hAPP(hAPP(c_List_Oappend(X2),X3),X4)!=hAPP(hAPP(c_List_Oappend(X2),X1),X5)), inference(split_conjunct,[status(thm)],[c_0_5038]), ['final']). 4.46/4.73 cnf(c_0_11818, plain, (X1=X2|hAPP(hAPP(c_Map_Omap__of(X3,X4),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X1),X5)),X6)),X2)=hAPP(hAPP(c_Map_Omap__of(X3,X4),X6),X2)), inference(split_conjunct,[status(thm)],[c_0_5821]), ['final']). 4.46/4.73 cnf(c_0_11819, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7106, c_0_6123]), c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_11820, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_7107]), ['final']). 4.46/4.73 cnf(c_0_11821, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7108]), ['final']). 4.46/4.73 cnf(c_0_11822, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_7109]), ['final']). 4.46/4.73 cnf(c_0_11823, plain, (X1=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2)),X3))|c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))!=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X4),X1)), inference(rw,[status(thm)],[c_0_7110, c_0_5644]), ['final']). 4.46/4.73 cnf(c_0_11824, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk132_3(X3,X2,X1)),esk134_3(X3,X2,X1))),X3))|c_Relation_Osingle__valued(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7111]), ['final']). 4.46/4.73 cnf(c_0_11825, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1)),X3)),X4)=hAPP(c_Option_Ooption_OSome(X2),esk464_4(X4,X3,X2,X1))|~class_Enum_Oenum(X1)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1))), inference(split_conjunct,[status(thm)],[c_0_7112]), ['final']). 4.46/4.73 cnf(c_0_11826, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk58_5(X2,X3,X4,X1,X5)),hAPP(X2,esk57_5(X2,X3,X4,X1,X5))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),X4),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_7113]), ['final']). 4.46/4.73 cnf(c_0_11827, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X1),X6),X2)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,X3)),X4))|~hBOOL(hAPP(hAPP(c_member(X5),X3),X6))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7114]), ['final']). 4.46/4.73 cnf(c_0_11828, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5207]), ['final']). 4.46/4.73 cnf(c_0_11829, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk132_3(X3,X2,X1)),esk133_3(X3,X2,X1))),X3))|c_Relation_Osingle__valued(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7111]), ['final']). 4.46/4.73 cnf(c_0_11830, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7115]), ['final']). 4.46/4.73 cnf(c_0_11831, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)),X5))|~c_Fun_Oinj__on(X1,X2,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_Set_Oimage(X1,X2,X4),X5)))), inference(rw,[status(thm)],[c_0_7116, c_0_4891]), ['final']). 4.46/4.73 cnf(c_0_11832, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X3,X1,X4),X5)))|hAPP(c_Set_Oimage(X3,X1,X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X3),X2),X4)),X5))), inference(rw,[status(thm)],[c_0_7117, c_0_4891]), ['final']). 4.46/4.73 cnf(c_0_11833, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk370_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk369_3(X1,X2,X3)))=X2|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))), inference(rw,[status(thm)],[c_0_7118, c_0_5100]), ['final']). 4.46/4.73 cnf(c_0_11834, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4),X3),X6)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X5),hAPP(X6,X2)))|~class_Complete__Lattice_Ocomplete__lattice(X4)|~class_Orderings_Olinorder(X4)), inference(split_conjunct,[status(thm)],[c_0_7119]), ['final']). 4.46/4.73 cnf(c_0_11835, plain, (c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7120]), ['final']). 4.46/4.73 cnf(c_0_11836, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7121]), ['final']). 4.46/4.73 cnf(c_0_11837, plain, (hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X6)),hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X6)),X7))=hAPP(c_Fun_Ocomp(X2,X2,X5,hAPP(X3,X6)),X7)|~c_Finite__Set_Ofolding__idem(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_7122]), ['final']). 4.46/4.73 cnf(c_0_11838, plain, (hAPP(c_List_Oset(X1),X2)=hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Oappend(X1),X3),X4))|hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)!=c_List_Opartition(X1,X5,X2)), inference(rw,[status(thm)],[c_0_7123, c_0_6608]), ['final']). 4.46/4.73 cnf(c_0_11839, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7124, c_0_6462]), c_0_6554]), ['final']). 4.46/4.73 cnf(c_0_11840, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X3))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X3),X2))), inference(rw,[status(thm)],[c_0_7125, c_0_5100]), ['final']). 4.46/4.73 cnf(c_0_11841, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_11842, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk303_5(X2,X3,X4,X1,X5)),hAPP(c_List_Oset(X1),X4)))|hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X5,X3),X2),X4)|~class_Orderings_Olinorder(X5)), inference(split_conjunct,[status(thm)],[c_0_7126]), ['final']). 4.46/4.73 cnf(c_0_11843, plain, (hAPP(c_Nat_OSuc,esk26_5(X1,X2,X3,X4,X5))=X2|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_6270]), ['final']). 4.46/4.73 cnf(c_0_11844, plain, (X1=hAPP(c_Nat_OSuc,esk391_5(X2,X1,X3,X4,X5))|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_6271]), ['final']). 4.46/4.73 cnf(c_0_11845, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk149_3(X2,X1,X3)),X3)),X2))|c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),esk147_2(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_7127]), ['final']). 4.46/4.73 cnf(c_0_11846, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X3),X4)),X5))=hAPP(hAPP(c_Set_Oinsert(X3),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X2),X5))), inference(split_conjunct,[status(thm)],[c_0_5871]), ['final']). 4.46/4.73 cnf(c_0_11847, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk44_4(X2,X3,X1,X4)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(X2,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7128]), ['final']). 4.46/4.73 cnf(c_0_11848, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk264_5(X2,X3,X4,X1,X5)),X4))|hAPP(X3,X2)=c_Groups_Ozero__class_Ozero(X5)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X3),X4)!=c_Groups_Ozero__class_Ozero(X5)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Oordered__ab__group__add(X5)), inference(split_conjunct,[status(thm)],[c_0_7129]), ['final']). 4.46/4.73 cnf(c_0_11849, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[c_0_7130, c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_11850, plain, (hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X1),X6),X5))=hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X3,X6))|~c_Finite__Set_Ofolding__idem(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_7131]), ['final']). 4.46/4.73 cnf(c_0_11851, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6606]), ['final']). 4.46/4.73 cnf(c_0_11852, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X3,X4),X2)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3,X1,hAPP(c_Relation_Oconverse(X1,X3),X4)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),X5)))))), inference(split_conjunct,[status(thm)],[c_0_6768]), ['final']). 4.46/4.73 cnf(c_0_11853, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X6),X3,c_Option_Ooption_ONone(X6),X5),hAPP(X1,X2))=hAPP(c_Option_Ooption_OSome(X6),X7)|hAPP(X5,X4)!=hAPP(c_Option_Ooption_OSome(X6),X7)|hAPP(X1,X2)!=hAPP(c_Option_Ooption_OSome(X3),X4)), inference(rw,[status(thm)],[c_0_7132, c_0_7133]), ['final']). 4.46/4.73 cnf(c_0_11854, plain, (X4=hAPP(c_Set_Oimage(X1,X2,esk171_4(X5,X1,X2,X4)),X5)|c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=X4|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),X5))|~c_Fun_Oinj__on(X2,X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_5259]), ['final']). 4.46/4.73 cnf(c_0_11855, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Map_Oran(X5,X1,X2))=c_Map_Oran(X5,X1,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X1)),X2),X3),hAPP(c_Option_Ooption_OSome(X1),X4)))|c_Option_Ooption_ONone(X1)!=hAPP(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7134]), ['final']). 4.46/4.73 cnf(c_0_11856, plain, (c_List_Oremove1(X1,X3,c_List_Olinorder__class_Osorted__list__of__set(X1,X2))=c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7135]), ['final']). 4.46/4.73 cnf(c_0_11857, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5)))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_7136]), ['final']). 4.46/4.73 cnf(c_0_11858, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5)))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_7137]), ['final']). 4.46/4.73 cnf(c_0_11859, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk387_3(X2,X3,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X2,c_Enum_Oenum__class_Oenum(X1)))))|c_Enum_Oall__n__lists(X1,X3,X2)|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_7138]), ['final']). 4.46/4.73 cnf(c_0_11860, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),X5),X3)=hAPP(c_Option_Ooption_OSome(X2),esk296_5(X5,X4,X3,X2,X1))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_List_Oset(tc_prod(X1,X2)),X5)))), inference(split_conjunct,[status(thm)],[c_0_7139]), ['final']). 4.46/4.73 cnf(c_0_11861, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5)))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_7140]), ['final']). 4.46/4.73 cnf(c_0_11862, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5)))|~class_Groups_Oordered__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_7141]), ['final']). 4.46/4.73 cnf(c_0_11863, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X5)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_7142]), ['final']). 4.46/4.73 cnf(c_0_11864, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X5)))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_7143]), ['final']). 4.46/4.73 cnf(c_0_11865, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X4,X2)),hAPP(X4,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than),X4)))), inference(rw,[status(thm)],[c_0_7144, c_0_6842]), ['final']). 4.46/4.73 cnf(c_0_11866, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk439_4(X4,X3,X2,X1)),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ORange(X3,X1),X4)))), inference(split_conjunct,[status(thm)],[c_0_7145]), ['final']). 4.46/4.73 cnf(c_0_11867, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk411_4(X4,X3,X2,X1)),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ORange(X3,X1),X4)))), inference(split_conjunct,[status(thm)],[c_0_7146]), ['final']). 4.46/4.73 cnf(c_0_11868, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk398_4(X4,X3,X2,X1))),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ODomain(X1,X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_7147]), ['final']). 4.46/4.73 cnf(c_0_11869, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Olist_OCons(X2),X3),hAPP(hAPP(c_List_Otake(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4))=hAPP(hAPP(c_List_Otake(X2),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7148]), ['final']). 4.46/4.73 cnf(c_0_11870, plain, (hAPP(c_List_Orev(tc_prod(X1,X3)),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4))=hAPP(hAPP(c_List_Ozip(X1,X3),hAPP(c_List_Orev(X1),X2)),hAPP(c_List_Orev(X3),X4))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)), inference(split_conjunct,[status(thm)],[c_0_7149]), ['final']). 4.46/4.73 cnf(c_0_11871, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))), inference(split_conjunct,[status(thm)],[c_0_7150]), ['final']). 4.46/4.73 cnf(c_0_11872, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7151]), ['final']). 4.46/4.73 cnf(c_0_11873, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Oone__class_Oone(X3)),X4))|~class_Rings_Olinordered__semidom(X3)), inference(split_conjunct,[status(thm)],[c_0_7152]), ['final']). 4.46/4.73 cnf(c_0_11874, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk414_7(X2,X3,X4,X5,X6,X7,X1)),X5))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X7,tc_fun(X6,tc_HOL_Obool))),X5),X4),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7153]), ['final']). 4.46/4.73 cnf(c_0_11875, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk306_4(X4,X3,X2,X1))),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ODomain(X1,X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_7154]), ['final']). 4.46/4.73 cnf(c_0_11876, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X4),X2)),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_7155]), ['final']). 4.46/4.73 cnf(c_0_11877, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk375_7(X2,X3,X4,X5,X6,X7,X1)),X7))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X3,tc_fun(X2,tc_HOL_Obool))),X7),X6),X5),X4))), inference(split_conjunct,[status(thm)],[c_0_7156]), ['final']). 4.46/4.73 cnf(c_0_11878, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),X4))), inference(split_conjunct,[status(thm)],[c_0_7157]), ['final']). 4.46/4.73 cnf(c_0_11879, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Oone__class_Oone(X3)),X4))|~class_Rings_Olinordered__semidom(X3)), inference(split_conjunct,[status(thm)],[c_0_7158]), ['final']). 4.46/4.73 cnf(c_0_11880, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_7159]), ['final']). 4.46/4.73 cnf(c_0_11881, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7160]), ['final']). 4.46/4.73 cnf(c_0_11882, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk302_3(X2,X3,X1)),X3)),X2))|hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7161]), ['final']). 4.46/4.73 cnf(c_0_11883, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_7162]), ['final']). 4.46/4.73 cnf(c_0_11884, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_List_Orev(X1),X2))|~class_Groups_Omonoid__add(X1)), inference(rw,[status(thm)],[c_0_7163, c_0_4713]), ['final']). 4.46/4.73 cnf(c_0_11885, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk17_3(X2,X3,X1)),X2))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6889]), ['final']). 4.46/4.73 cnf(c_0_11886, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk17_3(X2,X3,X1)),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6889]), ['final']). 4.46/4.73 cnf(c_0_11887, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk300_3(X2,X3,X1)),X3)),X2))|hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7164]), ['final']). 4.46/4.73 cnf(c_0_11888, plain, (hAPP(c_Set_Oimage(X1,X2,X3),X4)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk170_4(X4,X1,X2,hAPP(c_Set_Oimage(X1,X2,X3),X4))),hAPP(c_Set_Oimage(X1,X2,X3),X4))),X4))), inference(er,[status(thm)],[c_0_7165]), ['final']). 4.46/4.73 cnf(c_0_11889, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X1)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk214_2(X2,X1)),hAPP(X1,esk214_2(X2,X1))))), inference(rw,[status(thm)],[c_0_7166, c_0_4531]), ['final']). 4.46/4.73 cnf(c_0_11890, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk81_3(X2,X3,X1)),X3)),X2))|hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7167]), ['final']). 4.46/4.73 cnf(c_0_11891, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk332_3(X2,X3,X1)),X2))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6893]), ['final']). 4.46/4.73 cnf(c_0_11892, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk332_3(X2,X3,X1)),X3))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6893]), ['final']). 4.46/4.73 cnf(c_0_11893, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7168]), ['final']). 4.46/4.73 cnf(c_0_11894, plain, (hAPP(hAPP(c_Set_Oinsert(X1),esk405_5(X2,X3,X4,X5,X1)),esk406_5(X2,X3,X4,X5,X1))=hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_7169]), ['final']). 4.46/4.73 cnf(c_0_11895, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,X1,esk103_2(X2,X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),esk102_2(X2,X1)))=X2|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(rw,[status(thm)],[c_0_7170, c_0_4531]), ['final']). 4.46/4.73 cnf(c_0_11896, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk486_2(X1,X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))|hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7171]), ['final']). 4.46/4.73 cnf(c_0_11897, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_7172]), ['final']). 4.46/4.73 cnf(c_0_11898, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk455_5(X2,X3,X4,X5,X1)),hAPP(c_List_Oset(X1),X3)))|hAPP(hAPP(c_List_Omap(X1,X5),X4),X3)=hAPP(hAPP(c_List_Omap(X1,X5),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_7173]), ['final']). 4.46/4.73 cnf(c_0_11899, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)=hAPP(hAPP(c_Set_Oinsert(X1),esk288_5(X4,X3,X2,X5,X1)),esk289_5(X4,X3,X2,X5,X1))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_6789]), ['final']). 4.46/4.73 cnf(c_0_11900, plain, (c_Map_Omap__upds(X1,X4,X6,X2,X5)=c_Map_Omap__upds(X1,X4,X6,X2,hAPP(hAPP(c_List_Olist__update(X4,X5),X3),X7))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5)))), inference(split_conjunct,[status(thm)],[c_0_7174]), ['final']). 4.46/4.73 cnf(c_0_11901, plain, (hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),c_Transitive__Closure_Ortrancl(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_7175]), ['final']). 4.46/4.73 cnf(c_0_11902, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))),X3)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7176]), ['final']). 4.46/4.73 cnf(c_0_11903, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4))), inference(csr,[status(thm)],[c_0_7177, c_0_7178]), ['final']). 4.46/4.73 cnf(c_0_11904, plain, (c_Fun_Oinj__on(X1,tc_fun(X4,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X4,X2),X1),c_COMBK(X2,X4)),X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_7179]), ['final']). 4.46/4.73 cnf(c_0_11905, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk299_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),X4)))|hAPP(hAPP(c_List_Oappend(X1),X4),c_List_OtakeWhile(X1,X3,X2))=c_List_OtakeWhile(X1,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_7180]), ['final']). 4.46/4.73 cnf(c_0_11906, plain, (X1=hAPP(hAPP(X2,X3),X4)|hBOOL(hAPP(hAPP(c_member(X5),esk333_7(X4,X3,X6,X1,X2,X7,X5)),X6))|~c_Nitpick_Ofold__graph_H(X5,X7,X2,X1,X6,hAPP(hAPP(X2,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_6285]), ['final']). 4.46/4.73 cnf(c_0_11907, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7181, c_0_4609]), c_0_4609]), c_0_5120]), c_0_4609]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_11908, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X2)),c_Wellfounded_Ofinite__psubset(X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7182]), ['final']). 4.46/4.73 cnf(c_0_11909, plain, (hAPP(hAPP(c_List_Onth(X3),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Odrop(X3),X1),X4)),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)))), inference(split_conjunct,[status(thm)],[c_0_7183]), ['final']). 4.46/4.73 cnf(c_0_11910, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X5)))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X5))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7184]), ['final']). 4.46/4.73 cnf(c_0_11911, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X5),X4))),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7185]), ['final']). 4.46/4.73 cnf(c_0_11912, plain, (hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(X6,X2)))), inference(split_conjunct,[status(thm)],[c_0_7186]), ['final']). 4.46/4.73 cnf(c_0_11913, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,esk91_3(X1,X2,X3)))))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_7057]), ['final']). 4.46/4.73 cnf(c_0_11914, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk515_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))|hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7187]), ['final']). 4.46/4.73 cnf(c_0_11915, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),hAPP(c_Relation_Oconverse(X1,X1),X2))!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))), inference(rw,[status(thm)],[c_0_7188, c_0_6164]), ['final']). 4.46/4.73 cnf(c_0_11916, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),esk333_7(X3,X4,X2,X5,X6,X7,X1)),X2))|~c_Nitpick_Ofold__graph_H(X1,X7,X6,X5,X2,hAPP(hAPP(X6,X4),X3))), inference(split_conjunct,[status(thm)],[c_0_6285]), ['final']). 4.46/4.73 cnf(c_0_11917, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),X4)))|c_List_OtakeWhile(X2,X1,X3)=hAPP(hAPP(c_List_Otake(X2),X4),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk62_4(X1,X3,X2,X4)),X4))), inference(split_conjunct,[status(thm)],[c_0_6762]), ['final']). 4.46/4.73 cnf(c_0_11918, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OSigma(X1,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X1),X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7189]), ['final']). 4.46/4.73 cnf(c_0_11919, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X1),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7190]), ['final']). 4.46/4.73 cnf(c_0_11920, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7191, c_0_5670]), c_0_5320]), c_0_4531]), ['final']). 4.46/4.73 cnf(c_0_11921, plain, (c_SetInterval_Oord__class_OgreaterThanLessThan(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X4)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X5))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7192]), ['final']). 4.46/4.73 cnf(c_0_11922, plain, (hBOOL(hAPP(X1,esk180_4(X1,X2,X3,X4)))|hBOOL(hAPP(X1,esk179_4(X1,X2,X3,X4)))|~hBOOL(hAPP(X1,X5))|~hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6573]), ['final']). 4.46/4.73 cnf(c_0_11923, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X6),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),X3),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))))|~c_List_Olist__all2(X1,X2,X6,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_6520]), ['final']). 4.46/4.73 cnf(c_0_11924, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_7193]), ['final']). 4.46/4.73 cnf(c_0_11925, plain, (hAPP(c_Nat_OSuc,esk26_5(X1,X2,X3,X4,X5))=X2|X3=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_6270]), ['final']). 4.46/4.73 cnf(c_0_11926, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X4)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X5))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7194]), ['final']). 4.46/4.73 cnf(c_0_11927, plain, (X5=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(X2,hAPP(X3,X5)),hAPP(X3,X4))=hAPP(X3,X4)|~c_Finite__Set_Ofolding__one__idem(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X4))), inference(split_conjunct,[status(thm)],[c_0_7195]), ['final']). 4.46/4.73 cnf(c_0_11928, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X5)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_7196]), ['final']). 4.46/4.73 cnf(c_0_11929, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_7197]), ['final']). 4.46/4.73 cnf(c_0_11930, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X5))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7198]), ['final']). 4.46/4.73 cnf(c_0_11931, plain, (X1=hAPP(c_Nat_OSuc,esk391_5(X2,X1,X3,X4,X5))|X4=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_6271]), ['final']). 4.46/4.73 cnf(c_0_11932, plain, (hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X3),X4)))|c_Fun_Oinj__on(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X6),X5),X4)|~c_Fun_Oinj__on(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_7199]), ['final']). 4.46/4.73 cnf(c_0_11933, plain, (c_List_Olist_ONil(tc_List_Olist(X1))=X2|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X2))|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)))), inference(split_conjunct,[status(thm)],[c_0_7200]), ['final']). 4.46/4.73 cnf(c_0_11934, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))=c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7201]), ['final']). 4.46/4.73 cnf(c_0_11935, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))|~class_Int_Onumber(X1)|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_7202]), ['final']). 4.46/4.73 cnf(c_0_11936, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_7203]), ['final']). 4.46/4.73 cnf(c_0_11937, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))|~class_Rings_Olinordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7204]), ['final']). 4.46/4.73 cnf(c_0_11938, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4))), inference(csr,[status(thm)],[c_0_7205, c_0_7206]), ['final']). 4.46/4.73 cnf(c_0_11939, plain, (hAPP(c_Relation_ORange(X1,X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))=X4|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3), inference(rw,[status(thm)],[c_0_7207, c_0_6591]), ['final']). 4.46/4.73 cnf(c_0_11940, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4))=c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7208]), ['final']). 4.46/4.73 cnf(c_0_11941, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7209]), ['final']). 4.46/4.73 cnf(c_0_11942, plain, (c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7210]), ['final']). 4.46/4.73 cnf(c_0_11943, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))!=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7211]), ['final']). 4.46/4.73 cnf(c_0_11944, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))=X3|X4=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(rw,[status(thm)],[c_0_7212, c_0_5275]), ['final']). 4.46/4.73 cnf(c_0_11945, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))|~class_Orderings_Oord(X1)|~class_Int_Onumber(X1)), inference(split_conjunct,[status(thm)],[c_0_7213]), ['final']). 4.46/4.73 cnf(c_0_11946, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7214]), ['final']). 4.46/4.73 cnf(c_0_11947, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_7215]), ['final']). 4.46/4.73 cnf(c_0_11948, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_7216]), ['final']). 4.46/4.73 cnf(c_0_11949, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Oone__class_Oone(X1)))), inference(split_conjunct,[status(thm)],[c_0_7217]), ['final']). 4.46/4.73 cnf(c_0_11950, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Oone__class_Oone(X1)))), inference(split_conjunct,[status(thm)],[c_0_7218]), ['final']). 4.46/4.73 cnf(c_0_11951, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X4,tc_fun(X1,tc_HOL_Obool)),X3),X6)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk494_6(X3,X2,X1,X4,X5,X6)),esk495_6(X3,X2,X1,X4,X5,X6))))), inference(split_conjunct,[status(thm)],[c_0_6683]), ['final']). 4.46/4.73 cnf(c_0_11952, plain, (hBOOL(hAPP(c_List_Odistinct(X2),hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1)))|esk3_2(X1,X2)!=esk2_2(X1,X2)|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1))|~hBOOL(hAPP(c_List_Odistinct(X2),esk1_2(X1,X2)))), inference(rw,[status(thm)],[c_0_7219, c_0_4736]), ['final']). 4.46/4.73 cnf(c_0_11953, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Finite__Set_Ocard(X2),X3))),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(c_COMBK(X1,X2),X4)),X3)|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7220]), ['final']). 4.46/4.73 cnf(c_0_11954, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_7221]), ['final']). 4.46/4.73 cnf(c_0_11955, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7222, c_0_4836]), c_0_4836]), c_0_4836]), ['final']). 4.46/4.73 cnf(c_0_11956, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7223, c_0_4836]), c_0_4836]), c_0_4836]), ['final']). 4.46/4.73 cnf(c_0_11957, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X1,X1),c_Groups_Oabs__class_Oabs(X1)),X2))))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_7224]), ['final']). 4.46/4.73 cnf(c_0_11958, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk415_4(X1,X2,X3,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)))|hBOOL(hAPP(X2,X1))|~hBOOL(hAPP(hAPP(c_member(X4),X1),hAPP(c_List_Oset(X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_7225]), ['final']). 4.46/4.73 cnf(c_0_11959, plain, (X1=hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk57_5(X4,X5,X1,X3,X2)),esk58_5(X4,X5,X1,X3,X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),X1),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X5),X4)))), inference(split_conjunct,[status(thm)],[c_0_7113]), ['final']). 4.46/4.73 cnf(c_0_11960, plain, (X5=X4|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X5)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))|hAPP(c_Map_Omap__of(X1,X3),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X5))!=hAPP(c_Map_Omap__of(X1,X3),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_7226]), ['final']). 4.46/4.73 cnf(c_0_11961, plain, (hAPP(hAPP(X5,X8),hAPP(c_Set_Oimage(X2,X2,X7),X6))=hAPP(hAPP(X5,hAPP(c_Fun_Ocomp(X2,X1,X2,X8),X7)),X6)|~c_Finite__Set_Ofolding__image(X1,X2,X3,X4,X5)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6))|~c_Fun_Oinj__on(X2,X2,X7,X6)), inference(split_conjunct,[status(thm)],[c_0_7227]), ['final']). 4.46/4.73 cnf(c_0_11962, plain, (X2=c_List_Olist_ONil(X1)|hAPP(c_List_Ofoldl(X1,X1,c_Groups_Otimes__class_Otimes(X1),hAPP(c_List_Ohd(X1),X2)),hAPP(c_List_Otl(X1),X2))=hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(c_List_Oset(X1),X2))|~class_Lattices_Oab__semigroup__idem__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_7228]), ['final']). 4.46/4.73 cnf(c_0_11963, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2),X5)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk15_6(X3,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2),X5),X2,X5,X4,X1))))|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5))), inference(er,[status(thm)],[c_0_7229]), ['final']). 4.46/4.73 cnf(c_0_11964, plain, (hBOOL(hAPP(hAPP(X3,hAPP(hAPP(c_List_Onth(X1),X4),X6)),hAPP(hAPP(c_List_Onth(X2),X5),X6)))|~c_List_Olist__all2(X1,X2,X3,X4,X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)))), inference(split_conjunct,[status(thm)],[c_0_7230]), ['final']). 4.46/4.73 cnf(c_0_11965, plain, (hBOOL(hAPP(hAPP(X4,hAPP(hAPP(c_List_Onth(X2),X3),X1)),hAPP(hAPP(c_List_Onth(X5),X6),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))|~c_List_Olist__all2(X2,X5,X4,X3,X6)), inference(split_conjunct,[status(thm)],[c_0_7078]), ['final']). 4.46/4.73 cnf(c_0_11966, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk91_3(X2,X3,X1))),X3))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_7057]), ['final']). 4.46/4.73 cnf(c_0_11967, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk88_3(X2,X3,X1)),X3))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X1),c_Int_Onat),X2)),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Int_Oint),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_6966]), ['final']). 4.46/4.73 cnf(c_0_11968, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)))=hAPP(c_List_Oset(X1),X3)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)|~hBOOL(hAPP(c_List_Odistinct(X1),X3))), inference(rw,[status(thm)],[c_0_7231, c_0_7232]), ['final']). 4.46/4.73 cnf(c_0_11969, plain, (hAPP(hAPP(X3,X5),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X5),X6)),X4)|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_7233]), ['final']). 4.46/4.73 cnf(c_0_11970, plain, (hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_OImage(X1,X2,X5),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_7234]), ['final']). 4.46/4.73 cnf(c_0_11971, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Oone__class_Oone(X1)))), inference(split_conjunct,[status(thm)],[c_0_7235]), ['final']). 4.46/4.73 cnf(c_0_11972, plain, (hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X3,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7236]), ['final']). 4.46/4.73 cnf(c_0_11973, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk217_3(X2,X3,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X2,c_Enum_Oenum__class_Oenum(X1)))))|~c_Enum_Oex__n__lists(X1,X3,X2)|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_7237]), ['final']). 4.46/4.73 cnf(c_0_11974, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X2)),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7238]), ['final']). 4.46/4.73 cnf(c_0_11975, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7239]), ['final']). 4.46/4.73 cnf(c_0_11976, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),c_Groups_Oone__class_Oone(X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7240]), ['final']). 4.46/4.73 cnf(c_0_11977, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X4),X5)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),X5)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7241]), ['final']). 4.46/4.73 cnf(c_0_11978, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),X5)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X4),X5)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7242]), ['final']). 4.46/4.73 cnf(c_0_11979, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X1),X2))=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7243]), ['final']). 4.46/4.73 cnf(c_0_11980, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))),X3)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7244]), ['final']). 4.46/4.73 cnf(c_0_11981, plain, (hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_7167]), ['final']). 4.46/4.73 cnf(c_0_11982, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk297_2(X1,X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7245]), ['final']). 4.46/4.73 cnf(c_0_11983, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,X1,X2),c_Int_Oring__1__class_Oof__int(X1)),X3)),X4)=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,tc_Int_Oint),X3),X4))|~class_Rings_Oring__1(X1)|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_7246]), ['final']). 4.46/4.73 cnf(c_0_11984, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X3)),c_Big__Operators_Olinorder__class_OMin(X1,X2))=c_Big__Operators_Olinorder__class_OMin(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7247]), ['final']). 4.46/4.73 cnf(c_0_11985, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X3)),c_Big__Operators_Olattice__class_OInf__fin(X1,X2))=c_Big__Operators_Olattice__class_OInf__fin(X1,X2)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7248]), ['final']). 4.46/4.73 cnf(c_0_11986, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X3)),c_Big__Operators_Olattice__class_OSup__fin(X1,X2))=c_Big__Operators_Olattice__class_OSup__fin(X1,X2)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7249]), ['final']). 4.46/4.73 cnf(c_0_11987, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Big__Operators_Olinorder__class_OMax(X1,X2)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,X3)),c_Big__Operators_Olinorder__class_OMax(X1,X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7250]), ['final']). 4.46/4.73 cnf(c_0_11988, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,tc_Nat_Onat),X3),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X1)),X3)),X4)|~class_Groups_Ocomm__monoid__mult(X1)|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7251]), ['final']). 4.46/4.73 cnf(c_0_11989, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2)))|hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X4,X5),X3),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))|~class_Orderings_Olinorder(X4)), inference(split_conjunct,[status(thm)],[c_0_7252]), ['final']). 4.46/4.73 cnf(c_0_11990, plain, (X2=X3|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ODomain(X1,X1),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_7253]), ['final']). 4.46/4.73 cnf(c_0_11991, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|c_Map_Orestrict__map(X1,X4,X5,X3)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Orestrict__map(X1,X4,X5,X3)),X2),c_Option_Ooption_ONone(X4))), inference(split_conjunct,[status(thm)],[c_0_6486]), ['final']). 4.46/4.73 cnf(c_0_11992, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7254, c_0_5120]), c_0_5120]), c_0_5120]), ['final']). 4.46/4.73 cnf(c_0_11993, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)), inference(split_conjunct,[status(thm)],[c_0_7255]), ['final']). 4.46/4.73 cnf(c_0_11994, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_7256, c_0_5100])])]), c_0_7257]), c_0_7258]), ['final']). 4.46/4.73 cnf(c_0_11995, plain, (hAPP(hAPP(c_List_Oappend(X1),esk399_3(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),esk400_3(X2,X3,X1)))=X2|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_7259]), ['final']). 4.46/4.73 cnf(c_0_11996, plain, (hAPP(hAPP(c_List_Oappend(X1),esk226_3(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),esk227_3(X2,X3,X1)))=X2|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_7260]), ['final']). 4.46/4.73 cnf(c_0_11997, plain, (hAPP(hAPP(c_List_Oappend(X1),esk165_3(X3,X2,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk166_3(X3,X2,X1)))=X3|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_5872]), ['final']). 4.46/4.73 cnf(c_0_11998, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),c_Groups_Oone__class_Oone(X1))|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7261]), ['final']). 4.46/4.73 cnf(c_0_11999, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)), inference(split_conjunct,[status(thm)],[c_0_7262]), ['final']). 4.46/4.73 cnf(c_0_12000, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)|~class_Rings_Ocomm__semiring(X1)), inference(split_conjunct,[status(thm)],[c_0_7263]), ['final']). 4.46/4.73 cnf(c_0_12001, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)|~class_Rings_Odivision__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7264]), ['final']). 4.46/4.73 cnf(c_0_12002, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk405_5(X3,X4,X5,X2,X1),esk406_5(X3,X4,X5,X2,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)),X3))), inference(split_conjunct,[status(thm)],[c_0_7169]), ['final']). 4.46/4.73 cnf(c_0_12003, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk288_5(X3,X4,X5,X2,X1),esk289_5(X3,X4,X5,X2,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)),X3))), inference(split_conjunct,[status(thm)],[c_0_6789]), ['final']). 4.46/4.73 cnf(c_0_12004, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))|c_List_OtakeWhile(X2,X4,X3)=hAPP(hAPP(c_List_Otake(X2),X1),X3)|~hBOOL(hAPP(X4,hAPP(hAPP(c_List_Onth(X2),X3),esk62_4(X4,X3,X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_6762]), ['final']). 4.46/4.73 cnf(c_0_12005, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk492_4(X2,X3,X1,X4)),hAPP(c_List_Oset(X1),X2)))|c_List_Olist__ex1(X1,X3,X2)|~hBOOL(hAPP(X3,X4))|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_7265]), ['final']). 4.46/4.73 cnf(c_0_12006, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))),X4)=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(c_COMBK(X1,X2),X4)),X3))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7266]), ['final']). 4.46/4.73 cnf(c_0_12007, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7267, c_0_4609]), c_0_4609]), c_0_5120]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_12008, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3)|~class_Lattices_Odistrib__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7268]), ['final']). 4.46/4.73 cnf(c_0_12009, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4)),X3)|~class_Lattices_Odistrib__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7269]), ['final']). 4.46/4.73 cnf(c_0_12010, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7270]), ['final']). 4.46/4.73 cnf(c_0_12011, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))|~class_Rings_Odivision__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7271]), ['final']). 4.46/4.73 cnf(c_0_12012, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk163_4(X2,X3,X1,X4)),hAPP(c_List_Oset(X1),X2)))|c_List_Olist__ex1(X1,X3,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2)))|~hBOOL(hAPP(X3,X4))), inference(split_conjunct,[status(thm)],[c_0_7272]), ['final']). 4.46/4.73 cnf(c_0_12013, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))|~class_Int_Onumber(X1)|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_7202]), ['final']). 4.46/4.73 cnf(c_0_12014, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))|~class_Orderings_Oord(X1)|~class_Int_Onumber(X1)), inference(split_conjunct,[status(thm)],[c_0_7213]), ['final']). 4.46/4.73 cnf(c_0_12015, plain, (X3=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk284_3(X1,X2,X3)))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7273]), ['final']). 4.46/4.73 cnf(c_0_12016, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7274]), ['final']). 4.46/4.73 cnf(c_0_12017, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7275]), ['final']). 4.46/4.73 cnf(c_0_12018, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7276, c_0_4760]), c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_12019, plain, (hBOOL(hAPP(X1,X2))|~epred1_3(X1,X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3))), inference(er,[status(thm)],[c_0_7277]), ['final']). 4.46/4.73 cnf(c_0_12020, plain, (hBOOL(hAPP(X1,X2))|~epred2_3(X1,X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X3))), inference(er,[status(thm)],[c_0_7278]), ['final']). 4.46/4.73 cnf(c_0_12021, plain, (hBOOL(hAPP(X1,X2))|~epred1_3(X1,X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X2))), inference(er,[status(thm)],[c_0_7279]), ['final']). 4.46/4.73 cnf(c_0_12022, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7280, c_0_4760]), c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_12023, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7281, c_0_4760]), c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_12024, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2))))), inference(split_conjunct,[status(thm)],[c_0_7282]), ['final']). 4.46/4.73 cnf(c_0_12025, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk167_3(X2,X3,X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6997]), ['final']). 4.46/4.73 cnf(c_0_12026, plain, (hBOOL(hAPP(X1,X2))|~epred2_3(X1,X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X4))), inference(er,[status(thm)],[c_0_7283]), ['final']). 4.46/4.73 cnf(c_0_12027, plain, (hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6))=hAPP(X4,X5)|~c_Finite__Set_Ofolding__idem(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X5))), inference(split_conjunct,[status(thm)],[c_0_7284]), ['final']). 4.46/4.73 cnf(c_0_12028, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk23_3(X2,X3,X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7285]), ['final']). 4.46/4.73 cnf(c_0_12029, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7286]), ['final']). 4.46/4.73 cnf(c_0_12030, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X7,tc_fun(X8,tc_HOL_Obool))),X3),X4),X5),X6))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(hAPP(X4,X2),X5),X6))), inference(split_conjunct,[status(thm)],[c_0_7287]), ['final']). 4.46/4.73 cnf(c_0_12031, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7288]), ['final']). 4.46/4.73 cnf(c_0_12032, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7289, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), ['final']). 4.46/4.73 cnf(c_0_12033, plain, (c_List_Olist_ONil(X1)=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X3,X2))),X2)|hBOOL(hAPP(hAPP(c_member(X1),esk193_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))), inference(rw,[status(thm)],[c_0_7290, c_0_4916]), ['final']). 4.46/4.73 cnf(c_0_12034, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk459_3(X2,X3,X1)),X2))|c_Relation_Orefl__on(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2))))), inference(split_conjunct,[status(thm)],[c_0_7291]), ['final']). 4.46/4.73 cnf(c_0_12035, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk41_3(X2,X3,X1)),X3))|c_Relation_Orefl__on(X1,X3,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))), inference(split_conjunct,[status(thm)],[c_0_7292]), ['final']). 4.46/4.73 cnf(c_0_12036, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk489_4(X2,X3,X4,X1)),X3))|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Wellfounded_Omax__extp(X1,X4,X3,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_5595]), ['final']). 4.46/4.73 cnf(c_0_12037, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3))), inference(rw,[status(thm)],[c_0_7293, c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_12038, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_7294]), ['final']). 4.46/4.73 cnf(c_0_12039, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))|~class_Lattices_Odistrib__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7295]), ['final']). 4.46/4.73 cnf(c_0_12040, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7296]), ['final']). 4.46/4.73 cnf(c_0_12041, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X1,X2,X3)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk532_3(X1,X2,X3)))|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,X1))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_12042, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk203_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X2))|~c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7184]), ['final']). 4.46/4.73 cnf(c_0_12043, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk202_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))|c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X2))|~c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7184]), ['final']). 4.46/4.73 cnf(c_0_12044, plain, (c_Option_Ooption_ONone(X1)=hAPP(X3,X2)|hAPP(c_Option_Ooption_OSome(X1),esk519_6(X2,X3,X4,X5,X6,X1))=hAPP(X3,X2)|c_Option_Ooption_ONone(X6)!=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X6),X1,c_Option_Ooption_ONone(X6),X4),hAPP(X3,X2))), inference(rw,[status(thm)],[c_0_7297, c_0_7133]), ['final']). 4.46/4.73 cnf(c_0_12045, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))|~class_Lattices_Odistrib__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7298]), ['final']). 4.46/4.73 cnf(c_0_12046, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))), inference(split_conjunct,[status(thm)],[c_0_7299]), ['final']). 4.46/4.73 cnf(c_0_12047, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_7300]), ['final']). 4.46/4.73 cnf(c_0_12048, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7301]), ['final']). 4.46/4.73 cnf(c_0_12049, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk263_3(X1,X2,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),X2),hAPP(hAPP(c_Relation_Orel__comp(X3,X3,X3),X1),c_Transitive__Closure_Ortrancl(X3,X1))))), inference(rw,[status(thm)],[c_0_7302, c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_12050, plain, (hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),esk346_4(X2,X3,X1,X4)),X3))|c_Hoare__Mirabelle_Otriple__valid(X1,X4,X5)|~hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X5),X2))|~c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_7303]), ['final']). 4.46/4.73 cnf(c_0_12051, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7304]), ['final']). 4.46/4.73 cnf(c_0_12052, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7085]), ['final']). 4.46/4.73 cnf(c_0_12053, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk436_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(er,[status(thm)],[c_0_7305]), ['final']). 4.46/4.73 cnf(c_0_12054, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_7306]), ['final']). 4.46/4.73 cnf(c_0_12055, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_7307]), ['final']). 4.46/4.73 cnf(c_0_12056, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel1(X1,X2)),c_List_Olistrel1(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7308]), ['final']). 4.46/4.73 cnf(c_0_12057, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel(X1,X2)),c_List_Olistrel(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7309]), ['final']). 4.46/4.73 cnf(c_0_12058, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk395_4(X2,X3,X4,X1)),X3))|hBOOL(hAPP(X2,X4))|~hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_7310]), ['final']). 4.46/4.73 cnf(c_0_12059, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk115_3(X2,X3,X1)),esk116_3(X2,X3,X1)))|hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7311]), ['final']). 4.46/4.73 cnf(c_0_12060, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X2,X1,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|epred1_3(X3,X1,X2)|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_12061, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk258_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(er,[status(thm)],[c_0_7312]), ['final']). 4.46/4.73 cnf(c_0_12062, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))|~c_Relation_Orefl__on(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_7292]), ['final']). 4.46/4.73 cnf(c_0_12063, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2))))|~c_Equiv__Relations_Oequiv(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7313]), ['final']). 4.46/4.73 cnf(c_0_12064, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|X1!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_7314]), ['final']). 4.46/4.73 cnf(c_0_12065, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X4)))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,X3))))), inference(split_conjunct,[status(thm)],[c_0_7315]), ['final']). 4.46/4.73 cnf(c_0_12066, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,X1))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_12067, plain, (c_Relation_Orefl__on(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk459_3(X2,X3,X1)),esk459_3(X2,X3,X1))),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2))))), inference(split_conjunct,[status(thm)],[c_0_7291]), ['final']). 4.46/4.73 cnf(c_0_12068, plain, (c_Relation_Orefl__on(X1,X3,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk41_3(X2,X3,X1)),esk41_3(X2,X3,X1))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))), inference(split_conjunct,[status(thm)],[c_0_7292]), ['final']). 4.46/4.73 cnf(c_0_12069, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk74_3(X2,X3,X1)),X2))|c_Relation_Orefl__on(X1,X3,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk73_3(X2,X3,X1)),esk73_3(X2,X3,X1))),X2))), inference(split_conjunct,[status(thm)],[c_0_4937]), ['final']). 4.46/4.73 cnf(c_0_12070, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2))=hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7316]), ['final']). 4.46/4.73 cnf(c_0_12071, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X4),X3)))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,X3))))), inference(split_conjunct,[status(thm)],[c_0_7315]), ['final']). 4.46/4.73 cnf(c_0_12072, plain, (hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))))), inference(split_conjunct,[status(thm)],[c_0_7317]), ['final']). 4.46/4.73 cnf(c_0_12073, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5471]), ['final']). 4.46/4.73 cnf(c_0_12074, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X3),X4))|~class_Groups_Osemigroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7318]), ['final']). 4.46/4.73 cnf(c_0_12075, plain, (hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X3,X6))=hAPP(X4,X5)|~c_Finite__Set_Ofolding__idem(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X5))), inference(split_conjunct,[status(thm)],[c_0_7319]), ['final']). 4.46/4.73 cnf(c_0_12076, plain, (hBOOL(hAPP(X1,esk445_2(X1,X2)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk444_2(X1,X2)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,esk443_2(X1,X2)))|~hBOOL(hAPP(X1,X3))), inference(rw,[status(thm)],[c_0_7320, c_0_6410]), ['final']). 4.46/4.73 cnf(c_0_12077, plain, (hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),X3),hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X3),X2)|~class_Groups_Oab__semigroup__add(X1)), inference(rw,[status(thm)],[c_0_7321, c_0_4713]), ['final']). 4.46/4.73 cnf(c_0_12078, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[c_0_7322, c_0_4436]), ['final']). 4.46/4.73 cnf(c_0_12079, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X4,X6)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5))|~hBOOL(hAPP(hAPP(c_member(X2),X6),X3))), inference(split_conjunct,[status(thm)],[c_0_6888]), ['final']). 4.46/4.73 cnf(c_0_12080, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(X5,X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(X3),X6),X4))), inference(split_conjunct,[status(thm)],[c_0_6890]), ['final']). 4.46/4.73 cnf(c_0_12081, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7323]), ['final']). 4.46/4.73 cnf(c_0_12082, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),hAPP(c_Set_Oimage(X1,X2,X3),X4)))|~c_Fun_Oinj__on(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X5),X4))), inference(split_conjunct,[status(thm)],[c_0_7324]), ['final']). 4.46/4.73 cnf(c_0_12083, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7325, c_0_4517]), c_0_4517]), ['final']). 4.46/4.73 cnf(c_0_12084, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7326]), ['final']). 4.46/4.73 cnf(c_0_12085, plain, (X2=X4|X3=X5|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)), inference(split_conjunct,[status(thm)],[c_0_7327]), ['final']). 4.46/4.73 cnf(c_0_12086, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_7328]), ['final']). 4.46/4.73 cnf(c_0_12087, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(c_Finite__Set_Ocard(X1),X3)=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7115]), ['final']). 4.46/4.73 cnf(c_0_12088, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7329]), ['final']). 4.46/4.73 cnf(c_0_12089, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(c_Nat_OSuc,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7330]), ['final']). 4.46/4.73 cnf(c_0_12090, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X4)),X3))|~c_Relation_Orefl__on(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_7331]), ['final']). 4.46/4.73 cnf(c_0_12091, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Ouminus__class_Ouminus(X1)),X3)),X4)|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7332]), ['final']). 4.46/4.73 cnf(c_0_12092, plain, (hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),X1))=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7333, c_0_4609]), c_0_4609]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_12093, plain, (c_Relation_Orefl__on(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X5))|~c_Relation_Orefl__on(X1,X2,X3)|~c_Relation_Orefl__on(X1,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_7334]), ['final']). 4.46/4.73 cnf(c_0_12094, plain, (c_Relation_Orefl__on(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X5))|~c_Relation_Orefl__on(X1,X2,X3)|~c_Relation_Orefl__on(X1,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_7335]), ['final']). 4.46/4.73 cnf(c_0_12095, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7336, c_0_5670]), c_0_5320]), c_0_4531]), ['final']). 4.46/4.73 cnf(c_0_12096, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X1)),X3)),X4)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X3),X4))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7337]), ['final']). 4.46/4.73 cnf(c_0_12097, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X1))), inference(er,[status(thm)],[c_0_7338]), ['final']). 4.46/4.73 cnf(c_0_12098, plain, (hAPP(hAPP(c_List_Oappend(X1),esk408_5(X2,X3,X4,X5,X1)),X4)=X2|hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)=X4|hAPP(hAPP(c_List_Oappend(X1),X5),X4)!=hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_7339]), ['final']). 4.46/4.73 cnf(c_0_12099, plain, (hAPP(hAPP(c_List_Oappend(X1),esk472_5(X2,X3,X4,X5,X1)),X2)=X4|hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)=X2|hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)!=hAPP(hAPP(c_List_Oappend(X1),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_7340]), ['final']). 4.46/4.73 cnf(c_0_12100, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|c_Groups_Ozero__class_Ozero(X1)!=hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~class_Groups_Ocomm__monoid__add(X1)), inference(rw,[status(thm)],[c_0_7341, c_0_4836]), ['final']). 4.46/4.73 cnf(c_0_12101, plain, (hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=hAPP(c_Finite__Set_Ocard(X1),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7342]), ['final']). 4.46/4.73 cnf(c_0_12102, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7343]), ['final']). 4.46/4.73 cnf(c_0_12103, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X1,X2,X3)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk532_3(X1,X2,X3)))|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_12104, plain, (X1=hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk408_5(X4,X3,X5,X1,X2))|hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)=X5|hAPP(hAPP(c_List_Oappend(X2),X1),X5)!=hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_7339]), ['final']). 4.46/4.73 cnf(c_0_12105, plain, (X1=hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk472_5(X4,X1,X5,X3,X2))|hAPP(hAPP(c_List_Olist_OCons(X2),X3),X5)=X4|hAPP(hAPP(c_List_Olist_OCons(X2),X3),X5)!=hAPP(hAPP(c_List_Oappend(X2),X1),X4)), inference(split_conjunct,[status(thm)],[c_0_7340]), ['final']). 4.46/4.73 cnf(c_0_12106, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),X2)),X2)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_6775]), ['final']). 4.46/4.73 cnf(c_0_12107, plain, (c_Wellfounded_Owf(X3,hAPP(c_Set_Oimage(tc_prod(X1,X1),tc_prod(X3,X3),c_Product__Type_Omap__pair(X1,X3,X1,X3,X4,X4)),X2))|~c_Wellfounded_Owf(X1,X2)|~c_Fun_Oinj__on(X1,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_7344]), ['final']). 4.46/4.73 cnf(c_0_12108, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_7345]), ['final']). 4.46/4.73 cnf(c_0_12109, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7346, c_0_4609]), c_0_4609]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_12110, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7347]), ['final']). 4.46/4.73 cnf(c_0_12111, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7348]), ['final']). 4.46/4.73 cnf(c_0_12112, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_7349]), ['final']). 4.46/4.73 cnf(c_0_12113, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7350]), ['final']). 4.46/4.73 cnf(c_0_12114, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk248_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),c_List_Oreplicate(X1,X4,X3))))|X4=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_7351]), ['final']). 4.46/4.73 cnf(c_0_12115, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_Predicate_Oconversep(X1,X1,X2)))|~c_Wellfounded_Oacyclic(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7352, c_0_4531]), c_0_4531]), ['final']). 4.46/4.73 cnf(c_0_12116, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X4,X6)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),X4)),X5))|~hBOOL(hAPP(hAPP(c_member(X2),X6),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6917]), ['final']). 4.46/4.73 cnf(c_0_12117, plain, (hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X4),c_List_Oremdups(X1,X5))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),hAPP(c_List_Oset(X1),X5))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7353]), ['final']). 4.46/4.73 cnf(c_0_12118, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk77_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),c_List_Oreplicate(X1,X4,X3))))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X4|hBOOL(hAPP(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_7354]), ['final']). 4.46/4.73 cnf(c_0_12119, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7355]), ['final']). 4.46/4.73 cnf(c_0_12120, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7356]), ['final']). 4.46/4.73 cnf(c_0_12121, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7357]), ['final']). 4.46/4.73 cnf(c_0_12122, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(X5,X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(X3),X6),X4))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6923]), ['final']). 4.46/4.73 cnf(c_0_12123, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)|~class_Divides_Oring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7358]), ['final']). 4.46/4.73 cnf(c_0_12124, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),c_List_Olist_Olist__size(X1,X5,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(X5,X2)))), inference(split_conjunct,[status(thm)],[c_0_7359]), ['final']). 4.46/4.73 cnf(c_0_12125, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),c_List_Olist_Olist__size(X1,X5,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(X5,X2)))), inference(split_conjunct,[status(thm)],[c_0_7360]), ['final']). 4.46/4.73 cnf(c_0_12126, plain, (hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X4|hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4))=hAPP(hAPP(X2,X5),hAPP(X3,X4))|~c_Finite__Set_Ofolding__one(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_7361]), ['final']). 4.46/4.73 cnf(c_0_12127, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7362]), ['final']). 4.46/4.73 cnf(c_0_12128, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk487_2(X1,X2)),X2))|hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))), inference(split_conjunct,[status(thm)],[c_0_7171]), ['final']). 4.46/4.73 cnf(c_0_12129, plain, (hBOOL(hAPP(X4,X2))|c_List_OtakeWhile(X1,X4,hAPP(hAPP(c_List_Oappend(X1),X3),X5))=c_List_OtakeWhile(X1,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7363]), ['final']). 4.46/4.73 cnf(c_0_12130, plain, (hAPP(hAPP(X3,hAPP(X6,X8)),hAPP(X6,X7))=hAPP(X6,X7)|~c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X8),X7))), inference(split_conjunct,[status(thm)],[c_0_7364]), ['final']). 4.46/4.73 cnf(c_0_12131, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X1)),hAPP(hAPP(c_Product__Type_OSigma(X4,X1),X3),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk383_4(X2,X1,X3,X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(split_conjunct,[status(thm)],[c_0_6903]), ['final']). 4.46/4.73 cnf(c_0_12132, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X2),X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X2),X1)))=c_Random_Olog(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7365]), ['final']). 4.46/4.73 cnf(c_0_12133, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))), inference(split_conjunct,[status(thm)],[c_0_7366]), ['final']). 4.46/4.73 cnf(c_0_12134, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Relation_OId__on(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(er,[status(thm)],[c_0_7367]), ['final']). 4.46/4.73 cnf(c_0_12135, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X2,X3,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X3=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X1,X3,X2)|~hBOOL(hAPP(X1,esk534_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_12136, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))|hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(rw,[status(thm)],[c_0_7368, c_0_4836]), ['final']). 4.46/4.73 cnf(c_0_12137, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),hAPP(hAPP(c_COMBC(X2,X4,X1),X5),X6))=hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X4,X1)),X3),X5),X6)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7369]), ['final']). 4.46/4.73 cnf(c_0_12138, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X1,X2,X3)))|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,esk532_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_12139, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X1,X3))))|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk311_4(X3,X2,X1,X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6638]), ['final']). 4.46/4.73 cnf(c_0_12140, plain, (c_Fun_Oinj__on(X4,X2,hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~c_Fun_Oinj__on(X4,X1,X5,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_7370]), ['final']). 4.46/4.73 cnf(c_0_12141, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X5),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X3)))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5207]), ['final']). 4.46/4.73 cnf(c_0_12142, plain, (hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,X1)),X4),X5),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X4),hAPP(hAPP(c_COMBC(X2,X3,X1),X5),X6))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7371]), ['final']). 4.46/4.73 cnf(c_0_12143, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X1),X2),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X1),X4),X3)|hAPP(X2,esk518_5(X4,X2,X3,X3,X1))!=hAPP(X4,esk518_5(X4,X2,X3,X3,X1))|~class_Groups_Ocomm__monoid__add(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~c_Nat__Transfer_Onat__set(X3)), inference(er,[status(thm)],[c_0_7372]), ['final']). 4.46/4.73 cnf(c_0_12144, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X3|hAPP(hAPP(c_List_Olist__update(X1,c_List_Obutlast(X1,X2)),X3),X4)=c_List_Obutlast(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5885]), ['final']). 4.46/4.73 cnf(c_0_12145, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X2),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X4),X3)|hAPP(X2,esk9_5(X4,X2,X3,X3,X1))!=hAPP(X4,esk9_5(X4,X2,X3,X3,X1))|~class_Groups_Ocomm__monoid__add(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~c_Nat__Transfer_Onat__set(X3)), inference(er,[status(thm)],[c_0_7373]), ['final']). 4.46/4.73 cnf(c_0_12146, plain, (X2=X4|~class_Rings_Olinordered__semidom(X1)|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))), inference(split_conjunct,[status(thm)],[c_0_7374]), ['final']). 4.46/4.73 cnf(c_0_12147, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odivmod__int(X1,X2)=hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_7375]), ['final']). 4.46/4.73 cnf(c_0_12148, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_7376]), ['final']). 4.46/4.73 cnf(c_0_12149, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_7377]), ['final']). 4.46/4.73 cnf(c_0_12150, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_5363]), ['final']). 4.46/4.73 cnf(c_0_12151, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk538_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk536_3(X1,X2,X3)))|epred2_3(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5124]), ['final']). 4.46/4.73 cnf(c_0_12152, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk422_2(X2,X1)),esk422_2(X2,X1))=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))), inference(rw,[status(thm)],[c_0_7378, c_0_5689]), ['final']). 4.46/4.73 cnf(c_0_12153, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7304]), ['final']). 4.46/4.73 cnf(c_0_12154, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7085]), ['final']). 4.46/4.73 cnf(c_0_12155, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7085]), ['final']). 4.46/4.73 cnf(c_0_12156, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X2,X1,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_12157, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7379]), ['final']). 4.46/4.73 cnf(c_0_12158, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))), inference(split_conjunct,[status(thm)],[c_0_7380]), ['final']). 4.46/4.73 cnf(c_0_12159, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6846]), ['final']). 4.46/4.73 cnf(c_0_12160, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6840]), ['final']). 4.46/4.73 cnf(c_0_12161, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_12162, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7304]), ['final']). 4.46/4.73 cnf(c_0_12163, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_7381]), ['final']). 4.46/4.73 cnf(c_0_12164, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_7382]), ['final']). 4.46/4.73 cnf(c_0_12165, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|c_Map_Orestrict__map(X1,X4,X5,X3)=c_Map_Orestrict__map(X1,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),X5),X2),X6),X3)), inference(split_conjunct,[status(thm)],[c_0_5067]), ['final']). 4.46/4.73 cnf(c_0_12166, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7383]), ['final']). 4.46/4.73 cnf(c_0_12167, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))), inference(split_conjunct,[status(thm)],[c_0_7384]), ['final']). 4.46/4.73 cnf(c_0_12168, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6808]), ['final']). 4.46/4.73 cnf(c_0_12169, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))), inference(split_conjunct,[status(thm)],[c_0_7385]), ['final']). 4.46/4.73 cnf(c_0_12170, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))), inference(split_conjunct,[status(thm)],[c_0_7386]), ['final']). 4.46/4.73 cnf(c_0_12171, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_7387]), ['final']). 4.46/4.73 cnf(c_0_12172, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7388]), ['final']). 4.46/4.73 cnf(c_0_12173, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6812]), ['final']). 4.46/4.73 cnf(c_0_12174, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))), inference(split_conjunct,[status(thm)],[c_0_7389]), ['final']). 4.46/4.73 cnf(c_0_12175, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_7390]), ['final']). 4.46/4.73 cnf(c_0_12176, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7391]), ['final']). 4.46/4.73 cnf(c_0_12177, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Rings_Oordered__cancel__semiring(X1)), inference(split_conjunct,[status(thm)],[c_0_7392]), ['final']). 4.46/4.73 cnf(c_0_12178, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Oordered__cancel__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_7393]), ['final']). 4.46/4.73 cnf(c_0_12179, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7394, c_0_4436]), c_0_4436]), ['final']). 4.46/4.73 cnf(c_0_12180, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_7395]), ['final']). 4.46/4.73 cnf(c_0_12181, plain, (hAPP(X6,hAPP(hAPP(c_Set_Oinsert(X2),X8),X7))=hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,X7))|~c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))), inference(split_conjunct,[status(thm)],[c_0_7396]), ['final']). 4.46/4.73 cnf(c_0_12182, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)=X3|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6404]), ['final']). 4.46/4.73 cnf(c_0_12183, plain, (X3=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6411]), ['final']). 4.46/4.73 cnf(c_0_12184, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7391]), ['final']). 4.46/4.73 cnf(c_0_12185, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_7397]), ['final']). 4.46/4.73 cnf(c_0_12186, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))), inference(split_conjunct,[status(thm)],[c_0_7398]), ['final']). 4.46/4.73 cnf(c_0_12187, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_7399]), ['final']). 4.46/4.73 cnf(c_0_12188, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X4)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7400]), ['final']). 4.46/4.73 cnf(c_0_12189, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7401]), ['final']). 4.46/4.73 cnf(c_0_12190, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1))), inference(split_conjunct,[status(thm)],[c_0_7402]), ['final']). 4.46/4.73 cnf(c_0_12191, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7403]), ['final']). 4.46/4.73 cnf(c_0_12192, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7404]), ['final']). 4.46/4.73 cnf(c_0_12193, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_7405]), ['final']). 4.46/4.73 cnf(c_0_12194, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_7406]), ['final']). 4.46/4.73 cnf(c_0_12195, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_7407]), ['final']). 4.46/4.73 cnf(c_0_12196, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X3))), inference(split_conjunct,[status(thm)],[c_0_7408]), ['final']). 4.46/4.73 cnf(c_0_12197, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7409]), ['final']). 4.46/4.73 cnf(c_0_12198, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7410]), ['final']). 4.46/4.73 cnf(c_0_12199, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7411]), ['final']). 4.46/4.73 cnf(c_0_12200, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))), inference(split_conjunct,[status(thm)],[c_0_7412]), ['final']). 4.46/4.73 cnf(c_0_12201, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))), inference(split_conjunct,[status(thm)],[c_0_7413]), ['final']). 4.46/4.73 cnf(c_0_12202, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))), inference(split_conjunct,[status(thm)],[c_0_7414]), ['final']). 4.46/4.73 cnf(c_0_12203, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_7415]), ['final']). 4.46/4.73 cnf(c_0_12204, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X5,X6)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(X3),X6),X4))), inference(split_conjunct,[status(thm)],[c_0_7416]), ['final']). 4.46/4.73 cnf(c_0_12205, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7417]), ['final']). 4.46/4.73 cnf(c_0_12206, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7418]), ['final']). 4.46/4.73 cnf(c_0_12207, plain, (X1=c_List_Olist_ONil(X2)|hBOOL(hAPP(hAPP(c_member(X2),hAPP(c_Product__Type_Ofst(X2,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X2,X1),X3))),hAPP(c_List_Oset(X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_7419]), ['final']). 4.46/4.73 cnf(c_0_12208, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Oordered__cancel__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))), inference(split_conjunct,[status(thm)],[c_0_7420]), ['final']). 4.46/4.73 cnf(c_0_12209, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7421]), ['final']). 4.46/4.73 cnf(c_0_12210, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7422]), ['final']). 4.46/4.73 cnf(c_0_12211, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X4)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7423]), ['final']). 4.46/4.73 cnf(c_0_12212, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk91_3(X1,X2,X3))),X2))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_7057]), ['final']). 4.46/4.73 cnf(c_0_12213, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk525_5(X2,X3,X1,X4,X5)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X5,X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_7424]), ['final']). 4.46/4.73 cnf(c_0_12214, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))), inference(split_conjunct,[status(thm)],[c_0_7425]), ['final']). 4.46/4.73 cnf(c_0_12215, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_7426]), ['final']). 4.46/4.73 cnf(c_0_12216, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_7427]), ['final']). 4.46/4.73 cnf(c_0_12217, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7428]), ['final']). 4.46/4.73 cnf(c_0_12218, plain, (X1=hAPP(c_Relation_OImage(X2,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),esk371_4(X3,X4,X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_7429]), ['final']). 4.46/4.73 cnf(c_0_12219, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7430]), ['final']). 4.46/4.73 cnf(c_0_12220, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_7431]), ['final']). 4.46/4.73 cnf(c_0_12221, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7421]), ['final']). 4.46/4.73 cnf(c_0_12222, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7422]), ['final']). 4.46/4.73 cnf(c_0_12223, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_7432]), ['final']). 4.46/4.73 cnf(c_0_12224, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,X1,X2),c_Int_Oring__1__class_Oof__int(X1)),X3)),X4)=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Int_Oint),X3),X4))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7433]), ['final']). 4.46/4.73 cnf(c_0_12225, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))=X2|~class_Fields_Ofield(X1)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7434, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), ['final']). 4.46/4.73 cnf(c_0_12226, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hBOOL(hAPP(X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))), inference(split_conjunct,[status(thm)],[c_0_7317]), ['final']). 4.46/4.73 cnf(c_0_12227, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_7435]), ['final']). 4.46/4.73 cnf(c_0_12228, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7436]), ['final']). 4.46/4.73 cnf(c_0_12229, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X2),c_Lazy__Sequence_Osmall__lazy_H(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Lazy__Sequence_Osmall__lazy_H(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7437]), ['final']). 4.46/4.73 cnf(c_0_12230, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk75_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7438]), ['final']). 4.46/4.73 cnf(c_0_12231, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2))|~class_Lattices_Oab__semigroup__idem__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7439]), ['final']). 4.46/4.73 cnf(c_0_12232, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7440]), ['final']). 4.46/4.73 cnf(c_0_12233, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1)), inference(split_conjunct,[status(thm)],[c_0_7441]), ['final']). 4.46/4.73 cnf(c_0_12234, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6))))), inference(split_conjunct,[status(thm)],[c_0_7442]), ['final']). 4.46/4.73 cnf(c_0_12235, plain, (hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X6)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6))))), inference(split_conjunct,[status(thm)],[c_0_7443]), ['final']). 4.46/4.73 cnf(c_0_12236, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk319_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))|c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7444]), ['final']). 4.46/4.73 cnf(c_0_12237, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk212_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7445]), ['final']). 4.46/4.73 cnf(c_0_12238, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X1,X2,X3)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,X1))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_12239, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_List_Olist_OCons(X1),hAPP(c_List_Ohd(X1),X2)),hAPP(hAPP(c_List_Otake(X1),X3),hAPP(c_List_Otl(X1),X2)))=hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X3)),X2)), inference(split_conjunct,[status(thm)],[c_0_7446]), ['final']). 4.46/4.73 cnf(c_0_12240, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),X2))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk432_3(X2,X3,X1)),esk433_3(X2,X3,X1))), inference(split_conjunct,[status(thm)],[c_0_6921]), ['final']). 4.46/4.73 cnf(c_0_12241, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X5),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X3),X5))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7447, c_0_4891]), c_0_4891]), ['final']). 4.46/4.73 cnf(c_0_12242, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk532_3(X2,X1,X3)))|epred1_3(X3,X1,X2)|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_12243, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk208_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7448]), ['final']). 4.46/4.73 cnf(c_0_12244, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7449]), ['final']). 4.46/4.73 cnf(c_0_12245, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7450]), ['final']). 4.46/4.73 cnf(c_0_12246, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk482_2(X2,X1)),esk482_2(X2,X1))),X2))|c_Relation_Oirrefl(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7451]), ['final']). 4.46/4.73 cnf(c_0_12247, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Onth(X2),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X3)),X1)), inference(split_conjunct,[status(thm)],[c_0_7452]), ['final']). 4.46/4.73 cnf(c_0_12248, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X2))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7453, c_0_7454]), c_0_7455]), ['final']). 4.46/4.73 cnf(c_0_12249, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7456, c_0_4609]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_12250, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),c_Big__Operators_Olinorder__class_OMax(X1,X3)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7457]), ['final']). 4.46/4.73 cnf(c_0_12251, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Big__Operators_Olinorder__class_OMin(X1,X3)),c_Big__Operators_Olinorder__class_OMin(X1,X2)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7458]), ['final']). 4.46/4.73 cnf(c_0_12252, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X3),X4)),hAPP(c_Finite__Set_Ocard(X1),X2))=hAPP(c_Finite__Set_Ocard(tc_sum(X3,X1)),c_Sum__Type_OPlus(X3,X1,X4,X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7459]), ['final']). 4.46/4.73 cnf(c_0_12253, plain, (hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,X7))=hAPP(X6,X7)|~c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))|~hBOOL(hAPP(hAPP(c_member(X2),X8),X7))), inference(split_conjunct,[status(thm)],[c_0_7460]), ['final']). 4.46/4.73 cnf(c_0_12254, plain, (c_List_Olist__all2(X4,X2,hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),X4),X3),X5),X6,X7)|~c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Omap(X4,X1),X5),X6),X7)), inference(split_conjunct,[status(thm)],[c_0_7461]), ['final']). 4.46/4.73 cnf(c_0_12255, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))=X3|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)), inference(er,[status(thm)],[c_0_7462]), ['final']). 4.46/4.73 cnf(c_0_12256, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7463, c_0_7464]), c_0_7465]), ['final']). 4.46/4.73 cnf(c_0_12257, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk70_4(X2,X3,X1,X4)),X4))|c_Fun_Oinj__on(X1,X3,X2,c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X4))|c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))=X4), inference(split_conjunct,[status(thm)],[c_0_7466]), ['final']). 4.46/4.73 cnf(c_0_12258, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X1)))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X1)))))), inference(split_conjunct,[status(thm)],[c_0_7467]), ['final']). 4.46/4.73 cnf(c_0_12259, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7468, c_0_7464]), c_0_7465]), ['final']). 4.46/4.73 cnf(c_0_12260, plain, (c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),X4)|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool)),X4),c_List_Oset(X1)))), inference(rw,[status(thm)],[c_0_7469, c_0_7470]), ['final']). 4.46/4.73 cnf(c_0_12261, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X4,c_Groups_Otimes__class_Otimes(X1)),X2),c_Groups_Oone__class_Oone(X1)),X3)=c_Groups_Oone__class_Oone(X1)|c_Groups_Oone__class_Oone(X1)!=hAPP(X2,esk233_4(X2,X3,X4,X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_6817]), ['final']). 4.46/4.73 cnf(c_0_12262, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7471]), ['final']). 4.46/4.73 cnf(c_0_12263, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X2),c_Product__Type_Osnd(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))=X4|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)), inference(er,[status(thm)],[c_0_7472]), ['final']). 4.46/4.73 cnf(c_0_12264, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X2))=c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7473, c_0_7454]), c_0_7455]), ['final']). 4.46/4.73 cnf(c_0_12265, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Int_Onat)),X1)=X1|~c_Nat__Transfer_Onat__set(X1)), inference(rw,[status(thm)],[c_0_7474, c_0_6899]), ['final']). 4.46/4.73 cnf(c_0_12266, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X1,hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Com_Ocom,c_Com_Ocom_OBODY),X2)))|~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),X1),hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Com_Ocom,c_Com_Ocom_OBODY),X2))),hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,c_Option_Othe(tc_Com_Ocom)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom),c_Com_Obody),X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7475, c_0_6899]), c_0_6899]), c_0_6899]), c_0_6899]), ['final']). 4.46/4.73 cnf(c_0_12267, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4))=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7476]), ['final']). 4.46/4.73 cnf(c_0_12268, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))), inference(split_conjunct,[status(thm)],[c_0_7477]), ['final']). 4.46/4.73 cnf(c_0_12269, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk67_4(hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),X1,X3,X2)),hAPP(c_List_Oset(X1),X3)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)), inference(er,[status(thm)],[c_0_7478]), ['final']). 4.46/4.73 cnf(c_0_12270, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk161_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|X3=X2|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)), inference(split_conjunct,[status(thm)],[c_0_7479]), ['final']). 4.46/4.73 cnf(c_0_12271, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7480]), ['final']). 4.46/4.73 cnf(c_0_12272, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7480]), ['final']). 4.46/4.73 cnf(c_0_12273, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_7481]), ['final']). 4.46/4.73 cnf(c_0_12274, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X4),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),hAPP(c_List_Oset(X2),X3))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_List_Odistinct(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7482]), ['final']). 4.46/4.73 cnf(c_0_12275, plain, (hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X3))),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))), inference(rw,[status(thm)],[c_0_7483, c_0_4517]), ['final']). 4.46/4.73 cnf(c_0_12276, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))|hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_4650]), ['final']). 4.46/4.73 cnf(c_0_12277, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(X5,X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7484]), ['final']). 4.46/4.73 cnf(c_0_12278, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),X2)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1), inference(rw,[status(thm)],[c_0_7485, c_0_5645]), ['final']). 4.46/4.73 cnf(c_0_12279, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7486]), ['final']). 4.46/4.73 cnf(c_0_12280, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7486]), ['final']). 4.46/4.73 cnf(c_0_12281, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Int_Oring__1__class_OInts(X1)))), inference(split_conjunct,[status(thm)],[c_0_7487]), ['final']). 4.46/4.73 cnf(c_0_12282, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Rings_Osemiring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Nat_Osemiring__1__class_ONats(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Nat_Osemiring__1__class_ONats(X1)))), inference(split_conjunct,[status(thm)],[c_0_7488]), ['final']). 4.46/4.73 cnf(c_0_12283, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))), inference(split_conjunct,[status(thm)],[c_0_7489]), ['final']). 4.46/4.73 cnf(c_0_12284, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(X5,X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7490]), ['final']). 4.46/4.73 cnf(c_0_12285, plain, (c_List_Olist__ex1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~c_List_Olist__ex1(X1,X2,X4)|~c_List_Olist__all(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X3))),X4)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7491, c_0_5671]), c_0_7040]), c_0_4934]), ['final']). 4.46/4.73 cnf(c_0_12286, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7492]), ['final']). 4.46/4.73 cnf(c_0_12287, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Oappend(X2),hAPP(c_List_Otl(X2),X1)),hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(c_List_Ohd(X2),X1)),c_List_Olist_ONil(X2)))=hAPP(c_List_Orotate1(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_7493]), ['final']). 4.46/4.73 cnf(c_0_12288, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Int_Oring__1__class_OInts(X1)))), inference(split_conjunct,[status(thm)],[c_0_7494]), ['final']). 4.46/4.73 cnf(c_0_12289, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Rings_Osemiring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Nat_Osemiring__1__class_ONats(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Nat_Osemiring__1__class_ONats(X1)))), inference(split_conjunct,[status(thm)],[c_0_7495]), ['final']). 4.46/4.73 cnf(c_0_12290, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Int_Oring__1__class_OInts(X1)))), inference(split_conjunct,[status(thm)],[c_0_7496]), ['final']). 4.46/4.73 cnf(c_0_12291, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7497]), ['final']). 4.46/4.73 cnf(c_0_12292, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7498]), ['final']). 4.46/4.73 cnf(c_0_12293, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7499]), ['final']). 4.46/4.73 cnf(c_0_12294, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5)))|~c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_7500]), ['final']). 4.46/4.73 cnf(c_0_12295, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)))), inference(split_conjunct,[status(thm)],[c_0_7501]), ['final']). 4.46/4.73 cnf(c_0_12296, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7502]), ['final']). 4.46/4.73 cnf(c_0_12297, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7497]), ['final']). 4.46/4.73 cnf(c_0_12298, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7502]), ['final']). 4.46/4.73 cnf(c_0_12299, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk516_2(X1,X2)),X2))|hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))), inference(split_conjunct,[status(thm)],[c_0_7187]), ['final']). 4.46/4.73 cnf(c_0_12300, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(hAPP(c_List_Oappend(X1),X3),c_List_Oremove1(X1,X2,X4))=c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7503]), ['final']). 4.46/4.73 cnf(c_0_12301, plain, (hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),esk116_3(X1,X3,X2)),hAPP(hAPP(c_Set_Oinsert(X2),esk115_3(X1,X3,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7311]), ['final']). 4.46/4.73 cnf(c_0_12302, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_7504]), ['final']). 4.46/4.73 cnf(c_0_12303, plain, (hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7505]), ['final']). 4.46/4.73 cnf(c_0_12304, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X2)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Complete__Lattice_OInf__class_OInf(X1,X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7506]), ['final']). 4.46/4.73 cnf(c_0_12305, plain, (c_List_Olist__all2(X2,X5,X1,X3,X4)|~hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk384_5(X1,X4,X5,X3,X2))),hAPP(hAPP(c_List_Onth(X5),X4),esk384_5(X1,X4,X5,X3,X2))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X4)), inference(split_conjunct,[status(thm)],[c_0_7077]), ['final']). 4.46/4.73 cnf(c_0_12306, plain, (c_List_Olist__all2(X2,X5,X1,X3,X4)|~hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk293_5(X4,X3,X1,X5,X2))),hAPP(hAPP(c_List_Onth(X5),X4),esk293_5(X4,X3,X1,X5,X2))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X4)), inference(split_conjunct,[status(thm)],[c_0_7078]), ['final']). 4.46/4.73 cnf(c_0_12307, plain, (hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Omap(X2,X4),X5),X3)),X1)=hAPP(X5,hAPP(hAPP(c_List_Onth(X2),X3),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_7507]), ['final']). 4.46/4.73 cnf(c_0_12308, plain, (hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X3))),X4)=hAPP(c_List_Ofilter(X1,X2),X4)|hBOOL(hAPP(X2,X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7508, c_0_5671]), c_0_7509]), c_0_6074]), ['final']). 4.46/4.73 cnf(c_0_12309, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),hAPP(c_List_Oset(tc_Nat_Onat),X2)))), inference(split_conjunct,[status(thm)],[c_0_7510]), ['final']). 4.46/4.73 cnf(c_0_12310, plain, (esk496_4(hAPP(X1,X2),X1,X3,X4)=X2|~c_Fun_Oinj__on(X4,X3,X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_7511]), c_0_7512])]), ['final']). 4.46/4.73 cnf(c_0_12311, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7326]), ['final']). 4.46/4.73 cnf(c_0_12312, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_Relation_Oconverse(X2,X1),X5)))), inference(split_conjunct,[status(thm)],[c_0_7001]), ['final']). 4.46/4.73 cnf(c_0_12313, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Owf(X1,X3)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X1),X2)),hAPP(c_Relation_ORange(X1,X1),X3))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_7513]), ['final']). 4.46/4.73 cnf(c_0_12314, plain, (hAPP(X1,X2)=hAPP(c_Option_Ooption_OSome(X3),esk87_7(X4,X2,X1,X5,X6,X7,X3))|hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X7),X3,c_Option_Ooption_ONone(X7),X5),hAPP(X1,X2))!=hAPP(c_Option_Ooption_OSome(X7),X4)), inference(rw,[status(thm)],[c_0_7514, c_0_7133]), ['final']). 4.46/4.73 cnf(c_0_12315, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X1,X2,X3)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_12316, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X5),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_OImage(X3,X1,X4),hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_7234]), ['final']). 4.46/4.73 cnf(c_0_12317, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X5),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_7515]), ['final']). 4.46/4.73 cnf(c_0_12318, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk532_3(X2,X1,X3)))|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_12319, plain, (c_List_Olist_ONil(X1)=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)|~hBOOL(hAPP(X2,hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7516, c_0_4916]), c_0_4916]), ['final']). 4.46/4.73 cnf(c_0_12320, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,X3,X4),X5))), inference(split_conjunct,[status(thm)],[c_0_7517]), ['final']). 4.46/4.73 cnf(c_0_12321, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X3))|~hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1,X2,X3),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_7518]), ['final']). 4.46/4.73 cnf(c_0_12322, plain, (hAPP(c_Random_Opick(X2,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X2)),X3),X4)),X1)=hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X2),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_6803]), ['final']). 4.46/4.73 cnf(c_0_12323, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(c_Set_Oimage(X1,X4,X5),X3)=hAPP(c_Set_Oimage(X1,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X4),X5),X2),X6)),X3)), inference(split_conjunct,[status(thm)],[c_0_6799]), ['final']). 4.46/4.73 cnf(c_0_12324, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Odrop(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)=hAPP(hAPP(c_List_Odrop(X2),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7519]), ['final']). 4.46/4.73 cnf(c_0_12325, plain, (c_Relation_Ototal__on(X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))|~c_Relation_Ototal__on(X1,X2,X3)), inference(rw,[status(thm)],[c_0_7520, c_0_5689]), ['final']). 4.46/4.73 cnf(c_0_12326, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_HOL_Obool,X1),X2),c_Option_Ooption_OSome(X1))))|hBOOL(hAPP(X2,c_Option_Ooption_ONone(X1)))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X1)),X2))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_7521]), ['final']). 4.46/4.73 cnf(c_0_12327, plain, (c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X1))|hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X2),X1))|esk433_3(X1,X2,X3)!=esk432_3(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_6921]), ['final']). 4.46/4.73 cnf(c_0_12328, plain, (X2=X4|~class_Rings_Olinordered__semidom(X1)|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),hAPP(c_Nat_OSuc,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))), inference(split_conjunct,[status(thm)],[c_0_7522]), ['final']). 4.46/4.73 cnf(c_0_12329, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk377_5(X2,X3,X4,X1,X5)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X5),X4),X3)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X5)|~class_Orderings_Olinorder(X5)), inference(split_conjunct,[status(thm)],[c_0_7114]), ['final']). 4.46/4.73 cnf(c_0_12330, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk368_5(X2,X3,X1,X4,X5)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5),X3),X2)))|~class_Complete__Lattice_Ocomplete__lattice(X5)|~class_Orderings_Olinorder(X5)), inference(split_conjunct,[status(thm)],[c_0_7119]), ['final']). 4.46/4.73 cnf(c_0_12331, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_7523]), ['final']). 4.46/4.73 cnf(c_0_12332, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X1),X2),c_List_Oupto(X3,X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X3,X4))|~class_Groups_Ocomm__monoid__add(X1)), inference(rw,[status(thm)],[c_0_7524, c_0_7525]), ['final']). 4.46/4.73 cnf(c_0_12333, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(c_List_Onth(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7526]), ['final']). 4.46/4.73 cnf(c_0_12334, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_7527]), ['final']). 4.46/4.73 cnf(c_0_12335, plain, (hAPP(X1,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=esk92_3(X1,X3,X4)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X1),X3)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X4),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(rw,[status(thm)],[c_0_7528, c_0_4836]), ['final']). 4.46/4.73 cnf(c_0_12336, plain, (hBOOL(hAPP(hAPP(hAPP(X1,esk477_7(X2,X3,X1,X4,X5,X6,X7)),X3),X2))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X6,tc_fun(X5,tc_HOL_Obool))),X4),X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7529]), ['final']). 4.46/4.73 cnf(c_0_12337, plain, (hBOOL(hAPP(hAPP(hAPP(X1,esk430_7(X2,X3,X1,X4,X5,X6,X7)),X3),X2))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X6,tc_fun(X5,tc_HOL_Obool))),X4),X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7530]), ['final']). 4.46/4.73 cnf(c_0_12338, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7531, c_0_4436]), c_0_4436]), ['final']). 4.46/4.73 cnf(c_0_12339, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7532, c_0_5120]), c_0_5120]), c_0_5120]), ['final']). 4.46/4.73 cnf(c_0_12340, plain, (c_List_Olist__ex1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~c_List_Olist__all(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X3))),X4)|~hBOOL(hAPP(X2,X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7533, c_0_5671]), c_0_7040]), c_0_4934]), ['final']). 4.46/4.73 cnf(c_0_12341, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X2)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7534]), ['final']). 4.46/4.73 cnf(c_0_12342, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X3)|hAPP(X1,esk380_5(X1,X2,X3,X4,X5))!=c_Groups_Oone__class_Oone(X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))|~class_Groups_Ocomm__monoid__mult(X5)), inference(split_conjunct,[status(thm)],[c_0_6471]), ['final']). 4.46/4.73 cnf(c_0_12343, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X2)|hAPP(X1,esk181_5(X1,X2,X3,X4,X5))!=c_Groups_Oone__class_Oone(X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))|~class_Groups_Ocomm__monoid__mult(X5)), inference(split_conjunct,[status(thm)],[c_0_6472]), ['final']). 4.46/4.73 cnf(c_0_12344, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X5),X1),X3)|hAPP(X1,esk447_5(X1,X2,X3,X4,X5))!=c_Groups_Ozero__class_Ozero(X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))|~class_Groups_Ocomm__monoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6473]), ['final']). 4.46/4.73 cnf(c_0_12345, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)|c_Groups_Ozero__class_Ozero(X1)!=hAPP(X2,esk146_5(X2,X3,X4,X5,X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6478]), ['final']). 4.46/4.73 cnf(c_0_12346, plain, (hBOOL(hAPP(hAPP(hAPP(X5,X8),X6),X7))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X4),X5),X6),X7))|~hBOOL(hAPP(hAPP(c_member(X1),X8),X4))), inference(split_conjunct,[status(thm)],[c_0_7535]), ['final']). 4.46/4.73 cnf(c_0_12347, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),hAPP(c_Nat_OSuc,X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))), inference(split_conjunct,[status(thm)],[c_0_7536]), ['final']). 4.46/4.73 cnf(c_0_12348, plain, (c_Option_Ooption_ONone(X6)=hAPP(X4,X3)|c_Option_Ooption_ONone(X1)=hAPP(X2,esk519_6(X3,X4,X2,X5,X1,X6))|c_Option_Ooption_ONone(X1)!=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X6,c_Option_Ooption_ONone(X1),X2),hAPP(X4,X3))), inference(rw,[status(thm)],[c_0_7537, c_0_7133]), ['final']). 4.46/4.73 cnf(c_0_12349, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk421_5(X2,X3,X1,X4,X5)),X3))|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_7538]), ['final']). 4.46/4.73 cnf(c_0_12350, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk8_4(X3,X4,X2,X1)),esk7_4(X3,X4,X2,X1))=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),X4),hAPP(c_Relation_Oconverse(X2,X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_6816]), ['final']). 4.46/4.73 cnf(c_0_12351, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|c_Divides_Odivmod__int(X2,X1)=hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7375]), ['final']). 4.46/4.73 cnf(c_0_12352, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7539]), ['final']). 4.46/4.73 cnf(c_0_12353, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)), inference(split_conjunct,[status(thm)],[c_0_7540]), ['final']). 4.46/4.73 cnf(c_0_12354, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7541]), ['final']). 4.46/4.73 cnf(c_0_12355, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)), inference(split_conjunct,[status(thm)],[c_0_7542]), ['final']). 4.46/4.73 cnf(c_0_12356, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X3))=hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2),X3)|~class_Groups_Omonoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7543]), ['final']). 4.46/4.73 cnf(c_0_12357, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7085]), ['final']). 4.46/4.73 cnf(c_0_12358, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7304]), ['final']). 4.46/4.73 cnf(c_0_12359, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7544, c_0_4609]), c_0_5120]), c_0_4836]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_12360, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))|~class_Groups_Oordered__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7545]), ['final']). 4.46/4.73 cnf(c_0_12361, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)), inference(split_conjunct,[status(thm)],[c_0_7546]), ['final']). 4.46/4.73 cnf(c_0_12362, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))|~class_Groups_Oordered__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7547]), ['final']). 4.46/4.73 cnf(c_0_12363, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X1))), inference(er,[status(thm)],[c_0_7548]), ['final']). 4.46/4.73 cnf(c_0_12364, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk377_5(X3,X2,X4,X5,X1))),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X1),X4),X2)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7114]), ['final']). 4.46/4.73 cnf(c_0_12365, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(X3,esk368_5(X3,X4,X5,X2,X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X1),X4),X3)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7119]), ['final']). 4.46/4.73 cnf(c_0_12366, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),X4)))|c_List_OtakeWhile(X2,X1,X3)=hAPP(hAPP(c_List_Otake(X2),X4),X3)|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk62_4(X1,X3,X2,X4))))), inference(split_conjunct,[status(thm)],[c_0_6762]), ['final']). 4.46/4.73 cnf(c_0_12367, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__ring__strict(X1)), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_7549])]), ['final']). 4.46/4.73 cnf(c_0_12368, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)), inference(split_conjunct,[status(thm)],[c_0_7550]), ['final']). 4.46/4.73 cnf(c_0_12369, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2)),X3)|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7551]), ['final']). 4.46/4.73 cnf(c_0_12370, plain, (c_List_Olist__all2(X4,X5,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X6),hAPP(hAPP(c_List_Olist_OCons(X5),X3),X7))|~hBOOL(hAPP(hAPP(X1,X2),X3))|~c_List_Olist__all2(X4,X5,X1,X6,X7)), inference(split_conjunct,[status(thm)],[c_0_7552]), ['final']). 4.46/4.73 cnf(c_0_12371, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3),X7),X4),X6)=hAPP(hAPP(X5,X7),X6)|~c_Finite__Set_Ofolding__image(X1,X2,X3,X4,X5)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6))), inference(split_conjunct,[status(thm)],[c_0_7553]), ['final']). 4.46/4.73 cnf(c_0_12372, plain, (hAPP(hAPP(X3,X4),X2)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X1,X6),X4),X7),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Big__Operators_Ocomm__monoid__big(X5,X1,X6,X7,X3)), inference(split_conjunct,[status(thm)],[c_0_7554]), ['final']). 4.46/4.73 cnf(c_0_12373, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X4,X5)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X2),X5),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6911]), ['final']). 4.46/4.73 cnf(c_0_12374, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7555, c_0_4760]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_12375, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7556, c_0_4609]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_12376, plain, (hBOOL(hAPP(hAPP(c_member(X3),X6),hAPP(c_List_Oset(X3),X4)))|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(hAPP(c_Map_Omap__of(X3,X1),hAPP(hAPP(c_List_Ozip(X3,X1),X4),X5)),X6)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)), inference(split_conjunct,[status(thm)],[c_0_6700]), ['final']). 4.46/4.73 cnf(c_0_12377, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk274_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_5065]), ['final']). 4.46/4.73 cnf(c_0_12378, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)))), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_7557])]), ['final']). 4.46/4.73 cnf(c_0_12379, plain, (hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_7558]), ['final']). 4.46/4.73 cnf(c_0_12380, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_7559, c_0_4436]), ['final']). 4.46/4.73 cnf(c_0_12381, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X2)=c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7560]), ['final']). 4.46/4.73 cnf(c_0_12382, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X2)=c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7561]), ['final']). 4.46/4.73 cnf(c_0_12383, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk57_5(X2,X3,X4,X5,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X5)),X4),hAPP(hAPP(c_Product__Type_OSigma(X1,X5),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_7113]), ['final']). 4.46/4.73 cnf(c_0_12384, plain, (X6=X5|~c_Relation_Osingle__valued(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X6)),X3))), inference(split_conjunct,[status(thm)],[c_0_7562]), ['final']). 4.46/4.73 cnf(c_0_12385, plain, (X1=hAPP(X2,esk496_4(X1,X2,X3,X4))|~hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_Set_Oimage(X4,X3,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5321]), ['final']). 4.46/4.73 cnf(c_0_12386, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X3|c_List_Olast(X1,X2)=c_List_Olast(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))|X2=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_5430]), ['final']). 4.46/4.73 cnf(c_0_12387, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(X1),X2))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X1))), inference(split_conjunct,[status(thm)],[c_0_7563]), ['final']). 4.46/4.73 cnf(c_0_12388, plain, (X3=hAPP(X4,X2)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Finite__Set_Ofolding__one(X1,X5,X4)), inference(split_conjunct,[status(thm)],[c_0_6613]), ['final']). 4.46/4.73 cnf(c_0_12389, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk222_3(X2,X3,X1)),X3))|c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))=X3|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_7564]), ['final']). 4.46/4.73 cnf(c_0_12390, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X5),X4)))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7565]), ['final']). 4.46/4.73 cnf(c_0_12391, plain, (c_List_Obutlast(X2,hAPP(hAPP(c_List_Otake(X2),X1),X3))=hAPP(hAPP(c_List_Otake(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_7566]), ['final']). 4.46/4.73 cnf(c_0_12392, plain, (X1=X2|X3=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X4),X2)),hAPP(hAPP(c_List_Olist_OCons(X5),X3),X1))),c_List_Olistrel1(X5,X6)))), inference(split_conjunct,[status(thm)],[c_0_6296]), ['final']). 4.46/4.73 cnf(c_0_12393, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Code__Numeral_Onat__of,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7567, c_0_5334]), c_0_7568]), c_0_4836]), ['final']). 4.46/4.73 cnf(c_0_12394, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_5989]), ['final']). 4.46/4.73 cnf(c_0_12395, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7569]), ['final']). 4.46/4.73 cnf(c_0_12396, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,esk167_3(X1,X2,X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_6997]), ['final']). 4.46/4.73 cnf(c_0_12397, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,esk23_3(X1,X2,X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7285]), ['final']). 4.46/4.73 cnf(c_0_12398, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X2,X3,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|epred1_3(X1,X3,X2)|~hBOOL(hAPP(X1,esk534_3(X2,X3,X1)))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_12399, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X1,X2,X3)))|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,esk532_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X1))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_12400, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,X2),X5),X4)=hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4))|~c_Finite__Set_Ofolding__one__idem(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_7570]), ['final']). 4.46/4.73 cnf(c_0_12401, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_7571]), ['final']). 4.46/4.73 cnf(c_0_12402, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)=X2|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7572, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), ['final']). 4.46/4.73 cnf(c_0_12403, plain, (esk45_3(X4,X3,X1)=X2|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(X4,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7128]), ['final']). 4.46/4.73 cnf(c_0_12404, plain, (hAPP(X1,esk87_7(X2,X3,X4,X1,X5,X6,X7))=hAPP(c_Option_Ooption_OSome(X6),X2)|hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X6),X7,c_Option_Ooption_ONone(X6),X1),hAPP(X4,X3))!=hAPP(c_Option_Ooption_OSome(X6),X2)), inference(rw,[status(thm)],[c_0_7573, c_0_7133]), ['final']). 4.46/4.73 cnf(c_0_12405, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X6),hAPP(hAPP(c_List_Oappend(X2),X5),X7))|~c_List_Olist__all2(X1,X2,X3,X4,X5)|~c_List_Olist__all2(X1,X2,X3,X6,X7)), inference(split_conjunct,[status(thm)],[c_0_7574]), ['final']). 4.46/4.73 cnf(c_0_12406, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))=X2|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7575, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), ['final']). 4.46/4.73 cnf(c_0_12407, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7576, c_0_4609]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_12408, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7577, c_0_5120]), c_0_5120]), c_0_5120]), ['final']). 4.46/4.73 cnf(c_0_12409, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7578]), ['final']). 4.46/4.73 cnf(c_0_12410, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_7579]), ['final']). 4.46/4.73 cnf(c_0_12411, plain, (hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk452_2(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_List_Oset(tc_Nat_Onat),X1)))), inference(er,[status(thm)],[c_0_7580]), ['final']). 4.46/4.73 cnf(c_0_12412, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X5),X3)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7581]), ['final']). 4.46/4.73 cnf(c_0_12413, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X5)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7581]), ['final']). 4.46/4.73 cnf(c_0_12414, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7582]), ['final']). 4.46/4.73 cnf(c_0_12415, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_7583]), ['final']). 4.46/4.73 cnf(c_0_12416, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7584]), ['final']). 4.46/4.73 cnf(c_0_12417, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))), inference(split_conjunct,[status(thm)],[c_0_7585]), ['final']). 4.46/4.73 cnf(c_0_12418, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7586]), ['final']). 4.46/4.73 cnf(c_0_12419, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X3)=c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X2,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7587]), ['final']). 4.46/4.73 cnf(c_0_12420, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7391]), ['final']). 4.46/4.73 cnf(c_0_12421, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7391]), ['final']). 4.46/4.73 cnf(c_0_12422, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7391]), ['final']). 4.46/4.73 cnf(c_0_12423, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X4),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3)|~class_Divides_Oring__div(X1)|c_Divides_Odiv__class_Omod(X1,X2,X3)!=c_Divides_Odiv__class_Omod(X1,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_7588]), ['final']). 4.46/4.73 cnf(c_0_12424, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7589]), ['final']). 4.46/4.73 cnf(c_0_12425, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7590]), ['final']). 4.46/4.73 cnf(c_0_12426, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7591]), ['final']). 4.46/4.73 cnf(c_0_12427, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_7592]), ['final']). 4.46/4.73 cnf(c_0_12428, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7391]), ['final']). 4.46/4.73 cnf(c_0_12429, plain, (hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),esk151_3(X2,X3,X1)),X3))|c_Hoare__Mirabelle_Otriple__valid(X1,X2,X4)|~hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7593]), ['final']). 4.46/4.73 cnf(c_0_12430, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7421]), ['final']). 4.46/4.73 cnf(c_0_12431, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7421]), ['final']). 4.46/4.73 cnf(c_0_12432, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(X1)),c_Option_Ooption_ONone(X1)),hAPP(hAPP(c_List_Omap(X1,tc_Option_Ooption(X1)),c_Option_Ooption_OSome(X1)),c_Enum_Oenum__class_Oenum(X1)))=c_Enum_Oenum__class_Oenum(tc_Option_Ooption(X1))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_7594]), ['final']). 4.46/4.73 cnf(c_0_12433, plain, (hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=X4|hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=hAPP(c_List_Orev(X1),X4)), inference(rw,[status(thm)],[c_0_7595, c_0_7596]), ['final']). 4.46/4.73 cnf(c_0_12434, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[c_0_7597, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_12435, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[c_0_7598, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_12436, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7599, c_0_4760]), c_0_4436]), c_0_4436]), ['final']). 4.46/4.73 cnf(c_0_12437, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[c_0_7600, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_12438, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7421]), ['final']). 4.46/4.73 cnf(c_0_12439, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7421]), ['final']). 4.46/4.73 cnf(c_0_12440, plain, (hAPP(X4,hAPP(c_Product__Type_Osnd(X3,X1),X5))=hAPP(X6,hAPP(c_Product__Type_Osnd(X3,X1),X5))|hAPP(c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X4),X5)!=hAPP(c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X6),X5)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7601, c_0_4825]), c_0_4825]), ['final']). 4.46/4.73 cnf(c_0_12441, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7602]), ['final']). 4.46/4.73 cnf(c_0_12442, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7603, c_0_4760]), c_0_4436]), c_0_4436]), ['final']). 4.46/4.73 cnf(c_0_12443, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7604, c_0_4760]), c_0_4609]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_12444, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[c_0_7605, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_12445, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[c_0_7606, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_12446, plain, (X1=c_List_Olist_ONil(X2)|c_Random_Oselect__weight(X2,hAPP(hAPP(c_List_Omap(X2,tc_prod(tc_Code__Numeral_Ocode__numeral,X2)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X1))=c_Random_Oselect(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_7607]), ['final']). 4.46/4.73 cnf(c_0_12447, plain, (hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X3),X5))=hAPP(X6,hAPP(c_Product__Type_Ofst(X1,X3),X5))|hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),X5)!=hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X6,c_Fun_Oid(X3)),X5)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7608, c_0_6862]), c_0_6862]), ['final']). 4.46/4.73 cnf(c_0_12448, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk396_4(X2,X3,X4,X1)))|hBOOL(hAPP(X2,X4))|~hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_7310]), ['final']). 4.46/4.73 cnf(c_0_12449, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk336_3(X2,X3,X1)),c_List_Olists(X1,X2)))|c_List_Olist_ONil(X1)=X3|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7609]), ['final']). 4.46/4.73 cnf(c_0_12450, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_Fun_Oid(X1)),hAPP(c_Set_Oimage(X2,X1,X3),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)|~class_Groups_Ocomm__monoid__add(X1)|~c_Fun_Oinj__on(X2,X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_7610]), ['final']). 4.46/4.73 cnf(c_0_12451, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7611, c_0_4436]), c_0_4760]), c_0_4436]), ['final']). 4.46/4.73 cnf(c_0_12452, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[c_0_7612, c_0_4760]), ['final']). 4.46/4.73 cnf(c_0_12453, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7613, c_0_4436]), c_0_4760]), c_0_4436]), ['final']). 4.46/4.73 cnf(c_0_12454, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk538_3(X2,X1,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk536_3(X2,X1,X3)),X1))|epred2_3(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5124]), ['final']). 4.46/4.73 cnf(c_0_12455, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X1),c_Fun_Oid(X1)),hAPP(c_Set_Oimage(X2,X1,X3),X4))|~class_Groups_Ocomm__monoid__mult(X1)|~c_Fun_Oinj__on(X2,X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_7614]), ['final']). 4.46/4.73 cnf(c_0_12456, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),esk359_2(X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7615]), ['final']). 4.46/4.73 cnf(c_0_12457, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7616]), ['final']). 4.46/4.73 cnf(c_0_12458, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X4)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7617]), ['final']). 4.46/4.73 cnf(c_0_12459, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_7618, c_0_4436]), ['final']). 4.46/4.73 cnf(c_0_12460, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2,X1),tc_HOL_Obool))))), inference(rw,[status(thm)],[c_0_7619, c_0_4836]), ['final']). 4.46/4.73 cnf(c_0_12461, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7620]), ['final']). 4.46/4.73 cnf(c_0_12462, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7621]), ['final']). 4.46/4.73 cnf(c_0_12463, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBS(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Oord__class_Oless__eq(X2)),X3)),X4)))|~class_Orderings_Oorder(X2)|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_7023]), ['final']). 4.46/4.73 cnf(c_0_12464, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7582]), ['final']). 4.46/4.73 cnf(c_0_12465, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,esk421_5(X3,X4,X5,X2,X1))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_7538]), ['final']). 4.46/4.73 cnf(c_0_12466, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))=c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3),X4)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7622]), ['final']). 4.46/4.73 cnf(c_0_12467, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X1,X2)),hAPP(hAPP(c_Set_Oinsert(X4),X3),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X1,X2)),X5)|c_Option_Ooption_ONone(X1)!=hAPP(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7623]), ['final']). 4.46/4.73 cnf(c_0_12468, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7624]), ['final']). 4.46/4.73 cnf(c_0_12469, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2)),X3)=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[c_0_7625, c_0_5320]), ['final']). 4.46/4.73 cnf(c_0_12470, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7626]), ['final']). 4.46/4.73 cnf(c_0_12471, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Oone__class_Oone(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7627, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4912]), ['final']). 4.46/4.73 cnf(c_0_12472, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Oone__class_Oone(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7628, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_6631]), ['final']). 4.46/4.73 cnf(c_0_12473, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_7629]), ['final']). 4.46/4.73 cnf(c_0_12474, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X2)),X3))), inference(rw,[status(thm)],[c_0_7630, c_0_5320]), ['final']). 4.46/4.73 cnf(c_0_12475, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3))), inference(rw,[status(thm)],[c_0_7631, c_0_5320]), ['final']). 4.46/4.73 cnf(c_0_12476, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2)),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[c_0_7632, c_0_5320]), ['final']). 4.46/4.73 cnf(c_0_12477, plain, (hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_ORange(X1,X2),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_7633]), ['final']). 4.46/4.73 cnf(c_0_12478, plain, (c_Option_Ooption_ONone(X5)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X5),X1,c_Option_Ooption_ONone(X5),X6),hAPP(X3,X4))|c_Option_Ooption_ONone(X5)!=hAPP(X6,X2)|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(X3,X4)), inference(rw,[status(thm)],[c_0_7634, c_0_7133]), ['final']). 4.46/4.73 cnf(c_0_12479, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))|~hBOOL(hAPP(hAPP(X1,esk27_3(X2,X1,X3)),esk28_3(X2,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5126]), ['final']). 4.46/4.73 cnf(c_0_12480, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(X1),X3))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7635]), ['final']). 4.46/4.73 cnf(c_0_12481, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))|~hBOOL(hAPP(hAPP(X1,esk155_3(X2,X1,X3)),esk156_3(X2,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5128]), ['final']). 4.46/4.73 cnf(c_0_12482, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X1,X2,X3)),X2))|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,esk532_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_12483, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),esk532_3(X2,X3,X1)))|X3=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X1,X3,X2)|~hBOOL(hAPP(X1,esk534_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.73 cnf(c_0_12484, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),X3)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber(X1)), inference(er,[status(thm)],[c_0_7636]), ['final']). 4.46/4.73 cnf(c_0_12485, plain, (hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7637]), ['final']). 4.46/4.73 cnf(c_0_12486, plain, (hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7638]), ['final']). 4.46/4.73 cnf(c_0_12487, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7639, c_0_5120]), c_0_5120]), c_0_5120]), ['final']). 4.46/4.73 cnf(c_0_12488, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk477_7(X2,X3,X4,X5,X6,X7,X1)),X5))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X7,tc_fun(X6,tc_HOL_Obool))),X5),X4),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7529]), ['final']). 4.46/4.73 cnf(c_0_12489, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk430_7(X2,X3,X4,X5,X6,X7,X1)),X5))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X7,tc_fun(X6,tc_HOL_Obool))),X5),X4),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7530]), ['final']). 4.46/4.73 cnf(c_0_12490, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7480]), ['final']). 4.46/4.73 cnf(c_0_12491, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7640]), ['final']). 4.46/4.73 cnf(c_0_12492, plain, (X3=hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Finite__Set_Ofolding__one(X1,X5,X4)), inference(split_conjunct,[status(thm)],[c_0_6660]), ['final']). 4.46/4.73 cnf(c_0_12493, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7641]), ['final']). 4.46/4.73 cnf(c_0_12494, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_5868]), ['final']). 4.46/4.73 cnf(c_0_12495, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7486]), ['final']). 4.46/4.73 cnf(c_0_12496, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7480]), ['final']). 4.46/4.73 cnf(c_0_12497, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7480]), ['final']). 4.46/4.73 cnf(c_0_12498, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7486]), ['final']). 4.46/4.73 cnf(c_0_12499, plain, (hAPP(c_List_Ofilter(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))=hAPP(hAPP(c_List_Olist_OCons(X3),X2),hAPP(c_List_Ofilter(X3,X1),X4))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_7642]), ['final']). 4.46/4.73 cnf(c_0_12500, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7643]), ['final']). 4.46/4.73 cnf(c_0_12501, plain, (hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7644]), ['final']). 4.46/4.73 cnf(c_0_12502, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3))=hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7645]), ['final']). 4.46/4.73 cnf(c_0_12503, plain, (hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7646]), ['final']). 4.46/4.73 cnf(c_0_12504, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),X3)),c_Divides_Odiv__class_Omod(X1,X2,X3))|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7647]), ['final']). 4.46/4.73 cnf(c_0_12505, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7486]), ['final']). 4.46/4.73 cnf(c_0_12506, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7480]), ['final']). 4.46/4.73 cnf(c_0_12507, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7486]), ['final']). 4.46/4.73 cnf(c_0_12508, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7497]), ['final']). 4.46/4.73 cnf(c_0_12509, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),X3))|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7648]), ['final']). 4.46/4.73 cnf(c_0_12510, plain, (hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7649]), ['final']). 4.46/4.73 cnf(c_0_12511, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X4),X3))|~class_Orderings_Oord(X2)), inference(split_conjunct,[status(thm)],[c_0_7650]), ['final']). 4.46/4.73 cnf(c_0_12512, plain, (c_List_Olist_ONil(X1)=X2|hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Odrop(X1),X3),X2))=hAPP(hAPP(c_List_Onth(X1),X2),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))), inference(split_conjunct,[status(thm)],[c_0_7651]), ['final']). 4.46/4.73 cnf(c_0_12513, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X4|hAPP(hAPP(X2,X5),hAPP(X3,X4))=hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4))|~c_Finite__Set_Ofolding__one__idem(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_7652]), ['final']). 4.46/4.73 cnf(c_0_12514, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))),c_Divides_Odiv__class_Omod(X1,X3,X2))=X3|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7653]), ['final']). 4.46/4.73 cnf(c_0_12515, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7497]), ['final']). 4.46/4.73 cnf(c_0_12516, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7497]), ['final']). 4.46/4.73 cnf(c_0_12517, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7497]), ['final']). 4.46/4.73 cnf(c_0_12518, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7502]), ['final']). 4.46/4.73 cnf(c_0_12519, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7654, c_0_4609]), c_0_5120]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_12520, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7655]), ['final']). 4.46/4.73 cnf(c_0_12521, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7656]), ['final']). 4.46/4.73 cnf(c_0_12522, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7657, c_0_5580]), c_0_5580]), ['final']). 4.46/4.73 cnf(c_0_12523, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(er,[status(thm)],[c_0_7658]), ['final']). 4.46/4.73 cnf(c_0_12524, plain, (c_List_Oupto(X1,X2)=hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X1),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7659]), ['final']). 4.46/4.73 cnf(c_0_12525, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7502]), ['final']). 4.46/4.73 cnf(c_0_12526, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7502]), ['final']). 4.46/4.73 cnf(c_0_12527, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7502]), ['final']). 4.46/4.73 cnf(c_0_12528, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2))=c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),X2))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7660]), ['final']). 4.46/4.73 cnf(c_0_12529, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X3,X3,hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X3),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot)),c_fequal)),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_5588]), ['final']). 4.46/4.73 cnf(c_0_12530, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3)=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7661]), ['final']). 4.46/4.73 cnf(c_0_12531, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2))=c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),X2))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7662]), ['final']). 4.46/4.73 cnf(c_0_12532, plain, (hAPP(X2,X3)=c_Groups_Ozero__class_Ozero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk264_5(X3,X2,X4,X5,X1))))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)!=c_Groups_Ozero__class_Ozero(X1)|~hBOOL(hAPP(hAPP(c_member(X5),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7129]), ['final']). 4.46/4.73 cnf(c_0_12533, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7663]), ['final']). 4.46/4.73 cnf(c_0_12534, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7664]), ['final']). 4.46/4.73 cnf(c_0_12535, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))), inference(er,[status(thm)],[c_0_7665]), ['final']). 4.46/4.73 cnf(c_0_12536, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7666]), ['final']). 4.46/4.73 cnf(c_0_12537, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7667]), ['final']). 4.46/4.73 cnf(c_0_12538, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_7668]), ['final']). 4.46/4.73 cnf(c_0_12539, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7669]), ['final']). 4.46/4.73 cnf(c_0_12540, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7670]), ['final']). 4.46/4.73 cnf(c_0_12541, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7671]), ['final']). 4.46/4.73 cnf(c_0_12542, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Groups_Otimes__class_Otimes(X1)),X3),X2)=hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~class_Lattices_Oab__semigroup__idem__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7672]), ['final']). 4.46/4.73 cnf(c_0_12543, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk538_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|epred2_3(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5124]), ['final']). 4.46/4.73 cnf(c_0_12544, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X3))=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1)), inference(er,[status(thm)],[c_0_7673]), ['final']). 4.46/4.73 cnf(c_0_12545, plain, (hBOOL(hAPP(hAPP(c_member(X1),X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_7674]), ['final']). 4.46/4.73 cnf(c_0_12546, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk536_3(X2,X1,X3)))|epred2_3(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5124]), ['final']). 4.46/4.73 cnf(c_0_12547, plain, (X5=X3|hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))!=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))|~hBOOL(hAPP(hAPP(c_member(X2),X6),X4))), inference(split_conjunct,[status(thm)],[c_0_7675]), ['final']). 4.46/4.73 cnf(c_0_12548, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7676]), ['final']). 4.46/4.73 cnf(c_0_12549, plain, (hAPP(X5,X6)=hAPP(X3,X6)|hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)!=hAPP(hAPP(c_List_Omap(X1,X2),X5),X4)|~hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),X4)))), inference(split_conjunct,[status(thm)],[c_0_7173]), ['final']). 4.46/4.73 cnf(c_0_12550, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk135_3(X2,X1,X3))=X1|hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_7677]), ['final']). 4.46/4.73 cnf(c_0_12551, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7678]), ['final']). 4.46/4.73 cnf(c_0_12552, plain, (hBOOL(hAPP(c_List_Odistinct(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool)),c_List_Oset(X1)),c_Enum_Osublists(X1,X2))))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7679]), ['final']). 4.46/4.73 cnf(c_0_12553, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,esk213_4(X2,X3,X1,X4))))|hAPP(c_Nat_OSuc,X2)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X1),X3)), inference(split_conjunct,[status(thm)],[c_0_7680]), ['final']). 4.46/4.73 cnf(c_0_12554, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_7681]), ['final']). 4.46/4.73 cnf(c_0_12555, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7682, c_0_5120]), c_0_6071]), ['final']). 4.46/4.73 cnf(c_0_12556, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk90_3(X2,X1,X3))|hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_7683]), ['final']). 4.46/4.73 cnf(c_0_12557, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk119_5(X2,X3,X1,X4,X5)),X2))|~hBOOL(hAPP(hAPP(c_member(X5),X4),c_Map_Oran(X1,X5,c_Map_Orestrict__map(X1,X5,X3,X2))))), inference(split_conjunct,[status(thm)],[c_0_7684]), ['final']). 4.46/4.73 cnf(c_0_12558, plain, (c_List_Olist__all2(X3,X2,X4,hAPP(hAPP(c_List_Omap(X1,X3),X5),X6),X7)|~c_List_Olist__all2(X1,X2,hAPP(hAPP(c_COMBB(X3,tc_fun(X2,tc_HOL_Obool),X1),X4),X5),X6,X7)), inference(split_conjunct,[status(thm)],[c_0_7461]), ['final']). 4.46/4.73 cnf(c_0_12559, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))), inference(rw,[status(thm)],[c_0_7685, c_0_5266]), ['final']). 4.46/4.73 cnf(c_0_12560, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk353_2(X2,X1)),hAPP(c_Relation_OImage(X1,X1,X2),esk353_2(X2,X1))))|c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7686]), ['final']). 4.46/4.73 cnf(c_0_12561, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7687]), ['final']). 4.46/4.73 cnf(c_0_12562, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2))), inference(csr,[status(thm)],[c_0_7688, c_0_7689]), ['final']). 4.46/4.73 cnf(c_0_12563, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3))))), inference(split_conjunct,[status(thm)],[c_0_7317]), ['final']). 4.46/4.73 cnf(c_0_12564, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2))),hAPP(c_Finite__Set_Ocard(X1),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7690]), ['final']). 4.46/4.73 cnf(c_0_12565, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk24_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7691]), ['final']). 4.46/4.73 cnf(c_0_12566, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X3),X4),X2)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X1,c_Groups_Otimes__class_Otimes(X3)),X4),c_Groups_Oone__class_Oone(X3)),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Groups_Ocomm__monoid__mult(X3)), inference(split_conjunct,[status(thm)],[c_0_4965]), ['final']). 4.46/4.73 cnf(c_0_12567, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X4),X2)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X1,c_Groups_Oplus__class_Oplus(X3)),X4),c_Groups_Ozero__class_Ozero(X3)),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Groups_Ocomm__monoid__add(X3)), inference(split_conjunct,[status(thm)],[c_0_7692]), ['final']). 4.46/4.73 cnf(c_0_12568, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2)), inference(split_conjunct,[status(thm)],[c_0_7693]), ['final']). 4.46/4.73 cnf(c_0_12569, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7694]), ['final']). 4.46/4.73 cnf(c_0_12570, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7695]), ['final']). 4.46/4.73 cnf(c_0_12571, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(X4,X2))), inference(rw,[status(thm)],[c_0_7696, c_0_4531]), ['final']). 4.46/4.73 cnf(c_0_12572, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(X4,X2)=hAPP(c_Map_Omap__upds(X1,X5,X4,X3,X6),X2)), inference(split_conjunct,[status(thm)],[c_0_7697]), ['final']). 4.46/4.73 cnf(c_0_12573, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk298_2(X1,X2)),X2))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))), inference(split_conjunct,[status(thm)],[c_0_7245]), ['final']). 4.46/4.73 cnf(c_0_12574, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),hAPP(c_Finite__Set_Ocard(X2),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(c_COMBK(X1,X2),X4)),X3)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7698]), ['final']). 4.46/4.73 cnf(c_0_12575, plain, (X3=X4|~hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hAPP(hAPP(c_List_Onth(X1),X2),X4)!=hAPP(hAPP(c_List_Onth(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_7699]), ['final']). 4.46/4.73 cnf(c_0_12576, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(rw,[status(thm)],[c_0_7700, c_0_4531]), ['final']). 4.46/4.73 cnf(c_0_12577, plain, (hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),esk395_4(X1,X3,X4,X2)),esk396_4(X1,X3,X4,X2))))|~hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))), inference(split_conjunct,[status(thm)],[c_0_7310]), ['final']). 4.46/4.73 cnf(c_0_12578, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_7701]), ['final']). 4.46/4.73 cnf(c_0_12579, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))|~class_Lattices_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_7702]), ['final']). 4.46/4.73 cnf(c_0_12580, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2))=hAPP(c_Nat_OSuc,X2)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7703, c_0_7704]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_12581, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,X2)=X3|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6563]), ['final']). 4.46/4.73 cnf(c_0_12582, plain, (X3=c_Big__Operators_Olinorder__class_OMax(X1,X2)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6564]), ['final']). 4.46/4.73 cnf(c_0_12583, plain, (X3=c_Big__Operators_Olattice__class_OSup__fin(X1,X2)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6562]), ['final']). 4.46/4.73 cnf(c_0_12584, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_6037]), ['final']). 4.46/4.73 cnf(c_0_12585, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk335_3(X2,X3,X1)),esk336_3(X2,X3,X1))=X3|c_List_Olist_ONil(X1)=X3|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7609]), ['final']). 4.46/4.73 cnf(c_0_12586, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_7376]), ['final']). 4.46/4.73 cnf(c_0_12587, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7705]), ['final']). 4.46/4.73 cnf(c_0_12588, plain, (X3=c_Big__Operators_Olinorder__class_OMin(X1,X2)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6565]), ['final']). 4.46/4.73 cnf(c_0_12589, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))), inference(rw,[status(thm)],[c_0_7706, c_0_4945]), ['final']). 4.46/4.73 cnf(c_0_12590, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X5),X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7707]), ['final']). 4.46/4.73 cnf(c_0_12591, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk164_5(X3,X2,X4,X5,X1))),X3))), inference(split_conjunct,[status(thm)],[c_0_6888]), ['final']). 4.46/4.73 cnf(c_0_12592, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_7377]), ['final']). 4.46/4.73 cnf(c_0_12593, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_7708]), ['final']). 4.46/4.73 cnf(c_0_12594, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6808]), ['final']). 4.46/4.73 cnf(c_0_12595, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_7709]), ['final']). 4.46/4.73 cnf(c_0_12596, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(X3,esk138_5(X3,X4,X5,X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_6890]), ['final']). 4.46/4.73 cnf(c_0_12597, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X4),X5)),hAPP(X5,X3)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_member(X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7710]), ['final']). 4.46/4.73 cnf(c_0_12598, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6812]), ['final']). 4.46/4.73 cnf(c_0_12599, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_7711]), ['final']). 4.46/4.73 cnf(c_0_12600, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6846]), ['final']). 4.46/4.73 cnf(c_0_12601, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_7712]), ['final']). 4.46/4.73 cnf(c_0_12602, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_7713]), ['final']). 4.46/4.73 cnf(c_0_12603, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X2),X1)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X2)))), inference(split_conjunct,[status(thm)],[c_0_7714]), ['final']). 4.46/4.73 cnf(c_0_12604, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X5,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X4),X5)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_member(X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7715]), ['final']). 4.46/4.73 cnf(c_0_12605, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7716]), ['final']). 4.46/4.73 cnf(c_0_12606, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk235_5(X2,X3,X4,X5,X1)),X4))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X5,tc_HOL_Obool)),X4),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7717]), ['final']). 4.46/4.73 cnf(c_0_12607, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_6840]), ['final']). 4.46/4.73 cnf(c_0_12608, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_7390]), ['final']). 4.46/4.73 cnf(c_0_12609, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_7395]), ['final']). 4.46/4.73 cnf(c_0_12610, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7718]), ['final']). 4.46/4.73 cnf(c_0_12611, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7719]), ['final']). 4.46/4.73 cnf(c_0_12612, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_7720]), ['final']). 4.46/4.73 cnf(c_0_12613, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=X3|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6431]), ['final']). 4.46/4.73 cnf(c_0_12614, plain, (c_List_Olistrelp(X4,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6))|~hBOOL(hAPP(hAPP(X1,X2),X3))|~c_List_Olistrelp(X4,X1,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_7721]), ['final']). 4.46/4.73 cnf(c_0_12615, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk111_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X1)))), inference(split_conjunct,[status(thm)],[c_0_5383]), ['final']). 4.46/4.73 cnf(c_0_12616, plain, (c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_7722]), ['final']). 4.46/4.73 cnf(c_0_12617, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X2),hAPP(c_Int_Oring__1__class_Oof__int(X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)))=hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Oring__1(X2)), inference(split_conjunct,[status(thm)],[c_0_4495]), ['final']). 4.46/4.73 cnf(c_0_12618, plain, (X3=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6436]), ['final']). 4.46/4.73 cnf(c_0_12619, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk188_3(X2,X3,X1)),X2))|hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5209]), ['final']). 4.46/4.73 cnf(c_0_12620, plain, (hAPP(X1,X2)=hAPP(X3,X2)|~class_HOL_Oequal(X4)|~class_Enum_Oenum(X5)|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X5,X4)),X1),X3))), inference(csr,[status(thm)],[c_0_7723, c_0_7724]), ['final']). 4.46/4.73 cnf(c_0_12621, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omin(X1),X2),X3)|~class_Orderings_Olinorder(X1)), inference(rw,[status(thm)],[c_0_7725, c_0_7726]), ['final']). 4.46/4.73 cnf(c_0_12622, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omax(X1),X2),X3)|~class_Orderings_Olinorder(X1)), inference(rw,[status(thm)],[c_0_7727, c_0_7726]), ['final']). 4.46/4.73 cnf(c_0_12623, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremove1(X1,X2,X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7728]), ['final']). 4.46/4.73 cnf(c_0_12624, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)|~c_Nat__Transfer_Ois__nat(X2)|~c_Nat__Transfer_Ois__nat(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7729, c_0_5120]), c_0_5120]), ['final']). 4.46/4.73 cnf(c_0_12625, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7730, c_0_4609]), c_0_4609]), c_0_4609]), ['final']). 4.46/4.73 cnf(c_0_12626, plain, (hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,X1)),X3),X4),X5)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X3,X5)),hAPP(X4,X5))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7731]), ['final']). 4.46/4.73 cnf(c_0_12627, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(X2,X3)),hAPP(X4,X3))=hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,X1)),X2),X4),X3)|~class_Groups_Ominus(X1)), inference(split_conjunct,[status(thm)],[c_0_7732]), ['final']). 4.46/4.73 cnf(c_0_12628, plain, (c_Option_Ooption_ONone(X1)=X2|hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Map_Odom(X3,X1,X5))=c_Map_Odom(X3,X1,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X1)),X5),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_5637]), ['final']). 4.46/4.73 cnf(c_0_12629, plain, (hAPP(hAPP(X1,X2),esk129_7(X2,X3,X4,X5,X1,X6,X7))=X3|~hBOOL(hAPP(hAPP(c_member(X7),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X6,X1,X5,X4),X3))|~c_Finite__Set_Ofun__left__comm(X7,X6,X1)), inference(split_conjunct,[status(thm)],[c_0_6352]), ['final']). 4.46/4.73 cnf(c_0_12630, plain, (c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X6),X4))|c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X6|~c_Fun_Oinj__on(X1,X2,X3,hAPP(X4,esk339_6(X4,X3,X2,X1,X5,X6)))), inference(split_conjunct,[status(thm)],[c_0_6771]), ['final']). 4.46/4.73 cnf(c_0_12631, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X4,X1,X3)),c_List_Olist_Olist__size(X4,X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,esk43_4(X2,X1,X3,X4))),hAPP(X2,esk43_4(X2,X1,X3,X4))))), inference(split_conjunct,[status(thm)],[c_0_6839]), ['final']). 4.46/4.73 cnf(c_0_12632, plain, (c_List_Olist_ONil(X3)=hAPP(hAPP(c_List_Odrop(X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),c_List_OtakeWhile(X3,X1,X2))),X2)|~hBOOL(hAPP(X1,esk193_3(X2,X1,X3)))), inference(rw,[status(thm)],[c_0_7733, c_0_4916]), ['final']). 4.46/4.73 cnf(c_0_12633, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_7734, c_0_4436]), ['final']). 4.46/4.73 cnf(c_0_12634, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X2,X3)),hAPP(X4,X3))=hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,X1)),X2),X4),X3)|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7735]), ['final']). 4.46/4.73 cnf(c_0_12635, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))=hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_7736, c_0_5120]), ['final']). 4.46/4.73 cnf(c_0_12636, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7737]), ['final']). 4.46/4.73 cnf(c_0_12637, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_7738, c_0_4912]), ['final']). 4.46/4.73 cnf(c_0_12638, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2,X1),tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_7739]), ['final']). 4.46/4.73 cnf(c_0_12639, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_7740]), ['final']). 4.46/4.73 cnf(c_0_12640, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7741]), ['final']). 4.46/4.73 cnf(c_0_12641, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(rw,[status(thm)],[c_0_7742, c_0_5902]), ['final']). 4.46/4.73 cnf(c_0_12642, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_7743]), ['final']). 4.46/4.73 cnf(c_0_12643, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),X2)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7744]), ['final']). 4.46/4.73 cnf(c_0_12644, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X5,X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),X4)))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_7745]), ['final']). 4.46/4.73 cnf(c_0_12645, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Oremdups(X1,X3))=c_List_Oremdups(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7746]), ['final']). 4.46/4.73 cnf(c_0_12646, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),hAPP(c_List_Oset(X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))), inference(er,[status(thm)],[c_0_7747]), ['final']). 4.46/4.73 cnf(c_0_12647, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7748, c_0_4436]), c_0_4500]), c_0_4760]), c_0_5765]), c_0_4436]), ['final']). 4.46/4.73 cnf(c_0_12648, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X4,X3))))|X2=X4|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7749]), ['final']). 4.46/4.73 cnf(c_0_12649, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4)), inference(split_conjunct,[status(thm)],[c_0_7750]), ['final']). 4.46/4.73 cnf(c_0_12650, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_7751, c_0_4443]), ['final']). 4.46/4.74 cnf(c_0_12651, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7752, c_0_4436]), c_0_4500]), c_0_4760]), c_0_5765]), c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_12652, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7753, c_0_4500]), c_0_4760]), c_0_5765]), ['final']). 4.46/4.74 cnf(c_0_12653, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7754, c_0_4500]), c_0_4760]), c_0_5765]), ['final']). 4.46/4.74 cnf(c_0_12654, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7755, c_0_4436]), c_0_4500]), c_0_4760]), c_0_5765]), c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_12655, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)=c_Nat_Osemiring__1__class_Oof__nat__aux(X1,hAPP(hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_Groups_Oone__class_Oone(X1)),X2,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7756]), ['final']). 4.46/4.74 cnf(c_0_12656, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk199_3(X1,X2,X3)),X3))|hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X2,X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7757]), ['final']). 4.46/4.74 cnf(c_0_12657, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X3,tc_fun(X2,tc_HOL_Obool))),X6),X1),X5),X4))|~hBOOL(hAPP(hAPP(hAPP(X1,esk375_7(X2,X3,X4,X5,X1,X6,X7)),X5),X4))), inference(split_conjunct,[status(thm)],[c_0_7156]), ['final']). 4.46/4.74 cnf(c_0_12658, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X6,tc_fun(X5,tc_HOL_Obool))),X4),X1),X3),X2))|~hBOOL(hAPP(hAPP(hAPP(X1,esk414_7(X2,X3,X1,X4,X5,X6,X7)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7153]), ['final']). 4.46/4.74 cnf(c_0_12659, plain, (hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)=hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_7758]), ['final']). 4.46/4.74 cnf(c_0_12660, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7759, c_0_4609]), c_0_4500]), c_0_4760]), c_0_5765]), c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_12661, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7760, c_0_4436]), c_0_4436]), c_0_4500]), c_0_4760]), c_0_5765]), ['final']). 4.46/4.74 cnf(c_0_12662, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7761, c_0_4500]), c_0_4760]), c_0_5765]), ['final']). 4.46/4.74 cnf(c_0_12663, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7762, c_0_4500]), c_0_4760]), c_0_5765]), ['final']). 4.46/4.74 cnf(c_0_12664, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X2)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_7763, c_0_5902]), ['final']). 4.46/4.74 cnf(c_0_12665, plain, (hBOOL(hAPP(X2,X3))|hAPP(c_List_Ofilter(X4,X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X1,X5),X3),X6))=hAPP(c_List_Ofilter(X4,X2),X6)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7764]), ['final']). 4.46/4.74 cnf(c_0_12666, plain, (hAPP(X5,X2)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X6),X1,c_Option_Ooption_ONone(X6),X5),hAPP(X3,X4))|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(X3,X4)), inference(rw,[status(thm)],[c_0_7765, c_0_7133]), ['final']). 4.46/4.74 cnf(c_0_12667, plain, (hAPP(hAPP(c_List_Oappend(X1),esk472_5(X2,X3,X4,X5,X1)),X2)=X4|c_List_Olist_ONil(X1)=X3|hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)!=hAPP(hAPP(c_List_Oappend(X1),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_7340]), ['final']). 4.46/4.74 cnf(c_0_12668, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_7766]), ['final']). 4.46/4.74 cnf(c_0_12669, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7767, c_0_4436]), c_0_4436]), c_0_4500]), c_0_4760]), c_0_5765]), ['final']). 4.46/4.74 cnf(c_0_12670, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7768, c_0_4436]), c_0_4436]), c_0_4500]), c_0_4760]), c_0_5765]), ['final']). 4.46/4.74 cnf(c_0_12671, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_7769]), ['final']). 4.46/4.74 cnf(c_0_12672, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7770]), ['final']). 4.46/4.74 cnf(c_0_12673, plain, (c_List_Olist_ONil(X1)=X2|c_List_Olast(X1,X2)=hAPP(hAPP(c_List_Onth(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_7771]), ['final']). 4.46/4.74 cnf(c_0_12674, plain, (hAPP(hAPP(c_List_Oappend(X1),esk408_5(X2,X3,X4,X5,X1)),X4)=X2|X5=c_List_Olist_ONil(X1)|hAPP(hAPP(c_List_Oappend(X1),X5),X4)!=hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_7339]), ['final']). 4.46/4.74 cnf(c_0_12675, plain, (X1=hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk472_5(X4,X1,X5,X3,X2))|c_List_Olist_ONil(X2)=X1|hAPP(hAPP(c_List_Olist_OCons(X2),X3),X5)!=hAPP(hAPP(c_List_Oappend(X2),X1),X4)), inference(split_conjunct,[status(thm)],[c_0_7340]), ['final']). 4.46/4.74 cnf(c_0_12676, plain, (X1=hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk408_5(X4,X3,X5,X1,X2))|X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Oappend(X2),X1),X5)!=hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_7339]), ['final']). 4.46/4.74 cnf(c_0_12677, plain, (c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))|~c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))), inference(rw,[status(thm)],[c_0_7772, c_0_5266]), ['final']). 4.46/4.74 cnf(c_0_12678, plain, (c_Hoare__Mirabelle_Otriple__valid(X1,X2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5))|~c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(c_Nat_OSuc,X2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_7773]), ['final']). 4.46/4.74 cnf(c_0_12679, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))), inference(split_conjunct,[status(thm)],[c_0_7774]), ['final']). 4.46/4.74 cnf(c_0_12680, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))), inference(split_conjunct,[status(thm)],[c_0_7775]), ['final']). 4.46/4.74 cnf(c_0_12681, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7776]), ['final']). 4.46/4.74 cnf(c_0_12682, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7777]), ['final']). 4.46/4.74 cnf(c_0_12683, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7778]), ['final']). 4.46/4.74 cnf(c_0_12684, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,X2))=c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7779]), ['final']). 4.46/4.74 cnf(c_0_12685, plain, (hBOOL(hAPP(c_Predicate_OPowp(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Set_OPow(X1),X2)))), inference(rw,[status(thm)],[c_0_7780, c_0_4945]), ['final']). 4.46/4.74 cnf(c_0_12686, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7781]), ['final']). 4.46/4.74 cnf(c_0_12687, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7782]), ['final']). 4.46/4.74 cnf(c_0_12688, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7783]), ['final']). 4.46/4.74 cnf(c_0_12689, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7784]), ['final']). 4.46/4.74 cnf(c_0_12690, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,X2))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7785]), ['final']). 4.46/4.74 cnf(c_0_12691, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7786]), ['final']). 4.46/4.74 cnf(c_0_12692, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7787]), ['final']). 4.46/4.74 cnf(c_0_12693, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7788]), ['final']). 4.46/4.74 cnf(c_0_12694, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),X2)=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7789]), ['final']). 4.46/4.74 cnf(c_0_12695, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk538_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|epred2_3(X3,X2,X1)|~hBOOL(hAPP(X3,esk535_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_5124]), ['final']). 4.46/4.74 cnf(c_0_12696, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk536_3(X2,X3,X1)))|epred2_3(X1,X3,X2)|~hBOOL(hAPP(X1,esk537_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5124]), ['final']). 4.46/4.74 cnf(c_0_12697, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk76_2(X1,X2)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))|~hBOOL(hAPP(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_7438]), ['final']). 4.46/4.74 cnf(c_0_12698, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_7790, c_0_5765]), ['final']). 4.46/4.74 cnf(c_0_12699, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~class_Rings_Olinordered__idom(X3)|~class_Int_Onumber__ring(X3)), inference(split_conjunct,[status(thm)],[c_0_7791]), ['final']). 4.46/4.74 cnf(c_0_12700, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~class_Rings_Olinordered__idom(X3)|~class_Int_Onumber__ring(X3)), inference(split_conjunct,[status(thm)],[c_0_7792]), ['final']). 4.46/4.74 cnf(c_0_12701, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7793]), ['final']). 4.46/4.74 cnf(c_0_12702, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7794]), ['final']). 4.46/4.74 cnf(c_0_12703, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,X2))=c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7795]), ['final']). 4.46/4.74 cnf(c_0_12704, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7501]), ['final']). 4.46/4.74 cnf(c_0_12705, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7796]), ['final']). 4.46/4.74 cnf(c_0_12706, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7797]), ['final']). 4.46/4.74 cnf(c_0_12707, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(X2,esk93_4(X2,X3,X1,X4))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(X2,X4)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7798, c_0_4836]), c_0_4836]), ['final']). 4.46/4.74 cnf(c_0_12708, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3),X5),X4),X7)=hAPP(X6,X7)|~c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))), inference(split_conjunct,[status(thm)],[c_0_7799]), ['final']). 4.46/4.74 cnf(c_0_12709, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7800, c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), ['final']). 4.46/4.74 cnf(c_0_12710, plain, (hBOOL(hAPP(X1,X5))|~hBOOL(hAPP(X1,esk12_4(X1,X2,X3,X4)))|~hBOOL(hAPP(X1,esk11_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6476]), ['final']). 4.46/4.74 cnf(c_0_12711, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7801]), ['final']). 4.46/4.74 cnf(c_0_12712, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7802]), ['final']). 4.46/4.74 cnf(c_0_12713, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7803]), ['final']). 4.46/4.74 cnf(c_0_12714, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7804]), ['final']). 4.46/4.74 cnf(c_0_12715, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7805]), ['final']). 4.46/4.74 cnf(c_0_12716, plain, (hBOOL(hAPP(X1,X2))|c_List_OtakeWhile(X3,X1,X4)=c_List_OtakeWhile(X3,X1,hAPP(hAPP(c_List_Oappend(X3),X4),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5)))), inference(split_conjunct,[status(thm)],[c_0_7806]), ['final']). 4.46/4.74 cnf(c_0_12717, plain, (hBOOL(hAPP(X1,esk396_4(X1,X2,X3,X4)))|hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7310]), ['final']). 4.46/4.74 cnf(c_0_12718, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk177_3(X2,X3,X1)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7807]), ['final']). 4.46/4.74 cnf(c_0_12719, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk260_3(X2,X3,X1)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7808]), ['final']). 4.46/4.74 cnf(c_0_12720, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7809]), ['final']). 4.46/4.74 cnf(c_0_12721, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))), inference(rw,[status(thm)],[c_0_7810, c_0_5884]), ['final']). 4.46/4.74 cnf(c_0_12722, plain, (c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=X3|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6614]), ['final']). 4.46/4.74 cnf(c_0_12723, plain, (c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=X3|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6620]), ['final']). 4.46/4.74 cnf(c_0_12724, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Complete__Lattice_OSup__class_OSup(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7811]), ['final']). 4.46/4.74 cnf(c_0_12725, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk536_3(X2,X1,X3)),X1))|epred2_3(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5124]), ['final']). 4.46/4.74 cnf(c_0_12726, plain, (X3=c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6618]), ['final']). 4.46/4.74 cnf(c_0_12727, plain, (X3=c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6619]), ['final']). 4.46/4.74 cnf(c_0_12728, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7812]), ['final']). 4.46/4.74 cnf(c_0_12729, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7813]), ['final']). 4.46/4.74 cnf(c_0_12730, plain, (X3=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),c_List_Oremove1(X1,X2,X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~c_List_Olinorder__class_Osorted(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_7814]), ['final']). 4.46/4.74 cnf(c_0_12731, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk538_3(X2,X1,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|epred2_3(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5124]), ['final']). 4.46/4.74 cnf(c_0_12732, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7815]), ['final']). 4.46/4.74 cnf(c_0_12733, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2))|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7816]), ['final']). 4.46/4.74 cnf(c_0_12734, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3))|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_7817]), ['final']). 4.46/4.74 cnf(c_0_12735, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_7818]), ['final']). 4.46/4.74 cnf(c_0_12736, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk135_3(X2,X3,X1))=X3|hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_7677]), ['final']). 4.46/4.74 cnf(c_0_12737, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk458_5(X2,X3,X1,X4,X5)),X2))|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Relation_OImage(X1,X5,X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_7069]), ['final']). 4.46/4.74 cnf(c_0_12738, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk216_5(X2,X3,X1,X4,X5)),X2))|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Relation_OImage(X1,X5,X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_7070]), ['final']). 4.46/4.74 cnf(c_0_12739, plain, (hAPP(hAPP(c_List_Oappend(X4),X3),c_List_OtakeWhile(X4,X1,X2))=c_List_OtakeWhile(X4,X1,hAPP(hAPP(c_List_Oappend(X4),X3),X2))|~hBOOL(hAPP(X1,esk299_4(X2,X1,X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_7180]), ['final']). 4.46/4.74 cnf(c_0_12740, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk318_3(X2,X3,X1)),X3))|c_Big__Operators_Olinorder__class_OMax(X1,X3)=X2|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7819]), ['final']). 4.46/4.74 cnf(c_0_12741, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),esk90_3(X3,X2,X1))|hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_7683]), ['final']). 4.46/4.74 cnf(c_0_12742, plain, (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X6,tc_HOL_Obool)),X5),X1),X3))|~hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),X5))), inference(split_conjunct,[status(thm)],[c_0_7820]), ['final']). 4.46/4.74 cnf(c_0_12743, plain, (hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Oappend(X2),X3),X4)),X1)=hAPP(hAPP(c_List_Onth(X2),X3),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6855]), ['final']). 4.46/4.74 cnf(c_0_12744, plain, (c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))|~c_Predicate_Oreflp(X1,X2)), inference(rw,[status(thm)],[c_0_7821, c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_12745, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk343_3(X2,X3,X1)),X3))|c_Big__Operators_Olinorder__class_OMin(X1,X3)=X2|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7822]), ['final']). 4.46/4.74 cnf(c_0_12746, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X4),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4),X3)|~class_Divides_Oring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7823]), ['final']). 4.46/4.74 cnf(c_0_12747, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)|c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))), inference(split_conjunct,[status(thm)],[c_0_7824]), ['final']). 4.46/4.74 cnf(c_0_12748, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_5502]), ['final']). 4.46/4.74 cnf(c_0_12749, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7825]), ['final']). 4.46/4.74 cnf(c_0_12750, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))|hAPP(c_Map_Omap__add(X1,X3,X4,X5),X2)=hAPP(X5,X2)), inference(split_conjunct,[status(thm)],[c_0_7826]), ['final']). 4.46/4.74 cnf(c_0_12751, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3),X4)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7827]), ['final']). 4.46/4.74 cnf(c_0_12752, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3),X4)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7828]), ['final']). 4.46/4.74 cnf(c_0_12753, plain, (hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_7691]), ['final']). 4.46/4.74 cnf(c_0_12754, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7829]), ['final']). 4.46/4.74 cnf(c_0_12755, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))|hAPP(c_Map_Omap__add(X1,X3,X5,X4),X2)=hAPP(X5,X2)), inference(split_conjunct,[status(thm)],[c_0_7830]), ['final']). 4.46/4.74 cnf(c_0_12756, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7831, c_0_4836]), c_0_4836]), ['final']). 4.46/4.74 cnf(c_0_12757, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))|hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2))))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_7317]), ['final']). 4.46/4.74 cnf(c_0_12758, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Wellfounded_Oless__than))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7832]), ['final']). 4.46/4.74 cnf(c_0_12759, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3),X4)|~class_Divides_Oring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7833]), ['final']). 4.46/4.74 cnf(c_0_12760, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7834]), ['final']). 4.46/4.74 cnf(c_0_12761, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X1),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7835]), ['final']). 4.46/4.74 cnf(c_0_12762, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X1),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7836]), ['final']). 4.46/4.74 cnf(c_0_12763, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))|~c_Nat__Transfer_Onat__set(X2)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2))), inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_7837, c_0_5120]), c_0_7838]), ['final']). 4.46/4.74 cnf(c_0_12764, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7839]), ['final']). 4.46/4.74 cnf(c_0_12765, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7840]), ['final']). 4.46/4.74 cnf(c_0_12766, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))), inference(split_conjunct,[status(thm)],[c_0_7501]), ['final']). 4.46/4.74 cnf(c_0_12767, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_7841]), ['final']). 4.46/4.74 cnf(c_0_12768, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)|X5=c_Groups_Ozero__class_Ozero(X1)|X3=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5)|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_7842]), ['final']). 4.46/4.74 cnf(c_0_12769, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_7843]), ['final']). 4.46/4.74 cnf(c_0_12770, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_Groups_Oab__semigroup__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_7844]), ['final']). 4.46/4.74 cnf(c_0_12771, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))|~class_Rings_Odivision__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7845]), ['final']). 4.46/4.74 cnf(c_0_12772, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|X3=X5|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5),X6)))), inference(split_conjunct,[status(thm)],[c_0_7846]), ['final']). 4.46/4.74 cnf(c_0_12773, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X6=X4|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5),X6)))), inference(split_conjunct,[status(thm)],[c_0_7847]), ['final']). 4.46/4.74 cnf(c_0_12774, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X1,X2,X3)),X2))|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,esk532_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X1))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.74 cnf(c_0_12775, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),esk532_3(X2,X3,X1)))|epred1_3(X1,X3,X2)|~hBOOL(hAPP(X1,esk534_3(X2,X3,X1)))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.74 cnf(c_0_12776, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X5)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)|X3=c_Groups_Ozero__class_Ozero(X1)|X5=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_7842]), ['final']). 4.46/4.74 cnf(c_0_12777, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_7848]), ['final']). 4.46/4.74 cnf(c_0_12778, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Nat__Transfer_Otsub(X1,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7849, c_0_5120]), c_0_5120]), c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_12779, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)=hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7850]), ['final']). 4.46/4.74 cnf(c_0_12780, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X1,X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7851]), ['final']). 4.46/4.74 cnf(c_0_12781, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Wellfounded_Omax__extp(X1,X4,X5,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(X4,esk489_4(X3,X5,X4,X1)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_5595]), ['final']). 4.46/4.74 cnf(c_0_12782, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7852]), ['final']). 4.46/4.74 cnf(c_0_12783, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_7853]), ['final']). 4.46/4.74 cnf(c_0_12784, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)|~class_Groups_Oab__semigroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7854]), ['final']). 4.46/4.74 cnf(c_0_12785, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7855]), ['final']). 4.46/4.74 cnf(c_0_12786, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3)|~class_Rings_Ocomm__semiring__1(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(hAPP(c_member(X2),X4),X3))|hAPP(X5,X4)!=c_Groups_Ozero__class_Ozero(X1)), inference(split_conjunct,[status(thm)],[c_0_7856]), ['final']). 4.46/4.74 cnf(c_0_12787, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|~class_Rings_Olinordered__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))), inference(split_conjunct,[status(thm)],[c_0_7857]), ['final']). 4.46/4.74 cnf(c_0_12788, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))), inference(split_conjunct,[status(thm)],[c_0_7858]), ['final']). 4.46/4.74 cnf(c_0_12789, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~class_Rings_Olinordered__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7859]), ['final']). 4.46/4.74 cnf(c_0_12790, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4)|~class_Lattices_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_7860]), ['final']). 4.46/4.74 cnf(c_0_12791, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4)|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7861]), ['final']). 4.46/4.74 cnf(c_0_12792, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4)|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7862]), ['final']). 4.46/4.74 cnf(c_0_12793, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4)|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_7863]), ['final']). 4.46/4.74 cnf(c_0_12794, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7087]), ['final']). 4.46/4.74 cnf(c_0_12795, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7864]), ['final']). 4.46/4.74 cnf(c_0_12796, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))), inference(split_conjunct,[status(thm)],[c_0_7865]), ['final']). 4.46/4.74 cnf(c_0_12797, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7097]), ['final']). 4.46/4.74 cnf(c_0_12798, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7866]), ['final']). 4.46/4.74 cnf(c_0_12799, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7867]), ['final']). 4.46/4.74 cnf(c_0_12800, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7868]), ['final']). 4.46/4.74 cnf(c_0_12801, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7869]), ['final']). 4.46/4.74 cnf(c_0_12802, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7870]), ['final']). 4.46/4.74 cnf(c_0_12803, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7108]), ['final']). 4.46/4.74 cnf(c_0_12804, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7871]), ['final']). 4.46/4.74 cnf(c_0_12805, plain, (~hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))|~c_Fun_Oinj__on(X4,X1,X2,hAPP(hAPP(c_Set_Oinsert(X4),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_6671]), ['final']). 4.46/4.74 cnf(c_0_12806, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7872]), ['final']). 4.46/4.74 cnf(c_0_12807, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X2)=c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7873]), ['final']). 4.46/4.74 cnf(c_0_12808, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X3)=c_Divides_Odiv__class_Omod(X1,X2,X3)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7874]), ['final']). 4.46/4.74 cnf(c_0_12809, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_7875]), ['final']). 4.46/4.74 cnf(c_0_12810, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7876]), ['final']). 4.46/4.74 cnf(c_0_12811, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk176_2(X2,X1)),X2))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2))), inference(split_conjunct,[status(thm)],[c_0_7877]), ['final']). 4.46/4.74 cnf(c_0_12812, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5367]), ['final']). 4.46/4.74 cnf(c_0_12813, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_7878]), ['final']). 4.46/4.74 cnf(c_0_12814, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7879]), ['final']). 4.46/4.74 cnf(c_0_12815, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X4)=c_Divides_Odiv__class_Omod(X1,X2,X4)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7880]), ['final']). 4.46/4.74 cnf(c_0_12816, plain, (hBOOL(hAPP(X2,X4))|~hBOOL(hAPP(hAPP(c_member(X1),esk395_4(X2,X3,X4,X1)),esk396_4(X2,X3,X4,X1)))|~hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_7310]), ['final']). 4.46/4.74 cnf(c_0_12817, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Odrop(X1),X6),X4),hAPP(hAPP(c_List_Odrop(X2),X6),X5))|~c_List_Olist__all2(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_7881]), ['final']). 4.46/4.74 cnf(c_0_12818, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Otake(X1),X6),X4),hAPP(hAPP(c_List_Otake(X2),X6),X5))|~c_List_Olist__all2(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_7882]), ['final']). 4.46/4.74 cnf(c_0_12819, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_fequal),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X3))))), inference(er,[status(thm)],[c_0_7883]), ['final']). 4.46/4.74 cnf(c_0_12820, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7884]), ['final']). 4.46/4.74 cnf(c_0_12821, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7885]), ['final']). 4.46/4.74 cnf(c_0_12822, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7886]), ['final']). 4.46/4.74 cnf(c_0_12823, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7887]), ['final']). 4.46/4.74 cnf(c_0_12824, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_7152]), ['final']). 4.46/4.74 cnf(c_0_12825, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7888]), ['final']). 4.46/4.74 cnf(c_0_12826, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7889]), ['final']). 4.46/4.74 cnf(c_0_12827, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7890]), ['final']). 4.46/4.74 cnf(c_0_12828, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))), inference(split_conjunct,[status(thm)],[c_0_7891]), ['final']). 4.46/4.74 cnf(c_0_12829, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7892]), ['final']). 4.46/4.74 cnf(c_0_12830, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_7158]), ['final']). 4.46/4.74 cnf(c_0_12831, plain, (hAPP(hAPP(c_List_Onth(X2),c_List_OtakeWhile(X2,X3,X4)),X1)=hAPP(hAPP(c_List_Onth(X2),X4),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X4))))), inference(split_conjunct,[status(thm)],[c_0_7893]), ['final']). 4.46/4.74 cnf(c_0_12832, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7894]), ['final']). 4.46/4.74 cnf(c_0_12833, plain, (hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Finite__Set_Ocard(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(rw,[status(thm)],[c_0_7895, c_0_4836]), ['final']). 4.46/4.74 cnf(c_0_12834, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7896]), ['final']). 4.46/4.74 cnf(c_0_12835, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),X2))=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7897]), ['final']). 4.46/4.74 cnf(c_0_12836, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk37_2(X1,X2)),X2))|c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_7898]), ['final']). 4.46/4.74 cnf(c_0_12837, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7899]), ['final']). 4.46/4.74 cnf(c_0_12838, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X1),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk416_4(X2,X3,X4,X1))))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_6918]), ['final']). 4.46/4.74 cnf(c_0_12839, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X1),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk344_4(X2,X3,X4,X1))))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_6922]), ['final']). 4.46/4.74 cnf(c_0_12840, plain, (c_Map_Omap__upds(X1,X3,X5,hAPP(hAPP(c_List_Oappend(X1),X2),X6),X4)=c_Map_Omap__upds(X1,X3,X5,X2,X4)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)), inference(split_conjunct,[status(thm)],[c_0_7900]), ['final']). 4.46/4.74 cnf(c_0_12841, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk188_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_5209]), ['final']). 4.46/4.74 cnf(c_0_12842, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),X2)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7901]), ['final']). 4.46/4.74 cnf(c_0_12843, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk309_2(X2,X1))))|hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,X2))), inference(rw,[status(thm)],[c_0_7902, c_0_5644]), ['final']). 4.46/4.74 cnf(c_0_12844, plain, (hAPP(hAPP(X3,X4),hAPP(hAPP(X3,X5),X6))=hAPP(hAPP(X3,X5),hAPP(hAPP(X3,X4),X6))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7903]), ['final']). 4.46/4.74 cnf(c_0_12845, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_7904]), ['final']). 4.46/4.74 cnf(c_0_12846, plain, (c_Map_Omap__upds(X3,X1,X5,X4,hAPP(hAPP(c_List_Oappend(X1),X2),X6))=c_Map_Omap__upds(X3,X1,X5,X4,X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)), inference(split_conjunct,[status(thm)],[c_0_7905]), ['final']). 4.46/4.74 cnf(c_0_12847, plain, (c_List_Olinorder__class_Osort__key(X2,X1,X3,hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),c_List_Olinorder__class_Osort__key(X2,X1,X3,X5))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7906]), ['final']). 4.46/4.74 cnf(c_0_12848, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_7907]), ['final']). 4.46/4.74 cnf(c_0_12849, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_7908]), ['final']). 4.46/4.74 cnf(c_0_12850, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7909, c_0_4448]), c_0_7704]), c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_12851, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7910]), ['final']). 4.46/4.74 cnf(c_0_12852, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X3), inference(split_conjunct,[status(thm)],[c_0_7911]), ['final']). 4.46/4.74 cnf(c_0_12853, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X3))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))|~class_Groups_Omonoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7912]), ['final']). 4.46/4.74 cnf(c_0_12854, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_7913]), ['final']). 4.46/4.74 cnf(c_0_12855, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Oremove1(X1,X2,X3)),X4)=c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7503]), ['final']). 4.46/4.74 cnf(c_0_12856, plain, (hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2))=c_List_Osublist(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)),X1)|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_7914]), ['final']). 4.46/4.74 cnf(c_0_12857, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7915]), ['final']). 4.46/4.74 cnf(c_0_12858, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3))=X3|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)!=X2), inference(er,[status(thm)],[c_0_7916]), ['final']). 4.46/4.74 cnf(c_0_12859, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3))=X4|hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))), inference(rw,[status(thm)],[c_0_7917, c_0_4891]), ['final']). 4.46/4.74 cnf(c_0_12860, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),hAPP(c_Set_Oimage(X2,X1,X3),X4)),X3)=X4|~c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))), inference(rw,[status(thm)],[c_0_7918, c_0_4891]), ['final']). 4.46/4.74 cnf(c_0_12861, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|hAPP(c_Set_Oimage(X3,X1,X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X3),X2),X4)))), inference(rw,[status(thm)],[c_0_7919, c_0_4891]), ['final']). 4.46/4.74 cnf(c_0_12862, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7920]), ['final']). 4.46/4.74 cnf(c_0_12863, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,esk420_5(X3,X4,X5,X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_6967]), ['final']). 4.46/4.74 cnf(c_0_12864, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7921]), ['final']). 4.46/4.74 cnf(c_0_12865, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2)),X3))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7922]), ['final']). 4.46/4.74 cnf(c_0_12866, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7923]), ['final']). 4.46/4.74 cnf(c_0_12867, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)))|~c_Fun_Oinj__on(X1,X2,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(rw,[status(thm)],[c_0_7924, c_0_4891]), ['final']). 4.46/4.74 cnf(c_0_12868, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_COMBB(X3,tc_HOL_Obool,X1),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(X3),hAPP(X5,X2)),X4))), inference(rw,[status(thm)],[c_0_7925, c_0_4891]), ['final']). 4.46/4.74 cnf(c_0_12869, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),X4))|~hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X5),X4),X2)))), inference(rw,[status(thm)],[c_0_7926, c_0_4891]), ['final']). 4.46/4.74 cnf(c_0_12870, plain, (X1=hAPP(X2,X3)|~hBOOL(hAPP(hAPP(c_member(X4),X3),hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,X4),hAPP(hAPP(c_Set_Oinsert(X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X2)))), inference(rw,[status(thm)],[c_0_7927, c_0_4891]), ['final']). 4.46/4.74 cnf(c_0_12871, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7928]), ['final']). 4.46/4.74 cnf(c_0_12872, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|epred1_3(X2,X1,X3)|~hBOOL(hAPP(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.74 cnf(c_0_12873, plain, (X1=hAPP(hAPP(c_Product__Type_OPair(X2,X2),esk16_3(X3,X1,X2)),esk16_3(X3,X1,X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X1),c_Relation_OId__on(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_7929]), ['final']). 4.46/4.74 cnf(c_0_12874, plain, (c_List_Olast(tc_Nat_Onat,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[c_0_7930, c_0_4517]), ['final']). 4.46/4.74 cnf(c_0_12875, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(c_COMBK(X1,X2),X4))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X1),X4),X3))), inference(rw,[status(thm)],[c_0_7931, c_0_4891]), ['final']). 4.46/4.74 cnf(c_0_12876, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(c_COMBK(X1,X2),X4))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))), inference(rw,[status(thm)],[c_0_7932, c_0_4891]), ['final']). 4.46/4.74 cnf(c_0_12877, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))), inference(split_conjunct,[status(thm)],[c_0_7933]), ['final']). 4.46/4.74 cnf(c_0_12878, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|c_Option_Ooption_ONone(X2)=hAPP(X3,esk402_3(X3,X2,X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Map_Odom(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_7934]), ['final']). 4.46/4.74 cnf(c_0_12879, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7448]), ['final']). 4.46/4.74 cnf(c_0_12880, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_5250]), ['final']). 4.46/4.74 cnf(c_0_12881, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk190_3(X2,X3,X1)),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5502]), ['final']). 4.46/4.74 cnf(c_0_12882, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk338_3(X2,X3,X1)),X3))|hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)))), inference(split_conjunct,[status(thm)],[c_0_7935]), ['final']). 4.46/4.74 cnf(c_0_12883, plain, (c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=X4|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))))), inference(split_conjunct,[status(thm)],[c_0_7936]), ['final']). 4.46/4.74 cnf(c_0_12884, plain, (hAPP(hAPP(c_List_Omap(X5,X4),X3),X2)=hAPP(hAPP(c_List_Omap(X5,X4),X1),X2)|hAPP(X1,esk455_5(X1,X2,X3,X4,X5))!=hAPP(X3,esk455_5(X1,X2,X3,X4,X5))), inference(split_conjunct,[status(thm)],[c_0_7173]), ['final']). 4.46/4.74 cnf(c_0_12885, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=X4|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)), inference(er,[status(thm)],[c_0_7937]), ['final']). 4.46/4.74 cnf(c_0_12886, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk149_3(X2,X1,X3)),esk147_2(X2,X1)))|c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),esk147_2(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_7127]), ['final']). 4.46/4.74 cnf(c_0_12887, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))))), inference(split_conjunct,[status(thm)],[c_0_7938]), ['final']). 4.46/4.74 cnf(c_0_12888, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2))=hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)|~class_Orderings_Olinorder(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7939, c_0_7454]), c_0_7455]), ['final']). 4.46/4.74 cnf(c_0_12889, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1)), inference(split_conjunct,[status(thm)],[c_0_7441]), ['final']). 4.46/4.74 cnf(c_0_12890, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremove1(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_7728]), ['final']). 4.46/4.74 cnf(c_0_12891, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,c_Wellfounded_Oacc(X1,X3))))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3))))), inference(split_conjunct,[status(thm)],[c_0_7940]), ['final']). 4.46/4.74 cnf(c_0_12892, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),X5)=hAPP(hAPP(X4,X5),X6)|~c_Finite__Set_Ofolding(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_7941]), ['final']). 4.46/4.74 cnf(c_0_12893, plain, (c_Divides_OnegDivAlg(X1,X2)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))), inference(rw,[status(thm)],[c_0_7942, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_12894, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk337_4(X2,X3,X4,X1)),X3))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X2)=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_7943]), ['final']). 4.46/4.74 cnf(c_0_12895, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1)), inference(split_conjunct,[status(thm)],[c_0_7944]), ['final']). 4.46/4.74 cnf(c_0_12896, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7945]), ['final']). 4.46/4.74 cnf(c_0_12897, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk266_4(X2,X3,X1,X4)),X3))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X2)=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_7946]), ['final']). 4.46/4.74 cnf(c_0_12898, plain, (hAPP(X4,hAPP(X5,X9))=hAPP(X7,hAPP(X8,X9))|hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5)!=hAPP(c_Fun_Ocomp(X6,X2,X3,X7),X8)), inference(split_conjunct,[status(thm)],[c_0_7947]), ['final']). 4.46/4.74 cnf(c_0_12899, plain, (X5=hAPP(X3,hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),X5))|~c_Fun_Oinj__on(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_7948]), ['final']). 4.46/4.74 cnf(c_0_12900, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))), inference(csr,[status(thm)],[c_0_7949, c_0_6524]), ['final']). 4.46/4.74 cnf(c_0_12901, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_7950]), ['final']). 4.46/4.74 cnf(c_0_12902, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_7950]), ['final']). 4.46/4.74 cnf(c_0_12903, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7951, c_0_4436]), c_0_7952]), ['final']). 4.46/4.74 cnf(c_0_12904, plain, (c_Nitpick_Oless__eq__frac(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_7953, c_0_6281]), ['final']). 4.46/4.74 cnf(c_0_12905, plain, (c_Nitpick_Oless__frac(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_7954, c_0_6281]), ['final']). 4.46/4.74 cnf(c_0_12906, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Olinorder__class_Oinsort__insert__key(X2,X1,X3,X5,X4)))|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7955]), ['final']). 4.46/4.74 cnf(c_0_12907, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk367_4(X2,X3,X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Set_Oimage(X1,X5,X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_7956]), ['final']). 4.46/4.74 cnf(c_0_12908, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7957, c_0_4436]), c_0_7958]), c_0_4834]), ['final']). 4.46/4.74 cnf(c_0_12909, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_7959]), ['final']). 4.46/4.74 cnf(c_0_12910, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))|~c_Wellfounded_Oacyclic(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_Predicate_Oconversep(X1,X1,X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7960, c_0_4531]), c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_12911, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk351_3(X2,X3,X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OSup__class_OSup(X1,X3)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7961]), ['final']). 4.46/4.74 cnf(c_0_12912, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk48_3(X2,X3,X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Complete__Lattice_OInf__class_OInf(X1,X2)))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7962]), ['final']). 4.46/4.74 cnf(c_0_12913, plain, (X3=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X2),tc_List_Olist(X2)),X1),c_List_Orotate1(X2)),X3)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))), inference(rw,[status(thm)],[c_0_7963, c_0_5902]), ['final']). 4.46/4.74 cnf(c_0_12914, plain, (hAPP(hAPP(X2,X5),hAPP(X3,X4))=hAPP(X3,X4)|~c_Finite__Set_Ofolding__one__idem(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))), inference(split_conjunct,[status(thm)],[c_0_7964]), ['final']). 4.46/4.74 cnf(c_0_12915, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))), inference(rw,[status(thm)],[c_0_7965, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_12916, plain, (X2=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7966]), ['final']). 4.46/4.74 cnf(c_0_12917, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)),hAPP(X5,X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7967]), ['final']). 4.46/4.74 cnf(c_0_12918, plain, (hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(X6,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X6)))), inference(split_conjunct,[status(thm)],[c_0_7968]), ['final']). 4.46/4.74 cnf(c_0_12919, plain, (hBOOL(hAPP(c_List_Odistinct(X2),hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)))|~c_Fun_Oinj__on(X1,X2,X3,hAPP(c_List_Oset(X1),X4))|~hBOOL(hAPP(c_List_Odistinct(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_7969]), ['final']). 4.46/4.74 cnf(c_0_12920, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk169_4(X2,X3,X1,X4)),X3))|c_Groups_Ozero__class_Ozero(X4)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X2),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Rings_Ono__zero__divisors(X4)|~class_Rings_Ocomm__semiring__1(X4)), inference(split_conjunct,[status(thm)],[c_0_7970]), ['final']). 4.46/4.74 cnf(c_0_12921, plain, (c_List_Olast(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))=X3|X2=c_List_Olist_ONil(X1)), inference(er,[status(thm)],[c_0_7971]), ['final']). 4.46/4.74 cnf(c_0_12922, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(X5,X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7972]), ['final']). 4.46/4.74 cnf(c_0_12923, plain, (hAPP(X1,esk119_5(X2,X1,X3,X4,X5))=hAPP(c_Option_Ooption_OSome(X5),X4)|~hBOOL(hAPP(hAPP(c_member(X5),X4),c_Map_Oran(X3,X5,c_Map_Orestrict__map(X3,X5,X1,X2))))), inference(split_conjunct,[status(thm)],[c_0_7684]), ['final']). 4.46/4.74 cnf(c_0_12924, plain, (~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_7973]), ['final']). 4.46/4.74 cnf(c_0_12925, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2))),X3)=X3|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(rw,[status(thm)],[c_0_7974, c_0_5671]), ['final']). 4.46/4.74 cnf(c_0_12926, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[c_0_7975, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_12927, plain, (hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~c_Relation_Orefl__on(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3))), inference(split_conjunct,[status(thm)],[c_0_7976]), ['final']). 4.46/4.74 cnf(c_0_12928, plain, (hBOOL(hAPP(hAPP(c_member(X1),X5),X2))|~c_Relation_Orefl__on(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3))), inference(split_conjunct,[status(thm)],[c_0_7977]), ['final']). 4.46/4.74 cnf(c_0_12929, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)=c_Int_OMin|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[c_0_7978, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_12930, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_7979]), ['final']). 4.46/4.74 cnf(c_0_12931, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk504_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|c_List_Olist_ONil(tc_List_Olist(X1))=c_List_Otranspose(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7980]), ['final']). 4.46/4.74 cnf(c_0_12932, plain, (hBOOL(hAPP(X2,X4))|c_List_Olist_ONil(X1)!=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))), inference(rw,[status(thm)],[c_0_7981, c_0_4916]), ['final']). 4.46/4.74 cnf(c_0_12933, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2))|~c_Nitpick_Orefl_H(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7982]), ['final']). 4.46/4.74 cnf(c_0_12934, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7578]), ['final']). 4.46/4.74 cnf(c_0_12935, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_7579]), ['final']). 4.46/4.74 cnf(c_0_12936, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7983]), ['final']). 4.46/4.74 cnf(c_0_12937, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7984]), ['final']). 4.46/4.74 cnf(c_0_12938, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[c_0_7985, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_12939, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_7986]), ['final']). 4.46/4.74 cnf(c_0_12940, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X2),X4)))|~hBOOL(hAPP(X1,esk272_3(X1,X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2)))), inference(split_conjunct,[status(thm)],[c_0_6866]), ['final']). 4.46/4.74 cnf(c_0_12941, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7987]), ['final']). 4.46/4.74 cnf(c_0_12942, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7586]), ['final']). 4.46/4.74 cnf(c_0_12943, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_7592]), ['final']). 4.46/4.74 cnf(c_0_12944, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|c_List_Oinsert(X1,X2,X3)=hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_7988]), ['final']). 4.46/4.74 cnf(c_0_12945, plain, (hAPP(c_Set_Oimage(X1,X4,hAPP(c_COMBK(X4,X1),X5)),X3)=hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7989]), ['final']). 4.46/4.74 cnf(c_0_12946, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7990]), ['final']). 4.46/4.74 cnf(c_0_12947, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk114_4(X2,X3,X4,X1)),X3))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X2)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_7991]), ['final']). 4.46/4.74 cnf(c_0_12948, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7992]), ['final']). 4.46/4.74 cnf(c_0_12949, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7993]), ['final']). 4.46/4.74 cnf(c_0_12950, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk207_4(X2,X3,X1,X4)),X3))|c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_7994]), ['final']). 4.46/4.74 cnf(c_0_12951, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7995]), ['final']). 4.46/4.74 cnf(c_0_12952, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7996]), ['final']). 4.46/4.74 cnf(c_0_12953, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_7997]), ['final']). 4.46/4.74 cnf(c_0_12954, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk47_3(X2,X3,X1)),c_Groups_Oone__class_Oone(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7998]), ['final']). 4.46/4.74 cnf(c_0_12955, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7999]), ['final']). 4.46/4.74 cnf(c_0_12956, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8000]), ['final']). 4.46/4.74 cnf(c_0_12957, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk461_3(X2,X3,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_8001]), ['final']). 4.46/4.74 cnf(c_0_12958, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8002]), ['final']). 4.46/4.74 cnf(c_0_12959, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))), inference(split_conjunct,[status(thm)],[c_0_8003]), ['final']). 4.46/4.74 cnf(c_0_12960, plain, (hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,X4),X3))), inference(split_conjunct,[status(thm)],[c_0_8004]), ['final']). 4.46/4.74 cnf(c_0_12961, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk47_3(X2,X3,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7998]), ['final']). 4.46/4.74 cnf(c_0_12962, plain, (hBOOL(hAPP(X1,esk492_4(X2,X1,X3,X4)))|c_List_Olist__ex1(X3,X1,X2)|~hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_7265]), ['final']). 4.46/4.74 cnf(c_0_12963, plain, (hBOOL(hAPP(X1,esk163_4(X2,X1,X3,X4)))|c_List_Olist__ex1(X3,X1,X2)|~hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),X2)))|~hBOOL(hAPP(X1,X4))), inference(split_conjunct,[status(thm)],[c_0_7272]), ['final']). 4.46/4.74 cnf(c_0_12964, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk370_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5242]), ['final']). 4.46/4.74 cnf(c_0_12965, plain, (hAPP(c_Option_Ooption_OSome(X3),X4)=hAPP(c_Map_Omap__add(X6,X3,X5,X1),X2)|hAPP(X1,X2)!=c_Option_Ooption_ONone(X3)|hAPP(c_Option_Ooption_OSome(X3),X4)!=hAPP(X5,X2)), inference(split_conjunct,[status(thm)],[c_0_8005]), ['final']). 4.46/4.74 cnf(c_0_12966, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),X5))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8006]), ['final']). 4.46/4.74 cnf(c_0_12967, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3)), inference(split_conjunct,[status(thm)],[c_0_7910]), ['final']). 4.46/4.74 cnf(c_0_12968, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_8007]), ['final']). 4.46/4.74 cnf(c_0_12969, plain, (hAPP(c_Set_Oimage(X2,X1,c_Fun_Othe__inv__into(X1,X2,X4,X3)),hAPP(c_Set_Oimage(X1,X2,X3),X4))=X4|~c_Fun_Oinj__on(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8008]), ['final']). 4.46/4.74 cnf(c_0_12970, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8009]), ['final']). 4.46/4.74 cnf(c_0_12971, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8010]), ['final']). 4.46/4.74 cnf(c_0_12972, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8011]), ['final']). 4.46/4.74 cnf(c_0_12973, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(X3,X5)),hAPP(X4,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))|~class_Orderings_Oord(X2)), inference(split_conjunct,[status(thm)],[c_0_8012]), ['final']). 4.46/4.74 cnf(c_0_12974, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8013]), ['final']). 4.46/4.74 cnf(c_0_12975, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8014]), ['final']). 4.46/4.74 cnf(c_0_12976, plain, (hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X6,X7,X8,X1,X4),X2),X5))|~hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(X4,X3),X5))), inference(split_conjunct,[status(thm)],[c_0_8015]), ['final']). 4.46/4.74 cnf(c_0_12977, plain, (hBOOL(hAPP(X1,X7))|~hBOOL(hAPP(X1,esk219_5(X1,X2,X3,X4,X5)))|~hBOOL(hAPP(hAPP(c_member(X4),X6),X3))|~hBOOL(hAPP(hAPP(c_member(X5),X7),hAPP(X2,X6)))), inference(split_conjunct,[status(thm)],[c_0_6516]), ['final']). 4.46/4.74 cnf(c_0_12978, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X2)),hAPP(c_List_Olexn(X1,X5),X3)))), inference(split_conjunct,[status(thm)],[c_0_8016]), ['final']). 4.46/4.74 cnf(c_0_12979, plain, (X1=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X3),X4)),hAPP(c_List_Olexn(X2,X5),X1)))), inference(split_conjunct,[status(thm)],[c_0_8016]), ['final']). 4.46/4.74 cnf(c_0_12980, plain, (hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1,X2,X5),X3),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_7518]), ['final']). 4.46/4.74 cnf(c_0_12981, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OField(X1),X2)),hAPP(c_Relation_OField(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8017]), ['final']). 4.46/4.74 cnf(c_0_12982, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Ofilter(X2,X5),X4)))|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8018]), ['final']). 4.46/4.74 cnf(c_0_12983, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(X2,X4)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|esk93_4(X2,X3,X1,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8019, c_0_4836]), c_0_4836]), ['final']). 4.46/4.74 cnf(c_0_12984, plain, (hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X1,X2))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_8020]), ['final']). 4.46/4.74 cnf(c_0_12985, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk370_3(X1,X2,X3)),X1))|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_5242]), ['final']). 4.46/4.74 cnf(c_0_12986, plain, (c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(c_Nat_OSuc,X2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5))|~c_Hoare__Mirabelle_Otriple__valid(X1,X2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5))), inference(split_conjunct,[status(thm)],[c_0_7773]), ['final']). 4.46/4.74 cnf(c_0_12987, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8021]), ['final']). 4.46/4.74 cnf(c_0_12988, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8022]), ['final']). 4.46/4.74 cnf(c_0_12989, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8023]), ['final']). 4.46/4.74 cnf(c_0_12990, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(c_COMBK(X1,X2),c_Groups_Ozero__class_Ozero(X1))),X3))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Omonoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8024]), ['final']). 4.46/4.74 cnf(c_0_12991, plain, (hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X1,X2))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_8025]), ['final']). 4.46/4.74 cnf(c_0_12992, plain, (X1=X2|hAPP(X3,X2)=hAPP(c_Option_Ooption_OSome(X4),X5)|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6,tc_Option_Ooption(X4)),X3),X1),hAPP(c_Option_Ooption_OSome(X4),X7)),X2)!=hAPP(c_Option_Ooption_OSome(X4),X5)), inference(split_conjunct,[status(thm)],[c_0_7053]), ['final']). 4.46/4.74 cnf(c_0_12993, plain, (X1=X2|hAPP(X3,X4)=hAPP(c_Option_Ooption_OSome(X5),X2)|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6,tc_Option_Ooption(X5)),X3),X7),hAPP(c_Option_Ooption_OSome(X5),X1)),X4)!=hAPP(c_Option_Ooption_OSome(X5),X2)), inference(split_conjunct,[status(thm)],[c_0_7053]), ['final']). 4.46/4.74 cnf(c_0_12994, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X1),X4),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk63_5(X3,X2,X4,X5,X1))),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6917]), ['final']). 4.46/4.74 cnf(c_0_12995, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8026]), ['final']). 4.46/4.74 cnf(c_0_12996, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8027]), ['final']). 4.46/4.74 cnf(c_0_12997, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olistsp(X1,X2)),c_List_Olistsp(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8028]), ['final']). 4.46/4.74 cnf(c_0_12998, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(X3,esk243_5(X3,X4,X5,X2,X1))))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6923]), ['final']). 4.46/4.74 cnf(c_0_12999, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_8029]), ['final']). 4.46/4.74 cnf(c_0_13000, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)|~class_Lattices_Olattice(X1)), inference(rw,[status(thm)],[c_0_8030, c_0_7726]), ['final']). 4.46/4.74 cnf(c_0_13001, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),X2)))), inference(split_conjunct,[status(thm)],[c_0_5498]), ['final']). 4.46/4.74 cnf(c_0_13002, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olists(X1,X2)),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8031]), ['final']). 4.46/4.74 cnf(c_0_13003, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)))), inference(split_conjunct,[status(thm)],[c_0_7418]), ['final']). 4.46/4.74 cnf(c_0_13004, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)))), inference(split_conjunct,[status(thm)],[c_0_8032]), ['final']). 4.46/4.74 cnf(c_0_13005, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(split_conjunct,[status(thm)],[c_0_8033]), ['final']). 4.46/4.74 cnf(c_0_13006, plain, (c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omin(X1),X2),X3)|~class_Orderings_Olinorder(X1)), inference(rw,[status(thm)],[c_0_8034, c_0_7726]), ['final']). 4.46/4.74 cnf(c_0_13007, plain, (c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omax(X1),X2),X3)|~class_Orderings_Olinorder(X1)), inference(rw,[status(thm)],[c_0_8035, c_0_7726]), ['final']). 4.46/4.74 cnf(c_0_13008, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)|~class_Lattices_Olattice(X1)), inference(rw,[status(thm)],[c_0_8036, c_0_7726]), ['final']). 4.46/4.74 cnf(c_0_13009, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[c_0_8037, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_13010, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_8038]), ['final']). 4.46/4.74 cnf(c_0_13011, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_8039, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_13012, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk145_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)))|c_List_Olist__all(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_8040]), ['final']). 4.46/4.74 cnf(c_0_13013, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X3),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk483_4(X2,X1,X3,X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(split_conjunct,[status(thm)],[c_0_6909]), ['final']). 4.46/4.74 cnf(c_0_13014, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X3),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk265_4(X2,X1,X3,X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(split_conjunct,[status(thm)],[c_0_6911]), ['final']). 4.46/4.74 cnf(c_0_13015, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk120_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|hBOOL(hAPP(c_List_Olistsp(X1,X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8041]), ['final']). 4.46/4.74 cnf(c_0_13016, plain, (X1=X2|hAPP(hAPP(c_List_Omap(X3,X4),X5),X1)!=hAPP(hAPP(c_List_Omap(X3,X4),X5),X2)|~c_Fun_Oinj__on(X3,X4,X5,hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Oappend(X3),X2),X1)))), inference(rw,[status(thm)],[c_0_8042, c_0_6608]), ['final']). 4.46/4.74 cnf(c_0_13017, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_8043, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_13018, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_8044]), ['final']). 4.46/4.74 cnf(c_0_13019, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk97_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|hAPP(c_List_Ofilter(X1,X3),X2)=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_8045]), ['final']). 4.46/4.74 cnf(c_0_13020, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk536_3(X2,X3,X1)),X3))|epred2_3(X1,X3,X2)|~hBOOL(hAPP(X1,esk537_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5124]), ['final']). 4.46/4.74 cnf(c_0_13021, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))), inference(split_conjunct,[status(thm)],[c_0_8046]), ['final']). 4.46/4.74 cnf(c_0_13022, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_8047]), ['final']). 4.46/4.74 cnf(c_0_13023, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk538_3(X2,X1,X3)))|epred2_3(X3,X1,X2)|~hBOOL(hAPP(X3,esk535_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_5124]), ['final']). 4.46/4.74 cnf(c_0_13024, plain, (hAPP(hAPP(c_Set_Oinsert(X2),X3),hAPP(c_List_Oset(X2),X4))=hAPP(c_List_Oset(X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X5),X3),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8048]), ['final']). 4.46/4.74 cnf(c_0_13025, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Oacc(X1,X3)),c_Wellfounded_Oacc(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8049]), ['final']). 4.46/4.74 cnf(c_0_13026, plain, (hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4)),X1)=X4|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_8050]), ['final']). 4.46/4.74 cnf(c_0_13027, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_HOL_Obool,X1),X2),c_Option_Ooption_OSome(X1))))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X1)),X2))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_8051]), ['final']). 4.46/4.74 cnf(c_0_13028, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk69_2(X3,X1)),X2))|X3=c_List_Olist_ONil(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk68_2(X3,X1))))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5314]), ['final']). 4.46/4.74 cnf(c_0_13029, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(X1,esk44_4(X1,X2,X3,X4))|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(X1,X4)|~hBOOL(hAPP(hAPP(c_member(X3),X4),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7128]), ['final']). 4.46/4.74 cnf(c_0_13030, plain, (c_Fun_Oinj__on(X1,X2,esk389_4(X3,X2,X4,X1),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X4)),hAPP(c_Finite__Set_Ocard(X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_6856]), ['final']). 4.46/4.74 cnf(c_0_13031, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)|hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber(X1)), inference(split_conjunct,[status(thm)],[c_0_5359]), ['final']). 4.46/4.74 cnf(c_0_13032, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3)))), inference(split_conjunct,[status(thm)],[c_0_8052]), ['final']). 4.46/4.74 cnf(c_0_13033, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_8053]), ['final']). 4.46/4.74 cnf(c_0_13034, plain, (c_Fun_Oinj__on(X4,X2,hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5),X6)|~c_Fun_Oinj__on(X1,X2,X3,hAPP(c_Set_Oimage(X4,X1,X5),X6))|~c_Fun_Oinj__on(X4,X1,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_8054]), ['final']). 4.46/4.74 cnf(c_0_13035, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OSup__class_OSup(X1,X2)),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7961]), ['final']). 4.46/4.74 cnf(c_0_13036, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Complete__Lattice_OInf__class_OInf(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7962]), ['final']). 4.46/4.74 cnf(c_0_13037, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),X3))|hAPP(c_Finite__Set_Ocard(X1),X3)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_8055])]), ['final']). 4.46/4.74 cnf(c_0_13038, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8056]), ['final']). 4.46/4.74 cnf(c_0_13039, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8057]), ['final']). 4.46/4.74 cnf(c_0_13040, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8058]), ['final']). 4.46/4.74 cnf(c_0_13041, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8059]), ['final']). 4.46/4.74 cnf(c_0_13042, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk466_2(X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))|c_List_Olinorder__class_Osorted(X2,X1)|~class_Orderings_Olinorder(X2)), inference(split_conjunct,[status(thm)],[c_0_6908]), ['final']). 4.46/4.74 cnf(c_0_13043, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,esk320_4(X3,X2,X4,X1))),hAPP(X3,esk320_4(X3,X2,X4,X1))))|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_8012]), ['final']). 4.46/4.74 cnf(c_0_13044, plain, (hBOOL(hAPP(X1,X6))|~hBOOL(hAPP(X1,esk221_5(X1,X2,X3,X4,X5)))|~hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X5,tc_HOL_Obool)),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6516]), ['final']). 4.46/4.74 cnf(c_0_13045, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk192_2(X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))|c_List_Olinorder__class_Osorted(X2,X1)|~class_Orderings_Olinorder(X2)), inference(split_conjunct,[status(thm)],[c_0_8060]), ['final']). 4.46/4.74 cnf(c_0_13046, plain, (X3=X4|hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)!=hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)), inference(split_conjunct,[status(thm)],[c_0_8061]), ['final']). 4.46/4.74 cnf(c_0_13047, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_7635]), ['final']). 4.46/4.74 cnf(c_0_13048, plain, (hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X5,X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3))=hAPP(c_Set_Oimage(X1,X4,X5),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8062]), ['final']). 4.46/4.74 cnf(c_0_13049, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk116_3(X2,X3,X1)))|hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7311]), ['final']). 4.46/4.74 cnf(c_0_13050, plain, (hAPP(X4,X6)=hAPP(X4,X5)|~c_Equiv__Relations_Ocongruent(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X3))), inference(split_conjunct,[status(thm)],[c_0_8063]), ['final']). 4.46/4.74 cnf(c_0_13051, plain, (hBOOL(hAPP(X1,esk294_4(X2,X3,X4,X1)))|c_Wellfounded_Owf(tc_prod(X2,X4),c_Recdef_Osame__fst(X2,X4,X1,X3))), inference(split_conjunct,[status(thm)],[c_0_8064]), ['final']). 4.46/4.74 cnf(c_0_13052, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk236_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)))|~c_List_Olist__ex(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_8065]), ['final']). 4.46/4.74 cnf(c_0_13053, plain, (hAPP(hAPP(c_List_Olist_OCons(X5),X3),X4)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),X3),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X2,esk303_5(X3,X2,X4,X5,X1))))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7126]), ['final']). 4.46/4.74 cnf(c_0_13054, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Oring__1__class_Oof__int(X3),X1)),hAPP(c_Int_Oring__1__class_Oof__int(X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~class_Rings_Olinordered__idom(X3)), inference(split_conjunct,[status(thm)],[c_0_8066]), ['final']). 4.46/4.74 cnf(c_0_13055, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~class_Rings_Olinordered__semidom(X3)), inference(split_conjunct,[status(thm)],[c_0_8067]), ['final']). 4.46/4.74 cnf(c_0_13056, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Oring__1__class_Oof__int(X3),X1)),hAPP(c_Int_Oring__1__class_Oof__int(X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~class_Rings_Olinordered__idom(X3)), inference(split_conjunct,[status(thm)],[c_0_8068]), ['final']). 4.46/4.74 cnf(c_0_13057, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk150_3(X3,X1,X4))),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|~c_Wellfounded_Owf(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_7127]), ['final']). 4.46/4.74 cnf(c_0_13058, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_8069, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_13059, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_8070, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_13060, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[c_0_8071, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_13061, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~class_Rings_Olinordered__semidom(X3)), inference(split_conjunct,[status(thm)],[c_0_8072]), ['final']). 4.46/4.74 cnf(c_0_13062, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8073, c_0_5120]), c_0_5120]), c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13063, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8074, c_0_5120]), c_0_5120]), c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13064, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[c_0_8075, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_13065, plain, (hBOOL(hAPP(X4,X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|c_List_Opartition(X1,X4,X5)!=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X6)), inference(split_conjunct,[status(thm)],[c_0_8076]), ['final']). 4.46/4.74 cnf(c_0_13066, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3))=c_SetInterval_Oord__class_OgreaterThanLessThan(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8077]), ['final']). 4.46/4.74 cnf(c_0_13067, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_7950]), ['final']). 4.46/4.74 cnf(c_0_13068, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8078, c_0_4836]), c_0_4836]), c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_13069, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8079, c_0_5120]), c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13070, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3))=c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8080]), ['final']). 4.46/4.74 cnf(c_0_13071, plain, (X1=hAPP(c_Set_Oimage(X2,X3,X4),esk525_5(X5,X4,X2,X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_Set_Oimage(X2,X3,X4),X5)))), inference(split_conjunct,[status(thm)],[c_0_7424]), ['final']). 4.46/4.74 cnf(c_0_13072, plain, (hAPP(c_Relation_OImage(X1,X1,c_Transitive__Closure_Ortrancl(X1,X2)),X3)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X2),X3)),X3))), inference(split_conjunct,[status(thm)],[c_0_8081]), ['final']). 4.46/4.74 cnf(c_0_13073, plain, (hBOOL(hAPP(hAPP(c_member(X4),X3),X5))|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),X5)))|~c_Fun_Oinj__on(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_8082]), ['final']). 4.46/4.74 cnf(c_0_13074, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8083, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), ['final']). 4.46/4.74 cnf(c_0_13075, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8084, c_0_5120]), c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13076, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X6,tc_HOL_Obool))),X1),X4),X2),X3))|~hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(X4,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8085]), ['final']). 4.46/4.74 cnf(c_0_13077, plain, (hBOOL(hAPP(hAPP(X4,X6),X5))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X3))), inference(split_conjunct,[status(thm)],[c_0_8086]), ['final']). 4.46/4.74 cnf(c_0_13078, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_8087]), ['final']). 4.46/4.74 cnf(c_0_13079, plain, (c_List_Olist_ONil(X2)=hAPP(hAPP(c_List_Otake(X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_8088]), ['final']). 4.46/4.74 cnf(c_0_13080, plain, (hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Otake(X3),X2),X4)),X1)=hAPP(hAPP(c_List_Onth(X3),X4),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8089]), ['final']). 4.46/4.74 cnf(c_0_13081, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_8090]), ['final']). 4.46/4.74 cnf(c_0_13082, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_4650]), ['final']). 4.46/4.74 cnf(c_0_13083, plain, (c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8091]), ['final']). 4.46/4.74 cnf(c_0_13084, plain, (c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8092]), ['final']). 4.46/4.74 cnf(c_0_13085, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Complete__Lattice_OSup__class_OSup(X1,X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8093]), ['final']). 4.46/4.74 cnf(c_0_13086, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2))=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8094]), ['final']). 4.46/4.74 cnf(c_0_13087, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X2))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_8095]), ['final']). 4.46/4.74 cnf(c_0_13088, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8096]), ['final']). 4.46/4.74 cnf(c_0_13089, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8097]), ['final']). 4.46/4.74 cnf(c_0_13090, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Ofinite__psubset(X1)))), inference(split_conjunct,[status(thm)],[c_0_7182]), ['final']). 4.46/4.74 cnf(c_0_13091, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_8098]), ['final']). 4.46/4.74 cnf(c_0_13092, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2))=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8099]), ['final']). 4.46/4.74 cnf(c_0_13093, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk374_5(X2,X3,X4,X5,X1)),X4))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X4),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7820]), ['final']). 4.46/4.74 cnf(c_0_13094, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk371_4(X2,X3,X4,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_7429]), ['final']). 4.46/4.74 cnf(c_0_13095, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk500_4(X2,X3,X4,X1)),X3))|c_Equiv__Relations_Ocongruent(X1,X4,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_6253]), ['final']). 4.46/4.74 cnf(c_0_13096, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),X3)=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X3))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8100]), ['final']). 4.46/4.74 cnf(c_0_13097, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3))|~class_Orderings_Olinorder(X1)), inference(rw,[status(thm)],[c_0_8101, c_0_5670]), ['final']). 4.46/4.74 cnf(c_0_13098, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8102]), ['final']). 4.46/4.74 cnf(c_0_13099, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk335_3(X2,X3,X1)),X2))|c_List_Olist_ONil(X1)=X3|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7609]), ['final']). 4.46/4.74 cnf(c_0_13100, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~class_Rings_Olinordered__semidom(X2)), inference(split_conjunct,[status(thm)],[c_0_8103]), ['final']). 4.46/4.74 cnf(c_0_13101, plain, (hAPP(X2,X4)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7807]), ['final']). 4.46/4.74 cnf(c_0_13102, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),X3)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X3))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8104]), ['final']). 4.46/4.74 cnf(c_0_13103, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[c_0_8105, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13104, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(X2,X4)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7808]), ['final']). 4.46/4.74 cnf(c_0_13105, plain, (hBOOL(hAPP(hAPP(c_member(X6),X2),c_SetInterval_Oord_OatLeastLessThan(X6,X4,X1,X5,X3)))|~hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(X4,X5),X2))), inference(split_conjunct,[status(thm)],[c_0_8106]), ['final']). 4.46/4.74 cnf(c_0_13106, plain, (hBOOL(hAPP(hAPP(c_member(X6),X3),c_SetInterval_Oord_OgreaterThanAtMost(X6,X4,X1,X2,X5)))|~hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(X4,X3),X5))), inference(split_conjunct,[status(thm)],[c_0_8107]), ['final']). 4.46/4.74 cnf(c_0_13107, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk16_3(X2,X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),c_Relation_OId__on(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7929]), ['final']). 4.46/4.74 cnf(c_0_13108, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk386_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|hAPP(c_List_Ofilter(X1,X3),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_8108]), ['final']). 4.46/4.74 cnf(c_0_13109, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))=X3|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk222_3(X2,X3,X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7564]), ['final']). 4.46/4.74 cnf(c_0_13110, plain, (hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_8109]), ['final']). 4.46/4.74 cnf(c_0_13111, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|c_List_Osublist(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)),X1)=c_List_Olist_ONil(X2)), inference(split_conjunct,[status(thm)],[c_0_7914]), ['final']). 4.46/4.74 cnf(c_0_13112, plain, (hAPP(hAPP(c_List_Otake(X2),X1),X3)=hAPP(hAPP(c_List_Otake(X2),X1),c_List_Obutlast(X2,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_8110]), ['final']). 4.46/4.74 cnf(c_0_13113, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7987]), ['final']). 4.46/4.74 cnf(c_0_13114, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7681]), ['final']). 4.46/4.74 cnf(c_0_13115, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8111]), ['final']). 4.46/4.74 cnf(c_0_13116, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_8112]), ['final']). 4.46/4.74 cnf(c_0_13117, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk329_2(X2,X1))))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5910]), ['final']). 4.46/4.74 cnf(c_0_13118, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk488_5(X2,X3,X4,X1,X5)),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3))|~c_Wellfounded_Omax__extp(X1,X4,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_5595]), ['final']). 4.46/4.74 cnf(c_0_13119, plain, (X1=X2|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8113, c_0_4609]), c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_13120, plain, (c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))=hAPP(X4,X5)|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)!=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3))), inference(split_conjunct,[status(thm)],[c_0_7946]), ['final']). 4.46/4.74 cnf(c_0_13121, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8114]), ['final']). 4.46/4.74 cnf(c_0_13122, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),c_List_Oreplicate(X2,X1,X3))))), inference(er,[status(thm)],[c_0_8115]), ['final']). 4.46/4.74 cnf(c_0_13123, plain, (c_List_Olinorder__class_Oinsort__insert__key(X4,X1,X2,X3,X5)=X5|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),hAPP(c_List_Oset(X4),X5))))), inference(split_conjunct,[status(thm)],[c_0_8116]), ['final']). 4.46/4.74 cnf(c_0_13124, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3))=hAPP(c_List_Oset(X1),c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X2,X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8117]), ['final']). 4.46/4.74 cnf(c_0_13125, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5207]), ['final']). 4.46/4.74 cnf(c_0_13126, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7326]), ['final']). 4.46/4.74 cnf(c_0_13127, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_COMBI(X1)),hAPP(c_List_Oset(X1),X2))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8118]), ['final']). 4.46/4.74 cnf(c_0_13128, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8119]), ['final']). 4.46/4.74 cnf(c_0_13129, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Oaccp(X1,X3)),c_Wellfounded_Oaccp(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8120]), ['final']). 4.46/4.74 cnf(c_0_13130, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8121]), ['final']). 4.46/4.74 cnf(c_0_13131, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X3)),X1),X2),hAPP(c_Option_Ooption_OSome(X3),X4))=X1|hAPP(X1,X2)!=hAPP(c_Option_Ooption_OSome(X3),X4)), inference(split_conjunct,[status(thm)],[c_0_8122]), ['final']). 4.46/4.74 cnf(c_0_13132, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk361_2(X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))|hBOOL(hAPP(c_List_Odistinct(X2),X1))), inference(split_conjunct,[status(thm)],[c_0_7699]), ['final']). 4.46/4.74 cnf(c_0_13133, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3)))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5207]), ['final']). 4.46/4.74 cnf(c_0_13134, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3)))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7326]), ['final']). 4.46/4.74 cnf(c_0_13135, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)!=c_Groups_Ozero__class_Ozero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Groups_Oordered__comm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5331]), ['final']). 4.46/4.74 cnf(c_0_13136, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)!=c_Groups_Ozero__class_Ozero(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1))|~class_Groups_Oordered__comm__monoid__add(X2)), inference(split_conjunct,[status(thm)],[c_0_5331]), ['final']). 4.46/4.74 cnf(c_0_13137, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk360_2(X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))|hBOOL(hAPP(c_List_Odistinct(X2),X1))), inference(split_conjunct,[status(thm)],[c_0_7699]), ['final']). 4.46/4.74 cnf(c_0_13138, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))|~class_Power_Opower(X1)), inference(split_conjunct,[status(thm)],[c_0_8123]), ['final']). 4.46/4.74 cnf(c_0_13139, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_8124]), ['final']). 4.46/4.74 cnf(c_0_13140, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_OMin,X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8125, c_0_4609]), c_0_5134]), ['final']). 4.46/4.74 cnf(c_0_13141, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4))|hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_8126]), ['final']). 4.46/4.74 cnf(c_0_13142, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[c_0_8127, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_13143, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X2))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7534]), ['final']). 4.46/4.74 cnf(c_0_13144, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X6)))), inference(split_conjunct,[status(thm)],[c_0_8128]), ['final']). 4.46/4.74 cnf(c_0_13145, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_OPow(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8129]), ['final']). 4.46/4.74 cnf(c_0_13146, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Omax__ext(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_5587]), ['final']). 4.46/4.74 cnf(c_0_13147, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X2)),c_Wellfounded_Omax__ext(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_5587]), ['final']). 4.46/4.74 cnf(c_0_13148, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8130]), ['final']). 4.46/4.74 cnf(c_0_13149, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8131]), ['final']). 4.46/4.74 cnf(c_0_13150, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8132]), ['final']). 4.46/4.74 cnf(c_0_13151, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8133]), ['final']). 4.46/4.74 cnf(c_0_13152, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8134]), ['final']). 4.46/4.74 cnf(c_0_13153, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8135]), ['final']). 4.46/4.74 cnf(c_0_13154, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8136]), ['final']). 4.46/4.74 cnf(c_0_13155, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_8098]), ['final']). 4.46/4.74 cnf(c_0_13156, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8137]), ['final']). 4.46/4.74 cnf(c_0_13157, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_8138]), ['final']). 4.46/4.74 cnf(c_0_13158, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_8139]), ['final']). 4.46/4.74 cnf(c_0_13159, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_8140]), ['final']). 4.46/4.74 cnf(c_0_13160, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=c_Groups_Ozero__class_Ozero(X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_8141, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_13161, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_8142]), ['final']). 4.46/4.74 cnf(c_0_13162, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_8143]), ['final']). 4.46/4.74 cnf(c_0_13163, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_8144]), ['final']). 4.46/4.74 cnf(c_0_13164, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8145]), ['final']). 4.46/4.74 cnf(c_0_13165, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_8146]), ['final']). 4.46/4.74 cnf(c_0_13166, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8147]), ['final']). 4.46/4.74 cnf(c_0_13167, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8148]), ['final']). 4.46/4.74 cnf(c_0_13168, plain, (hAPP(c_Set_Oimage(X1,X2,X3),X4)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|c_Fun_Oinj__on(X2,X1,esk170_4(X4,X1,X2,hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X4))), inference(er,[status(thm)],[c_0_8149]), ['final']). 4.46/4.74 cnf(c_0_13169, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2))),X3)=c_List_Oremove1(X1,X2,X3)|~hBOOL(hAPP(c_List_Odistinct(X1),X3))), inference(rw,[status(thm)],[c_0_8150, c_0_5671]), ['final']). 4.46/4.74 cnf(c_0_13170, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X1))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))), inference(rw,[status(thm)],[c_0_8151, c_0_5884]), ['final']). 4.46/4.74 cnf(c_0_13171, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4)),X3))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8152]), ['final']). 4.46/4.74 cnf(c_0_13172, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Orderings_Opreorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8153]), ['final']). 4.46/4.74 cnf(c_0_13173, plain, (hBOOL(hAPP(X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk101_1(X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_8154]), ['final']). 4.46/4.74 cnf(c_0_13174, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Rings_Odivision__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8155]), ['final']). 4.46/4.74 cnf(c_0_13175, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X2)),X3))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8156]), ['final']). 4.46/4.74 cnf(c_0_13176, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4)),X3))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8157]), ['final']). 4.46/4.74 cnf(c_0_13177, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X2)),X3))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8158]), ['final']). 4.46/4.74 cnf(c_0_13178, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8159]), ['final']). 4.46/4.74 cnf(c_0_13179, plain, (hAPP(c_Option_Ooption_OSome(X1),X2)=hAPP(X3,X4)|hAPP(X5,X4)=hAPP(c_Option_Ooption_OSome(X1),X2)|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(c_Map_Omap__add(X6,X1,X3,X5),X4)), inference(split_conjunct,[status(thm)],[c_0_8160]), ['final']). 4.46/4.74 cnf(c_0_13180, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8161, c_0_4760]), c_0_4760]), ['final']). 4.46/4.74 cnf(c_0_13181, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(c_List_Olistsp(X1,X3),X2))), inference(rw,[status(thm)],[c_0_8162, c_0_4945]), ['final']). 4.46/4.74 cnf(c_0_13182, plain, (c_Fun_Oinj__on(X1,X2,X3,c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X4))|c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))=X4|~c_Fun_Oinj__on(X1,X2,X3,esk70_4(X3,X2,X1,X4))), inference(split_conjunct,[status(thm)],[c_0_7466]), ['final']). 4.46/4.74 cnf(c_0_13183, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8163]), ['final']). 4.46/4.74 cnf(c_0_13184, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8164]), ['final']). 4.46/4.74 cnf(c_0_13185, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8165]), ['final']). 4.46/4.74 cnf(c_0_13186, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8166]), ['final']). 4.46/4.74 cnf(c_0_13187, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[c_0_8167, c_0_6292]), ['final']). 4.46/4.74 cnf(c_0_13188, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_5196]), ['final']). 4.46/4.74 cnf(c_0_13189, plain, (~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)))))), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_8168])]), ['final']). 4.46/4.74 cnf(c_0_13190, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8169]), ['final']). 4.46/4.74 cnf(c_0_13191, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X3)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8170]), ['final']). 4.46/4.74 cnf(c_0_13192, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8171]), ['final']). 4.46/4.74 cnf(c_0_13193, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X3)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8172]), ['final']). 4.46/4.74 cnf(c_0_13194, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3))),c_Groups_Ozero__class_Ozero(X2)))|~class_Rings_Olinordered__ring__strict(X2)), inference(split_conjunct,[status(thm)],[c_0_5196]), ['final']). 4.46/4.74 cnf(c_0_13195, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3))))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,c_Wellfounded_Oacc(X1,X3))))), inference(split_conjunct,[status(thm)],[c_0_8173]), ['final']). 4.46/4.74 cnf(c_0_13196, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3))=c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8174]), ['final']). 4.46/4.74 cnf(c_0_13197, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)|~class_Rings_Oring(X1)), inference(split_conjunct,[status(thm)],[c_0_8175]), ['final']). 4.46/4.74 cnf(c_0_13198, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3)))|~hBOOL(hAPP(c_Predicate_OPowp(X1,X3),X2))), inference(rw,[status(thm)],[c_0_8176, c_0_4945]), ['final']). 4.46/4.74 cnf(c_0_13199, plain, (X2=hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_8177]), ['final']). 4.46/4.74 cnf(c_0_13200, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X1,X2)),c_Predicate_OPowp(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8178]), ['final']). 4.46/4.74 cnf(c_0_13201, plain, (hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk273_3(X1,X3,X2))))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_6866]), ['final']). 4.46/4.74 cnf(c_0_13202, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Oremove1(X2,X5,X4)))|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8179]), ['final']). 4.46/4.74 cnf(c_0_13203, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),X4))), inference(split_conjunct,[status(thm)],[c_0_8180]), ['final']). 4.46/4.74 cnf(c_0_13204, plain, (hAPP(hAPP(c_Set_Oinsert(X1),esk33_3(X2,X3,X1)),esk34_3(X2,X3,X1))=X3|hAPP(c_Nat_OSuc,X2)!=hAPP(c_Finite__Set_Ocard(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_5438]), ['final']). 4.46/4.74 cnf(c_0_13205, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_8181]), ['final']). 4.46/4.74 cnf(c_0_13206, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk397_2(X1,X2)),X1))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1)))), inference(split_conjunct,[status(thm)],[c_0_8182]), ['final']). 4.46/4.74 cnf(c_0_13207, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2))=hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)|~class_Orderings_Olinorder(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8183, c_0_7464]), c_0_7465]), ['final']). 4.46/4.74 cnf(c_0_13208, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_8184, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_13209, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8185]), ['final']). 4.46/4.74 cnf(c_0_13210, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8186]), ['final']). 4.46/4.74 cnf(c_0_13211, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(X1,esk498_3(X1,X2,X3)),esk499_3(X1,X2,X3)))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6578]), ['final']). 4.46/4.74 cnf(c_0_13212, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(X1,esk409_3(X1,X2,X3)),esk410_3(X1,X2,X3)))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_4513]), ['final']). 4.46/4.74 cnf(c_0_13213, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Rings_Odivision__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8187]), ['final']). 4.46/4.74 cnf(c_0_13214, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_8188]), ['final']). 4.46/4.74 cnf(c_0_13215, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_8189]), ['final']). 4.46/4.74 cnf(c_0_13216, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_8190]), ['final']). 4.46/4.74 cnf(c_0_13217, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_8191]), ['final']). 4.46/4.74 cnf(c_0_13218, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(X1,esk378_3(X1,X2,X3)),esk379_3(X1,X2,X3)))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_5086]), ['final']). 4.46/4.74 cnf(c_0_13219, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(X1,esk246_3(X1,X2,X3)),esk247_3(X1,X2,X3)))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_5045]), ['final']). 4.46/4.74 cnf(c_0_13220, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(X1,esk229_3(X1,X2,X3)),esk230_3(X1,X2,X3)))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_4519]), ['final']). 4.46/4.74 cnf(c_0_13221, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(X1,esk38_3(X1,X2,X3)),esk39_3(X1,X2,X3)))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6517]), ['final']). 4.46/4.74 cnf(c_0_13222, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_8192]), ['final']). 4.46/4.74 cnf(c_0_13223, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk277_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|X2=c_List_OtakeWhile(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8193]), ['final']). 4.46/4.74 cnf(c_0_13224, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk92_3(X2,X3,X1)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(rw,[status(thm)],[c_0_8194, c_0_4836]), ['final']). 4.46/4.74 cnf(c_0_13225, plain, (c_List_OtakeWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))=hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_OtakeWhile(X3,X1,X4))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_8195]), ['final']). 4.46/4.74 cnf(c_0_13226, plain, (X3=c_List_Olist_ONil(X1)|hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)!=c_List_Olist_ONil(X1)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))), inference(rw,[status(thm)],[c_0_8196, c_0_4736]), ['final']). 4.46/4.74 cnf(c_0_13227, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_8197]), ['final']). 4.46/4.74 cnf(c_0_13228, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8198]), ['final']). 4.46/4.74 cnf(c_0_13229, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))), inference(split_conjunct,[status(thm)],[c_0_8199]), ['final']). 4.46/4.74 cnf(c_0_13230, plain, (c_Divides_OnegDivAlg(X1,X2)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_8200, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_13231, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),X2)), inference(split_conjunct,[status(thm)],[c_0_8201]), ['final']). 4.46/4.74 cnf(c_0_13232, plain, (X2=X3|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8202]), ['final']). 4.46/4.74 cnf(c_0_13233, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin))), inference(rw,[status(thm)],[c_0_8203, c_0_4760]), ['final']). 4.46/4.74 cnf(c_0_13234, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin))), inference(rw,[status(thm)],[c_0_8204, c_0_4760]), ['final']). 4.46/4.74 cnf(c_0_13235, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8205, c_0_4436]), c_0_4760]), c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_13236, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8206, c_0_4436]), c_0_4760]), c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_13237, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8207]), ['final']). 4.46/4.74 cnf(c_0_13238, plain, (c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))=c_Nitpick_Onorm__frac(X2,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5477]), ['final']). 4.46/4.74 cnf(c_0_13239, plain, (hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),X4)))|~c_List_Olist__all(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))), inference(split_conjunct,[status(thm)],[c_0_8040]), ['final']). 4.46/4.74 cnf(c_0_13240, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin))), inference(rw,[status(thm)],[c_0_8208, c_0_4760]), ['final']). 4.46/4.74 cnf(c_0_13241, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8209, c_0_4609]), c_0_4760]), c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_13242, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))), inference(rw,[status(thm)],[c_0_8210, c_0_4760]), ['final']). 4.46/4.74 cnf(c_0_13243, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))), inference(rw,[status(thm)],[c_0_8211, c_0_4760]), ['final']). 4.46/4.74 cnf(c_0_13244, plain, (X5=X7|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5))!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X6),X4),hAPP(c_Option_Ooption_OSome(X2),X7))), inference(split_conjunct,[status(thm)],[c_0_8212]), ['final']). 4.46/4.74 cnf(c_0_13245, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))), inference(rw,[status(thm)],[c_0_8213, c_0_4760]), ['final']). 4.46/4.74 cnf(c_0_13246, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8214, c_0_4436]), c_0_4436]), c_0_4760]), ['final']). 4.46/4.74 cnf(c_0_13247, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8215, c_0_4436]), c_0_4436]), c_0_4760]), ['final']). 4.46/4.74 cnf(c_0_13248, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_8216]), ['final']). 4.46/4.74 cnf(c_0_13249, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|~c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X6),hAPP(hAPP(c_List_Oappend(X2),X5),X7))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)), inference(split_conjunct,[status(thm)],[c_0_8217]), ['final']). 4.46/4.74 cnf(c_0_13250, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|~c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X6),X4),hAPP(hAPP(c_List_Oappend(X2),X7),X5))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X7)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X6)), inference(split_conjunct,[status(thm)],[c_0_8217]), ['final']). 4.46/4.74 cnf(c_0_13251, plain, (c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Oinj__on(X1,X2,X3,X5)), inference(split_conjunct,[status(thm)],[c_0_8218]), ['final']). 4.46/4.74 cnf(c_0_13252, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk6_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))|c_List_Olist__all(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8219]), ['final']). 4.46/4.74 cnf(c_0_13253, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)))), inference(split_conjunct,[status(thm)],[c_0_7296]), ['final']). 4.46/4.74 cnf(c_0_13254, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8220, c_0_4836]), c_0_4836]), ['final']). 4.46/4.74 cnf(c_0_13255, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8221, c_0_4836]), c_0_4836]), ['final']). 4.46/4.74 cnf(c_0_13256, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_8222]), ['final']). 4.46/4.74 cnf(c_0_13257, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk517_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|c_List_Olist__all(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8223]), ['final']). 4.46/4.74 cnf(c_0_13258, plain, (hBOOL(hAPP(c_List_Odistinct(tc_prod(X1,X3)),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8224]), ['final']). 4.46/4.74 cnf(c_0_13259, plain, (hBOOL(hAPP(c_List_Odistinct(tc_prod(X3,X1)),hAPP(hAPP(c_List_Ozip(X3,X1),X4),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8225]), ['final']). 4.46/4.74 cnf(c_0_13260, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk113_3(X2,X3,X1)))|hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_8226]), ['final']). 4.46/4.74 cnf(c_0_13261, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))), inference(split_conjunct,[status(thm)],[c_0_7492]), ['final']). 4.46/4.74 cnf(c_0_13262, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk252_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|c_List_Olist__all(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8227]), ['final']). 4.46/4.74 cnf(c_0_13263, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[c_0_8228, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13264, plain, (c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))|~c_FunDef_Oreduction__pair(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_6199]), ['final']). 4.46/4.74 cnf(c_0_13265, plain, (hBOOL(hAPP(X2,X4))|~c_Enum_Oall__n__lists(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X3,c_Enum_Oenum__class_Oenum(X1)))))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_7138]), ['final']). 4.46/4.74 cnf(c_0_13266, plain, (hBOOL(hAPP(hAPP(X1,esk231_4(X2,X3,X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X6,X7,X4,X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8015]), ['final']). 4.46/4.74 cnf(c_0_13267, plain, (hBOOL(hAPP(hAPP(X1,X2),esk231_4(X3,X2,X4,X1)))|~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X6,X7,X1,X4),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8015]), ['final']). 4.46/4.74 cnf(c_0_13268, plain, (c_Equiv__Relations_Ocongruent(X4,X5,X6,hAPP(X7,X8))|~c_Equiv__Relations_Oequiv(X1,X2,X3)|~c_Equiv__Relations_Ocongruent2(X1,X4,X5,X3,X6,X7)|~hBOOL(hAPP(hAPP(c_member(X1),X8),X2))), inference(split_conjunct,[status(thm)],[c_0_8229]), ['final']). 4.46/4.74 cnf(c_0_13269, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|X3=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8230]), ['final']). 4.46/4.74 cnf(c_0_13270, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8231]), ['final']). 4.46/4.74 cnf(c_0_13271, plain, (hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8232]), ['final']). 4.46/4.74 cnf(c_0_13272, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8233]), ['final']). 4.46/4.74 cnf(c_0_13273, plain, (hAPP(c_Set_Oimage(X1,X1,X3),X2)=X2|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X1,X3),X2)),X2))|~c_Fun_Oinj__on(X1,X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8234]), ['final']). 4.46/4.74 cnf(c_0_13274, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=c_Transitive__Closure_Ortrancl(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Transitive__Closure_Ortrancl(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_8235]), ['final']). 4.46/4.74 cnf(c_0_13275, plain, (c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),c_Map_Omap__add(X1,X2,X4,X3),c_Map_Odom(X1,X2,X3))|~c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),X3,c_Map_Odom(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_8236]), ['final']). 4.46/4.74 cnf(c_0_13276, plain, (hBOOL(hAPP(hAPP(c_member(X5),X2),c_SetInterval_Oord_OatLeastAtMost(X5,X1,X4,X3)))|~hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(X1,X4),X2))), inference(split_conjunct,[status(thm)],[c_0_8237]), ['final']). 4.46/4.74 cnf(c_0_13277, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Obutlast(X1,X2)),hAPP(hAPP(c_List_Olist_OCons(X1),c_List_Olast(X1,X2)),c_List_Olist_ONil(X1)))=X2|X2=c_List_Olist_ONil(X1)), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_8238])]), ['final']). 4.46/4.74 cnf(c_0_13278, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)|~class_Rings_Oring(X1)), inference(split_conjunct,[status(thm)],[c_0_8239]), ['final']). 4.46/4.74 cnf(c_0_13279, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)|~class_Rings_Odivision__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8240]), ['final']). 4.46/4.74 cnf(c_0_13280, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))|~class_Rings_Oring(X1)), inference(split_conjunct,[status(thm)],[c_0_8241]), ['final']). 4.46/4.74 cnf(c_0_13281, plain, (hBOOL(hAPP(hAPP(c_member(X5),X3),c_SetInterval_Oord_OgreaterThanLessThan(X5,X1,X2,X4)))|~hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(X1,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8242]), ['final']). 4.46/4.74 cnf(c_0_13282, plain, (hBOOL(hAPP(X1,esk298_2(X1,X2)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))), inference(split_conjunct,[status(thm)],[c_0_7245]), ['final']). 4.46/4.74 cnf(c_0_13283, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,X2))=c_Big__Operators_Olinorder__class_OMax(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8243]), ['final']). 4.46/4.74 cnf(c_0_13284, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(X3,esk135_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_7677]), ['final']). 4.46/4.74 cnf(c_0_13285, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(X3,esk90_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_7683]), ['final']). 4.46/4.74 cnf(c_0_13286, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8244]), ['final']). 4.46/4.74 cnf(c_0_13287, plain, (hAPP(c_Fun_Othe__inv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(X3,X4))=X4|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_8245]), ['final']). 4.46/4.74 cnf(c_0_13288, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,X2))=c_Big__Operators_Olinorder__class_OMin(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8246]), ['final']). 4.46/4.74 cnf(c_0_13289, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,X2)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,X2))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8247]), ['final']). 4.46/4.74 cnf(c_0_13290, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,X2))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8248]), ['final']). 4.46/4.74 cnf(c_0_13291, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X1),esk449_2(X2,X1)),X2))), inference(csr,[status(thm)],[c_0_8249, c_0_8250]), ['final']). 4.46/4.74 cnf(c_0_13292, plain, (X1=X2|hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Olist__update(X3,X4),X2),X5)),X1)=hAPP(hAPP(c_List_Onth(X3),X4),X1)), inference(split_conjunct,[status(thm)],[c_0_8251]), ['final']). 4.46/4.74 cnf(c_0_13293, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_8038]), ['final']). 4.46/4.74 cnf(c_0_13294, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8252]), ['final']). 4.46/4.74 cnf(c_0_13295, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8253]), ['final']). 4.46/4.74 cnf(c_0_13296, plain, (X1=X2|c_List_Oremove1(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))=hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_Oremove1(X3,X1,X4))), inference(split_conjunct,[status(thm)],[c_0_5965]), ['final']). 4.46/4.74 cnf(c_0_13297, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X2),X3)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X1!=esk44_4(X2,X3,X4,X1)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(X2,X1)|~hBOOL(hAPP(hAPP(c_member(X4),X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7128]), ['final']). 4.46/4.74 cnf(c_0_13298, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X4)),c_List_Olists(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_7155]), ['final']). 4.46/4.74 cnf(c_0_13299, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X4),X2)),c_List_Olists(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_7155]), ['final']). 4.46/4.74 cnf(c_0_13300, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X2)),c_List_Olists(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_7238]), ['final']). 4.46/4.74 cnf(c_0_13301, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8254]), ['final']). 4.46/4.74 cnf(c_0_13302, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8255]), ['final']). 4.46/4.74 cnf(c_0_13303, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk206_2(X1,X2))=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))), inference(rw,[status(thm)],[c_0_8256, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13304, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Odrop(X1),X3),X4))))), inference(split_conjunct,[status(thm)],[c_0_8257]), ['final']). 4.46/4.74 cnf(c_0_13305, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),X3),X4))))), inference(split_conjunct,[status(thm)],[c_0_8258]), ['final']). 4.46/4.74 cnf(c_0_13306, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk45_3(X2,X3,X1)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7128]), ['final']). 4.46/4.74 cnf(c_0_13307, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8259]), ['final']). 4.46/4.74 cnf(c_0_13308, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|c_SMT_Oz3div(X2,X1)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_8260]), ['final']). 4.46/4.74 cnf(c_0_13309, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Oring(X1)), inference(split_conjunct,[status(thm)],[c_0_8261]), ['final']). 4.46/4.74 cnf(c_0_13310, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5429]), ['final']). 4.46/4.74 cnf(c_0_13311, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8262]), ['final']). 4.46/4.74 cnf(c_0_13312, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(c_List_Otl(X2),c_List_Oreplicate(X2,X1,X3))=c_List_Oreplicate(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3)), inference(split_conjunct,[status(thm)],[c_0_8263]), ['final']). 4.46/4.74 cnf(c_0_13313, plain, (hAPP(c_Option_Ooption_OSome(X3),X4)=hAPP(c_Map_Omap__add(X5,X3,X6,X1),X2)|hAPP(X1,X2)!=hAPP(c_Option_Ooption_OSome(X3),X4)), inference(split_conjunct,[status(thm)],[c_0_8005]), ['final']). 4.46/4.74 cnf(c_0_13314, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),hAPP(c_List_Oset(tc_prod(X3,X3)),hAPP(hAPP(c_List_Ozip(X3,X3),X4),X4))))), inference(split_conjunct,[status(thm)],[c_0_5111]), ['final']). 4.46/4.74 cnf(c_0_13315, plain, (c_Enum_Oex__n__lists(X3,X1,X4)|~hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3)),X2),hAPP(c_List_Oset(tc_List_Olist(X3)),c_Enum_On__lists(X3,X4,c_Enum_Oenum__class_Oenum(X3)))))|~class_Enum_Oenum(X3)), inference(split_conjunct,[status(thm)],[c_0_7237]), ['final']). 4.46/4.74 cnf(c_0_13316, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_8264]), ['final']). 4.46/4.74 cnf(c_0_13317, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8265]), ['final']). 4.46/4.74 cnf(c_0_13318, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5921]), ['final']). 4.46/4.74 cnf(c_0_13319, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8266]), ['final']). 4.46/4.74 cnf(c_0_13320, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[c_0_8267, c_0_5134]), ['final']). 4.46/4.74 cnf(c_0_13321, plain, (c_List_Olist_ONil(X1)=X2|hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))=hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Otl(X1),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_8268]), ['final']). 4.46/4.74 cnf(c_0_13322, plain, (c_Map_Omap__add(X1,X2,X4,X3)=c_Map_Omap__add(X1,X2,X3,X4)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),c_Map_Odom(X1,X2,X4))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_8269]), ['final']). 4.46/4.74 cnf(c_0_13323, plain, (c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk37_2(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7898]), ['final']). 4.46/4.74 cnf(c_0_13324, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|~hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3)))))), inference(split_conjunct,[status(thm)],[c_0_8270]), ['final']). 4.46/4.74 cnf(c_0_13325, plain, (c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X1)))|~class_Orderings_Owellorder(X1)), inference(rw,[status(thm)],[c_0_8271, c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_13326, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_8272, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_13327, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk121_3(X2,X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))), inference(split_conjunct,[status(thm)],[c_0_8273]), ['final']). 4.46/4.74 cnf(c_0_13328, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk211_3(X2,X3,X1)),X2))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5487]), ['final']). 4.46/4.74 cnf(c_0_13329, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk210_3(X2,X3,X1)),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5487]), ['final']). 4.46/4.74 cnf(c_0_13330, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_8274]), ['final']). 4.46/4.74 cnf(c_0_13331, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_8275]), ['final']). 4.46/4.74 cnf(c_0_13332, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_8276, c_0_4448]), ['final']). 4.46/4.74 cnf(c_0_13333, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8277]), ['final']). 4.46/4.74 cnf(c_0_13334, plain, (hBOOL(hAPP(X1,esk116_3(X1,X2,X3)))|hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))|~hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7311]), ['final']). 4.46/4.74 cnf(c_0_13335, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)), inference(split_conjunct,[status(thm)],[c_0_7546]), ['final']). 4.46/4.74 cnf(c_0_13336, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_8278]), ['final']). 4.46/4.74 cnf(c_0_13337, plain, (X1=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X1))|~c_List_Onat__list(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8279, c_0_5787]), c_0_5788]), ['final']). 4.46/4.74 cnf(c_0_13338, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8009]), ['final']). 4.46/4.74 cnf(c_0_13339, plain, (hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X5)),hAPP(X3,X5))=hAPP(X3,X5)|~c_Finite__Set_Ofolding__idem(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8280]), ['final']). 4.46/4.74 cnf(c_0_13340, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X3)|~class_Divides_Oring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8281]), ['final']). 4.46/4.74 cnf(c_0_13341, plain, (~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X3,hAPP(c_Nat_OSuc,esk305_3(X3,X2,X1)))),hAPP(X3,esk305_3(X3,X2,X1)))),X2))), inference(split_conjunct,[status(thm)],[c_0_8282]), ['final']). 4.46/4.74 cnf(c_0_13342, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk52_1(X1)))|hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))), inference(split_conjunct,[status(thm)],[c_0_8283]), ['final']). 4.46/4.74 cnf(c_0_13343, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8009]), ['final']). 4.46/4.74 cnf(c_0_13344, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8010]), ['final']). 4.46/4.74 cnf(c_0_13345, plain, (~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X3,hAPP(c_Nat_OSuc,esk5_3(X2,X1,X3)))),hAPP(X3,esk5_3(X2,X1,X3)))),X2))), inference(split_conjunct,[status(thm)],[c_0_6939]), ['final']). 4.46/4.74 cnf(c_0_13346, plain, (hBOOL(hAPP(hAPP(X1,esk374_5(X2,X1,X3,X4,X5)),X2))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X4,tc_HOL_Obool)),X3),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7820]), ['final']). 4.46/4.74 cnf(c_0_13347, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk150_3(X2,X1,X3)),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7127]), ['final']). 4.46/4.74 cnf(c_0_13348, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(X2,X4))), inference(split_conjunct,[status(thm)],[c_0_8284]), ['final']). 4.46/4.74 cnf(c_0_13349, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8285]), ['final']). 4.46/4.74 cnf(c_0_13350, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8286]), ['final']). 4.46/4.74 cnf(c_0_13351, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X5)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8287]), ['final']). 4.46/4.74 cnf(c_0_13352, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X5)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8288]), ['final']). 4.46/4.74 cnf(c_0_13353, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8289]), ['final']). 4.46/4.74 cnf(c_0_13354, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8290]), ['final']). 4.46/4.74 cnf(c_0_13355, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk213_4(X2,X3,X4,X1)),X3))|hAPP(c_Nat_OSuc,X2)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_7680]), ['final']). 4.46/4.74 cnf(c_0_13356, plain, (c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,X3,hAPP(X2,X4))=c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,hAPP(c_Nat_OSuc,X3),X4)|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8291]), ['final']). 4.46/4.74 cnf(c_0_13357, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X2,X1,X3)|~hBOOL(hAPP(X2,esk532_3(X3,X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.74 cnf(c_0_13358, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X3=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X1,X3,X2)|~hBOOL(hAPP(X1,esk534_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.74 cnf(c_0_13359, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8013]), ['final']). 4.46/4.74 cnf(c_0_13360, plain, (c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X1,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_8292]), ['final']). 4.46/4.74 cnf(c_0_13361, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X7)|hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)!=hAPP(hAPP(c_List_Omap(X5,X2),X6),X7)), inference(split_conjunct,[status(thm)],[c_0_8293]), ['final']). 4.46/4.74 cnf(c_0_13362, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Ois__nat(X1)|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))), inference(rw,[status(thm)],[c_0_8294, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13363, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_5564]), ['final']). 4.46/4.74 cnf(c_0_13364, plain, (c_Nitpick_Onorm__frac(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(er,[status(thm)],[c_0_8295]), ['final']). 4.46/4.74 cnf(c_0_13365, plain, (hAPP(c_Finite__Set_Ocard(X1),X3)=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_8296]), ['final']). 4.46/4.74 cnf(c_0_13366, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|epred2_3(X2,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_5124]), ['final']). 4.46/4.74 cnf(c_0_13367, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk239_3(X2,X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7809]), ['final']). 4.46/4.74 cnf(c_0_13368, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk239_3(X2,X3,X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7809]), ['final']). 4.46/4.74 cnf(c_0_13369, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk364_3(X2,X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Complete__Lattice_OSup__class_OSup(X1,X2)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7811]), ['final']). 4.46/4.74 cnf(c_0_13370, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk493_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olist__ex1(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_7265]), ['final']). 4.46/4.74 cnf(c_0_13371, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4))), inference(split_conjunct,[status(thm)],[c_0_7459]), ['final']). 4.46/4.74 cnf(c_0_13372, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[c_0_8297, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_13373, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X2)),c_Wellfounded_Ofinite__psubset(X1)))), inference(split_conjunct,[status(thm)],[c_0_7182]), ['final']). 4.46/4.74 cnf(c_0_13374, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))))), inference(split_conjunct,[status(thm)],[c_0_7986]), ['final']). 4.46/4.74 cnf(c_0_13375, plain, (c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8298]), ['final']). 4.46/4.74 cnf(c_0_13376, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(tc_sum(X3,X1)),c_Sum__Type_OPlus(X3,X1,X4,X2))), inference(split_conjunct,[status(thm)],[c_0_7459]), ['final']). 4.46/4.74 cnf(c_0_13377, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk352_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olist__ex(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8299]), ['final']). 4.46/4.74 cnf(c_0_13378, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk162_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olist__ex1(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_7272]), ['final']). 4.46/4.74 cnf(c_0_13379, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),esk364_3(X3,X2,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7811]), ['final']). 4.46/4.74 cnf(c_0_13380, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X3)),X3)=X3|~c_Equiv__Relations_Oequiv(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8300]), ['final']). 4.46/4.74 cnf(c_0_13381, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8301]), ['final']). 4.46/4.74 cnf(c_0_13382, plain, (X3=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Lattices_Oboolean__algebra(X1)|c_Orderings_Obot__class_Obot(X1)!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)!=c_Orderings_Otop__class_Otop(X1)), inference(split_conjunct,[status(thm)],[c_0_8302]), ['final']). 4.46/4.74 cnf(c_0_13383, plain, (c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8303]), ['final']). 4.46/4.74 cnf(c_0_13384, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8304, c_0_5120]), c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13385, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)|~class_Lattices_Oab__semigroup__idem__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_8305]), ['final']). 4.46/4.74 cnf(c_0_13386, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2))=hAPP(c_SetInterval_Oord__class_OatLeast(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8306]), ['final']). 4.46/4.74 cnf(c_0_13387, plain, (hBOOL(hAPP(X1,esk199_3(X2,X1,X3)))|hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7757]), ['final']). 4.46/4.74 cnf(c_0_13388, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),c_Orderings_Otop__class_Otop(X1)),X2)=c_Complete__Lattice_OInf__class_OInf(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8307]), ['final']). 4.46/4.74 cnf(c_0_13389, plain, (c_Complete__Lattice_OSup__class_OSup(X1,X2)=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),c_Orderings_Obot__class_Obot(X1)),X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8308]), ['final']). 4.46/4.74 cnf(c_0_13390, plain, (X2=X3|hAPP(X1,X2)!=hAPP(X1,X3)|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5))|~hBOOL(hAPP(hAPP(c_member(X4),X2),X5))|~c_Typedef_Otype__definition(X6,X4,X7,X1,X5)), inference(split_conjunct,[status(thm)],[c_0_8309]), ['final']). 4.46/4.74 cnf(c_0_13391, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2))=hAPP(c_SetInterval_Oord__class_OatMost(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8310]), ['final']). 4.46/4.74 cnf(c_0_13392, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8311]), ['final']). 4.46/4.74 cnf(c_0_13393, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8312]), ['final']). 4.46/4.74 cnf(c_0_13394, plain, (hAPP(c_SetInterval_Oord__class_OlessThan(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8313]), ['final']). 4.46/4.74 cnf(c_0_13395, plain, (hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),esk112_3(X1,X3,X2)),esk113_3(X1,X3,X2))))|~hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8226]), ['final']). 4.46/4.74 cnf(c_0_13396, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),X5)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7565]), ['final']). 4.46/4.74 cnf(c_0_13397, plain, (c_Option_Ooption_ONone(X1)!=hAPP(hAPP(c_Map_Omap__of(X2,X1),hAPP(hAPP(c_List_Ozip(X2,X1),X3),X4)),X5)|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_List_Oset(X2),X3)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)), inference(split_conjunct,[status(thm)],[c_0_6957]), ['final']). 4.46/4.74 cnf(c_0_13398, plain, (hBOOL(hAPP(hAPP(X1,X2),esk488_5(X3,X4,X1,X5,X2)))|~hBOOL(hAPP(hAPP(c_member(X5),X2),X4))|~c_Wellfounded_Omax__extp(X5,X1,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_5595]), ['final']). 4.46/4.74 cnf(c_0_13399, plain, (hBOOL(hAPP(X1,X2))|hAPP(c_List_Ofilter(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))=hAPP(c_List_Ofilter(X3,X1),X4)), inference(split_conjunct,[status(thm)],[c_0_7642]), ['final']). 4.46/4.74 cnf(c_0_13400, plain, (hAPP(hAPP(c_List_Onth(X1),X2),esk361_2(X2,X1))=hAPP(hAPP(c_List_Onth(X1),X2),esk360_2(X2,X1))|hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7699]), ['final']). 4.46/4.74 cnf(c_0_13401, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3))|~class_Lattices_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_8314]), ['final']). 4.46/4.74 cnf(c_0_13402, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_8315]), ['final']). 4.46/4.74 cnf(c_0_13403, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8316]), ['final']). 4.46/4.74 cnf(c_0_13404, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8317]), ['final']). 4.46/4.74 cnf(c_0_13405, plain, (c_Fun_Oinj__on(X2,X1,c_Fun_Othe__inv__into(X1,X2,X4,X3),hAPP(c_Set_Oimage(X1,X2,X3),X4))|~c_Fun_Oinj__on(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8318]), ['final']). 4.46/4.74 cnf(c_0_13406, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk202_3(X2,X3,X1)),esk203_3(X2,X3,X1)))|~c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7184]), ['final']). 4.46/4.74 cnf(c_0_13407, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X3,X1)),c_Sum__Type_OPlus(X3,X1,X4,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8319]), ['final']). 4.46/4.74 cnf(c_0_13408, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),X2))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8320]), ['final']). 4.46/4.74 cnf(c_0_13409, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))=X3|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8321]), ['final']). 4.46/4.74 cnf(c_0_13410, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))=X3|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8322]), ['final']). 4.46/4.74 cnf(c_0_13411, plain, (hBOOL(hAPP(hAPP(X3,X5),X6))|hBOOL(hAPP(hAPP(X4,X5),X6))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4),X5),X6))), inference(split_conjunct,[status(thm)],[c_0_8323]), ['final']). 4.46/4.74 cnf(c_0_13412, plain, (hBOOL(hAPP(c_List_Odistinct(tc_prod(X1,X3)),c_Enum_Oproduct(X1,X3,X2,X4)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8324]), ['final']). 4.46/4.74 cnf(c_0_13413, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8325]), ['final']). 4.46/4.74 cnf(c_0_13414, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1)=c_List_Olist_ONil(X2)|esk357_2(X1,X2)!=c_List_Olist_ONil(X2)), inference(rw,[status(thm)],[c_0_8326, c_0_4736]), ['final']). 4.46/4.74 cnf(c_0_13415, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1)=c_List_Olist_ONil(X2)|esk195_2(X1,X2)!=c_List_Olist_ONil(X2)), inference(rw,[status(thm)],[c_0_8327, c_0_4736]), ['final']). 4.46/4.74 cnf(c_0_13416, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8233]), ['final']). 4.46/4.74 cnf(c_0_13417, plain, (X2=X3|hAPP(hAPP(c_List_Onth(X1),X2),esk161_3(X1,X3,X2))!=hAPP(hAPP(c_List_Onth(X1),X3),esk161_3(X1,X3,X2))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_7479]), ['final']). 4.46/4.74 cnf(c_0_13418, plain, (c_Fun_Oinj__on(X3,X2,X4,hAPP(c_Set_Oimage(X1,X3,X5),X6))|~c_Fun_Oinj__on(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),X6)), inference(split_conjunct,[status(thm)],[c_0_8328]), ['final']). 4.46/4.74 cnf(c_0_13419, plain, (hAPP(X3,X4)=hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X4)),hAPP(X3,X4))|~c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8329]), ['final']). 4.46/4.74 cnf(c_0_13420, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8330]), ['final']). 4.46/4.74 cnf(c_0_13421, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8331]), ['final']). 4.46/4.74 cnf(c_0_13422, plain, (hBOOL(hAPP(hAPP(X6,X2),X3))|~hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X1),X6))), inference(split_conjunct,[status(thm)],[c_0_8332]), ['final']). 4.46/4.74 cnf(c_0_13423, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk309_2(X1,X2)),X1))|hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_5409]), ['final']). 4.46/4.74 cnf(c_0_13424, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2)=X3|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8333]), ['final']). 4.46/4.74 cnf(c_0_13425, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2)=X3|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8334]), ['final']). 4.46/4.74 cnf(c_0_13426, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk301_2(X1,X2)),c_Int_OInteg))|hBOOL(hAPP(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_8335]), ['final']). 4.46/4.74 cnf(c_0_13427, plain, (hBOOL(hAPP(X1,esk76_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))|~hBOOL(hAPP(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_7438]), ['final']). 4.46/4.74 cnf(c_0_13428, plain, (c_Option_Ooption_ONone(X4)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X4),X1,c_Option_Ooption_ONone(X4),X6),hAPP(X2,X3))|c_Option_Ooption_ONone(X1)!=hAPP(X2,X3)), inference(rw,[status(thm)],[c_0_8336, c_0_7133]), ['final']). 4.46/4.74 cnf(c_0_13429, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8337]), ['final']). 4.46/4.74 cnf(c_0_13430, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))=X1), inference(split_conjunct,[status(thm)],[c_0_8338]), ['final']). 4.46/4.74 cnf(c_0_13431, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8339]), ['final']). 4.46/4.74 cnf(c_0_13432, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X3))|~class_Groups_Omonoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8340]), ['final']). 4.46/4.74 cnf(c_0_13433, plain, (c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=X3|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),hAPP(c_COMBK(X1,X2),X4))=X4|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8341]), ['final']). 4.46/4.74 cnf(c_0_13434, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8342]), ['final']). 4.46/4.74 cnf(c_0_13435, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8343]), ['final']). 4.46/4.74 cnf(c_0_13436, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8344]), ['final']). 4.46/4.74 cnf(c_0_13437, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))), inference(rw,[status(thm)],[c_0_8345, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_13438, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))=c_Groups_Osgn__class_Osgn(X1,X2)|c_Groups_Ozero__class_Ozero(X1)=X2|~class_Groups_Osgn__if(X1)), inference(split_conjunct,[status(thm)],[c_0_8346]), ['final']). 4.46/4.74 cnf(c_0_13439, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))|X4=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1),X2),hAPP(c_COMBK(X1,X3),X4))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8347]), ['final']). 4.46/4.74 cnf(c_0_13440, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_8348]), ['final']). 4.46/4.74 cnf(c_0_13441, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8349]), ['final']). 4.46/4.74 cnf(c_0_13442, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8350]), ['final']). 4.46/4.74 cnf(c_0_13443, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X3,X4)),X1),X2))|hAPP(X1,esk469_4(X2,X1,X3,X4))!=hAPP(X2,esk469_4(X2,X1,X3,X4))|~class_Enum_Oenum(X3)|~class_HOL_Oequal(X4)), inference(split_conjunct,[status(thm)],[c_0_5373]), ['final']). 4.46/4.74 cnf(c_0_13444, plain, (X1=X2|hAPP(hAPP(c_List_Oappend(X3),X1),hAPP(hAPP(c_List_Olist_OCons(X3),X4),c_List_Olist_ONil(X3)))!=hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X5),c_List_Olist_ONil(X3)))), inference(split_conjunct,[status(thm)],[c_0_8351]), ['final']). 4.46/4.74 cnf(c_0_13445, plain, (X1=X2|hAPP(hAPP(c_List_Oappend(X3),X4),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3)))!=hAPP(hAPP(c_List_Oappend(X3),X5),hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_Olist_ONil(X3)))), inference(split_conjunct,[status(thm)],[c_0_8351]), ['final']). 4.46/4.74 cnf(c_0_13446, plain, (X3=X2|hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_5514]), ['final']). 4.46/4.74 cnf(c_0_13447, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk196_2(X2,X1)))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5930]), ['final']). 4.46/4.74 cnf(c_0_13448, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_7296]), ['final']). 4.46/4.74 cnf(c_0_13449, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_8216]), ['final']). 4.46/4.74 cnf(c_0_13450, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7786]), ['final']). 4.46/4.74 cnf(c_0_13451, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|X3=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_8352]), ['final']). 4.46/4.74 cnf(c_0_13452, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))|~c_Wellfounded_OwfP(X1,X2)), inference(rw,[status(thm)],[c_0_8353, c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_13453, plain, (c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))|~c_Wellfounded_OwfP(X1,X2)), inference(rw,[status(thm)],[c_0_8354, c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_13454, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),c_Divides_OposDivAlg(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_8355]), ['final']). 4.46/4.74 cnf(c_0_13455, plain, (hAPP(X1,esk417_1(X1))=hAPP(X1,esk418_1(X1))|hBOOL(hAPP(hAPP(X1,esk417_1(X1)),esk418_1(X1)))|c_Equiv__Relations_Oequivp(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_8356]), ['final']). 4.46/4.74 cnf(c_0_13456, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7802]), ['final']). 4.46/4.74 cnf(c_0_13457, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_8144]), ['final']). 4.46/4.74 cnf(c_0_13458, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_8143]), ['final']). 4.46/4.74 cnf(c_0_13459, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1)),X3),X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8357]), ['final']). 4.46/4.74 cnf(c_0_13460, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),c_Divides_OnegDivAlg(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_8358]), ['final']). 4.46/4.74 cnf(c_0_13461, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk467_2(X1,X2)),esk466_2(X1,X2)))|c_List_Olinorder__class_Osorted(X2,X1)|~class_Orderings_Olinorder(X2)), inference(split_conjunct,[status(thm)],[c_0_6908]), ['final']). 4.46/4.74 cnf(c_0_13462, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk191_2(X1,X2)),esk192_2(X1,X2)))|c_List_Olinorder__class_Osorted(X2,X1)|~class_Orderings_Olinorder(X2)), inference(split_conjunct,[status(thm)],[c_0_8060]), ['final']). 4.46/4.74 cnf(c_0_13463, plain, (X2=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4)))), inference(split_conjunct,[status(thm)],[c_0_8359]), ['final']). 4.46/4.74 cnf(c_0_13464, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8360]), ['final']). 4.46/4.74 cnf(c_0_13465, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8361]), ['final']). 4.46/4.74 cnf(c_0_13466, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8362]), ['final']). 4.46/4.74 cnf(c_0_13467, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8363]), ['final']). 4.46/4.74 cnf(c_0_13468, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X1)),X2))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_HOL_Obool,X1),X2),c_Option_Ooption_OSome(X1))))|~hBOOL(hAPP(X2,c_Option_Ooption_ONone(X1)))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_8051]), ['final']). 4.46/4.74 cnf(c_0_13469, plain, (hAPP(X1,X2)=c_Option_Ooption_ONone(X3)|hAPP(X1,X2)=hAPP(c_Option_Ooption_OSome(X3),X4)|hAPP(c_Option_Ooption_OSome(X3),X4)!=hAPP(c_Map_Omap__add(X5,X3,X6,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_8160]), ['final']). 4.46/4.74 cnf(c_0_13470, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8364]), ['final']). 4.46/4.74 cnf(c_0_13471, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8365]), ['final']). 4.46/4.74 cnf(c_0_13472, plain, (X1=hAPP(c_List_Ofilter(X2,X3),esk529_5(X4,X3,X1,X5,X2))|hAPP(hAPP(c_List_Olist_OCons(X2),X5),X1)!=hAPP(c_List_Ofilter(X2,X3),X4)), inference(split_conjunct,[status(thm)],[c_0_5072]), ['final']). 4.46/4.74 cnf(c_0_13473, plain, (X1=hAPP(c_List_Ofilter(X2,X3),esk153_5(X1,X4,X5,X3,X2))|hAPP(c_List_Ofilter(X2,X3),X5)!=hAPP(hAPP(c_List_Olist_OCons(X2),X4),X1)), inference(split_conjunct,[status(thm)],[c_0_5090]), ['final']). 4.46/4.74 cnf(c_0_13474, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8366, c_0_5120]), c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13475, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8367, c_0_5120]), c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13476, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6))|hAPP(hAPP(X5,X7),X6)=X4|~c_Big__Operators_Ocomm__monoid__big(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_8368]), ['final']). 4.46/4.74 cnf(c_0_13477, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_8369, c_0_4912]), ['final']). 4.46/4.74 cnf(c_0_13478, plain, (c_List_Olast(X2,X3)=c_List_Olast(X2,hAPP(hAPP(c_List_Odrop(X2),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_8370]), ['final']). 4.46/4.74 cnf(c_0_13479, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8371]), ['final']). 4.46/4.74 cnf(c_0_13480, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_8372]), ['final']). 4.46/4.74 cnf(c_0_13481, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8373, c_0_4836]), c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13482, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))=hAPP(c_Set_Oimage(X1,X3,hAPP(c_COMBK(X3,X1),X4)),X2)), inference(split_conjunct,[status(thm)],[c_0_8374]), ['final']). 4.46/4.74 cnf(c_0_13483, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,X2)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8375]), ['final']). 4.46/4.74 cnf(c_0_13484, plain, (c_Divides_Odivmod__int(X2,X1)=c_Divides_OnegDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_7375]), ['final']). 4.46/4.74 cnf(c_0_13485, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)))), inference(split_conjunct,[status(thm)],[c_0_8376]), ['final']). 4.46/4.74 cnf(c_0_13486, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))=hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8377, c_0_5120]), c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13487, plain, (hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[c_0_8378, c_0_4517]), ['final']). 4.46/4.74 cnf(c_0_13488, plain, (c_List_Olist_ONil(X1)=X2|hAPP(c_List_Ohd(X3),hAPP(hAPP(c_List_Omap(X1,X3),X4),X2))=hAPP(X4,hAPP(c_List_Ohd(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8379]), ['final']). 4.46/4.74 cnf(c_0_13489, plain, (X5=X6|~c_Fun_Oinj__on(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X6),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|hAPP(X3,X5)!=hAPP(X3,X6)), inference(split_conjunct,[status(thm)],[c_0_8380]), ['final']). 4.46/4.74 cnf(c_0_13490, plain, (c_List_Olist__all2(X1,X2,X3,X5,X4)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3),esk491_5(X4,X5,X3,X2,X1)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)), inference(split_conjunct,[status(thm)],[c_0_6520]), ['final']). 4.46/4.74 cnf(c_0_13491, plain, (c_List_Olist__all2(X1,X2,X3,X5,X4)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3),esk168_5(X3,X4,X5,X2,X1)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5)), inference(split_conjunct,[status(thm)],[c_0_6519]), ['final']). 4.46/4.74 cnf(c_0_13492, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_8381, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_13493, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8382]), ['final']). 4.46/4.74 cnf(c_0_13494, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X2),X4)))|~hBOOL(hAPP(X1,esk253_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2)))), inference(split_conjunct,[status(thm)],[c_0_7018]), ['final']). 4.46/4.74 cnf(c_0_13495, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X4,X2))|c_List_Opartition(X1,X4,X5)!=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X6),X3)), inference(split_conjunct,[status(thm)],[c_0_8076]), ['final']). 4.46/4.74 cnf(c_0_13496, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))), inference(er,[status(thm)],[c_0_8383]), ['final']). 4.46/4.74 cnf(c_0_13497, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[c_0_8384, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13498, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_4650]), ['final']). 4.46/4.74 cnf(c_0_13499, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))), inference(split_conjunct,[status(thm)],[c_0_5921]), ['final']). 4.46/4.74 cnf(c_0_13500, plain, (X2=c_List_Olist_ONil(X1)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olistrel(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8385]), ['final']). 4.46/4.74 cnf(c_0_13501, plain, (X2=c_List_Olist_ONil(X1)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olistrel(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8386]), ['final']). 4.46/4.74 cnf(c_0_13502, plain, (c_List_Olinorder__class_Osort__key(X2,X1,X3,hAPP(c_List_Ofilter(X2,X4),X5))=hAPP(c_List_Ofilter(X2,X4),c_List_Olinorder__class_Osort__key(X2,X1,X3,X5))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8387]), ['final']). 4.46/4.74 cnf(c_0_13503, plain, (hAPP(X1,esk169_4(X1,X2,X3,X4))=c_Groups_Ozero__class_Ozero(X4)|c_Groups_Ozero__class_Ozero(X4)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X4),X1),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))|~class_Rings_Ono__zero__divisors(X4)|~class_Rings_Ocomm__semiring__1(X4)), inference(split_conjunct,[status(thm)],[c_0_7970]), ['final']). 4.46/4.74 cnf(c_0_13504, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~c_Nat__Transfer_Onat__set(X1)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8388]), ['final']). 4.46/4.74 cnf(c_0_13505, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_8389]), ['final']). 4.46/4.74 cnf(c_0_13506, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Int_OMin),X1)=c_Int_OMin|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8390, c_0_4609]), c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_13507, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),esk121_3(X3,X2,X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))), inference(split_conjunct,[status(thm)],[c_0_8273]), ['final']). 4.46/4.74 cnf(c_0_13508, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8391]), ['final']). 4.46/4.74 cnf(c_0_13509, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8392]), ['final']). 4.46/4.74 cnf(c_0_13510, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_List_Oappend(X1),X3),c_List_Obutlast(X1,X2))=c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8393]), ['final']). 4.46/4.74 cnf(c_0_13511, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk69_2(X2,X1)),esk68_2(X2,X1))=X2|X2=c_List_Olist_ONil(X1)|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5314]), ['final']). 4.46/4.74 cnf(c_0_13512, plain, (hAPP(c_Set_Oimage(X1,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_8394]), ['final']). 4.46/4.74 cnf(c_0_13513, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Obutlast(X1,X2))=c_List_Obutlast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5964]), ['final']). 4.46/4.74 cnf(c_0_13514, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,esk199_3(X2,X1,X3)),X3)))|~hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7757]), ['final']). 4.46/4.74 cnf(c_0_13515, plain, (hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,esk487_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))), inference(split_conjunct,[status(thm)],[c_0_7171]), ['final']). 4.46/4.74 cnf(c_0_13516, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OInf__fin(X1,X2))=X3|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8395]), ['final']). 4.46/4.74 cnf(c_0_13517, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,X2))=X3|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8396]), ['final']). 4.46/4.74 cnf(c_0_13518, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8397, c_0_4448]), c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_13519, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8398]), ['final']). 4.46/4.74 cnf(c_0_13520, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8399]), ['final']). 4.46/4.74 cnf(c_0_13521, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))=c_List_Olist_ONil(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[c_0_8400, c_0_5884]), ['final']). 4.46/4.74 cnf(c_0_13522, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X4))), inference(split_conjunct,[status(thm)],[c_0_6764]), ['final']). 4.46/4.74 cnf(c_0_13523, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X4))), inference(split_conjunct,[status(thm)],[c_0_6769]), ['final']). 4.46/4.74 cnf(c_0_13524, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk262_4(X2,X3,X4,X1)),X2))|c_Fun_Oinj__on(X1,X4,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8401]), ['final']). 4.46/4.74 cnf(c_0_13525, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk261_4(X2,X3,X4,X1)),X2))|c_Fun_Oinj__on(X1,X4,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8401]), ['final']). 4.46/4.74 cnf(c_0_13526, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Nat_OSuc,X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8402]), ['final']). 4.46/4.74 cnf(c_0_13527, plain, (hAPP(X4,X5)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)|~hBOOL(hAPP(hAPP(c_member(X2),X5),X3))), inference(split_conjunct,[status(thm)],[c_0_7994]), ['final']). 4.46/4.74 cnf(c_0_13528, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))), inference(split_conjunct,[status(thm)],[c_0_8403]), ['final']). 4.46/4.74 cnf(c_0_13529, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_8404]), ['final']). 4.46/4.74 cnf(c_0_13530, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1))),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(er,[status(thm)],[c_0_8405]), ['final']). 4.46/4.74 cnf(c_0_13531, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(X1,esk91_3(X2,X3,X1)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_7057]), ['final']). 4.46/4.74 cnf(c_0_13532, plain, (hBOOL(hAPP(X1,esk113_3(X1,X2,X3)))|hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8226]), ['final']). 4.46/4.74 cnf(c_0_13533, plain, (hAPP(X1,esk92_3(X1,X2,X3))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8406, c_0_4836]), c_0_4836]), ['final']). 4.46/4.74 cnf(c_0_13534, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_8407]), ['final']). 4.46/4.74 cnf(c_0_13535, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_8408]), ['final']). 4.46/4.74 cnf(c_0_13536, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_8409]), ['final']). 4.46/4.74 cnf(c_0_13537, plain, (hBOOL(hAPP(hAPP(c_member(X3),X4),c_Map_Oran(X5,X3,X1)))|hAPP(X1,X2)!=hAPP(c_Option_Ooption_OSome(X3),X4)), inference(split_conjunct,[status(thm)],[c_0_8410]), ['final']). 4.46/4.74 cnf(c_0_13538, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Wellfounded_Oless__than))), inference(split_conjunct,[status(thm)],[c_0_7832]), ['final']). 4.46/4.74 cnf(c_0_13539, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),c_List_Olist_ONil(X2))=hAPP(hAPP(c_List_Olist_OCons(X2),X4),c_List_Olist_ONil(X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8411]), ['final']). 4.46/4.74 cnf(c_0_13540, plain, (c_Finite__Set_Ofun__left__comm(X4,X2,hAPP(hAPP(c_COMBB(X1,tc_fun(X2,X2),X4),X3),X5))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8412]), ['final']). 4.46/4.74 cnf(c_0_13541, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|c_List_Oremove1(X1,X2,X3)=X3), inference(split_conjunct,[status(thm)],[c_0_8413]), ['final']). 4.46/4.74 cnf(c_0_13542, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_8414]), ['final']). 4.46/4.74 cnf(c_0_13543, plain, (c_Finite__Set_Ofun__left__comm__idem(X4,X2,hAPP(hAPP(c_COMBB(X1,tc_fun(X2,X2),X4),X3),X5))|~c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8415]), ['final']). 4.46/4.74 cnf(c_0_13544, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2,X1)),hAPP(c_Relation_Oconverse(X1,X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_8416]), ['final']). 4.46/4.74 cnf(c_0_13545, plain, (hBOOL(hAPP(X1,esk20_3(X1,X2,X3)))|c_List_Olist__ex1(X2,X1,c_Enum_Oenum__class_Oenum(X2))|~hBOOL(hAPP(X1,X3))|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_8417]), ['final']). 4.46/4.74 cnf(c_0_13546, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8418]), ['final']). 4.46/4.74 cnf(c_0_13547, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Oring__char__0(X1)|~hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(X1)),c_Int_Oring__1__class_OInts(X1)))), inference(er,[status(thm)],[c_0_8419]), ['final']). 4.46/4.74 cnf(c_0_13548, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(X4,X2)=hAPP(c_Fun_Ooverride__on(X1,X5,X4,X6,X3),X2)), inference(split_conjunct,[status(thm)],[c_0_8420]), ['final']). 4.46/4.74 cnf(c_0_13549, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X3,X4))))), inference(split_conjunct,[status(thm)],[c_0_8421]), ['final']). 4.46/4.74 cnf(c_0_13550, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X4,X3))))), inference(split_conjunct,[status(thm)],[c_0_8422]), ['final']). 4.46/4.74 cnf(c_0_13551, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(c_COMBK(X1,X2),c_Groups_Oone__class_Oone(X1))),X3)=c_Groups_Oone__class_Oone(X1)|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_8423]), ['final']). 4.46/4.74 cnf(c_0_13552, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8418]), ['final']). 4.46/4.74 cnf(c_0_13553, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(c_COMBK(X1,X2),c_Groups_Ozero__class_Ozero(X1))),X3)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8424]), ['final']). 4.46/4.74 cnf(c_0_13554, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_OtakeWhile(X1,X4,X3))))), inference(split_conjunct,[status(thm)],[c_0_8425]), ['final']). 4.46/4.74 cnf(c_0_13555, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7791]), ['final']). 4.46/4.74 cnf(c_0_13556, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7792]), ['final']). 4.46/4.74 cnf(c_0_13557, plain, (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X4,tc_HOL_Obool)),X3),X1),X2))|~hBOOL(hAPP(hAPP(X1,esk235_5(X2,X1,X3,X4,X5)),X2))), inference(split_conjunct,[status(thm)],[c_0_7717]), ['final']). 4.46/4.74 cnf(c_0_13558, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_8426, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_13559, plain, (X1=c_List_Olist_ONil(X2)|hBOOL(hAPP(hAPP(c_member(X2),hAPP(c_List_Ohd(X2),X1)),hAPP(c_List_Oset(X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_8427]), ['final']). 4.46/4.74 cnf(c_0_13560, plain, (c_List_Oremdups(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=c_List_Oremdups(X1,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7746]), ['final']). 4.46/4.74 cnf(c_0_13561, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_8428]), ['final']). 4.46/4.74 cnf(c_0_13562, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),hAPP(c_List_Oset(tc_Nat_Onat),X2)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_5338]), ['final']). 4.46/4.74 cnf(c_0_13563, plain, (hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8429, c_0_7704]), c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_13564, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,X3))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X4)), inference(rw,[status(thm)],[c_0_8430, c_0_5580]), ['final']). 4.46/4.74 cnf(c_0_13565, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),X4)!=c_Option_Ooption_ONone(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))))), inference(rw,[status(thm)],[c_0_8431, c_0_5275]), ['final']). 4.46/4.74 cnf(c_0_13566, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Relation_OId__on(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8432]), ['final']). 4.46/4.74 cnf(c_0_13567, plain, (X1=hAPP(X2,esk367_4(X3,X2,X4,X1))|~hBOOL(hAPP(hAPP(c_member(X5),X1),hAPP(c_Set_Oimage(X4,X5,X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_7956]), ['final']). 4.46/4.74 cnf(c_0_13568, plain, (X3=X2|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_8433]), ['final']). 4.46/4.74 cnf(c_0_13569, plain, (hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Map_Odom(X5,X3,X1))=c_Map_Odom(X5,X3,X1)|hAPP(X1,X2)!=hAPP(c_Option_Ooption_OSome(X3),X4)), inference(split_conjunct,[status(thm)],[c_0_8434]), ['final']). 4.46/4.74 cnf(c_0_13570, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|X3=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_5917]), ['final']). 4.46/4.74 cnf(c_0_13571, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4))=X4), inference(split_conjunct,[status(thm)],[c_0_8435]), ['final']). 4.46/4.74 cnf(c_0_13572, plain, (hAPP(X4,X2)=hAPP(c_Map_Omap__add(X1,X3,X5,X4),X2)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_8436]), ['final']). 4.46/4.74 cnf(c_0_13573, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_7878]), ['final']). 4.46/4.74 cnf(c_0_13574, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7879]), ['final']). 4.46/4.74 cnf(c_0_13575, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7884]), ['final']). 4.46/4.74 cnf(c_0_13576, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8021]), ['final']). 4.46/4.74 cnf(c_0_13577, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8026]), ['final']). 4.46/4.74 cnf(c_0_13578, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8023]), ['final']). 4.46/4.74 cnf(c_0_13579, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8027]), ['final']). 4.46/4.74 cnf(c_0_13580, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X3,X2),X4),X5)))|~hBOOL(hAPP(X1,esk514_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_8437]), ['final']). 4.46/4.74 cnf(c_0_13581, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7886]), ['final']). 4.46/4.74 cnf(c_0_13582, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7890]), ['final']). 4.46/4.74 cnf(c_0_13583, plain, (esk493_3(X3,X4,X1)=X2|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X4,X2))|~c_List_Olist__ex1(X1,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_7265]), ['final']). 4.46/4.74 cnf(c_0_13584, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8022]), ['final']). 4.46/4.74 cnf(c_0_13585, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),X1)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_8438]), ['final']). 4.46/4.74 cnf(c_0_13586, plain, (X2=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_8439]), ['final']). 4.46/4.74 cnf(c_0_13587, plain, (X2=esk162_3(X3,X4,X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X4,X2))|~c_List_Olist__ex1(X1,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_7272]), ['final']). 4.46/4.74 cnf(c_0_13588, plain, (hBOOL(hAPP(hAPP(X2,X3),X5))|~c_Equiv__Relations_Oequivp(X1,X2)|~hBOOL(hAPP(hAPP(X2,X3),X4))|~hBOOL(hAPP(hAPP(X2,X4),X5))), inference(split_conjunct,[status(thm)],[c_0_8440]), ['final']). 4.46/4.74 cnf(c_0_13589, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))!=c_Groups_Osgn__class_Osgn(X1,X2)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8441]), ['final']). 4.46/4.74 cnf(c_0_13590, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_8442]), ['final']). 4.46/4.74 cnf(c_0_13591, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)))|~class_Rings_Olinordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8443]), ['final']). 4.46/4.74 cnf(c_0_13592, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_8444]), ['final']). 4.46/4.74 cnf(c_0_13593, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(c_List_Orev(X1),X4),hAPP(c_List_Orev(X2),X5))|~c_List_Olist__all2(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_8445]), ['final']). 4.46/4.74 cnf(c_0_13594, plain, (c_List_Olinorder__class_Osorted(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),esk467_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk466_2(X2,X1))))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6908]), ['final']). 4.46/4.74 cnf(c_0_13595, plain, (c_List_Olinorder__class_Osorted(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),esk191_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk192_2(X2,X1))))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8060]), ['final']). 4.46/4.74 cnf(c_0_13596, plain, (hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(hAPP(c_member(X1),esk112_3(X2,X3,X1)),esk113_3(X2,X3,X1)))|~hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_8226]), ['final']). 4.46/4.74 cnf(c_0_13597, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1)), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_8446])]), ['final']). 4.46/4.74 cnf(c_0_13598, plain, (hBOOL(hAPP(hAPP(c_member(X5),X4),c_Map_Odom(X5,X1,X3)))|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8447]), ['final']). 4.46/4.74 cnf(c_0_13599, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8448]), ['final']). 4.46/4.74 cnf(c_0_13600, plain, (hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))=X2|hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_8449]), ['final']). 4.46/4.74 cnf(c_0_13601, plain, (hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),hAPP(X3,X5))=X5|~c_Fun_Oinj__on(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))), inference(split_conjunct,[status(thm)],[c_0_8450]), ['final']). 4.46/4.74 cnf(c_0_13602, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|epred1_3(X2,X1,X3)|~hBOOL(hAPP(X2,esk532_3(X3,X1,X2)))|~hBOOL(hAPP(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.74 cnf(c_0_13603, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|epred1_3(X1,X3,X2)|~hBOOL(hAPP(X1,esk534_3(X2,X3,X1)))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.74 cnf(c_0_13604, plain, (X1=hAPP(hAPP(c_List_Onth(X2),X3),esk111_3(X3,X1,X2))|~hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_List_Oset(X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_5383]), ['final']). 4.46/4.74 cnf(c_0_13605, plain, (X2=c_List_Oremove1(X1,X3,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8451]), ['final']). 4.46/4.74 cnf(c_0_13606, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[c_0_8452, c_0_4443]), ['final']). 4.46/4.74 cnf(c_0_13607, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8453]), ['final']). 4.46/4.74 cnf(c_0_13608, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk96_3(X2,X3,X1)),X2))|hBOOL(hAPP(c_Predicate_OPowp(X1,X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8454]), ['final']). 4.46/4.74 cnf(c_0_13609, plain, (X3=X1|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8455]), ['final']). 4.46/4.74 cnf(c_0_13610, plain, (hAPP(c_Option_Ooption_OSome(X1),esk431_5(X2,X3,X4,X5,X1))=X3|hAPP(hAPP(c_Option_Omap(X1,X5),X4),X3)!=hAPP(c_Option_Ooption_OSome(X5),X2)), inference(split_conjunct,[status(thm)],[c_0_8456]), ['final']). 4.46/4.74 cnf(c_0_13611, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8457]), ['final']). 4.46/4.74 cnf(c_0_13612, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8458]), ['final']). 4.46/4.74 cnf(c_0_13613, plain, (hBOOL(hAPP(X1,esk178_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X4),X5),X2))|~hBOOL(hAPP(X1,X5))), inference(split_conjunct,[status(thm)],[c_0_6573]), ['final']). 4.46/4.74 cnf(c_0_13614, plain, (hBOOL(hAPP(X1,esk178_4(X1,X2,X3,X4)))|~hBOOL(hAPP(X1,X5))|~hBOOL(hAPP(hAPP(c_member(X4),X5),X3))), inference(split_conjunct,[status(thm)],[c_0_6573]), ['final']). 4.46/4.74 cnf(c_0_13615, plain, (c_Fun_Oinj__on(X1,X2,X3,hAPP(c_List_Oset(X1),X4))|~hBOOL(hAPP(c_List_Odistinct(X2),hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_7969]), ['final']). 4.46/4.74 cnf(c_0_13616, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk236_3(X3,X1,X2))))|~c_List_Olist__ex(X2,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_8065]), ['final']). 4.46/4.74 cnf(c_0_13617, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8459]), ['final']). 4.46/4.74 cnf(c_0_13618, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk100_1(X1)))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))), inference(split_conjunct,[status(thm)],[c_0_8154]), ['final']). 4.46/4.74 cnf(c_0_13619, plain, (hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,esk516_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))), inference(split_conjunct,[status(thm)],[c_0_7187]), ['final']). 4.46/4.74 cnf(c_0_13620, plain, (c_Relation_Osingle__valued(X1,X1,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2))|~c_Relation_Osingle__valued(X1,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8460]), ['final']). 4.46/4.74 cnf(c_0_13621, plain, (hAPP(X1,esk261_4(X2,X1,X3,X4))=hAPP(X1,esk262_4(X2,X1,X3,X4))|c_Fun_Oinj__on(X4,X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8401]), ['final']). 4.46/4.74 cnf(c_0_13622, plain, (hAPP(c_Nat_OSuc,X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8461]), ['final']). 4.46/4.74 cnf(c_0_13623, plain, (X1=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk385_1(X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_8462]), ['final']). 4.46/4.74 cnf(c_0_13624, plain, (c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_8463]), ['final']). 4.46/4.74 cnf(c_0_13625, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_7907]), ['final']). 4.46/4.74 cnf(c_0_13626, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_8464]), ['final']). 4.46/4.74 cnf(c_0_13627, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X3)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1)), inference(er,[status(thm)],[c_0_8465]), ['final']). 4.46/4.74 cnf(c_0_13628, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,X3))))), inference(split_conjunct,[status(thm)],[c_0_8466]), ['final']). 4.46/4.74 cnf(c_0_13629, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk47_3(X2,X3,X1)),X3)),X2))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7998]), ['final']). 4.46/4.74 cnf(c_0_13630, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5207]), ['final']). 4.46/4.74 cnf(c_0_13631, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),esk461_3(X3,X2,X1))))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_8001]), ['final']). 4.46/4.74 cnf(c_0_13632, plain, (c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~c_Fun_Oinj__on(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8467]), ['final']). 4.46/4.74 cnf(c_0_13633, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Olinorder__class_Osort__key(X2,X1,X3,X4)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8468]), ['final']). 4.46/4.74 cnf(c_0_13634, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2)=c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_List_Oset(X1),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8469]), ['final']). 4.46/4.74 cnf(c_0_13635, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2)=c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_List_Oset(X1),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8470]), ['final']). 4.46/4.74 cnf(c_0_13636, plain, (~class_Rings_Olinordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_8471]), ['final']). 4.46/4.74 cnf(c_0_13637, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),X2)|~class_Rings_Ocomm__ring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8472]), ['final']). 4.46/4.74 cnf(c_0_13638, plain, (c_Equiv__Relations_Oequiv(X1,hAPP(c_Relation_ODomain(X1,X1),X2),X2)|hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X2)),X2)!=X2), inference(er,[status(thm)],[c_0_8473]), ['final']). 4.46/4.74 cnf(c_0_13639, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X1),X6),X2),X3))|~hBOOL(hAPP(hAPP(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8474]), ['final']). 4.46/4.74 cnf(c_0_13640, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk490_1(X1)),hAPP(c_List_Oset(tc_Nat_Onat),X1)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_8475]), ['final']). 4.46/4.74 cnf(c_0_13641, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1)))), inference(er,[status(thm)],[c_0_8476]), ['final']). 4.46/4.74 cnf(c_0_13642, plain, (hAPP(c_List_Ofilter(X1,X2),c_List_Oremove1(X1,X3,X4))=hAPP(c_List_Ofilter(X1,X2),X4)|hBOOL(hAPP(X2,X3))), inference(rw,[status(thm)],[c_0_8477, c_0_8478]), ['final']). 4.46/4.74 cnf(c_0_13643, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X6),X1),X2),X3))|~hBOOL(hAPP(hAPP(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8474]), ['final']). 4.46/4.74 cnf(c_0_13644, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_7950]), ['final']). 4.46/4.74 cnf(c_0_13645, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk53_1(X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_8283]), ['final']). 4.46/4.74 cnf(c_0_13646, plain, (X4=X3|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_8479]), ['final']). 4.46/4.74 cnf(c_0_13647, plain, (~c_Wellfounded_Oacyclic(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))), inference(rw,[status(thm)],[c_0_8480, c_0_5266]), ['final']). 4.46/4.74 cnf(c_0_13648, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_8103]), ['final']). 4.46/4.74 cnf(c_0_13649, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8481]), ['final']). 4.46/4.74 cnf(c_0_13650, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_8482]), ['final']). 4.46/4.74 cnf(c_0_13651, plain, (X2=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))), inference(rw,[status(thm)],[c_0_8483, c_0_5689]), ['final']). 4.46/4.74 cnf(c_0_13652, plain, (hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))))), inference(split_conjunct,[status(thm)],[c_0_7317]), ['final']). 4.46/4.74 cnf(c_0_13653, plain, (X4=hAPP(hAPP(c_List_Onth(X2),X1),X3)|X1!=hAPP(hAPP(c_List_Olist__update(X2,X1),X3),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))), inference(split_conjunct,[status(thm)],[c_0_8484]), ['final']). 4.46/4.74 cnf(c_0_13654, plain, (c_Relation_Ototal__on(X1,X3,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk131_3(X2,X3,X1)),esk130_3(X2,X3,X1))),X2))), inference(split_conjunct,[status(thm)],[c_0_6336]), ['final']). 4.46/4.74 cnf(c_0_13655, plain, (X1=c_List_Olist_ONil(X2)|hAPP(X3,c_List_Olast(X2,X1))=c_List_Olast(X4,hAPP(hAPP(c_List_Omap(X2,X4),X3),X1))), inference(split_conjunct,[status(thm)],[c_0_8485]), ['final']). 4.46/4.74 cnf(c_0_13656, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_8486]), ['final']). 4.46/4.74 cnf(c_0_13657, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_8487]), ['final']). 4.46/4.74 cnf(c_0_13658, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_8488]), ['final']). 4.46/4.74 cnf(c_0_13659, plain, (hAPP(c_Finite__Set_Ocard(X2),hAPP(c_Set_Oimage(X1,X2,X3),X4))=hAPP(c_Finite__Set_Ocard(X1),X4)|~c_Fun_Oinj__on(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8489]), ['final']). 4.46/4.74 cnf(c_0_13660, plain, (c_Relation_Ototal__on(X1,X3,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk130_3(X2,X3,X1)),esk131_3(X2,X3,X1))),X2))), inference(split_conjunct,[status(thm)],[c_0_6336]), ['final']). 4.46/4.74 cnf(c_0_13661, plain, (c_Relation_Ototal__on(X1,X2,X3)|~c_Relation_Ototal__on(X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))), inference(rw,[status(thm)],[c_0_8490, c_0_5689]), ['final']). 4.46/4.74 cnf(c_0_13662, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))), inference(rw,[status(thm)],[c_0_8491, c_0_5266]), ['final']). 4.46/4.74 cnf(c_0_13663, plain, (c_Relation_Osingle__valued(X1,X4,hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X4),X3),X5))|~c_Relation_Osingle__valued(X1,X2,X3)|~c_Relation_Osingle__valued(X2,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_8492]), ['final']). 4.46/4.74 cnf(c_0_13664, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X1,X3))=c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8493]), ['final']). 4.46/4.74 cnf(c_0_13665, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))), inference(rw,[status(thm)],[c_0_8494, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_13666, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))), inference(rw,[status(thm)],[c_0_8495, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_13667, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))), inference(rw,[status(thm)],[c_0_8496, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_13668, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))), inference(rw,[status(thm)],[c_0_8497, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_13669, plain, (c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8498]), ['final']). 4.46/4.74 cnf(c_0_13670, plain, (X1=X2|X2=X3|hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_8499]), ['final']). 4.46/4.74 cnf(c_0_13671, plain, (X3=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_8500]), ['final']). 4.46/4.74 cnf(c_0_13672, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))|~class_Enum_Oenum(X1)|~class_Orderings_Oorder(X2)), inference(split_conjunct,[status(thm)],[c_0_5192]), ['final']). 4.46/4.74 cnf(c_0_13673, plain, (c_Random_Ominus__shift(X3,X1,X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X3),X1)),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8501]), ['final']). 4.46/4.74 cnf(c_0_13674, plain, (c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X2,X1),X3)=c_Lazy__Sequence_Oproduct(X2,X1,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X2,X3),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X1,X3))|~class_Lazy__Sequence_Osmall__lazy(X1)|~class_Lazy__Sequence_Osmall__lazy(X2)), inference(split_conjunct,[status(thm)],[c_0_8502]), ['final']). 4.46/4.74 cnf(c_0_13675, plain, (c_List_Olist_ONil(X1)=X2|hBOOL(hAPP(hAPP(c_member(X1),c_List_Olast(X1,X2)),hAPP(c_List_Oset(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_8503]), ['final']). 4.46/4.74 cnf(c_0_13676, plain, (X1=X2|X2=X3|hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_8499]), ['final']). 4.46/4.74 cnf(c_0_13677, plain, (X3=X2|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))|~c_List_Olinorder__class_Osorted(X1,X3)|~hBOOL(hAPP(c_List_Odistinct(X1),X3))|hAPP(c_List_Oset(X1),X3)!=hAPP(c_List_Oset(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_8504]), ['final']). 4.46/4.74 cnf(c_0_13678, plain, (hBOOL(hAPP(X1,esk404_4(X2,X3,X1,X4)))|c_FunDef_OTHE__default(X3,X2,X1)=c_HOL_OThe(X3,X1)|~hBOOL(hAPP(X1,X4))), inference(split_conjunct,[status(thm)],[c_0_8505]), ['final']). 4.46/4.74 cnf(c_0_13679, plain, (X1=c_List_Olist_ONil(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))), inference(split_conjunct,[status(thm)],[c_0_8506]), ['final']). 4.46/4.74 cnf(c_0_13680, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),esk190_3(X3,X2,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(rw,[status(thm)],[c_0_8507, c_0_6164]), ['final']). 4.46/4.74 cnf(c_0_13681, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),esk338_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_7935]), ['final']). 4.46/4.74 cnf(c_0_13682, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_7585]), ['final']). 4.46/4.74 cnf(c_0_13683, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_7585]), ['final']). 4.46/4.74 cnf(c_0_13684, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_Olinorder__class_Osort__key(X2,X1,X4,X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8508]), ['final']). 4.46/4.74 cnf(c_0_13685, plain, (hBOOL(hAPP(X1,X2))|c_List_Olist__ex1(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))|~c_List_Olist__ex1(X3,X1,X4)), inference(split_conjunct,[status(thm)],[c_0_5229]), ['final']). 4.46/4.74 cnf(c_0_13686, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(c_List_Orev(X1),X4),X5)|~c_List_Olist__all2(X1,X2,X3,X4,hAPP(c_List_Orev(X2),X5))), inference(split_conjunct,[status(thm)],[c_0_8509]), ['final']). 4.46/4.74 cnf(c_0_13687, plain, (c_List_Olist__all2(X1,X2,X3,X4,hAPP(c_List_Orev(X2),X5))|~c_List_Olist__all2(X1,X2,X3,hAPP(c_List_Orev(X1),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_8509]), ['final']). 4.46/4.74 cnf(c_0_13688, plain, (c_Wellfounded_Owf(tc_prod(X3,X1),c_Recdef_Osame__fst(X3,X1,X4,X2))|~c_Wellfounded_Owf(X1,hAPP(X2,esk294_4(X3,X2,X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_8064]), ['final']). 4.46/4.74 cnf(c_0_13689, plain, (c_Hoare__Mirabelle_Otriple__valid(X1,X2,X5)|~c_Hoare__Mirabelle_Otriple__valid(X1,X2,esk346_4(X3,X4,X1,X2))|~hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X5),X3))|~c_Hoare__Mirabelle_Ohoare__valids(X1,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_7303]), ['final']). 4.46/4.74 cnf(c_0_13690, plain, (c_Big__Operators_Olinorder__class_OMax(X1,X3)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk318_3(X2,X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7819]), ['final']). 4.46/4.74 cnf(c_0_13691, plain, (hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),esk348_3(X2,X3,X1)),X2))|c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_7303]), ['final']). 4.46/4.74 cnf(c_0_13692, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Odivision__ring(X1)), inference(er,[status(thm)],[c_0_8510]), ['final']). 4.46/4.74 cnf(c_0_13693, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X2))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8511]), ['final']). 4.46/4.74 cnf(c_0_13694, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))|~hBOOL(hAPP(X2,esk206_2(X1,X2)))), inference(rw,[status(thm)],[c_0_8512, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13695, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk206_2(X1,X2))=X1|hBOOL(hAPP(X2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))|~hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_8513, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13696, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk98_1(X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8514]), ['final']). 4.46/4.74 cnf(c_0_13697, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),c_List_Olists(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_7238]), ['final']). 4.46/4.74 cnf(c_0_13698, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),c_List_Oreplicate(X3,X5,X2))))|~hBOOL(hAPP(X1,X4))), inference(split_conjunct,[status(thm)],[c_0_7351]), ['final']). 4.46/4.74 cnf(c_0_13699, plain, (hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),c_List_Oreplicate(X3,X5,X2))))), inference(split_conjunct,[status(thm)],[c_0_7354]), ['final']). 4.46/4.74 cnf(c_0_13700, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7990]), ['final']). 4.46/4.74 cnf(c_0_13701, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),esk423_1(X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8515]), ['final']). 4.46/4.74 cnf(c_0_13702, plain, (hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=X5|~c_Typedef_Otype__definition(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_8516]), ['final']). 4.46/4.74 cnf(c_0_13703, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(rw,[status(thm)],[c_0_8517, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_13704, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(c_Divides_OnegateSnd,X3)))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_8518]), ['final']). 4.46/4.74 cnf(c_0_13705, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7995]), ['final']). 4.46/4.74 cnf(c_0_13706, plain, (c_Big__Operators_Olinorder__class_OMin(X1,X3)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk343_3(X2,X3,X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7822]), ['final']). 4.46/4.74 cnf(c_0_13707, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7996]), ['final']). 4.46/4.74 cnf(c_0_13708, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_7997]), ['final']). 4.46/4.74 cnf(c_0_13709, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X3)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Odivision__ring(X1)), inference(er,[status(thm)],[c_0_8519]), ['final']). 4.46/4.74 cnf(c_0_13710, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8520]), ['final']). 4.46/4.74 cnf(c_0_13711, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8521]), ['final']). 4.46/4.74 cnf(c_0_13712, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8522]), ['final']). 4.46/4.74 cnf(c_0_13713, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8188]), ['final']). 4.46/4.74 cnf(c_0_13714, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8189]), ['final']). 4.46/4.74 cnf(c_0_13715, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8523]), ['final']). 4.46/4.74 cnf(c_0_13716, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))), inference(split_conjunct,[status(thm)],[c_0_8096]), ['final']). 4.46/4.74 cnf(c_0_13717, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8524]), ['final']). 4.46/4.74 cnf(c_0_13718, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8190]), ['final']). 4.46/4.74 cnf(c_0_13719, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8191]), ['final']). 4.46/4.74 cnf(c_0_13720, plain, (X4=X5|hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)!=hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_8525]), ['final']). 4.46/4.74 cnf(c_0_13721, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1)), inference(er,[status(thm)],[c_0_8526]), ['final']). 4.46/4.74 cnf(c_0_13722, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk328_2(X2,X1)))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5944]), ['final']). 4.46/4.74 cnf(c_0_13723, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk528_5(X3,X4,X5,X6,X1))))|~hBOOL(hAPP(X4,X2))|hAPP(hAPP(c_List_Olist_OCons(X1),X6),X5)!=hAPP(c_List_Ofilter(X1,X4),X3)), inference(split_conjunct,[status(thm)],[c_0_5072]), ['final']). 4.46/4.74 cnf(c_0_13724, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk152_5(X3,X4,X5,X6,X1))))|~hBOOL(hAPP(X6,X2))|hAPP(c_List_Ofilter(X1,X6),X5)!=hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_5090]), ['final']). 4.46/4.74 cnf(c_0_13725, plain, (hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk415_4(X4,X1,X3,X2))))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_7225]), ['final']). 4.46/4.74 cnf(c_0_13726, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=X4|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_8527]), ['final']). 4.46/4.74 cnf(c_0_13727, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk148_2(X2,X1)),esk147_2(X2,X1)))|c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7127]), ['final']). 4.46/4.74 cnf(c_0_13728, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_8528]), ['final']). 4.46/4.74 cnf(c_0_13729, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3)))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8066]), ['final']). 4.46/4.74 cnf(c_0_13730, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_8072]), ['final']). 4.46/4.74 cnf(c_0_13731, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8529]), ['final']). 4.46/4.74 cnf(c_0_13732, plain, (hAPP(hAPP(X3,X4),hAPP(hAPP(X3,X4),X5))=hAPP(hAPP(X3,X4),X5)|~c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8530]), ['final']). 4.46/4.74 cnf(c_0_13733, plain, (c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=X4|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))!=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))), inference(split_conjunct,[status(thm)],[c_0_8531]), ['final']). 4.46/4.74 cnf(c_0_13734, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3)))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8068]), ['final']). 4.46/4.74 cnf(c_0_13735, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))|~c_Wellfounded_Owf(X1,X2)), inference(rw,[status(thm)],[c_0_8532, c_0_5266]), ['final']). 4.46/4.74 cnf(c_0_13736, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,esk91_3(X1,X3,X2)))|~hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))), inference(split_conjunct,[status(thm)],[c_0_7057]), ['final']). 4.46/4.74 cnf(c_0_13737, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk176_2(X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2))), inference(split_conjunct,[status(thm)],[c_0_7877]), ['final']). 4.46/4.74 cnf(c_0_13738, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_List_Oset(X2),c_List_Oreplicate(X2,X1,X3))=hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_8533]), ['final']). 4.46/4.74 cnf(c_0_13739, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8534]), ['final']). 4.46/4.74 cnf(c_0_13740, plain, (esk407_2(hAPP(c_List_Oset(X1),X2),X1)=X2|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_8535]), c_0_8536])]), ['final']). 4.46/4.74 cnf(c_0_13741, plain, (X6=X7|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X6))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X7))), inference(split_conjunct,[status(thm)],[c_0_8537]), ['final']). 4.46/4.74 cnf(c_0_13742, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8538]), ['final']). 4.46/4.74 cnf(c_0_13743, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8539]), ['final']). 4.46/4.74 cnf(c_0_13744, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X3,X5),X2)))), inference(split_conjunct,[status(thm)],[c_0_8540]), ['final']). 4.46/4.74 cnf(c_0_13745, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),X2))|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8541]), ['final']). 4.46/4.74 cnf(c_0_13746, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8130]), ['final']). 4.46/4.74 cnf(c_0_13747, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8131]), ['final']). 4.46/4.74 cnf(c_0_13748, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_8542]), ['final']). 4.46/4.74 cnf(c_0_13749, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8543]), ['final']). 4.46/4.74 cnf(c_0_13750, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[c_0_8544, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13751, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8147]), ['final']). 4.46/4.74 cnf(c_0_13752, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8148]), ['final']). 4.46/4.74 cnf(c_0_13753, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))!=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3),X4)), inference(rw,[status(thm)],[c_0_8545, c_0_4517]), ['final']). 4.46/4.74 cnf(c_0_13754, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X1)),X2))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_HOL_Obool,X1),X2),c_Option_Ooption_OSome(X1))))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_7521]), ['final']). 4.46/4.74 cnf(c_0_13755, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X1),X2),X3)))|~c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X1),X2),X3)))|~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8546, c_0_5580]), c_0_5580]), c_0_5580]), ['final']). 4.46/4.74 cnf(c_0_13756, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_8547]), ['final']). 4.46/4.74 cnf(c_0_13757, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))|~hBOOL(hAPP(X2,esk187_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_5209]), ['final']). 4.46/4.74 cnf(c_0_13758, plain, (hAPP(hAPP(c_List_Onth(X3),c_List_Oreplicate(X3,X2,X4)),X1)=X4|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8548]), ['final']). 4.46/4.74 cnf(c_0_13759, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))|c_List_Olist_ONil(tc_Nat_Onat)!=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))), inference(rw,[status(thm)],[c_0_8549, c_0_4517]), ['final']). 4.46/4.74 cnf(c_0_13760, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_5329]), ['final']). 4.46/4.74 cnf(c_0_13761, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))|~class_Rings_Ocomm__ring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8550]), ['final']). 4.46/4.74 cnf(c_0_13762, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8551]), ['final']). 4.46/4.74 cnf(c_0_13763, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8552]), ['final']). 4.46/4.74 cnf(c_0_13764, plain, (hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[c_0_8553, c_0_6178]), ['final']). 4.46/4.74 cnf(c_0_13765, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk524_1(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_8554]), ['final']). 4.46/4.74 cnf(c_0_13766, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|c_Groups_Ozero__class_Ozero(X2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3))|~class_Rings_Olinordered__ring__strict(X2)), inference(split_conjunct,[status(thm)],[c_0_5329]), ['final']). 4.46/4.74 cnf(c_0_13767, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8555]), ['final']). 4.46/4.74 cnf(c_0_13768, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8556]), ['final']). 4.46/4.74 cnf(c_0_13769, plain, (X3=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X3,X4))))), inference(split_conjunct,[status(thm)],[c_0_8557]), ['final']). 4.46/4.74 cnf(c_0_13770, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=X2|~class_Groups_Oabs__if(X1)), inference(split_conjunct,[status(thm)],[c_0_8558]), ['final']). 4.46/4.74 cnf(c_0_13771, plain, (c_Partial__Function_Oflat__lub(X1,X3,X2)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_5143]), ['final']). 4.46/4.74 cnf(c_0_13772, plain, (c_List_Olist__ex(X2,X1,X3)|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_8065]), ['final']). 4.46/4.74 cnf(c_0_13773, plain, (c_Hoare__Mirabelle_Otriple__valid(X1,X2,X4)|~c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(c_Nat_OSuc,X2),esk151_3(X2,X3,X1))|~hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7593]), ['final']). 4.46/4.74 cnf(c_0_13774, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8559, c_0_4436]), c_0_7958]), c_0_4834]), ['final']). 4.46/4.74 cnf(c_0_13775, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8560, c_0_4436]), c_0_7952]), ['final']). 4.46/4.74 cnf(c_0_13776, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8561]), ['final']). 4.46/4.74 cnf(c_0_13777, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),X1))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),X1),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8562, c_0_5554])]), ['final']). 4.46/4.74 cnf(c_0_13778, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_8563]), ['final']). 4.46/4.74 cnf(c_0_13779, plain, (hBOOL(hAPP(X2,X4))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_8041]), ['final']). 4.46/4.74 cnf(c_0_13780, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3)=c_Divides_Odiv__class_Omod(X1,X2,X3)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8564]), ['final']). 4.46/4.74 cnf(c_0_13781, plain, (c_Divides_Odiv__class_Omod(X1,X2,X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2),X3)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8565]), ['final']). 4.46/4.74 cnf(c_0_13782, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X1,hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,X2)))|hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),esk283_2(X2,X1)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))|~hBOOL(hAPP(c_Com_OWT,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8566, c_0_5580]), c_0_5555])]), ['final']). 4.46/4.74 cnf(c_0_13783, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(X1),esk302_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7161]), ['final']). 4.46/4.74 cnf(c_0_13784, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(X1),esk300_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7164]), ['final']). 4.46/4.74 cnf(c_0_13785, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(X1),esk81_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7167]), ['final']). 4.46/4.74 cnf(c_0_13786, plain, (hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X5,X1,X4),X2),X3))|~hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(X4,X3))), inference(split_conjunct,[status(thm)],[c_0_8567]), ['final']). 4.46/4.74 cnf(c_0_13787, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(X1,esk45_3(X1,X2,X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7128]), ['final']). 4.46/4.74 cnf(c_0_13788, plain, (hBOOL(hAPP(hAPP(X1,esk453_3(X2,X1,X3)),X2))|hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8568]), ['final']). 4.46/4.74 cnf(c_0_13789, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8569]), ['final']). 4.46/4.74 cnf(c_0_13790, plain, (X3=X2|hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_8569]), ['final']). 4.46/4.74 cnf(c_0_13791, plain, (hBOOL(hAPP(hAPP(X1,esk240_3(X2,X1,X3)),X2))|hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8570]), ['final']). 4.46/4.74 cnf(c_0_13792, plain, (hBOOL(hAPP(X2,X4))|hAPP(c_List_Ofilter(X1,X2),X3)!=X3|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_8108]), ['final']). 4.46/4.74 cnf(c_0_13793, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7616]), ['final']). 4.46/4.74 cnf(c_0_13794, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk131_3(X2,X3,X1)),X3))|c_Relation_Ototal__on(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_6336]), ['final']). 4.46/4.74 cnf(c_0_13795, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk130_3(X2,X3,X1)),X3))|c_Relation_Ototal__on(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_6336]), ['final']). 4.46/4.74 cnf(c_0_13796, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8571]), ['final']). 4.46/4.74 cnf(c_0_13797, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X2))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_8572]), ['final']). 4.46/4.74 cnf(c_0_13798, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X2))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8573]), ['final']). 4.46/4.74 cnf(c_0_13799, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))=c_SMT_Oz3mod(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_8574]), ['final']). 4.46/4.74 cnf(c_0_13800, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|X3=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8575]), ['final']). 4.46/4.74 cnf(c_0_13801, plain, (X2=X3|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8576]), ['final']). 4.46/4.74 cnf(c_0_13802, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Rings_Oidom(X1)), inference(er,[status(thm)],[c_0_8577]), ['final']). 4.46/4.74 cnf(c_0_13803, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X3))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_8578]), ['final']). 4.46/4.74 cnf(c_0_13804, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X3))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8579]), ['final']). 4.46/4.74 cnf(c_0_13805, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)))|~class_Lattices_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_8580]), ['final']). 4.46/4.74 cnf(c_0_13806, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8581]), ['final']). 4.46/4.74 cnf(c_0_13807, plain, (X2=X4|~class_Orderings_Olinorder(X1)|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)!=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_8582]), ['final']). 4.46/4.74 cnf(c_0_13808, plain, (X5=X3|~class_Orderings_Olinorder(X1)|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)!=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_8583]), ['final']). 4.46/4.74 cnf(c_0_13809, plain, (~hBOOL(hAPP(hAPP(c_member(X1),esk405_5(X2,X3,X4,X5,X1)),esk406_5(X2,X3,X4,X5,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_7169]), ['final']). 4.46/4.74 cnf(c_0_13810, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)))|~class_Lattices_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_8584]), ['final']). 4.46/4.74 cnf(c_0_13811, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8585]), ['final']). 4.46/4.74 cnf(c_0_13812, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8586]), ['final']). 4.46/4.74 cnf(c_0_13813, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8587]), ['final']). 4.46/4.74 cnf(c_0_13814, plain, (~hBOOL(hAPP(hAPP(c_member(X1),esk288_5(X2,X3,X4,X5,X1)),esk289_5(X2,X3,X4,X5,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_6789]), ['final']). 4.46/4.74 cnf(c_0_13815, plain, (X6=hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),X5)|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X6))), inference(split_conjunct,[status(thm)],[c_0_8588]), ['final']). 4.46/4.74 cnf(c_0_13816, plain, (hBOOL(hAPP(c_List_Odistinct(X2),c_List_Olinorder__class_Oinsort__insert__key(X2,X1,X4,X5,X3)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_List_Odistinct(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8589]), ['final']). 4.46/4.74 cnf(c_0_13817, plain, (X1=hAPP(X2,esk431_5(X1,X3,X2,X4,X5))|hAPP(hAPP(c_Option_Omap(X5,X4),X2),X3)!=hAPP(c_Option_Ooption_OSome(X4),X1)), inference(split_conjunct,[status(thm)],[c_0_8456]), ['final']). 4.46/4.74 cnf(c_0_13818, plain, (c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1)=c_Int_OMin|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[c_0_8590, c_0_6631]), ['final']). 4.46/4.74 cnf(c_0_13819, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,esk394_1(X1)))), inference(rw,[status(thm)],[c_0_8591, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13820, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_7739]), ['final']). 4.46/4.74 cnf(c_0_13821, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2,X1),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_7739]), ['final']). 4.46/4.74 cnf(c_0_13822, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))), inference(split_conjunct,[status(thm)],[c_0_8592]), ['final']). 4.46/4.74 cnf(c_0_13823, plain, (X6=hAPP(X3,hAPP(X4,X6))|~c_Typedef_Otype__definition(X1,X2,X3,X4,X5)|~hBOOL(hAPP(hAPP(c_member(X2),X6),X5))), inference(split_conjunct,[status(thm)],[c_0_8593]), ['final']). 4.46/4.74 cnf(c_0_13824, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3))|~class_Lattices_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_8594]), ['final']). 4.46/4.74 cnf(c_0_13825, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk393_1(X1)))|hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5516]), ['final']). 4.46/4.74 cnf(c_0_13826, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_8253]), ['final']). 4.46/4.74 cnf(c_0_13827, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))), inference(split_conjunct,[status(thm)],[c_0_8255]), ['final']). 4.46/4.74 cnf(c_0_13828, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X2)),X3))|~class_Lattices_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_8594]), ['final']). 4.46/4.74 cnf(c_0_13829, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_8595]), ['final']). 4.46/4.74 cnf(c_0_13830, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|c_Option_Ooption_ONone(X4)=hAPP(c_Map_Orestrict__map(X1,X4,X5,X3),X2)), inference(split_conjunct,[status(thm)],[c_0_8596]), ['final']). 4.46/4.74 cnf(c_0_13831, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))), inference(split_conjunct,[status(thm)],[c_0_8262]), ['final']). 4.46/4.74 cnf(c_0_13832, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))), inference(rw,[status(thm)],[c_0_8597, c_0_6178]), ['final']). 4.46/4.74 cnf(c_0_13833, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X3)))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_8595]), ['final']). 4.46/4.74 cnf(c_0_13834, plain, (hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OlessThan(X4,X1,X3)))|~hBOOL(hAPP(hAPP(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8598]), ['final']). 4.46/4.74 cnf(c_0_13835, plain, (hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatMost(X4,X1,X3)))|~hBOOL(hAPP(hAPP(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8599]), ['final']). 4.46/4.74 cnf(c_0_13836, plain, (hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThan(X4,X1,X2)))|~hBOOL(hAPP(hAPP(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8600]), ['final']). 4.46/4.74 cnf(c_0_13837, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1)))), inference(split_conjunct,[status(thm)],[c_0_8601]), ['final']). 4.46/4.74 cnf(c_0_13838, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),c_Groups_Ozero__class_Ozero(X1))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber(X1)), inference(er,[status(thm)],[c_0_8602]), ['final']). 4.46/4.74 cnf(c_0_13839, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_8265]), ['final']). 4.46/4.74 cnf(c_0_13840, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))), inference(rw,[status(thm)],[c_0_8603, c_0_5134]), ['final']). 4.46/4.74 cnf(c_0_13841, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))), inference(split_conjunct,[status(thm)],[c_0_8266]), ['final']). 4.46/4.74 cnf(c_0_13842, plain, (c_List_Olist_ONil(tc_Nat_Onat)=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[c_0_8604, c_0_4517]), ['final']). 4.46/4.74 cnf(c_0_13843, plain, (hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeast(X4,X1,X2)))|~hBOOL(hAPP(hAPP(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8605]), ['final']). 4.46/4.74 cnf(c_0_13844, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X4))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~hBOOL(hAPP(hAPP(X2,X4),X3))), inference(split_conjunct,[status(thm)],[c_0_8570]), ['final']). 4.46/4.74 cnf(c_0_13845, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8606, c_0_4836]), c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13846, plain, (hAPP(c_Nat_OSuc,X2)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))), inference(split_conjunct,[status(thm)],[c_0_8607]), ['final']). 4.46/4.74 cnf(c_0_13847, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8608, c_0_5334]), c_0_5334]), ['final']). 4.46/4.74 cnf(c_0_13848, plain, (X3=c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),X3))), inference(rw,[status(thm)],[c_0_8609, c_0_6292]), ['final']). 4.46/4.74 cnf(c_0_13849, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(X1),esk24_3(X2,X3,X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7691]), ['final']). 4.46/4.74 cnf(c_0_13850, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk319_3(X2,X3,X1)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7444]), ['final']). 4.46/4.74 cnf(c_0_13851, plain, (X1=X2|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X2),X6),X1)=hAPP(X5,X1)), inference(split_conjunct,[status(thm)],[c_0_8610]), ['final']). 4.46/4.74 cnf(c_0_13852, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8611]), ['final']). 4.46/4.74 cnf(c_0_13853, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8612]), ['final']). 4.46/4.74 cnf(c_0_13854, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8613, c_0_5334]), c_0_5334]), ['final']). 4.46/4.74 cnf(c_0_13855, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk212_3(X3,X2,X1)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7445]), ['final']). 4.46/4.74 cnf(c_0_13856, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk208_3(X3,X2,X1)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7448]), ['final']). 4.46/4.74 cnf(c_0_13857, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|epred2_3(X1,X3,X2)|~hBOOL(hAPP(X1,esk537_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5124]), ['final']). 4.46/4.74 cnf(c_0_13858, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|epred2_3(X2,X1,X3)|~hBOOL(hAPP(X2,esk535_3(X3,X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_5124]), ['final']). 4.46/4.74 cnf(c_0_13859, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=X1|X2=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8614, c_0_4836]), c_0_4836]), c_0_4836]), ['final']). 4.46/4.74 cnf(c_0_13860, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8615]), ['final']). 4.46/4.74 cnf(c_0_13861, plain, (hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)!=hAPP(hAPP(c_List_Odrop(X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),c_List_OtakeWhile(X3,X1,X5))),X5)|~hBOOL(hAPP(X1,X2))), inference(rw,[status(thm)],[c_0_8616, c_0_4916]), ['final']). 4.46/4.74 cnf(c_0_13862, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X3))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)))), inference(rw,[status(thm)],[c_0_8617, c_0_5902]), ['final']). 4.46/4.74 cnf(c_0_13863, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))=X2|c_Groups_Oone__class_Oone(X1)=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_5528]), ['final']). 4.46/4.74 cnf(c_0_13864, plain, (c_Fun_Oinj__on(X1,X1,X3,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X1,X1,X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_8618]), ['final']). 4.46/4.74 cnf(c_0_13865, plain, (~class_Int_Oring__char__0(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),X2)),X2)), inference(split_conjunct,[status(thm)],[c_0_8619]), ['final']). 4.46/4.74 cnf(c_0_13866, plain, (c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(c_List_Oset(X1),X2))=c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),c_List_Oremdups(X1,X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8620]), ['final']). 4.46/4.74 cnf(c_0_13867, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8621]), ['final']). 4.46/4.74 cnf(c_0_13868, plain, (c_List_Olist_ONil(tc_Nat_Onat)=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[c_0_8622, c_0_4517]), ['final']). 4.46/4.74 cnf(c_0_13869, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_8389]), ['final']). 4.46/4.74 cnf(c_0_13870, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[c_0_8623, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13871, plain, (c_Groups_Oone__class_Oone(X1)=c_Groups_Osgn__class_Osgn(X1,X2)|c_Groups_Ozero__class_Ozero(X1)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Osgn__if(X1)), inference(split_conjunct,[status(thm)],[c_0_8346]), ['final']). 4.46/4.74 cnf(c_0_13872, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),c_Groups_Ozero__class_Ozero(X1))|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber(X1)), inference(er,[status(thm)],[c_0_8624]), ['final']). 4.46/4.74 cnf(c_0_13873, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8625]), ['final']). 4.46/4.74 cnf(c_0_13874, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_8626]), ['final']). 4.46/4.74 cnf(c_0_13875, plain, (hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk512_3(X3,X2,X1)),esk513_3(X3,X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_8437]), ['final']). 4.46/4.74 cnf(c_0_13876, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~c_List_Olist__all2(X4,X5,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X6),hAPP(hAPP(c_List_Olist_OCons(X5),X3),X7))), inference(split_conjunct,[status(thm)],[c_0_7552]), ['final']). 4.46/4.74 cnf(c_0_13877, plain, (hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X6)),X5))|~c_Typedef_Otype__definition(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_8627]), ['final']). 4.46/4.74 cnf(c_0_13878, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8628]), ['final']). 4.46/4.74 cnf(c_0_13879, plain, (X1=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_8629]), ['final']). 4.46/4.74 cnf(c_0_13880, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_8630]), ['final']). 4.46/4.74 cnf(c_0_13881, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_8631]), ['final']). 4.46/4.74 cnf(c_0_13882, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OSup__class_OSup(X1,X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk351_3(X2,X3,X1)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7961]), ['final']). 4.46/4.74 cnf(c_0_13883, plain, (hBOOL(hAPP(X1,X2))|c_List_Olist_ONil(X3)=c_List_OtakeWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_8195]), ['final']). 4.46/4.74 cnf(c_0_13884, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),X2)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8632]), ['final']). 4.46/4.74 cnf(c_0_13885, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,X3))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4))), inference(rw,[status(thm)],[c_0_8633, c_0_5580]), ['final']). 4.46/4.74 cnf(c_0_13886, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Complete__Lattice_OInf__class_OInf(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk48_3(X3,X2,X1)))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7962]), ['final']). 4.46/4.74 cnf(c_0_13887, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8337]), ['final']). 4.46/4.74 cnf(c_0_13888, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8342]), ['final']). 4.46/4.74 cnf(c_0_13889, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8343]), ['final']). 4.46/4.74 cnf(c_0_13890, plain, (hAPP(X1,X2)=c_Option_Ooption_ONone(X3)|hBOOL(hAPP(hAPP(c_member(X4),X2),c_Map_Odom(X4,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_8634]), ['final']). 4.46/4.74 cnf(c_0_13891, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2))=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8635]), ['final']). 4.46/4.74 cnf(c_0_13892, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2))), inference(rw,[status(thm)],[c_0_8636, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13893, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8344]), ['final']). 4.46/4.74 cnf(c_0_13894, plain, (hBOOL(hAPP(X1,esk297_2(X1,X2)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7245]), ['final']). 4.46/4.74 cnf(c_0_13895, plain, (hBOOL(hAPP(X1,esk75_2(X1,X2)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7438]), ['final']). 4.46/4.74 cnf(c_0_13896, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oabs__if(X1)), inference(split_conjunct,[status(thm)],[c_0_8558]), ['final']). 4.46/4.74 cnf(c_0_13897, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8637]), ['final']). 4.46/4.74 cnf(c_0_13898, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X3),X2)=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))!=hAPP(X2,esk337_4(X2,X3,X1,X4))), inference(split_conjunct,[status(thm)],[c_0_7943]), ['final']). 4.46/4.74 cnf(c_0_13899, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X3),X2)=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))!=hAPP(X2,esk266_4(X2,X3,X4,X1))), inference(split_conjunct,[status(thm)],[c_0_7946]), ['final']). 4.46/4.74 cnf(c_0_13900, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_8638]), ['final']). 4.46/4.74 cnf(c_0_13901, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)=hAPP(c_Groups_Oabs__class_Oabs(X1),X2)|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_8639]), ['final']). 4.46/4.74 cnf(c_0_13902, plain, (X3=hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=c_Map_Odom(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8640]), ['final']). 4.46/4.74 cnf(c_0_13903, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))|~class_Orderings_Oord(X2)), inference(split_conjunct,[status(thm)],[c_0_7650]), ['final']). 4.46/4.74 cnf(c_0_13904, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=X1|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8641, c_0_4836]), c_0_4836]), ['final']). 4.46/4.74 cnf(c_0_13905, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8642, c_0_4836]), c_0_4836]), ['final']). 4.46/4.74 cnf(c_0_13906, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))), inference(split_conjunct,[status(thm)],[c_0_8643]), ['final']). 4.46/4.74 cnf(c_0_13907, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))), inference(split_conjunct,[status(thm)],[c_0_8643]), ['final']). 4.46/4.74 cnf(c_0_13908, plain, (hAPP(c_Finite__Set_Ofold1(X1,X2),X4)=hAPP(X3,X4)|~c_Big__Operators_Osemilattice__big(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_8644]), ['final']). 4.46/4.74 cnf(c_0_13909, plain, (hAPP(c_Finite__Set_Ofold1(X1,X2),X4)=hAPP(X3,X4)|~c_Finite__Set_Ofolding__one(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_8645]), ['final']). 4.46/4.74 cnf(c_0_13910, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8646]), ['final']). 4.46/4.74 cnf(c_0_13911, plain, (hAPP(c_Nat_OSuc,esk397_2(X1,X2))=X2|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1)))), inference(split_conjunct,[status(thm)],[c_0_8182]), ['final']). 4.46/4.74 cnf(c_0_13912, plain, (X2=hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_8647]), ['final']). 4.46/4.74 cnf(c_0_13913, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[c_0_8648, c_0_5884]), ['final']). 4.46/4.74 cnf(c_0_13914, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7777]), ['final']). 4.46/4.74 cnf(c_0_13915, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7777]), ['final']). 4.46/4.74 cnf(c_0_13916, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8649]), ['final']). 4.46/4.74 cnf(c_0_13917, plain, (X1=c_List_Olist_ONil(X2)|hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Oappend(X2),X1),X3))=hAPP(c_List_Ohd(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_8650]), ['final']). 4.46/4.74 cnf(c_0_13918, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8649]), ['final']). 4.46/4.74 cnf(c_0_13919, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,esk187_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5209]), ['final']). 4.46/4.74 cnf(c_0_13920, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,esk135_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_7677]), ['final']). 4.46/4.74 cnf(c_0_13921, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8651]), ['final']). 4.46/4.74 cnf(c_0_13922, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(er,[status(thm)],[c_0_8652]), ['final']). 4.46/4.74 cnf(c_0_13923, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8653, c_0_5334]), c_0_7568]), ['final']). 4.46/4.74 cnf(c_0_13924, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,esk90_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_7683]), ['final']). 4.46/4.74 cnf(c_0_13925, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7783]), ['final']). 4.46/4.74 cnf(c_0_13926, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7783]), ['final']). 4.46/4.74 cnf(c_0_13927, plain, (esk210_3(X1,X2,X3)=esk211_3(X1,X2,X3)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X2),X1)=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5487]), ['final']). 4.46/4.74 cnf(c_0_13928, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8654]), ['final']). 4.46/4.74 cnf(c_0_13929, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(X2,X3))=hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,X1)),X2),X3)|~class_Groups_Ouminus(X1)), inference(split_conjunct,[status(thm)],[c_0_8655]), ['final']). 4.46/4.74 cnf(c_0_13930, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))=X2|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8656]), ['final']). 4.46/4.74 cnf(c_0_13931, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7784]), ['final']). 4.46/4.74 cnf(c_0_13932, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7784]), ['final']). 4.46/4.74 cnf(c_0_13933, plain, (c_List_Olist__ex1(X3,X2,X1)|esk163_4(X1,X2,X3,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),X1)))|~hBOOL(hAPP(X2,X4))), inference(split_conjunct,[status(thm)],[c_0_7272]), ['final']). 4.46/4.74 cnf(c_0_13934, plain, (X2=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|hAPP(c_Finite__Set_Ocard(X1),X2)!=hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_8657]), ['final']). 4.46/4.74 cnf(c_0_13935, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X3)=X2|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8658]), ['final']). 4.46/4.74 cnf(c_0_13936, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X3)=X2|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8659]), ['final']). 4.46/4.74 cnf(c_0_13937, plain, (c_List_Olist__ex1(X4,X3,X2)|X1!=esk492_4(X2,X3,X4,X1)|~hBOOL(hAPP(X3,X1))|~hBOOL(hAPP(hAPP(c_member(X4),X1),hAPP(c_List_Oset(X4),X2)))), inference(split_conjunct,[status(thm)],[c_0_7265]), ['final']). 4.46/4.74 cnf(c_0_13938, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))=X2|hAPP(c_List_Orev(X1),X2)!=hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_5904]), ['final']). 4.46/4.74 cnf(c_0_13939, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3))=X2|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8660]), ['final']). 4.46/4.74 cnf(c_0_13940, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3))=X2|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8661]), ['final']). 4.46/4.74 cnf(c_0_13941, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8662]), ['final']). 4.46/4.74 cnf(c_0_13942, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8663]), ['final']). 4.46/4.74 cnf(c_0_13943, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)|~class_Lattices_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_8664]), ['final']). 4.46/4.74 cnf(c_0_13944, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8663]), ['final']). 4.46/4.74 cnf(c_0_13945, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8665]), ['final']). 4.46/4.74 cnf(c_0_13946, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8666]), ['final']). 4.46/4.74 cnf(c_0_13947, plain, (hAPP(X4,X2)=hAPP(c_Fun_Ooverride__on(X1,X5,X6,X4,X3),X2)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8420]), ['final']). 4.46/4.74 cnf(c_0_13948, plain, (c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),X4,c_Map_Odom(X1,X2,X4))|~c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),c_Map_Omap__add(X1,X2,X3,X4),c_Map_Odom(X1,X2,X4))), inference(split_conjunct,[status(thm)],[c_0_8236]), ['final']). 4.46/4.74 cnf(c_0_13949, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk424_2(X1,X2)),X1))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))), inference(split_conjunct,[status(thm)],[c_0_8515]), ['final']). 4.46/4.74 cnf(c_0_13950, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8667]), ['final']). 4.46/4.74 cnf(c_0_13951, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8668]), ['final']). 4.46/4.74 cnf(c_0_13952, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8669]), ['final']). 4.46/4.74 cnf(c_0_13953, plain, (hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X1),X3),X2))|~hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_8670]), ['final']). 4.46/4.74 cnf(c_0_13954, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk204_1(X1)))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5527]), ['final']). 4.46/4.74 cnf(c_0_13955, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk99_2(X1,X2)),X1))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))), inference(split_conjunct,[status(thm)],[c_0_8514]), ['final']). 4.46/4.74 cnf(c_0_13956, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_8671]), ['final']). 4.46/4.74 cnf(c_0_13957, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)=X3|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_8672]), ['final']). 4.46/4.74 cnf(c_0_13958, plain, (hAPP(c_Map_Omap__add(X5,X1,X4,X2),X3)=c_Option_Ooption_ONone(X1)|c_Option_Ooption_ONone(X1)!=hAPP(X2,X3)|c_Option_Ooption_ONone(X1)!=hAPP(X4,X3)), inference(split_conjunct,[status(thm)],[c_0_8673]), ['final']). 4.46/4.74 cnf(c_0_13959, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2))|c_Random_Ominus__shift(X3,X1,X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_8501]), ['final']). 4.46/4.74 cnf(c_0_13960, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8674]), ['final']). 4.46/4.74 cnf(c_0_13961, plain, (c_Hoare__Mirabelle_Otriple__valid(X1,esk347_3(X4,X3,X1),X2)|c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X4)|~hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7303]), ['final']). 4.46/4.74 cnf(c_0_13962, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Relation_ODomain(X1,X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_8675]), ['final']). 4.46/4.74 cnf(c_0_13963, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X2),hAPP(c_Relation_ORange(X1,X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_8676]), ['final']). 4.46/4.74 cnf(c_0_13964, plain, (X3=c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X2,X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_8677]), ['final']). 4.46/4.74 cnf(c_0_13965, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8678]), ['final']). 4.46/4.74 cnf(c_0_13966, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_8679]), ['final']). 4.46/4.74 cnf(c_0_13967, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X1)))), inference(rw,[status(thm)],[c_0_8680, c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_13968, plain, (hBOOL(hAPP(X3,X4))|X1!=c_List_OtakeWhile(X2,X3,X1)|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_8193]), ['final']). 4.46/4.74 cnf(c_0_13969, plain, (c_Nitpick_Orefl_H(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk330_2(X2,X1)),esk330_2(X2,X1))),X2))), inference(split_conjunct,[status(thm)],[c_0_7982]), ['final']). 4.46/4.74 cnf(c_0_13970, plain, (hBOOL(hAPP(X1,esk248_4(X1,X2,X3,X4)))|X3=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_7351]), ['final']). 4.46/4.74 cnf(c_0_13971, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|X2=c_Groups_Oone__class_Oone(tc_Int_Oint)|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_8681]), ['final']). 4.46/4.74 cnf(c_0_13972, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8682]), ['final']). 4.46/4.74 cnf(c_0_13973, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_8683]), ['final']). 4.46/4.74 cnf(c_0_13974, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_8684]), ['final']). 4.46/4.74 cnf(c_0_13975, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8685]), ['final']). 4.46/4.74 cnf(c_0_13976, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X3=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_8686]), ['final']). 4.46/4.74 cnf(c_0_13977, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8391]), ['final']). 4.46/4.74 cnf(c_0_13978, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2)))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8392]), ['final']). 4.46/4.74 cnf(c_0_13979, plain, (hBOOL(hAPP(X1,esk205_1(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))), inference(rw,[status(thm)],[c_0_8687, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_13980, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_8688]), ['final']). 4.46/4.74 cnf(c_0_13981, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8689]), ['final']). 4.46/4.74 cnf(c_0_13982, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Int_Oring__1__class_OInts(X1)))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8690]), ['final']). 4.46/4.74 cnf(c_0_13983, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Nat_Onat),X1),X2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(X1,esk177_3(X1,X2,X3))!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7807]), ['final']). 4.46/4.74 cnf(c_0_13984, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(X1,esk260_3(X1,X2,X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7808]), ['final']). 4.46/4.74 cnf(c_0_13985, plain, (hBOOL(hAPP(X4,X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(X4,esk10_4(X4,X3,X5,X1)))), inference(split_conjunct,[status(thm)],[c_0_6476]), ['final']). 4.46/4.74 cnf(c_0_13986, plain, (c_Divides_Odivmod__int(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(er,[status(thm)],[c_0_8691]), ['final']). 4.46/4.74 cnf(c_0_13987, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8692]), ['final']). 4.46/4.74 cnf(c_0_13988, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8693]), ['final']). 4.46/4.74 cnf(c_0_13989, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1))=hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X1)|~c_Nat__Transfer_Onat__set(X1)), inference(split_conjunct,[status(thm)],[c_0_8694]), ['final']). 4.46/4.74 cnf(c_0_13990, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Relation_OImage(X1,X1,X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_8695]), ['final']). 4.46/4.74 cnf(c_0_13991, plain, (hBOOL(hAPP(X4,X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(X4,esk10_4(X4,X5,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_6476]), ['final']). 4.46/4.74 cnf(c_0_13992, plain, (X4=X5|hAPP(c_Set_Oimage(X1,X2,X3),X4)!=hAPP(c_Set_Oimage(X1,X2,X3),X5)|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_8696]), ['final']). 4.46/4.74 cnf(c_0_13993, plain, (c_Fun_Oinj__on(X1,X2,X3,X5)|~c_Fun_Oinj__on(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X4))), inference(split_conjunct,[status(thm)],[c_0_8697]), ['final']). 4.46/4.74 cnf(c_0_13994, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~c_List_Olistrelp(X4,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6))), inference(split_conjunct,[status(thm)],[c_0_8698]), ['final']). 4.46/4.74 cnf(c_0_13995, plain, (hBOOL(hAPP(X1,X2))|hAPP(c_List_Ofilter(X3,X1),c_List_Oreplicate(X3,X4,X2))=c_List_Olist_ONil(X3)), inference(split_conjunct,[status(thm)],[c_0_8699]), ['final']). 4.46/4.74 cnf(c_0_13996, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk67_4(hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),X1,X3,X2)))), inference(er,[status(thm)],[c_0_8700]), ['final']). 4.46/4.74 cnf(c_0_13997, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2))|c_List_Olist_ONil(X1)!=hAPP(hAPP(c_List_Odrop(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_8701]), ['final']). 4.46/4.74 cnf(c_0_13998, plain, (hBOOL(hAPP(hAPP(X3,esk215_2(X4,X3)),X4))|~hBOOL(hAPP(c_Predicate_ORangeP(X1,X2,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8702]), ['final']). 4.46/4.74 cnf(c_0_13999, plain, (hBOOL(hAPP(hAPP(X3,X4),esk51_2(X4,X3)))|~hBOOL(hAPP(c_Predicate_ODomainP(X1,X2,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8703]), ['final']). 4.46/4.74 cnf(c_0_14000, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X3)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8704]), ['final']). 4.46/4.74 cnf(c_0_14001, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8705]), ['final']). 4.46/4.74 cnf(c_0_14002, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1)))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(er,[status(thm)],[c_0_8706]), ['final']). 4.46/4.74 cnf(c_0_14003, plain, (c_List_Olist_ONil(X1)=hAPP(hAPP(c_List_Odrop(X1),X3),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_8701]), ['final']). 4.46/4.74 cnf(c_0_14004, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|X2=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4651]), ['final']). 4.46/4.74 cnf(c_0_14005, plain, (c_Groups_Ozero__class_Ozero(X1)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8707]), ['final']). 4.46/4.74 cnf(c_0_14006, plain, (X5=X4|hAPP(c_Set_Oimage(X1,X2,X3),X4)!=hAPP(c_Set_Oimage(X1,X2,X3),X5)|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_8708]), ['final']). 4.46/4.74 cnf(c_0_14007, plain, (X3=X2|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_fequal),esk172_3(X1,X2,X3)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)), inference(split_conjunct,[status(thm)],[c_0_5407]), ['final']). 4.46/4.74 cnf(c_0_14008, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8709]), ['final']). 4.46/4.74 cnf(c_0_14009, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Odrop(X1),X3),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8710]), ['final']). 4.46/4.74 cnf(c_0_14010, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Otake(X1),X3),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8711]), ['final']). 4.46/4.74 cnf(c_0_14011, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk234_2(X2,X1))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8712]), ['final']). 4.46/4.74 cnf(c_0_14012, plain, (c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))|~c_List_Olist__all(X1,X2,X3)|~hBOOL(hAPP(X2,X4))), inference(split_conjunct,[status(thm)],[c_0_8713]), ['final']). 4.46/4.74 cnf(c_0_14013, plain, (hAPP(c_List_Ofilter(X3,X1),c_List_Oreplicate(X3,X4,X2))=c_List_Oreplicate(X3,X4,X2)|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_8699]), ['final']). 4.46/4.74 cnf(c_0_14014, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7824]), ['final']). 4.46/4.74 cnf(c_0_14015, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[c_0_8714, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_14016, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,X2))=c_Groups_Ozero__class_Ozero(X1)|~class_Power_Opower(X1)|~class_Rings_Osemiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_8715]), ['final']). 4.46/4.74 cnf(c_0_14017, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8716, c_0_5120]), c_0_5120]), c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_14018, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7693]), ['final']). 4.46/4.74 cnf(c_0_14019, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk245_2(X2,X1))=X1|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5968]), ['final']). 4.46/4.74 cnf(c_0_14020, plain, (X1=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk54_2(X2,X1))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5970]), ['final']). 4.46/4.74 cnf(c_0_14021, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_8717, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_14022, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8718]), ['final']). 4.46/4.74 cnf(c_0_14023, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8719]), ['final']). 4.46/4.74 cnf(c_0_14024, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|~c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X6),X4),hAPP(hAPP(c_List_Olist_OCons(X2),X7),X5))), inference(split_conjunct,[status(thm)],[c_0_7552]), ['final']). 4.46/4.74 cnf(c_0_14025, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|c_Groups_Osgn__class_Osgn(X1,X2)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8720]), ['final']). 4.46/4.74 cnf(c_0_14026, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1)|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),hAPP(c_List_Oset(tc_Nat_Onat),X1)))), inference(split_conjunct,[status(thm)],[c_0_8475]), ['final']). 4.46/4.74 cnf(c_0_14027, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_8721]), ['final']). 4.46/4.74 cnf(c_0_14028, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_8722]), ['final']). 4.46/4.74 cnf(c_0_14029, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_8721]), ['final']). 4.46/4.74 cnf(c_0_14030, plain, (c_Relation_Osingle__valued(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))|~c_Relation_Osingle__valued(X1,X2,X4)), inference(split_conjunct,[status(thm)],[c_0_8723]), ['final']). 4.46/4.74 cnf(c_0_14031, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Osort__key(X1,X3,X4,X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))|~class_Orderings_Olinorder(X3)), inference(split_conjunct,[status(thm)],[c_0_8724]), ['final']). 4.46/4.74 cnf(c_0_14032, plain, (hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk309_2(X2,X3)))|~hBOOL(hAPP(X3,X1))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5409]), ['final']). 4.46/4.74 cnf(c_0_14033, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_8725]), ['final']). 4.46/4.74 cnf(c_0_14034, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2))), inference(rw,[status(thm)],[c_0_8726, c_0_4443]), ['final']). 4.46/4.74 cnf(c_0_14035, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8727, c_0_5120]), c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_14036, plain, (hBOOL(hAPP(X1,esk413_3(X2,X1,X3)))|hAPP(c_List_Ofilter(X3,X1),X2)=c_List_OtakeWhile(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5154]), ['final']). 4.46/4.74 cnf(c_0_14037, plain, (c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X4),X3))|~c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,X4)), inference(split_conjunct,[status(thm)],[c_0_8728]), ['final']). 4.46/4.74 cnf(c_0_14038, plain, (c_List_Olist_ONil(X1)=X2|hBOOL(hAPP(c_List_Odistinct(X1),c_List_Obutlast(X1,X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8729]), ['final']). 4.46/4.74 cnf(c_0_14039, plain, (c_List_Olist_ONil(X1)=X3|c_List_Olist_ONil(tc_List_Olist(X1))!=c_List_Otranspose(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))), inference(split_conjunct,[status(thm)],[c_0_7980]), ['final']). 4.46/4.74 cnf(c_0_14040, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))), inference(rw,[status(thm)],[c_0_8730, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_14041, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[c_0_8731, c_0_6178]), ['final']). 4.46/4.74 cnf(c_0_14042, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))), inference(rw,[status(thm)],[c_0_8732, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_14043, plain, (hBOOL(hAPP(X2,X1))|~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Int_OInteg))|~hBOOL(hAPP(X2,hAPP(c_Int_ORep__Integ,esk342_2(X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_8733]), ['final']). 4.46/4.74 cnf(c_0_14044, plain, (X1=X2|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8734, c_0_5120]), c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_14045, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))=c_Groups_Ozero__class_Ozero(X1)|hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber(X1)), inference(er,[status(thm)],[c_0_8735]), ['final']). 4.46/4.74 cnf(c_0_14046, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))), inference(split_conjunct,[status(thm)],[c_0_8736]), ['final']). 4.46/4.74 cnf(c_0_14047, plain, (hAPP(hAPP(c_List_Onth(X1),X5),X4)=X2|hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=hAPP(hAPP(c_List_Odrop(X1),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_8737]), ['final']). 4.46/4.74 cnf(c_0_14048, plain, (hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_7683]), ['final']). 4.46/4.74 cnf(c_0_14049, plain, (c_Divides_OposDivAlg(X2,X1)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_4535]), ['final']). 4.46/4.74 cnf(c_0_14050, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Big__Operators_Olattice__class_OSup__fin(X1,X2)=c_Complete__Lattice_OSup__class_OSup(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8738]), ['final']). 4.46/4.74 cnf(c_0_14051, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_8739]), ['final']). 4.46/4.74 cnf(c_0_14052, plain, (c_Orderings_Otop__class_Otop(X1)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2)|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_8740]), ['final']). 4.46/4.74 cnf(c_0_14053, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2)|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8741]), ['final']). 4.46/4.74 cnf(c_0_14054, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Complete__Lattice_OInf__class_OInf(X1,X2)=c_Big__Operators_Olattice__class_OInf__fin(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8742]), ['final']). 4.46/4.74 cnf(c_0_14055, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8743]), ['final']). 4.46/4.74 cnf(c_0_14056, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=c_Orderings_Otop__class_Otop(X1)|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_8744]), ['final']). 4.46/4.74 cnf(c_0_14057, plain, (X2=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8745]), ['final']). 4.46/4.74 cnf(c_0_14058, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_7907]), ['final']). 4.46/4.74 cnf(c_0_14059, plain, (X2=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8746]), ['final']). 4.46/4.74 cnf(c_0_14060, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X2)|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8747]), ['final']). 4.46/4.74 cnf(c_0_14061, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_8748]), ['final']). 4.46/4.74 cnf(c_0_14062, plain, (hBOOL(hAPP(X2,X4))|~c_List_Olist__all(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_8219]), ['final']). 4.46/4.74 cnf(c_0_14063, plain, (X1=c_List_Olist_ONil(X2)|c_List_Olast(X2,X1)=c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1))), inference(split_conjunct,[status(thm)],[c_0_8749]), ['final']). 4.46/4.74 cnf(c_0_14064, plain, (X1=c_List_Olist_ONil(X2)|c_List_Olast(X2,X1)=c_List_Olast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1))), inference(split_conjunct,[status(thm)],[c_0_8750]), ['final']). 4.46/4.74 cnf(c_0_14065, plain, (c_Nitpick_Ounknown(tc_HOL_Obool)|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))|~c_Nitpick_Owf_H(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8751]), ['final']). 4.46/4.74 cnf(c_0_14066, plain, (c_Divides_OposDivAlg(X2,X1)=c_Divides_Odivmod__int(X2,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7375]), ['final']). 4.46/4.74 cnf(c_0_14067, plain, (c_Orderings_Oord_Omin(X1,hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1)))=c_Orderings_Oord__class_Omax(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8752]), ['final']). 4.46/4.74 cnf(c_0_14068, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8753]), ['final']). 4.46/4.74 cnf(c_0_14069, plain, (c_Orderings_Oord_Omax(X1,hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1)))=c_Orderings_Oord__class_Omin(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8754]), ['final']). 4.46/4.74 cnf(c_0_14070, plain, (hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),c_Enum_On__lists(X1,X3,X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8755]), ['final']). 4.46/4.74 cnf(c_0_14071, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)!=c_Groups_Ozero__class_Ozero(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))|~class_Int_Oring__char__0(X1)), inference(split_conjunct,[status(thm)],[c_0_5492]), ['final']). 4.46/4.74 cnf(c_0_14072, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofilter(X1,X3),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8756]), ['final']). 4.46/4.74 cnf(c_0_14073, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(c_Set_Oimage(X2,X1,X3),X4))),hAPP(c_Finite__Set_Ocard(X2),X4)))|~c_Fun_Oinj__on(X2,X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8757]), ['final']). 4.46/4.74 cnf(c_0_14074, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Osgn__class_Osgn(X1,X2))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8758]), ['final']). 4.46/4.74 cnf(c_0_14075, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~class_Power_Opower(X1)|~class_Rings_Ono__zero__divisors(X1)|~class_Rings_Ozero__neq__one(X1)|~class_Rings_Omult__zero(X1)), inference(er,[status(thm)],[c_0_8759]), ['final']). 4.46/4.74 cnf(c_0_14076, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5593]), ['final']). 4.46/4.74 cnf(c_0_14077, plain, (hAPP(c_List_Oset(X2),c_List_Olinorder__class_Osort__key(X2,X1,X3,X4))=hAPP(c_List_Oset(X2),X4)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8760]), ['final']). 4.46/4.74 cnf(c_0_14078, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X4)|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_8761]), ['final']). 4.46/4.74 cnf(c_0_14079, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_8762]), ['final']). 4.46/4.74 cnf(c_0_14080, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8763, c_0_4836]), c_0_4836]), ['final']). 4.46/4.74 cnf(c_0_14081, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3))=X2|~c_Equiv__Relations_Oequiv(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8764]), ['final']). 4.46/4.74 cnf(c_0_14082, plain, (hAPP(X4,X2)=hAPP(c_Map_Orestrict__map(X1,X5,X4,X3),X2)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8765]), ['final']). 4.46/4.74 cnf(c_0_14083, plain, (hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4,X5,X1),X3),X2))|~hBOOL(hAPP(hAPP(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8766]), ['final']). 4.46/4.74 cnf(c_0_14084, plain, (hBOOL(hAPP(X4,X2))|~hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X4))), inference(split_conjunct,[status(thm)],[c_0_8767]), ['final']). 4.46/4.74 cnf(c_0_14085, plain, (c_List_Olist__ex(X1,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X4,X2))), inference(split_conjunct,[status(thm)],[c_0_8299]), ['final']). 4.46/4.74 cnf(c_0_14086, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(rw,[status(thm)],[c_0_8768, c_0_4836]), ['final']). 4.46/4.74 cnf(c_0_14087, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_8090]), ['final']). 4.46/4.74 cnf(c_0_14088, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X2),X1)=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))|hAPP(X1,esk114_4(X1,X2,X3,X4))!=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_7991]), ['final']). 4.46/4.74 cnf(c_0_14089, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Relation_OField(X1),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_8769]), ['final']). 4.46/4.74 cnf(c_0_14090, plain, (hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,esk515_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7187]), ['final']). 4.46/4.74 cnf(c_0_14091, plain, (hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,esk486_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7171]), ['final']). 4.46/4.74 cnf(c_0_14092, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)=hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8770]), ['final']). 4.46/4.74 cnf(c_0_14093, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|c_Int_OMin=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_8771, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_14094, plain, (c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)|hAPP(X1,esk207_4(X1,X2,X3,X4))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_7994]), ['final']). 4.46/4.74 cnf(c_0_14095, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)=hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omax(X1)),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8772]), ['final']). 4.46/4.74 cnf(c_0_14096, plain, (~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_8773, c_0_4760]), ['final']). 4.46/4.74 cnf(c_0_14097, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|X2=c_Int_OMin|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_8774, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_14098, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)))|~hBOOL(hAPP(X1,esk370_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5242]), ['final']). 4.46/4.74 cnf(c_0_14099, plain, (c_Enum_Oenum__class_Oenum(tc_prod(X2,X1))=c_Enum_Oproduct(X2,X1,c_Enum_Oenum__class_Oenum(X2),c_Enum_Oenum__class_Oenum(X1))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_8775]), ['final']). 4.46/4.74 cnf(c_0_14100, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1)))|~epred2_3(X2,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_8776]), ['final']). 4.46/4.74 cnf(c_0_14101, plain, (c_List_Oremdups(X1,c_List_Oremove1(X1,X3,X2))=c_List_Oremove1(X1,X3,c_List_Oremdups(X1,X2))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8777]), ['final']). 4.46/4.74 cnf(c_0_14102, plain, (X1=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Int_OMin=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)!=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_8778, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_14103, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_8779]), ['final']). 4.46/4.74 cnf(c_0_14104, plain, (hBOOL(hAPP(X1,esk97_3(X2,X1,X3)))|hAPP(c_List_Ofilter(X3,X1),X2)=c_List_Olist_ONil(X3)), inference(split_conjunct,[status(thm)],[c_0_8045]), ['final']). 4.46/4.74 cnf(c_0_14105, plain, (X3=X1|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_8780]), ['final']). 4.46/4.74 cnf(c_0_14106, plain, (X3=X2|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)), inference(split_conjunct,[status(thm)],[c_0_8781]), ['final']). 4.46/4.74 cnf(c_0_14107, plain, (c_Predicate_Oreflp(X1,X2)|~c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))), inference(rw,[status(thm)],[c_0_8782, c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_14108, plain, (X1=c_Groups_Oone__class_Oone(tc_Int_Oint)|X1=c_Int_OMin|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)!=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_8783, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_14109, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8784]), ['final']). 4.46/4.74 cnf(c_0_14110, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_8482]), ['final']). 4.46/4.74 cnf(c_0_14111, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)))|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_8487]), ['final']). 4.46/4.74 cnf(c_0_14112, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)))|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_8486]), ['final']). 4.46/4.74 cnf(c_0_14113, plain, (hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|esk452_2(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(er,[status(thm)],[c_0_8785]), ['final']). 4.46/4.74 cnf(c_0_14114, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8786]), ['final']). 4.46/4.74 cnf(c_0_14115, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8607]), ['final']). 4.46/4.74 cnf(c_0_14116, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)))|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_8488]), ['final']). 4.46/4.74 cnf(c_0_14117, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)|hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))!=X2), inference(split_conjunct,[status(thm)],[c_0_8449]), ['final']). 4.46/4.74 cnf(c_0_14118, plain, (X3=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X1,X3,X2)|~hBOOL(hAPP(X1,esk534_3(X2,X3,X1)))|~hBOOL(hAPP(X1,esk532_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.74 cnf(c_0_14119, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1)), inference(er,[status(thm)],[c_0_8787]), ['final']). 4.46/4.74 cnf(c_0_14120, plain, (hBOOL(hAPP(hAPP(X3,X5),X6))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4),X5),X6))), inference(split_conjunct,[status(thm)],[c_0_8788]), ['final']). 4.46/4.74 cnf(c_0_14121, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8789]), ['final']). 4.46/4.74 cnf(c_0_14122, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8790]), ['final']). 4.46/4.74 cnf(c_0_14123, plain, (hBOOL(hAPP(X2,X4))|~hBOOL(hAPP(c_Predicate_OPowp(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_8454]), ['final']). 4.46/4.74 cnf(c_0_14124, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5515]), ['final']). 4.46/4.74 cnf(c_0_14125, plain, (hBOOL(hAPP(hAPP(X4,X5),X6))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4),X5),X6))), inference(split_conjunct,[status(thm)],[c_0_8791]), ['final']). 4.46/4.74 cnf(c_0_14126, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3))), inference(split_conjunct,[status(thm)],[c_0_8090]), ['final']). 4.46/4.74 cnf(c_0_14127, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))), inference(split_conjunct,[status(thm)],[c_0_8547]), ['final']). 4.46/4.74 cnf(c_0_14128, plain, (X1=X2|hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)!=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1)), inference(split_conjunct,[status(thm)],[c_0_8792]), ['final']). 4.46/4.74 cnf(c_0_14129, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8793]), ['final']). 4.46/4.74 cnf(c_0_14130, plain, (c_Divides_OposDivAlg(X1,X2)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4535]), ['final']). 4.46/4.74 cnf(c_0_14131, plain, (~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8794, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), ['final']). 4.46/4.74 cnf(c_0_14132, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),esk468_2(X2,X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_8795]), ['final']). 4.46/4.74 cnf(c_0_14133, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))=c_Divides_Opdivmod(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5952]), ['final']). 4.46/4.74 cnf(c_0_14134, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_8796]), ['final']). 4.46/4.74 cnf(c_0_14135, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8797]), ['final']). 4.46/4.74 cnf(c_0_14136, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk139_2(X2,X1)),X2))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2), inference(split_conjunct,[status(thm)],[c_0_8798]), ['final']). 4.46/4.74 cnf(c_0_14137, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),hAPP(c_Relation_Oconverse(X2,X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_8416]), ['final']). 4.46/4.74 cnf(c_0_14138, plain, (hAPP(c_List_Ofilter(X1,X2),X3)!=c_List_Olist_ONil(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4))), inference(split_conjunct,[status(thm)],[c_0_8045]), ['final']). 4.46/4.74 cnf(c_0_14139, plain, (c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1))=c_List_Omonoid__add__class_Olistsum(X1)|~class_Groups_Omonoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8799]), ['final']). 4.46/4.74 cnf(c_0_14140, plain, (X3=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8800]), ['final']). 4.46/4.74 cnf(c_0_14141, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,X2),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_8801]), ['final']). 4.46/4.74 cnf(c_0_14142, plain, (hBOOL(hAPP(hAPP(X2,X4),X3))|~c_Equiv__Relations_Oequivp(X1,X2)|~hBOOL(hAPP(hAPP(X2,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8802]), ['final']). 4.46/4.74 cnf(c_0_14143, plain, (hAPP(c_Finite__Set_Ocard(X1),esk34_3(X2,X3,X1))=X2|hAPP(c_Nat_OSuc,X2)!=hAPP(c_Finite__Set_Ocard(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_5438]), ['final']). 4.46/4.74 cnf(c_0_14144, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omax(X1)),X2)=c_Big__Operators_Olinorder__class_OMax(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8803]), ['final']). 4.46/4.74 cnf(c_0_14145, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2)=c_Big__Operators_Olattice__class_OSup__fin(X1,X2)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8804]), ['final']). 4.46/4.74 cnf(c_0_14146, plain, (hBOOL(hAPP(X2,X4))|hBOOL(hAPP(X3,X4))|~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8805]), ['final']). 4.46/4.74 cnf(c_0_14147, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)))), inference(rw,[status(thm)],[c_0_8806, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_14148, plain, (X2=hAPP(hAPP(c_List_Otake(X1),X3),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_8807]), ['final']). 4.46/4.74 cnf(c_0_14149, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2)=c_Big__Operators_Olattice__class_OInf__fin(X1,X2)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8808]), ['final']). 4.46/4.74 cnf(c_0_14150, plain, (c_Big__Operators_Olinorder__class_OMin(X1,X2)=hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8809]), ['final']). 4.46/4.74 cnf(c_0_14151, plain, (c_Fun_Oinj__on(X1,X3,X4,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|hAPP(c_Finite__Set_Ocard(X1),X2)!=hAPP(c_Finite__Set_Ocard(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2))), inference(split_conjunct,[status(thm)],[c_0_8810]), ['final']). 4.46/4.74 cnf(c_0_14152, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_8811]), ['final']). 4.46/4.74 cnf(c_0_14153, plain, (c_List_Oremdups(X1,X2)=X2|hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)), inference(rw,[status(thm)],[c_0_8812, c_0_8813]), ['final']). 4.46/4.74 cnf(c_0_14154, plain, (X2=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8814]), ['final']). 4.46/4.74 cnf(c_0_14155, plain, (X2=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8815]), ['final']). 4.46/4.74 cnf(c_0_14156, plain, (X3=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Lattices_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_8816]), ['final']). 4.46/4.74 cnf(c_0_14157, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_8817]), ['final']). 4.46/4.74 cnf(c_0_14158, plain, (c_List_Olistrelp(X1,X2,X3,X4)|~c_List_Olistrelp(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X4))), inference(split_conjunct,[status(thm)],[c_0_8698]), ['final']). 4.46/4.74 cnf(c_0_14159, plain, (c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))=c_Smallcheck_Osmall_H(X3,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6673]), ['final']). 4.46/4.74 cnf(c_0_14160, plain, (c_Wellfounded_Owf(tc_prod(X1,X3),c_Wellfounded_Olex__prod(X1,X3,X2,X4))|~c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Owf(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8818]), ['final']). 4.46/4.74 cnf(c_0_14161, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)))|~c_Nat__Transfer_Onat__set(X1)), inference(split_conjunct,[status(thm)],[c_0_8819]), ['final']). 4.46/4.74 cnf(c_0_14162, plain, (X3=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8820]), ['final']). 4.46/4.74 cnf(c_0_14163, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=X2|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_8821]), ['final']). 4.46/4.74 cnf(c_0_14164, plain, (X2=hAPP(c_Groups_Oabs__class_Oabs(X1),X2)|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_8822]), ['final']). 4.46/4.74 cnf(c_0_14165, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)=X3|~class_Groups_Ogroup__add(X1)|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_8823]), ['final']). 4.46/4.74 cnf(c_0_14166, plain, (esk34_3(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(c_Finite__Set_Ocard(X2),X1)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_8824]), c_0_4836]), ['final']). 4.46/4.74 cnf(c_0_14167, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_8626]), ['final']). 4.46/4.74 cnf(c_0_14168, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))), inference(split_conjunct,[status(thm)],[c_0_8611]), ['final']). 4.46/4.74 cnf(c_0_14169, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8825, c_0_5334]), c_0_5334]), ['final']). 4.46/4.74 cnf(c_0_14170, plain, (X2=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5538]), ['final']). 4.46/4.74 cnf(c_0_14171, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X4,X5),X2),X3)))|~class_Orderings_Olinorder(X4)), inference(split_conjunct,[status(thm)],[c_0_7252]), ['final']). 4.46/4.74 cnf(c_0_14172, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X3,X4),X5),X2)))|~class_Orderings_Olinorder(X3)), inference(split_conjunct,[status(thm)],[c_0_7252]), ['final']). 4.46/4.74 cnf(c_0_14173, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))), inference(split_conjunct,[status(thm)],[c_0_8826]), ['final']). 4.46/4.74 cnf(c_0_14174, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8827, c_0_5120]), c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_14175, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))), inference(split_conjunct,[status(thm)],[c_0_8615]), ['final']). 4.46/4.74 cnf(c_0_14176, plain, (c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))|~c_Wellfounded_Oacyclic(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8828]), ['final']). 4.46/4.74 cnf(c_0_14177, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X3,X1,X2)))|~hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,X2))), inference(split_conjunct,[status(thm)],[c_0_8829]), ['final']). 4.46/4.74 cnf(c_0_14178, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|c_Groups_Ozero__class_Ozero(X3)=c_Nitpick_Osetsum_H(X1,X3,X4,X2)|~class_Groups_Ocomm__monoid__add(X3)), inference(split_conjunct,[status(thm)],[c_0_4939]), ['final']). 4.46/4.74 cnf(c_0_14179, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8830]), ['final']). 4.46/4.74 cnf(c_0_14180, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8831, c_0_5334]), c_0_5334]), ['final']). 4.46/4.74 cnf(c_0_14181, plain, (c_List_Olist__ex(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_8832]), ['final']). 4.46/4.74 cnf(c_0_14182, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8833]), ['final']). 4.46/4.74 cnf(c_0_14183, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),c_Relation_OId__on(X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_8432]), ['final']). 4.46/4.74 cnf(c_0_14184, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk399_3(X3,X2,X1))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7259]), ['final']). 4.46/4.74 cnf(c_0_14185, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk227_3(X3,X2,X1))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7260]), ['final']). 4.46/4.74 cnf(c_0_14186, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~epred2_3(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8776]), ['final']). 4.46/4.74 cnf(c_0_14187, plain, (X2=esk403_3(X3,X4,X1)|X3=c_FunDef_OTHE__default(X4,X3,X1)|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_8505]), ['final']). 4.46/4.74 cnf(c_0_14188, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X3,X2))|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8834]), ['final']). 4.46/4.74 cnf(c_0_14189, plain, (c_Wellfounded_Oacyclic(X1,X3)|~c_Wellfounded_Oacyclic(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8835]), ['final']). 4.46/4.74 cnf(c_0_14190, plain, (c_Wellfounded_Owf(X1,X3)|~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8836]), ['final']). 4.46/4.74 cnf(c_0_14191, plain, (c_Wellfounded_OwfP(X1,X3)|~c_Wellfounded_OwfP(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8837]), ['final']). 4.46/4.74 cnf(c_0_14192, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)=X4|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_8838]), ['final']). 4.46/4.74 cnf(c_0_14193, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X1)=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Osemiring__0(X2)|~class_Power_Opower(X2)), inference(split_conjunct,[status(thm)],[c_0_8839]), ['final']). 4.46/4.74 cnf(c_0_14194, plain, (c_Orderings_Obot__class_Obot(X1)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2)|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_8840]), ['final']). 4.46/4.74 cnf(c_0_14195, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=c_Orderings_Obot__class_Obot(X1)|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_8841]), ['final']). 4.46/4.74 cnf(c_0_14196, plain, (X3=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3)), inference(split_conjunct,[status(thm)],[c_0_8842]), ['final']). 4.46/4.74 cnf(c_0_14197, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))), inference(rw,[status(thm)],[c_0_8843, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_14198, plain, (c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))|~c_List_Olist__ex(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8844]), ['final']). 4.46/4.74 cnf(c_0_14199, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=hAPP(c_Groups_Oabs__class_Oabs(X1),X2)|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_8845]), ['final']). 4.46/4.74 cnf(c_0_14200, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8846]), ['final']). 4.46/4.74 cnf(c_0_14201, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2))=hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8847]), ['final']). 4.46/4.74 cnf(c_0_14202, plain, (hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8848]), ['final']). 4.46/4.74 cnf(c_0_14203, plain, (hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8849]), ['final']). 4.46/4.74 cnf(c_0_14204, plain, (c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X4),X3))|~c_List_Olist__ex(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8844]), ['final']). 4.46/4.74 cnf(c_0_14205, plain, (c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))|~c_List_Olist__ex(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8832]), ['final']). 4.46/4.74 cnf(c_0_14206, plain, (c_Equiv__Relations_Oequiv(tc_List_Olist(X1),c_List_Olists(X1,X2),c_List_Olistrel(X1,X3))|~c_Equiv__Relations_Oequiv(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8850]), ['final']). 4.46/4.74 cnf(c_0_14207, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)))), inference(split_conjunct,[status(thm)],[c_0_8851]), ['final']). 4.46/4.74 cnf(c_0_14208, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_8739]), ['final']). 4.46/4.74 cnf(c_0_14209, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nitpick_Onat__gcd(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1))=c_Nitpick_Onat__gcd(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_6000]), ['final']). 4.46/4.74 cnf(c_0_14210, plain, (c_Relation_Orefl__on(tc_List_Olist(X1),c_List_Olists(X1,X2),c_List_Olistrel(X1,X3))|~c_Relation_Orefl__on(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8852]), ['final']). 4.46/4.74 cnf(c_0_14211, plain, (X3=X4|hAPP(c_Product__Type_Osnd(X1,X2),X3)!=hAPP(c_Product__Type_Osnd(X1,X2),X4)|hAPP(c_Product__Type_Ofst(X1,X2),X4)!=hAPP(c_Product__Type_Ofst(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_8853]), ['final']). 4.46/4.74 cnf(c_0_14212, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X2)=X2|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_8854, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_14213, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=X2|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_8855, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_14214, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)|~c_List_Olist__all2(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_8856]), ['final']). 4.46/4.74 cnf(c_0_14215, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Oimage(X2,X1,X3),X4)))|~c_Fun_Oinj__on(X2,X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8857]), ['final']). 4.46/4.74 cnf(c_0_14216, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))), inference(split_conjunct,[status(thm)],[c_0_6764]), ['final']). 4.46/4.74 cnf(c_0_14217, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8858]), ['final']). 4.46/4.74 cnf(c_0_14218, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8859]), ['final']). 4.46/4.74 cnf(c_0_14219, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))), inference(split_conjunct,[status(thm)],[c_0_6769]), ['final']). 4.46/4.74 cnf(c_0_14220, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatLeastLessThan(X4,X5,X1,X6,X3)))), inference(split_conjunct,[status(thm)],[c_0_8106]), ['final']). 4.46/4.74 cnf(c_0_14221, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8860]), ['final']). 4.46/4.74 cnf(c_0_14222, plain, (X1=c_Int_OMin|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))!=c_Int_OMin), inference(rw,[status(thm)],[c_0_8861, c_0_4760]), ['final']). 4.46/4.74 cnf(c_0_14223, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OgreaterThanAtMost(X4,X1,X5,X6,X3)))), inference(split_conjunct,[status(thm)],[c_0_8107]), ['final']). 4.46/4.74 cnf(c_0_14224, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeastLessThan(X4,X1,X5,X2,X6)))), inference(split_conjunct,[status(thm)],[c_0_8106]), ['final']). 4.46/4.74 cnf(c_0_14225, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThanAtMost(X4,X5,X1,X2,X6)))), inference(split_conjunct,[status(thm)],[c_0_8107]), ['final']). 4.46/4.74 cnf(c_0_14226, plain, (hBOOL(hAPP(c_Predicate_ORangeP(X4,X5,X1),X3))|~hBOOL(hAPP(hAPP(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8702]), ['final']). 4.46/4.74 cnf(c_0_14227, plain, (hBOOL(hAPP(c_Predicate_ODomainP(X4,X5,X1),X2))|~hBOOL(hAPP(hAPP(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8703]), ['final']). 4.46/4.74 cnf(c_0_14228, plain, (c_List_Olist_ONil(X1)=X2|c_List_Olast(X1,X2)=hAPP(c_List_Ohd(X1),hAPP(c_List_Orev(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8862]), ['final']). 4.46/4.74 cnf(c_0_14229, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_8863, c_0_5120])]), ['final']). 4.46/4.74 cnf(c_0_14230, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8864]), ['final']). 4.46/4.74 cnf(c_0_14231, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(er,[status(thm)],[c_0_8865]), ['final']). 4.46/4.74 cnf(c_0_14232, plain, (hBOOL(hAPP(X1,esk403_3(X2,X3,X1)))|X2=c_FunDef_OTHE__default(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_8505]), ['final']). 4.46/4.74 cnf(c_0_14233, plain, (X3=c_List_Oinsert(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7988]), ['final']). 4.46/4.74 cnf(c_0_14234, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|~hBOOL(hAPP(X1,X2))), inference(er,[status(thm)],[c_0_8866]), ['final']). 4.46/4.74 cnf(c_0_14235, plain, (c_Fun_Oinj__on(tc_Nat_Onat,X1,c_Nat_Osemiring__1__class_Oof__nat(X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))|~class_Nat_Osemiring__char__0(X1)), inference(split_conjunct,[status(thm)],[c_0_8867]), ['final']). 4.46/4.74 cnf(c_0_14236, plain, (hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Oone__class_Oone(X1)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8868]), ['final']). 4.46/4.74 cnf(c_0_14237, plain, (hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Oone__class_Oone(X1)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8869]), ['final']). 4.46/4.74 cnf(c_0_14238, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8870]), ['final']). 4.46/4.74 cnf(c_0_14239, plain, (c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3)=c_Divides_Odiv__class_Omod(X1,X2,X3)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8871]), ['final']). 4.46/4.74 cnf(c_0_14240, plain, (X2=X1|hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)!=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)), inference(split_conjunct,[status(thm)],[c_0_8872]), ['final']). 4.46/4.74 cnf(c_0_14241, plain, (hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(X1)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8873]), ['final']). 4.46/4.74 cnf(c_0_14242, plain, (hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8874]), ['final']). 4.46/4.74 cnf(c_0_14243, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8875]), ['final']). 4.46/4.74 cnf(c_0_14244, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(c_List_Orev(X1),X2))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8876]), ['final']). 4.46/4.74 cnf(c_0_14245, plain, (X1=X2|hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X1),X4),X5)!=hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X2),X6),X7)), inference(split_conjunct,[status(thm)],[c_0_8877]), ['final']). 4.46/4.74 cnf(c_0_14246, plain, (X1=X2|hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X4),X1),X5)!=hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X6),X2),X7)), inference(split_conjunct,[status(thm)],[c_0_8877]), ['final']). 4.46/4.74 cnf(c_0_14247, plain, (X1=X2|hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X4),X5),X1)!=hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X6),X7),X2)), inference(split_conjunct,[status(thm)],[c_0_8877]), ['final']). 4.46/4.74 cnf(c_0_14248, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Osublist(X1,X2,X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8878]), ['final']). 4.46/4.74 cnf(c_0_14249, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_8879]), ['final']). 4.46/4.74 cnf(c_0_14250, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8880]), ['final']). 4.46/4.74 cnf(c_0_14251, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8881]), ['final']). 4.46/4.74 cnf(c_0_14252, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremove1(X1,X3,X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8882]), ['final']). 4.46/4.74 cnf(c_0_14253, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_OtakeWhile(X1,X3,X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8883]), ['final']). 4.46/4.74 cnf(c_0_14254, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oinsert(X1,X3,X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8884]), ['final']). 4.46/4.74 cnf(c_0_14255, plain, (c_FunDef_Oreduction__pair(X3,hAPP(hAPP(c_FunDef_Orp__inv__image(X1,X3),X2),X4))|~c_FunDef_Oreduction__pair(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8885]), ['final']). 4.46/4.74 cnf(c_0_14256, plain, (c_Wellfounded_Owf(X3,hAPP(hAPP(c_Relation_Oinv__image(X1,X3),X2),X4))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8886]), ['final']). 4.46/4.74 cnf(c_0_14257, plain, (hBOOL(hAPP(X1,X2))|hAPP(c_List_Ofilter(X3,X1),X4)!=hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5)), inference(split_conjunct,[status(thm)],[c_0_5090]), ['final']). 4.46/4.74 cnf(c_0_14258, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8887]), ['final']). 4.46/4.74 cnf(c_0_14259, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(X1,esk376_1(X1)))), inference(rw,[status(thm)],[c_0_8888, c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_14260, plain, (hAPP(c_Set_Oimage(X2,X1,X4),X5)=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|~c_Typedef_Otype__definition(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_8889]), ['final']). 4.46/4.74 cnf(c_0_14261, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X1),c_Divides_Odivmod__int(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_8890]), ['final']). 4.46/4.74 cnf(c_0_14262, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(X1,esk109_1(X1)))), inference(rw,[status(thm)],[c_0_8891, c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_14263, plain, (X2=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8892]), ['final']). 4.46/4.74 cnf(c_0_14264, plain, (X3=X2|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8893]), ['final']). 4.46/4.74 cnf(c_0_14265, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_8894]), ['final']). 4.46/4.74 cnf(c_0_14266, plain, (X2=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8895]), ['final']). 4.46/4.74 cnf(c_0_14267, plain, (X3=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8896]), ['final']). 4.46/4.74 cnf(c_0_14268, plain, (X3=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8897]), ['final']). 4.46/4.74 cnf(c_0_14269, plain, (c_SMT_Oz3div(X2,X1)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_8260]), ['final']). 4.46/4.74 cnf(c_0_14270, plain, (X2=X1|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_8898]), ['final']). 4.46/4.74 cnf(c_0_14271, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_8180]), ['final']). 4.46/4.74 cnf(c_0_14272, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_8180]), ['final']). 4.46/4.74 cnf(c_0_14273, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_8899]), ['final']). 4.46/4.74 cnf(c_0_14274, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8900]), ['final']). 4.46/4.74 cnf(c_0_14275, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Otl(X1),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8901]), ['final']). 4.46/4.74 cnf(c_0_14276, plain, (c_List_Olist_ONil(X1)=X2|hAPP(c_List_Ohd(X1),X2)=c_List_Olast(X1,hAPP(c_List_Orev(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8902]), ['final']). 4.46/4.74 cnf(c_0_14277, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_8284]), ['final']). 4.46/4.74 cnf(c_0_14278, plain, (hBOOL(hAPP(c_List_Odistinct(X1),esk407_2(X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5506]), ['final']). 4.46/4.74 cnf(c_0_14279, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Osorted__list__of__set(X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8903]), ['final']). 4.46/4.74 cnf(c_0_14280, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Odrop(X1),X3),X2))|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8904]), ['final']). 4.46/4.74 cnf(c_0_14281, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8905]), ['final']). 4.46/4.74 cnf(c_0_14282, plain, (hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X4|~c_Finite__Set_Ofolding__one(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8906]), ['final']). 4.46/4.74 cnf(c_0_14283, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Otake(X1),X3),X2))|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8907]), ['final']). 4.46/4.74 cnf(c_0_14284, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)))|~hBOOL(hAPP(X1,esk370_3(X2,X3,X1)))|~hBOOL(hAPP(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_5242]), ['final']). 4.46/4.74 cnf(c_0_14285, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(er,[status(thm)],[c_0_8908]), ['final']). 4.46/4.74 cnf(c_0_14286, plain, (X1=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X4),X4)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X2),X1)|~class_Groups_Oab__group__add(X3)), inference(er,[status(thm)],[c_0_8909]), ['final']). 4.46/4.74 cnf(c_0_14287, plain, (hBOOL(hAPP(X2,X3))|c_List_Olist__ex(X1,X2,X4)|~c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8832]), ['final']). 4.46/4.74 cnf(c_0_14288, plain, (hBOOL(hAPP(X1,X2))|c_List_Olist__ex1(X3,X1,X4)|~c_List_Olist__ex1(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_5229]), ['final']). 4.46/4.74 cnf(c_0_14289, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8910]), ['final']). 4.46/4.74 cnf(c_0_14290, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(X1,esk52_1(X1)))), inference(split_conjunct,[status(thm)],[c_0_8283]), ['final']). 4.46/4.74 cnf(c_0_14291, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X2)|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8911]), ['final']). 4.46/4.74 cnf(c_0_14292, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8912]), ['final']). 4.46/4.74 cnf(c_0_14293, plain, (c_Finite__Set_Ofun__left__comm(X1,tc_List_Olist(X1),c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8913]), ['final']). 4.46/4.74 cnf(c_0_14294, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|hAPP(X1,X2)!=hAPP(X1,X3)|~c_Equiv__Relations_Oequivp(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_8356]), ['final']). 4.46/4.74 cnf(c_0_14295, plain, (hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X1),X4),X2))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_8914]), ['final']). 4.46/4.74 cnf(c_0_14296, plain, (hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),X1),X2))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_8915]), ['final']). 4.46/4.74 cnf(c_0_14297, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatLeastAtMost(X4,X1,X5,X3)))), inference(split_conjunct,[status(thm)],[c_0_8237]), ['final']). 4.46/4.74 cnf(c_0_14298, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OgreaterThanLessThan(X4,X1,X5,X3)))), inference(split_conjunct,[status(thm)],[c_0_8242]), ['final']). 4.46/4.74 cnf(c_0_14299, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeastAtMost(X4,X1,X2,X5)))), inference(split_conjunct,[status(thm)],[c_0_8237]), ['final']). 4.46/4.74 cnf(c_0_14300, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThanLessThan(X4,X1,X2,X5)))), inference(split_conjunct,[status(thm)],[c_0_8242]), ['final']). 4.46/4.74 cnf(c_0_14301, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X1,hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,X2)))|~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X1,hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,esk283_2(X2,X1)))))|~hBOOL(hAPP(c_Com_OWT,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8916, c_0_5580]), c_0_5555]), c_0_5580])]), ['final']). 4.46/4.74 cnf(c_0_14302, plain, (hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_8917]), ['final']). 4.46/4.74 cnf(c_0_14303, plain, (X2=hAPP(c_List_Orotate1(X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_8918]), ['final']). 4.46/4.74 cnf(c_0_14304, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__no__zero__divisors(X1)), inference(er,[status(thm)],[c_0_8919]), ['final']). 4.46/4.74 cnf(c_0_14305, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8920]), ['final']). 4.46/4.74 cnf(c_0_14306, plain, (epred1_3(X1,X3,X2)|~hBOOL(hAPP(X1,esk534_3(X2,X3,X1)))|~hBOOL(hAPP(X1,esk532_3(X2,X3,X1)))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5089]), ['final']). 4.46/4.74 cnf(c_0_14307, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8921]), ['final']). 4.46/4.74 cnf(c_0_14308, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8922]), ['final']). 4.46/4.74 cnf(c_0_14309, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2)=c_Groups_Oone__class_Oone(X1)|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_8923]), ['final']). 4.46/4.74 cnf(c_0_14310, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X2)=c_Orderings_Otop__class_Otop(X1)|~class_Lattices_Obounded__lattice__top(X1)), inference(split_conjunct,[status(thm)],[c_0_8924]), ['final']). 4.46/4.74 cnf(c_0_14311, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)|~class_Rings_Omult__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_8925]), ['final']). 4.46/4.74 cnf(c_0_14312, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8926]), ['final']). 4.46/4.74 cnf(c_0_14313, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ozero__class_Ozero(X1)),X2)|~class_Rings_Odivision__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8927]), ['final']). 4.46/4.74 cnf(c_0_14314, plain, (hAPP(c_List_Oset(X1),esk407_2(X2,X1))=X2|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5506]), ['final']). 4.46/4.74 cnf(c_0_14315, plain, (hAPP(c_List_Oset(X1),c_List_Olinorder__class_Osorted__list__of__set(X1,X2))=X2|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8903]), ['final']). 4.46/4.74 cnf(c_0_14316, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_List_Onth(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_List_Ohd(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_8928]), ['final']). 4.46/4.74 cnf(c_0_14317, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8929]), ['final']). 4.46/4.74 cnf(c_0_14318, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X1,X2)))|~hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,X2))), inference(split_conjunct,[status(thm)],[c_0_8930]), ['final']). 4.46/4.74 cnf(c_0_14319, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)=X3|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)|~class_Rings_Oring__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_5550]), ['final']). 4.46/4.74 cnf(c_0_14320, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ono__zero__divisors(X1)|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_8931]), ['final']). 4.46/4.74 cnf(c_0_14321, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[c_0_8932, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_14322, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_8372]), ['final']). 4.46/4.74 cnf(c_0_14323, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_8372]), ['final']). 4.46/4.74 cnf(c_0_14324, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X3))|X1!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X3)|~class_Lattices_Osemilattice__inf(X2)), inference(split_conjunct,[status(thm)],[c_0_8933]), ['final']). 4.46/4.74 cnf(c_0_14325, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X1))|X1!=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X3),X1)|~class_Lattices_Osemilattice__sup(X2)), inference(split_conjunct,[status(thm)],[c_0_8816]), ['final']). 4.46/4.74 cnf(c_0_14326, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|~c_List_Olist__all2(X1,X2,X3,hAPP(c_List_Orev(X1),X4),hAPP(c_List_Orev(X2),X5))), inference(split_conjunct,[status(thm)],[c_0_8445]), ['final']). 4.46/4.74 cnf(c_0_14327, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),c_List_OtakeWhile(X3,X1,X4))))), inference(split_conjunct,[status(thm)],[c_0_8425]), ['final']). 4.46/4.74 cnf(c_0_14328, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X1,hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X2))))|~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X2))),X1),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X2)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8934, c_0_5580]), c_0_5580]), ['final']). 4.46/4.74 cnf(c_0_14329, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,X1)))|~hBOOL(hAPP(c_Com_OWT,X1))), inference(rw,[status(thm)],[c_0_8935, c_0_5580]), ['final']). 4.46/4.74 cnf(c_0_14330, plain, (c_List_Olist_ONil(X1)=X3|hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)!=c_List_Olist_ONil(X1)), inference(rw,[status(thm)],[c_0_8936, c_0_5902]), ['final']). 4.46/4.74 cnf(c_0_14331, plain, (X1=X2|c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X2)!=hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))|~class_Orderings_Oorder(X3)), inference(split_conjunct,[status(thm)],[c_0_8937]), ['final']). 4.46/4.74 cnf(c_0_14332, plain, (X1=X2|c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)!=hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))|~class_Orderings_Oorder(X3)), inference(split_conjunct,[status(thm)],[c_0_8937]), ['final']). 4.46/4.74 cnf(c_0_14333, plain, (c_Groups_Oone__class_Oone(X1)=c_Groups_Osgn__class_Osgn(X1,X2)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_8938]), ['final']). 4.46/4.74 cnf(c_0_14334, plain, (X2=esk19_2(X1,X3)|~hBOOL(hAPP(X1,X2))|~c_List_Olist__ex1(X3,X1,c_Enum_Oenum__class_Oenum(X3))|~class_Enum_Oenum(X3)), inference(split_conjunct,[status(thm)],[c_0_8417]), ['final']). 4.46/4.74 cnf(c_0_14335, plain, (c_List_Olist__ex(X1,X2,X3)|c_List_Olist__ex(X1,X2,X4)|~c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8844]), ['final']). 4.46/4.74 cnf(c_0_14336, plain, (c_Equiv__Relations_Oequivp(X2,X1)|hAPP(X1,esk417_1(X1))!=hAPP(X1,esk418_1(X1))|~hBOOL(hAPP(hAPP(X1,esk417_1(X1)),esk418_1(X1)))), inference(split_conjunct,[status(thm)],[c_0_8356]), ['final']). 4.46/4.74 cnf(c_0_14337, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Olinordered__ab__group__add(X1)), inference(er,[status(thm)],[c_0_8939]), ['final']). 4.46/4.74 cnf(c_0_14338, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_8940]), ['final']). 4.46/4.74 cnf(c_0_14339, plain, (hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(er,[status(thm)],[c_0_8941]), ['final']). 4.46/4.74 cnf(c_0_14340, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,esk206_2(X2,X1)))), inference(rw,[status(thm)],[c_0_8942, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_14341, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)=c_Nat__Transfer_Otsub(X2,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8943]), ['final']). 4.46/4.74 cnf(c_0_14342, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))), inference(split_conjunct,[status(thm)],[c_0_8786]), ['final']). 4.46/4.74 cnf(c_0_14343, plain, (c_List_Olist__ex1(X2,X1,c_Enum_Oenum__class_Oenum(X2))|esk20_3(X1,X2,X3)!=X3|~hBOOL(hAPP(X1,X3))|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_8417]), ['final']). 4.46/4.74 cnf(c_0_14344, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X3),hAPP(hAPP(c_List_Omap(X1,X3),X4),X2)))), inference(split_conjunct,[status(thm)],[c_0_7969]), ['final']). 4.46/4.74 cnf(c_0_14345, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_5491]), ['final']). 4.46/4.74 cnf(c_0_14346, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8944]), ['final']). 4.46/4.74 cnf(c_0_14347, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__no__zero__divisors(X1)), inference(er,[status(thm)],[c_0_8945]), ['final']). 4.46/4.74 cnf(c_0_14348, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_8946]), ['final']). 4.46/4.74 cnf(c_0_14349, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8947]), ['final']). 4.46/4.74 cnf(c_0_14350, plain, (hBOOL(hAPP(X1,esk19_2(X1,X2)))|~c_List_Olist__ex1(X2,X1,c_Enum_Oenum__class_Oenum(X2))|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_8417]), ['final']). 4.46/4.74 cnf(c_0_14351, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)|~class_Rings_Ono__zero__divisors(X1)|~class_Rings_Ozero__neq__one(X1)|~class_Rings_Omult__zero(X1)|~class_Power_Opower(X1)), inference(split_conjunct,[status(thm)],[c_0_5533]), ['final']). 4.46/4.74 cnf(c_0_14352, plain, (~c_Relation_Oirrefl(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_7451]), ['final']). 4.46/4.74 cnf(c_0_14353, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_8948]), ['final']). 4.46/4.74 cnf(c_0_14354, plain, (~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_8949]), ['final']). 4.46/4.74 cnf(c_0_14355, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X3|hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,esk77_4(X1,X2,X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_7354]), ['final']). 4.46/4.74 cnf(c_0_14356, plain, (~hBOOL(hAPP(hAPP(c_member(X1),esk33_3(X2,X3,X1)),esk34_3(X2,X3,X1)))|hAPP(c_Nat_OSuc,X2)!=hAPP(c_Finite__Set_Ocard(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_5438]), ['final']). 4.46/4.74 cnf(c_0_14357, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Odivision__ring__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_8950]), ['final']). 4.46/4.74 cnf(c_0_14358, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_8951]), ['final']). 4.46/4.74 cnf(c_0_14359, plain, (hBOOL(hAPP(hAPP(X3,X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OlessThan(X1,X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_8598]), ['final']). 4.46/4.74 cnf(c_0_14360, plain, (hBOOL(hAPP(hAPP(X3,X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatMost(X1,X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_8599]), ['final']). 4.46/4.74 cnf(c_0_14361, plain, (hBOOL(hAPP(hAPP(X3,X4),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OgreaterThan(X1,X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_8600]), ['final']). 4.46/4.74 cnf(c_0_14362, plain, (hBOOL(hAPP(hAPP(X3,X4),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatLeast(X1,X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_8605]), ['final']). 4.46/4.74 cnf(c_0_14363, plain, (c_Orderings_Otop__class_Otop(X1)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Orderings_Otop__class_Otop(X1))|~class_Lattices_Obounded__lattice__top(X1)), inference(split_conjunct,[status(thm)],[c_0_8952]), ['final']). 4.46/4.74 cnf(c_0_14364, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[c_0_8953, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_14365, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Orderings_Otop__class_Otop(X1)))|~class_Orderings_Otop(X1)), inference(split_conjunct,[status(thm)],[c_0_8954]), ['final']). 4.46/4.74 cnf(c_0_14366, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8955]), ['final']). 4.46/4.74 cnf(c_0_14367, plain, (hBOOL(hAPP(X1,esk100_1(X1)))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))), inference(split_conjunct,[status(thm)],[c_0_8154]), ['final']). 4.46/4.74 cnf(c_0_14368, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)!=X3|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8956]), ['final']). 4.46/4.74 cnf(c_0_14369, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),c_Groups_Ozero__class_Ozero(X1))|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8957]), ['final']). 4.46/4.74 cnf(c_0_14370, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)!=X2|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8958]), ['final']). 4.46/4.74 cnf(c_0_14371, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_6707]), ['final']). 4.46/4.74 cnf(c_0_14372, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X4))), inference(split_conjunct,[status(thm)],[c_0_6707]), ['final']). 4.46/4.74 cnf(c_0_14373, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_8959]), ['final']). 4.46/4.74 cnf(c_0_14374, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=hAPP(c_List_Ohd(X3),c_List_Oreplicate(X3,X1,X2))), inference(split_conjunct,[status(thm)],[c_0_8960]), ['final']). 4.46/4.74 cnf(c_0_14375, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8961]), ['final']). 4.46/4.74 cnf(c_0_14376, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk524_1(X1))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_8554]), ['final']). 4.46/4.74 cnf(c_0_14377, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5942]), ['final']). 4.46/4.74 cnf(c_0_14378, plain, (c_Wellfounded_Owf(tc_List_Olist(X1),hAPP(c_List_Olexn(X1,X2),X3))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8962]), ['final']). 4.46/4.74 cnf(c_0_14379, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)!=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))), inference(split_conjunct,[status(thm)],[c_0_8963]), ['final']). 4.46/4.74 cnf(c_0_14380, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)=X1), inference(split_conjunct,[status(thm)],[c_0_8917]), ['final']). 4.46/4.74 cnf(c_0_14381, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2))|~class_Orderings_Oorder(X1)), inference(er,[status(thm)],[c_0_8964]), ['final']). 4.46/4.74 cnf(c_0_14382, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Omult__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_8965]), ['final']). 4.46/4.74 cnf(c_0_14383, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)!=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))), inference(split_conjunct,[status(thm)],[c_0_8963]), ['final']). 4.46/4.74 cnf(c_0_14384, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)), inference(er,[status(thm)],[c_0_8966]), ['final']). 4.46/4.74 cnf(c_0_14385, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(csr,[status(thm)],[c_0_8967, c_0_8250]), ['final']). 4.46/4.74 cnf(c_0_14386, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X2)),c_Sum__Type_OPlus(X1,X2,X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_8968]), ['final']). 4.46/4.74 cnf(c_0_14387, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8969]), ['final']). 4.46/4.74 cnf(c_0_14388, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8970]), ['final']). 4.46/4.74 cnf(c_0_14389, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8971]), ['final']). 4.46/4.74 cnf(c_0_14390, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_List_Olist_ONil(tc_List_Olist(X2))=c_Enum_On__lists(X2,X1,c_List_Olist_ONil(X2))), inference(split_conjunct,[status(thm)],[c_0_8972]), ['final']). 4.46/4.74 cnf(c_0_14391, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X2)),c_Sum__Type_OPlus(X1,X2,X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_8973]), ['final']). 4.46/4.74 cnf(c_0_14392, plain, (hAPP(hAPP(X3,X7),X7)=X7|~c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_8974]), ['final']). 4.46/4.74 cnf(c_0_14393, plain, (c_Relation_Ototal__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3))|~c_Relation_Ototal__on(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8975]), ['final']). 4.46/4.74 cnf(c_0_14394, plain, (c_Relation_Orefl__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3))|~c_Relation_Orefl__on(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8976]), ['final']). 4.46/4.74 cnf(c_0_14395, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2)=c_Groups_Oone__class_Oone(X1)|~class_Rings_Odivision__ring__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_8977]), ['final']). 4.46/4.74 cnf(c_0_14396, plain, (X2=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8978]), ['final']). 4.46/4.74 cnf(c_0_14397, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8979]), ['final']). 4.46/4.74 cnf(c_0_14398, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk412_1(X1)),X1))|c_Nat__Transfer_Onat__set(X1)), inference(split_conjunct,[status(thm)],[c_0_8980]), ['final']). 4.46/4.74 cnf(c_0_14399, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X2)),X1))|~hBOOL(hAPP(X1,c_Option_Ooption_ONone(X2)))|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_7521]), ['final']). 4.46/4.74 cnf(c_0_14400, plain, (X1=X2|c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X3))!=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),X4)), inference(rw,[status(thm)],[c_0_8981, c_0_4517]), ['final']). 4.46/4.74 cnf(c_0_14401, plain, (X4=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)|~class_Groups_Ocancel__semigroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8982]), ['final']). 4.46/4.74 cnf(c_0_14402, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Oone__class_Oone(X1)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8983]), ['final']). 4.46/4.74 cnf(c_0_14403, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),esk204_1(X1))))|~hBOOL(hAPP(X1,X2))), inference(rw,[status(thm)],[c_0_8984, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_14404, plain, (X4=X3|~class_Groups_Ocancel__ab__semigroup__add(X1)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)), inference(split_conjunct,[status(thm)],[c_0_8985]), ['final']). 4.46/4.74 cnf(c_0_14405, plain, (X3=X4|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)|~class_Groups_Ocancel__semigroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8986]), ['final']). 4.46/4.74 cnf(c_0_14406, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2)=c_Groups_Oone__class_Oone(X1)|~class_Rings_Odivision__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8987]), ['final']). 4.46/4.74 cnf(c_0_14407, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X4),X3))|~class_Orderings_Oord(X2)), inference(split_conjunct,[status(thm)],[c_0_7650]), ['final']). 4.46/4.74 cnf(c_0_14408, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_7741]), ['final']). 4.46/4.74 cnf(c_0_14409, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_7635]), ['final']). 4.46/4.74 cnf(c_0_14410, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_7635]), ['final']). 4.46/4.74 cnf(c_0_14411, plain, (c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))|~c_Nat__Transfer_Onat__set(X1)|~c_Nat__Transfer_Onat__set(X2)), inference(split_conjunct,[status(thm)],[c_0_8988]), ['final']). 4.46/4.74 cnf(c_0_14412, plain, (c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))|~c_Nat__Transfer_Onat__set(X1)|~c_Nat__Transfer_Onat__set(X2)), inference(split_conjunct,[status(thm)],[c_0_8989]), ['final']). 4.46/4.74 cnf(c_0_14413, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_8990]), ['final']). 4.46/4.74 cnf(c_0_14414, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_7741]), ['final']). 4.46/4.74 cnf(c_0_14415, plain, (hBOOL(hAPP(X1,esk217_3(X2,X1,X3)))|~c_Enum_Oex__n__lists(X3,X1,X2)|~class_Enum_Oenum(X3)), inference(split_conjunct,[status(thm)],[c_0_7237]), ['final']). 4.46/4.74 cnf(c_0_14416, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X2,X3,X1)))|~hBOOL(hAPP(c_Com_OWT,X1))), inference(split_conjunct,[status(thm)],[c_0_8991]), ['final']). 4.46/4.74 cnf(c_0_14417, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oab__group__add(X1)), inference(er,[status(thm)],[c_0_8992]), ['final']). 4.46/4.74 cnf(c_0_14418, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_8993]), ['final']). 4.46/4.74 cnf(c_0_14419, plain, (c_List_Olist_ONil(X1)=X2|c_List_Olinorder__class_Osorted(X1,c_List_Obutlast(X1,X2))|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8994]), ['final']). 4.46/4.74 cnf(c_0_14420, plain, (c_List_Olinorder__class_Osorted(X1,esk68_2(X2,X1))|X2=c_List_Olist_ONil(X1)|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5314]), ['final']). 4.46/4.74 cnf(c_0_14421, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_List_Olast(X2,c_List_Oreplicate(X2,X1,X3))=X3), inference(split_conjunct,[status(thm)],[c_0_8995]), ['final']). 4.46/4.74 cnf(c_0_14422, plain, (c_List_Olist_ONil(X1)=X3|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Olist_ONil(X1)!=hAPP(hAPP(c_List_Otake(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_8996]), ['final']). 4.46/4.74 cnf(c_0_14423, plain, (X5=X4|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|hAPP(X3,X4)!=hAPP(X3,X5)), inference(split_conjunct,[status(thm)],[c_0_8997]), ['final']). 4.46/4.74 cnf(c_0_14424, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X1)|~class_Power_Opower(X1)), inference(split_conjunct,[status(thm)],[c_0_8998]), ['final']). 4.46/4.74 cnf(c_0_14425, plain, (X2=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=X1), inference(split_conjunct,[status(thm)],[c_0_8999]), ['final']). 4.46/4.74 cnf(c_0_14426, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)=X2|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_9000]), ['final']). 4.46/4.74 cnf(c_0_14427, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)=X2|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_9001]), ['final']). 4.46/4.74 cnf(c_0_14428, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=X2|~class_Groups_Omonoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_9002]), ['final']). 4.46/4.74 cnf(c_0_14429, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|c_List_Oupto(X1,X2)=c_List_Olist_ONil(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_7659]), ['final']). 4.46/4.74 cnf(c_0_14430, plain, (X1=X2|hAPP(hAPP(c_Product__Type_OPair(X3,X4),X2),X5)!=hAPP(hAPP(c_Product__Type_OPair(X3,X4),X1),X6)), inference(split_conjunct,[status(thm)],[c_0_9003]), ['final']). 4.46/4.74 cnf(c_0_14431, plain, (X1=X2|hAPP(hAPP(c_Product__Type_OPair(X3,X4),X5),X2)!=hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X1)), inference(split_conjunct,[status(thm)],[c_0_9003]), ['final']). 4.46/4.74 cnf(c_0_14432, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Nat__Transfer_Otsub(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_8943]), ['final']). 4.46/4.74 cnf(c_0_14433, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9004]), ['final']). 4.46/4.74 cnf(c_0_14434, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=X2|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_9005]), ['final']). 4.46/4.74 cnf(c_0_14435, plain, (X2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9006]), ['final']). 4.46/4.74 cnf(c_0_14436, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9007]), ['final']). 4.46/4.74 cnf(c_0_14437, plain, (X2=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2)|~class_Lattices_Obounded__lattice__top(X1)), inference(split_conjunct,[status(thm)],[c_0_9008]), ['final']). 4.46/4.74 cnf(c_0_14438, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X4))|~hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Osort__key(X1,X2,X3,X4)))|~class_Orderings_Olinorder(X2)), inference(split_conjunct,[status(thm)],[c_0_8724]), ['final']). 4.46/4.74 cnf(c_0_14439, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk99_2(X1,X2)),X2))), inference(split_conjunct,[status(thm)],[c_0_8514]), ['final']). 4.46/4.74 cnf(c_0_14440, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk424_2(X1,X2)),X2))), inference(split_conjunct,[status(thm)],[c_0_8515]), ['final']). 4.46/4.74 cnf(c_0_14441, plain, (hAPP(X1,X2)=hAPP(X1,X3)|~hBOOL(hAPP(hAPP(X1,X2),X3))|~c_Equiv__Relations_Oequivp(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_8356]), ['final']). 4.46/4.74 cnf(c_0_14442, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_9009]), ['final']). 4.46/4.74 cnf(c_0_14443, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_9010]), ['final']). 4.46/4.74 cnf(c_0_14444, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Groups_Omonoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_9011]), ['final']). 4.46/4.74 cnf(c_0_14445, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_9012]), ['final']). 4.46/4.74 cnf(c_0_14446, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Orderings_Otop__class_Otop(X1))=X2|~class_Lattices_Obounded__lattice__top(X1)), inference(split_conjunct,[status(thm)],[c_0_9013]), ['final']). 4.46/4.74 cnf(c_0_14447, plain, (X2=X3|c_Groups_Ozero__class_Ozero(X1)=X3|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Odivision__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_9014]), ['final']). 4.46/4.74 cnf(c_0_14448, plain, (c_Wellfounded_Owf(X1,X2)|c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))!=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)), inference(split_conjunct,[status(thm)],[c_0_9015]), ['final']). 4.46/4.74 cnf(c_0_14449, plain, (c_Wellfounded_OwfP(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))), inference(rw,[status(thm)],[c_0_9016, c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_14450, plain, (c_SMT_Oz3mod(X2,X1)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_8574]), ['final']). 4.46/4.74 cnf(c_0_14451, plain, (X2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_9017]), ['final']). 4.46/4.74 cnf(c_0_14452, plain, (X2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9018]), ['final']). 4.46/4.74 cnf(c_0_14453, plain, (X2=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Oone__class_Oone(X1))|~class_Rings_Odivision__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_9019]), ['final']). 4.46/4.74 cnf(c_0_14454, plain, (X6=hAPP(X4,hAPP(X3,X6))|~c_Typedef_Otype__definition(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_9020]), ['final']). 4.46/4.74 cnf(c_0_14455, plain, (c_List_Olist__all(X2,X1,X3)|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk145_3(X3,X1,X2))))), inference(split_conjunct,[status(thm)],[c_0_8040]), ['final']). 4.46/4.74 cnf(c_0_14456, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X4,X1,X5),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8567]), ['final']). 4.46/4.74 cnf(c_0_14457, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9021]), ['final']). 4.46/4.74 cnf(c_0_14458, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_9022]), ['final']). 4.46/4.74 cnf(c_0_14459, plain, (X2=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_9023]), ['final']). 4.46/4.74 cnf(c_0_14460, plain, (X2=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_9024]), ['final']). 4.46/4.74 cnf(c_0_14461, plain, (hBOOL(hAPP(hAPP(X3,X5),X4))|~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9025]), ['final']). 4.46/4.74 cnf(c_0_14462, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk453_3(X3,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_8568]), ['final']). 4.46/4.74 cnf(c_0_14463, plain, (X2=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9026]), ['final']). 4.46/4.74 cnf(c_0_14464, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X2,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7481]), ['final']). 4.46/4.74 cnf(c_0_14465, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk240_3(X3,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_8570]), ['final']). 4.46/4.74 cnf(c_0_14466, plain, (hBOOL(hAPP(X2,esk356_2(X2,X1)))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X2))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_9027]), ['final']). 4.46/4.74 cnf(c_0_14467, plain, (hBOOL(hAPP(X2,esk310_2(X2,X1)))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X2))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_9028]), ['final']). 4.46/4.74 cnf(c_0_14468, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8948]), ['final']). 4.46/4.74 cnf(c_0_14469, plain, (hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[c_0_9029, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_14470, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_8929]), ['final']). 4.46/4.74 cnf(c_0_14471, plain, (c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9030]), ['final']). 4.46/4.74 cnf(c_0_14472, plain, (c_Lazy__Sequence_Osmall__lazy_H(X1,X2)=c_Lazy__Sequence_Oempty(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7437]), ['final']). 4.46/4.74 cnf(c_0_14473, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9031]), ['final']). 4.46/4.74 cnf(c_0_14474, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(c_List_Olistsp(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_8284]), ['final']). 4.46/4.74 cnf(c_0_14475, plain, (c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_9032]), ['final']). 4.46/4.74 cnf(c_0_14476, plain, (c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9033]), ['final']). 4.46/4.74 cnf(c_0_14477, plain, (c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9034]), ['final']). 4.46/4.74 cnf(c_0_14478, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9035]), ['final']). 4.46/4.74 cnf(c_0_14479, plain, (X2=c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9036]), ['final']). 4.46/4.74 cnf(c_0_14480, plain, (c_Power_Opower_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1))=c_Power_Opower__class_Opower(X1)|~class_Power_Opower(X1)), inference(split_conjunct,[status(thm)],[c_0_9037]), ['final']). 4.46/4.74 cnf(c_0_14481, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1)), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9038])]), ['final']). 4.46/4.74 cnf(c_0_14482, plain, (X2=c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9039]), ['final']). 4.46/4.74 cnf(c_0_14483, plain, (X3=X4|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4))), inference(split_conjunct,[status(thm)],[c_0_5940]), ['final']). 4.46/4.74 cnf(c_0_14484, plain, (~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_9040]), ['final']). 4.46/4.74 cnf(c_0_14485, plain, (~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_9041]), ['final']). 4.46/4.74 cnf(c_0_14486, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9042]), ['final']). 4.46/4.74 cnf(c_0_14487, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Ois__nat(X1)|~c_Nat__Transfer_Ois__nat(X2)), inference(split_conjunct,[status(thm)],[c_0_9043]), ['final']). 4.46/4.74 cnf(c_0_14488, plain, (X3=hAPP(c_Option_Ooption_OSome(X1),X2)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Option_Oset(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_9044]), ['final']). 4.46/4.74 cnf(c_0_14489, plain, (X3=X4|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),X3))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9045]), ['final']). 4.46/4.74 cnf(c_0_14490, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Ois__nat(X1)|~c_Nat__Transfer_Ois__nat(X2)), inference(split_conjunct,[status(thm)],[c_0_9046]), ['final']). 4.46/4.74 cnf(c_0_14491, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Ois__nat(X1)|~c_Nat__Transfer_Ois__nat(X2)), inference(split_conjunct,[status(thm)],[c_0_9047]), ['final']). 4.46/4.74 cnf(c_0_14492, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_9048]), ['final']). 4.46/4.74 cnf(c_0_14493, plain, (hBOOL(hAPP(X3,X4))|X4=X2|~hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5990]), ['final']). 4.46/4.74 cnf(c_0_14494, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_List_Oset(X3),c_List_Oreplicate(X3,X4,X2))))), inference(split_conjunct,[status(thm)],[c_0_5450]), ['final']). 4.46/4.74 cnf(c_0_14495, plain, (epred2_3(X1,X3,X2)|~hBOOL(hAPP(X1,esk537_3(X2,X3,X1)))|~hBOOL(hAPP(X1,esk535_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5124]), ['final']). 4.46/4.74 cnf(c_0_14496, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=X2|~class_Groups_Ogroup__add(X1)), inference(er,[status(thm)],[c_0_9049]), ['final']). 4.46/4.74 cnf(c_0_14497, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_8859]), ['final']). 4.46/4.74 cnf(c_0_14498, plain, (X1=hAPP(c_Int_ORep__Integ,esk200_1(X1))|~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Int_OInteg))), inference(split_conjunct,[status(thm)],[c_0_9050]), ['final']). 4.46/4.74 cnf(c_0_14499, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X1,X3),tc_HOL_Obool))!=c_Sum__Type_OPlus(X1,X3,X2,X4)), inference(split_conjunct,[status(thm)],[c_0_5922]), ['final']). 4.46/4.74 cnf(c_0_14500, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X3,X2),tc_HOL_Obool))!=c_Sum__Type_OPlus(X3,X2,X4,X1)), inference(split_conjunct,[status(thm)],[c_0_5922]), ['final']). 4.46/4.74 cnf(c_0_14501, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(X1)|~class_Power_Opower(X1)|~class_Rings_Ono__zero__divisors(X1)|~class_Rings_Ozero__neq__one(X1)|~class_Rings_Omult__zero(X1)), inference(er,[status(thm)],[c_0_9051]), ['final']). 4.46/4.74 cnf(c_0_14502, plain, (X1=X2|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9052, c_0_5334]), c_0_5334]), ['final']). 4.46/4.74 cnf(c_0_14503, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)!=X3), inference(split_conjunct,[status(thm)],[c_0_9053]), ['final']). 4.46/4.74 cnf(c_0_14504, plain, (hBOOL(hAPP(X1,esk493_3(X2,X1,X3)))|~c_List_Olist__ex1(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7265]), ['final']). 4.46/4.74 cnf(c_0_14505, plain, (hBOOL(hAPP(X1,esk352_3(X2,X1,X3)))|~c_List_Olist__ex(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8299]), ['final']). 4.46/4.74 cnf(c_0_14506, plain, (hBOOL(hAPP(X1,esk162_3(X2,X1,X3)))|~c_List_Olist__ex1(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7272]), ['final']). 4.46/4.74 cnf(c_0_14507, plain, (X1=X2|c_Random_Oinc__shift(X2,X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), inference(split_conjunct,[status(thm)],[c_0_6001]), ['final']). 4.46/4.74 cnf(c_0_14508, plain, (hBOOL(hAPP(X1,esk286_2(X2,X1)))|~hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_9054]), ['final']). 4.46/4.74 cnf(c_0_14509, plain, (c_List_Olist__ex(X1,X2,hAPP(c_List_Orev(X1),X3))|~c_List_Olist__ex(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9055]), ['final']). 4.46/4.74 cnf(c_0_14510, plain, (c_List_Olist__all(X1,X2,hAPP(c_List_Orev(X1),X3))|~c_List_Olist__all(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9056]), ['final']). 4.46/4.74 cnf(c_0_14511, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8753]), ['final']). 4.46/4.74 cnf(c_0_14512, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5593]), ['final']). 4.46/4.74 cnf(c_0_14513, plain, (hAPP(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))=X4|~c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_9057]), ['final']). 4.46/4.74 cnf(c_0_14514, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=X1|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[c_0_9058, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_14515, plain, (hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_9054]), ['final']). 4.46/4.74 cnf(c_0_14516, plain, (c_Fun_Oinj__on(X1,X3,X5,X6)|~c_Fun_Oinj__on(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),X6)), inference(split_conjunct,[status(thm)],[c_0_9059]), ['final']). 4.46/4.74 cnf(c_0_14517, plain, (X1=X3|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_9060]), ['final']). 4.46/4.74 cnf(c_0_14518, plain, (X3=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)), inference(split_conjunct,[status(thm)],[c_0_9061]), ['final']). 4.46/4.74 cnf(c_0_14519, plain, (c_List_Olinorder__class_Osorted(X1,X3)|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8541]), ['final']). 4.46/4.74 cnf(c_0_14520, plain, (~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1))))), inference(er,[status(thm)],[c_0_9062]), ['final']). 4.46/4.74 cnf(c_0_14521, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_9063, c_0_4836]), ['final']). 4.46/4.74 cnf(c_0_14522, plain, (c_Orderings_Otop__class_Otop(X1)=hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,X1)),X3)|~class_Orderings_Otop(X1)), inference(split_conjunct,[status(thm)],[c_0_9064]), ['final']). 4.46/4.74 cnf(c_0_14523, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_9065]), ['final']). 4.46/4.74 cnf(c_0_14524, plain, (X2=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_9066]), ['final']). 4.46/4.74 cnf(c_0_14525, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|X2=X3|c_List_Oreplicate(X4,X1,X2)!=c_List_Oreplicate(X4,X5,X3)), inference(split_conjunct,[status(thm)],[c_0_9067]), ['final']). 4.46/4.74 cnf(c_0_14526, plain, (hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5990]), ['final']). 4.46/4.74 cnf(c_0_14527, plain, (c_List_Olist_ONil(X2)=c_List_Olinorder__class_Osort__key(X2,X1,X3,c_List_Olist_ONil(X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9068]), ['final']). 4.46/4.74 cnf(c_0_14528, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X3),X1))|~hBOOL(hAPP(X1,X2))|~class_Enum_Oenum(X3)), inference(split_conjunct,[status(thm)],[c_0_9028]), ['final']). 4.46/4.74 cnf(c_0_14529, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5338]), ['final']). 4.46/4.74 cnf(c_0_14530, plain, (~class_Rings_Olinordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_9069]), ['final']). 4.46/4.74 cnf(c_0_14531, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Orderings_Obot__class_Obot(X1)),X2))|~class_Orderings_Obot(X1)), inference(split_conjunct,[status(thm)],[c_0_9070]), ['final']). 4.46/4.74 cnf(c_0_14532, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))), inference(split_conjunct,[status(thm)],[c_0_9071]), ['final']). 4.46/4.74 cnf(c_0_14533, plain, (c_FunDef_OTHE__default(X3,X2,X4)=c_HOL_OThe(X3,X4)|X1!=esk404_4(X2,X3,X4,X1)|~hBOOL(hAPP(X4,X1))), inference(split_conjunct,[status(thm)],[c_0_8505]), ['final']). 4.46/4.74 cnf(c_0_14534, plain, (X1=X2|hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)!=hAPP(hAPP(c_List_Olist_OCons(X3),X1),X5)), inference(split_conjunct,[status(thm)],[c_0_9072]), ['final']). 4.46/4.74 cnf(c_0_14535, plain, (X1=X2|hAPP(hAPP(c_List_Olist_OCons(X3),X4),X2)!=hAPP(hAPP(c_List_Olist_OCons(X3),X5),X1)), inference(split_conjunct,[status(thm)],[c_0_9072]), ['final']). 4.46/4.74 cnf(c_0_14536, plain, (X2=X4|hAPP(hAPP(c_List_Oappend(X1),X2),X3)!=hAPP(hAPP(c_List_Oappend(X1),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_9073]), ['final']). 4.46/4.74 cnf(c_0_14537, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),esk393_1(X1))))), inference(rw,[status(thm)],[c_0_9074, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_14538, plain, (hBOOL(hAPP(hAPP(c_member(X3),X2),X1))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_9075]), ['final']). 4.46/4.74 cnf(c_0_14539, plain, (X4=X3|hAPP(hAPP(c_List_Oappend(X1),X2),X3)!=hAPP(hAPP(c_List_Oappend(X1),X2),X4)), inference(split_conjunct,[status(thm)],[c_0_9076]), ['final']). 4.46/4.74 cnf(c_0_14540, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4))), inference(split_conjunct,[status(thm)],[c_0_6671]), ['final']). 4.46/4.74 cnf(c_0_14541, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X2),X2))|~class_HOL_Oequal(X1)), inference(split_conjunct,[status(thm)],[c_0_9077]), ['final']). 4.46/4.74 cnf(c_0_14542, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2))|~class_Orderings_Opreorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9078]), ['final']). 4.46/4.74 cnf(c_0_14543, plain, (c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X2))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9079]), ['final']). 4.46/4.74 cnf(c_0_14544, plain, (c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X2))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9080]), ['final']). 4.46/4.74 cnf(c_0_14545, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))|~c_Wellfounded_Oacyclic(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9081]), ['final']). 4.46/4.74 cnf(c_0_14546, plain, (hAPP(X3,X4)=X5|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5)!=X3), inference(split_conjunct,[status(thm)],[c_0_9082]), ['final']). 4.46/4.74 cnf(c_0_14547, plain, (X2=X3|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_9083]), ['final']). 4.46/4.74 cnf(c_0_14548, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X6))), inference(split_conjunct,[status(thm)],[c_0_9084]), ['final']). 4.46/4.74 cnf(c_0_14549, plain, (X2=c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9085]), ['final']). 4.46/4.74 cnf(c_0_14550, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_8900]), ['final']). 4.46/4.74 cnf(c_0_14551, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X2,X1)))|~hBOOL(hAPP(c_Com_OWT,X1))), inference(split_conjunct,[status(thm)],[c_0_9086]), ['final']). 4.46/4.74 cnf(c_0_14552, plain, (hAPP(c_Nat_OSuc,esk244_1(X1))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_9087]), ['final']). 4.46/4.74 cnf(c_0_14553, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_8905]), ['final']). 4.46/4.74 cnf(c_0_14554, plain, (c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=c_Random_Olog(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), inference(split_conjunct,[status(thm)],[c_0_7365]), ['final']). 4.46/4.74 cnf(c_0_14555, plain, (c_Option_Ooption_ONone(X1)=hAPP(X2,X3)|hAPP(c_Map_Omap__add(X4,X1,X2,X5),X3)!=c_Option_Ooption_ONone(X1)), inference(split_conjunct,[status(thm)],[c_0_8673]), ['final']). 4.46/4.74 cnf(c_0_14556, plain, (c_Option_Ooption_ONone(X1)=hAPP(X2,X3)|hAPP(c_Map_Omap__add(X4,X1,X5,X2),X3)!=c_Option_Ooption_ONone(X1)), inference(split_conjunct,[status(thm)],[c_0_8673]), ['final']). 4.46/4.74 cnf(c_0_14557, plain, (hBOOL(hAPP(X2,X4))|~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9088]), ['final']). 4.46/4.74 cnf(c_0_14558, plain, (hBOOL(hAPP(X3,X4))|~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9089]), ['final']). 4.46/4.74 cnf(c_0_14559, plain, (X4=hAPP(hAPP(X2,X4),X4)|~c_Finite__Set_Ofolding__one__idem(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9090]), ['final']). 4.46/4.74 cnf(c_0_14560, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Otl(X1),X2))|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9091]), ['final']). 4.46/4.74 cnf(c_0_14561, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_9092]), ['final']). 4.46/4.74 cnf(c_0_14562, plain, (X1=c_Orderings_Otop__class_Otop(X2)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X3)!=c_Orderings_Otop__class_Otop(X2)|~class_Lattices_Obounded__lattice__top(X2)), inference(split_conjunct,[status(thm)],[c_0_9093]), ['final']). 4.46/4.74 cnf(c_0_14563, plain, (X1=c_Orderings_Otop__class_Otop(X2)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X3),X1)!=c_Orderings_Otop__class_Otop(X2)|~class_Lattices_Obounded__lattice__top(X2)), inference(split_conjunct,[status(thm)],[c_0_9093]), ['final']). 4.46/4.74 cnf(c_0_14564, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_9094, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_14565, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))), inference(rw,[status(thm)],[c_0_9095, c_0_6178]), ['final']). 4.46/4.74 cnf(c_0_14566, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(er,[status(thm)],[c_0_9096]), ['final']). 4.46/4.74 cnf(c_0_14567, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8601]), ['final']). 4.46/4.74 cnf(c_0_14568, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(rw,[status(thm)],[c_0_9097, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_14569, plain, (c_Complete__Lattice_OSup__class_OSup(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9098]), ['final']). 4.46/4.74 cnf(c_0_14570, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2)=c_Orderings_Obot__class_Obot(X1)|~class_Lattices_Obounded__lattice__bot(X1)), inference(split_conjunct,[status(thm)],[c_0_9099]), ['final']). 4.46/4.74 cnf(c_0_14571, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1))=c_Orderings_Obot__class_Obot(X1)|~class_Lattices_Obounded__lattice__bot(X1)), inference(split_conjunct,[status(thm)],[c_0_9100]), ['final']). 4.46/4.74 cnf(c_0_14572, plain, (X1=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9101]), ['final']). 4.46/4.74 cnf(c_0_14573, plain, (X4=X5|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X5))), inference(split_conjunct,[status(thm)],[c_0_9102]), ['final']). 4.46/4.74 cnf(c_0_14574, plain, (c_Wellfounded_Owf(X1,X3)|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9103]), ['final']). 4.46/4.74 cnf(c_0_14575, plain, (c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),esk292_2(X2,X1)),c_Wellfounded_Oacc(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_9104]), ['final']). 4.46/4.74 cnf(c_0_14576, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X2))=c_Groups_Osgn__class_Osgn(X1,X2)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_9105]), ['final']). 4.46/4.74 cnf(c_0_14577, plain, (X3=X2|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|~class_Int_Oring__char__0(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_9106]), ['final']). 4.46/4.74 cnf(c_0_14578, plain, (hBOOL(hAPP(c_Predicate_OPowp(X3,X1),X2))|~hBOOL(hAPP(X1,esk96_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8454]), ['final']). 4.46/4.74 cnf(c_0_14579, plain, (hBOOL(hAPP(c_List_Olistsp(X3,X1),X2))|~hBOOL(hAPP(X1,esk120_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8041]), ['final']). 4.46/4.74 cnf(c_0_14580, plain, (X2=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2)|~class_Lattices_Obounded__lattice__bot(X1)), inference(split_conjunct,[status(thm)],[c_0_9107]), ['final']). 4.46/4.74 cnf(c_0_14581, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~c_Wellfounded_OwfP(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9108]), ['final']). 4.46/4.74 cnf(c_0_14582, plain, (c_Groups_Ozero__class_Ozero(X1)=c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_9109]), ['final']). 4.46/4.74 cnf(c_0_14583, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Nitpick_Ocard_H(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5012]), ['final']). 4.46/4.74 cnf(c_0_14584, plain, (X2=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1))|~class_Lattices_Obounded__lattice__bot(X1)), inference(split_conjunct,[status(thm)],[c_0_9110]), ['final']). 4.46/4.74 cnf(c_0_14585, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(c_Finite__Set_Ocard(X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9111]), ['final']). 4.46/4.74 cnf(c_0_14586, plain, (c_Fun_Oid(X2)=hAPP(X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))|~c_Finite__Set_Ofolding(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_9112]), ['final']). 4.46/4.74 cnf(c_0_14587, plain, (c_Groups_Ozero__class_Ozero(X1)=c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Oone__class_Oone(X1))|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_9113]), ['final']). 4.46/4.74 cnf(c_0_14588, plain, (c_Nitpick_Owf_H(X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))|~c_Wellfounded_Oacyclic(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8751]), ['final']). 4.46/4.74 cnf(c_0_14589, plain, (hBOOL(hAPP(X1,c_Option_Ooption_ONone(X2)))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X2)),X1))|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_8051]), ['final']). 4.46/4.74 cnf(c_0_14590, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X1)=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_9114]), ['final']). 4.46/4.74 cnf(c_0_14591, plain, (hBOOL(hAPP(hAPP(X2,X3),X3))|~c_Predicate_Oreflp(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9115]), ['final']). 4.46/4.74 cnf(c_0_14592, plain, (hBOOL(hAPP(hAPP(X2,X3),X3))|~c_Equiv__Relations_Oequivp(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9116]), ['final']). 4.46/4.74 cnf(c_0_14593, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)=X3|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9117]), ['final']). 4.46/4.74 cnf(c_0_14594, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(split_conjunct,[status(thm)],[c_0_9118]), ['final']). 4.46/4.74 cnf(c_0_14595, plain, (hAPP(c_List_Ofilter(X3,X1),X2)=X2|~hBOOL(hAPP(X1,esk386_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8108]), ['final']). 4.46/4.74 cnf(c_0_14596, plain, (hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X2))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_9119]), ['final']). 4.46/4.74 cnf(c_0_14597, plain, (hAPP(c_Option_Ooption_OSome(X1),esk268_2(X1,X2))=X2|c_Option_Ooption_ONone(X1)=X2), inference(split_conjunct,[status(thm)],[c_0_9120]), ['final']). 4.46/4.74 cnf(c_0_14598, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8571]), ['final']). 4.46/4.74 cnf(c_0_14599, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2)), inference(split_conjunct,[status(thm)],[c_0_9121]), ['final']). 4.46/4.74 cnf(c_0_14600, plain, (c_Option_Ooption_ONone(X1)=X2|X2=hAPP(c_Option_Ooption_OSome(X1),esk259_2(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_9122]), ['final']). 4.46/4.74 cnf(c_0_14601, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Oremove1(X1,X3,X2))|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9123]), ['final']). 4.46/4.74 cnf(c_0_14602, plain, (c_List_Olinorder__class_Osorted(X1,c_List_OtakeWhile(X1,X3,X2))|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9124]), ['final']). 4.46/4.74 cnf(c_0_14603, plain, (c_List_Olinorder__class_Osorted(X1,esk407_2(X2,X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5506]), ['final']). 4.46/4.74 cnf(c_0_14604, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osorted__list__of__set(X1,X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8903]), ['final']). 4.46/4.74 cnf(c_0_14605, plain, (X2=X3|hAPP(X1,X2)!=hAPP(X1,X3)|~c_Typedef_Otype__definition(X4,X5,X1,X6,X7)), inference(split_conjunct,[status(thm)],[c_0_9125]), ['final']). 4.46/4.74 cnf(c_0_14606, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X2),X1))|~hBOOL(hAPP(X1,esk509_2(X1,X2)))|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_9126]), ['final']). 4.46/4.74 cnf(c_0_14607, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X2),X1))|~hBOOL(hAPP(X1,esk182_2(X1,X2)))|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_9119]), ['final']). 4.46/4.74 cnf(c_0_14608, plain, (c_List_Olist_ONil(tc_Int_Oint)=c_List_Oupto(X2,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9127]), ['final']). 4.46/4.74 cnf(c_0_14609, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_9128]), ['final']). 4.46/4.74 cnf(c_0_14610, plain, (c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=c_Random_Olog(X2,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7365]), ['final']). 4.46/4.74 cnf(c_0_14611, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X3,X4,X1),X5),X2))), inference(split_conjunct,[status(thm)],[c_0_8567]), ['final']). 4.46/4.74 cnf(c_0_14612, plain, (hBOOL(hAPP(X1,X2))|~c_List_Olist__all(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_8713]), ['final']). 4.46/4.74 cnf(c_0_14613, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|~class_Rings_Oring__1__no__zero__divisors(X1)|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_9129]), ['final']). 4.46/4.74 cnf(c_0_14614, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[c_0_9130, c_0_5120]), ['final']). 4.46/4.74 cnf(c_0_14615, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5556]), ['final']). 4.46/4.74 cnf(c_0_14616, plain, (c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X2)|~c_Hoare__Mirabelle_Otriple__valid(X1,esk347_3(X2,X3,X1),esk348_3(X2,X3,X1))), inference(split_conjunct,[status(thm)],[c_0_7303]), ['final']). 4.46/4.74 cnf(c_0_14617, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))|~class_Orderings_Opreorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8153]), ['final']). 4.46/4.74 cnf(c_0_14618, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9131]), ['final']). 4.46/4.74 cnf(c_0_14619, plain, (c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olex(X1,X2))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9132]), ['final']). 4.46/4.74 cnf(c_0_14620, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2)=X2|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9133]), ['final']). 4.46/4.74 cnf(c_0_14621, plain, (X2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Lattices_Oab__semigroup__idem__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_9134]), ['final']). 4.46/4.74 cnf(c_0_14622, plain, (X2=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2)|~class_Lattices_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_9135]), ['final']). 4.46/4.74 cnf(c_0_14623, plain, (c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olenlex(X1,X2))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9136]), ['final']). 4.46/4.74 cnf(c_0_14624, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,esk301_2(X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_8335]), ['final']). 4.46/4.74 cnf(c_0_14625, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Oacyclic(X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_9137]), ['final']). 4.46/4.74 cnf(c_0_14626, plain, (X2=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2)|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9138]), ['final']). 4.46/4.74 cnf(c_0_14627, plain, (X2=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2)|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_9139]), ['final']). 4.46/4.74 cnf(c_0_14628, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))|hAPP(X4,X2)!=c_Option_Ooption_ONone(X3)), inference(split_conjunct,[status(thm)],[c_0_8634]), ['final']). 4.46/4.74 cnf(c_0_14629, plain, (~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_9140]), ['final']). 4.46/4.74 cnf(c_0_14630, plain, (~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_9141]), ['final']). 4.46/4.74 cnf(c_0_14631, plain, (epred2_3(X1,X2,X3)|~hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_8776]), ['final']). 4.46/4.74 cnf(c_0_14632, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5567]), ['final']). 4.46/4.74 cnf(c_0_14633, plain, (c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8728]), ['final']). 4.46/4.74 cnf(c_0_14634, plain, (c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_8728]), ['final']). 4.46/4.74 cnf(c_0_14635, plain, (c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_8713]), ['final']). 4.46/4.74 cnf(c_0_14636, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Ois__nat(X1)), inference(split_conjunct,[status(thm)],[c_0_9142]), ['final']). 4.46/4.74 cnf(c_0_14637, plain, (c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Ozero__class_Ozero(X1))=X2|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_9143]), ['final']). 4.46/4.74 cnf(c_0_14638, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))=X3|hAPP(c_Relation_ORange(X1,X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5983]), ['final']). 4.46/4.74 cnf(c_0_14639, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))|hAPP(c_Relation_ODomain(X1,X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5984]), ['final']). 4.46/4.74 cnf(c_0_14640, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_9144]), ['final']). 4.46/4.74 cnf(c_0_14641, plain, (X3=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)!=X2|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)), inference(split_conjunct,[status(thm)],[c_0_5558]), ['final']). 4.46/4.74 cnf(c_0_14642, plain, (X3=X2|hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)!=hAPP(c_Int_Oring__1__class_Oof__int(X1),X3)|~class_Int_Oring__char__0(X1)), inference(split_conjunct,[status(thm)],[c_0_9145]), ['final']). 4.46/4.74 cnf(c_0_14643, plain, (X3=X2|hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)!=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_9146]), ['final']). 4.46/4.74 cnf(c_0_14644, plain, (X3=X2|hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))!=hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_9147]), ['final']). 4.46/4.74 cnf(c_0_14645, plain, (X2=X3|hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)!=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_9148]), ['final']). 4.46/4.74 cnf(c_0_14646, plain, (X3=X2|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)|~class_Nat_Osemiring__char__0(X1)), inference(split_conjunct,[status(thm)],[c_0_9149]), ['final']). 4.46/4.74 cnf(c_0_14647, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2))), inference(split_conjunct,[status(thm)],[c_0_8793]), ['final']). 4.46/4.74 cnf(c_0_14648, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))|~epred1_3(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9150]), ['final']). 4.46/4.74 cnf(c_0_14649, plain, (hBOOL(hAPP(hAPP(c_fconj,X1),X2))|~hBOOL(X1)|~hBOOL(X2)), inference(split_conjunct,[status(thm)],[c_0_9151]), ['final']). 4.46/4.74 cnf(c_0_14650, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_Enum_Oenum__class_Oenum(X1)))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_9152]), ['final']). 4.46/4.74 cnf(c_0_14651, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8625]), ['final']). 4.46/4.74 cnf(c_0_14652, plain, (c_Fun_Oinj__on(X1,X1,c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_9153]), ['final']). 4.46/4.74 cnf(c_0_14653, plain, (X1=X2|hAPP(X1,esk160_2(X1,X2))!=hAPP(X2,esk160_2(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_9154]), ['final']). 4.46/4.74 cnf(c_0_14654, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_9155, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_14655, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_9156]), ['final']). 4.46/4.74 cnf(c_0_14656, plain, (c_Orderings_Obot__class_Obot(X1)=X2|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)!=c_Orderings_Obot__class_Obot(X1)|~class_Lattices_Obounded__lattice__bot(X1)), inference(split_conjunct,[status(thm)],[c_0_9157]), ['final']). 4.46/4.74 cnf(c_0_14657, plain, (c_Fun_Oinj__on(X4,X3,X2,X1)|esk261_4(X1,X2,X3,X4)!=esk262_4(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8401]), ['final']). 4.46/4.74 cnf(c_0_14658, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8829]), ['final']). 4.46/4.74 cnf(c_0_14659, plain, (X1=c_Orderings_Obot__class_Obot(X2)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X3)!=c_Orderings_Obot__class_Obot(X2)|~class_Lattices_Obounded__lattice__bot(X2)), inference(split_conjunct,[status(thm)],[c_0_9157]), ['final']). 4.46/4.74 cnf(c_0_14660, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_8829]), ['final']). 4.46/4.74 cnf(c_0_14661, plain, (hBOOL(hAPP(c_Com_OWT,X3))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_9158]), ['final']). 4.46/4.74 cnf(c_0_14662, plain, (c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7184]), ['final']). 4.46/4.74 cnf(c_0_14663, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Oone__class_Oone(X1))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_9159]), ['final']). 4.46/4.74 cnf(c_0_14664, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_9118]), ['final']). 4.46/4.74 cnf(c_0_14665, plain, (c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7184]), ['final']). 4.46/4.74 cnf(c_0_14666, plain, (c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7448]), ['final']). 4.46/4.74 cnf(c_0_14667, plain, (c_Nat__Transfer_Onat__set(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk412_1(X1)))), inference(split_conjunct,[status(thm)],[c_0_8980]), ['final']). 4.46/4.74 cnf(c_0_14668, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(c_List_Omonoid__add__class_Olistsum(X1),c_List_Olist_ONil(X1))|~class_Groups_Omonoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_9160]), ['final']). 4.46/4.74 cnf(c_0_14669, plain, (c_Orderings_Otop__class_Otop(X1)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1))|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_9161]), ['final']). 4.46/4.74 cnf(c_0_14670, plain, (c_Orderings_Obot__class_Obot(X1)=c_Complete__Lattice_OInf__class_OInf(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9162]), ['final']). 4.46/4.74 cnf(c_0_14671, plain, (c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X2))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9163]), ['final']). 4.46/4.74 cnf(c_0_14672, plain, (c_Wellfounded_Owf(X1,c_Wellfounded_Omlex__prod(X1,X3,X2))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9164]), ['final']). 4.46/4.74 cnf(c_0_14673, plain, (c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))|~c_Nat__Transfer_Ois__nat(X1)|~c_Nat__Transfer_Ois__nat(X2)), inference(split_conjunct,[status(thm)],[c_0_9165]), ['final']). 4.46/4.74 cnf(c_0_14674, plain, (c_Enum_Oall__n__lists(X3,X1,X2)|~hBOOL(hAPP(X1,esk387_3(X2,X1,X3)))|~class_Enum_Oenum(X3)), inference(split_conjunct,[status(thm)],[c_0_7138]), ['final']). 4.46/4.74 cnf(c_0_14675, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_9166]), ['final']). 4.46/4.74 cnf(c_0_14676, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_5524]), ['final']). 4.46/4.74 cnf(c_0_14677, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2)=X2|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9167]), ['final']). 4.46/4.74 cnf(c_0_14678, plain, (X2=c_List_OtakeWhile(X3,X1,X2)|~hBOOL(hAPP(X1,esk277_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8193]), ['final']). 4.46/4.74 cnf(c_0_14679, plain, (c_List_Olist_ONil(X1)=X4|hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)!=c_List_Olist_ONil(X2)), inference(split_conjunct,[status(thm)],[c_0_9168]), ['final']). 4.46/4.74 cnf(c_0_14680, plain, (c_List_Olist_ONil(X1)=X2|c_List_Olist_ONil(X1)!=hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_9169]), ['final']). 4.46/4.74 cnf(c_0_14681, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_9170]), ['final']). 4.46/4.74 cnf(c_0_14682, plain, (X2=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9171]), ['final']). 4.46/4.74 cnf(c_0_14683, plain, (X3=X2|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)!=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)), inference(split_conjunct,[status(thm)],[c_0_9172]), ['final']). 4.46/4.74 cnf(c_0_14684, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_9173]), ['final']). 4.46/4.74 cnf(c_0_14685, plain, (X4=c_Option_Ooption_ONone(X1)|hAPP(hAPP(c_Option_Omap(X1,X2),X3),X4)!=c_Option_Ooption_ONone(X2)), inference(split_conjunct,[status(thm)],[c_0_9174]), ['final']). 4.46/4.74 cnf(c_0_14686, plain, (X2=X3|hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)!=hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9175]), ['final']). 4.46/4.74 cnf(c_0_14687, plain, (c_Orderings_Obot__class_Obot(X1)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1))|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_9176]), ['final']). 4.46/4.74 cnf(c_0_14688, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_9173]), ['final']). 4.46/4.74 cnf(c_0_14689, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=X1|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_9177]), ['final']). 4.46/4.74 cnf(c_0_14690, plain, (X2=X3|hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)!=hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9178]), ['final']). 4.46/4.74 cnf(c_0_14691, plain, (X2=X3|hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)!=hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9179]), ['final']). 4.46/4.74 cnf(c_0_14692, plain, (X2=X3|hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)!=hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9180]), ['final']). 4.46/4.74 cnf(c_0_14693, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Oremdups(X1,X2))|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9181]), ['final']). 4.46/4.74 cnf(c_0_14694, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_9182]), ['final']). 4.46/4.74 cnf(c_0_14695, plain, (hBOOL(X1)|hBOOL(hAPP(hAPP(c_fimplies,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9183]), ['final']). 4.46/4.74 cnf(c_0_14696, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Oring__char__0(X1)), inference(split_conjunct,[status(thm)],[c_0_5571]), ['final']). 4.46/4.74 cnf(c_0_14697, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Oring__char__0(X1)), inference(er,[status(thm)],[c_0_9184]), ['final']). 4.46/4.74 cnf(c_0_14698, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9185]), ['final']). 4.46/4.74 cnf(c_0_14699, plain, (hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X2)))|hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1)!=hAPP(c_Com_Obody,X2)), inference(split_conjunct,[status(thm)],[c_0_9186]), ['final']). 4.46/4.74 cnf(c_0_14700, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8685]), ['final']). 4.46/4.74 cnf(c_0_14701, plain, (X2=X3|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5559]), ['final']). 4.46/4.74 cnf(c_0_14702, plain, (X3=X2|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_9187]), ['final']). 4.46/4.74 cnf(c_0_14703, plain, (c_Relation_Ototal__on(X1,X2,X3)|~c_Relation_Ototal__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3))), inference(split_conjunct,[status(thm)],[c_0_8975]), ['final']). 4.46/4.74 cnf(c_0_14704, plain, (hBOOL(hAPP(X3,X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9075]), ['final']). 4.46/4.74 cnf(c_0_14705, plain, (X2=X3|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3)))), inference(split_conjunct,[status(thm)],[c_0_5981]), ['final']). 4.46/4.74 cnf(c_0_14706, plain, (c_Relation_Orefl__on(X1,X2,X3)|~c_Relation_Orefl__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3))), inference(split_conjunct,[status(thm)],[c_0_8976]), ['final']). 4.46/4.74 cnf(c_0_14707, plain, (c_Groups_Ozero__class_Ozero(X1)=c_Divides_Odiv__class_Omod(X1,X2,X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_9188]), ['final']). 4.46/4.74 cnf(c_0_14708, plain, (X1=X2|c_Nitpick_Opair__box_OPairBox(X3,X4,X1,X5)!=c_Nitpick_Opair__box_OPairBox(X3,X4,X2,X6)), inference(split_conjunct,[status(thm)],[c_0_9189]), ['final']). 4.46/4.74 cnf(c_0_14709, plain, (X1=X2|c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X1)!=c_Nitpick_Opair__box_OPairBox(X3,X4,X6,X2)), inference(split_conjunct,[status(thm)],[c_0_9189]), ['final']). 4.46/4.74 cnf(c_0_14710, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_9190]), ['final']). 4.46/4.74 cnf(c_0_14711, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_9190]), ['final']). 4.46/4.74 cnf(c_0_14712, plain, (X3=X2|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X2),X3))|~class_HOL_Oequal(X1)), inference(split_conjunct,[status(thm)],[c_0_9191]), ['final']). 4.46/4.74 cnf(c_0_14713, plain, (hBOOL(hAPP(c_Com_OWT,X2))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_9086]), ['final']). 4.46/4.74 cnf(c_0_14714, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~c_Nat__Transfer_Ois__nat(X1)), inference(split_conjunct,[status(thm)],[c_0_9192]), ['final']). 4.46/4.74 cnf(c_0_14715, plain, (c_List_Olinorder__class_Osorted__list__of__set(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_List_Olist_ONil(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9193]), ['final']). 4.46/4.74 cnf(c_0_14716, plain, (c_List_Olist_ONil(X1)=X2|c_List_Olist_ONil(X1)!=hAPP(hAPP(c_List_Oappend(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_9194]), ['final']). 4.46/4.74 cnf(c_0_14717, plain, (X1=c_List_Olist_ONil(X2)|c_List_Olist_ONil(X2)!=hAPP(hAPP(c_List_Oappend(X2),X3),X1)), inference(split_conjunct,[status(thm)],[c_0_9194]), ['final']). 4.46/4.74 cnf(c_0_14718, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Olinordered__ab__group__add(X1)), inference(er,[status(thm)],[c_0_9195]), ['final']). 4.46/4.74 cnf(c_0_14719, plain, (c_Complete__Lattice_OInf__class_OInf(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9196]), ['final']). 4.46/4.74 cnf(c_0_14720, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Finite__Set_Ofinite(X1)), inference(split_conjunct,[status(thm)],[c_0_9197]), ['final']). 4.46/4.74 cnf(c_0_14721, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_9198]), ['final']). 4.46/4.74 cnf(c_0_14722, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=hAPP(c_Groups_Oabs__class_Oabs(X1),X2)|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_9199]), ['final']). 4.46/4.74 cnf(c_0_14723, plain, (epred1_3(X1,X3,X2)|~hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_9150]), ['final']). 4.46/4.74 cnf(c_0_14724, plain, (c_Wellfounded_OwfP(X1,X2)|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk251_2(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_9200]), ['final']). 4.46/4.74 cnf(c_0_14725, plain, (hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk271_1(X1))=hAPP(c_Com_Obody,X1)|~hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X1)))), inference(split_conjunct,[status(thm)],[c_0_9186]), ['final']). 4.46/4.74 cnf(c_0_14726, plain, (hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk269_1(X1))=hAPP(c_Com_Obody,X1)|~hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X1)))), inference(split_conjunct,[status(thm)],[c_0_9201]), ['final']). 4.46/4.74 cnf(c_0_14727, plain, (hBOOL(X1)|hBOOL(X2)|~hBOOL(hAPP(hAPP(c_fdisj,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9202]), ['final']). 4.46/4.74 cnf(c_0_14728, plain, (c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))|~c_Nat__Transfer_Ois__nat(X1)), inference(split_conjunct,[status(thm)],[c_0_9203]), ['final']). 4.46/4.74 cnf(c_0_14729, plain, (hBOOL(hAPP(c_List_Odistinct(X2),X1))|esk360_2(X1,X2)!=esk361_2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7699]), ['final']). 4.46/4.74 cnf(c_0_14730, plain, (X2=X1|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_9204]), ['final']). 4.46/4.74 cnf(c_0_14731, plain, (c_List_Olist__all(X3,X1,X2)|~hBOOL(hAPP(X1,esk517_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8223]), ['final']). 4.46/4.74 cnf(c_0_14732, plain, (c_List_Olist__all(X3,X1,X2)|~hBOOL(hAPP(X1,esk252_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8227]), ['final']). 4.46/4.74 cnf(c_0_14733, plain, (c_List_Olist__all(X3,X1,X2)|~hBOOL(hAPP(X1,esk6_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_8219]), ['final']). 4.46/4.74 cnf(c_0_14734, plain, (~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_9205]), ['final']). 4.46/4.74 cnf(c_0_14735, plain, (hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3)=c_Orderings_Obot__class_Obot(X1)|~class_Orderings_Obot(X1)), inference(split_conjunct,[status(thm)],[c_0_9206]), ['final']). 4.46/4.74 cnf(c_0_14736, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_9207]), ['final']). 4.46/4.74 cnf(c_0_14737, plain, (~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(X1)))), inference(split_conjunct,[status(thm)],[c_0_9208]), ['final']). 4.46/4.74 cnf(c_0_14738, plain, (c_List_Olist__ex(X1,X2,X3)|~c_List_Olist__ex(X1,X2,hAPP(c_List_Orev(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_9055]), ['final']). 4.46/4.74 cnf(c_0_14739, plain, (c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,hAPP(c_List_Orev(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_9056]), ['final']). 4.46/4.74 cnf(c_0_14740, plain, (X2=X3|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(c_Option_Ooption_OSome(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_9209]), ['final']). 4.46/4.74 cnf(c_0_14741, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1)), inference(er,[status(thm)],[c_0_9210]), ['final']). 4.46/4.74 cnf(c_0_14742, plain, (X3=X2|hAPP(c_List_Orev(X1),X2)!=hAPP(c_List_Orev(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_9211]), ['final']). 4.46/4.74 cnf(c_0_14743, plain, (X2=c_List_Olist_ONil(X1)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_9212]), ['final']). 4.46/4.74 cnf(c_0_14744, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|X1!=hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1)|~class_Groups_Olinordered__ab__group__add(X2)), inference(split_conjunct,[status(thm)],[c_0_5572]), ['final']). 4.46/4.74 cnf(c_0_14745, plain, (hBOOL(hAPP(X1,X2))|~epred1_3(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)), inference(er,[status(thm)],[c_0_9213]), ['final']). 4.46/4.74 cnf(c_0_14746, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Wellfounded_Omax__extp(X1,X3,X2,X4)), inference(split_conjunct,[status(thm)],[c_0_5595]), ['final']). 4.46/4.74 cnf(c_0_14747, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Wellfounded_Omax__extp(X1,X3,X4,X2)), inference(split_conjunct,[status(thm)],[c_0_5595]), ['final']). 4.46/4.74 cnf(c_0_14748, plain, (X2=c_List_Oremdups(X1,X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9214]), ['final']). 4.46/4.74 cnf(c_0_14749, plain, (c_List_Olist_ONil(tc_List_Olist(X1))=c_List_Otranspose(X1,X2)|c_List_Olist_ONil(X1)!=esk504_2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_7980]), ['final']). 4.46/4.74 cnf(c_0_14750, plain, (X4=c_List_Olist_ONil(X2)|~c_List_Olist__all2(X1,X2,X3,c_List_Olist_ONil(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_9215]), ['final']). 4.46/4.74 cnf(c_0_14751, plain, (X4=c_List_Olist_ONil(X1)|~c_List_Olist__all2(X1,X2,X3,X4,c_List_Olist_ONil(X2))), inference(split_conjunct,[status(thm)],[c_0_5986]), ['final']). 4.46/4.74 cnf(c_0_14752, plain, (c_Finite__Set_Ofun__left__comm(X1,X1,c_Groups_Otimes__class_Otimes(X1))|~class_Groups_Oab__semigroup__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_9216]), ['final']). 4.46/4.74 cnf(c_0_14753, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Orderings_Oord__class_Omax(X1))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9217]), ['final']). 4.46/4.74 cnf(c_0_14754, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Orderings_Oord__class_Omin(X1))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9218]), ['final']). 4.46/4.74 cnf(c_0_14755, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Groups_Otimes__class_Otimes(X1))|~class_Lattices_Oab__semigroup__idem__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_9219]), ['final']). 4.46/4.74 cnf(c_0_14756, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1))|~class_Lattices_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_9220]), ['final']). 4.46/4.74 cnf(c_0_14757, plain, (c_Orderings_Oord_Omin(X1,c_Orderings_Oord__class_Oless__eq(X1))=c_Orderings_Oord__class_Omin(X1)|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_9221]), ['final']). 4.46/4.74 cnf(c_0_14758, plain, (X2=c_List_Olist_ONil(X1)|hAPP(hAPP(c_List_Oappend(X1),X2),X3)!=X3), inference(split_conjunct,[status(thm)],[c_0_9222]), ['final']). 4.46/4.74 cnf(c_0_14759, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_9223]), ['final']). 4.46/4.74 cnf(c_0_14760, plain, (c_Relation_Ototal__on(X3,X2,X1)|esk130_3(X1,X2,X3)!=esk131_3(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_6336]), ['final']). 4.46/4.74 cnf(c_0_14761, plain, (c_Relation_Osingle__valued(X3,X2,X1)|esk134_3(X1,X2,X3)!=esk133_3(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7111]), ['final']). 4.46/4.74 cnf(c_0_14762, plain, (c_Hoare__Mirabelle_Otriple__valid(X1,X2,X3)|~c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(c_Nat_OSuc,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_9224]), ['final']). 4.46/4.74 cnf(c_0_14763, plain, (c_Orderings_Oord_Omax(X1,c_Orderings_Oord__class_Oless__eq(X1))=c_Orderings_Oord__class_Omax(X1)|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_9225]), ['final']). 4.46/4.74 cnf(c_0_14764, plain, (X3=c_List_Olist_ONil(X2)|X1!=hAPP(hAPP(c_List_Oappend(X2),X1),X3)), inference(split_conjunct,[status(thm)],[c_0_9226]), ['final']). 4.46/4.74 cnf(c_0_14765, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)!=X1), inference(split_conjunct,[status(thm)],[c_0_9227]), ['final']). 4.46/4.74 cnf(c_0_14766, plain, (hBOOL(hAPP(hAPP(c_fdisj,X1),X2))|~hBOOL(X1)), inference(split_conjunct,[status(thm)],[c_0_9228]), ['final']). 4.46/4.74 cnf(c_0_14767, plain, (X1=X2|c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X2,X4)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X1,X5)), inference(split_conjunct,[status(thm)],[c_0_9229]), ['final']). 4.46/4.74 cnf(c_0_14768, plain, (X1=X2|c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X1)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X5,X2)), inference(split_conjunct,[status(thm)],[c_0_9229]), ['final']). 4.46/4.74 cnf(c_0_14769, plain, (X1=X2|c_List_Oreplicate(X3,X1,X4)!=c_List_Oreplicate(X3,X2,X5)), inference(split_conjunct,[status(thm)],[c_0_9067]), ['final']). 4.46/4.74 cnf(c_0_14770, plain, (X1=X2|c_Com_Ocom_OCond(X2,X3,X4)!=c_Com_Ocom_OCond(X1,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_9230]), ['final']). 4.46/4.74 cnf(c_0_14771, plain, (c_Groups_Ozero__class_Ozero(X1)=c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Osgn__if(X1)), inference(split_conjunct,[status(thm)],[c_0_9231]), ['final']). 4.46/4.74 cnf(c_0_14772, plain, (hBOOL(hAPP(hAPP(c_fdisj,X2),X1))|~hBOOL(X1)), inference(split_conjunct,[status(thm)],[c_0_9232]), ['final']). 4.46/4.74 cnf(c_0_14773, plain, (hBOOL(hAPP(hAPP(c_fimplies,X2),X1))|~hBOOL(X1)), inference(split_conjunct,[status(thm)],[c_0_9233]), ['final']). 4.46/4.74 cnf(c_0_14774, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1)|esk490_1(X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_8475]), ['final']). 4.46/4.74 cnf(c_0_14775, plain, (X1=X2|c_Com_Ocom_OCond(X3,X1,X4)!=c_Com_Ocom_OCond(X5,X2,X6)), inference(split_conjunct,[status(thm)],[c_0_9230]), ['final']). 4.46/4.74 cnf(c_0_14776, plain, (X1=X2|c_Com_Ocom_OCond(X3,X4,X2)!=c_Com_Ocom_OCond(X5,X6,X1)), inference(split_conjunct,[status(thm)],[c_0_9230]), ['final']). 4.46/4.74 cnf(c_0_14777, plain, (X1=X2|c_Com_Ocom_OLocal(X1,X3,X4)!=c_Com_Ocom_OLocal(X2,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_9234]), ['final']). 4.46/4.74 cnf(c_0_14778, plain, (X1=X2|c_Com_Ocom_OLocal(X3,X1,X4)!=c_Com_Ocom_OLocal(X5,X2,X6)), inference(split_conjunct,[status(thm)],[c_0_9234]), ['final']). 4.46/4.74 cnf(c_0_14779, plain, (X1=X2|c_Com_Ocom_OLocal(X3,X4,X1)!=c_Com_Ocom_OLocal(X5,X6,X2)), inference(split_conjunct,[status(thm)],[c_0_9234]), ['final']). 4.46/4.74 cnf(c_0_14780, plain, (hBOOL(hAPP(c_List_Odistinct(X2),X1))|X1!=c_List_Oremdups(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_9235]), ['final']). 4.46/4.74 cnf(c_0_14781, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_9236]), ['final']). 4.46/4.74 cnf(c_0_14782, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X1),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_9236]), ['final']). 4.46/4.74 cnf(c_0_14783, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))!=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_9237]), ['final']). 4.46/4.74 cnf(c_0_14784, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9238]), ['final']). 4.46/4.74 cnf(c_0_14785, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Oone__class_Oone(tc_Int_Oint))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9239]), ['final']). 4.46/4.74 cnf(c_0_14786, plain, (~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2))), inference(er,[status(thm)],[c_0_9240]), ['final']). 4.46/4.74 cnf(c_0_14787, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9241]), ['final']). 4.46/4.74 cnf(c_0_14788, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9242]), ['final']). 4.46/4.74 cnf(c_0_14789, plain, (~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2))), inference(er,[status(thm)],[c_0_9243]), ['final']). 4.46/4.74 cnf(c_0_14790, plain, (class_Lazy__Sequence_Osmall__lazy(tc_prod(X2,X1))|~class_Lazy__Sequence_Osmall__lazy(X1)|~class_Lazy__Sequence_Osmall__lazy(X2)), inference(split_conjunct,[status(thm)],[c_0_9244]), ['final']). 4.46/4.74 cnf(c_0_14791, plain, (class_HOL_Oequal(tc_fun(X1,X2))|~class_Enum_Oenum(X1)|~class_HOL_Oequal(X2)), inference(split_conjunct,[status(thm)],[c_0_9245]), ['final']). 4.46/4.74 cnf(c_0_14792, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_9246]), ['final']). 4.46/4.74 cnf(c_0_14793, plain, (c_Orderings_Obot__class_Obot(X1)=c_Complete__Lattice_OSup__class_OSup(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9247]), ['final']). 4.46/4.74 cnf(c_0_14794, plain, (class_Finite__Set_Ofinite(tc_sum(X2,X1))|~class_Finite__Set_Ofinite(X1)|~class_Finite__Set_Ofinite(X2)), inference(split_conjunct,[status(thm)],[c_0_9248]), ['final']). 4.46/4.74 cnf(c_0_14795, plain, (class_Finite__Set_Ofinite(tc_prod(X2,X1))|~class_Finite__Set_Ofinite(X1)|~class_Finite__Set_Ofinite(X2)), inference(split_conjunct,[status(thm)],[c_0_9249]), ['final']). 4.46/4.74 cnf(c_0_14796, plain, (class_Finite__Set_Ofinite(tc_fun(X2,X1))|~class_Finite__Set_Ofinite(X1)|~class_Finite__Set_Ofinite(X2)), inference(split_conjunct,[status(thm)],[c_0_9250]), ['final']). 4.46/4.74 cnf(c_0_14797, plain, (class_Smallcheck_Osmall(tc_prod(X1,X2))|~class_Smallcheck_Osmall(X1)|~class_Smallcheck_Osmall(X2)), inference(split_conjunct,[status(thm)],[c_0_9251]), ['final']). 4.46/4.74 cnf(c_0_14798, plain, (X4=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(c_Set_Oimage(X1,X2,X3),X4)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_9252]), ['final']). 4.46/4.74 cnf(c_0_14799, plain, (hAPP(c_Com_Obody,X1)=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X1)))), inference(split_conjunct,[status(thm)],[c_0_9253]), ['final']). 4.46/4.74 cnf(c_0_14800, plain, (class_Enum_Oenum(tc_sum(X1,X2))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_9254]), ['final']). 4.46/4.74 cnf(c_0_14801, plain, (class_Enum_Oenum(tc_prod(X1,X2))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_9255]), ['final']). 4.46/4.74 cnf(c_0_14802, plain, (class_Enum_Oenum(tc_fun(X2,X1))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_9256]), ['final']). 4.46/4.74 cnf(c_0_14803, plain, (c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X1,X2))|~c_Nat__Transfer_Ois__nat(X1)|~c_Nat__Transfer_Ois__nat(X2)), inference(split_conjunct,[status(thm)],[c_0_9257]), ['final']). 4.46/4.74 cnf(c_0_14804, plain, (hBOOL(hAPP(c_Com_OWT,X1))|hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1)!=hAPP(c_Com_Obody,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9258, c_0_5554])]), ['final']). 4.46/4.74 cnf(c_0_14805, plain, (~class_Orderings_Olinorder(X1)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),X5)!=c_List_Olist_ONil(X2)), inference(split_conjunct,[status(thm)],[c_0_9259]), ['final']). 4.46/4.74 cnf(c_0_14806, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(split_conjunct,[status(thm)],[c_0_8990]), ['final']). 4.46/4.74 cnf(c_0_14807, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9081]), ['final']). 4.46/4.74 cnf(c_0_14808, plain, (hBOOL(X1)|~hBOOL(X2)|~hBOOL(hAPP(hAPP(c_fimplies,X2),X1))), inference(split_conjunct,[status(thm)],[c_0_9260]), ['final']). 4.46/4.74 cnf(c_0_14809, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Oreplicate(X1,X2,X3)!=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_9261]), ['final']). 4.46/4.74 cnf(c_0_14810, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Osgn__class_Osgn(X1,X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_5573]), ['final']). 4.46/4.74 cnf(c_0_14811, plain, (c_Nat__Transfer_Ois__nat(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_9192]), ['final']). 4.46/4.74 cnf(c_0_14812, plain, (X2=c_List_Olist_ONil(X1)|hAPP(c_List_Oset(X1),X2)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_9262]), ['final']). 4.46/4.74 cnf(c_0_14813, plain, (c_Option_Ooption_ONone(X1)=X2|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=c_Option_Oset(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9263]), ['final']). 4.46/4.74 cnf(c_0_14814, plain, (hBOOL(X1)|hBOOL(hAPP(c_fNot,X1))), inference(split_conjunct,[status(thm)],[c_0_9264]), ['final']). 4.46/4.74 cnf(c_0_14815, plain, (X2=c_List_Olist_ONil(X1)|hAPP(c_List_Orotate1(X1),X2)!=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_9265]), ['final']). 4.46/4.74 cnf(c_0_14816, plain, (X2=c_List_Olist_ONil(X1)|hAPP(c_List_Orev(X1),X2)!=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_9266]), ['final']). 4.46/4.74 cnf(c_0_14817, plain, (c_Nitpick_Owf_H(X1,X2)|~c_Nitpick_Ounknown(tc_HOL_Obool)|~c_Wellfounded_Oacyclic(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8751]), ['final']). 4.46/4.74 cnf(c_0_14818, plain, (c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3)|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9267]), ['final']). 4.46/4.74 cnf(c_0_14819, plain, (c_Wellfounded_Owf(X2,X1)|esk353_2(X1,X2)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_7686]), ['final']). 4.46/4.74 cnf(c_0_14820, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_9268, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_14821, plain, (c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9269]), ['final']). 4.46/4.74 cnf(c_0_14822, plain, (~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2))), inference(split_conjunct,[status(thm)],[c_0_9270]), ['final']). 4.46/4.74 cnf(c_0_14823, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1))|~class_Orderings_Olinorder(X1)), inference(er,[status(thm)],[c_0_9271]), ['final']). 4.46/4.74 cnf(c_0_14824, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_fequal,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9272]), ['final']). 4.46/4.74 cnf(c_0_14825, plain, (X1=X2|c_Com_Ocom_OSemi(X2,X3)!=c_Com_Ocom_OSemi(X1,X4)), inference(split_conjunct,[status(thm)],[c_0_9273]), ['final']). 4.46/4.74 cnf(c_0_14826, plain, (X1=X2|c_Com_Ocom_OSemi(X3,X1)!=c_Com_Ocom_OSemi(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_9273]), ['final']). 4.46/4.74 cnf(c_0_14827, plain, (c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X1))|~c_List_Onat__list(X1)), inference(split_conjunct,[status(thm)],[c_0_9274]), ['final']). 4.46/4.74 cnf(c_0_14828, plain, (X2=X1|hAPP(c_Code__Numeral_Onat__of,X1)!=hAPP(c_Code__Numeral_Onat__of,X2)), inference(split_conjunct,[status(thm)],[c_0_9275]), ['final']). 4.46/4.74 cnf(c_0_14829, plain, (X1=X2|hAPP(c_Int_ORep__Integ,X1)!=hAPP(c_Int_ORep__Integ,X2)), inference(split_conjunct,[status(thm)],[c_0_9276]), ['final']). 4.46/4.74 cnf(c_0_14830, plain, (X1=X2|c_Com_Ocom_OWhile(X1,X3)!=c_Com_Ocom_OWhile(X2,X4)), inference(split_conjunct,[status(thm)],[c_0_9277]), ['final']). 4.46/4.74 cnf(c_0_14831, plain, (X1=X2|c_Com_Ocom_OWhile(X3,X1)!=c_Com_Ocom_OWhile(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_9277]), ['final']). 4.46/4.74 cnf(c_0_14832, plain, (X1=X2|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9278, c_0_5334]), c_0_5334]), ['final']). 4.46/4.74 cnf(c_0_14833, plain, (X2=X1|hAPP(c_Nat_OSuc,X1)!=hAPP(c_Nat_OSuc,X2)), inference(split_conjunct,[status(thm)],[c_0_9279]), ['final']). 4.46/4.74 cnf(c_0_14834, plain, (class_Orderings_Otop(tc_fun(X2,X1))|~class_Orderings_Otop(X1)), inference(split_conjunct,[status(thm)],[c_0_9280]), ['final']). 4.46/4.74 cnf(c_0_14835, plain, (class_Groups_Ouminus(tc_fun(X2,X1))|~class_Groups_Ouminus(X1)), inference(split_conjunct,[status(thm)],[c_0_9281]), ['final']). 4.46/4.74 cnf(c_0_14836, plain, (class_Lattices_Odistrib__lattice(tc_fun(X2,X1))|~class_Lattices_Odistrib__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9282]), ['final']). 4.46/4.74 cnf(c_0_14837, plain, (class_Orderings_Oord(tc_fun(X2,X1))|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_9283]), ['final']). 4.46/4.74 cnf(c_0_14838, plain, (class_Lattices_Oboolean__algebra(tc_fun(X2,X1))|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_9284]), ['final']). 4.46/4.74 cnf(c_0_14839, plain, (class_Orderings_Opreorder(tc_fun(X2,X1))|~class_Orderings_Opreorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9285]), ['final']). 4.46/4.74 cnf(c_0_14840, plain, (class_Lattices_Obounded__lattice__top(tc_fun(X2,X1))|~class_Lattices_Obounded__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9286]), ['final']). 4.46/4.74 cnf(c_0_14841, plain, (class_Lattices_Obounded__lattice(tc_fun(X2,X1))|~class_Lattices_Obounded__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9287]), ['final']). 4.46/4.74 cnf(c_0_14842, plain, (class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9288]), ['final']). 4.46/4.74 cnf(c_0_14843, plain, (hBOOL(X1)|~hBOOL(hAPP(hAPP(c_fconj,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9289]), ['final']). 4.46/4.74 cnf(c_0_14844, plain, (hBOOL(X2)|~hBOOL(hAPP(hAPP(c_fconj,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9290]), ['final']). 4.46/4.74 cnf(c_0_14845, plain, (class_Lattices_Osemilattice__sup(tc_fun(X2,X1))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9291]), ['final']). 4.46/4.74 cnf(c_0_14846, plain, (class_Lattices_Osemilattice__inf(tc_fun(X2,X1))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9292]), ['final']). 4.46/4.74 cnf(c_0_14847, plain, (class_Lattices_Olattice(tc_fun(X2,X1))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9293]), ['final']). 4.46/4.74 cnf(c_0_14848, plain, (class_Orderings_Obot(tc_fun(X2,X1))|~class_Orderings_Obot(X1)), inference(split_conjunct,[status(thm)],[c_0_9294]), ['final']). 4.46/4.74 cnf(c_0_14849, plain, (X2=c_List_Olist_ONil(X1)|c_List_Oremdups(X1,X2)!=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_9295]), ['final']). 4.46/4.74 cnf(c_0_14850, plain, (class_Orderings_Oorder(tc_fun(X2,X1))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9296]), ['final']). 4.46/4.74 cnf(c_0_14851, plain, (class_Lattices_Obounded__lattice__bot(tc_fun(X2,X1))|~class_Lattices_Obounded__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9297]), ['final']). 4.46/4.74 cnf(c_0_14852, plain, (class_Groups_Ominus(tc_fun(X2,X1))|~class_Groups_Ominus(X1)), inference(split_conjunct,[status(thm)],[c_0_9298]), ['final']). 4.46/4.74 cnf(c_0_14853, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|~c_Int_Oiszero(X1,X2)|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9299]), ['final']). 4.46/4.74 cnf(c_0_14854, plain, (X2=X3|~c_List_Olist__all2(X1,X1,c_fequal,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_5994]), ['final']). 4.46/4.74 cnf(c_0_14855, plain, (c_Orderings_Oord__class_Omax(X1)=c_Lattices_Osemilattice__sup__class_Osup(X1)|~class_Lattices_Osemilattice__sup(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9300]), ['final']). 4.46/4.74 cnf(c_0_14856, plain, (c_Lattices_Osemilattice__inf__class_Oinf(X1)=c_Orderings_Oord__class_Omin(X1)|~class_Lattices_Osemilattice__inf(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9301]), ['final']). 4.46/4.74 cnf(c_0_14857, plain, (~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_9302]), ['final']). 4.46/4.74 cnf(c_0_14858, plain, (c_List_Onat__list(X1)|~c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X1))), inference(split_conjunct,[status(thm)],[c_0_9274]), ['final']). 4.46/4.74 cnf(c_0_14859, plain, (class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X1))|~class_Lazy__Sequence_Osmall__lazy(X1)), inference(split_conjunct,[status(thm)],[c_0_9303]), ['final']). 4.46/4.74 cnf(c_0_14860, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9304]), ['final']). 4.46/4.74 cnf(c_0_14861, plain, (class_Finite__Set_Ofinite(tc_Option_Ooption(X1))|~class_Finite__Set_Ofinite(X1)), inference(split_conjunct,[status(thm)],[c_0_9305]), ['final']). 4.46/4.74 cnf(c_0_14862, plain, (class_Enum_Oenum(tc_Option_Ooption(X1))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_9306]), ['final']). 4.46/4.74 cnf(c_0_14863, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Nitpick_Owf_H(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8751]), ['final']). 4.46/4.74 cnf(c_0_14864, plain, (X2=X1|hAPP(c_Com_Ocom_OBODY,X1)!=hAPP(c_Com_Ocom_OBODY,X2)), inference(split_conjunct,[status(thm)],[c_0_9307]), ['final']). 4.46/4.74 cnf(c_0_14865, plain, (c_fequal=c_HOL_Oequal__class_Oequal(X1)|~class_HOL_Oequal(X1)), inference(split_conjunct,[status(thm)],[c_0_9308]), ['final']). 4.46/4.74 cnf(c_0_14866, plain, (~hBOOL(hAPP(c_fNot,X1))|~hBOOL(X1)), inference(split_conjunct,[status(thm)],[c_0_9309]), ['final']). 4.46/4.74 cnf(c_0_14867, plain, (~class_Rings_Osemiring__1(X1)|~c_Int_Oiszero(X1,c_Groups_Oone__class_Oone(X1))), inference(split_conjunct,[status(thm)],[c_0_9310]), ['final']). 4.46/4.74 cnf(c_0_14868, plain, (~class_Rings_Ozero__neq__one(X1)|c_Groups_Ozero__class_Ozero(X1)!=c_Groups_Oone__class_Oone(X1)), inference(split_conjunct,[status(thm)],[c_0_9311]), ['final']). 4.46/4.74 cnf(c_0_14869, negated_conjecture, (~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Com_Ocom,c_Com_Ocom_OBODY),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,v_y)))), inference(rw,[status(thm)],[c_0_9312, c_0_6899]), ['final']). 4.46/4.74 cnf(c_0_14870, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9313, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4760]), ['final']). 4.46/4.74 cnf(c_0_14871, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9314, c_0_4760]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), ['final']). 4.46/4.74 cnf(c_0_14872, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))), inference(rw,[status(thm)],[c_0_9315, c_0_5765]), ['final']). 4.46/4.74 cnf(c_0_14873, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))), inference(rw,[status(thm)],[c_0_9316, c_0_5765]), ['final']). 4.46/4.74 cnf(c_0_14874, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)!=c_Int_OMin), inference(rw,[status(thm)],[c_0_9317, c_0_5765]), ['final']). 4.46/4.74 cnf(c_0_14875, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9318, c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), c_0_4760]), ['final']). 4.46/4.74 cnf(c_0_14876, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Wellfounded_Omax__ext(X1,X3)))), inference(er,[status(thm)],[c_0_9319]), ['final']). 4.46/4.74 cnf(c_0_14877, plain, (~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot)),c_fequal)),X2),X2))), inference(er,[status(thm)],[c_0_9320]), ['final']). 4.46/4.74 cnf(c_0_14878, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olex(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_9321]), ['final']). 4.46/4.74 cnf(c_0_14879, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olistrel1(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_9322]), ['final']). 4.46/4.74 cnf(c_0_14880, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olex(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_9323]), ['final']). 4.46/4.74 cnf(c_0_14881, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olexord(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_9324]), ['final']). 4.46/4.74 cnf(c_0_14882, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olistrel1(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_9325]), ['final']). 4.46/4.74 cnf(c_0_14883, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,c_List_Olist_ONil(tc_fun(X1,tc_Nat_Onat)))))), inference(split_conjunct,[status(thm)],[c_0_9326]), ['final']). 4.46/4.74 cnf(c_0_14884, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9327, c_0_4760]), c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_14885, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9328, c_0_4436]), c_0_4760]), ['final']). 4.46/4.74 cnf(c_0_14886, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_9329, c_0_4760]), ['final']). 4.46/4.74 cnf(c_0_14887, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1)))))), inference(split_conjunct,[status(thm)],[c_0_9330]), ['final']). 4.46/4.74 cnf(c_0_14888, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))), inference(split_conjunct,[status(thm)],[c_0_9331]), ['final']). 4.46/4.74 cnf(c_0_14889, plain, (hAPP(c_COMBK(tc_Option_Ooption(X1),X2),c_Option_Ooption_ONone(X1))!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X2,tc_Option_Ooption(X1)),X3),X4),hAPP(c_Option_Ooption_OSome(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_9332]), ['final']). 4.46/4.74 cnf(c_0_14890, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))!=c_List_Olist_ONil(X1)), inference(er,[status(thm)],[c_0_9333]), ['final']). 4.46/4.74 cnf(c_0_14891, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9334, c_0_5334]), c_0_7568])]), ['final']). 4.46/4.74 cnf(c_0_14892, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1))), inference(split_conjunct,[status(thm)],[c_0_9335]), ['final']). 4.46/4.74 cnf(c_0_14893, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2))), inference(split_conjunct,[status(thm)],[c_0_9336]), ['final']). 4.46/4.74 cnf(c_0_14894, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_9337]), ['final']). 4.46/4.74 cnf(c_0_14895, plain, (hAPP(c_Set_OPow(X1),X2)!=hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_9338]), ['final']). 4.46/4.74 cnf(c_0_14896, plain, (~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_9339]), ['final']). 4.46/4.74 cnf(c_0_14897, plain, (~hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2))), inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_9340, c_0_4531])]), ['final']). 4.46/4.74 cnf(c_0_14898, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2))), inference(er,[status(thm)],[c_0_9341]), ['final']). 4.46/4.74 cnf(c_0_14899, plain, (~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3))), inference(split_conjunct,[status(thm)],[c_0_9342]), ['final']). 4.46/4.74 cnf(c_0_14900, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_9343]), ['final']). 4.46/4.74 cnf(c_0_14901, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1))), inference(er,[status(thm)],[c_0_9344]), ['final']). 4.46/4.74 cnf(c_0_14902, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_9345]), ['final']). 4.46/4.74 cnf(c_0_14903, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9346]), ['final']). 4.46/4.74 cnf(c_0_14904, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(rw,[status(thm)],[c_0_9347, c_0_5334]), ['final']). 4.46/4.74 cnf(c_0_14905, plain, (~c_Wellfounded_Omax__extp(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(er,[status(thm)],[c_0_9348]), ['final']). 4.46/4.74 cnf(c_0_14906, plain, (~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_9349]), ['final']). 4.46/4.74 cnf(c_0_14907, plain, (~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_9350]), ['final']). 4.46/4.74 cnf(c_0_14908, plain, (c_Com_Ocom_OLocal(X1,X2,X3)!=c_Com_Ocom_OCond(X4,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_9351]), ['final']). 4.46/4.74 cnf(c_0_14909, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_9352]), ['final']). 4.46/4.74 cnf(c_0_14910, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_9353, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_14911, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1))), inference(split_conjunct,[status(thm)],[c_0_9354]), ['final']). 4.46/4.74 cnf(c_0_14912, plain, (c_List_Olist_ONil(X1)!=hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_9355]), ['final']). 4.46/4.74 cnf(c_0_14913, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Int_OMin))), inference(rw,[status(thm)],[c_0_9356, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_14914, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_9357]), ['final']). 4.46/4.74 cnf(c_0_14915, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Int_OMin))), inference(rw,[status(thm)],[c_0_9358, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_14916, plain, (c_Com_Ocom_OLocal(X1,X2,X3)!=c_Com_Ocom_OWhile(X4,X5)), inference(split_conjunct,[status(thm)],[c_0_9359]), ['final']). 4.46/4.74 cnf(c_0_14917, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Int_OMin))), inference(rw,[status(thm)],[c_0_9360, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_14918, plain, (c_Com_Ocom_OSemi(X1,X2)!=c_Com_Ocom_OCond(X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_9361]), ['final']). 4.46/4.74 cnf(c_0_14919, plain, (c_Com_Ocom_OSemi(X1,X2)!=c_Com_Ocom_OLocal(X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_9362]), ['final']). 4.46/4.74 cnf(c_0_14920, plain, (c_Com_Ocom_OLocal(X1,X2,X3)!=hAPP(c_Com_Ocom_OBODY,X4)), inference(split_conjunct,[status(thm)],[c_0_9363]), ['final']). 4.46/4.74 cnf(c_0_14921, plain, (hAPP(c_Com_Ocom_OBODY,X1)!=c_Com_Ocom_OCond(X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_9364]), ['final']). 4.46/4.74 cnf(c_0_14922, plain, (c_Com_Ocom_OWhile(X1,X2)!=c_Com_Ocom_OCond(X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_9365]), ['final']). 4.46/4.74 cnf(c_0_14923, plain, (X1!=hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)), inference(split_conjunct,[status(thm)],[c_0_9366]), ['final']). 4.46/4.74 cnf(c_0_14924, plain, (c_Option_Ooption_ONone(X1)!=hAPP(c_Option_Ooption_OSome(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_9367]), ['final']). 4.46/4.74 cnf(c_0_14925, plain, (c_Com_Ocom_OSemi(X1,X2)!=hAPP(c_Com_Ocom_OBODY,X3)), inference(split_conjunct,[status(thm)],[c_0_9368]), ['final']). 4.46/4.74 cnf(c_0_14926, plain, (c_Lazy__Sequence_Olazy__sequence_OEmpty(X1)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9369]), ['final']). 4.46/4.74 cnf(c_0_14927, plain, (c_Com_Ocom_OWhile(X1,X2)!=hAPP(c_Com_Ocom_OBODY,X3)), inference(split_conjunct,[status(thm)],[c_0_9370]), ['final']). 4.46/4.74 cnf(c_0_14928, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_9371]), ['final']). 4.46/4.74 cnf(c_0_14929, plain, (c_Com_Ocom_OWhile(X1,X2)!=c_Com_Ocom_OSemi(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_9372]), ['final']). 4.46/4.74 cnf(c_0_14930, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_9373]), ['final']). 4.46/4.74 cnf(c_0_14931, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_9374]), ['final']). 4.46/4.74 cnf(c_0_14932, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))!=hAPP(c_Set_OPow(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_9375]), ['final']). 4.46/4.74 cnf(c_0_14933, plain, (c_Com_Ocom_OSKIP!=c_Com_Ocom_OCond(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9376]), ['final']). 4.46/4.74 cnf(c_0_14934, plain, (c_Com_Ocom_OSKIP!=c_Com_Ocom_OLocal(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9377]), ['final']). 4.46/4.74 cnf(c_0_14935, hypothesis, (~hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,v_y)),v_F))), inference(split_conjunct,[status(thm)],[c_0_9378]), ['final']). 4.46/4.74 cnf(c_0_14936, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X1)), inference(split_conjunct,[status(thm)],[c_0_9379]), ['final']). 4.46/4.74 cnf(c_0_14937, plain, (~c_List_Olist__ex(X1,X2,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_9380]), ['final']). 4.46/4.74 cnf(c_0_14938, plain, (~c_List_Olist__ex1(X1,X2,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_9381]), ['final']). 4.46/4.74 cnf(c_0_14939, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_9382]), ['final']). 4.46/4.74 cnf(c_0_14940, plain, (c_Com_Ocom_OSKIP!=hAPP(c_Com_Ocom_OBODY,X1)), inference(split_conjunct,[status(thm)],[c_0_9383]), ['final']). 4.46/4.74 cnf(c_0_14941, plain, (c_Com_Ocom_OSKIP!=c_Com_Ocom_OSemi(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9384]), ['final']). 4.46/4.74 cnf(c_0_14942, plain, (c_Com_Ocom_OSKIP!=c_Com_Ocom_OWhile(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9385]), ['final']). 4.46/4.74 cnf(c_0_14943, plain, (X1!=hAPP(c_Nat_OSuc,X1)), inference(split_conjunct,[status(thm)],[c_0_9386]), ['final']). 4.46/4.74 cnf(c_0_14944, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[fact_int__0__neq__1]), ['final']). 4.46/4.74 cnf(c_0_14945, plain, (c_Int_OMin!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_9387, c_0_4436]), ['final']). 4.46/4.74 cnf(c_0_14946, plain, (~hBOOL(c_fFalse)), inference(split_conjunct,[status(thm)],[c_0_9388]), ['final']). 4.46/4.74 cnf(c_0_14947, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_HOL_Obool,X1),c_Transitive__Closure_Ortrancl(X1,X2)),hAPP(hAPP(c_COMBC(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),X3))),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_HOL_Obool,X1),c_Transitive__Closure_Ortrancl(X1,X2)),hAPP(c_Product__Type_OPair(X1,X1),X4)))))=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9389, c_0_6095]), c_0_6095]), c_0_4961]), c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_14948, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X1,tc_Nat_Onat)),X2),c_Product__Type_Osnd(X1,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))))))=hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X1,tc_Nat_Onat)),X2),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(X1,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X4))),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9390, c_0_6095]), c_0_6095]), ['final']). 4.46/4.74 cnf(c_0_14949, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9391, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), c_0_6071]), ['final']). 4.46/4.74 cnf(c_0_14950, plain, (hAPP(c_Set_Oimage(X1,tc_prod(X2,X3),hAPP(hAPP(c_COMBS(X1,X3,tc_prod(X2,X3)),hAPP(hAPP(c_COMBB(X2,tc_fun(X3,tc_prod(X2,X3)),X1),c_Product__Type_OPair(X2,X3)),X4)),X5)),X6)=hAPP(hAPP(c_Product__Type_OSigma(X2,X3),hAPP(c_Set_Oimage(X1,X2,X4),X6)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),c_Set_Oimage(X1,X3,X5)),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),c_Set_Ovimage(X1,X2,X4)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),c_Set_Oinsert(X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))),X6)))), inference(split_conjunct,[status(thm)],[c_0_9392]), ['final']). 4.46/4.74 cnf(c_0_14951, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9393, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), c_0_4609]), c_0_4609]), c_0_4500]), c_0_4760]), c_0_5765]), c_0_4609]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_14952, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X3))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9394, c_0_5580]), c_0_5580]), c_0_5580]), ['final']). 4.46/4.74 cnf(c_0_14953, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X5)),X4))=c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),X1),c_If(tc_Option_Ooption(X2))),X4)),X3)),X5))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9395, c_0_4531]), c_0_5671]), c_0_4531]), c_0_6074]), ['final']). 4.46/4.74 cnf(c_0_14954, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(c_Set_Oimage(X2,X1,X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5)))=hAPP(c_Set_Oimage(X2,X1,hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBS(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X5)),X3)),X6)),X4)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9396, c_0_4531]), c_0_5671]), c_0_4531]), c_0_6074]), ['final']). 4.46/4.74 cnf(c_0_14955, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X1,tc_Nat_Onat)),X2),c_Product__Type_Osnd(X1,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X4))))=hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X1,tc_Nat_Onat)),X2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X1,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X1,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_9397]), ['final']). 4.46/4.74 cnf(c_0_14956, plain, (hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,X4),X5),hAPP(hAPP(c_COMBC(X2,tc_fun(X6,tc_fun(X7,X4)),tc_fun(X3,X4)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X6,X7)),tc_fun(tc_fun(X6,tc_fun(X7,X4)),tc_fun(X3,X4)),X2),c_Product__Type_Oscomp(X3,X6,X7,X4)),X8)),X9))=hAPP(hAPP(c_Product__Type_Oscomp(X1,X6,X7,X4),hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,tc_prod(X6,X7)),X5),X8)),X9)), inference(split_conjunct,[status(thm)],[c_0_9398]), ['final']). 4.46/4.74 cnf(c_0_14957, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X3))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9399, c_0_4836]), c_0_6071]), ['final']). 4.46/4.74 cnf(c_0_14958, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,c_List_Otranspose(X1,X2)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X1)))),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9400, c_0_5101]), c_0_9401]), c_0_5670]), c_0_5580]), c_0_5671]), ['final']). 4.46/4.74 cnf(c_0_14959, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),tc_Option_Ooption(X2),X1,hAPP(c_Option_Omap(X3,X2),X4)),X5)),X6),hAPP(c_Option_Ooption_OSome(X2),hAPP(X4,X7)))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),tc_Option_Ooption(X2),X1,hAPP(c_Option_Omap(X3,X2),X4)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),X5),X6),hAPP(c_Option_Ooption_OSome(X3),X7)))), inference(split_conjunct,[status(thm)],[c_0_9402]), ['final']). 4.46/4.74 cnf(c_0_14960, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9403, c_0_4448]), c_0_4448]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4760]), c_0_4760]), c_0_4784]), c_0_4784]), ['final']). 4.46/4.74 cnf(c_0_14961, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9404, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.74 cnf(c_0_14962, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_Set_Oimage(X3,X1,X4),X5)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_Oimage(X6,X2,X7),X8)))=hAPP(c_Set_Oimage(tc_prod(X3,X6),tc_prod(X1,X2),c_Product__Type_Omap__pair(X3,X1,X6,X2,X4,X7)),hAPP(hAPP(c_Product__Type_OSigma(X3,X6),X5),hAPP(c_COMBK(tc_fun(X6,tc_HOL_Obool),X3),X8)))), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9405])]), ['final']). 4.46/4.74 cnf(c_0_14963, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9406, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.74 cnf(c_0_14964, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,hAPP(c_Fun_Ocomp(X2,tc_HOL_Obool,X1,X4),X3),X5))),X5))=hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X4,hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)))),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9407, c_0_4916]), c_0_4916]), ['final']). 4.46/4.74 cnf(c_0_14965, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9408, c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), ['final']). 4.46/4.74 cnf(c_0_14966, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9409]), ['final']). 4.46/4.74 cnf(c_0_14967, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9410]), ['final']). 4.46/4.74 cnf(c_0_14968, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_9411]), ['final']). 4.46/4.74 cnf(c_0_14969, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),X3))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Osublist(X1,X2,X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9412, c_0_4945]), c_0_5320]), c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_14970, plain, (hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),hAPP(c_Fun_Ocomp(X3,tc_fun(X2,X2),X1,X4),X5)),X7),hAPP(c_List_Orev(X1),X6))=hAPP(c_List_Ofoldl(X2,X3,hAPP(c_COMBC(X3,X2,X2),X4),X7),hAPP(c_List_Orev(X3),hAPP(hAPP(c_List_Omap(X1,X3),X5),X6)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9413, c_0_4713]), c_0_4713]), ['final']). 4.46/4.74 cnf(c_0_14971, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9414, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_4784]), ['final']). 4.46/4.74 cnf(c_0_14972, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9415, c_0_4760]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4784]), ['final']). 4.46/4.74 cnf(c_0_14973, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X5))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBS(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_9416]), ['final']). 4.46/4.74 cnf(c_0_14974, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X5))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBS(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_9417]), ['final']). 4.46/4.74 cnf(c_0_14975, plain, (hAPP(hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3),hAPP(c_Product__Type_OPair(X1,X2),X4))=hAPP(c_Relation_OImage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9418, c_0_6095]), c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_14976, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool),tc_Nat_Onat),X4),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2)))), inference(rw,[status(thm)],[c_0_9419, c_0_6965]), ['final']). 4.46/4.74 cnf(c_0_14977, plain, (hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Omap(X1,tc_prod(X1,X2)),hAPP(hAPP(c_COMBS(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2)),X3)),X4))=c_Map_Orestrict__map(X1,X2,hAPP(c_Fun_Ocomp(X2,tc_Option_Ooption(X2),X1,c_Option_Ooption_OSome(X2)),X3),hAPP(c_List_Oset(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_9420]), ['final']). 4.46/4.74 cnf(c_0_14978, plain, (c_List_Omaps(tc_List_Olist(X1),X2,hAPP(c_List_Omap(X1,X2),X3),X4)=hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X4))), inference(rw,[status(thm)],[c_0_9421, c_0_5669]), ['final']). 4.46/4.74 cnf(c_0_14979, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),hAPP(c_Product__Type_Omap__pair(X1,X1,X5,X3,c_Fun_Oid(X1),X6),X7))=hAPP(c_Product__Type_Omap__pair(X2,X2,X5,X3,c_Fun_Oid(X2),X6),hAPP(c_Product__Type_Omap__pair(X1,X2,X5,X5,X4,c_Fun_Oid(X5)),X7))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9422, c_0_6862]), c_0_6862]), c_0_4825]), c_0_4825]), ['final']). 4.46/4.74 cnf(c_0_14980, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X4,hAPP(c_Fun_Ocomp(X5,X2,X1,X6),X7),hAPP(c_Fun_Ocomp(X8,X4,X3,X9),X10)),X11)=hAPP(c_Product__Type_Omap__pair(X5,X2,X8,X4,X6,X9),hAPP(c_Product__Type_Omap__pair(X1,X5,X3,X8,X7,X10),X11))), inference(split_conjunct,[status(thm)],[c_0_9423]), ['final']). 4.46/4.74 cnf(c_0_14981, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9424, c_0_4784]), c_0_9425]), c_0_4784]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_4760]), c_0_4760]), ['final']). 4.46/4.74 cnf(c_0_14982, plain, (hAPP(c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X4),hAPP(c_Product__Type_Omap__pair(X5,X3,X1,X1,X6,c_Fun_Oid(X1)),X7))=hAPP(hAPP(c_Product__Type_OPair(X3,X2),hAPP(X6,hAPP(c_Product__Type_Ofst(X5,X1),X7))),hAPP(X4,hAPP(c_Product__Type_Osnd(X5,X1),X7)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9426, c_0_6862]), c_0_4825]), ['final']). 4.46/4.74 cnf(c_0_14983, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),hAPP(c_Product__Type_Omap__pair(X1,X1,X5,X3,c_Fun_Oid(X1),X6),X7))=hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X5),X7))),hAPP(X6,hAPP(c_Product__Type_Osnd(X1,X5),X7)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9427, c_0_6862]), c_0_4825]), ['final']). 4.46/4.74 cnf(c_0_14984, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9428, c_0_4784]), c_0_9425]), c_0_4784]), c_0_4760]), c_0_4500]), c_0_4760]), c_0_5765]), ['final']). 4.46/4.74 cnf(c_0_14985, plain, (hAPP(hAPP(X1,X2),hAPP(c_List_Ofoldl(X4,X3,hAPP(c_COMBC(X3,X4,X4),X1),X6),hAPP(c_List_Orev(X3),X5)))=hAPP(c_List_Ofoldl(X4,X3,hAPP(c_COMBC(X3,X4,X4),X1),X6),hAPP(c_List_Orev(X3),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9429, c_0_4713]), c_0_4713]), ['final']). 4.46/4.74 cnf(c_0_14986, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist__update(X1,X3),X4),X5)),hAPP(hAPP(c_List_Olist__update(X2,X6),X4),X7))=hAPP(hAPP(c_List_Olist__update(tc_prod(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X6)),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X7))), inference(split_conjunct,[status(thm)],[c_0_9430]), ['final']). 4.46/4.74 cnf(c_0_14987, plain, (hAPP(c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X4),hAPP(c_Product__Type_Omap__pair(X3,X3,X5,X1,c_Fun_Oid(X3),X6),X7))=hAPP(c_Product__Type_Omap__pair(X3,X3,X5,X2,c_Fun_Oid(X3),hAPP(c_Fun_Ocomp(X1,X2,X5,X4),X6)),X7)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9431, c_0_4825]), c_0_4825]), c_0_4825]), ['final']). 4.46/4.74 cnf(c_0_14988, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,hAPP(c_Fun_Ocomp(X4,X2,X1,X5),X6),c_Fun_Oid(X3)),X7)=hAPP(c_Product__Type_Omap__pair(X4,X2,X3,X3,X5,c_Fun_Oid(X3)),hAPP(c_Product__Type_Omap__pair(X1,X4,X3,X3,X6,c_Fun_Oid(X3)),X7))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9432, c_0_6862]), c_0_6862]), c_0_6862]), ['final']). 4.46/4.74 cnf(c_0_14989, plain, (hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9433, c_0_4500]), c_0_4760]), c_0_5765]), ['final']). 4.46/4.74 cnf(c_0_14990, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9434, c_0_4448]), c_0_4448]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4760]), c_0_4448]), c_0_4784]), c_0_4784]), ['final']). 4.46/4.74 cnf(c_0_14991, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5))=hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X3),tc_List_Olist(X3)),X2),c_List_Orotate1(X3)),X5))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9435, c_0_5902]), c_0_5902]), ['final']). 4.46/4.74 cnf(c_0_14992, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6))=hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X5)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X6))), inference(split_conjunct,[status(thm)],[c_0_9436]), ['final']). 4.46/4.74 cnf(c_0_14993, plain, (hAPP(c_Set_Oimage(X1,tc_List_Olist(X1),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))),X2)=c_List_Oset__Cons(X1,X2,hAPP(c_fequal,c_List_Olist_ONil(X1)))), inference(rw,[status(thm)],[c_0_9437, c_0_5580]), ['final']). 4.46/4.74 cnf(c_0_14994, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1))), inference(split_conjunct,[status(thm)],[c_0_9438]), ['final']). 4.46/4.74 cnf(c_0_14995, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6),hAPP(X4,X7))=hAPP(c_Fun_Ocomp(X3,X2,X1,X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X3),X5),X6),X7))), inference(split_conjunct,[status(thm)],[c_0_9439]), ['final']). 4.46/4.74 cnf(c_0_14996, plain, (hAPP(c_Fun_Ocomp(X1,X2,tc_prod(X1,X3),X4),c_Product__Type_Ofst(X1,X3))=hAPP(c_Fun_Ocomp(tc_prod(X2,X5),X2,tc_prod(X1,X3),c_Product__Type_Ofst(X2,X5)),c_Product__Type_Omap__pair(X1,X2,X3,X5,X4,X6))), inference(split_conjunct,[status(thm)],[c_0_9440]), ['final']). 4.46/4.74 cnf(c_0_14997, plain, (hAPP(c_Fun_Ocomp(X1,X2,tc_prod(X3,X1),X4),c_Product__Type_Osnd(X3,X1))=hAPP(c_Fun_Ocomp(tc_prod(X5,X2),X2,tc_prod(X3,X1),c_Product__Type_Osnd(X5,X2)),c_Product__Type_Omap__pair(X3,X5,X1,X2,X6,X4))), inference(split_conjunct,[status(thm)],[c_0_9441]), ['final']). 4.46/4.74 cnf(c_0_14998, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X3))), inference(split_conjunct,[status(thm)],[c_0_9442]), ['final']). 4.46/4.74 cnf(c_0_14999, plain, (c_List_Otranspose(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_List_Olist(X1)),hAPP(c_List_Omap(X2,X1),X3)),X4))=hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_List_Olist(X1)),hAPP(c_List_Omap(X2,X1),X3)),c_List_Otranspose(X2,X4))), inference(split_conjunct,[status(thm)],[c_0_9443]), ['final']). 4.46/4.74 cnf(c_0_15000, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(c_Fun_Ocomp(X4,tc_fun(X2,X3),X1,X5),X6)),X7)=hAPP(hAPP(X5,hAPP(X6,hAPP(c_Product__Type_Ofst(X1,X2),X7))),hAPP(c_Product__Type_Osnd(X1,X2),X7))), inference(split_conjunct,[status(thm)],[c_0_9444]), ['final']). 4.46/4.74 cnf(c_0_15001, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),hAPP(c_List_Ofilter(X3,hAPP(c_Fun_Ocomp(X1,tc_HOL_Obool,X3,X2),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_9445]), ['final']). 4.46/4.74 cnf(c_0_15002, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2))=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2))), inference(rw,[status(thm)],[c_0_9446, c_0_4736]), ['final']). 4.46/4.74 cnf(c_0_15003, plain, (hAPP(hAPP(c_List_Omap(X1,tc_prod(X1,X1)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1))),X2)=hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2)), inference(split_conjunct,[status(thm)],[c_0_9447]), ['final']). 4.46/4.74 cnf(c_0_15004, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Map_Odom(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),c_Option_Ooption_ONone(X2)))), inference(er,[status(thm)],[c_0_9448]), ['final']). 4.46/4.74 cnf(c_0_15005, plain, (c_List_Olist_Olist__size(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,X3)),hAPP(c_Nat_OSuc,c_List_Olist_Olist__size(X1,X2,X4)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9449, c_0_4836]), c_0_5643]), c_0_5644]), ['final']). 4.46/4.74 cnf(c_0_15006, plain, (hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X3,X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,X3)),hAPP(c_Nat_OSuc,hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),X4)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9450, c_0_4836]), c_0_5643]), c_0_5644]), ['final']). 4.46/4.74 cnf(c_0_15007, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_Fun_Ocomp(X4,tc_fun(X2,tc_HOL_Obool),X1,X5),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X6),X3)),X5)), inference(split_conjunct,[status(thm)],[c_0_9451]), ['final']). 4.46/4.74 cnf(c_0_15008, plain, (hAPP(c_Fun_Ocomp(X1,X2,X3,hAPP(c_Fun_Ocomp(X4,X2,X1,X5),X6)),X7)=hAPP(c_Fun_Ocomp(X4,X2,X3,X5),hAPP(c_Fun_Ocomp(X1,X4,X3,X6),X7))), inference(split_conjunct,[status(thm)],[c_0_9452]), ['final']). 4.46/4.74 cnf(c_0_15009, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Olist__update(X1,X4),X5),X6))=hAPP(hAPP(c_List_Olist__update(X2,hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)),X5),hAPP(X3,X6))), inference(split_conjunct,[status(thm)],[c_0_9453]), ['final']). 4.46/4.74 cnf(c_0_15010, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,tc_HOL_Obool),X1),X5),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X6),X3)),X5)), inference(split_conjunct,[status(thm)],[c_0_9454]), ['final']). 4.46/4.74 cnf(c_0_15011, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X1,X4),X5)),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),X3),X6),X4))), inference(split_conjunct,[status(thm)],[c_0_9455]), ['final']). 4.46/4.74 cnf(c_0_15012, plain, (hAPP(c_Relation_ORange(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3))=hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X1)),hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9456, c_0_4531]), c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_15013, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),c_Option_Ooption_ONone(X2))=c_Map_Orestrict__map(X1,X2,X3,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_9457]), ['final']). 4.46/4.74 cnf(c_0_15014, plain, (hAPP(hAPP(c_Option_Omap(X1,X2),hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6)=hAPP(hAPP(c_Option_Omap(X3,X2),X4),hAPP(hAPP(c_Option_Omap(X1,X3),X5),X6))), inference(split_conjunct,[status(thm)],[c_0_9458]), ['final']). 4.46/4.74 cnf(c_0_15015, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(X5,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9459]), ['final']). 4.46/4.74 cnf(c_0_15016, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(X5,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9460]), ['final']). 4.46/4.74 cnf(c_0_15017, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),c_Relation_ORange(X1,X2))=hAPP(c_Relation_ORange(X1,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3))), inference(split_conjunct,[status(thm)],[c_0_9461]), ['final']). 4.46/4.74 cnf(c_0_15018, plain, (hAPP(c_Relation_ODomain(X1,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),c_Relation_ODomain(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_9462]), ['final']). 4.46/4.74 cnf(c_0_15019, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X1,X2,X3))=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X2,X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9463, c_0_4836]), c_0_5643]), c_0_5644]), c_0_5645]), c_0_9464]), ['final']). 4.46/4.74 cnf(c_0_15020, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(c_Fun_Ocomp(X4,X1,X2,X5),X6))=hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,X2),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X4),X3),X5)),X6)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9465, c_0_4891]), c_0_4891]), c_0_4891]), ['final']). 4.46/4.74 cnf(c_0_15021, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))=hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(X3,X4)),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9466]), ['final']). 4.46/4.74 cnf(c_0_15022, plain, (hAPP(c_List_Ofoldl(X1,X2,X3,X4),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X6))=hAPP(c_List_Ofoldl(X1,X2,X3,hAPP(hAPP(X3,X4),X5)),X6)), inference(split_conjunct,[status(thm)],[c_0_9467]), ['final']). 4.46/4.74 cnf(c_0_15023, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Otake(X1),X4),X5))=hAPP(hAPP(c_List_Otake(X2),X4),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9468]), ['final']). 4.46/4.74 cnf(c_0_15024, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5))=hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(hAPP(c_List_Odrop(X3),X2),X5))), inference(split_conjunct,[status(thm)],[c_0_9469]), ['final']). 4.46/4.74 cnf(c_0_15025, plain, (c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))=hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))), inference(rw,[status(thm)],[c_0_9470, c_0_6292]), ['final']). 4.46/4.74 cnf(c_0_15026, plain, (hAPP(c_Set_Oimage(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6)=hAPP(c_Set_Oimage(X3,X2,X4),hAPP(c_Set_Oimage(X1,X3,X5),X6))), inference(split_conjunct,[status(thm)],[c_0_9471]), ['final']). 4.46/4.74 cnf(c_0_15027, plain, (c_List_Omaps(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))=hAPP(hAPP(c_List_Oappend(X2),hAPP(X3,X4)),c_List_Omaps(X1,X2,X3,X5))), inference(split_conjunct,[status(thm)],[c_0_9472]), ['final']). 4.46/4.74 cnf(c_0_15028, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9473]), ['final']). 4.46/4.74 cnf(c_0_15029, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9474]), ['final']). 4.46/4.74 cnf(c_0_15030, plain, (hAPP(c_Relation_Oconverse(X1,X1),hAPP(hAPP(c_Relation_Oinv__image(X2,X1),X3),X4))=hAPP(hAPP(c_Relation_Oinv__image(X2,X1),hAPP(c_Relation_Oconverse(X2,X2),X3)),X4)), inference(split_conjunct,[status(thm)],[c_0_9475]), ['final']). 4.46/4.74 cnf(c_0_15031, plain, (c_List_Olist_Olist__size(X1,hAPP(c_Fun_Ocomp(X2,tc_Nat_Onat,X1,X3),X4),X5)=c_List_Olist_Olist__size(X2,X3,hAPP(hAPP(c_List_Omap(X1,X2),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9476]), ['final']). 4.46/4.74 cnf(c_0_15032, plain, (hAPP(hAPP(X1,X2),hAPP(hAPP(c_Power_Opower_Opower(X3,X4,X1),X2),X5))=hAPP(hAPP(c_Power_Opower_Opower(X3,X4,X1),X2),hAPP(c_Nat_OSuc,X5))), inference(split_conjunct,[status(thm)],[c_0_9477]), ['final']). 4.46/4.74 cnf(c_0_15033, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X1,X2,X3))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X2,X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9478, c_0_4836]), c_0_5643]), c_0_5644]), c_0_5645]), c_0_9479]), ['final']). 4.46/4.74 cnf(c_0_15034, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Relation_OField(X1))=hAPP(c_Relation_OField(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2))), inference(rw,[status(thm)],[c_0_9480, c_0_7470]), ['final']). 4.46/4.74 cnf(c_0_15035, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2))), inference(split_conjunct,[status(thm)],[c_0_9481]), ['final']). 4.46/4.74 cnf(c_0_15036, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2))), inference(split_conjunct,[status(thm)],[c_0_9482]), ['final']). 4.46/4.74 cnf(c_0_15037, plain, (hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X2),X2,hAPP(X3,X5),c_Option_Ooption_OSome(X2)),hAPP(X4,X5))), inference(split_conjunct,[status(thm)],[c_0_9483]), ['final']). 4.46/4.74 cnf(c_0_15038, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4))=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X3)),X4)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9484, c_0_4891]), c_0_4891]), ['final']). 4.46/4.74 cnf(c_0_15039, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),X5)=hAPP(hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X2),X5)),hAPP(c_Product__Type_Osnd(X1,X2),X5))), inference(split_conjunct,[status(thm)],[c_0_9485]), ['final']). 4.46/4.74 cnf(c_0_15040, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),c_Set_Oimage(X1,X2,X4))=hAPP(c_Set_Oimage(X1,X2,X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))), inference(split_conjunct,[status(thm)],[c_0_9486]), ['final']). 4.46/4.74 cnf(c_0_15041, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X5))=hAPP(hAPP(c_Set_Oinsert(X2),hAPP(X3,X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9487]), ['final']). 4.46/4.74 cnf(c_0_15042, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))), inference(rw,[status(thm)],[c_0_9488, c_0_4891]), ['final']). 4.46/4.74 cnf(c_0_15043, plain, (hAPP(c_List_Orotate1(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))), inference(split_conjunct,[status(thm)],[c_0_9489]), ['final']). 4.46/4.74 cnf(c_0_15044, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),X2),c_List_Olist_ONil(X1)),X3)=hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X2,X1,X4),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X3)), inference(er,[status(thm)],[c_0_9490]), ['final']). 4.46/4.74 cnf(c_0_15045, plain, (hAPP(hAPP(c_List_Omap(X1,X2),hAPP(c_COMBK(X2,X1),X3)),X4)=c_List_Oreplicate(X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_9491]), ['final']). 4.46/4.74 cnf(c_0_15046, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Otl(X1),X4))=hAPP(c_List_Otl(X2),hAPP(hAPP(c_List_Omap(X1,X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9492]), ['final']). 4.46/4.74 cnf(c_0_15047, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1))), inference(split_conjunct,[status(thm)],[c_0_9493]), ['final']). 4.46/4.74 cnf(c_0_15048, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))), inference(split_conjunct,[status(thm)],[c_0_9494]), ['final']). 4.46/4.74 cnf(c_0_15049, plain, (hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_List_Oset(X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9495]), ['final']). 4.46/4.74 cnf(c_0_15050, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Obutlast(X2,X4))), inference(split_conjunct,[status(thm)],[c_0_9496]), ['final']). 4.46/4.74 cnf(c_0_15051, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_9497]), ['final']). 4.46/4.74 cnf(c_0_15052, plain, (hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),hAPP(c_Nat_OSuc,X4))=hAPP(hAPP(X3,X4),hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9498]), ['final']). 4.46/4.74 cnf(c_0_15053, plain, (c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)), inference(rw,[status(thm)],[c_0_9499, c_0_5689]), ['final']). 4.46/4.74 cnf(c_0_15054, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1)), inference(split_conjunct,[status(thm)],[c_0_9500]), ['final']). 4.46/4.74 cnf(c_0_15055, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(X1))=c_List_Opartition(X1,X2,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_9501]), ['final']). 4.46/4.74 cnf(c_0_15056, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))), inference(split_conjunct,[status(thm)],[c_0_9502]), ['final']). 4.46/4.74 cnf(c_0_15057, plain, (hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),X5),X6)=hAPP(hAPP(X4,X6),hAPP(X5,X6))), inference(split_conjunct,[status(thm)],[c_0_9503]), ['final']). 4.46/4.74 cnf(c_0_15058, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Orev(X1),X3))=hAPP(c_List_Orev(X1),hAPP(c_List_Ofilter(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9504]), ['final']). 4.46/4.74 cnf(c_0_15059, plain, (hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),X2)=hAPP(c_Set_OPow(X1),X2)), inference(rw,[status(thm)],[c_0_9505, c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_15060, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))=hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9506]), ['final']). 4.46/4.74 cnf(c_0_15061, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(tc_List_Olist(X1)))=c_Enum_On__lists(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_9507]), ['final']). 4.46/4.74 cnf(c_0_15062, plain, (c_Fun_Oid(tc_prod(X1,X2))=hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_9508]), ['final']). 4.46/4.74 cnf(c_0_15063, plain, (c_List_Oremove1(X1,X2,c_List_Oremove1(X1,X3,X4))=c_List_Oremove1(X1,X3,c_List_Oremove1(X1,X2,X4))), inference(split_conjunct,[status(thm)],[c_0_9509]), ['final']). 4.46/4.74 cnf(c_0_15064, plain, (hAPP(c_New__DSequence_Opos__union(X1,X2,X3),X4)=c_Lazy__Sequence_Oappend(X1,hAPP(X2,X4),hAPP(X3,X4))), inference(split_conjunct,[status(thm)],[c_0_9510]), ['final']). 4.46/4.74 cnf(c_0_15065, plain, (c_Enum_Osublists(X1,c_List_Olist_ONil(X1))=hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(tc_List_Olist(X1)))), inference(split_conjunct,[status(thm)],[c_0_9511]), ['final']). 4.46/4.74 cnf(c_0_15066, plain, (hAPP(c_List_Olexn(X1,X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_9512]), ['final']). 4.46/4.74 cnf(c_0_15067, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X1)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X1)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBC(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X1)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))))),c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1))))),c_List_Olex(X1,X2)))))=c_List_Olenlex(X1,X2)), inference(rw,[status(thm)],[c_0_9513, c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_15068, plain, (hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X1)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),tc_List_Olist(X1)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_List_Olist(X1)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_List_Olist(X1)),c_COMBS(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_List_Olist(X1)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),X1),c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X1)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_List_Olist(X1)),c_COMBB(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_List_Olist(X1),tc_HOL_Obool,tc_List_Olist(X1))),c_fequal))),c_List_Olist_OCons(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2))),X3))))=c_List_Oset__Cons(X1,X2,X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9514, c_0_4945]), c_0_4945]), c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_15069, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))=c_Divides_Oadjust(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9515, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_15070, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X3))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBC(X3,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X1,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X3),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X1,X3)))),c_Product__Type_OPair(X1,X3)))),X4))))),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X3,X2)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X3,X2),tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X3,X2)))),hAPP(c_COMBC(X3,X2,tc_prod(X3,X2)),c_Product__Type_OPair(X3,X2))))),X5))))=hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5)), inference(rw,[status(thm)],[c_0_9516, c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_15071, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_COMBS(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(X2,X1)),c_Product__Type_OPair(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),c_Relation_Oinv__image(X1,X2))))),c_Relation_Oinv__image(X1,X2)))=c_FunDef_Orp__inv__image(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9517]), ['final']). 4.46/4.74 cnf(c_0_15072, plain, (c_List_Opartition(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_fun(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_List_Olist(X1)),c_COMBS(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_List_Olist(X1)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_List_Olist(X1)),hAPP(c_If(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(X2,X3)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_List_Olist(X1)),c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(c_List_Olist_OCons(X1),X3))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_List_Olist(X1)),c_COMBB(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1))),c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(c_List_Olist_OCons(X1),X3)))),c_List_Opartition(X1,X2,X4))), inference(split_conjunct,[status(thm)],[c_0_9518]), ['final']). 4.46/4.74 cnf(c_0_15073, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3)),X1)))=hAPP(c_Divides_Oadjust(X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9519, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), c_0_4760]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_15074, plain, (hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_9520]), ['final']). 4.46/4.74 cnf(c_0_15075, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X1,tc_List_Olist(X1)),tc_prod(X1,tc_List_Olist(X1))),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),c_Product__Type_Omap__pair(tc_prod(X1,tc_List_Olist(X1)),tc_List_Olist(X1),tc_prod(X1,tc_List_Olist(X1)),tc_List_Olist(X1),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)))),c_Wellfounded_Olex__prod(X1,tc_List_Olist(X1),X2,hAPP(c_List_Olexn(X1,X2),X3)))),c_Nitpick_Oprod(tc_List_Olist(X1),tc_List_Olist(X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),hAPP(c_Nat_OSuc,X3)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),hAPP(c_Nat_OSuc,X3))))=hAPP(c_List_Olexn(X1,X2),hAPP(c_Nat_OSuc,X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9521, c_0_4961]), c_0_6201]), c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_15076, plain, (hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X1,X2)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X1,X2),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X1,X2)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(X1,X2)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(X1,X2),tc_fun(tc_Nat_Onat,tc_prod(X1,X2)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X1,X2)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X1,X2)),c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X2,tc_prod(X1,X2)),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_prod(X1,X2)),tc_Nat_Onat),c_Product__Type_OPair(X1,X2)),hAPP(c_List_Onth(X1),X3))),hAPP(c_List_Onth(X2),X4)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)))))=hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9522, c_0_4986]), c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_15077, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),c_Nitpick_Oint__lcm(hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2)),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X3)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X1),tc_Int_Oint),c_Nitpick_Ofrac(X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2)))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X3)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X3))))))),c_COMBI(tc_Int_Oint)))=c_Nitpick_Oplus__frac(X1,X2,X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9523, c_0_6281]), c_0_6281]), c_0_6281]), c_0_6281]), c_0_6281]), c_0_6281]), ['final']). 4.46/4.74 cnf(c_0_15078, plain, (c_Map_Omap__upds(X1,X2,X3,X4,X5)=hAPP(c_List_Ofoldl(tc_fun(X1,tc_Option_Ooption(X2)),tc_prod(X1,X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_prod(X1,X2),tc_fun(X1,tc_Option_Ooption(X2))),tc_fun(X1,tc_Option_Ooption(X2))),c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X1,tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X1,tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),tc_fun(X1,tc_Option_Ooption(X2))),c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(X1,tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),tc_fun(X1,tc_Option_Ooption(X2))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2)))),X1),c_COMBB(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)),X2))),c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2))))),c_Option_Ooption_OSome(X2))),X3),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9524]), ['final']). 4.46/4.74 cnf(c_0_15079, plain, (c_Map_Omap__add(X1,X2,X3,hAPP(c_Map_Omap__of(X1,X2),X4))=hAPP(c_List_Ofoldl(tc_fun(X1,tc_Option_Ooption(X2)),tc_prod(X1,X2),hAPP(c_COMBC(tc_prod(X1,X2),tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),X1),c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))),X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),X1),c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),X1,tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)))))),c_Option_Ooption_OSome(X2)))),X3),hAPP(c_List_Orev(tc_prod(X1,X2)),X4))), inference(rw,[status(thm)],[c_0_9525, c_0_4713]), ['final']). 4.46/4.74 cnf(c_0_15080, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X4)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X2),c_Set_Oinsert(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_9526]), ['final']). 4.46/4.74 cnf(c_0_15081, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,X1))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2)))))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),X2)))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))))=c_Divides_Odivmod__int__rel(X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9527, c_0_5320]), c_0_5320]), c_0_5320]), ['final']). 4.46/4.74 cnf(c_0_15082, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X2,X2)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X2,X2),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X2,X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X2),tc_fun(X1,tc_prod(X2,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X2,X2)),tc_fun(tc_fun(X1,X2),tc_fun(X1,tc_prod(X2,X2))),X1),c_COMBB(X2,tc_prod(X2,X2),X1)),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_prod(X2,X2)),X1),c_Product__Type_OPair(X2,X2)),X3))),X3)))),X4))=hAPP(hAPP(c_Relation_Oinv__image(X2,X1),X4),X3)), inference(rw,[status(thm)],[c_0_9528, c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_15083, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),c_List_Ohd(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X1)))),X3)))),c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),X4),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Otl(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X1)))),X3)))))=c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9529, c_0_5669]), c_0_9530]), c_0_5669]), c_0_9531]), ['final']). 4.46/4.74 cnf(c_0_15084, plain, (c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBC(X1,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),X1),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X1),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),X1),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3)=hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),X3)), inference(rw,[status(thm)],[c_0_9532, c_0_9533]), ['final']). 4.46/4.74 cnf(c_0_15085, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,tc_fun(X2,tc_HOL_Obool)),X7),X8)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X3,X6),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X3,X6),X4),hAPP(c_COMBK(tc_fun(X6,tc_HOL_Obool),X3),X7))),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X6,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3,tc_fun(X6,tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),tc_fun(X6,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),tc_fun(tc_fun(X6,tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),tc_fun(X6,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X3),c_COMBB(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X6)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),c_Product__Type_OSigma(X1,X2)),X5))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X6),c_COMBK(tc_fun(X2,tc_HOL_Obool),X1)),X8))))), inference(split_conjunct,[status(thm)],[c_0_9534]), ['final']). 4.46/4.74 cnf(c_0_15086, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),X3),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5))=hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X1,X2)),X1,c_List_Olist_ONil(tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2)))),X1),c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),X1),c_List_Olist_OCons(tc_prod(X1,X2))),hAPP(hAPP(c_COMBC(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2)),X4)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2))),c_List_Ozip(X1,X2)),X5))),X3)), inference(split_conjunct,[status(thm)],[c_0_9535]), ['final']). 4.46/4.74 cnf(c_0_15087, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X3),hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X3)),hAPP(c_List_Ofilter(tc_List_Olist(X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X3),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X3)))),X4)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3))),c_List_Otranspose(X3,X4)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9536, c_0_5101]), c_0_5101]), c_0_4836]), c_0_5670]), c_0_5580]), c_0_5671]), c_0_5101]), c_0_5101]), c_0_9401]), ['final']). 4.46/4.74 cnf(c_0_15088, plain, (hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X1),X2))))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),X3)))=hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9537, c_0_4945]), c_0_5320]), c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_15089, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X1,X3,X4),X5))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X3,X4)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5)))))=hAPP(c_Nat_Onat_Onat__rec(X1,X3,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X5))), inference(rw,[status(thm)],[c_0_9538, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_15090, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)),X5)=hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X1,X2)),X2,c_List_Olist_ONil(tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2)))),X2),c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(X2))),hAPP(hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),X2),c_List_Olist_OCons(tc_prod(X1,X2))),hAPP(c_Product__Type_OPair(X1,X2),X3)))),hAPP(c_List_Ozip(X1,X2),X4))),X5)), inference(split_conjunct,[status(thm)],[c_0_9539]), ['final']). 4.46/4.74 cnf(c_0_15091, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X2,X1)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X2,X1),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X2,X1)))),hAPP(c_COMBC(X2,X1,tc_prod(X2,X1)),c_Product__Type_OPair(X2,X1))))),X3))=hAPP(c_Relation_Oconverse(X2,X1),X3)), inference(rw,[status(thm)],[c_0_9540, c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_15092, plain, (hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2)),c_Set_OPow(X1))))=hAPP(c_Set_OPow(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))), inference(rw,[status(thm)],[c_0_9541, c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_15093, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X3),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X4)),tc_fun(X2,X3),X1),hAPP(c_COMBB(tc_prod(X1,X4),X3,X2),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X4),tc_fun(X2,tc_prod(X1,X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X1,X4)),tc_fun(tc_fun(X2,X4),tc_fun(X2,tc_prod(X1,X4))),X1),c_COMBB(X4,tc_prod(X1,X4),X2)),c_Product__Type_OPair(X1,X4))),X6)))),hAPP(hAPP(c_List_Ozip(X1,X2),X7),X8))=hAPP(hAPP(c_List_Omap(tc_prod(X1,X4),X3),X5),hAPP(hAPP(c_List_Ozip(X1,X4),X7),hAPP(hAPP(c_List_Omap(X2,X4),X6),X8)))), inference(split_conjunct,[status(thm)],[c_0_9542]), ['final']). 4.46/4.74 cnf(c_0_15094, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9543, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.74 cnf(c_0_15095, plain, (hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X1),X2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))=hAPP(c_List_Oset(X1),X2)), inference(rw,[status(thm)],[c_0_9544, c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_15096, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X1,X3,X4,X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))))=c_Nat_Onat_Onat__case(X1,X3,X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X5))), inference(rw,[status(thm)],[c_0_9545, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_15097, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),tc_prod(X3,X4)),c_Product__Type_Omap__pair(X1,X3,X2,X4,X5,X6)),hAPP(hAPP(c_List_Ozip(X1,X2),X7),X8))=hAPP(hAPP(c_List_Ozip(X3,X4),hAPP(hAPP(c_List_Omap(X1,X3),X5),X7)),hAPP(hAPP(c_List_Omap(X2,X4),X6),X8))), inference(rw,[status(thm)],[c_0_9546, c_0_9547]), ['final']). 4.46/4.74 cnf(c_0_15098, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9548, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.74 cnf(c_0_15099, plain, (hAPP(hAPP(c_Nitpick_Ofrac(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2))),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X3)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2))),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X3))))=c_Nitpick_Otimes__frac(X1,X2,X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9549, c_0_6281]), c_0_6281]), c_0_6281]), c_0_6281]), ['final']). 4.46/4.74 cnf(c_0_15100, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)),c_Int_Onat)),X2))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9550, c_0_4609]), c_0_5101]), c_0_5101]), ['final']). 4.46/4.74 cnf(c_0_15101, plain, (hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X1,X1)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(tc_prod(X1,X1),tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_HOL_Obool)),tc_prod(X1,X1)),c_COMBB(tc_prod(X1,X1),tc_HOL_Obool,X1)),c_fequal)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1))))=c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))), inference(rw,[status(thm)],[c_0_9551, c_0_4531]), ['final']). 4.46/4.74 cnf(c_0_15102, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),X3)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X4),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X3,X4)),c_Int_Onat))))=hAPP(c_Nat_Onat_Onat__rec(X1,X3,X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))), inference(rw,[status(thm)],[c_0_9552, c_0_4609]), ['final']). 4.46/4.74 cnf(c_0_15103, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X4,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X4,tc_fun(X2,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X6))),X7)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),X5),X7))), inference(split_conjunct,[status(thm)],[c_0_9553]), ['final']). 4.46/4.75 cnf(c_0_15104, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X6),X7))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X6)),hAPP(hAPP(c_COMBC(X2,tc_fun(X5,tc_fun(X1,tc_HOL_Obool)),tc_fun(X5,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X1,tc_HOL_Obool)),tc_fun(X5,tc_fun(X1,tc_HOL_Obool))),X2),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X4))),X7)))), inference(split_conjunct,[status(thm)],[c_0_9554]), ['final']). 4.46/4.75 cnf(c_0_15105, plain, (c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)), inference(rw,[status(thm)],[c_0_9555, c_0_5120]), ['final']). 4.46/4.75 cnf(c_0_15106, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat)),c_Int_Onat)),X2))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9556, c_0_4609]), c_0_4986]), c_0_4986]), ['final']). 4.46/4.75 cnf(c_0_15107, plain, (c_List_Omaps(tc_List_Olist(X1),tc_List_Olist(X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),tc_List_Olist(X1)),c_List_Omap(X1,tc_List_Olist(X1))),hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)))),X2),c_Enum_On__lists(X1,X3,X2))=c_Enum_On__lists(X1,hAPP(c_Nat_OSuc,X3),X2)), inference(rw,[status(thm)],[c_0_9557, c_0_5669]), ['final']). 4.46/4.75 cnf(c_0_15108, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9558, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), ['final']). 4.46/4.75 cnf(c_0_15109, plain, (hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Omap(tc_prod(X1,X3),tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X3,tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,X2),tc_fun(X3,tc_prod(X1,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(tc_fun(X3,X2),tc_fun(X3,tc_prod(X1,X2))),X1),c_COMBB(X2,tc_prod(X1,X2),X3)),c_Product__Type_OPair(X1,X2))),X4))),X5))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),tc_Option_Ooption(X2),X1,hAPP(c_Option_Omap(X3,X2),X4)),hAPP(c_Map_Omap__of(X1,X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9559]), ['final']). 4.46/4.75 cnf(c_0_15110, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)))))=hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9560, c_0_5580]), c_0_5580]), c_0_5580]), ['final']). 4.46/4.75 cnf(c_0_15111, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),tc_prod(X1,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X1,X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X3),tc_fun(X2,tc_prod(X1,X3))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X1,X3)),tc_fun(tc_fun(X2,X3),tc_fun(X2,tc_prod(X1,X3))),X1),c_COMBB(X3,tc_prod(X1,X3),X2)),c_Product__Type_OPair(X1,X3))),X4))),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6))=hAPP(hAPP(c_List_Ozip(X1,X3),X5),hAPP(hAPP(c_List_Omap(X2,X3),X4),X6))), inference(split_conjunct,[status(thm)],[c_0_9561]), ['final']). 4.46/4.75 cnf(c_0_15112, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X2)),c_List_Olists(X1,hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X2,X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9562, c_0_6105]), c_0_5320]), c_0_4531]), ['final']). 4.46/4.75 cnf(c_0_15113, plain, (hAPP(c_Set_Oimage(X1,tc_prod(X1,X1),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1))),X2)=c_Relation_OId__on(X1,X2)), inference(rw,[status(thm)],[c_0_9563, c_0_9564]), ['final']). 4.46/4.75 cnf(c_0_15114, plain, (c_New__DSequence_Oneg__bind(X1,X2,hAPP(hAPP(hAPP(X3,X4),X5),X6),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))))),X7),X4)),X5)),X6))=hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X1,X2,X3,X7),X4),X5),X6)), inference(split_conjunct,[status(thm)],[c_0_9565]), ['final']). 4.46/4.75 cnf(c_0_15115, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X2)),c_Int_Onat))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9566, c_0_4609]), c_0_5101]), c_0_5101]), ['final']). 4.46/4.75 cnf(c_0_15116, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X2)),c_Int_Onat))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9567, c_0_4609]), c_0_4986]), c_0_4986]), ['final']). 4.46/4.75 cnf(c_0_15117, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X1,tc_Nat_Onat)),X2),c_Product__Type_Osnd(X1,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))))=c_List_Osublist(X1,X3,X2)), inference(rw,[status(thm)],[c_0_9568, c_0_6095]), ['final']). 4.46/4.75 cnf(c_0_15118, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq))=c_FunDef_Omin__weak), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9569, c_0_5580]), c_0_6382]), ['final']). 4.46/4.75 cnf(c_0_15119, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq))=c_FunDef_Omax__weak), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9570, c_0_5580]), c_0_6382]), ['final']). 4.46/4.75 cnf(c_0_15120, plain, (c_Enum_Osublists(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_Enum_Osublists(X1,X3)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(X1)),tc_fun(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),tc_List_Olist(tc_List_Olist(X1))),c_List_Oappend(tc_List_Olist(X1))),hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(c_List_Olist_OCons(X1),X2)))),c_COMBI(tc_List_Olist(tc_List_Olist(X1)))))), inference(split_conjunct,[status(thm)],[c_0_9571]), ['final']). 4.46/4.75 cnf(c_0_15121, plain, (c_New__Random__Sequence_Oneg__decr__bind(X1,X2,X3,X4,X5,X6,X7)=c_New__DSequence_Oneg__decr__bind(X1,X2,hAPP(hAPP(hAPP(X3,X5),X6),X7),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))))),X4),X5)),X6)),X7))), inference(split_conjunct,[status(thm)],[c_0_9572]), ['final']). 4.46/4.75 cnf(c_0_15122, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X3),X4),hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Omap(X5,X1),X6),X7)),X8))=hAPP(hAPP(c_List_Omap(tc_prod(X5,X2),X3),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X2,X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,X3),X5),hAPP(c_COMBB(tc_prod(X1,X2),X3,X2),X4)),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_prod(X1,X2)),X5),c_Product__Type_OPair(X1,X2)),X6)))),hAPP(hAPP(c_List_Ozip(X5,X2),X7),X8))), inference(split_conjunct,[status(thm)],[c_0_9573]), ['final']). 4.46/4.75 cnf(c_0_15123, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9574, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_6186]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4609]), ['final']). 4.46/4.75 cnf(c_0_15124, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Nitpick_OFrac), inference(split_conjunct,[status(thm)],[fact_Nitpick_OFrac__def]), ['final']). 4.46/4.75 cnf(c_0_15125, plain, (hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),X3))),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1)),c_member(X2))),X4)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9575, c_0_4945]), c_0_4531]), ['final']). 4.46/4.75 cnf(c_0_15126, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Map_Odom(X1,X3,X4))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X3,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),c_Map_Odom(X1,X3,X4))))=c_Map_Odom(X1,X3,c_Fun_Ooverride__on(X1,tc_Option_Ooption(X3),X5,X4,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9576, c_0_4945]), c_0_4531]), c_0_4945]), c_0_4531]), c_0_6382]), ['final']). 4.46/4.75 cnf(c_0_15127, plain, (c_Lazy__Sequence_Oproduct(X1,X2,X3,X4)=hAPP(c_Lazy__Sequence_Obind(X1,tc_prod(X1,X2),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X1,X2))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X1,X2)),X1),c_Lazy__Sequence_Obind(X2,tc_prod(X1,X2),X4)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X1,X2))),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X1,X2)),X2),c_Lazy__Sequence_Osingle(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2))))), inference(split_conjunct,[status(thm)],[c_0_9577]), ['final']). 4.46/4.75 cnf(c_0_15128, plain, (c_New__DSequence_Opos__bind(X1,X2,hAPP(hAPP(hAPP(X3,X4),X5),X6),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))))),X7),X4)),X5)),X6))=hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X1,X2,X3,X7),X4),X5),X6)), inference(split_conjunct,[status(thm)],[c_0_9578]), ['final']). 4.46/4.75 cnf(c_0_15129, plain, (c_New__DSequence_Opos__decr__bind(X1,X2,hAPP(hAPP(hAPP(X3,X4),X5),X6),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))))),X7),X4)),X5)),X6))=c_New__Random__Sequence_Opos__decr__bind(X1,X2,X3,X7,X4,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_9579]), ['final']). 4.46/4.75 cnf(c_0_15130, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_Set_Oinsert(X2),X5),X6)))=hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_Set_Oinsert(X2),X5),X6)))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X6))))), inference(split_conjunct,[status(thm)],[c_0_9580]), ['final']). 4.46/4.75 cnf(c_0_15131, plain, (c_Fun_Oinj__on(tc_fun(X1,X2),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,X2)),c_Set_OCollect(tc_prod(X1,X2))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,X2)),c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool)),hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBC(X2,X2,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,X2),tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_9581]), ['final']). 4.46/4.75 cnf(c_0_15132, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X5,X3),tc_HOL_Obool),tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2,X5),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X5,X3),tc_HOL_Obool),tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X1),c_Relation_Orel__comp(X2,X5,X3)),X6)),X7))=hAPP(hAPP(c_Relation_Orel__comp(X2,X5,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X5),tc_HOL_Obool)),X4),X6)),X7)), inference(split_conjunct,[status(thm)],[c_0_9582]), ['final']). 4.46/4.75 cnf(c_0_15133, plain, (c_Random_Oselect__weight(X1,X2)=hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X1)),X2)))),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_9583]), ['final']). 4.46/4.75 cnf(c_0_15134, plain, (c_List_Omap__filter(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),X1),c_If(tc_Option_Ooption(X2))),X3)),hAPP(hAPP(c_COMBB(X2,tc_Option_Ooption(X2),X1),c_Option_Ooption_OSome(X2)),X4))),c_Option_Ooption_ONone(X2)),X5)=hAPP(hAPP(c_List_Omap(X1,X2),X4),hAPP(c_List_Ofilter(X1,X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9584]), ['final']). 4.46/4.75 cnf(c_0_15135, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X1)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))),c_List_Olist_ONil(X1))),c_List_Osublist(X1,X4,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X2),c_Nat_OSuc)))=c_List_Osublist(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9585, c_0_6095]), c_0_4531]), ['final']). 4.46/4.75 cnf(c_0_15136, plain, (c_Wellfounded_Omlex__prod(tc_List_Olist(X1),c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Olex(X1,X2))=c_List_Olenlex(X1,X2)), inference(rw,[status(thm)],[c_0_9586, c_0_9587]), ['final']). 4.46/4.75 cnf(c_0_15137, plain, (c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),X1),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)=hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),X2)), inference(rw,[status(thm)],[c_0_9588, c_0_9533]), ['final']). 4.46/4.75 cnf(c_0_15138, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olists(X1,X2)),c_List_Olists(X1,X3))=c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9589, c_0_4945]), c_0_4945]), c_0_4945]), c_0_4945]), ['final']). 4.46/4.75 cnf(c_0_15139, plain, (c_List_Omeasures(X1,X2)=hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),X1),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(tc_fun(X1,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(X1,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),X1),c_List_Omap(tc_fun(X1,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(X1,tc_Nat_Onat),X1,tc_Nat_Onat),c_COMBI(tc_fun(X1,tc_Nat_Onat))))),X2))), inference(split_conjunct,[status(thm)],[c_0_9590]), ['final']). 4.46/4.75 cnf(c_0_15140, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9591, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4784]), ['final']). 4.46/4.75 cnf(c_0_15141, plain, (hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X1),X2)),c_Code__Numeral_Onat__of)))=c_Random_Oselect(X1,X2)), inference(rw,[status(thm)],[c_0_9592, c_0_5334]), ['final']). 4.46/4.75 cnf(c_0_15142, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9593, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), c_0_4784]), c_0_9594]), c_0_4760]), ['final']). 4.46/4.75 cnf(c_0_15143, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_OCollect(X1)),hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1))))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)), inference(rw,[status(thm)],[c_0_9595, c_0_6173]), ['final']). 4.46/4.75 cnf(c_0_15144, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),X3)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X4),c_Int_Onat)))=c_Nat_Onat_Onat__case(X1,X3,X4,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))), inference(rw,[status(thm)],[c_0_9596, c_0_4609]), ['final']). 4.46/4.75 cnf(c_0_15145, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)))))=hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X1))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9597, c_0_5580]), c_0_5580]), ['final']). 4.46/4.75 cnf(c_0_15146, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Osublist(X1,X2,X3)),c_List_Osublist(X1,X4,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X3),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))))=c_List_Osublist(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X4),X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9598, c_0_6095]), c_0_4531]), ['final']). 4.46/4.75 cnf(c_0_15147, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9599, c_0_4784]), c_0_9594]), c_0_5714]), c_0_4784]), c_0_4500]), c_0_4760]), c_0_5765]), c_0_4760]), ['final']). 4.46/4.75 cnf(c_0_15148, plain, (hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),c_Relation_OImage(X1,X1,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3)=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X2)), inference(rw,[status(thm)],[c_0_9600, c_0_9564]), ['final']). 4.46/4.75 cnf(c_0_15149, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9601, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.75 cnf(c_0_15150, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),hAPP(c_Fun_Ocomp(tc_prod(X2,X4),X2,X1,c_Product__Type_Ofst(X2,X4)),X5))),hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,X1),X6),hAPP(c_Fun_Ocomp(tc_prod(X2,X4),X4,X1,c_Product__Type_Osnd(X2,X4)),X5)))=hAPP(hAPP(c_COMBB(tc_prod(X2,X4),tc_HOL_Obool,X1),hAPP(hAPP(c_Product__Type_OSigma(X2,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X2),X6))),X5)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9602, c_0_4891]), c_0_4891]), c_0_4891]), ['final']). 4.46/4.75 cnf(c_0_15151, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9603, c_0_4500]), c_0_4760]), c_0_5765]), c_0_4609]), c_0_4760]), c_0_4784]), c_0_4784]), c_0_5714]), c_0_4609]), c_0_4609]), c_0_4609]), ['final']). 4.46/4.75 cnf(c_0_15152, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X1)))=c_Wellfounded_Ofinite__psubset(X1)), inference(rw,[status(thm)],[c_0_9604, c_0_4531]), ['final']). 4.46/4.75 cnf(c_0_15153, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9605, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_6013]), ['final']). 4.46/4.75 cnf(c_0_15154, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9606, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), ['final']). 4.46/4.75 cnf(c_0_15155, plain, (hAPP(hAPP(c_List_Omap(X1,X2),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2)),X3)),hAPP(c_List_Ofilter(X1,c_Map_Odom(X1,X2,X3)),X4))=c_List_Omap__filter(X1,X2,X3,X4)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9607, c_0_5671]), c_0_9608]), ['final']). 4.46/4.75 cnf(c_0_15156, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),tc_prod(X3,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X3,X2)),hAPP(hAPP(c_COMBB(X3,tc_fun(X2,tc_prod(X3,X2)),X1),c_Product__Type_OPair(X3,X2)),X4))),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6))=hAPP(hAPP(c_List_Ozip(X3,X2),hAPP(hAPP(c_List_Omap(X1,X3),X4),X5)),X6)), inference(split_conjunct,[status(thm)],[c_0_9609]), ['final']). 4.46/4.75 cnf(c_0_15157, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),tc_prod(X2,X1),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X2,X1)),hAPP(c_COMBC(X2,X1,tc_prod(X2,X1)),c_Product__Type_OPair(X2,X1)))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))=hAPP(hAPP(c_Product__Type_OSigma(X2,X1),X4),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9610]), ['final']). 4.46/4.75 cnf(c_0_15158, plain, (c_List_Omaps(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X2),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_List_Olist(X2),tc_List_Olist(X2)),X1),c_List_Olist_OCons(X2)),X3)),c_List_Olist_ONil(X2)),X4)=hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)), inference(rw,[status(thm)],[c_0_9611, c_0_5669]), ['final']). 4.46/4.75 cnf(c_0_15159, plain, (c_Lazy__Sequence_Ohb__not__seq(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),X2)))=hAPP(c_New__DSequence_Opos__not__seq(X1),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9612, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), ['final']). 4.46/4.75 cnf(c_0_15160, plain, (hAPP(c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Oappend(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1)))),X2)=hAPP(c_List_Orotate1(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_9613]), ['final']). 4.46/4.75 cnf(c_0_15161, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),X3),hAPP(hAPP(c_List_Oappend(X2),X4),X5))=hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)),X3)),X4)),hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)),X3)),X5))), inference(split_conjunct,[status(thm)],[c_0_9614]), ['final']). 4.46/4.75 cnf(c_0_15162, plain, (hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X4))),hAPP(hAPP(c_List_Ozip(X1,X2),X5),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X4)))=hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X5)),X4)), inference(split_conjunct,[status(thm)],[c_0_9615]), ['final']). 4.46/4.75 cnf(c_0_15163, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X6,tc_prod(X1,X2)),X7),X8))=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X6,X3),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_prod(X1,X2)),tc_fun(X6,X3),X5),hAPP(c_COMBB(tc_prod(X1,X2),X3,X6),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4))),X7)),X8)), inference(split_conjunct,[status(thm)],[c_0_9616]), ['final']). 4.46/4.75 cnf(c_0_15164, plain, (c_List_Oset__Cons(X1,hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(c_fequal,X4)))=hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(c_fequal,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9617, c_0_5580]), c_0_5580]), ['final']). 4.46/4.75 cnf(c_0_15165, plain, (hAPP(hAPP(c_Product__Type_OSigma(tc_Int_Oint,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_Set_OCollect(tc_Int_Oint)),c_Orderings_Oord__class_Oless(tc_Int_Oint)))=c_Int_Oint__ge__less__than(X1)), inference(rw,[status(thm)],[c_0_9618, c_0_9619]), ['final']). 4.46/4.75 cnf(c_0_15166, plain, (hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool)))=hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[c_0_9620, c_0_6013]), ['final']). 4.46/4.75 cnf(c_0_15167, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,X3),X1),X5),X6))=hAPP(hAPP(c_COMBS(tc_prod(X1,X2),X2,X3),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,X3),tc_prod(X1,X2)),X5),hAPP(hAPP(c_COMBB(X1,X4,tc_prod(X1,X2)),X6),c_Product__Type_Ofst(X1,X2)))),c_Product__Type_Osnd(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_9621]), ['final']). 4.46/4.75 cnf(c_0_15168, plain, (c_HOL_OThe(tc_prod(X1,X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_fequal,X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_fequal,X4))))=hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)), inference(rw,[status(thm)],[c_0_9622, c_0_4961]), ['final']). 4.46/4.75 cnf(c_0_15169, plain, (c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_fequal,X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_fequal,X4))))=hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)), inference(rw,[status(thm)],[c_0_9623, c_0_4961]), ['final']). 4.46/4.75 cnf(c_0_15170, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),c_Int_OMin)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9624, c_0_4784]), c_0_4784]), c_0_4784]), c_0_4760]), c_0_4760]), ['final']). 4.46/4.75 cnf(c_0_15171, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat),X3),hAPP(c_List_Onth(X1),X2))))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X3),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9625, c_0_5320]), c_0_4531]), ['final']). 4.46/4.75 cnf(c_0_15172, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X2)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2)), inference(rw,[status(thm)],[c_0_9626, c_0_9627]), ['final']). 4.46/4.75 cnf(c_0_15173, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X2)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9628, c_0_6381]), c_0_9629]), ['final']). 4.46/4.75 cnf(c_0_15174, plain, (hAPP(c_List_Ofoldl(X1,X2,X3,X4),hAPP(hAPP(c_List_Omap(X5,X2),X6),X7))=hAPP(c_List_Ofoldl(X1,X5,hAPP(hAPP(c_COMBC(X1,tc_fun(X5,X2),tc_fun(X5,X1)),hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_fun(tc_fun(X5,X2),tc_fun(X5,X1)),X1),c_COMBB(X2,X1,X5)),X3)),X6),X4),X7)), inference(split_conjunct,[status(thm)],[c_0_9630]), ['final']). 4.46/4.75 cnf(c_0_15175, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2))),X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)), inference(rw,[status(thm)],[c_0_9631, c_0_5643]), ['final']). 4.46/4.75 cnf(c_0_15176, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2))),X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)),X2)), inference(rw,[status(thm)],[c_0_9632, c_0_4784]), ['final']). 4.46/4.75 cnf(c_0_15177, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9633, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4609]), ['final']). 4.46/4.75 cnf(c_0_15178, plain, (c_Nitpick_OAbs__Frac(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2)))),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2))))=c_Nitpick_Ouminus__frac(X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9634, c_0_6281]), c_0_6281]), ['final']). 4.46/4.75 cnf(c_0_15179, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X3,tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),X3),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool))),X5)),X6))), inference(split_conjunct,[status(thm)],[c_0_9635]), ['final']). 4.46/4.75 cnf(c_0_15180, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))),c_Transitive__Closure_Ortrancl(X1,X2))=c_Transitive__Closure_Ortrancl(X1,X2)), inference(rw,[status(thm)],[c_0_9636, c_0_9637]), ['final']). 4.46/4.75 cnf(c_0_15181, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9638, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4835]), c_0_4834]), c_0_4609]), ['final']). 4.46/4.75 cnf(c_0_15182, plain, (hAPP(c_List_Orev(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),c_List_Orotate1(X1)),X2))=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),hAPP(c_List_Orev(X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9639, c_0_5902]), c_0_5902]), ['final']). 4.46/4.75 cnf(c_0_15183, plain, (hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4),X5)=c_Nat_Onat_Onat__case(tc_List_Olist(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_List_Olist(X1),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X1),X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X1,tc_List_Olist(X1)),c_List_Olist__update(X1,X3)),X5)),X4)), inference(split_conjunct,[status(thm)],[c_0_9640]), ['final']). 4.46/4.75 cnf(c_0_15184, plain, (c_HOL_OThe(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X1,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,tc_HOL_Obool),X1),c_fequal),X4)),X5)))=hAPP(c_Fun_Othe__inv__into(X1,X3,X2,X4),X5)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9641, c_0_4945]), c_0_5320]), ['final']). 4.46/4.75 cnf(c_0_15185, plain, (hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3))),c_Option_Ooption_OSome(X2)))=c_Map_Oran(X1,X2,X3)), inference(rw,[status(thm)],[c_0_9642, c_0_4531]), ['final']). 4.46/4.75 cnf(c_0_15186, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X6),X7))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),X6),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(tc_prod(X1,X3),tc_HOL_Obool),X5),hAPP(c_Relation_Orel__comp(X1,X2,X3),X4)),X7))), inference(split_conjunct,[status(thm)],[c_0_9643]), ['final']). 4.46/4.75 cnf(c_0_15187, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9644, c_0_4436]), c_0_4436]), c_0_4784]), c_0_4784]), c_0_4784]), c_0_4760]), c_0_9645]), c_0_4436]), c_0_4500]), c_0_4760]), c_0_5765]), ['final']). 4.46/4.75 cnf(c_0_15188, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),X5),X6))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4),c_Relation_OImage(X2,X1,X3)),X6))))), inference(split_conjunct,[status(thm)],[c_0_9646]), ['final']). 4.46/4.75 cnf(c_0_15189, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)=hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3)),hAPP(hAPP(c_List_Otake(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3))), inference(rw,[status(thm)],[c_0_9647, c_0_5902]), ['final']). 4.46/4.75 cnf(c_0_15190, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(X1),X1,c_List_Omap__filter(X2,X1,X3,X4),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Omap__filter(X2,X1,X3,X4))),hAPP(X3,X5))=c_List_Omap__filter(X2,X1,X3,hAPP(hAPP(c_List_Olist_OCons(X2),X5),X4))), inference(split_conjunct,[status(thm)],[c_0_9648]), ['final']). 4.46/4.75 cnf(c_0_15191, plain, (hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))=hAPP(c_List_Olist_Olist__case(tc_List_Olist(X1),X1,hAPP(c_List_Otl(X1),X3),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Oappend(X1)),X3))),X2)), inference(split_conjunct,[status(thm)],[c_0_9649]), ['final']). 4.46/4.75 cnf(c_0_15192, plain, (hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=c_Nat_Onat_Onat__case(tc_List_Olist(X1),c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_List_Olist(X1),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X1),X3)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Otake(X1)),X4)),X2)), inference(split_conjunct,[status(thm)],[c_0_9650]), ['final']). 4.46/4.75 cnf(c_0_15193, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9651, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), c_0_4784]), c_0_4609]), ['final']). 4.46/4.75 cnf(c_0_15194, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),hAPP(c_Relation_OField(X1),X2)),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_Relation_OField(X1),X2)))))), inference(rw,[status(thm)],[c_0_9652, c_0_5266]), ['final']). 4.46/4.75 cnf(c_0_15195, plain, (c_Product__Type_Omap__pair(X1,X2,X3,X4,hAPP(c_Fun_Ocomp(X5,X2,X1,X6),X7),hAPP(c_Fun_Ocomp(X8,X4,X3,X9),X10))=hAPP(c_Fun_Ocomp(tc_prod(X5,X8),tc_prod(X2,X4),tc_prod(X1,X3),c_Product__Type_Omap__pair(X5,X2,X8,X4,X6,X9)),c_Product__Type_Omap__pair(X1,X5,X3,X8,X7,X10))), inference(split_conjunct,[status(thm)],[c_0_9653]), ['final']). 4.46/4.75 cnf(c_0_15196, plain, (hAPP(hAPP(c_List_Olist__update(tc_prod(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)),X5),X6)=hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist__update(X1,X3),X5),hAPP(c_Product__Type_Ofst(X1,X2),X6))),hAPP(hAPP(c_List_Olist__update(X2,X4),X5),hAPP(c_Product__Type_Osnd(X1,X2),X6)))), inference(split_conjunct,[status(thm)],[c_0_9654]), ['final']). 4.46/4.75 cnf(c_0_15197, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)))),c_Nitpick_Onat__gcd(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)))))=c_Nitpick_Oint__lcm(X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9655, c_0_5120]), c_0_5120]), c_0_9656]), c_0_5120]), c_0_5120]), ['final']). 4.46/4.75 cnf(c_0_15198, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X1),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),X3))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X4))),c_Com_Ocom_OWhile(X4,X5)),X3)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9657, c_0_5671]), c_0_5580]), ['final']). 4.46/4.75 cnf(c_0_15199, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9658, c_0_4784]), c_0_5764]), c_0_9659]), c_0_4760]), c_0_4760]), ['final']). 4.46/4.75 cnf(c_0_15200, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9660, c_0_4760]), c_0_4912]), c_0_4760]), c_0_4912]), c_0_4784]), c_0_5764]), c_0_9659]), c_0_4760]), ['final']). 4.46/4.75 cnf(c_0_15201, plain, (c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3))=c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(hAPP(c_COMBS(tc_prod(X1,X2),X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),tc_prod(X1,X2)),X3),c_Product__Type_Ofst(X1,X2))),c_Product__Type_Osnd(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_9661]), ['final']). 4.46/4.75 cnf(c_0_15202, plain, (c_Map_Orestrict__map(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=c_Map_Orestrict__map(X1,X2,X3,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_9662]), ['final']). 4.46/4.75 cnf(c_0_15203, plain, (c_HOL_OThe(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3))=c_HOL_OThe(tc_prod(X1,X2),hAPP(hAPP(c_COMBS(tc_prod(X1,X2),X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),tc_prod(X1,X2)),X3),c_Product__Type_Ofst(X1,X2))),c_Product__Type_Osnd(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_9663]), ['final']). 4.46/4.75 cnf(c_0_15204, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X3),X5))))), inference(split_conjunct,[status(thm)],[c_0_9664]), ['final']). 4.46/4.75 cnf(c_0_15205, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X3),tc_HOL_Obool),X1),c_Relation_Oconverse(X3,X2)),X5))=hAPP(c_Relation_Oconverse(X3,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_prod(X3,X2),tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9665]), ['final']). 4.46/4.75 cnf(c_0_15206, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X3),tc_HOL_Obool),X1),c_Relation_Oconverse(X3,X2)),X5))=hAPP(c_Relation_Oconverse(X3,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X3,X2),tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9666]), ['final']). 4.46/4.75 cnf(c_0_15207, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(c_List_Orev(tc_List_Olist(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Orev(X1)),X2)))=hAPP(c_List_Orev(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2))), inference(rw,[status(thm)],[c_0_9667, c_0_9668]), ['final']). 4.46/4.75 cnf(c_0_15208, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,tc_prod(X1,X2),esk157_4(X3,X4,X1,X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X4),X3))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_9669]), ['final']). 4.46/4.75 cnf(c_0_15209, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9670, c_0_4912]), c_0_4912]), c_0_4760]), c_0_4500]), c_0_4760]), c_0_5765]), ['final']). 4.46/4.75 cnf(c_0_15210, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3))),X3))), inference(split_conjunct,[status(thm)],[c_0_9671]), ['final']). 4.46/4.75 cnf(c_0_15211, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5)), inference(split_conjunct,[status(thm)],[c_0_9672]), ['final']). 4.46/4.75 cnf(c_0_15212, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))),X3))), inference(split_conjunct,[status(thm)],[c_0_9673]), ['final']). 4.46/4.75 cnf(c_0_15213, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5)), inference(split_conjunct,[status(thm)],[c_0_9674]), ['final']). 4.46/4.75 cnf(c_0_15214, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_9675]), ['final']). 4.46/4.75 cnf(c_0_15215, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9676, c_0_5580]), c_0_5120]), ['final']). 4.46/4.75 cnf(c_0_15216, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),c_List_Orotate1(X1)),X4)=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9677, c_0_5902]), c_0_5902]), c_0_5902]), ['final']). 4.46/4.75 cnf(c_0_15217, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3))),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))))), inference(split_conjunct,[status(thm)],[c_0_9678]), ['final']). 4.46/4.75 cnf(c_0_15218, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X6),X5))=hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),X4),X6)),X5)), inference(split_conjunct,[status(thm)],[c_0_9679]), ['final']). 4.46/4.75 cnf(c_0_15219, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X6))=hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X2),tc_HOL_Obool)),X5),X6))), inference(split_conjunct,[status(thm)],[c_0_9680]), ['final']). 4.46/4.75 cnf(c_0_15220, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))),c_List_Olexord(X1,X5)))), inference(er,[status(thm)],[c_0_9681]), ['final']). 4.46/4.75 cnf(c_0_15221, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ORange(X2,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ORange(X2,X1),X3)),hAPP(c_Relation_ORange(X2,X1),X4))))), inference(split_conjunct,[status(thm)],[c_0_9682]), ['final']). 4.46/4.75 cnf(c_0_15222, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4))))), inference(split_conjunct,[status(thm)],[c_0_9683]), ['final']). 4.46/4.75 cnf(c_0_15223, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ORange(X2,X1),X3)),hAPP(c_Relation_ORange(X2,X1),X4))),hAPP(c_Relation_ORange(X2,X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4))))), inference(split_conjunct,[status(thm)],[c_0_9684]), ['final']). 4.46/4.75 cnf(c_0_15224, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4))),hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))))), inference(split_conjunct,[status(thm)],[c_0_9685]), ['final']). 4.46/4.75 cnf(c_0_15225, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),c_fequal))),X2))=c_Relation_OId__on(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9686]), ['final']). 4.46/4.75 cnf(c_0_15226, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Product__Type_OSigma(X1,X2)),X4))), inference(split_conjunct,[status(thm)],[c_0_9687]), ['final']). 4.46/4.75 cnf(c_0_15227, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_Map_Omap__of(X1,X2),X3)),hAPP(c_Product__Type_Ofst(X1,X2),X4)),hAPP(c_Option_Ooption_OSome(X2),hAPP(c_Product__Type_Osnd(X1,X2),X4)))=hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_9688]), ['final']). 4.46/4.75 cnf(c_0_15228, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3))=c_List_Omaps(tc_List_Olist(X1),X1,c_List_Ofilter(X1,X2),X3)), inference(rw,[status(thm)],[c_0_9689, c_0_5669]), ['final']). 4.46/4.75 cnf(c_0_15229, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool)),X2))), inference(split_conjunct,[status(thm)],[c_0_9690]), ['final']). 4.46/4.75 cnf(c_0_15230, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)), inference(rw,[status(thm)],[c_0_9691, c_0_5580]), ['final']). 4.46/4.75 cnf(c_0_15231, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9692, c_0_9693]), c_0_9694]), ['final']). 4.46/4.75 cnf(c_0_15232, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),esk362_1(X1)),esk363_1(X1)))))=X1), inference(rw,[status(thm)],[c_0_9695, c_0_5580]), ['final']). 4.46/4.75 cnf(c_0_15233, plain, (hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X4)=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9696]), ['final']). 4.46/4.75 cnf(c_0_15234, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),X2),c_Set_OPow(X1)),X4))),hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4))))), inference(split_conjunct,[status(thm)],[c_0_9697]), ['final']). 4.46/4.75 cnf(c_0_15235, plain, (c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak))), inference(split_conjunct,[status(thm)],[fact_max__rpair__set]), ['final']). 4.46/4.75 cnf(c_0_15236, plain, (c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak))), inference(split_conjunct,[status(thm)],[fact_min__rpair__set]), ['final']). 4.46/4.75 cnf(c_0_15237, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak))), inference(split_conjunct,[status(thm)],[c_0_9698]), ['final']). 4.46/4.75 cnf(c_0_15238, plain, (c_Enum_Oproduct(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4),X5)=hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),hAPP(hAPP(c_List_Omap(X2,tc_prod(X1,X2)),hAPP(c_Product__Type_OPair(X1,X2),X3)),X5)),c_Enum_Oproduct(X1,X2,X4,X5))), inference(split_conjunct,[status(thm)],[c_0_9699]), ['final']). 4.46/4.75 cnf(c_0_15239, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))=c_Int_Oint__ge__less__than2(X1)), inference(rw,[status(thm)],[c_0_9700, c_0_4531]), ['final']). 4.46/4.75 cnf(c_0_15240, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_9701]), ['final']). 4.46/4.75 cnf(c_0_15241, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X3)))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X3)))), inference(split_conjunct,[status(thm)],[c_0_9702]), ['final']). 4.46/4.75 cnf(c_0_15242, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_9703]), ['final']). 4.46/4.75 cnf(c_0_15243, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5))),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5))))), inference(split_conjunct,[status(thm)],[c_0_9704]), ['final']). 4.46/4.75 cnf(c_0_15244, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5))))), inference(split_conjunct,[status(thm)],[c_0_9705]), ['final']). 4.46/4.75 cnf(c_0_15245, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Ofilter(X1,X2),X3)),hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),X3)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9706, c_0_5671]), c_0_9707]), ['final']). 4.46/4.75 cnf(c_0_15246, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3)),hAPP(hAPP(c_List_Odrop(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X4))=hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9708]), ['final']). 4.46/4.75 cnf(c_0_15247, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X4))=hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9709]), ['final']). 4.46/4.75 cnf(c_0_15248, plain, (c_Map_Odom(X1,X2,X3)=c_Map_Odom(X1,X4,hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_Option_Ooption(X4)),hAPP(hAPP(c_COMBB(tc_fun(X2,X4),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X4)),X1),c_Option_Omap(X2,X4)),X5)),X3))), inference(split_conjunct,[status(thm)],[c_0_9710]), ['final']). 4.46/4.75 cnf(c_0_15249, plain, (c_Lazy__Sequence_Ohb__flat(X1,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1))),X2,X3))=c_Lazy__Sequence_Oappend(tc_Option_Ooption(X1),hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)),tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)),c_Lazy__Sequence_Ohit__bound(X1),c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)))),X2),c_Lazy__Sequence_Ohb__flat(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_9711]), ['final']). 4.46/4.75 cnf(c_0_15250, plain, (c_Random_Opick(X1,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X2))=c_Random_Opick(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9712]), ['final']). 4.46/4.75 cnf(c_0_15251, plain, (c_Random_Oselect__weight(X1,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X2))=c_Random_Oselect__weight(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9713]), ['final']). 4.46/4.75 cnf(c_0_15252, plain, (c_List_OtakeWhile(tc_prod(X1,X2),hAPP(c_Fun_Ocomp(X1,tc_HOL_Obool,tc_prod(X1,X2),X3),c_Product__Type_Ofst(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))=hAPP(hAPP(c_List_Ozip(X1,X2),c_List_OtakeWhile(X1,X3,X4)),X5)), inference(split_conjunct,[status(thm)],[c_0_9714]), ['final']). 4.46/4.75 cnf(c_0_15253, plain, (c_List_OtakeWhile(tc_prod(X1,X2),hAPP(c_Fun_Ocomp(X2,tc_HOL_Obool,tc_prod(X1,X2),X3),c_Product__Type_Osnd(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))=hAPP(hAPP(c_List_Ozip(X1,X2),X4),c_List_OtakeWhile(X2,X3,X5))), inference(split_conjunct,[status(thm)],[c_0_9715]), ['final']). 4.46/4.75 cnf(c_0_15254, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4))),hAPP(X5,hAPP(c_Product__Type_Osnd(X2,X3),X4))))=c_Product__Type_Oprod_Oprod__size(X2,X3,X1,X5,X4)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9716, c_0_4836]), c_0_5643]), c_0_5644]), c_0_5645]), ['final']). 4.46/4.75 cnf(c_0_15255, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))),c_List_Olexord(X1,X4)))), inference(er,[status(thm)],[c_0_9717]), ['final']). 4.46/4.75 cnf(c_0_15256, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),X1),c_Int_Onat)))=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9718, c_0_5320]), c_0_4531]), c_0_4531]), ['final']). 4.46/4.75 cnf(c_0_15257, plain, (hAPP(c_List_Oset(X1),hAPP(c_List_Ofilter(X1,X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X3)),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9719, c_0_4945]), c_0_5320]), c_0_4531]), ['final']). 4.46/4.75 cnf(c_0_15258, plain, (hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X1),X2)))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X1),X2)), inference(rw,[status(thm)],[c_0_9720, c_0_9721]), ['final']). 4.46/4.75 cnf(c_0_15259, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X4))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X5)),X4)), inference(split_conjunct,[status(thm)],[c_0_9722]), ['final']). 4.46/4.75 cnf(c_0_15260, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9723]), ['final']). 4.46/4.75 cnf(c_0_15261, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9724]), ['final']). 4.46/4.75 cnf(c_0_15262, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=c_Nat_Onat_Onat__case(tc_List_Olist(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Odrop(X1)),X4),X2)), inference(split_conjunct,[status(thm)],[c_0_9725]), ['final']). 4.46/4.75 cnf(c_0_15263, plain, (c_Divides_Odivmod__int(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))=c_Divides_Opdivmod(X1,X2)), inference(rw,[status(thm)],[c_0_9726, c_0_9727]), ['final']). 4.46/4.75 cnf(c_0_15264, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9728, c_0_4531]), c_0_5320]), c_0_4531]), ['final']). 4.46/4.75 cnf(c_0_15265, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3))=hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)), inference(rw,[status(thm)],[c_0_9729, c_0_6151]), ['final']). 4.46/4.75 cnf(c_0_15266, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X3)),X4))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(er,[status(thm)],[c_0_9730]), ['final']). 4.46/4.75 cnf(c_0_15267, plain, (c_New__Random__Sequence_Oneg__map(X1,X2,X3,X4)=c_New__Random__Sequence_Oneg__bind(X1,X2,X4,hAPP(c_Fun_Ocomp(X2,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))))),X1,c_New__Random__Sequence_Oneg__single(X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_9731]), ['final']). 4.46/4.75 cnf(c_0_15268, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),hAPP(c_COMBC(X1,X2,X1),X3)),X4),X5)=hAPP(c_List_Ofoldl(X1,X2,X3,X4),X5)), inference(rw,[status(thm)],[c_0_9732, c_0_9733]), ['final']). 4.46/4.75 cnf(c_0_15269, plain, (c_Map_Omap__add(X1,X2,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X4),X5),hAPP(c_Option_Ooption_OSome(X2),X6)))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__add(X1,X2,X3,X4)),X5),hAPP(c_Option_Ooption_OSome(X2),X6))), inference(split_conjunct,[status(thm)],[c_0_9734]), ['final']). 4.46/4.75 cnf(c_0_15270, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,X3),X1),hAPP(c_COMBB(tc_prod(X1,X2),X3,X2),X4)),c_Product__Type_OPair(X1,X2)))=X4), inference(split_conjunct,[status(thm)],[c_0_9735]), ['final']). 4.46/4.75 cnf(c_0_15271, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool))),X4))), inference(split_conjunct,[status(thm)],[c_0_9736]), ['final']). 4.46/4.75 cnf(c_0_15272, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool))),X4))), inference(split_conjunct,[status(thm)],[c_0_9737]), ['final']). 4.46/4.75 cnf(c_0_15273, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2),X3)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))), inference(rw,[status(thm)],[c_0_9738, c_0_5100]), ['final']). 4.46/4.75 cnf(c_0_15274, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4))),c_Map_Odom(X1,X2,X5))=c_Map_Odom(X1,X2,c_Map_Omap__upds(X1,X2,X5,X4,X3))), inference(split_conjunct,[status(thm)],[c_0_9739]), ['final']). 4.46/4.75 cnf(c_0_15275, plain, (c_FunDef_Opair__leq=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Transitive__Closure_Ortrancl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool))))), inference(rw,[status(thm)],[c_0_9740, c_0_5689]), ['final']). 4.46/4.75 cnf(c_0_15276, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_Ovimage(X2,X4,X5)),X6))=hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6)),X5)), inference(rw,[status(thm)],[c_0_9741, c_0_4891]), ['final']). 4.46/4.75 cnf(c_0_15277, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_Ovimage(X2,X4,X5)),X6))=hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6)),X5)), inference(rw,[status(thm)],[c_0_9742, c_0_4891]), ['final']). 4.46/4.75 cnf(c_0_15278, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Relation_OImage(X4,X2,X5)),X6))=hAPP(c_Relation_OImage(X4,X2,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6))), inference(split_conjunct,[status(thm)],[c_0_9743]), ['final']). 4.46/4.75 cnf(c_0_15279, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),c_List_Orotate1(X1)),X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9744, c_0_5902]), c_0_5902]), ['final']). 4.46/4.75 cnf(c_0_15280, plain, (c_New__Random__Sequence_Opos__map(X1,X2,X3,X4)=c_New__Random__Sequence_Opos__bind(X1,X2,X4,hAPP(c_Fun_Ocomp(X2,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))))),X1,c_New__Random__Sequence_Opos__single(X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_9745]), ['final']). 4.46/4.75 cnf(c_0_15281, plain, (hAPP(c_Relation_OField(X1),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(c_Relation_OField(X1),X4)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9746, c_0_7464]), c_0_7464]), c_0_7465]), ['final']). 4.46/4.75 cnf(c_0_15282, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))))), inference(split_conjunct,[status(thm)],[c_0_9747]), ['final']). 4.46/4.75 cnf(c_0_15283, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3))))), inference(split_conjunct,[status(thm)],[c_0_9748]), ['final']). 4.46/4.75 cnf(c_0_15284, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X5),X4))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X5)),X4)), inference(split_conjunct,[status(thm)],[c_0_9749]), ['final']). 4.46/4.75 cnf(c_0_15285, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9750]), ['final']). 4.46/4.75 cnf(c_0_15286, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))=c_Transitive__Closure_Ortrancl(X1,X2)), inference(rw,[status(thm)],[c_0_9751, c_0_9694]), ['final']). 4.46/4.75 cnf(c_0_15287, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_9752]), ['final']). 4.46/4.75 cnf(c_0_15288, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_9753]), ['final']). 4.46/4.75 cnf(c_0_15289, plain, (hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(c_fequal,c_List_Olist_ONil(X1)))=hAPP(c_fequal,c_List_Olist_ONil(X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9754, c_0_5580]), c_0_5580]), ['final']). 4.46/4.75 cnf(c_0_15290, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_OPow(X1),X3))),hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))))), inference(split_conjunct,[status(thm)],[c_0_9755]), ['final']). 4.46/4.75 cnf(c_0_15291, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_9756]), ['final']). 4.46/4.75 cnf(c_0_15292, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X5),X4))=hAPP(c_Relation_OImage(X2,X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X5)),X4)), inference(split_conjunct,[status(thm)],[c_0_9757]), ['final']). 4.46/4.75 cnf(c_0_15293, plain, (c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)),X1)),X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9758, c_0_5101]), c_0_5101]), ['final']). 4.46/4.75 cnf(c_0_15294, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X2),c_Product__Type_Osnd(X1,X2)),X3))=X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9759])]), c_0_9760]), c_0_9760])]), ['final']). 4.46/4.75 cnf(c_0_15295, plain, (c_Fun_Oinj__on(tc_prod(X1,X2),tc_prod(X2,X1),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X2,X1)),hAPP(c_COMBC(X2,X1,tc_prod(X2,X1)),c_Product__Type_OPair(X2,X1))),X3)), inference(split_conjunct,[status(thm)],[c_0_9761]), ['final']). 4.46/4.75 cnf(c_0_15296, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),X3)),hAPP(hAPP(c_Nat_Ocompow(X1,X1),X4),X3))=hAPP(hAPP(c_Nat_Ocompow(X1,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)),X3)), inference(split_conjunct,[status(thm)],[c_0_9762]), ['final']). 4.46/4.75 cnf(c_0_15297, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9763]), ['final']). 4.46/4.75 cnf(c_0_15298, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2)),X5))), inference(split_conjunct,[status(thm)],[c_0_9764]), ['final']). 4.46/4.75 cnf(c_0_15299, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2)),X5))), inference(split_conjunct,[status(thm)],[c_0_9765]), ['final']). 4.46/4.75 cnf(c_0_15300, plain, (c_Lazy__Sequence_Ohb__flat(X2,c_Lazy__Sequence_Ohb__map(X1,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))),X5),X4),hAPP(X3,X4)))=hAPP(c_New__DSequence_Oneg__bind(X1,X2,X3,X5),X4)), inference(rw,[status(thm)],[c_0_9766, c_0_6597]), ['final']). 4.46/4.75 cnf(c_0_15301, plain, (hAPP(c_Option_Omap(X1,X2),hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),tc_Option_Ooption(X2),tc_Option_Ooption(X1),hAPP(c_Option_Omap(X3,X2),X4)),hAPP(c_Option_Omap(X1,X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9767]), ['final']). 4.46/4.75 cnf(c_0_15302, plain, (hAPP(c_List_Omap(X1,X2),hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5))=hAPP(c_Fun_Ocomp(tc_List_Olist(X3),tc_List_Olist(X2),tc_List_Olist(X1),hAPP(c_List_Omap(X3,X2),X4)),hAPP(c_List_Omap(X1,X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9768]), ['final']). 4.46/4.75 cnf(c_0_15303, plain, (c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat)),X1)),X2)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9769, c_0_4986]), c_0_4986]), ['final']). 4.46/4.75 cnf(c_0_15304, plain, (hAPP(c_Relation_Oconverse(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X1,X2),X3)),hAPP(c_Relation_Oconverse(X1,X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9770]), ['final']). 4.46/4.75 cnf(c_0_15305, plain, (hAPP(c_Relation_Oconverse(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X1,X2),X3)),hAPP(c_Relation_Oconverse(X1,X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9771]), ['final']). 4.46/4.75 cnf(c_0_15306, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2))=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X3)),X2)), inference(rw,[status(thm)],[c_0_9772, c_0_9773]), ['final']). 4.46/4.75 cnf(c_0_15307, plain, (c_List_Opartition(X1,X2,X3)=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3)),hAPP(c_List_Ofilter(X1,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X1,c_fNot),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_9774]), ['final']). 4.46/4.75 cnf(c_0_15308, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X5),X4))=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X5)),X4)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9775, c_0_4891]), c_0_4891]), c_0_4891]), ['final']). 4.46/4.75 cnf(c_0_15309, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X5),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4),c_Set_Oimage(X1,X2,X3)),X6))), inference(split_conjunct,[status(thm)],[c_0_9776]), ['final']). 4.46/4.75 cnf(c_0_15310, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X3),X5))=hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9777]), ['final']). 4.46/4.75 cnf(c_0_15311, plain, (c_Map_Omap__upds(X1,X2,X3,X4,X5)=c_Map_Omap__add(X1,X2,X3,hAPP(c_Map_Omap__of(X1,X2),hAPP(c_List_Orev(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))))), inference(split_conjunct,[status(thm)],[c_0_9778]), ['final']). 4.46/4.75 cnf(c_0_15312, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X5),X4))=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X5)),X4)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9779, c_0_4891]), c_0_4891]), c_0_4891]), ['final']). 4.46/4.75 cnf(c_0_15313, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X5),X4))=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),X5)),X4)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9780, c_0_4891]), c_0_4891]), c_0_4891]), ['final']). 4.46/4.75 cnf(c_0_15314, plain, (hAPP(hAPP(c_List_Odrop(tc_prod(X1,X2)),X3),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))=hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Odrop(X1),X3),X4)),hAPP(hAPP(c_List_Odrop(X2),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9781]), ['final']). 4.46/4.75 cnf(c_0_15315, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X1,X2))),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))), inference(rw,[status(thm)],[c_0_9782, c_0_4986]), ['final']). 4.46/4.75 cnf(c_0_15316, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9783, c_0_5320]), c_0_4531]), ['final']). 4.46/4.75 cnf(c_0_15317, plain, (hAPP(c_List_Oset(tc_prod(X1,X2)),c_Enum_Oproduct(X1,X2,X3,X4))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_List_Oset(X1),X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_List_Oset(X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_9784]), ['final']). 4.46/4.75 cnf(c_0_15318, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_9785]), ['final']). 4.46/4.75 cnf(c_0_15319, plain, (hAPP(c_Finite__Set_Ocard(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9786]), ['final']). 4.46/4.75 cnf(c_0_15320, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_Oimage(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oinsert(X1),X3)),hAPP(c_Set_OPow(X1),X2)))=hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_9787]), ['final']). 4.46/4.75 cnf(c_0_15321, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),c_List_Oreplicate(X1,X3,X4)),c_List_Oreplicate(X2,X5,X6))=c_List_Oreplicate(tc_prod(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X3),X5),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X6))), inference(rw,[status(thm)],[c_0_9788, c_0_4986]), ['final']). 4.46/4.75 cnf(c_0_15322, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(X1))),c_List_Olistrel(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_9789]), ['final']). 4.46/4.75 cnf(c_0_15323, plain, (c_Map_Odom(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),X3),hAPP(c_Option_Ooption_OSome(X2),X4)))=hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(er,[status(thm)],[c_0_9790]), ['final']). 4.46/4.75 cnf(c_0_15324, plain, (hAPP(c_List_Oset(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)),c_List_Oset(X1))), inference(rw,[status(thm)],[c_0_9791, c_0_4736]), ['final']). 4.46/4.75 cnf(c_0_15325, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),X3)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),X3))), inference(split_conjunct,[status(thm)],[c_0_9792]), ['final']). 4.46/4.75 cnf(c_0_15326, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2))),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2))),X3)), inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9793, c_0_5671]), c_0_5671])]), ['final']). 4.46/4.75 cnf(c_0_15327, plain, (hAPP(c_Relation_Oconverse(X1,X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5))=hAPP(hAPP(c_Relation_Orel__comp(X2,X3,X1),hAPP(c_Relation_Oconverse(X3,X2),X5)),hAPP(c_Relation_Oconverse(X1,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9794]), ['final']). 4.46/4.75 cnf(c_0_15328, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(c_Nat_OSuc,X2)),c_List_Orotate1(X1)),X3)=hAPP(c_List_Orotate1(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9795, c_0_5902]), c_0_5902]), ['final']). 4.46/4.75 cnf(c_0_15329, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5))=hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(c_List_Ofilter(X3,hAPP(c_Fun_Ocomp(X1,tc_HOL_Obool,X3,X2),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_9796]), ['final']). 4.46/4.75 cnf(c_0_15330, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Relation_OId__on(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2))))), inference(split_conjunct,[status(thm)],[c_0_9797]), ['final']). 4.46/4.75 cnf(c_0_15331, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))), inference(split_conjunct,[status(thm)],[c_0_9798]), ['final']). 4.46/4.75 cnf(c_0_15332, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),X2),X3)=hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3))), inference(rw,[status(thm)],[c_0_9799, c_0_4736]), ['final']). 4.46/4.75 cnf(c_0_15333, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)),X3)=hAPP(c_Option_Ooption_OSome(X2),X4)), inference(er,[status(thm)],[c_0_9800]), ['final']). 4.46/4.75 cnf(c_0_15334, plain, (c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))=c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_9801]), ['final']). 4.46/4.75 cnf(c_0_15335, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ORange(X2,X1),X3)),hAPP(c_Relation_ORange(X2,X1),X4))=hAPP(c_Relation_ORange(X2,X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9802]), ['final']). 4.46/4.75 cnf(c_0_15336, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4))=hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9803]), ['final']). 4.46/4.75 cnf(c_0_15337, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))=c_Wellfounded_Opred__nat), inference(rw,[status(thm)],[c_0_9804, c_0_4531]), ['final']). 4.46/4.75 cnf(c_0_15338, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),c_Predicate_Oconversep(X2,X1,X3)),c_Predicate_Oconversep(X2,X1,X4))=c_Predicate_Oconversep(X2,X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_fun(X1,tc_HOL_Obool))),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9805]), ['final']). 4.46/4.75 cnf(c_0_15339, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),X1),c_Set_OPow(X2)),X4))=hAPP(c_Set_OPow(X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9806]), ['final']). 4.46/4.75 cnf(c_0_15340, plain, (c_Predicate_Oconversep(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_fun(X1,tc_HOL_Obool))),c_Predicate_Oconversep(X1,X2,X3)),c_Predicate_Oconversep(X1,X2,X4))), inference(split_conjunct,[status(thm)],[c_0_9807]), ['final']). 4.46/4.75 cnf(c_0_15341, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))))), inference(rw,[status(thm)],[c_0_9808, c_0_7232]), ['final']). 4.46/4.75 cnf(c_0_15342, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool))),X4))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9809]), ['final']). 4.46/4.75 cnf(c_0_15343, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool))),X4))), inference(split_conjunct,[status(thm)],[c_0_9810]), ['final']). 4.46/4.75 cnf(c_0_15344, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_Set_Oinsert(X1),X2)),X5))), inference(split_conjunct,[status(thm)],[c_0_9811]), ['final']). 4.46/4.75 cnf(c_0_15345, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel1(X1,c_Transitive__Closure_Ortrancl(X1,X2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2))))), inference(split_conjunct,[status(thm)],[c_0_9812]), ['final']). 4.46/4.75 cnf(c_0_15346, plain, (hAPP(c_Relation_ORange(X1,X2),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))=hAPP(hAPP(c_Set_Oinsert(X2),X4),hAPP(c_Relation_ORange(X1,X2),X5))), inference(split_conjunct,[status(thm)],[c_0_9813]), ['final']). 4.46/4.75 cnf(c_0_15347, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3))), inference(rw,[status(thm)],[c_0_9814, c_0_9815]), ['final']). 4.46/4.75 cnf(c_0_15348, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3)), inference(split_conjunct,[status(thm)],[c_0_9816]), ['final']). 4.46/4.75 cnf(c_0_15349, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))=hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X5))), inference(split_conjunct,[status(thm)],[c_0_9817]), ['final']). 4.46/4.75 cnf(c_0_15350, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3)), inference(split_conjunct,[status(thm)],[c_0_9818]), ['final']). 4.46/4.75 cnf(c_0_15351, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9819]), ['final']). 4.46/4.75 cnf(c_0_15352, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))), inference(rw,[status(thm)],[c_0_9820, c_0_4800]), ['final']). 4.46/4.75 cnf(c_0_15353, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9821]), ['final']). 4.46/4.75 cnf(c_0_15354, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9822]), ['final']). 4.46/4.75 cnf(c_0_15355, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9823]), ['final']). 4.46/4.75 cnf(c_0_15356, plain, (c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Omap(X3,X1),X4),X5))=hAPP(hAPP(c_List_Omap(X3,X1),X4),c_List_OtakeWhile(X3,hAPP(c_Fun_Ocomp(X1,tc_HOL_Obool,X3,X2),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9824]), ['final']). 4.46/4.75 cnf(c_0_15357, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3))=hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9825, c_0_4531]), c_0_4531]), ['final']). 4.46/4.75 cnf(c_0_15358, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Oappend(X1),c_List_Oreplicate(X1,X3,X2)),X4))=hAPP(hAPP(c_List_Oappend(X1),c_List_Oreplicate(X1,X3,X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9826]), ['final']). 4.46/4.75 cnf(c_0_15359, plain, (hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3))=hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)),hAPP(c_List_Orev(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_9827]), ['final']). 4.46/4.75 cnf(c_0_15360, plain, (hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3))=hAPP(hAPP(c_List_Odrop(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)),hAPP(c_List_Orev(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_9828]), ['final']). 4.46/4.75 cnf(c_0_15361, plain, (c_List_Osplice(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))=hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X4),c_List_Osplice(X1,X3,X5)))), inference(split_conjunct,[status(thm)],[c_0_9829]), ['final']). 4.46/4.75 cnf(c_0_15362, plain, (hAPP(hAPP(c_List_Onth(X1),X2),X3)=hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Oappend(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)),X3))), inference(split_conjunct,[status(thm)],[c_0_9830]), ['final']). 4.46/4.75 cnf(c_0_15363, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X4)),X5),hAPP(X3,X5))=c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4))), inference(split_conjunct,[status(thm)],[c_0_9831]), ['final']). 4.46/4.75 cnf(c_0_15364, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))),hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(c_List_Oset(X1),X2))))), inference(split_conjunct,[status(thm)],[c_0_9832]), ['final']). 4.46/4.75 cnf(c_0_15365, plain, (c_Fun_Ocomp(X1,X1,X2,hAPP(hAPP(c_Nat_Ocompow(X1,X1),X3),X4))=hAPP(hAPP(c_Nat_Ocompow(tc_fun(X2,X1),tc_fun(X2,X1)),X3),c_Fun_Ocomp(X1,X1,X2,X4))), inference(split_conjunct,[status(thm)],[c_0_9833]), ['final']). 4.46/4.75 cnf(c_0_15366, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X4,X5,X6),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X7),X8))=hAPP(hAPP(c_Product__Type_OPair(X2,X4),hAPP(X5,X7)),hAPP(X6,X8))), inference(split_conjunct,[status(thm)],[c_0_9834]), ['final']). 4.46/4.75 cnf(c_0_15367, hypothesis, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),v_F),hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,c_Option_Othe(tc_Com_Ocom)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom),c_Com_Obody),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9835, c_0_6899]), c_0_6899]), ['final']). 4.46/4.75 cnf(c_0_15368, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),c_Int_Onat),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X1)=X1), inference(rw,[status(thm)],[c_0_9836, c_0_6899]), ['final']). 4.46/4.75 cnf(c_0_15369, hypothesis, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Com_Ocom,c_Com_Ocom_OBODY),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),v_F)), inference(rw,[status(thm)],[c_0_9837, c_0_6899]), ['final']). 4.46/4.75 cnf(c_0_15370, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),c_Set_Ovimage(X2,X1,X4))=hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4)), inference(rw,[status(thm)],[c_0_9838, c_0_4891]), ['final']). 4.46/4.75 cnf(c_0_15371, plain, (c_HOL_OThe(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),hAPP(c_fequal,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=c_Set_Othe__elem(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9839]), ['final']). 4.46/4.75 cnf(c_0_15372, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),c_List_OtakeWhile(X2,X3,X1)),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X1))),X1))), inference(rw,[status(thm)],[c_0_9840, c_0_4916]), ['final']). 4.46/4.75 cnf(c_0_15373, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),hAPP(c_List_Onth(X1),X2)),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))=X2), inference(rw,[status(thm)],[c_0_9841, c_0_4517]), ['final']). 4.46/4.75 cnf(c_0_15374, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X6)),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_9842]), ['final']). 4.46/4.75 cnf(c_0_15375, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)),X4))=hAPP(hAPP(c_List_Otake(X1),X3),hAPP(hAPP(c_List_Odrop(X1),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9843]), ['final']). 4.46/4.75 cnf(c_0_15376, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X1),X3)),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9844, c_0_4986]), c_0_4986]), ['final']). 4.46/4.75 cnf(c_0_15377, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),X2)), inference(split_conjunct,[status(thm)],[c_0_9845]), ['final']). 4.46/4.75 cnf(c_0_15378, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X3)),X2)), inference(split_conjunct,[status(thm)],[c_0_9846]), ['final']). 4.46/4.75 cnf(c_0_15379, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9847]), ['final']). 4.46/4.75 cnf(c_0_15380, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9848]), ['final']). 4.46/4.75 cnf(c_0_15381, plain, (c_Nitpick_Opair__box_Opair__box__size(X1,X2,X3,X4,c_Nitpick_Opair__box_OPairBox(X1,X2,X5,X6))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X3,X5)),hAPP(c_Nat_OSuc,hAPP(X4,X6)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9849, c_0_4836]), c_0_5643]), c_0_5644]), ['final']). 4.46/4.75 cnf(c_0_15382, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Otake(X1),X3),X4))=hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)),hAPP(hAPP(c_List_Odrop(X1),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9850]), ['final']). 4.46/4.75 cnf(c_0_15383, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9851]), ['final']). 4.46/4.75 cnf(c_0_15384, plain, (hAPP(c_Set_Oimage(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3)),hAPP(c_Set_OPow(X1),X4))=hAPP(c_Set_OPow(X2),hAPP(c_Set_Oimage(X1,X2,X3),X4))), inference(er,[status(thm)],[c_0_9852]), ['final']). 4.46/4.75 cnf(c_0_15385, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_9853]), ['final']). 4.46/4.75 cnf(c_0_15386, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_9854]), ['final']). 4.46/4.75 cnf(c_0_15387, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_9855]), ['final']). 4.46/4.75 cnf(c_0_15388, plain, (c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X1),hAPP(hAPP(c_Option_Omap(X2,X1),X3),X4),c_Lazy__Sequence_Ohb__map(X2,X1,X3,X5))=c_Lazy__Sequence_Ohb__map(X2,X1,X3,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X2),X4,X5))), inference(split_conjunct,[status(thm)],[c_0_9856]), ['final']). 4.46/4.75 cnf(c_0_15389, plain, (hAPP(c_fequal,hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X2)), inference(rw,[status(thm)],[c_0_9857, c_0_5580]), ['final']). 4.46/4.75 cnf(c_0_15390, plain, (c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X1)),X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9858, c_0_5101]), c_0_5101]), ['final']). 4.46/4.75 cnf(c_0_15391, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X1,tc_Nat_Onat),X3),X2)))=c_List_Olist_Olist__size(X1,X3,X2)), inference(rw,[status(thm)],[c_0_9859, c_0_5100]), ['final']). 4.46/4.75 cnf(c_0_15392, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),hAPP(c_COMBK(X1,tc_Nat_Onat),X2)),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))=c_List_Oreplicate(X1,X3,X2)), inference(rw,[status(thm)],[c_0_9860, c_0_4517]), ['final']). 4.46/4.75 cnf(c_0_15393, plain, (hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),X3),X4))=c_Map_Omap__add(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X4),hAPP(c_Map_Omap__of(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9861]), ['final']). 4.46/4.75 cnf(c_0_15394, plain, (c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))), inference(rw,[status(thm)],[c_0_9862, c_0_5689]), ['final']). 4.46/4.75 cnf(c_0_15395, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9863, c_0_4836]), c_0_5644]), ['final']). 4.46/4.75 cnf(c_0_15396, plain, (c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1))), inference(rw,[status(thm)],[c_0_9864, c_0_5320]), ['final']). 4.46/4.75 cnf(c_0_15397, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel(X1,X2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2))))), inference(split_conjunct,[status(thm)],[c_0_9865]), ['final']). 4.46/4.75 cnf(c_0_15398, plain, (hAPP(c_Lazy__Sequence_Obind(X1,X2,hAPP(X3,X4)),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)),X5),X4))=hAPP(c_New__DSequence_Opos__bind(X1,X2,X3,X5),X4)), inference(split_conjunct,[status(thm)],[c_0_9866]), ['final']). 4.46/4.75 cnf(c_0_15399, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),X1,hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1)),X2)=hAPP(c_List_Orev(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_9867]), ['final']). 4.46/4.75 cnf(c_0_15400, plain, (c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X1)),X2)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9868, c_0_4986]), c_0_4986]), ['final']). 4.46/4.75 cnf(c_0_15401, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_9869]), ['final']). 4.46/4.75 cnf(c_0_15402, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X3)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9870]), ['final']). 4.46/4.75 cnf(c_0_15403, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X3)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9871]), ['final']). 4.46/4.75 cnf(c_0_15404, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist__update(X1,X3),X4),X5))=hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(c_Nat_OSuc,X4)),X5)), inference(split_conjunct,[status(thm)],[c_0_9872]), ['final']). 4.46/4.75 cnf(c_0_15405, plain, (hAPP(c_List_Ofoldl(X1,X2,X3,X4),hAPP(hAPP(c_List_Oappend(X2),X5),X6))=hAPP(c_List_Ofoldl(X1,X2,X3,hAPP(c_List_Ofoldl(X1,X2,X3,X4),X5)),X6)), inference(split_conjunct,[status(thm)],[c_0_9873]), ['final']). 4.46/4.75 cnf(c_0_15406, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X3)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9874, c_0_6462]), c_0_6462]), ['final']). 4.46/4.75 cnf(c_0_15407, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3)),X4))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(er,[status(thm)],[c_0_9875]), ['final']). 4.46/4.75 cnf(c_0_15408, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))))), inference(split_conjunct,[status(thm)],[c_0_9876]), ['final']). 4.46/4.75 cnf(c_0_15409, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OField(X1),X2)),hAPP(c_Relation_OField(X1),X3))=hAPP(c_Relation_OField(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9877]), ['final']). 4.46/4.75 cnf(c_0_15410, plain, (hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),X3),c_Option_Ooption_ONone(X2)),X4)=c_Option_Ooption_ONone(X2)), inference(split_conjunct,[status(thm)],[c_0_9878]), ['final']). 4.46/4.75 cnf(c_0_15411, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2))), inference(rw,[status(thm)],[c_0_9879, c_0_5884]), ['final']). 4.46/4.75 cnf(c_0_15412, plain, (hAPP(hAPP(c_Nat_Ocompow(X1,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4)=hAPP(hAPP(c_Nat_Ocompow(X1,X1),X3),hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9880]), ['final']). 4.46/4.75 cnf(c_0_15413, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Osplice(X1,X2,X3))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3))), inference(rw,[status(thm)],[c_0_9881, c_0_9707]), ['final']). 4.46/4.75 cnf(c_0_15414, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Ofilter(X1,X2),X3)),hAPP(c_List_Ofilter(X1,X2),X4))=hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9882]), ['final']). 4.46/4.75 cnf(c_0_15415, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))), inference(rw,[status(thm)],[c_0_9883, c_0_5689]), ['final']). 4.46/4.75 cnf(c_0_15416, plain, (hAPP(c_Option_Omap(X1,X2),X3)=c_Option_Ooption_Ooption__case(tc_Option_Ooption(X2),X1,c_Option_Ooption_ONone(X2),hAPP(hAPP(c_COMBB(X2,tc_Option_Ooption(X2),X1),c_Option_Ooption_OSome(X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_9884]), ['final']). 4.46/4.75 cnf(c_0_15417, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))), inference(rw,[status(thm)],[c_0_9885, c_0_5689]), ['final']). 4.46/4.75 cnf(c_0_15418, plain, (hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X1),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3)))=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9886, c_0_4517]), c_0_4517]), ['final']). 4.46/4.75 cnf(c_0_15419, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9887])])]), c_0_9888]), c_0_4836]), c_0_9889]), ['final']). 4.46/4.75 cnf(c_0_15420, plain, (hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3))=hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_9890]), ['final']). 4.46/4.75 cnf(c_0_15421, plain, (hAPP(c_Set_OPow(X1),hAPP(c_List_Oset(X1),X2))=hAPP(c_Set_Oimage(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),c_List_Oset(X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_Osublists(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_9891]), ['final']). 4.46/4.75 cnf(c_0_15422, plain, (c_Fun_Oinj__on(X1,tc_prod(X2,X1),esk157_4(X3,X4,X2,X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_9669]), ['final']). 4.46/4.75 cnf(c_0_15423, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X3)),X2)), inference(split_conjunct,[status(thm)],[c_0_9892]), ['final']). 4.46/4.75 cnf(c_0_15424, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_9893]), ['final']). 4.46/4.75 cnf(c_0_15425, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_9894]), ['final']). 4.46/4.75 cnf(c_0_15426, plain, (X1=hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Oappend(X2),X3),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X4))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_9895]), ['final']). 4.46/4.75 cnf(c_0_15427, plain, (c_Random_Oselect__weight(X1,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X1)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X1),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X2)),X3))=c_Random_Oselect__weight(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_9896]), ['final']). 4.46/4.75 cnf(c_0_15428, plain, (c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool))=hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(X1)),c_Option_Ooption_ONone(X1)),hAPP(c_Set_Oimage(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_9897]), ['final']). 4.46/4.75 cnf(c_0_15429, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X1,X2))=c_List_Olex(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9898]), ['final']). 4.46/4.75 cnf(c_0_15430, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)), inference(rw,[status(thm)],[c_0_9899, c_0_5902]), ['final']). 4.46/4.75 cnf(c_0_15431, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))), inference(split_conjunct,[status(thm)],[c_0_9900]), ['final']). 4.46/4.75 cnf(c_0_15432, plain, (c_Option_Ooption_ONone(X1)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X2,c_Option_Ooption_ONone(X1),hAPP(c_COMBK(tc_Option_Ooption(X1),X2),c_Option_Ooption_ONone(X1))),hAPP(X4,X5))), inference(rw,[status(thm)],[c_0_9901, c_0_7133]), ['final']). 4.46/4.75 cnf(c_0_15433, plain, (c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_9902]), ['final']). 4.46/4.75 cnf(c_0_15434, plain, (c_List_Olist_ONil(X1)=hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),c_List_Oreplicate(tc_List_Olist(X1),X2,c_List_Olist_ONil(X1)))), inference(rw,[status(thm)],[c_0_9903, c_0_4736]), ['final']). 4.46/4.75 cnf(c_0_15435, plain, (hAPP(c_Lazy__Sequence_Oyield(X1),c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3))=hAPP(c_Option_Ooption_OSome(tc_prod(X1,tc_Lazy__Sequence_Olazy__sequence(X1))),hAPP(hAPP(c_Product__Type_OPair(X1,tc_Lazy__Sequence_Olazy__sequence(X1)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9904]), ['final']). 4.46/4.75 cnf(c_0_15436, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))=X1), inference(rw,[status(thm)],[c_0_9905, c_0_4760]), ['final']). 4.46/4.75 cnf(c_0_15437, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9906, c_0_4609]), c_0_5120]), c_0_4836]), ['final']). 4.46/4.75 cnf(c_0_15438, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),X3)), inference(rw,[status(thm)],[c_0_9907, c_0_6074]), ['final']). 4.46/4.75 cnf(c_0_15439, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_COMBB(X3,tc_HOL_Obool,X1),hAPP(hAPP(c_Set_Oinsert(X3),hAPP(X4,X2)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X4)))), inference(rw,[status(thm)],[c_0_9908, c_0_4891]), ['final']). 4.46/4.75 cnf(c_0_15440, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X4),X3))),X4))), inference(rw,[status(thm)],[c_0_9909, c_0_4891]), ['final']). 4.46/4.75 cnf(c_0_15441, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X3)=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))), inference(rw,[status(thm)],[c_0_9910, c_0_4891]), ['final']). 4.46/4.75 cnf(c_0_15442, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1))=X2), inference(rw,[status(thm)],[c_0_9911, c_0_4891]), ['final']). 4.46/4.75 cnf(c_0_15443, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_COMBI(X1))=X2), inference(rw,[status(thm)],[c_0_9912, c_0_4891]), ['final']). 4.46/4.75 cnf(c_0_15444, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(rw,[status(thm)],[c_0_9913, c_0_4891]), ['final']). 4.46/4.75 cnf(c_0_15445, plain, (hAPP(hAPP(c_Nat_Ocompow(X1,X1),hAPP(c_Nat_OSuc,X2)),X3)=hAPP(c_Fun_Ocomp(X1,X1,X1,X3),hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9914]), ['final']). 4.46/4.75 cnf(c_0_15446, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9915]), ['final']). 4.46/4.75 cnf(c_0_15447, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_fequal,X2)),X3)=c_List_Oreplicate(X1,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,hAPP(c_fequal,X2)),X3)),X2)), inference(split_conjunct,[status(thm)],[c_0_9916]), ['final']). 4.46/4.75 cnf(c_0_15448, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Olist_OCons(X1),X3),hAPP(hAPP(c_List_Otake(X1),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9917]), ['final']). 4.46/4.75 cnf(c_0_15449, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),hAPP(c_Map_Omap__of(X2,X1),X3)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_9918]), ['final']). 4.46/4.75 cnf(c_0_15450, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))), inference(split_conjunct,[status(thm)],[c_0_9919]), ['final']). 4.46/4.75 cnf(c_0_15451, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X3),X2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_9920]), ['final']). 4.46/4.75 cnf(c_0_15452, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X3)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_9921]), ['final']). 4.46/4.75 cnf(c_0_15453, plain, (c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olistsp(X1,X2)),c_List_Olistsp(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_9922]), ['final']). 4.46/4.75 cnf(c_0_15454, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)),X3))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3))), inference(rw,[status(thm)],[c_0_9923, c_0_9924]), ['final']). 4.46/4.75 cnf(c_0_15455, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Oreplicate(X1,X2,X3)),c_List_Oreplicate(X1,X4,X3))=c_List_Oreplicate(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_9925]), ['final']). 4.46/4.75 cnf(c_0_15456, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),X3))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3))), inference(rw,[status(thm)],[c_0_9926, c_0_9927]), ['final']). 4.46/4.75 cnf(c_0_15457, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3)), inference(split_conjunct,[status(thm)],[c_0_9928]), ['final']). 4.46/4.75 cnf(c_0_15458, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X3)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3)), inference(split_conjunct,[status(thm)],[c_0_9929]), ['final']). 4.46/4.75 cnf(c_0_15459, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9930]), ['final']). 4.46/4.75 cnf(c_0_15460, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_9931]), ['final']). 4.46/4.75 cnf(c_0_15461, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_9932]), c_0_9933]), c_0_9933]), ['final']). 4.46/4.75 cnf(c_0_15462, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))))=hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9934, c_0_5120]), c_0_5120]), ['final']). 4.46/4.75 cnf(c_0_15463, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X2),X3)),X4))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(er,[status(thm)],[c_0_9935]), ['final']). 4.46/4.75 cnf(c_0_15464, plain, (hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_OPow(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_9936]), ['final']). 4.46/4.75 cnf(c_0_15465, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),c_Map_Odom(X1,X2,X4))=c_Map_Odom(X1,X2,c_Map_Omap__add(X1,X2,X4,X3))), inference(split_conjunct,[status(thm)],[c_0_9937]), ['final']). 4.46/4.75 cnf(c_0_15466, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X2),hAPP(c_COMBK(tc_fun(X2,X2),X1),c_COMBI(X2))),X3)=hAPP(c_Product__Type_Osnd(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_9938]), ['final']). 4.46/4.75 cnf(c_0_15467, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)))))), inference(er,[status(thm)],[c_0_9939]), ['final']). 4.46/4.75 cnf(c_0_15468, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X1)),hAPP(c_fequal,hAPP(c_Nat_OSuc,X1)))=hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))), inference(rw,[status(thm)],[c_0_9940, c_0_5580]), ['final']). 4.46/4.75 cnf(c_0_15469, plain, (c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),c_List_Otranspose(X1,X2))))), inference(split_conjunct,[status(thm)],[c_0_9941]), ['final']). 4.46/4.75 cnf(c_0_15470, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(er,[status(thm)],[c_0_9942]), ['final']). 4.46/4.75 cnf(c_0_15471, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3))),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_9943]), ['final']). 4.46/4.75 cnf(c_0_15472, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_Enum_Osublists(X1,X2))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))), inference(rw,[status(thm)],[c_0_9944, c_0_4836]), ['final']). 4.46/4.75 cnf(c_0_15473, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3))),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_9945]), ['final']). 4.46/4.75 cnf(c_0_15474, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[c_0_9946, c_0_9947]), ['final']). 4.46/4.75 cnf(c_0_15475, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)), inference(rw,[status(thm)],[c_0_9948, c_0_6410]), ['final']). 4.46/4.75 cnf(c_0_15476, plain, (c_Relation_Oirrefl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))), inference(rw,[status(thm)],[c_0_9949, c_0_5689]), ['final']). 4.46/4.75 cnf(c_0_15477, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))), inference(split_conjunct,[status(thm)],[c_0_9950]), ['final']). 4.46/4.75 cnf(c_0_15478, plain, (hAPP(c_Product__Type_Ofst(X1,X2),hAPP(c_Product__Type_Omap__pair(X3,X1,X4,X2,X5,X6),X7))=hAPP(X5,hAPP(c_Product__Type_Ofst(X3,X4),X7))), inference(split_conjunct,[status(thm)],[c_0_9951]), ['final']). 4.46/4.75 cnf(c_0_15479, plain, (hAPP(c_Product__Type_Osnd(X1,X2),hAPP(c_Product__Type_Omap__pair(X3,X1,X4,X2,X5,X6),X7))=hAPP(X6,hAPP(c_Product__Type_Osnd(X3,X4),X7))), inference(split_conjunct,[status(thm)],[c_0_9952]), ['final']). 4.46/4.75 cnf(c_0_15480, plain, (hAPP(c_Product__Type_Osnd(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Opartition(X1,X2,X3))=hAPP(c_List_Ofilter(X1,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X1,c_fNot),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_9953]), ['final']). 4.46/4.75 cnf(c_0_15481, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)=c_List_Obutlast(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9954]), ['final']). 4.46/4.75 cnf(c_0_15482, plain, (hAPP(c_Relation_ORange(X1,X1),X2)=hAPP(c_Relation_ORange(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))), inference(rw,[status(thm)],[c_0_9955, c_0_5266]), ['final']). 4.46/4.75 cnf(c_0_15483, plain, (hAPP(c_Relation_ODomain(X1,X1),X2)=hAPP(c_Relation_ODomain(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))), inference(rw,[status(thm)],[c_0_9956, c_0_5266]), ['final']). 4.46/4.75 cnf(c_0_15484, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X3))),hAPP(c_List_Oset(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_9957]), ['final']). 4.46/4.75 cnf(c_0_15485, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X2,X3))),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_9958]), ['final']). 4.46/4.75 cnf(c_0_15486, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Ortrancl(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_9959]), ['final']). 4.46/4.75 cnf(c_0_15487, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))), inference(split_conjunct,[status(thm)],[c_0_9960]), ['final']). 4.46/4.75 cnf(c_0_15488, plain, (hAPP(c_List_Oset(X1),X2)=hAPP(c_List_Oset(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X2))), inference(rw,[status(thm)],[c_0_9961, c_0_5902]), ['final']). 4.46/4.75 cnf(c_0_15489, plain, (c_Fun_Oinj__on(X1,tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_9962]), ['final']). 4.46/4.75 cnf(c_0_15490, plain, (c_List_Oremdups(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=c_List_Oremdups(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Oremdups(X2,X4)))), inference(split_conjunct,[status(thm)],[c_0_9963]), ['final']). 4.46/4.75 cnf(c_0_15491, plain, (c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))), inference(split_conjunct,[status(thm)],[c_0_9964]), ['final']). 4.46/4.75 cnf(c_0_15492, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X1),X2)),hAPP(c_Relation_ORange(X1,X1),X2))=hAPP(c_Relation_OField(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_9965]), ['final']). 4.46/4.75 cnf(c_0_15493, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Oimage(tc_Nat_Onat,X1,X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X3))))), inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_9966, c_0_4531])]), ['final']). 4.46/4.75 cnf(c_0_15494, plain, (hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,X4),X5),X6),X7)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X4),X6),hAPP(X5,X7))), inference(split_conjunct,[status(thm)],[c_0_9967]), ['final']). 4.46/4.75 cnf(c_0_15495, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9968, c_0_6071]), c_0_9969]), c_0_4836]), c_0_6071]), c_0_5884]), ['final']). 4.46/4.75 cnf(c_0_15496, plain, (hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)=hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X5)),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_9970]), ['final']). 4.46/4.75 cnf(c_0_15497, plain, (c_Predicate_Opred__comp(X1,X2,X3,c_Predicate_Oconversep(X2,X1,X4),c_Predicate_Oconversep(X3,X2,X5))=c_Predicate_Oconversep(X3,X1,c_Predicate_Opred__comp(X3,X2,X1,X5,X4))), inference(split_conjunct,[status(thm)],[c_0_9971]), ['final']). 4.46/4.75 cnf(c_0_15498, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))=c_List_Obutlast(X1,X2)), inference(er,[status(thm)],[c_0_9972]), ['final']). 4.46/4.75 cnf(c_0_15499, plain, (hAPP(X1,hAPP(hAPP(hAPP(c_Nat_Ocompow(X2,X2),X3),X1),X4))=hAPP(hAPP(hAPP(c_Nat_Ocompow(X2,X2),X3),X1),hAPP(X1,X4))), inference(split_conjunct,[status(thm)],[c_0_9973]), ['final']). 4.46/4.75 cnf(c_0_15500, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),X4)=hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9974]), ['final']). 4.46/4.75 cnf(c_0_15501, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4))=hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4)), inference(split_conjunct,[status(thm)],[c_0_9975]), ['final']). 4.46/4.75 cnf(c_0_15502, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X4)=hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Odrop(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9976]), ['final']). 4.46/4.75 cnf(c_0_15503, plain, (hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Otake(X1),X3),X4))=hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X2),X3)),X4)), inference(rw,[status(thm)],[c_0_9977, c_0_4986]), ['final']). 4.46/4.75 cnf(c_0_15504, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),X2)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,X2))=c_Code__Numeral_Odiv__mod__code__numeral(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9978]), ['final']). 4.46/4.75 cnf(c_0_15505, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9979]), ['final']). 4.46/4.75 cnf(c_0_15506, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9980]), ['final']). 4.46/4.75 cnf(c_0_15507, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),X3)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9981]), ['final']). 4.46/4.75 cnf(c_0_15508, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_9982]), ['final']). 4.46/4.75 cnf(c_0_15509, plain, (hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))=hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Orev(X1),X3)),hAPP(c_List_Orev(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9983]), ['final']). 4.46/4.75 cnf(c_0_15510, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9984]), ['final']). 4.46/4.75 cnf(c_0_15511, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))), inference(split_conjunct,[status(thm)],[c_0_9985]), ['final']). 4.46/4.75 cnf(c_0_15512, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))), inference(split_conjunct,[status(thm)],[c_0_9986]), ['final']). 4.46/4.75 cnf(c_0_15513, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2), inference(split_conjunct,[status(thm)],[c_0_9987]), ['final']). 4.46/4.75 cnf(c_0_15514, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))), inference(split_conjunct,[status(thm)],[c_0_9988]), ['final']). 4.46/4.75 cnf(c_0_15515, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9989, c_0_4836]), c_0_5644]), ['final']). 4.46/4.75 cnf(c_0_15516, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X1)),hAPP(c_fequal,X1))=hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9990, c_0_5580]), c_0_9991]), ['final']). 4.46/4.75 cnf(c_0_15517, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_9992]), ['final']). 4.46/4.75 cnf(c_0_15518, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))=X2), inference(split_conjunct,[status(thm)],[c_0_9993]), ['final']). 4.46/4.75 cnf(c_0_15519, plain, (hAPP(hAPP(X1,X2),X3)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X5,X6),X1),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9994]), ['final']). 4.46/4.75 cnf(c_0_15520, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1))))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9995, c_0_5334]), c_0_4836]), c_0_5644]), ['final']). 4.46/4.75 cnf(c_0_15521, plain, (c_Map_Orestrict__map(X1,X2,c_Map_Orestrict__map(X1,X2,X3,X4),X5)=c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9996]), ['final']). 4.46/4.75 cnf(c_0_15522, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)=hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)), inference(split_conjunct,[status(thm)],[c_0_9997]), ['final']). 4.46/4.75 cnf(c_0_15523, plain, (c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))=hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9998, c_0_5689]), c_0_5689]), ['final']). 4.46/4.75 cnf(c_0_15524, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(hAPP(c_List_Oappend(X1),X2),X3))=X3), inference(er,[status(thm)],[c_0_9999]), ['final']). 4.46/4.75 cnf(c_0_15525, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[c_0_10000, c_0_10001]), ['final']). 4.46/4.75 cnf(c_0_15526, plain, (c_List_OtakeWhile(X1,X2,X3)=hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)), inference(split_conjunct,[status(thm)],[c_0_10002]), ['final']). 4.46/4.75 cnf(c_0_15527, plain, (c_Hoare__Mirabelle_Otriple_Otriple__case(X1,X2,X3,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X4),X5),X6))=hAPP(hAPP(hAPP(X3,X4),X5),X6)), inference(split_conjunct,[status(thm)],[c_0_10003]), ['final']). 4.46/4.75 cnf(c_0_15528, plain, (hAPP(hAPP(hAPP(X1,X2),X3),X4)=c_Hoare__Mirabelle_Otriple_Otriple__rec(X5,X6,X1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_10004]), ['final']). 4.46/4.75 cnf(c_0_15529, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_Enum_On__lists(X1,X2,X3))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)), inference(split_conjunct,[status(thm)],[c_0_10005]), ['final']). 4.46/4.75 cnf(c_0_15530, plain, (c_Nitpick_Onorm__frac(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_10006]), c_0_10007]), ['final']). 4.46/4.75 cnf(c_0_15531, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1))))), inference(split_conjunct,[status(thm)],[c_0_10008]), ['final']). 4.46/4.75 cnf(c_0_15532, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X3)))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)), inference(rw,[status(thm)],[c_0_10009, c_0_5580]), ['final']). 4.46/4.75 cnf(c_0_15533, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X3)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)), inference(rw,[status(thm)],[c_0_10010, c_0_5580]), ['final']). 4.46/4.75 cnf(c_0_15534, plain, (hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X2)),X3))=hAPP(hAPP(c_List_Otake(X1),X2),hAPP(c_List_Otl(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_10011]), ['final']). 4.46/4.75 cnf(c_0_15535, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))=hAPP(hAPP(c_List_Otake(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_10012]), ['final']). 4.46/4.75 cnf(c_0_15536, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_10013]), ['final']). 4.46/4.75 cnf(c_0_15537, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(hAPP(c_List_Oappend(X1),X2),X3))=X2), inference(er,[status(thm)],[c_0_10014]), ['final']). 4.46/4.75 cnf(c_0_15538, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X1)))), inference(rw,[status(thm)],[c_0_10015, c_0_4531]), ['final']). 4.46/4.75 cnf(c_0_15539, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X1)))), inference(rw,[status(thm)],[c_0_10016, c_0_4531]), ['final']). 4.46/4.75 cnf(c_0_15540, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_10017]), ['final']). 4.46/4.75 cnf(c_0_15541, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))), inference(split_conjunct,[status(thm)],[c_0_10018]), ['final']). 4.46/4.75 cnf(c_0_15542, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),X2)))), inference(split_conjunct,[status(thm)],[c_0_10019]), ['final']). 4.46/4.75 cnf(c_0_15543, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10020, c_0_4436]), c_0_4834]), c_0_4436]), c_0_4834]), ['final']). 4.46/4.75 cnf(c_0_15544, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10021]), ['final']). 4.46/4.75 cnf(c_0_15545, plain, (hAPP(hAPP(c_List_Onth(X1),X2),X3)=hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X2)),hAPP(c_Nat_OSuc,X3))), inference(split_conjunct,[status(thm)],[c_0_10022]), ['final']). 4.46/4.75 cnf(c_0_15546, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1)), inference(er,[status(thm)],[c_0_10023]), ['final']). 4.46/4.75 cnf(c_0_15547, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(rw,[status(thm)],[c_0_10024, c_0_6965]), ['final']). 4.46/4.75 cnf(c_0_15548, plain, (hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))=hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))), inference(er,[status(thm)],[c_0_10025]), ['final']). 4.46/4.75 cnf(c_0_15549, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Odrop(X1),X2),X4)), inference(split_conjunct,[status(thm)],[c_0_10026]), ['final']). 4.46/4.75 cnf(c_0_15550, plain, (hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)), inference(rw,[status(thm)],[c_0_10027, c_0_6292]), ['final']). 4.46/4.75 cnf(c_0_15551, plain, (c_Product__Type_Oprod_Oprod__rec(X1,X2,X3,X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6))=hAPP(hAPP(X4,X5),X6)), inference(split_conjunct,[status(thm)],[c_0_10028]), ['final']). 4.46/4.75 cnf(c_0_15552, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Otake(X2),X3),X1)),hAPP(hAPP(c_List_Odrop(X2),X3),X1))), inference(split_conjunct,[status(thm)],[c_0_10029]), ['final']). 4.46/4.75 cnf(c_0_15553, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(c_Product__Type_Ofst(X1,X2),X3)),hAPP(c_Product__Type_Osnd(X1,X2),X3))=X3), inference(split_conjunct,[status(thm)],[c_0_10030]), ['final']). 4.46/4.75 cnf(c_0_15554, plain, (c_Map_Omap__upds(X1,X2,c_Map_Omap__add(X1,X2,X3,X4),X5,X6)=c_Map_Omap__add(X1,X2,X3,c_Map_Omap__upds(X1,X2,X4,X5,X6))), inference(split_conjunct,[status(thm)],[c_0_10031]), ['final']). 4.46/4.75 cnf(c_0_15555, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4))=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(er,[status(thm)],[c_0_10032]), ['final']). 4.46/4.75 cnf(c_0_15556, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4)=c_Nat_Onat_Onat__case(X1,X2,hAPP(c_List_Onth(X1),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_10033]), ['final']). 4.46/4.75 cnf(c_0_15557, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10034, c_0_5134]), c_0_7525]), ['final']). 4.46/4.75 cnf(c_0_15558, plain, (hAPP(c_Map_Orestrict__map(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),X3),X4)=c_Option_Ooption_ONone(X2)), inference(split_conjunct,[status(thm)],[c_0_10035]), ['final']). 4.46/4.75 cnf(c_0_15559, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_10036]), ['final']). 4.46/4.75 cnf(c_0_15560, plain, (hAPP(hAPP(c_List_Otake(X1),X2),c_List_Oreplicate(X1,X3,X4))=c_List_Oreplicate(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X2),X3),X4)), inference(rw,[status(thm)],[c_0_10037, c_0_4986]), ['final']). 4.46/4.75 cnf(c_0_15561, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),c_List_Oreplicate(X1,X3,X4))=c_List_Oreplicate(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2),X4)), inference(split_conjunct,[status(thm)],[c_0_10038]), ['final']). 4.46/4.75 cnf(c_0_15562, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_10039]), ['final']). 4.46/4.75 cnf(c_0_15563, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Otl(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_10040]), ['final']). 4.46/4.75 cnf(c_0_15564, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)), inference(rw,[status(thm)],[c_0_10041, c_0_4517]), ['final']). 4.46/4.75 cnf(c_0_15565, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X2)))))), inference(er,[status(thm)],[c_0_10042]), ['final']). 4.46/4.75 cnf(c_0_15566, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10043]), ['final']). 4.46/4.75 cnf(c_0_15567, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))), inference(split_conjunct,[status(thm)],[c_0_10044]), ['final']). 4.46/4.75 cnf(c_0_15568, plain, (hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X1,X3),hAPP(c_Product__Type_OPair(X2,X1),X4)),X5)=hAPP(X5,X4)), inference(split_conjunct,[status(thm)],[c_0_10045]), ['final']). 4.46/4.75 cnf(c_0_15569, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),X3)=X3), inference(rw,[status(thm)],[c_0_10046, c_0_5689]), ['final']). 4.46/4.75 cnf(c_0_15570, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),X4)=c_Map_Odom(X1,X2,c_Map_Orestrict__map(X1,X2,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_10047]), ['final']). 4.46/4.75 cnf(c_0_15571, plain, (c_List_Olistset(X1,c_List_Olist_ONil(tc_fun(X1,tc_HOL_Obool)))=hAPP(c_fequal,c_List_Olist_ONil(X1))), inference(rw,[status(thm)],[c_0_10048, c_0_5580]), ['final']). 4.46/4.75 cnf(c_0_15572, plain, (hAPP(c_List_Olist_Olist__case(X1,X2,X3,X4),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X6))=hAPP(hAPP(X4,X5),X6)), inference(split_conjunct,[status(thm)],[c_0_10049]), ['final']). 4.46/4.75 cnf(c_0_15573, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X2),X3),c_Transitive__Closure_Ortrancl(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_HOL_Obool))))=X3), inference(rw,[status(thm)],[c_0_10050, c_0_5689]), ['final']). 4.46/4.75 cnf(c_0_15574, plain, (hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[c_0_10051, c_0_5884]), ['final']). 4.46/4.75 cnf(c_0_15575, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X3)), inference(split_conjunct,[status(thm)],[c_0_10052]), ['final']). 4.46/4.75 cnf(c_0_15576, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_10053]), ['final']). 4.46/4.75 cnf(c_0_15577, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_10054]), ['final']). 4.46/4.75 cnf(c_0_15578, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_10055]), ['final']). 4.46/4.75 cnf(c_0_15579, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X4)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10056]), ['final']). 4.46/4.75 cnf(c_0_15580, plain, (hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)), inference(rw,[status(thm)],[c_0_10057, c_0_6292]), ['final']). 4.46/4.75 cnf(c_0_15581, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))=hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10058]), ['final']). 4.46/4.75 cnf(c_0_15582, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBB(X2,tc_Option_Ooption(X2),X1),c_Option_Ooption_OSome(X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_10059]), ['final']). 4.46/4.75 cnf(c_0_15583, plain, (c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))=c_Transitive__Closure_Ortrancl(X1,X2)), inference(rw,[status(thm)],[c_0_10060, c_0_5266]), ['final']). 4.46/4.75 cnf(c_0_15584, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X2))=c_Transitive__Closure_Ortrancl(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_10061]), ['final']). 4.46/4.75 cnf(c_0_15585, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))=c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))), inference(split_conjunct,[status(thm)],[c_0_10062]), ['final']). 4.46/4.75 cnf(c_0_15586, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X3))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(er,[status(thm)],[c_0_10063]), ['final']). 4.46/4.75 cnf(c_0_15587, plain, (c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_10064, c_0_4531]), ['final']). 4.46/4.75 cnf(c_0_15588, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X3)),X4)=X4), inference(er,[status(thm)],[c_0_10065]), ['final']). 4.46/4.75 cnf(c_0_15589, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)), inference(split_conjunct,[status(thm)],[c_0_10066]), ['final']). 4.46/4.75 cnf(c_0_15590, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Obutlast(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10067]), ['final']). 4.46/4.75 cnf(c_0_15591, plain, (c_Smallcheck_Osmall_H(X1,hAPP(c_Code__Numeral_Oint__of,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X2)))=hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10068]), ['final']). 4.46/4.75 cnf(c_0_15592, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4))=X2), inference(er,[status(thm)],[c_0_10069]), ['final']). 4.46/4.75 cnf(c_0_15593, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4))=X2), inference(er,[status(thm)],[c_0_10070]), ['final']). 4.46/4.75 cnf(c_0_15594, plain, (c_List_Olistrel1(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))=hAPP(c_Relation_Oconverse(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel1(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10071]), ['final']). 4.46/4.75 cnf(c_0_15595, plain, (c_Map_Omap__add(X1,X2,c_Map_Omap__add(X1,X2,X3,X4),X5)=c_Map_Omap__add(X1,X2,X3,c_Map_Omap__add(X1,X2,X4,X5))), inference(split_conjunct,[status(thm)],[c_0_10072]), ['final']). 4.46/4.75 cnf(c_0_15596, plain, (hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,tc_prod(X2,X3)),X4),c_Product__Type_OPair(X2,X3))=X4), inference(split_conjunct,[status(thm)],[c_0_10073]), ['final']). 4.46/4.75 cnf(c_0_15597, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))), inference(split_conjunct,[status(thm)],[c_0_10074]), ['final']). 4.46/4.75 cnf(c_0_15598, plain, (c_List_Oreplicate(X1,X2,hAPP(X3,X4))=hAPP(hAPP(c_List_Omap(X5,X1),X3),c_List_Oreplicate(X5,X2,X4))), inference(split_conjunct,[status(thm)],[c_0_10075]), ['final']). 4.46/4.75 cnf(c_0_15599, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))))), inference(er,[status(thm)],[c_0_10076]), ['final']). 4.46/4.75 cnf(c_0_15600, plain, (c_Sum__Type_OPlus(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X1,X2),tc_HOL_Obool))), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_10077])]), ['final']). 4.46/4.75 cnf(c_0_15601, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),X2)), inference(rw,[status(thm)],[c_0_10078, c_0_5334]), ['final']). 4.46/4.75 cnf(c_0_15602, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_10079, c_0_6292]), ['final']). 4.46/4.75 cnf(c_0_15603, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X1),X2)), inference(rw,[status(thm)],[c_0_10080, c_0_5334]), ['final']). 4.46/4.75 cnf(c_0_15604, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X1),X2)), inference(rw,[status(thm)],[c_0_10081, c_0_5334]), ['final']). 4.46/4.75 cnf(c_0_15605, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),X2)), inference(rw,[status(thm)],[c_0_10082, c_0_5334]), ['final']). 4.46/4.75 cnf(c_0_15606, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_10083]), ['final']). 4.46/4.75 cnf(c_0_15607, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OSKIP),X3)))), inference(rw,[status(thm)],[c_0_10084, c_0_5580]), ['final']). 4.46/4.75 cnf(c_0_15608, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)=c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_Oimage(X1,tc_fun(X2,tc_HOL_Obool),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_10085]), ['final']). 4.46/4.75 cnf(c_0_15609, plain, (c_Option_Ooption_Ooption__size(X1,X2,hAPP(c_Option_Ooption_OSome(X1),X3))=hAPP(c_Nat_OSuc,hAPP(X2,X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10086, c_0_4836]), c_0_5644]), ['final']). 4.46/4.75 cnf(c_0_15610, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_10087]), ['final']). 4.46/4.75 cnf(c_0_15611, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_10088]), ['final']). 4.46/4.75 cnf(c_0_15612, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))), inference(er,[status(thm)],[c_0_10089]), ['final']). 4.46/4.75 cnf(c_0_15613, plain, (hAPP(c_Product__Type_Ofst(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Opartition(X1,X2,X3))=hAPP(c_List_Ofilter(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_10090]), ['final']). 4.46/4.75 cnf(c_0_15614, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_10091]), ['final']). 4.46/4.75 cnf(c_0_15615, plain, (c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10092]), ['final']). 4.46/4.75 cnf(c_0_15616, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_10093]), ['final']). 4.46/4.75 cnf(c_0_15617, plain, (c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool))=c_Sum__Type_OPlus(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10094]), ['final']). 4.46/4.75 cnf(c_0_15618, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X1,X2,X3))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10095, c_0_4836]), c_0_5644]), ['final']). 4.46/4.75 cnf(c_0_15619, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))))), inference(split_conjunct,[status(thm)],[c_0_10096]), ['final']). 4.46/4.75 cnf(c_0_15620, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10097, c_0_5101]), c_0_5101]), ['final']). 4.46/4.75 cnf(c_0_15621, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10098, c_0_4986]), c_0_4986]), ['final']). 4.46/4.75 cnf(c_0_15622, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10099, c_0_5334]), c_0_5334]), c_0_5334]), ['final']). 4.46/4.75 cnf(c_0_15623, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10100, c_0_5334]), c_0_5334]), c_0_5334]), ['final']). 4.46/4.75 cnf(c_0_15624, plain, (c_List_Olists(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=hAPP(c_fequal,c_List_Olist_ONil(X1))), inference(rw,[status(thm)],[c_0_10101, c_0_5580]), ['final']). 4.46/4.75 cnf(c_0_15625, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10102]), ['final']). 4.46/4.75 cnf(c_0_15626, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X2)), inference(split_conjunct,[status(thm)],[c_0_10103]), ['final']). 4.46/4.75 cnf(c_0_15627, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1))))=hAPP(c_Nat_OSuc,c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10104, c_0_5334]), c_0_4836]), c_0_5644]), ['final']). 4.46/4.75 cnf(c_0_15628, plain, (c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,X1,X2)=c_Smallcheck_Ofull__small_H(X1,hAPP(c_Code__Numeral_Oint__of,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X2)))), inference(split_conjunct,[status(thm)],[c_0_10105]), ['final']). 4.46/4.75 cnf(c_0_15629, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_10106]), ['final']). 4.46/4.75 cnf(c_0_15630, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X1),c_COMBK(X1,X2)),X3)=hAPP(c_Product__Type_Ofst(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_10107]), ['final']). 4.46/4.75 cnf(c_0_15631, plain, (c_HOL_OThe(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2), inference(rw,[status(thm)],[c_0_10108, c_0_5670]), ['final']). 4.46/4.75 cnf(c_0_15632, plain, (c_Hilbert__Choice_OEps(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2), inference(rw,[status(thm)],[c_0_10109, c_0_5670]), ['final']). 4.46/4.75 cnf(c_0_15633, plain, (c_Nitpick_Opair__box_Opair__box__case(X1,X2,X3,X4,c_Nitpick_Opair__box_OPairBox(X1,X2,X5,X6))=hAPP(hAPP(X4,X5),X6)), inference(split_conjunct,[status(thm)],[c_0_10110]), ['final']). 4.46/4.75 cnf(c_0_15634, plain, (c_Nitpick_Opair__box_Opair__box__rec(X1,X2,X3,X4,c_Nitpick_Opair__box_OPairBox(X1,X2,X5,X6))=hAPP(hAPP(X4,X5),X6)), inference(split_conjunct,[status(thm)],[c_0_10111]), ['final']). 4.46/4.75 cnf(c_0_15635, plain, (hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3))), inference(er,[status(thm)],[c_0_10112]), ['final']). 4.46/4.75 cnf(c_0_15636, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))))), inference(rw,[status(thm)],[c_0_10113, c_0_6292]), ['final']). 4.46/4.75 cnf(c_0_15637, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))), inference(split_conjunct,[status(thm)],[c_0_10114]), ['final']). 4.46/4.75 cnf(c_0_15638, plain, (hAPP(c_List_Oset(X1),c_List_Oreplicate(X1,hAPP(c_Nat_OSuc,X2),X3))=hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10115]), ['final']). 4.46/4.75 cnf(c_0_15639, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(er,[status(thm)],[c_0_10116]), ['final']). 4.46/4.75 cnf(c_0_15640, plain, (hAPP(hAPP(c_Option_Omap(X1,X2),X3),hAPP(c_Option_Ooption_OSome(X1),X4))=hAPP(c_Option_Ooption_OSome(X2),hAPP(X3,X4))), inference(split_conjunct,[status(thm)],[c_0_10117]), ['final']). 4.46/4.75 cnf(c_0_15641, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(c_Nat_OSuc,X1)))), inference(split_conjunct,[status(thm)],[c_0_10118]), ['final']). 4.46/4.75 cnf(c_0_15642, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))))), inference(split_conjunct,[status(thm)],[c_0_10119]), ['final']). 4.46/4.75 cnf(c_0_15643, plain, (c_Hoare__Mirabelle_Otriple__valid(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Com_Ocom_OBODY,X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_10120]), ['final']). 4.46/4.75 cnf(c_0_15644, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))), inference(split_conjunct,[status(thm)],[c_0_10121]), ['final']). 4.46/4.75 cnf(c_0_15645, plain, (X1=hAPP(c_Relation_OImage(X2,X2,c_Transitive__Closure_Ortrancl(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),X1)), inference(rw,[status(thm)],[c_0_10122, c_0_5689]), ['final']). 4.46/4.75 cnf(c_0_15646, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))))), inference(er,[status(thm)],[c_0_10123]), ['final']). 4.46/4.75 cnf(c_0_15647, plain, (hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel)=c_Int_OInteg), inference(split_conjunct,[status(thm)],[fact_Integ__def]), ['final']). 4.46/4.75 cnf(c_0_15648, plain, (c_List_Oreplicate(X1,hAPP(c_Nat_OSuc,X2),X3)=hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Oreplicate(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_10124]), ['final']). 4.46/4.75 cnf(c_0_15649, plain, (hAPP(c_New__DSequence_Oneg__union(X1,X2,X3),X4)=c_Lazy__Sequence_Oappend(tc_Option_Ooption(X1),hAPP(X2,X4),hAPP(X3,X4))), inference(split_conjunct,[status(thm)],[c_0_10125]), ['final']). 4.46/4.75 cnf(c_0_15650, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Odrop(X1),X2),X3))=hAPP(hAPP(c_List_Odrop(X1),X2),c_List_Obutlast(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_10126]), ['final']). 4.46/4.75 cnf(c_0_15651, plain, (c_HOL_OThe(X1,c_Finite__Set_Ofold__graph(X2,X1,X3,X4,X5))=hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,X3),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_10127]), ['final']). 4.46/4.75 cnf(c_0_15652, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10128, c_0_6965]), c_0_6965]), ['final']). 4.46/4.75 cnf(c_0_15653, plain, (hAPP(c_Relation_OImage(X1,X1,c_Relation_OId__on(X1,X2)),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_10129]), ['final']). 4.46/4.75 cnf(c_0_15654, plain, (X1=c_Predicate_Opred__comp(X2,X2,X2,c_fequal,c_Predicate_Opred__comp(X2,X2,X2,X1,c_fequal))), inference(split_conjunct,[status(thm)],[c_0_10130]), ['final']). 4.46/4.75 cnf(c_0_15655, plain, (c_List_Olistset(X1,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X1,tc_HOL_Obool)),X2),X3))=c_List_Oset__Cons(X1,X2,c_List_Olistset(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_10131]), ['final']). 4.46/4.75 cnf(c_0_15656, plain, (hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1))), inference(rw,[status(thm)],[c_0_10132, c_0_5120]), ['final']). 4.46/4.75 cnf(c_0_15657, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X1,X2))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10133, c_0_4836]), c_0_5644]), ['final']). 4.46/4.75 cnf(c_0_15658, plain, (hAPP(hAPP(X1,X2),X3)=hAPP(hAPP(hAPP(c_COMBC(X4,X5,X6),X1),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_10134]), ['final']). 4.46/4.75 cnf(c_0_15659, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X2,X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X4))))=hAPP(X3,X4)), inference(rw,[status(thm)],[c_0_10135, c_0_5334]), ['final']). 4.46/4.75 cnf(c_0_15660, plain, (c_Map_Omap__add(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),X3)=X3), inference(split_conjunct,[status(thm)],[c_0_10136]), ['final']). 4.46/4.75 cnf(c_0_15661, plain, (c_List_Olast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))))=X3), inference(er,[status(thm)],[c_0_10137]), ['final']). 4.46/4.75 cnf(c_0_15662, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))=X1), inference(rw,[status(thm)],[c_0_10138, c_0_5334]), ['final']). 4.46/4.75 cnf(c_0_15663, plain, (X1=c_Map_Omap__add(X2,X3,X1,hAPP(c_COMBK(tc_Option_Ooption(X3),X2),c_Option_Ooption_ONone(X3)))), inference(split_conjunct,[status(thm)],[c_0_10139]), ['final']). 4.46/4.75 cnf(c_0_15664, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X1),hAPP(c_Code__Numeral_Onat__of,X2)))=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,X2)), inference(rw,[status(thm)],[c_0_10140, c_0_5334]), ['final']). 4.46/4.75 cnf(c_0_15665, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))))=X2), inference(er,[status(thm)],[c_0_10141]), ['final']). 4.46/4.75 cnf(c_0_15666, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3))=hAPP(c_List_Oset(X1),c_List_Oinsert(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_10142]), ['final']). 4.46/4.75 cnf(c_0_15667, plain, (c_Map_Oran(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10143]), ['final']). 4.46/4.75 cnf(c_0_15668, plain, (c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2))=c_List_Otranspose(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_10144]), ['final']). 4.46/4.75 cnf(c_0_15669, plain, (hAPP(c_Relation_ORange(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3))=hAPP(c_Relation_ODomain(X2,X1),X3)), inference(split_conjunct,[status(thm)],[c_0_10145]), ['final']). 4.46/4.75 cnf(c_0_15670, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10146, c_0_4609]), c_0_4609])])]), c_0_10147]), ['final']). 4.46/4.75 cnf(c_0_15671, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat))=c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[fact_UN__atMost__UNIV]), ['final']). 4.46/4.75 cnf(c_0_15672, plain, (c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[fact_UN__lessThan__UNIV]), ['final']). 4.46/4.75 cnf(c_0_15673, plain, (c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[fact_UN__atLeast__UNIV]), ['final']). 4.46/4.75 cnf(c_0_15674, plain, (c_Divides_Opdivmod(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))), inference(er,[status(thm)],[c_0_10148]), ['final']). 4.46/4.75 cnf(c_0_15675, plain, (hAPP(c_Relation_ORange(X1,X2),X3)=hAPP(c_Relation_ODomain(X2,X1),hAPP(c_Relation_Oconverse(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_10149]), ['final']). 4.46/4.75 cnf(c_0_15676, plain, (c_Product__Type_Omap__pair(X1,X1,X2,X2,c_COMBI(X1),c_COMBI(X2))=c_Fun_Oid(tc_prod(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10150]), ['final']). 4.46/4.75 cnf(c_0_15677, plain, (c_Fun_Oid(tc_prod(X1,X2))=c_Product__Type_Omap__pair(X1,X1,X2,X2,c_Fun_Oid(X1),c_Fun_Oid(X2))), inference(split_conjunct,[status(thm)],[c_0_10151]), ['final']). 4.46/4.75 cnf(c_0_15678, plain, (hAPP(hAPP(X1,X2),X3)=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X4,X5,X6,X1,c_Lazy__Sequence_Olazy__sequence_OInsert(X5,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_10152]), ['final']). 4.46/4.75 cnf(c_0_15679, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBI(tc_fun(X1,tc_HOL_Obool)))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)), inference(split_conjunct,[status(thm)],[c_0_10153]), ['final']). 4.46/4.75 cnf(c_0_15680, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBI(tc_fun(X1,tc_HOL_Obool)))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)), inference(split_conjunct,[status(thm)],[c_0_10154]), ['final']). 4.46/4.75 cnf(c_0_15681, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10155, c_0_10156]), c_0_5334]), c_0_5334]), c_0_5334]), ['final']). 4.46/4.75 cnf(c_0_15682, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X1,X2)),c_Nitpick_Opair__box_OPairBox(X1,X2,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_10157]), ['final']). 4.46/4.75 cnf(c_0_15683, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_10158]), ['final']). 4.46/4.75 cnf(c_0_15684, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_10159]), ['final']). 4.46/4.75 cnf(c_0_15685, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Hoare__Mirabelle_Otriple_Otriple__size(X1,X2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_10160]), ['final']). 4.46/4.75 cnf(c_0_15686, plain, (hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1))=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_10161]), ['final']). 4.46/4.75 cnf(c_0_15687, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)), inference(rw,[status(thm)],[c_0_10162, c_0_10163]), ['final']). 4.46/4.75 cnf(c_0_15688, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X3))), inference(split_conjunct,[status(thm)],[c_0_10164]), ['final']). 4.46/4.75 cnf(c_0_15689, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_10165]), ['final']). 4.46/4.75 cnf(c_0_15690, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_10166]), ['final']). 4.46/4.75 cnf(c_0_15691, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),X3),X4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_10167]), ['final']). 4.46/4.75 cnf(c_0_15692, plain, (hAPP(c_List_Ofilter(X1,X2),c_List_Oremdups(X1,X3))=c_List_Oremdups(X1,hAPP(c_List_Ofilter(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_10168]), ['final']). 4.46/4.75 cnf(c_0_15693, plain, (hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Ortrancl(X1,X2))=c_Transitive__Closure_Ortrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_10169]), ['final']). 4.46/4.75 cnf(c_0_15694, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_10170, c_0_4912]), ['final']). 4.46/4.75 cnf(c_0_15695, plain, (c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X1))=hAPP(c_Nat_OSuc,c_Nat_Onat_Onat__size(X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10171, c_0_4836]), c_0_5644]), ['final']). 4.46/4.75 cnf(c_0_15696, plain, (hAPP(c_Random_Oiterate(X1,X2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),X3),X4)=hAPP(c_Product__Type_OPair(X1,X2),X4)), inference(er,[status(thm)],[c_0_10172]), ['final']). 4.46/4.75 cnf(c_0_15697, plain, (hAPP(c_Option_Ooption_Ooption__case(X1,X2,X3,X4),hAPP(c_Option_Ooption_OSome(X2),X5))=hAPP(X4,X5)), inference(split_conjunct,[status(thm)],[c_0_10173]), ['final']). 4.46/4.75 cnf(c_0_15698, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_10174, c_0_4836])]), ['final']). 4.46/4.75 cnf(c_0_15699, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2), inference(split_conjunct,[status(thm)],[c_0_10175]), ['final']). 4.46/4.75 cnf(c_0_15700, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10176]), ['final']). 4.46/4.75 cnf(c_0_15701, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X1,X2,X3))=hAPP(c_Nat_OSuc,c_Com_Ocom_Ocom__size(X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10177, c_0_4836]), c_0_5644]), ['final']). 4.46/4.75 cnf(c_0_15702, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=c_Map_Odom(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)))), inference(split_conjunct,[status(thm)],[c_0_10178]), ['final']). 4.46/4.75 cnf(c_0_15703, plain, (hAPP(hAPP(c_List_Olist__update(X1,X2),X3),hAPP(hAPP(c_List_Onth(X1),X2),X3))=X2), inference(split_conjunct,[status(thm)],[c_0_10179]), ['final']). 4.46/4.75 cnf(c_0_15704, plain, (X1=hAPP(hAPP(c_List_Odrop(X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1))), inference(split_conjunct,[status(thm)],[c_0_10180]), ['final']). 4.46/4.75 cnf(c_0_15705, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X1)),c_Int_OInteg))), inference(split_conjunct,[status(thm)],[c_0_10181]), ['final']). 4.46/4.75 cnf(c_0_15706, plain, (c_Wellfounded_OwfP(X1,hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))), inference(rw,[status(thm)],[c_0_10182, c_0_10183]), ['final']). 4.46/4.75 cnf(c_0_15707, plain, (hAPP(X1,hAPP(X2,X3))=hAPP(hAPP(hAPP(c_COMBB(X4,X5,X6),X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_10184]), ['final']). 4.46/4.75 cnf(c_0_15708, plain, (hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))))), inference(rw,[status(thm)],[c_0_10185, c_0_4517]), ['final']). 4.46/4.75 cnf(c_0_15709, plain, (c_Lazy__Sequence_Oappend(X1,c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3),X4)=c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,c_Lazy__Sequence_Oappend(X1,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_10186]), ['final']). 4.46/4.75 cnf(c_0_15710, plain, (c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X2)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)), inference(split_conjunct,[status(thm)],[c_0_10187]), ['final']). 4.46/4.75 cnf(c_0_15711, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_10188]), ['final']). 4.46/4.75 cnf(c_0_15712, plain, (c_Option_Ooption_ONone(X1)=hAPP(hAPP(c_Map_Omap__of(X2,X1),c_List_Olist_ONil(tc_prod(X2,X1))),X3)), inference(split_conjunct,[status(thm)],[c_0_10189]), ['final']). 4.46/4.75 cnf(c_0_15713, plain, (c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel)), inference(split_conjunct,[status(thm)],[fact_equiv__intrel]), ['final']). 4.46/4.75 cnf(c_0_15714, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_10190]), ['final']). 4.46/4.75 cnf(c_0_15715, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X1))), inference(split_conjunct,[status(thm)],[c_0_10191]), ['final']). 4.46/4.75 cnf(c_0_15716, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))=c_List_Olist_ONil(X1)), inference(er,[status(thm)],[c_0_10192]), ['final']). 4.46/4.75 cnf(c_0_15717, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X4))), inference(split_conjunct,[status(thm)],[c_0_10193]), ['final']). 4.46/4.75 cnf(c_0_15718, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk501_1(X1)),c_Int_OInteg))), inference(split_conjunct,[status(thm)],[c_0_10194]), ['final']). 4.46/4.75 cnf(c_0_15719, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),X1))), inference(split_conjunct,[status(thm)],[c_0_10195]), ['final']). 4.46/4.75 cnf(c_0_15720, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X1))), inference(split_conjunct,[status(thm)],[c_0_10196]), ['final']). 4.46/4.75 cnf(c_0_15721, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1)))))), inference(split_conjunct,[status(thm)],[c_0_10197]), ['final']). 4.46/4.75 cnf(c_0_15722, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[fact_INT__greaterThan__UNIV]), ['final']). 4.46/4.75 cnf(c_0_15723, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1)))), inference(split_conjunct,[status(thm)],[c_0_10198]), ['final']). 4.46/4.75 cnf(c_0_15724, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_10199]), ['final']). 4.46/4.75 cnf(c_0_15725, plain, (c_Divides_Odivmod__int(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(er,[status(thm)],[c_0_10200]), ['final']). 4.46/4.75 cnf(c_0_15726, plain, (c_Option_Ooption_Ooption__rec(X1,X2,X3,X4,hAPP(c_Option_Ooption_OSome(X2),X5))=hAPP(X4,X5)), inference(split_conjunct,[status(thm)],[c_0_10201]), ['final']). 4.46/4.75 cnf(c_0_15727, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_10202]), ['final']). 4.46/4.75 cnf(c_0_15728, plain, (hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X1),X2),X3),X4),X5)=c_New__DSequence_Oneg__single(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_10203]), ['final']). 4.46/4.75 cnf(c_0_15729, plain, (c_New__DSequence_Opos__single(X1,X2)=hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X1),X2),X3),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_10204]), ['final']). 4.46/4.75 cnf(c_0_15730, plain, (c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=X3), inference(er,[status(thm)],[c_0_10205]), ['final']). 4.46/4.75 cnf(c_0_15731, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orotate1(X1),X2))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_10206]), ['final']). 4.46/4.75 cnf(c_0_15732, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orev(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_10207]), ['final']). 4.46/4.75 cnf(c_0_15733, plain, (X1=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X2,X3,X4),X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10208]), ['final']). 4.46/4.75 cnf(c_0_15734, plain, (c_Relation_Osingle__valued(X1,X1,c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))), inference(rw,[status(thm)],[c_0_10209, c_0_5689]), ['final']). 4.46/4.75 cnf(c_0_15735, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10210, c_0_6071]), c_0_6071]), c_0_5884]), ['final']). 4.46/4.75 cnf(c_0_15736, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_10211]), ['final']). 4.46/4.75 cnf(c_0_15737, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(er,[status(thm)],[c_0_10212]), ['final']). 4.46/4.75 cnf(c_0_15738, plain, (c_List_Osublist(X1,X2,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))=hAPP(hAPP(c_List_Otake(X1),X3),X2)), inference(rw,[status(thm)],[c_0_10213, c_0_6071]), ['final']). 4.46/4.75 cnf(c_0_15739, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))), inference(split_conjunct,[status(thm)],[c_0_10214]), ['final']). 4.46/4.75 cnf(c_0_15740, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(er,[status(thm)],[c_0_10215]), ['final']). 4.46/4.75 cnf(c_0_15741, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X1,X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10216]), ['final']). 4.46/4.75 cnf(c_0_15742, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),c_Int_OMin)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)), inference(rw,[status(thm)],[c_0_10217, c_0_4609]), ['final']). 4.46/4.75 cnf(c_0_15743, plain, (c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))=c_Divides_OnegateSnd), inference(rw,[status(thm)],[c_0_10218, c_0_4825]), ['final']). 4.46/4.75 cnf(c_0_15744, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10219, c_0_4836]), c_0_4836])]), ['final']). 4.46/4.75 cnf(c_0_15745, plain, (c_Wellfounded_Oless__than=hAPP(hAPP(c_Relation_Orel__comp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Wellfounded_Opred__nat),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))), inference(rw,[status(thm)],[c_0_10220, c_0_5266]), ['final']). 4.46/4.75 cnf(c_0_15746, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),c_List_Olist_ONil(X1)),X3)=c_List_Olist_ONil(tc_prod(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10221]), ['final']). 4.46/4.75 cnf(c_0_15747, plain, (X1=hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X2,X3),X4),X5),X1),X5)), inference(split_conjunct,[status(thm)],[c_0_10222]), ['final']). 4.46/4.75 cnf(c_0_15748, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)=X2), inference(split_conjunct,[status(thm)],[c_0_10223]), ['final']). 4.46/4.75 cnf(c_0_15749, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)=X1), inference(split_conjunct,[status(thm)],[c_0_10224]), ['final']). 4.46/4.75 cnf(c_0_15750, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),hAPP(X3,X4))=X3), inference(split_conjunct,[status(thm)],[c_0_10225]), ['final']). 4.46/4.75 cnf(c_0_15751, plain, (c_List_Olist_ONil(tc_prod(X1,X2))=hAPP(hAPP(c_List_Ozip(X1,X2),X3),c_List_Olist_ONil(X2))), inference(split_conjunct,[status(thm)],[c_0_10226]), ['final']). 4.46/4.75 cnf(c_0_15752, plain, (c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))=X2), inference(er,[status(thm)],[c_0_10227]), ['final']). 4.46/4.75 cnf(c_0_15753, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X1,X2))=hAPP(c_Nat_OSuc,c_Com_Ocom_Ocom__size(X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10228, c_0_4836]), c_0_5644]), ['final']). 4.46/4.75 cnf(c_0_15754, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_Set_OPow(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_10229]), ['final']). 4.46/4.75 cnf(c_0_15755, plain, (c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg)), inference(split_conjunct,[status(thm)],[fact_type__definition__Integ]), ['final']). 4.46/4.75 cnf(c_0_15756, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X1))), inference(split_conjunct,[status(thm)],[c_0_10230]), ['final']). 4.46/4.75 cnf(c_0_15757, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2)), inference(split_conjunct,[status(thm)],[c_0_10231]), ['final']). 4.46/4.75 cnf(c_0_15758, plain, (c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(rw,[status(thm)],[c_0_10232, c_0_10233]), ['final']). 4.46/4.75 cnf(c_0_15759, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_10234]), ['final']). 4.46/4.75 cnf(c_0_15760, plain, (hAPP(c_New__DSequence_Oneg__decr__bind(X1,X2,X3,X4),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Lazy__Sequence_Ohit__bound(X2)), inference(er,[status(thm)],[c_0_10235]), ['final']). 4.46/4.75 cnf(c_0_15761, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_10236]), ['final']). 4.46/4.75 cnf(c_0_15762, plain, (hAPP(c_New__DSequence_Opos__decr__bind(X1,X2,X3,X4),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Lazy__Sequence_Oempty(X2)), inference(er,[status(thm)],[c_0_10237]), ['final']). 4.46/4.75 cnf(c_0_15763, plain, (hAPP(c_Set_OPow(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=hAPP(c_fequal,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(rw,[status(thm)],[c_0_10238, c_0_5580]), ['final']). 4.46/4.75 cnf(c_0_15764, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X1)=hAPP(c_fequal,X1)), inference(rw,[status(thm)],[c_0_10239, c_0_5580]), ['final']). 4.46/4.75 cnf(c_0_15765, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_10240]), ['final']). 4.46/4.75 cnf(c_0_15766, plain, (hAPP(c_Relation_OField(X1),X2)=hAPP(c_Relation_OField(X1),hAPP(c_Relation_Oconverse(X1,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_10241]), ['final']). 4.46/4.75 cnf(c_0_15767, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_10242]), ['final']). 4.46/4.75 cnf(c_0_15768, plain, (c_Option_Ooption_ONone(X1)=hAPP(c_Map_Orestrict__map(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X4)), inference(split_conjunct,[status(thm)],[c_0_10243]), ['final']). 4.46/4.75 cnf(c_0_15769, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)), inference(split_conjunct,[status(thm)],[c_0_10244]), ['final']). 4.46/4.75 cnf(c_0_15770, plain, (X1=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)), inference(split_conjunct,[status(thm)],[c_0_10245]), ['final']). 4.46/4.75 cnf(c_0_15771, plain, (c_List_Oinsert(X1,X2,c_List_Oremdups(X1,X3))=c_List_Oremdups(X1,c_List_Oinsert(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_10246]), ['final']). 4.46/4.75 cnf(c_0_15772, plain, (hAPP(c_List_Orev(X1),c_List_Oreplicate(X1,X2,X3))=c_List_Oreplicate(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_10247]), ['final']). 4.46/4.75 cnf(c_0_15773, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_10248]), ['final']). 4.46/4.75 cnf(c_0_15774, plain, (hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[fact_greaterThan__0]), ['final']). 4.46/4.75 cnf(c_0_15775, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_10249]), ['final']). 4.46/4.75 cnf(c_0_15776, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10250]), ['final']). 4.46/4.75 cnf(c_0_15777, plain, (c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(X1))=c_Lazy__Sequence_Ohb__map(X2,X1,X3,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(X2)))), inference(split_conjunct,[status(thm)],[c_0_10251]), ['final']). 4.46/4.75 cnf(c_0_15778, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_10252]), ['final']). 4.46/4.75 cnf(c_0_15779, plain, (c_List_Oinsert(X1,X2,c_List_Olist_ONil(X1))=hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10253]), ['final']). 4.46/4.75 cnf(c_0_15780, plain, (c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[fact_transfer__morphism__nat__int]), ['final']). 4.46/4.75 cnf(c_0_15781, plain, (c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))), inference(rw,[status(thm)],[c_0_10254, c_0_4517]), ['final']). 4.46/4.75 cnf(c_0_15782, plain, (c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X4)), inference(split_conjunct,[status(thm)],[c_0_10255]), ['final']). 4.46/4.75 cnf(c_0_15783, plain, (hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X3), inference(split_conjunct,[status(thm)],[c_0_10256]), ['final']). 4.46/4.75 cnf(c_0_15784, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1)))), inference(split_conjunct,[status(thm)],[c_0_10257]), ['final']). 4.46/4.75 cnf(c_0_15785, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(rw,[status(thm)],[c_0_10258, c_0_5120]), ['final']). 4.46/4.75 cnf(c_0_15786, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))),X1)=X1), inference(er,[status(thm)],[c_0_10259]), ['final']). 4.46/4.75 cnf(c_0_15787, plain, (X1=hAPP(hAPP(c_Power_Opower_Opower(X2,X1,X3),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_10260]), ['final']). 4.46/4.75 cnf(c_0_15788, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2)))), inference(er,[status(thm)],[c_0_10261]), ['final']). 4.46/4.75 cnf(c_0_15789, plain, (X1=hAPP(c_Relation_Oconverse(X2,X3),hAPP(c_Relation_Oconverse(X3,X2),X1))), inference(split_conjunct,[status(thm)],[c_0_10262]), ['final']). 4.46/4.75 cnf(c_0_15790, plain, (c_HOL_OThe(X1,c_Finite__Set_Ofold1Set(X1,X2,X3))=hAPP(c_Finite__Set_Ofold1(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_10263]), ['final']). 4.46/4.75 cnf(c_0_15791, plain, (hAPP(c_Relation_ORange(X1,X1),c_Transitive__Closure_Ortrancl(X1,X2))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10264]), ['final']). 4.46/4.75 cnf(c_0_15792, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Ortrancl(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10265]), ['final']). 4.46/4.75 cnf(c_0_15793, plain, (c_Relation_OId__on(X1,X2)=hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId__on(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10266]), ['final']). 4.46/4.75 cnf(c_0_15794, plain, (c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(rw,[status(thm)],[c_0_10267, c_0_5334]), ['final']). 4.46/4.75 cnf(c_0_15795, plain, (c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[fact_inj__int]), ['final']). 4.46/4.75 cnf(c_0_15796, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_10268]), ['final']). 4.46/4.75 cnf(c_0_15797, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_10269]), ['final']). 4.46/4.75 cnf(c_0_15798, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than),X2))), inference(rw,[status(thm)],[c_0_10270, c_0_6842]), ['final']). 4.46/4.75 cnf(c_0_15799, plain, (c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10271]), ['final']). 4.46/4.75 cnf(c_0_15800, plain, (c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X2))=c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10272]), ['final']). 4.46/4.75 cnf(c_0_15801, plain, (c_List_Olist_ONil(X1)=hAPP(hAPP(c_List_Olist__update(X1,c_List_Olist_ONil(X1)),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_10273]), ['final']). 4.46/4.75 cnf(c_0_15802, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[fact_int__0__less__1]), ['final']). 4.46/4.75 cnf(c_0_15803, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]), ['final']). 4.46/4.75 cnf(c_0_15804, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X3)), inference(split_conjunct,[status(thm)],[c_0_10274]), ['final']). 4.46/4.75 cnf(c_0_15805, plain, (X1=hAPP(hAPP(c_Finite__Set_Ofold(X2,X3,X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10275]), ['final']). 4.46/4.75 cnf(c_0_15806, plain, (hAPP(hAPP(c_Nat_Ocompow(X1,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=c_Fun_Oid(X1)), inference(split_conjunct,[status(thm)],[c_0_10276]), ['final']). 4.46/4.75 cnf(c_0_15807, plain, (c_Enum_Oproduct(X1,X2,c_List_Olist_ONil(X1),X3)=c_List_Olist_ONil(tc_prod(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10277]), ['final']). 4.46/4.75 cnf(c_0_15808, plain, (hAPP(hAPP(c_Option_Omap(X1,X2),X3),c_Option_Ooption_ONone(X1))=c_Option_Ooption_ONone(X2)), inference(split_conjunct,[status(thm)],[c_0_10278]), ['final']). 4.46/4.75 cnf(c_0_15809, plain, (c_Nitpick_OAbs__Frac(X1,c_Nitpick_Onorm__frac(X2,X3))=hAPP(hAPP(c_Nitpick_Ofrac(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_10279]), ['final']). 4.46/4.75 cnf(c_0_15810, plain, (hAPP(c_List_Oset(X1),hAPP(c_List_Orotate1(X1),X2))=hAPP(c_List_Oset(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10280]), ['final']). 4.46/4.75 cnf(c_0_15811, plain, (hAPP(c_List_Oset(X1),X2)=hAPP(c_List_Oset(X1),hAPP(c_List_Orev(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_10281]), ['final']). 4.46/4.75 cnf(c_0_15812, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X1)),hAPP(c_Option_Ooption_OSome(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_10282]), ['final']). 4.46/4.75 cnf(c_0_15813, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2)), inference(split_conjunct,[status(thm)],[c_0_10283]), ['final']). 4.46/4.75 cnf(c_0_15814, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10284]), ['final']). 4.46/4.75 cnf(c_0_15815, plain, (c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orev(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10285]), ['final']). 4.46/4.75 cnf(c_0_15816, plain, (hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_10286]), ['final']). 4.46/4.75 cnf(c_0_15817, plain, (X1=hAPP(c_Fun_Ocomp(X2,X2,X3,c_Fun_Oid(X2)),X1)), inference(split_conjunct,[status(thm)],[c_0_10287]), ['final']). 4.46/4.75 cnf(c_0_15818, plain, (hAPP(c_List_Olist_Olist__case(X1,X2,X3,X4),c_List_Olist_ONil(X2))=X3), inference(split_conjunct,[status(thm)],[c_0_10288]), ['final']). 4.46/4.75 cnf(c_0_15819, plain, (hAPP(c_Fun_Ocomp(X1,X2,X1,X3),c_Fun_Oid(X1))=X3), inference(split_conjunct,[status(thm)],[c_0_10289]), ['final']). 4.46/4.75 cnf(c_0_15820, plain, (c_Fun_Ooverride__on(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=X3), inference(split_conjunct,[status(thm)],[c_0_10290]), ['final']). 4.46/4.75 cnf(c_0_15821, plain, (X1=hAPP(c_Option_Ooption_Ooption__case(X2,X3,X1,X4),c_Option_Ooption_ONone(X3))), inference(split_conjunct,[status(thm)],[c_0_10291]), ['final']). 4.46/4.75 cnf(c_0_15822, plain, (X1=hAPP(c_List_Ofoldl(X2,X3,X4,X1),c_List_Olist_ONil(X3))), inference(split_conjunct,[status(thm)],[c_0_10292]), ['final']). 4.46/4.75 cnf(c_0_15823, plain, (hAPP(c_Relation_ORange(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(er,[status(thm)],[c_0_10293]), ['final']). 4.46/4.75 cnf(c_0_15824, plain, (hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of)=c_Code__Numeral_Oint__of), inference(split_conjunct,[status(thm)],[fact_int__of__def]), ['final']). 4.46/4.75 cnf(c_0_15825, plain, (c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Nat_OSuc,X4))=hAPP(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_10294]), ['final']). 4.46/4.75 cnf(c_0_15826, plain, (hAPP(c_Relation_ODomain(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(er,[status(thm)],[c_0_10295]), ['final']). 4.46/4.75 cnf(c_0_15827, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oreplicate(X1,X2,X3))=X2), inference(split_conjunct,[status(thm)],[c_0_10296]), ['final']). 4.46/4.75 cnf(c_0_15828, plain, (hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=X2), inference(split_conjunct,[status(thm)],[c_0_10297]), ['final']). 4.46/4.75 cnf(c_0_15829, plain, (hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=X3), inference(split_conjunct,[status(thm)],[c_0_10298]), ['final']). 4.46/4.75 cnf(c_0_15830, plain, (X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_10299]), ['final']). 4.46/4.75 cnf(c_0_15831, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[fact_code__numeral__zero__minus__one]), ['final']). 4.46/4.75 cnf(c_0_15832, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_10300]), ['final']). 4.46/4.75 cnf(c_0_15833, plain, (c_Relation_Orefl__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10301]), ['final']). 4.46/4.75 cnf(c_0_15834, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1), inference(rw,[status(thm)],[c_0_10302, c_0_4836]), ['final']). 4.46/4.75 cnf(c_0_15835, plain, (c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X2)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_10303]), ['final']). 4.46/4.75 cnf(c_0_15836, plain, (hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral)),c_Int_Onat)=c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral)), inference(rw,[status(thm)],[c_0_10304, c_0_5334]), ['final']). 4.46/4.75 cnf(c_0_15837, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_10305]), ['final']). 4.46/4.75 cnf(c_0_15838, plain, (c_List_Olist__all2(X1,X2,X3,c_List_Olist_ONil(X1),c_List_Olist_ONil(X2))), inference(er,[status(thm)],[c_0_10306]), ['final']). 4.46/4.75 cnf(c_0_15839, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10307]), ['final']). 4.46/4.75 cnf(c_0_15840, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_10308]), ['final']). 4.46/4.75 cnf(c_0_15841, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_10309]), ['final']). 4.46/4.75 cnf(c_0_15842, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(rw,[status(thm)],[c_0_10310, c_0_4836]), ['final']). 4.46/4.75 cnf(c_0_15843, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_OMin)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_10311, c_0_4609]), ['final']). 4.46/4.75 cnf(c_0_15844, plain, (hAPP(c_List_Oset(X1),X2)=hAPP(c_List_Oset(X1),c_List_Oremdups(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10312]), ['final']). 4.46/4.75 cnf(c_0_15845, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(er,[status(thm)],[c_0_10313]), ['final']). 4.46/4.75 cnf(c_0_15846, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1)))), inference(split_conjunct,[status(thm)],[c_0_10314]), ['final']). 4.46/4.75 cnf(c_0_15847, plain, (c_Option_Ooption_Ooption__rec(X1,X2,X3,X4,c_Option_Ooption_ONone(X2))=X3), inference(split_conjunct,[status(thm)],[c_0_10315]), ['final']). 4.46/4.75 cnf(c_0_15848, plain, (c_Map_Omap__upds(X1,X2,X3,X4,c_List_Olist_ONil(X2))=X3), inference(split_conjunct,[status(thm)],[c_0_10316]), ['final']). 4.46/4.75 cnf(c_0_15849, plain, (X1=c_Map_Omap__upds(X2,X3,X1,c_List_Olist_ONil(X2),X4)), inference(split_conjunct,[status(thm)],[c_0_10317]), ['final']). 4.46/4.75 cnf(c_0_15850, plain, (hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2))), inference(er,[status(thm)],[c_0_10318]), ['final']). 4.46/4.75 cnf(c_0_15851, plain, (X1=c_Predicate_Oconversep(X2,X3,c_Predicate_Oconversep(X3,X2,X1))), inference(split_conjunct,[status(thm)],[c_0_10319]), ['final']). 4.46/4.75 cnf(c_0_15852, plain, (c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))=c_List_Olists(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10320]), ['final']). 4.46/4.75 cnf(c_0_15853, plain, (c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X1)=c_Lazy__Sequence_Osmall__lazy_H(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))), inference(split_conjunct,[status(thm)],[c_0_10321]), ['final']). 4.46/4.75 cnf(c_0_15854, plain, (hAPP(c_Option_Omap(X1,X1),c_COMBI(X1))=c_Fun_Oid(tc_Option_Ooption(X1))), inference(split_conjunct,[status(thm)],[c_0_10322]), ['final']). 4.46/4.75 cnf(c_0_15855, plain, (hAPP(c_List_Omap(X1,X1),c_Fun_Oid(X1))=c_Fun_Oid(tc_List_Olist(X1))), inference(split_conjunct,[status(thm)],[c_0_10323]), ['final']). 4.46/4.75 cnf(c_0_15856, plain, (c_Fun_Oid(tc_Option_Ooption(X1))=hAPP(c_Option_Omap(X1,X1),c_Fun_Oid(X1))), inference(split_conjunct,[status(thm)],[c_0_10324]), ['final']). 4.46/4.75 cnf(c_0_15857, plain, (X1=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))),X1)), inference(split_conjunct,[status(thm)],[c_0_10325]), ['final']). 4.46/4.75 cnf(c_0_15858, plain, (X1=c_Set_Othe__elem(X2,hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_10326]), ['final']). 4.46/4.75 cnf(c_0_15859, plain, (hAPP(c_Relation_OField(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10327]), ['final']). 4.46/4.75 cnf(c_0_15860, plain, (hAPP(c_Relation_OImage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10328]), ['final']). 4.46/4.75 cnf(c_0_15861, plain, (c_Fun_Oid(tc_List_Olist(X1))=hAPP(c_List_Omap(X1,X1),c_COMBI(X1))), inference(split_conjunct,[status(thm)],[c_0_10329]), ['final']). 4.46/4.75 cnf(c_0_15862, plain, (c_List_Omap__filter(X1,X2,X3,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X2)), inference(split_conjunct,[status(thm)],[c_0_10330]), ['final']). 4.46/4.75 cnf(c_0_15863, plain, (c_List_Olist_ONil(X1)=c_List_Omaps(X2,X1,X3,c_List_Olist_ONil(X2))), inference(split_conjunct,[status(thm)],[c_0_10331]), ['final']). 4.46/4.75 cnf(c_0_15864, plain, (c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_10332]), ['final']). 4.46/4.75 cnf(c_0_15865, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))=X2), inference(split_conjunct,[status(thm)],[c_0_10333]), ['final']). 4.46/4.75 cnf(c_0_15866, plain, (X1=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10334]), ['final']). 4.46/4.75 cnf(c_0_15867, plain, (c_List_Olist_ONil(X1)=hAPP(hAPP(c_List_Otake(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)), inference(split_conjunct,[status(thm)],[c_0_10335]), ['final']). 4.46/4.75 cnf(c_0_15868, plain, (c_List_Olist_ONil(X1)=hAPP(hAPP(c_List_Odrop(X1),X2),c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10336]), ['final']). 4.46/4.75 cnf(c_0_15869, plain, (c_List_Olist_ONil(X1)=hAPP(hAPP(c_List_Otake(X1),X2),c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10337]), ['final']). 4.46/4.75 cnf(c_0_15870, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(rw,[status(thm)],[c_0_10338, c_0_4986]), ['final']). 4.46/4.75 cnf(c_0_15871, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X1))), inference(split_conjunct,[status(thm)],[c_0_10339]), ['final']). 4.46/4.75 cnf(c_0_15872, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))=X1), inference(rw,[status(thm)],[c_0_10340, c_0_5120]), ['final']). 4.46/4.75 cnf(c_0_15873, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)), inference(split_conjunct,[status(thm)],[c_0_10341]), ['final']). 4.46/4.75 cnf(c_0_15874, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)), inference(split_conjunct,[status(thm)],[c_0_10342]), ['final']). 4.46/4.75 cnf(c_0_15875, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(rw,[status(thm)],[c_0_10343, c_0_4986]), ['final']). 4.46/4.75 cnf(c_0_15876, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_10344]), ['final']). 4.46/4.75 cnf(c_0_15877, plain, (hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2), inference(split_conjunct,[status(thm)],[c_0_10345]), ['final']). 4.46/4.75 cnf(c_0_15878, plain, (c_Fun_Oinj__on(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10346]), ['final']). 4.46/4.75 cnf(c_0_15879, plain, (hAPP(c_Relation_ORange(X1,X1),c_Relation_OId__on(X1,X2))=X2), inference(split_conjunct,[status(thm)],[c_0_10347]), ['final']). 4.46/4.75 cnf(c_0_15880, plain, (X1=hAPP(c_Relation_ODomain(X2,X2),c_Relation_OId__on(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_10348]), ['final']). 4.46/4.75 cnf(c_0_15881, plain, (c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10349]), ['final']). 4.46/4.75 cnf(c_0_15882, plain, (c_List_Oremdups(X1,c_List_Oremdups(X1,X2))=c_List_Oremdups(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_10350]), ['final']). 4.46/4.75 cnf(c_0_15883, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10351]), ['final']). 4.46/4.75 cnf(c_0_15884, plain, (c_List_Olist_ONil(tc_List_Olist(X1))=c_List_Otranspose(X1,c_List_Olist_ONil(tc_List_Olist(X1)))), inference(split_conjunct,[status(thm)],[c_0_10352]), ['final']). 4.46/4.75 cnf(c_0_15885, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1)))), inference(split_conjunct,[status(thm)],[c_0_10353]), ['final']). 4.46/4.75 cnf(c_0_15886, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_10354]), ['final']). 4.46/4.75 cnf(c_0_15887, plain, (hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_10355]), ['final']). 4.46/4.75 cnf(c_0_15888, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10356]), ['final']). 4.46/4.75 cnf(c_0_15889, plain, (hAPP(c_New__DSequence_Opos__single(X1,X2),X3)=hAPP(c_Lazy__Sequence_Osingle(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10357]), ['final']). 4.46/4.75 cnf(c_0_15890, plain, (hAPP(c_List_Ofilter(X1,X2),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_10358]), ['final']). 4.46/4.75 cnf(c_0_15891, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X1)),c_Option_Ooption_ONone(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_10359]), ['final']). 4.46/4.75 cnf(c_0_15892, plain, (X1=c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_OPow(X2),X1))), inference(split_conjunct,[status(thm)],[c_0_10360]), ['final']). 4.46/4.75 cnf(c_0_15893, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Olist_ONil(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_10361]), ['final']). 4.46/4.75 cnf(c_0_15894, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X1))), inference(split_conjunct,[status(thm)],[c_0_10362]), ['final']). 4.46/4.75 cnf(c_0_15895, plain, (hAPP(c_Set_OPow(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10363]), ['final']). 4.46/4.75 cnf(c_0_15896, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=X2), inference(split_conjunct,[status(thm)],[c_0_10364]), ['final']). 4.46/4.75 cnf(c_0_15897, plain, (c_Nat_Onat_Onat__case(X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2), inference(split_conjunct,[status(thm)],[c_0_10365]), ['final']). 4.46/4.75 cnf(c_0_15898, plain, (hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_10366]), ['final']). 4.46/4.75 cnf(c_0_15899, plain, (hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_10367]), ['final']). 4.46/4.75 cnf(c_0_15900, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2))), inference(split_conjunct,[status(thm)],[c_0_10368]), ['final']). 4.46/4.75 cnf(c_0_15901, plain, (X1=hAPP(hAPP(c_COMBK(X2,X3),X1),X4)), inference(split_conjunct,[status(thm)],[c_0_10369]), ['final']). 4.46/4.75 cnf(c_0_15902, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_10370]), ['final']). 4.46/4.75 cnf(c_0_15903, plain, (hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_10371]), ['final']). 4.46/4.75 cnf(c_0_15904, plain, (c_List_Olist__all2(X1,X1,c_fequal,X2,X2)), inference(er,[status(thm)],[c_0_10372]), ['final']). 4.46/4.75 cnf(c_0_15905, plain, (c_List_Osublist(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_10373]), ['final']). 4.46/4.75 cnf(c_0_15906, plain, (hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_card__UNIV__unit]), ['final']). 4.46/4.75 cnf(c_0_15907, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),X1),c_List_Olist_ONil(X2))), inference(split_conjunct,[status(thm)],[c_0_10374]), ['final']). 4.46/4.75 cnf(c_0_15908, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)), inference(split_conjunct,[status(thm)],[c_0_10375]), ['final']). 4.46/4.75 cnf(c_0_15909, plain, (X1=hAPP(c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),X1))), inference(split_conjunct,[status(thm)],[c_0_10376]), ['final']). 4.46/4.75 cnf(c_0_15910, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)), inference(split_conjunct,[status(thm)],[c_0_10377]), ['final']). 4.46/4.75 cnf(c_0_15911, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10378]), ['final']). 4.46/4.75 cnf(c_0_15912, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)=X1), inference(split_conjunct,[status(thm)],[c_0_10379]), ['final']). 4.46/4.75 cnf(c_0_15913, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)=X1), inference(split_conjunct,[status(thm)],[c_0_10380]), ['final']). 4.46/4.75 cnf(c_0_15914, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=X1), inference(split_conjunct,[status(thm)],[c_0_10381]), ['final']). 4.46/4.75 cnf(c_0_15915, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)), inference(split_conjunct,[status(thm)],[c_0_10382]), ['final']). 4.46/4.75 cnf(c_0_15916, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=X1), inference(rw,[status(thm)],[c_0_10383, c_0_5101]), ['final']). 4.46/4.75 cnf(c_0_15917, plain, (c_Relation_OId__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10384]), ['final']). 4.46/4.75 cnf(c_0_15918, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1), inference(split_conjunct,[status(thm)],[c_0_10385]), ['final']). 4.46/4.75 cnf(c_0_15919, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1), inference(rw,[status(thm)],[c_0_10386, c_0_5101]), ['final']). 4.46/4.75 cnf(c_0_15920, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2))), inference(split_conjunct,[status(thm)],[c_0_10387]), ['final']). 4.46/4.75 cnf(c_0_15921, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10388]), ['final']). 4.46/4.75 cnf(c_0_15922, plain, (X1=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_10389]), ['final']). 4.46/4.75 cnf(c_0_15923, plain, (X1=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[c_0_10390]), ['final']). 4.46/4.75 cnf(c_0_15924, plain, (c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10391]), ['final']). 4.46/4.75 cnf(c_0_15925, plain, (hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10392]), ['final']). 4.46/4.75 cnf(c_0_15926, plain, (X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10393]), ['final']). 4.46/4.75 cnf(c_0_15927, plain, (X1=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))), inference(split_conjunct,[status(thm)],[c_0_10394]), ['final']). 4.46/4.75 cnf(c_0_15928, plain, (c_Lazy__Sequence_Ohb__single(X1,X2)=hAPP(c_New__DSequence_Oneg__single(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_10395]), ['final']). 4.46/4.75 cnf(c_0_15929, plain, (c_Wellfounded_Owf(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10396]), ['final']). 4.46/4.75 cnf(c_0_15930, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10397]), ['final']). 4.46/4.75 cnf(c_0_15931, plain, (c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[fact_atLeast__0]), ['final']). 4.46/4.75 cnf(c_0_15932, plain, (c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10398]), ['final']). 4.46/4.75 cnf(c_0_15933, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10399]), ['final']). 4.46/4.75 cnf(c_0_15934, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X1))), inference(split_conjunct,[status(thm)],[c_0_10400]), ['final']). 4.46/4.75 cnf(c_0_15935, plain, (c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10401]), ['final']). 4.46/4.75 cnf(c_0_15936, plain, (c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10402]), ['final']). 4.46/4.75 cnf(c_0_15937, plain, (c_Relation_Orefl__on(X1,X2,c_Relation_OId__on(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10403]), ['final']). 4.46/4.75 cnf(c_0_15938, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1))), inference(split_conjunct,[status(thm)],[c_0_10404]), ['final']). 4.46/4.75 cnf(c_0_15939, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X1))), inference(split_conjunct,[status(thm)],[c_0_10405]), ['final']). 4.46/4.75 cnf(c_0_15940, plain, (c_List_OtakeWhile(X1,X2,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_10406]), ['final']). 4.46/4.75 cnf(c_0_15941, plain, (c_List_Olist_ONil(X1)=c_List_Osublist(X1,c_List_Olist_ONil(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10407]), ['final']). 4.46/4.75 cnf(c_0_15942, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_10408, c_0_4436]), ['final']). 4.46/4.75 cnf(c_0_15943, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_10409, c_0_4436]), ['final']). 4.46/4.75 cnf(c_0_15944, plain, (c_List_Olist_ONil(X1)=c_List_Oremove1(X1,X2,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10410]), ['final']). 4.46/4.75 cnf(c_0_15945, plain, (c_Option_Ooption_Ooption__size(X1,X2,c_Option_Ooption_ONone(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_10411]), ['final']). 4.46/4.75 cnf(c_0_15946, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))), inference(rw,[status(thm)],[c_0_10412, c_0_4609]), ['final']). 4.46/4.75 cnf(c_0_15947, plain, (c_List_Olist_Olist__size(X1,X2,c_List_Olist_ONil(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_10413]), ['final']). 4.46/4.75 cnf(c_0_15948, plain, (c_List_Olist_ONil(X1)=c_List_Oreplicate(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_10414]), ['final']). 4.46/4.75 cnf(c_0_15949, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_10415]), ['final']). 4.46/4.75 cnf(c_0_15950, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_10416]), ['final']). 4.46/4.75 cnf(c_0_15951, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10417]), ['final']). 4.46/4.75 cnf(c_0_15952, plain, (hBOOL(hAPP(hAPP(c_fequal,X1),X1))), inference(er,[status(thm)],[c_0_10418]), ['final']). 4.46/4.75 cnf(c_0_15953, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10419]), ['final']). 4.46/4.75 cnf(c_0_15954, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_10420]), ['final']). 4.46/4.75 cnf(c_0_15955, plain, (X1=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X1),X1)), inference(split_conjunct,[status(thm)],[c_0_10421]), ['final']). 4.46/4.75 cnf(c_0_15956, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olist_ONil(X1)))), inference(split_conjunct,[status(thm)],[c_0_10422]), ['final']). 4.46/4.75 cnf(c_0_15957, plain, (hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_10423]), ['final']). 4.46/4.75 cnf(c_0_15958, plain, (c_List_Olist_ONil(X1)=hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_9489]), ['final']). 4.46/4.75 cnf(c_0_15959, plain, (c_List_Olist_ONil(X1)=hAPP(c_List_Otl(X1),c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10424]), ['final']). 4.46/4.75 cnf(c_0_15960, plain, (c_FunDef_Opair__less=c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than)), inference(split_conjunct,[status(thm)],[fact_pair__less__def]), ['final']). 4.46/4.75 cnf(c_0_15961, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(c_List_Oset(X1),c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10425]), ['final']). 4.46/4.75 cnf(c_0_15962, plain, (X1=c_Lazy__Sequence_Oappend(X2,c_Lazy__Sequence_Olazy__sequence_OEmpty(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_10426]), ['final']). 4.46/4.75 cnf(c_0_15963, plain, (X1=c_List_Osplice(X2,c_List_Olist_ONil(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_10427]), ['final']). 4.46/4.75 cnf(c_0_15964, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[fact_int__1]), ['final']). 4.46/4.75 cnf(c_0_15965, plain, (X1=c_List_Osplice(X2,X1,c_List_Olist_ONil(X2))), inference(split_conjunct,[status(thm)],[c_0_10428]), ['final']). 4.46/4.75 cnf(c_0_15966, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=X1), inference(split_conjunct,[status(thm)],[c_0_10344]), ['final']). 4.46/4.75 cnf(c_0_15967, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), inference(split_conjunct,[status(thm)],[fact_code__numeral_Osize_I3_J]), ['final']). 4.46/4.75 cnf(c_0_15968, plain, (c_Option_Oset(X1,c_Option_Ooption_ONone(X1))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10429]), ['final']). 4.46/4.75 cnf(c_0_15969, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=X1), inference(rw,[status(thm)],[c_0_10430, c_0_4436]), ['final']). 4.46/4.75 cnf(c_0_15970, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10431, c_0_4436]), c_0_4436]), ['final']). 4.46/4.75 cnf(c_0_15971, plain, (c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)=c_FunDef_Omax__strict), inference(split_conjunct,[status(thm)],[fact_max__strict__def]), ['final']). 4.46/4.75 cnf(c_0_15972, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[fact_int__0]), ['final']). 4.46/4.75 cnf(c_0_15973, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10432]), ['final']). 4.46/4.75 cnf(c_0_15974, plain, (c_FunDef_Omin__strict=c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)), inference(split_conjunct,[status(thm)],[fact_min__strict__def]), ['final']). 4.46/4.75 cnf(c_0_15975, plain, (c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(er,[status(thm)],[c_0_10433]), ['final']). 4.46/4.75 cnf(c_0_15976, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_10434]), ['final']). 4.46/4.75 cnf(c_0_15977, plain, (c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1)), inference(split_conjunct,[status(thm)],[c_0_10435]), ['final']). 4.46/4.75 cnf(c_0_15978, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X1)), inference(split_conjunct,[status(thm)],[c_0_10436]), ['final']). 4.46/4.75 cnf(c_0_15979, plain, (hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2))), inference(split_conjunct,[status(thm)],[c_0_10437]), ['final']). 4.46/4.75 cnf(c_0_15980, plain, (c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)), inference(split_conjunct,[status(thm)],[c_0_10438]), ['final']). 4.46/4.75 cnf(c_0_15981, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1))), inference(split_conjunct,[status(thm)],[c_0_10439]), ['final']). 4.46/4.75 cnf(c_0_15982, plain, (c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10440]), ['final']). 4.46/4.75 cnf(c_0_15983, plain, (c_List_Olist__all(X1,X2,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10441]), ['final']). 4.46/4.75 cnf(c_0_15984, plain, (c_Wellfounded_Owf(X1,c_List_Omeasures(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10442]), ['final']). 4.46/4.75 cnf(c_0_15985, plain, (c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)), inference(split_conjunct,[status(thm)],[fact_wf__pair__less]), ['final']). 4.46/4.75 cnf(c_0_15986, plain, (c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X1))), inference(split_conjunct,[status(thm)],[c_0_10443]), ['final']). 4.46/4.75 cnf(c_0_15987, plain, (c_List_Olist_ONil(X1)=c_List_Obutlast(X1,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10444]), ['final']). 4.46/4.75 cnf(c_0_15988, plain, (c_List_Olist_ONil(X1)=c_List_Oremdups(X1,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10445]), ['final']). 4.46/4.75 cnf(c_0_15989, plain, (c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X2))=X2), inference(split_conjunct,[status(thm)],[c_0_10446]), ['final']). 4.46/4.75 cnf(c_0_15990, plain, (hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(er,[status(thm)],[c_0_10447]), ['final']). 4.46/4.75 cnf(c_0_15991, plain, (X1=c_HOL_OThe(X2,hAPP(c_fequal,X1))), inference(split_conjunct,[status(thm)],[c_0_10448]), ['final']). 4.46/4.75 cnf(c_0_15992, plain, (c_Nitpick_Onat__gcd(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1), inference(er,[status(thm)],[c_0_10449]), ['final']). 4.46/4.75 cnf(c_0_15993, plain, (c_Random_Oinc__shift(X1,X1)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), inference(er,[status(thm)],[c_0_10450]), ['final']). 4.46/4.75 cnf(c_0_15994, plain, (c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))), inference(split_conjunct,[status(thm)],[c_0_10451]), ['final']). 4.46/4.75 cnf(c_0_15995, plain, (hAPP(c_New__DSequence_Opos__empty(X1),X2)=c_Lazy__Sequence_Oempty(X1)), inference(split_conjunct,[status(thm)],[c_0_10452]), ['final']). 4.46/4.75 cnf(c_0_15996, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(rw,[status(thm)],[c_0_10453, c_0_4436]), ['final']). 4.46/4.75 cnf(c_0_15997, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), inference(rw,[status(thm)],[c_0_10454, c_0_5334]), ['final']). 4.46/4.75 cnf(c_0_15998, plain, (c_Predicate_Oconversep(X1,X1,c_fequal)=c_fequal), inference(split_conjunct,[status(thm)],[c_0_10455]), ['final']). 4.46/4.75 cnf(c_0_15999, plain, (X1=hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X1))), inference(split_conjunct,[status(thm)],[c_0_10456]), ['final']). 4.46/4.75 cnf(c_0_16000, plain, (hAPP(c_Code__Numeral_Onat__of,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1))=X1), inference(rw,[status(thm)],[c_0_10457, c_0_5334]), ['final']). 4.46/4.75 cnf(c_0_16001, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Onat__of,X1))=X1), inference(rw,[status(thm)],[c_0_10458, c_0_5334]), ['final']). 4.46/4.75 cnf(c_0_16002, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_10459]), ['final']). 4.46/4.75 cnf(c_0_16003, plain, (class_HOL_Oequal(tc_Nitpick_Opair__box(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10460]), ['final']). 4.46/4.75 cnf(c_0_16004, plain, (class_HOL_Oequal(tc_sum(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10461]), ['final']). 4.46/4.75 cnf(c_0_16005, plain, (class_HOL_Oequal(tc_prod(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10462]), ['final']). 4.46/4.75 cnf(c_0_16006, plain, (class_Nat_Osize(tc_Nitpick_Opair__box(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10463]), ['final']). 4.46/4.75 cnf(c_0_16007, plain, (class_Nat_Osize(tc_sum(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10464]), ['final']). 4.46/4.75 cnf(c_0_16008, plain, (class_Nat_Osize(tc_prod(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10465]), ['final']). 4.46/4.75 cnf(c_0_16009, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10466]), ['final']). 4.46/4.75 cnf(c_0_16010, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,X1))), inference(split_conjunct,[status(thm)],[c_0_10467]), ['final']). 4.46/4.75 cnf(c_0_16011, plain, (c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X1))), inference(split_conjunct,[status(thm)],[c_0_10468]), ['final']). 4.46/4.75 cnf(c_0_16012, plain, (c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X1))), inference(split_conjunct,[status(thm)],[c_0_10469]), ['final']). 4.46/4.75 cnf(c_0_16013, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_com_Osize_I9_J]), ['final']). 4.46/4.75 cnf(c_0_16014, plain, (hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_bool_Osize_I4_J]), ['final']). 4.46/4.75 cnf(c_0_16015, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue)), inference(split_conjunct,[status(thm)],[fact_bool_Osize_I3_J]), ['final']). 4.46/4.75 cnf(c_0_16016, plain, (hAPP(c_COMBI(X1),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_10470]), ['final']). 4.46/4.75 cnf(c_0_16017, plain, (X1=hAPP(c_Fun_Oid(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_10471]), ['final']). 4.46/4.75 cnf(c_0_16018, plain, (hAPP(c_Int_OAbs__Integ,esk501_1(X1))=X1), inference(split_conjunct,[status(thm)],[c_0_10194]), ['final']). 4.46/4.75 cnf(c_0_16019, hypothesis, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),v_F))), inference(split_conjunct,[status(thm)],[conj_2]), ['final']). 4.46/4.75 cnf(c_0_16020, plain, (X1=hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_10472]), ['final']). 4.46/4.75 cnf(c_0_16021, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP))), inference(split_conjunct,[status(thm)],[fact_WT_OSkip]), ['final']). 4.46/4.75 cnf(c_0_16022, plain, (c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than)), inference(split_conjunct,[status(thm)],[fact_wf__less__than]), ['final']). 4.46/4.75 cnf(c_0_16023, plain, (c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat)), inference(split_conjunct,[status(thm)],[fact_wf__pred__nat]), ['final']). 4.46/4.75 cnf(c_0_16024, plain, (c_Equiv__Relations_Oequivp(X1,c_fequal)), inference(split_conjunct,[status(thm)],[c_0_10473]), ['final']). 4.46/4.75 cnf(c_0_16025, plain, (class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X1))), inference(split_conjunct,[status(thm)],[c_0_10474]), ['final']). 4.46/4.75 cnf(c_0_16026, plain, (class_HOL_Oequal(tc_Option_Ooption(X1))), inference(split_conjunct,[status(thm)],[c_0_10475]), ['final']). 4.46/4.75 cnf(c_0_16027, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_code__numeral_Osize_I1_J]), ['final']). 4.46/4.75 cnf(c_0_16028, plain, (class_HOL_Oequal(tc_List_Olist(X1))), inference(split_conjunct,[status(thm)],[c_0_10476]), ['final']). 4.46/4.75 cnf(c_0_16029, plain, (class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X1))), inference(split_conjunct,[status(thm)],[c_0_10477]), ['final']). 4.46/4.75 cnf(c_0_16030, plain, (class_Nat_Osize(tc_Option_Ooption(X1))), inference(split_conjunct,[status(thm)],[c_0_10478]), ['final']). 4.46/4.75 cnf(c_0_16031, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[fact_nat_Osize_I1_J]), ['final']). 4.46/4.75 cnf(c_0_16032, plain, (class_Nat_Osize(tc_List_Olist(X1))), inference(split_conjunct,[status(thm)],[c_0_10479]), ['final']). 4.46/4.75 cnf(c_0_16033, plain, (c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J]), ['final']). 4.46/4.75 cnf(c_0_16034, plain, (c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J]), ['final']). 4.46/4.75 cnf(c_0_16035, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))), inference(split_conjunct,[status(thm)],[fact_finite__dom__body]), ['final']). 4.46/4.75 cnf(c_0_16036, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_HOL_Obool_Obool__size(c_fTrue)), inference(split_conjunct,[status(thm)],[fact_bool_Osize_I1_J]), ['final']). 4.46/4.75 cnf(c_0_16037, plain, (c_HOL_Obool_Obool__size(c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_bool_Osize_I2_J]), ['final']). 4.46/4.75 cnf(c_0_16038, plain, (c_Int_Oring__1__class_Oof__int(tc_Int_Oint)=c_Fun_Oid(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[fact_of__int__eq__id]), ['final']). 4.46/4.75 cnf(c_0_16039, plain, (c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J]), ['final']). 4.46/4.75 cnf(c_0_16040, plain, (hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies)=c_Com_Obody), inference(split_conjunct,[status(thm)],[fact_body__def]), ['final']). 4.46/4.75 cnf(c_0_16041, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_com_Osize_I1_J]), ['final']). 4.46/4.75 cnf(c_0_16042, plain, (class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(X1))), inference(split_conjunct,[status(thm)],[c_0_10480]), ['final']). 4.46/4.75 cnf(c_0_16043, plain, (class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X1))), inference(split_conjunct,[status(thm)],[c_0_10481]), ['final']). 4.46/4.75 cnf(c_0_16044, hypothesis, (hAPP(c_Com_Obody,v_pn)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y)), inference(split_conjunct,[status(thm)],[conj_5]), ['final']). 4.46/4.75 cnf(c_0_16045, plain, (c_Orderings_Obot__class_Obot(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_bot__nat__def]), ['final']). 4.46/4.75 cnf(c_0_16046, plain, (class_Rings_Oidom(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]), ['final']). 4.46/4.75 cnf(c_0_16047, plain, (class_Rings_Olinordered__ring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]), ['final']). 4.46/4.75 cnf(c_0_16048, plain, (class_Rings_Oordered__ring__abs(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]), ['final']). 4.46/4.75 cnf(c_0_16049, plain, (class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16050, plain, (class_Groups_Oab__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16051, plain, (class_Groups_Oab__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16052, plain, (class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring]), ['final']). 4.46/4.75 cnf(c_0_16053, plain, (class_Rings_Oordered__cancel__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]), ['final']). 4.46/4.75 cnf(c_0_16054, plain, (class_Rings_Oordered__cancel__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]), ['final']). 4.46/4.75 cnf(c_0_16055, plain, (class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit)), inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy]), ['final']). 4.46/4.75 cnf(c_0_16056, plain, (class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lazy__Sequence_Osmall__lazy]), ['final']). 4.46/4.75 cnf(c_0_16057, plain, (class_Rings_Olinordered__semiring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]), ['final']). 4.46/4.75 cnf(c_0_16058, plain, (class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring]), ['final']). 4.46/4.75 cnf(c_0_16059, plain, (class_Rings_Olinordered__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]), ['final']). 4.46/4.75 cnf(c_0_16060, plain, (class_Rings_Olinordered__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]), ['final']). 4.46/4.75 cnf(c_0_16061, plain, (class_Rings_Ocomm__ring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]), ['final']). 4.46/4.75 cnf(c_0_16062, plain, (class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16063, plain, (class_Groups_Osemigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Osemigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16064, plain, (class_Groups_Osemigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osemigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16065, plain, (class_Groups_Oabs__if(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]), ['final']). 4.46/4.75 cnf(c_0_16066, plain, (class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring]), ['final']). 4.46/4.75 cnf(c_0_16067, plain, (class_Rings_Ocomm__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]), ['final']). 4.46/4.75 cnf(c_0_16068, plain, (class_Rings_Ocomm__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]), ['final']). 4.46/4.75 cnf(c_0_16069, plain, (class_Power_Opower(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Power_Opower]), ['final']). 4.46/4.75 cnf(c_0_16070, plain, (class_Power_Opower(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]), ['final']). 4.46/4.75 cnf(c_0_16071, plain, (class_Power_Opower(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]), ['final']). 4.46/4.75 cnf(c_0_16072, plain, (class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors]), ['final']). 4.46/4.75 cnf(c_0_16073, plain, (class_Rings_Ono__zero__divisors(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]), ['final']). 4.46/4.75 cnf(c_0_16074, plain, (class_Rings_Ono__zero__divisors(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]), ['final']). 4.46/4.75 cnf(c_0_16075, plain, (class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1__no__zero__divisors]), ['final']). 4.46/4.75 cnf(c_0_16076, plain, (class_Rings_Oring__no__zero__divisors(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__no__zero__divisors]), ['final']). 4.46/4.75 cnf(c_0_16077, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict]), ['final']). 4.46/4.75 cnf(c_0_16078, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict]), ['final']). 4.46/4.75 cnf(c_0_16079, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]), ['final']). 4.46/4.75 cnf(c_0_16080, plain, (class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring]), ['final']). 4.46/4.75 cnf(c_0_16081, plain, (class_Rings_Osemiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]), ['final']). 4.46/4.75 cnf(c_0_16082, plain, (class_Rings_Osemiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]), ['final']). 4.46/4.75 cnf(c_0_16083, plain, (class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1__strict]), ['final']). 4.46/4.75 cnf(c_0_16084, plain, (class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one]), ['final']). 4.46/4.75 cnf(c_0_16085, plain, (class_Rings_Ozero__neq__one(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]), ['final']). 4.46/4.75 cnf(c_0_16086, plain, (class_Rings_Ozero__neq__one(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]), ['final']). 4.46/4.75 cnf(c_0_16087, plain, (class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring]), ['final']). 4.46/4.75 cnf(c_0_16088, plain, (class_Rings_Oordered__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]), ['final']). 4.46/4.75 cnf(c_0_16089, plain, (class_Rings_Oordered__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]), ['final']). 4.46/4.75 cnf(c_0_16090, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16091, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16092, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__ab__semigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16093, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16094, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16095, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16096, plain, (class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0]), ['final']). 4.46/4.75 cnf(c_0_16097, plain, (class_Rings_Osemiring__0(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]), ['final']). 4.46/4.75 cnf(c_0_16098, plain, (class_Rings_Osemiring__0(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]), ['final']). 4.46/4.75 cnf(c_0_16099, plain, (class_Groups_Oone(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oone]), ['final']). 4.46/4.75 cnf(c_0_16100, plain, (class_Groups_Oone(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]), ['final']). 4.46/4.75 cnf(c_0_16101, plain, (class_Groups_Oone(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]), ['final']). 4.46/4.75 cnf(c_0_16102, plain, (class_HOL_Oequal(tc_Product__Type_Ounit)), inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__HOL_Oequal]), ['final']). 4.46/4.75 cnf(c_0_16103, plain, (class_HOL_Oequal(tc_Code__Evaluation_Oterm)), inference(split_conjunct,[status(thm)],[arity_Code____Evaluation__Oterm__HOL_Oequal]), ['final']). 4.46/4.75 cnf(c_0_16104, plain, (class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__HOL_Oequal]), ['final']). 4.46/4.75 cnf(c_0_16105, plain, (class_HOL_Oequal(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__HOL_Oequal]), ['final']). 4.46/4.75 cnf(c_0_16106, plain, (class_HOL_Oequal(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__HOL_Oequal]), ['final']). 4.46/4.75 cnf(c_0_16107, plain, (class_Orderings_Owellorder(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Owellorder]), ['final']). 4.46/4.75 cnf(c_0_16108, plain, (class_Groups_Ouminus(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ouminus]), ['final']). 4.46/4.75 cnf(c_0_16109, plain, (class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16110, plain, (class_Groups_Ocancel__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16111, plain, (class_Groups_Ocancel__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16112, plain, (class_Rings_Olinordered__ring__strict(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]), ['final']). 4.46/4.75 cnf(c_0_16113, plain, (class_Lattices_Odistrib__lattice(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Odistrib__lattice]), ['final']). 4.46/4.75 cnf(c_0_16114, plain, (class_Lattices_Odistrib__lattice(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Odistrib__lattice]), ['final']). 4.46/4.75 cnf(c_0_16115, plain, (class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ozero]), ['final']). 4.46/4.75 cnf(c_0_16116, plain, (class_Groups_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]), ['final']). 4.46/4.75 cnf(c_0_16117, plain, (class_Groups_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]), ['final']). 4.46/4.75 cnf(c_0_16118, plain, (class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0]), ['final']). 4.46/4.75 cnf(c_0_16119, plain, (class_Nat_Osemiring__char__0(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Nat_Osemiring__char__0]), ['final']). 4.46/4.75 cnf(c_0_16120, plain, (class_Nat_Osemiring__char__0(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Nat_Osemiring__char__0]), ['final']). 4.46/4.75 cnf(c_0_16121, plain, (class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add]), ['final']). 4.46/4.75 cnf(c_0_16122, plain, (class_Groups_Omonoid__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]), ['final']). 4.46/4.75 cnf(c_0_16123, plain, (class_Groups_Omonoid__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]), ['final']). 4.46/4.75 cnf(c_0_16124, plain, (class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring]), ['final']). 4.46/4.75 cnf(c_0_16125, plain, (class_Rings_Oordered__comm__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]), ['final']). 4.46/4.75 cnf(c_0_16126, plain, (class_Rings_Oordered__comm__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]), ['final']). 4.46/4.75 cnf(c_0_16127, plain, (class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oord]), ['final']). 4.46/4.75 cnf(c_0_16128, plain, (class_Orderings_Oord(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]), ['final']). 4.46/4.75 cnf(c_0_16129, plain, (class_Orderings_Oord(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]), ['final']). 4.46/4.75 cnf(c_0_16130, plain, (class_Finite__Set_Ofinite(tc_Product__Type_Ounit)), inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite]), ['final']). 4.46/4.75 cnf(c_0_16131, plain, (class_Groups_Osgn__if(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]), ['final']). 4.46/4.75 cnf(c_0_16132, plain, (class_Nat_Osize(tc_Product__Type_Ounit)), inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Nat_Osize]), ['final']). 4.46/4.75 cnf(c_0_16133, plain, (class_Nat_Osize(tc_Code__Evaluation_Oterm)), inference(split_conjunct,[status(thm)],[arity_Code____Evaluation__Oterm__Nat_Osize]), ['final']). 4.46/4.75 cnf(c_0_16134, plain, (class_Nat_Osize(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Nat_Osize]), ['final']). 4.46/4.75 cnf(c_0_16135, plain, (class_Nat_Osize(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Nat_Osize]), ['final']). 4.46/4.75 cnf(c_0_16136, plain, (class_Rings_Oring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]), ['final']). 4.46/4.75 cnf(c_0_16137, plain, (class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16138, plain, (class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16139, plain, (class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__semigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16140, plain, (class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder]), ['final']). 4.46/4.75 cnf(c_0_16141, plain, (class_Orderings_Opreorder(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]), ['final']). 4.46/4.75 cnf(c_0_16142, plain, (class_Orderings_Opreorder(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]), ['final']). 4.46/4.75 cnf(c_0_16143, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16144, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16145, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add]), ['final']). 4.46/4.75 cnf(c_0_16146, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le]), ['final']). 4.46/4.75 cnf(c_0_16147, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le]), ['final']). 4.46/4.75 cnf(c_0_16148, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le]), ['final']). 4.46/4.75 cnf(c_0_16149, plain, (class_Smallcheck_Osmall(tc_Product__Type_Ounit)), inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Smallcheck_Osmall]), ['final']). 4.46/4.75 cnf(c_0_16150, plain, (class_Smallcheck_Osmall(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Smallcheck_Osmall]), ['final']). 4.46/4.75 cnf(c_0_16151, plain, (class_Groups_Oab__group__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]), ['final']). 4.46/4.75 cnf(c_0_16152, plain, (class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict]), ['final']). 4.46/4.75 cnf(c_0_16153, plain, (class_Rings_Olinordered__semiring__strict(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]), ['final']). 4.46/4.75 cnf(c_0_16154, plain, (class_Rings_Olinordered__semiring__strict(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]), ['final']). 4.46/4.75 cnf(c_0_16155, plain, (class_Lattices_Osemilattice__sup(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__sup]), ['final']). 4.46/4.75 cnf(c_0_16156, plain, (class_Lattices_Osemilattice__sup(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__sup]), ['final']). 4.46/4.75 cnf(c_0_16157, plain, (class_Int_Onumber(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Int_Onumber]), ['final']). 4.46/4.75 cnf(c_0_16158, plain, (class_Int_Onumber(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Int_Onumber]), ['final']). 4.46/4.75 cnf(c_0_16159, plain, (class_Int_Onumber(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber]), ['final']). 4.46/4.75 cnf(c_0_16160, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]), ['final']). 4.46/4.75 cnf(c_0_16161, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]), ['final']). 4.46/4.75 cnf(c_0_16162, plain, (class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult]), ['final']). 4.46/4.75 cnf(c_0_16163, plain, (class_Groups_Omonoid__mult(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]), ['final']). 4.46/4.75 cnf(c_0_16164, plain, (class_Groups_Omonoid__mult(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]), ['final']). 4.46/4.75 cnf(c_0_16165, plain, (class_Rings_Olinordered__idom(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]), ['final']). 4.46/4.75 cnf(c_0_16166, plain, (class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1]), ['final']). 4.46/4.75 cnf(c_0_16167, plain, (class_Rings_Ocomm__semiring__1(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]), ['final']). 4.46/4.75 cnf(c_0_16168, plain, (class_Rings_Ocomm__semiring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]), ['final']). 4.46/4.75 cnf(c_0_16169, plain, (class_Rings_Oordered__ring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]), ['final']). 4.46/4.75 cnf(c_0_16170, plain, (class_Lattices_Osemilattice__inf(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]), ['final']). 4.46/4.75 cnf(c_0_16171, plain, (class_Lattices_Osemilattice__inf(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__inf]), ['final']). 4.46/4.75 cnf(c_0_16172, plain, (class_Lattices_Olattice(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Olattice]), ['final']). 4.46/4.75 cnf(c_0_16173, plain, (class_Lattices_Olattice(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Olattice]), ['final']). 4.46/4.75 cnf(c_0_16174, plain, (class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult]), ['final']). 4.46/4.75 cnf(c_0_16175, plain, (class_Groups_Oab__semigroup__mult(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]), ['final']). 4.46/4.75 cnf(c_0_16176, plain, (class_Groups_Oab__semigroup__mult(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]), ['final']). 4.46/4.75 cnf(c_0_16177, plain, (class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero]), ['final']). 4.46/4.75 cnf(c_0_16178, plain, (class_Rings_Omult__zero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]), ['final']). 4.46/4.75 cnf(c_0_16179, plain, (class_Rings_Omult__zero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]), ['final']). 4.46/4.75 cnf(c_0_16180, plain, (class_Int_Oring__char__0(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]), ['final']). 4.46/4.75 cnf(c_0_16181, plain, (class_Orderings_Obot(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Obot]), ['final']). 4.46/4.75 cnf(c_0_16182, plain, (class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add__abs]), ['final']). 4.46/4.75 cnf(c_0_16183, plain, (class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oorder]), ['final']). 4.46/4.75 cnf(c_0_16184, plain, (class_Orderings_Oorder(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]), ['final']). 4.46/4.75 cnf(c_0_16185, plain, (class_Orderings_Oorder(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]), ['final']). 4.46/4.75 cnf(c_0_16186, plain, (class_Groups_Oordered__ab__group__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]), ['final']). 4.46/4.75 cnf(c_0_16187, plain, (class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1]), ['final']). 4.46/4.75 cnf(c_0_16188, plain, (class_Rings_Osemiring__1(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]), ['final']). 4.46/4.75 cnf(c_0_16189, plain, (class_Rings_Osemiring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]), ['final']). 4.46/4.75 cnf(c_0_16190, plain, (class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ominus]), ['final']). 4.46/4.75 cnf(c_0_16191, plain, (class_Groups_Ominus(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ominus]), ['final']). 4.46/4.75 cnf(c_0_16192, plain, (class_Groups_Ominus(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ominus]), ['final']). 4.46/4.75 cnf(c_0_16193, plain, (class_Enum_Oenum(tc_Product__Type_Ounit)), inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Enum_Oenum]), ['final']). 4.46/4.75 cnf(c_0_16194, plain, (class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add]), ['final']). 4.46/4.75 cnf(c_0_16195, plain, (class_Groups_Ocomm__monoid__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]), ['final']). 4.46/4.75 cnf(c_0_16196, plain, (class_Groups_Ocomm__monoid__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]), ['final']). 4.46/4.75 cnf(c_0_16197, plain, (class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult]), ['final']). 4.46/4.75 cnf(c_0_16198, plain, (class_Groups_Ocomm__monoid__mult(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]), ['final']). 4.46/4.75 cnf(c_0_16199, plain, (class_Groups_Ocomm__monoid__mult(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]), ['final']). 4.46/4.75 cnf(c_0_16200, plain, (class_Rings_Oring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]), ['final']). 4.46/4.75 cnf(c_0_16201, plain, (class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div]), ['final']). 4.46/4.75 cnf(c_0_16202, plain, (class_Divides_Osemiring__div(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]), ['final']). 4.46/4.75 cnf(c_0_16203, plain, (class_Divides_Osemiring__div(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]), ['final']). 4.46/4.75 cnf(c_0_16204, plain, (class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder]), ['final']). 4.46/4.75 cnf(c_0_16205, plain, (class_Orderings_Olinorder(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]), ['final']). 4.46/4.75 cnf(c_0_16206, plain, (class_Orderings_Olinorder(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]), ['final']). 4.46/4.75 cnf(c_0_16207, plain, (class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add]), ['final']). 4.46/4.75 cnf(c_0_16208, plain, (class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add]), ['final']). 4.46/4.75 cnf(c_0_16209, plain, (class_Groups_Oordered__comm__monoid__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__comm__monoid__add]), ['final']). 4.46/4.75 cnf(c_0_16210, plain, (class_Groups_Ogroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]), ['final']). 4.46/4.75 cnf(c_0_16211, plain, (class_Groups_Olinordered__ab__group__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]), ['final']). 4.46/4.75 cnf(c_0_16212, plain, (class_Orderings_Otop(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]), ['final']). 4.46/4.75 cnf(c_0_16213, plain, (class_HOL_Oequal(tc_Com_Ostate)), inference(split_conjunct,[status(thm)],[arity_Com__Ostate__HOL_Oequal]), ['final']). 4.46/4.75 cnf(c_0_16214, plain, (class_HOL_Oequal(tc_Com_Ocom)), inference(split_conjunct,[status(thm)],[arity_Com__Ocom__HOL_Oequal]), ['final']). 4.46/4.75 cnf(c_0_16215, plain, (class_HOL_Oequal(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__HOL_Oequal]), ['final']). 4.46/4.75 cnf(c_0_16216, plain, (class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom]), ['final']). 4.46/4.75 cnf(c_0_16217, plain, (class_Rings_Olinordered__semidom(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]), ['final']). 4.46/4.75 cnf(c_0_16218, plain, (class_Rings_Olinordered__semidom(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]), ['final']). 4.46/4.75 cnf(c_0_16219, plain, (class_Divides_Oring__div(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Oring__div]), ['final']). 4.46/4.75 cnf(c_0_16220, plain, (class_Groups_Ouminus(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]), ['final']). 4.46/4.75 cnf(c_0_16221, plain, (class_Int_Onumber__ring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]), ['final']). 4.46/4.75 cnf(c_0_16222, plain, (class_Lattices_Odistrib__lattice(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Odistrib__lattice]), ['final']). 4.46/4.75 cnf(c_0_16223, plain, (class_Orderings_Oord(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]), ['final']). 4.46/4.75 cnf(c_0_16224, plain, (class_Lattices_Oboolean__algebra(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]), ['final']). 4.46/4.75 cnf(c_0_16225, plain, (class_Finite__Set_Ofinite(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]), ['final']). 4.46/4.75 cnf(c_0_16226, plain, (class_Nat_Osize(tc_Com_Ostate)), inference(split_conjunct,[status(thm)],[arity_Com__Ostate__Nat_Osize]), ['final']). 4.46/4.75 cnf(c_0_16227, plain, (hBOOL(c_fTrue)), inference(split_conjunct,[status(thm)],[help_c__fTrue__1]), ['final']). 4.46/4.75 cnf(c_0_16228, plain, (class_Nat_Osize(tc_Com_Ocom)), inference(split_conjunct,[status(thm)],[arity_Com__Ocom__Nat_Osize]), ['final']). 4.46/4.75 cnf(c_0_16229, plain, (class_Nat_Osize(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Nat_Osize]), ['final']). 4.46/4.75 cnf(c_0_16230, plain, (class_Orderings_Opreorder(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]), ['final']). 4.46/4.75 cnf(c_0_16231, plain, (class_Lattices_Obounded__lattice__top(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__top]), ['final']). 4.46/4.75 cnf(c_0_16232, plain, (class_Lattices_Obounded__lattice(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice]), ['final']). 4.46/4.75 cnf(c_0_16233, plain, (class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice]), ['final']). 4.46/4.75 cnf(c_0_16234, plain, (class_Lattices_Osemilattice__sup(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__sup]), ['final']). 4.46/4.75 cnf(c_0_16235, plain, (class_Lattices_Osemilattice__inf(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]), ['final']). 4.46/4.75 cnf(c_0_16236, plain, (class_Lattices_Olattice(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]), ['final']). 4.46/4.75 cnf(c_0_16237, plain, (class_Orderings_Obot(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]), ['final']). 4.46/4.75 cnf(c_0_16238, plain, (class_Orderings_Oorder(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]), ['final']). 4.46/4.75 cnf(c_0_16239, plain, (class_Lattices_Obounded__lattice__bot(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__bot]), ['final']). 4.46/4.75 cnf(c_0_16240, plain, (class_Groups_Ominus(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ominus]), ['final']). 4.46/4.75 cnf(c_0_16241, plain, (class_Enum_Oenum(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Enum_Oenum]), ['final']). 4.46/4.75 4.46/4.75 # End clausification derivation 4.46/4.75 # Begin listing active clauses obtained from FOF to CNF conversion 4.46/4.75 cnf(i_0_4111, hypothesis, (c_Com_OWT__bodies)). 4.46/4.75 cnf(i_0_3920, hypothesis, (c_Hoare__Mirabelle_Ostate__not__singleton)). 4.46/4.75 cnf(i_0_83, plain, (class_Enum_Oenum(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_6863, plain, (c_Int_OPls=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.75 cnf(i_0_5588, plain, (class_Groups_Ominus(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_160, plain, (class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_4093, plain, (class_Orderings_Oorder(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_3212, plain, (class_Orderings_Obot(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_3856, plain, (class_Lattices_Olattice(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_4635, plain, (class_Lattices_Osemilattice__inf(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_957, plain, (c_Code__Numeral_Osubtract__code__numeral=c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_4297, plain, (class_Lattices_Osemilattice__sup(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_5715, plain, (class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_396, plain, (class_Lattices_Obounded__lattice(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_2189, plain, (class_Lattices_Obounded__lattice__top(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_2009, plain, (class_Orderings_Opreorder(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_1480, plain, (class_Nat_Osize(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_231, plain, (c_Code__Numeral_Oof__nat=c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_2198, plain, (class_Nat_Osize(tc_Com_Ocom))). 4.46/4.75 cnf(i_0_6701, plain, (hBOOL(c_fTrue))). 4.46/4.75 cnf(i_0_809, plain, (class_Nat_Osize(tc_Com_Ostate))). 4.46/4.75 cnf(i_0_5858, plain, (class_Finite__Set_Ofinite(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_3926, plain, (class_Lattices_Oboolean__algebra(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_4512, plain, (class_Orderings_Oord(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_3561, plain, (class_Lattices_Odistrib__lattice(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_6739, plain, (class_Int_Onumber__ring(tc_Int_Oint))). 4.46/4.75 cnf(i_0_2535, plain, (class_Groups_Ouminus(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_2222, plain, (class_Divides_Oring__div(tc_Int_Oint))). 4.46/4.75 cnf(i_0_5851, plain, (class_Rings_Olinordered__semidom(tc_Int_Oint))). 4.46/4.75 cnf(i_0_4523, plain, (class_Rings_Olinordered__semidom(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_4326, plain, (class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_3529, plain, (class_HOL_Oequal(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_2728, plain, (class_HOL_Oequal(tc_Com_Ocom))). 4.46/4.75 cnf(i_0_2950, plain, (class_HOL_Oequal(tc_Com_Ostate))). 4.46/4.75 cnf(i_0_2537, plain, (class_Orderings_Otop(tc_HOL_Obool))). 4.46/4.75 cnf(i_0_4177, plain, (class_Groups_Olinordered__ab__group__add(tc_Int_Oint))). 4.46/4.75 cnf(i_0_3747, plain, (class_Groups_Ogroup__add(tc_Int_Oint))). 4.46/4.75 cnf(i_0_6655, plain, (class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))). 4.46/4.75 cnf(i_0_2665, plain, (class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_2259, plain, (class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_4897, plain, (class_Orderings_Olinorder(tc_Int_Oint))). 4.46/4.75 cnf(i_0_1500, plain, (class_Orderings_Olinorder(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_508, plain, (class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_1119, plain, (class_Divides_Osemiring__div(tc_Int_Oint))). 4.46/4.75 cnf(i_0_6496, plain, (class_Divides_Osemiring__div(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_516, plain, (class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_1813, plain, (class_Rings_Oring(tc_Int_Oint))). 4.46/4.75 cnf(i_0_1301, plain, (class_Groups_Ocomm__monoid__mult(tc_Int_Oint))). 4.46/4.75 cnf(i_0_914, plain, (class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_5451, plain, (class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_4280, plain, (class_Groups_Ocomm__monoid__add(tc_Int_Oint))). 4.46/4.75 cnf(i_0_2364, plain, (class_Groups_Ocomm__monoid__add(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_5607, plain, (class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_4520, plain, (class_Enum_Oenum(tc_Product__Type_Ounit))). 4.46/4.75 cnf(i_0_1236, plain, (class_Groups_Ominus(tc_Int_Oint))). 4.46/4.75 cnf(i_0_2000, plain, (class_Groups_Ominus(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_4542, plain, (class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_5569, plain, (class_Rings_Osemiring__1(tc_Int_Oint))). 4.46/4.75 cnf(i_0_1788, plain, (class_Rings_Osemiring__1(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_5780, plain, (class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_7283, plain, (class_Groups_Oordered__ab__group__add(tc_Int_Oint))). 4.46/4.75 cnf(i_0_811, plain, (class_Orderings_Oorder(tc_Int_Oint))). 4.46/4.75 cnf(i_0_3099, plain, (class_Orderings_Oorder(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_4624, plain, (class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_7362, plain, (class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))). 4.46/4.75 cnf(i_0_171, plain, (class_Orderings_Obot(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_2209, plain, (class_Int_Oring__char__0(tc_Int_Oint))). 4.46/4.75 cnf(i_0_5026, plain, (class_Rings_Omult__zero(tc_Int_Oint))). 4.46/4.75 cnf(i_0_3116, plain, (class_Rings_Omult__zero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_3777, plain, (class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_207, plain, (class_Groups_Oab__semigroup__mult(tc_Int_Oint))). 4.46/4.75 cnf(i_0_2676, plain, (class_Groups_Oab__semigroup__mult(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_5467, plain, (class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_4641, plain, (class_Lattices_Olattice(tc_Int_Oint))). 4.46/4.75 cnf(i_0_6094, plain, (class_Lattices_Olattice(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_6534, plain, (class_Lattices_Osemilattice__inf(tc_Int_Oint))). 4.46/4.75 cnf(i_0_1079, plain, (class_Lattices_Osemilattice__inf(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_218, plain, (class_Rings_Oordered__ring(tc_Int_Oint))). 4.46/4.75 cnf(i_0_1082, plain, (class_Rings_Ocomm__semiring__1(tc_Int_Oint))). 4.46/4.75 cnf(i_0_778, plain, (class_Rings_Ocomm__semiring__1(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_2138, plain, (class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_5420, plain, (class_Rings_Olinordered__idom(tc_Int_Oint))). 4.46/4.75 cnf(i_0_6020, plain, (class_Groups_Omonoid__mult(tc_Int_Oint))). 4.46/4.75 cnf(i_0_1340, plain, (class_Groups_Omonoid__mult(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_4149, plain, (class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_5873, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))). 4.46/4.75 cnf(i_0_284, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_3583, plain, (class_Int_Onumber(tc_Int_Oint))). 4.46/4.75 cnf(i_0_7218, plain, (class_Int_Onumber(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_7123, plain, (class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_2383, plain, (class_Lattices_Osemilattice__sup(tc_Int_Oint))). 4.46/4.75 cnf(i_0_3093, plain, (class_Lattices_Osemilattice__sup(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_2800, plain, (class_Rings_Olinordered__semiring__strict(tc_Int_Oint))). 4.46/4.75 cnf(i_0_7375, plain, (class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_3984, plain, (class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_5730, plain, (class_Groups_Oab__group__add(tc_Int_Oint))). 4.46/4.75 cnf(i_0_5260, plain, (class_Smallcheck_Osmall(tc_Int_Oint))). 4.46/4.75 cnf(i_0_2481, plain, (class_Smallcheck_Osmall(tc_Product__Type_Ounit))). 4.46/4.75 cnf(i_0_4291, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))). 4.46/4.75 cnf(i_0_5700, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_4501, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_1208, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))). 4.46/4.75 cnf(i_0_720, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_6918, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_2087, plain, (class_Orderings_Opreorder(tc_Int_Oint))). 4.46/4.75 cnf(i_0_6457, plain, (class_Orderings_Opreorder(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_6311, plain, (class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_4475, plain, (class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))). 4.46/4.75 cnf(i_0_507, plain, (class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_5389, plain, (class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_2409, plain, (class_Rings_Oring__1(tc_Int_Oint))). 4.46/4.75 cnf(i_0_554, plain, (class_Nat_Osize(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_1552, plain, (class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_5088, plain, (class_Nat_Osize(tc_Code__Evaluation_Oterm))). 4.46/4.75 cnf(i_0_5497, plain, (class_Nat_Osize(tc_Product__Type_Ounit))). 4.46/4.75 cnf(i_0_4829, plain, (class_Groups_Osgn__if(tc_Int_Oint))). 4.46/4.75 cnf(i_0_6256, plain, (class_Finite__Set_Ofinite(tc_Product__Type_Ounit))). 4.46/4.75 cnf(i_0_1316, plain, (class_Orderings_Oord(tc_Int_Oint))). 4.46/4.75 cnf(i_0_6173, plain, (class_Orderings_Oord(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_2244, plain, (class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_655, plain, (class_Rings_Oordered__comm__semiring(tc_Int_Oint))). 4.46/4.75 cnf(i_0_3458, plain, (class_Rings_Oordered__comm__semiring(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_3886, plain, (class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_2709, plain, (class_Groups_Omonoid__add(tc_Int_Oint))). 4.46/4.75 cnf(i_0_4561, plain, (class_Groups_Omonoid__add(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_2226, plain, (class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_5819, plain, (class_Nat_Osemiring__char__0(tc_Int_Oint))). 4.46/4.75 cnf(i_0_7298, plain, (class_Nat_Osemiring__char__0(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_7127, plain, (class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_4109, plain, (class_Groups_Ozero(tc_Int_Oint))). 4.46/4.75 cnf(i_0_6998, plain, (class_Groups_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_6510, plain, (class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_3554, plain, (class_Lattices_Odistrib__lattice(tc_Int_Oint))). 4.46/4.75 cnf(i_0_7056, plain, (class_Lattices_Odistrib__lattice(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_2868, plain, (class_Rings_Olinordered__ring__strict(tc_Int_Oint))). 4.46/4.75 cnf(i_0_6957, plain, (class_Groups_Ocancel__semigroup__add(tc_Int_Oint))). 4.46/4.75 cnf(i_0_924, plain, (class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_4704, plain, (class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_2081, plain, (class_Groups_Ouminus(tc_Int_Oint))). 4.46/4.75 cnf(i_0_2593, plain, (class_Orderings_Owellorder(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_7444, plain, (class_HOL_Oequal(tc_Int_Oint))). 4.46/4.75 cnf(i_0_2053, plain, (class_HOL_Oequal(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_1226, plain, (class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_2534, plain, (class_HOL_Oequal(tc_Code__Evaluation_Oterm))). 4.46/4.75 cnf(i_0_3321, plain, (class_HOL_Oequal(tc_Product__Type_Ounit))). 4.46/4.75 cnf(i_0_1290, plain, (class_Groups_Oone(tc_Int_Oint))). 4.46/4.75 cnf(i_0_6694, plain, (class_Groups_Oone(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_4814, plain, (class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_7076, plain, (class_Rings_Osemiring__0(tc_Int_Oint))). 4.46/4.75 cnf(i_0_7279, plain, (class_Rings_Osemiring__0(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_1673, plain, (class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_2607, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))). 4.46/4.75 cnf(i_0_4178, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_2478, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_5666, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))). 4.46/4.75 cnf(i_0_2871, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_1395, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_2536, plain, (class_Rings_Oordered__semiring(tc_Int_Oint))). 4.46/4.75 cnf(i_0_1416, plain, (class_Rings_Oordered__semiring(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_2034, plain, (class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_1439, plain, (class_Rings_Ozero__neq__one(tc_Int_Oint))). 4.46/4.75 cnf(i_0_6967, plain, (class_Rings_Ozero__neq__one(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_7235, plain, (class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_5185, plain, (class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))). 4.46/4.75 cnf(i_0_4644, plain, (class_Rings_Osemiring(tc_Int_Oint))). 4.46/4.75 cnf(i_0_1564, plain, (class_Rings_Osemiring(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_2064, plain, (class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_1586, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))). 4.46/4.75 cnf(i_0_4066, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_2864, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_7096, plain, (class_Rings_Oring__no__zero__divisors(tc_Int_Oint))). 4.46/4.75 cnf(i_0_6005, plain, (class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))). 4.46/4.75 cnf(i_0_2372, plain, (class_Rings_Ono__zero__divisors(tc_Int_Oint))). 4.46/4.75 cnf(i_0_1857, plain, (class_Rings_Ono__zero__divisors(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_5367, plain, (class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_3776, plain, (class_Power_Opower(tc_Int_Oint))). 4.46/4.75 cnf(i_0_2137, plain, (class_Power_Opower(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_3411, plain, (class_Power_Opower(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_4445, plain, (class_Rings_Ocomm__semiring(tc_Int_Oint))). 4.46/4.75 cnf(i_0_2205, plain, (class_Rings_Ocomm__semiring(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_3880, plain, (class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_5415, plain, (class_Groups_Oabs__if(tc_Int_Oint))). 4.46/4.75 cnf(i_0_3125, plain, (class_Groups_Osemigroup__add(tc_Int_Oint))). 4.46/4.75 cnf(i_0_5368, plain, (class_Groups_Osemigroup__add(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_4356, plain, (class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_7335, plain, (class_Rings_Ocomm__ring__1(tc_Int_Oint))). 4.46/4.75 cnf(i_0_7183, plain, (class_Rings_Olinordered__semiring(tc_Int_Oint))). 4.46/4.75 cnf(i_0_4233, plain, (class_Rings_Olinordered__semiring(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_2680, plain, (class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_2861, plain, (class_Rings_Olinordered__semiring__1(tc_Int_Oint))). 4.46/4.75 cnf(i_0_3092, plain, (class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))). 4.46/4.75 cnf(i_0_6516, plain, (class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))). 4.46/4.75 cnf(i_0_3622, plain, (class_Rings_Oordered__cancel__semiring(tc_Int_Oint))). 4.46/4.75 cnf(i_0_6404, plain, (class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_4296, plain, (class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_3854, plain, (class_Groups_Oab__semigroup__add(tc_Int_Oint))). 4.46/4.75 cnf(i_0_4281, plain, (class_Groups_Oab__semigroup__add(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_3955, plain, (class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_4070, plain, (class_Rings_Oordered__ring__abs(tc_Int_Oint))). 4.46/4.75 cnf(i_0_7408, plain, (class_Rings_Olinordered__ring(tc_Int_Oint))). 4.46/4.75 cnf(i_0_6155, plain, (class_Rings_Oidom(tc_Int_Oint))). 4.46/4.75 cnf(i_0_127, plain, (c_Orderings_Obot__class_Obot(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_3134, hypothesis, (hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y)=hAPP(c_Com_Obody,v_pn))). 4.46/4.75 cnf(i_0_4277, plain, (class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X1)))). 4.46/4.75 cnf(i_0_6223, plain, (class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(X1)))). 4.46/4.75 cnf(i_0_6703, plain, (c_Orderings_Oord__class_Omin(tc_Nat_Onat)=c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_6779, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_6710, plain, (c_Orderings_Oord__class_Omax(tc_Nat_Onat)=c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_7290, plain, (hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies)=c_Com_Obody)). 4.46/4.75 cnf(i_0_4472, plain, (c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_1968, plain, (c_Int_Oring__1__class_Oof__int(tc_Int_Oint)=c_Fun_Oid(tc_Int_Oint))). 4.46/4.75 cnf(i_0_4010, plain, (c_HOL_Obool_Obool__size(c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_2613, plain, (c_HOL_Obool_Obool__size(c_fTrue)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_3460, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))))). 4.46/4.75 cnf(i_0_2625, plain, (c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 4.46/4.75 cnf(i_0_7418, plain, (c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))). 4.46/4.75 cnf(i_0_3577, plain, (class_Nat_Osize(tc_List_Olist(X1)))). 4.46/4.75 cnf(i_0_2219, plain, (c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_1576, plain, (class_Nat_Osize(tc_Option_Ooption(X1)))). 4.46/4.75 cnf(i_0_1958, plain, (class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)))). 4.46/4.75 cnf(i_0_2606, plain, (class_HOL_Oequal(tc_List_Olist(X1)))). 4.46/4.75 cnf(i_0_3549, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_5194, plain, (class_HOL_Oequal(tc_Option_Ooption(X1)))). 4.46/4.75 cnf(i_0_2184, plain, (class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X1)))). 4.46/4.75 cnf(i_0_483, plain, (c_Equiv__Relations_Oequivp(X1,c_fequal))). 4.46/4.75 cnf(i_0_87, plain, (c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat))). 4.46/4.75 cnf(i_0_6275, plain, (c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than))). 4.46/4.75 cnf(i_0_4456, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)))). 4.46/4.75 cnf(i_0_4843, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.75 cnf(i_0_3919, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X1)=X1)). 4.46/4.75 cnf(i_0_2229, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)=X1)). 4.46/4.75 cnf(i_0_2693, hypothesis, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),v_F)))). 4.46/4.75 cnf(i_0_7129, plain, (hAPP(c_Int_OAbs__Integ,esk501_1(X1))=X1)). 4.46/4.75 cnf(i_0_1461, plain, (hAPP(c_Set_OCollect(X1),X2)=X2)). 4.46/4.75 cnf(i_0_1231, plain, (hAPP(c_Fun_Oid(X1),X2)=X2)). 4.46/4.75 cnf(i_0_1974, plain, (hAPP(c_COMBI(X1),X2)=X2)). 4.46/4.75 cnf(i_0_2468, plain, (hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_1545, plain, (hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_6320, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_470, plain, (c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X1)))). 4.46/4.75 cnf(i_0_6649, plain, (c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X1)))). 4.46/4.75 cnf(i_0_520, plain, (c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_4003, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_5012, plain, (class_Nat_Osize(tc_prod(X1,X2)))). 4.46/4.75 cnf(i_0_6483, plain, (class_Nat_Osize(tc_sum(X1,X2)))). 4.46/4.75 cnf(i_0_4037, plain, (class_Nat_Osize(tc_Nitpick_Opair__box(X1,X2)))). 4.46/4.75 cnf(i_0_6661, plain, (class_HOL_Oequal(tc_prod(X1,X2)))). 4.46/4.75 cnf(i_0_4505, plain, (class_HOL_Oequal(tc_sum(X1,X2)))). 4.46/4.75 cnf(i_0_3546, plain, (class_HOL_Oequal(tc_Nitpick_Opair__box(X1,X2)))). 4.46/4.75 cnf(i_0_825, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_4335, plain, (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_4687, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Onat__of,X1))=X1)). 4.46/4.75 cnf(i_0_4225, plain, (hAPP(c_Code__Numeral_Onat__of,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1))=X1)). 4.46/4.75 cnf(i_0_4422, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X1))=X1)). 4.46/4.75 cnf(i_0_6308, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_3327, plain, (c_Predicate_Oconversep(X1,X1,c_fequal)=c_fequal)). 4.46/4.75 cnf(i_0_1953, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_4530, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_6804, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_5083, plain, (hAPP(c_New__DSequence_Opos__empty(X1),X2)=c_Lazy__Sequence_Oempty(X1))). 4.46/4.75 cnf(i_0_2412, plain, (c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))). 4.46/4.75 cnf(i_0_1243, plain, (c_Random_Oinc__shift(X1,X1)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_6029, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Int_OMin)). 4.46/4.75 cnf(i_0_7225, plain, (c_Nitpick_Onat__gcd(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1)). 4.46/4.75 cnf(i_0_2736, plain, (c_HOL_OThe(X1,hAPP(c_fequal,X2))=X2)). 4.46/4.75 cnf(i_0_3642, plain, (hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.75 cnf(i_0_5093, plain, (c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X2))=X2)). 4.46/4.75 cnf(i_0_959, plain, (c_List_Oremdups(X1,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.46/4.75 cnf(i_0_6528, plain, (c_List_Obutlast(X1,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.46/4.75 cnf(i_0_4026, plain, (c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X1)))). 4.46/4.75 cnf(i_0_2202, plain, (c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less))). 4.46/4.75 cnf(i_0_485, plain, (c_Wellfounded_Owf(X1,c_List_Omeasures(X1,X2)))). 4.46/4.75 cnf(i_0_4324, plain, (c_List_Olist__all(X1,X2,c_List_Olist_ONil(X1)))). 4.46/4.75 cnf(i_0_1859, plain, (c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X2)))). 4.46/4.75 cnf(i_0_3169, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1)))). 4.46/4.75 cnf(i_0_6364, plain, (c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2))). 4.46/4.75 cnf(i_0_6175, plain, (hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)))). 4.46/4.75 cnf(i_0_3605, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.75 cnf(i_0_5293, plain, (c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1))). 4.46/4.75 cnf(i_0_4385, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))). 4.46/4.75 cnf(i_0_6611, plain, (c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.75 cnf(i_0_5835, plain, (c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)=c_FunDef_Omin__strict)). 4.46/4.75 cnf(i_0_5393, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_2371, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.75 cnf(i_0_4629, plain, (c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)=c_FunDef_Omax__strict)). 4.46/4.75 cnf(i_0_7281, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_1423, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.75 cnf(i_0_5322, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)=X1)). 4.46/4.75 cnf(i_0_477, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=X1)). 4.46/4.75 cnf(i_0_1767, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=X1)). 4.46/4.75 cnf(i_0_1359, plain, (c_Option_Oset(X1,c_Option_Ooption_ONone(X1))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_4658, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_264, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=X1)). 4.46/4.75 cnf(i_0_1784, plain, (c_List_Osplice(X1,X2,c_List_Olist_ONil(X1))=X2)). 4.46/4.75 cnf(i_0_614, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Int_Oint))). 4.46/4.75 cnf(i_0_2016, plain, (c_List_Osplice(X1,c_List_Olist_ONil(X1),X2)=X2)). 4.46/4.75 cnf(i_0_4065, plain, (c_Lazy__Sequence_Oappend(X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),X2)=X2)). 4.46/4.75 cnf(i_0_2105, plain, (hAPP(c_List_Oset(X1),c_List_Olist_ONil(X1))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_3246, plain, (c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than)=c_FunDef_Opair__less)). 4.46/4.75 cnf(i_0_1867, plain, (hAPP(c_List_Otl(X1),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.46/4.75 cnf(i_0_4970, plain, (hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.46/4.75 cnf(i_0_2576, plain, (hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.46/4.75 cnf(i_0_881, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olist_ONil(X1))))). 4.46/4.75 cnf(i_0_6403, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X2)=X2)). 4.46/4.75 cnf(i_0_3528, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X2)=X2)). 4.46/4.75 cnf(i_0_6636, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_7308, plain, (hBOOL(hAPP(hAPP(c_fequal,X1),X1)))). 4.46/4.75 cnf(i_0_2526, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_5535, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_5975, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.75 cnf(i_0_779, plain, (c_List_Oreplicate(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)=c_List_Olist_ONil(X1))). 4.46/4.75 cnf(i_0_2523, plain, (c_List_Olist_Olist__size(X1,X2,c_List_Olist_ONil(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_7227, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)))). 4.46/4.75 cnf(i_0_1360, plain, (c_Option_Ooption_Ooption__size(X1,X2,c_Option_Ooption_ONone(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_2042, plain, (c_List_Oremove1(X1,X2,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.46/4.75 cnf(i_0_241, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.75 cnf(i_0_3423, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.75 cnf(i_0_3976, plain, (c_List_Osublist(X1,c_List_Olist_ONil(X1),X2)=c_List_Olist_ONil(X1))). 4.46/4.75 cnf(i_0_2843, plain, (c_List_OtakeWhile(X1,X2,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.46/4.75 cnf(i_0_1705, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X1)))). 4.46/4.75 cnf(i_0_7130, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)))). 4.46/4.75 cnf(i_0_844, plain, (c_Relation_Orefl__on(X1,X2,c_Relation_OId__on(X1,X2)))). 4.46/4.75 cnf(i_0_6594, plain, (c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X2)))). 4.46/4.75 cnf(i_0_6430, plain, (c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X2))). 4.46/4.75 cnf(i_0_629, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X1)))). 4.46/4.75 cnf(i_0_4414, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_1775, plain, (c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2))). 4.46/4.75 cnf(i_0_48, plain, (hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_5698, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_2762, plain, (c_Wellfounded_Owf(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_1855, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=X2)). 4.46/4.75 cnf(i_0_1342, plain, (hAPP(c_New__DSequence_Oneg__single(X1,X2),X3)=c_Lazy__Sequence_Ohb__single(X1,X2))). 4.46/4.75 cnf(i_0_3114, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))=X1)). 4.46/4.75 cnf(i_0_576, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=X2)). 4.46/4.75 cnf(i_0_3633, plain, (hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_6249, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)=X2)). 4.46/4.75 cnf(i_0_3590, plain, (c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_4673, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))=X1)). 4.46/4.75 cnf(i_0_1102, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1)). 4.46/4.75 cnf(i_0_4777, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_2562, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2)))). 4.46/4.75 cnf(i_0_2131, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1)). 4.46/4.75 cnf(i_0_3265, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1)). 4.46/4.75 cnf(i_0_3844, plain, (c_Relation_OId__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_4963, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1)). 4.46/4.75 cnf(i_0_2073, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=X1)). 4.46/4.75 cnf(i_0_2339, plain, (hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_5034, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=X1)). 4.46/4.75 cnf(i_0_1935, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)=X1)). 4.46/4.75 cnf(i_0_5970, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)=X1)). 4.46/4.75 cnf(i_0_6467, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_3436, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_2282, plain, (hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2))=X2)). 4.46/4.75 cnf(i_0_2997, plain, (hAPP(c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),X2))=X2)). 4.46/4.75 cnf(i_0_2794, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_4189, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1))=X2)). 4.46/4.75 cnf(i_0_5887, plain, (hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_7233, plain, (c_List_Osublist(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=c_List_Olist_ONil(X1))). 4.46/4.75 cnf(i_0_4138, plain, (c_List_Olist__all2(X1,X1,c_fequal,X2,X2))). 4.46/4.75 cnf(i_0_4657, plain, (hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=X2)). 4.46/4.75 cnf(i_0_3465, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)=X2)). 4.46/4.75 cnf(i_0_946, plain, (hAPP(hAPP(c_COMBK(X1,X2),X3),X4)=X3)). 4.46/4.75 cnf(i_0_346, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)))). 4.46/4.75 cnf(i_0_206, plain, (hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X2)=X2)). 4.46/4.75 cnf(i_0_6060, plain, (hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X2)=X2)). 4.46/4.75 cnf(i_0_4386, plain, (c_Nat_Onat_Onat__case(X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2)). 4.46/4.75 cnf(i_0_4292, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=X2)). 4.46/4.75 cnf(i_0_5995, plain, (hAPP(c_Set_OPow(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_2670, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_6780, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Olist_ONil(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_500, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_4132, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_OPow(X1),X2))=X2)). 4.46/4.75 cnf(i_0_4243, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X1)),c_Option_Ooption_ONone(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_7008, plain, (hAPP(c_List_Ofilter(X1,X2),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.46/4.75 cnf(i_0_7245, plain, (hAPP(c_New__DSequence_Opos__single(X1,X2),X3)=hAPP(c_Lazy__Sequence_Osingle(X1),X2))). 4.46/4.75 cnf(i_0_770, plain, (hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 4.46/4.75 cnf(i_0_1398, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_1027, plain, (hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X2))))). 4.46/4.75 cnf(i_0_4135, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X2))))). 4.46/4.75 cnf(i_0_2542, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))))). 4.46/4.75 cnf(i_0_1757, plain, (c_List_Otranspose(X1,c_List_Olist_ONil(tc_List_Olist(X1)))=c_List_Olist_ONil(tc_List_Olist(X1)))). 4.46/4.75 cnf(i_0_3244, plain, (c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X2))=c_Transitive__Closure_Ortrancl(X1,X2))). 4.46/4.75 cnf(i_0_251, plain, (c_List_Oremdups(X1,c_List_Oremdups(X1,X2))=c_List_Oremdups(X1,X2))). 4.46/4.75 cnf(i_0_6907, plain, (hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_1031, plain, (hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))). 4.46/4.75 cnf(i_0_2420, plain, (c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)))). 4.46/4.75 cnf(i_0_3075, plain, (hAPP(c_Relation_ODomain(X1,X1),c_Relation_OId__on(X1,X2))=X2)). 4.46/4.75 cnf(i_0_536, plain, (hAPP(c_Relation_ORange(X1,X1),c_Relation_OId__on(X1,X2))=X2)). 4.46/4.75 cnf(i_0_5543, plain, (c_Fun_Oinj__on(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1),X2))). 4.46/4.75 cnf(i_0_1080, plain, (hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2)). 4.46/4.75 cnf(i_0_265, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.75 cnf(i_0_5186, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_5738, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_1665, plain, (hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))=hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1))). 4.46/4.75 cnf(i_0_1694, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.75 cnf(i_0_3826, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_1289, plain, (hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))=hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X1))). 4.46/4.75 cnf(i_0_1604, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X1)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))). 4.46/4.75 cnf(i_0_4303, plain, (hAPP(c_Int_Onat,X1)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))). 4.46/4.75 cnf(i_0_285, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_147, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_208, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))=X1)). 4.46/4.75 cnf(i_0_5110, plain, (hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X1))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))). 4.46/4.75 cnf(i_0_3197, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_1533, plain, (hAPP(hAPP(c_List_Otake(X1),X2),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.46/4.75 cnf(i_0_1284, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.46/4.75 cnf(i_0_5008, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.46/4.75 cnf(i_0_4397, plain, (hAPP(hAPP(c_List_Otake(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=c_List_Olist_ONil(X1))). 4.46/4.75 cnf(i_0_93, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X2))))). 4.46/4.75 cnf(i_0_4302, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=X2)). 4.46/4.75 cnf(i_0_3879, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))=X2)). 4.46/4.75 cnf(i_0_4016, plain, (c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)))). 4.46/4.75 cnf(i_0_1551, plain, (c_List_Omaps(X1,X2,X3,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X2))). 4.46/4.75 cnf(i_0_2361, plain, (c_List_Omap__filter(X1,X2,X3,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X2))). 4.46/4.75 cnf(i_0_302, plain, (hAPP(c_List_Omap(X1,X1),c_COMBI(X1))=c_Fun_Oid(tc_List_Olist(X1)))). 4.46/4.75 cnf(i_0_5991, plain, (hAPP(c_Relation_OImage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_164, plain, (hAPP(c_Relation_OField(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_389, plain, (c_Set_Othe__elem(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2)). 4.46/4.75 cnf(i_0_5050, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2)=X2)). 4.46/4.75 cnf(i_0_1312, plain, (hAPP(c_Option_Omap(X1,X1),c_Fun_Oid(X1))=c_Fun_Oid(tc_Option_Ooption(X1)))). 4.46/4.75 cnf(i_0_5043, plain, (hAPP(c_List_Omap(X1,X1),c_Fun_Oid(X1))=c_Fun_Oid(tc_List_Olist(X1)))). 4.46/4.75 cnf(i_0_584, plain, (hAPP(c_Option_Omap(X1,X1),c_COMBI(X1))=c_Fun_Oid(tc_Option_Ooption(X1)))). 4.46/4.75 cnf(i_0_944, plain, (c_Lazy__Sequence_Osmall__lazy_H(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))=c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X1))). 4.46/4.75 cnf(i_0_1172, plain, (c_List_Olists(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_6667, plain, (c_Predicate_Oconversep(X1,X2,c_Predicate_Oconversep(X2,X1,X3))=X3)). 4.46/4.75 cnf(i_0_1515, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_OSuc,X1))). 4.46/4.75 cnf(i_0_1616, plain, (hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)))). 4.46/4.75 cnf(i_0_3310, plain, (c_Map_Omap__upds(X1,X2,X3,c_List_Olist_ONil(X1),X4)=X3)). 4.46/4.75 cnf(i_0_1150, plain, (c_Map_Omap__upds(X1,X2,X3,X4,c_List_Olist_ONil(X2))=X3)). 4.46/4.75 cnf(i_0_4341, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)=hAPP(c_Nat_OSuc,X1))). 4.46/4.75 cnf(i_0_4607, plain, (c_Option_Ooption_Ooption__rec(X1,X2,X3,X4,c_Option_Ooption_ONone(X2))=X3)). 4.46/4.75 cnf(i_0_2849, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X2)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2))). 4.46/4.75 cnf(i_0_6362, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))))). 4.46/4.75 cnf(i_0_4688, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_5872, plain, (hAPP(c_List_Oset(X1),c_List_Oremdups(X1,X2))=hAPP(c_List_Oset(X1),X2))). 4.46/4.75 cnf(i_0_6406, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_OMin)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.75 cnf(i_0_6397, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_2214, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))). 4.46/4.75 cnf(i_0_5781, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))))). 4.46/4.75 cnf(i_0_2004, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_4083, plain, (c_List_Olist__all2(X1,X2,X3,c_List_Olist_ONil(X1),c_List_Olist_ONil(X2)))). 4.46/4.75 cnf(i_0_6791, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))))). 4.46/4.75 cnf(i_0_3335, plain, (hAPP(c_Product__Type_Osnd(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4))=X4)). 4.46/4.75 cnf(i_0_2845, plain, (hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral)),c_Int_Onat)=c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_6036, plain, (c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X2)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))). 4.46/4.75 cnf(i_0_250, plain, (hAPP(c_Product__Type_Ofst(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4))=X3)). 4.46/4.75 cnf(i_0_698, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1)). 4.46/4.75 cnf(i_0_1751, plain, (c_Relation_Orefl__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_5571, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))). 4.46/4.75 cnf(i_0_4715, plain, (hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1,X2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))). 4.46/4.75 cnf(i_0_4000, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_440, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1)). 4.46/4.75 cnf(i_0_5843, plain, (hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=X3)). 4.46/4.75 cnf(i_0_2841, plain, (hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue)=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_2987, plain, (hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=X2)). 4.46/4.75 cnf(i_0_6042, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oreplicate(X1,X2,X3))=X2)). 4.46/4.75 cnf(i_0_1987, plain, (hAPP(c_Relation_ODomain(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_2948, plain, (c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Nat_OSuc,X4))=hAPP(X3,X4))). 4.46/4.75 cnf(i_0_3620, plain, (hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of)=c_Code__Numeral_Oint__of)). 4.46/4.75 cnf(i_0_6817, plain, (hAPP(c_Relation_ORange(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_838, plain, (hAPP(c_List_Ofoldl(X1,X2,X3,X4),c_List_Olist_ONil(X2))=X4)). 4.46/4.75 cnf(i_0_1358, plain, (hAPP(c_Option_Ooption_Ooption__case(X1,X2,X3,X4),c_Option_Ooption_ONone(X2))=X3)). 4.46/4.75 cnf(i_0_7188, plain, (c_Fun_Ooverride__on(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=X3)). 4.46/4.75 cnf(i_0_5944, plain, (hAPP(c_Fun_Ocomp(X1,X2,X1,X3),c_Fun_Oid(X1))=X3)). 4.46/4.75 cnf(i_0_5915, plain, (hAPP(c_List_Olist_Olist__case(X1,X2,X3,X4),c_List_Olist_ONil(X2))=X3)). 4.46/4.75 cnf(i_0_6317, plain, (hAPP(c_Fun_Ocomp(X1,X1,X2,c_Fun_Oid(X1)),X3)=X3)). 4.46/4.75 cnf(i_0_5787, plain, (hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))). 4.46/4.75 cnf(i_0_3881, plain, (c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orev(X1),X2))). 4.46/4.75 cnf(i_0_7363, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_796, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2)=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_4170, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X1)),hAPP(c_Option_Ooption_OSome(X1),X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_1850, plain, (hAPP(c_List_Oset(X1),hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Oset(X1),X2))). 4.46/4.75 cnf(i_0_6010, plain, (hAPP(c_List_Oset(X1),hAPP(c_List_Orotate1(X1),X2))=hAPP(c_List_Oset(X1),X2))). 4.46/4.75 cnf(i_0_4824, plain, (c_Nitpick_OAbs__Frac(X1,c_Nitpick_Onorm__frac(X2,X3))=hAPP(hAPP(c_Nitpick_Ofrac(X1),X2),X3))). 4.46/4.75 cnf(i_0_5483, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X2))). 4.46/4.75 cnf(i_0_619, plain, (hAPP(hAPP(c_Option_Omap(X1,X2),X3),c_Option_Ooption_ONone(X1))=c_Option_Ooption_ONone(X2))). 4.46/4.75 cnf(i_0_2995, plain, (c_Enum_Oproduct(X1,X2,c_List_Olist_ONil(X1),X3)=c_List_Olist_ONil(tc_prod(X1,X2)))). 4.46/4.75 cnf(i_0_3616, plain, (hAPP(hAPP(c_Nat_Ocompow(X1,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=c_Fun_Oid(X1))). 4.46/4.75 cnf(i_0_3065, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=X4)). 4.46/4.75 cnf(i_0_6539, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_3284, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 4.46/4.75 cnf(i_0_2601, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 4.46/4.75 cnf(i_0_3319, plain, (hAPP(hAPP(c_List_Olist__update(X1,c_List_Olist_ONil(X1)),X2),X3)=c_List_Olist_ONil(X1))). 4.46/4.75 cnf(i_0_3457, plain, (c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X2))=c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2)))). 4.46/4.75 cnf(i_0_6013, plain, (c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)))). 4.46/4.75 cnf(i_0_949, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than),X2)))). 4.46/4.75 cnf(i_0_3608, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2))))). 4.46/4.75 cnf(i_0_5814, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))))). 4.46/4.75 cnf(i_0_1625, plain, (c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_1716, plain, (c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_1664, plain, (hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId__on(X1,X2))=c_Relation_OId__on(X1,X2))). 4.46/4.75 cnf(i_0_6081, plain, (hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Ortrancl(X1,X2))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_2690, plain, (hAPP(c_Relation_ORange(X1,X1),c_Transitive__Closure_Ortrancl(X1,X2))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_5686, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))). 4.46/4.75 cnf(i_0_6154, plain, (c_HOL_OThe(X1,c_Finite__Set_Ofold1Set(X1,X2,X3))=hAPP(c_Finite__Set_Ofold1(X1,X2),X3))). 4.46/4.75 cnf(i_0_5028, plain, (hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3))=X3)). 4.46/4.75 cnf(i_0_1863, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))))). 4.46/4.75 cnf(i_0_5930, plain, (hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2)). 4.46/4.75 cnf(i_0_7324, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))),X1)=X1)). 4.46/4.75 cnf(i_0_3309, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=c_List_Olist_ONil(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_5158, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_2979, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))))). 4.46/4.75 cnf(i_0_4095, plain, (hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X3)). 4.46/4.75 cnf(i_0_138, plain, (c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X4))). 4.46/4.75 cnf(i_0_6444, plain, (c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))))). 4.46/4.75 cnf(i_0_3602, plain, (c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.75 cnf(i_0_2231, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))). 4.46/4.75 cnf(i_0_1526, plain, (c_List_Oinsert(X1,X2,c_List_Olist_ONil(X1))=hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))). 4.46/4.75 cnf(i_0_3550, plain, (c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X2))=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_4572, plain, (c_Lazy__Sequence_Ohb__map(X1,X2,X3,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(X1)))=c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(X2)))). 4.46/4.75 cnf(i_0_300, plain, (hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X1,X2))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))). 4.46/4.75 cnf(i_0_1782, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))))). 4.46/4.75 cnf(i_0_1495, plain, (hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_29, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X2))))). 4.46/4.75 cnf(i_0_2615, plain, (hAPP(c_List_Orev(X1),c_List_Oreplicate(X1,X2,X3))=c_List_Oreplicate(X1,X2,X3))). 4.46/4.75 cnf(i_0_2243, plain, (c_List_Oinsert(X1,X2,c_List_Oremdups(X1,X3))=c_List_Oremdups(X1,c_List_Oinsert(X1,X2,X3)))). 4.46/4.75 cnf(i_0_5976, plain, (hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)=X2)). 4.46/4.75 cnf(i_0_1114, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_6849, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))). 4.46/4.75 cnf(i_0_4417, plain, (hAPP(c_Map_Orestrict__map(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X4)=c_Option_Ooption_ONone(X2))). 4.46/4.75 cnf(i_0_699, plain, (c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 4.46/4.75 cnf(i_0_2132, plain, (hAPP(c_Relation_OField(X1),hAPP(c_Relation_Oconverse(X1,X1),X2))=hAPP(c_Relation_OField(X1),X2))). 4.46/4.75 cnf(i_0_6306, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))))). 4.46/4.75 cnf(i_0_4984, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X1)=hAPP(c_fequal,X1))). 4.46/4.75 cnf(i_0_4407, plain, (hAPP(c_Set_OPow(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=hAPP(c_fequal,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_2487, plain, (hAPP(c_New__DSequence_Opos__decr__bind(X1,X2,X3,X4),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Lazy__Sequence_Oempty(X2))). 4.46/4.75 cnf(i_0_361, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))). 4.46/4.75 cnf(i_0_344, plain, (hAPP(c_New__DSequence_Oneg__decr__bind(X1,X2,X3,X4),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Lazy__Sequence_Ohit__bound(X2))). 4.46/4.75 cnf(i_0_3593, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.75 cnf(i_0_4662, plain, (c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_1444, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))). 4.46/4.75 cnf(i_0_486, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X1)))). 4.46/4.75 cnf(i_0_2714, plain, (c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg))). 4.46/4.75 cnf(i_0_4190, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_Set_OPow(X1),X2))))). 4.46/4.75 cnf(i_0_43, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X1,X2))=hAPP(c_Nat_OSuc,c_Com_Ocom_Ocom__size(X2)))). 4.46/4.75 cnf(i_0_722, plain, (c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))=X2)). 4.46/4.75 cnf(i_0_1662, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),X3),c_List_Olist_ONil(X2))=c_List_Olist_ONil(tc_prod(X1,X2)))). 4.46/4.75 cnf(i_0_1812, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),hAPP(X3,X4))=X3)). 4.46/4.75 cnf(i_0_5162, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)=X1)). 4.46/4.75 cnf(i_0_929, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)=X2)). 4.46/4.75 cnf(i_0_1563, plain, (hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5),X4)=X5)). 4.46/4.75 cnf(i_0_856, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),c_List_Olist_ONil(X1)),X3)=c_List_Olist_ONil(tc_prod(X1,X2)))). 4.46/4.75 cnf(i_0_5357, plain, (hAPP(hAPP(c_Relation_Orel__comp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Wellfounded_Opred__nat),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))=c_Wellfounded_Oless__than)). 4.46/4.75 cnf(i_0_686, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_1871, plain, (c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))=c_Divides_OnegateSnd)). 4.46/4.75 cnf(i_0_1872, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),c_Int_OMin)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))). 4.46/4.75 cnf(i_0_126, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X1,X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))). 4.46/4.75 cnf(i_0_849, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.75 cnf(i_0_5644, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_3464, plain, (c_List_Osublist(X1,X2,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))=hAPP(hAPP(c_List_Otake(X1),X3),X2))). 4.46/4.75 cnf(i_0_3613, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_2908, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))). 4.46/4.75 cnf(i_0_1837, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 4.46/4.75 cnf(i_0_5581, plain, (c_Relation_Osingle__valued(X1,X1,c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))). 4.46/4.75 cnf(i_0_4378, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.75 cnf(i_0_337, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3),X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))=X5)). 4.46/4.75 cnf(i_0_3565, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))=X1)). 4.46/4.75 cnf(i_0_2033, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orev(X1),X2))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))). 4.46/4.75 cnf(i_0_581, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orotate1(X1),X2))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))). 4.46/4.75 cnf(i_0_1303, plain, (c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=X3)). 4.46/4.75 cnf(i_0_6196, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X2)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))). 4.46/4.75 cnf(i_0_5768, plain, (hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X1),X2),X3),X4),X5)=c_New__DSequence_Opos__single(X1,X2))). 4.46/4.75 cnf(i_0_740, plain, (hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X1),X2),X3),X4),X5)=c_New__DSequence_Oneg__single(X1,X2))). 4.46/4.75 cnf(i_0_5177, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))))). 4.46/4.75 cnf(i_0_6421, plain, (c_Option_Ooption_Ooption__rec(X1,X2,X3,X4,hAPP(c_Option_Ooption_OSome(X2),X5))=hAPP(X4,X5))). 4.46/4.75 cnf(i_0_1911, plain, (c_Divides_Odivmod__int(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 4.46/4.75 cnf(i_0_3136, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))))). 4.46/4.75 cnf(i_0_2199, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1))))). 4.46/4.75 cnf(i_0_4165, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_234, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1))))))). 4.46/4.75 cnf(i_0_6559, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X1)))). 4.46/4.75 cnf(i_0_5248, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),X1)))). 4.46/4.75 cnf(i_0_7128, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk501_1(X1)),c_Int_OInteg)))). 4.46/4.75 cnf(i_0_4025, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X4)))). 4.46/4.75 cnf(i_0_6271, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))=c_List_Olist_ONil(X1))). 4.46/4.75 cnf(i_0_6870, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))). 4.46/4.75 cnf(i_0_989, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_5107, plain, (c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel))). 4.46/4.75 cnf(i_0_1124, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),c_List_Olist_ONil(tc_prod(X1,X2))),X3)=c_Option_Ooption_ONone(X2))). 4.46/4.75 cnf(i_0_4834, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))))). 4.46/4.75 cnf(i_0_1961, plain, (c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X2)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))). 4.46/4.75 cnf(i_0_3476, plain, (c_Lazy__Sequence_Oappend(X1,c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3),X4)=c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,c_Lazy__Sequence_Oappend(X1,X3,X4)))). 4.46/4.75 cnf(i_0_95, plain, (hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))))). 4.46/4.75 cnf(i_0_6293, plain, (hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6)=hAPP(X4,hAPP(X5,X6)))). 4.46/4.75 cnf(i_0_1674, plain, (c_Wellfounded_OwfP(X1,hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))). 4.46/4.75 cnf(i_0_3115, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X1)),c_Int_OInteg)))). 4.46/4.75 cnf(i_0_446, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremdups(X1,X2))=hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2)))). 4.46/4.75 cnf(i_0_3155, plain, (hAPP(hAPP(c_List_Odrop(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=X3)). 4.46/4.75 cnf(i_0_1465, plain, (hAPP(hAPP(c_List_Olist__update(X1,X2),X3),hAPP(hAPP(c_List_Onth(X1),X2),X3))=X2)). 4.46/4.75 cnf(i_0_487, plain, (c_Map_Odom(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_5977, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X1,X2,X3))=hAPP(c_Nat_OSuc,c_Com_Ocom_Ocom__size(X3)))). 4.46/4.75 cnf(i_0_2738, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_910, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2)). 4.46/4.75 cnf(i_0_68, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 4.46/4.75 cnf(i_0_2527, plain, (hAPP(c_Option_Ooption_Ooption__case(X1,X2,X3,X4),hAPP(c_Option_Ooption_OSome(X2),X5))=hAPP(X4,X5))). 4.46/4.75 cnf(i_0_4916, plain, (hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6)=hAPP(X4,hAPP(X5,X6)))). 4.46/4.75 cnf(i_0_7101, plain, (hAPP(c_Random_Oiterate(X1,X2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),X3),X4)=hAPP(c_Product__Type_OPair(X1,X2),X4))). 4.46/4.75 cnf(i_0_3097, plain, (c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X1))=hAPP(c_Nat_OSuc,c_Nat_Onat_Onat__size(X1)))). 4.46/4.75 cnf(i_0_4944, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))). 4.46/4.75 cnf(i_0_1712, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.75 cnf(i_0_6666, plain, (c_Transitive__Closure_Ortrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))=hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)))). 4.46/4.75 cnf(i_0_5867, plain, (c_List_Oremdups(X1,hAPP(c_List_Ofilter(X1,X2),X3))=hAPP(c_List_Ofilter(X1,X2),c_List_Oremdups(X1,X3)))). 4.46/4.75 cnf(i_0_839, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))). 4.46/4.75 cnf(i_0_1308, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),X3),X4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_1252, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1))). 4.46/4.75 cnf(i_0_6633, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2))))). 4.46/4.75 cnf(i_0_1718, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))))). 4.46/4.75 cnf(i_0_4840, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X3)))). 4.46/4.75 cnf(i_0_5259, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))). 4.46/4.75 cnf(i_0_286, plain, (hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1))=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X1))). 4.46/4.75 cnf(i_0_3222, plain, (c_Hoare__Mirabelle_Otriple_Otriple__size(X1,X2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_5085, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X2)))). 4.46/4.75 cnf(i_0_808, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X2)))). 4.46/4.75 cnf(i_0_6560, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X1,X2)),c_Nitpick_Opair__box_OPairBox(X1,X2,X3,X4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_1005, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))). 4.46/4.75 cnf(i_0_7392, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBI(tc_fun(X1,tc_HOL_Obool)))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))). 4.46/4.75 cnf(i_0_1247, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBI(tc_fun(X1,tc_HOL_Obool)))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2))). 4.46/4.75 cnf(i_0_2643, plain, (c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X1,X2,X3,X4,c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X5,X6))=hAPP(hAPP(X4,X5),X6))). 4.46/4.75 cnf(i_0_570, plain, (c_Product__Type_Omap__pair(X1,X1,X2,X2,c_Fun_Oid(X1),c_Fun_Oid(X2))=c_Fun_Oid(tc_prod(X1,X2)))). 4.46/4.75 cnf(i_0_4525, plain, (c_Product__Type_Omap__pair(X1,X1,X2,X2,c_COMBI(X1),c_COMBI(X2))=c_Fun_Oid(tc_prod(X1,X2)))). 4.46/4.75 cnf(i_0_173, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3))=hAPP(c_Relation_ORange(X2,X1),X3))). 4.46/4.75 cnf(i_0_1729, plain, (c_Divides_Opdivmod(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)))). 4.46/4.75 cnf(i_0_2787, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat))=c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_347, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat))=c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_416, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat))=c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_4146, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)=c_Groups_Oone__class_Oone(tc_Int_Oint))). 4.46/4.75 cnf(i_0_7289, plain, (hAPP(c_Relation_ORange(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3))=hAPP(c_Relation_ODomain(X2,X1),X3))). 4.46/4.75 cnf(i_0_3342, plain, (c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2))=c_List_Otranspose(X1,X2))). 4.46/4.75 cnf(i_0_463, plain, (c_Map_Oran(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_293, plain, (hAPP(c_List_Oset(X1),c_List_Oinsert(X1,X2,X3))=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))). 4.46/4.75 cnf(i_0_3708, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))))=X2)). 4.46/4.75 cnf(i_0_5292, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X1),hAPP(c_Code__Numeral_Onat__of,X2)))=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,X2))). 4.46/4.75 cnf(i_0_276, plain, (c_Map_Omap__add(X1,X2,X3,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)))=X3)). 4.46/4.75 cnf(i_0_5427, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))=X1)). 4.46/4.75 cnf(i_0_3707, plain, (c_List_Olast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))))=X3)). 4.46/4.75 cnf(i_0_196, plain, (c_Map_Omap__add(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),X3)=X3)). 4.46/4.75 cnf(i_0_2936, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X2,X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X4))))=hAPP(X3,X4))). 4.46/4.75 cnf(i_0_5187, plain, (hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6)=hAPP(hAPP(X4,X6),X5))). 4.46/4.75 cnf(i_0_86, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X1,X2))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)))). 4.46/4.75 cnf(i_0_7069, plain, (hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))). 4.46/4.75 cnf(i_0_348, plain, (hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)))). 4.46/4.75 cnf(i_0_133, plain, (c_List_Oset__Cons(X1,X2,c_List_Olistset(X1,X3))=c_List_Olistset(X1,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.46/4.75 cnf(i_0_5294, plain, (hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)=X2)). 4.46/4.75 cnf(i_0_5928, plain, (c_Predicate_Opred__comp(X1,X1,X1,c_fequal,c_Predicate_Opred__comp(X1,X1,X1,X2,c_fequal))=X2)). 4.46/4.75 cnf(i_0_5256, plain, (hAPP(c_Relation_OImage(X1,X1,c_Relation_OId__on(X1,X2)),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.46/4.75 cnf(i_0_3907, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)))). 4.46/4.75 cnf(i_0_3098, plain, (c_HOL_OThe(X1,c_Finite__Set_Ofold__graph(X2,X1,X3,X4,X5))=hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,X3),X4),X5))). 4.46/4.75 cnf(i_0_1433, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Odrop(X1),X2),X3))=hAPP(hAPP(c_List_Odrop(X1),X2),c_List_Obutlast(X1,X3)))). 4.46/4.75 cnf(i_0_3948, plain, (c_Lazy__Sequence_Oappend(tc_Option_Ooption(X1),hAPP(X2,X3),hAPP(X4,X3))=hAPP(c_New__DSequence_Oneg__union(X1,X2,X4),X3))). 4.46/4.75 cnf(i_0_7169, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Oreplicate(X1,X3,X2))=c_List_Oreplicate(X1,hAPP(c_Nat_OSuc,X3),X2))). 4.46/4.75 cnf(i_0_1789, plain, (hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel)=c_Int_OInteg)). 4.46/4.75 cnf(i_0_4652, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))))). 4.46/4.75 cnf(i_0_5010, plain, (hAPP(c_Relation_OImage(X1,X1,c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),X2)=X2)). 4.46/4.75 cnf(i_0_1214, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1)))). 4.46/4.75 cnf(i_0_7344, plain, (c_Hoare__Mirabelle_Otriple__valid(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Com_Ocom_OBODY,X3)),X4)))). 4.46/4.75 cnf(i_0_3790, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))))). 4.46/4.75 cnf(i_0_2935, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(c_Nat_OSuc,X1))))). 4.46/4.75 cnf(i_0_4534, plain, (hAPP(hAPP(c_Option_Omap(X1,X2),X3),hAPP(c_Option_Ooption_OSome(X1),X4))=hAPP(c_Option_Ooption_OSome(X2),hAPP(X3,X4)))). 4.46/4.75 cnf(i_0_84, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(c_List_Otl(X1),X3))=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X2)),X3))). 4.46/4.75 cnf(i_0_4724, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 4.46/4.75 cnf(i_0_4707, plain, (hAPP(c_List_Oset(X1),c_List_Oreplicate(X1,hAPP(c_Nat_OSuc,X2),X3))=hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_2052, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.46/4.75 cnf(i_0_65, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)))))). 4.46/4.75 cnf(i_0_3563, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.46/4.75 cnf(i_0_4546, plain, (hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)))). 4.46/4.75 cnf(i_0_479, plain, (c_Nitpick_Opair__box_Opair__box__rec(X1,X2,X3,X4,c_Nitpick_Opair__box_OPairBox(X1,X2,X5,X6))=hAPP(hAPP(X4,X5),X6))). 4.46/4.75 cnf(i_0_3397, plain, (c_Nitpick_Opair__box_Opair__box__case(X1,X2,X3,X4,c_Nitpick_Opair__box_OPairBox(X1,X2,X5,X6))=hAPP(hAPP(X4,X5),X6))). 4.46/4.75 cnf(i_0_2037, plain, (hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))). 4.46/4.75 cnf(i_0_5809, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),X2,c_Product__Type_Osnd(X1,X2)),X3)=hAPP(c_Relation_ORange(X1,X2),X3))). 4.46/4.75 cnf(i_0_4895, plain, (hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2)=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_4347, plain, (c_Hilbert__Choice_OEps(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2)). 4.46/4.75 cnf(i_0_4455, plain, (c_HOL_OThe(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2)). 4.46/4.75 cnf(i_0_1560, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),X3)=hAPP(c_Relation_ODomain(X1,X2),X3))). 4.46/4.75 cnf(i_0_1830, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X1),c_COMBK(X1,X2)),X3)=hAPP(c_Product__Type_Ofst(X1,X2),X3))). 4.46/4.75 cnf(i_0_2608, plain, (c_List_Oremove1(X1,X2,hAPP(c_List_Ofilter(X1,X3),X4))=hAPP(c_List_Ofilter(X1,X3),c_List_Oremove1(X1,X2,X4)))). 4.46/4.75 cnf(i_0_6544, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))). 4.46/4.75 cnf(i_0_4790, plain, (c_Smallcheck_Ofull__small_H(X1,hAPP(c_Code__Numeral_Oint__of,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X2)))=c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,X1,X2))). 4.46/4.75 cnf(i_0_1999, plain, (hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))). 4.46/4.75 cnf(i_0_1227, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1))))=hAPP(c_Nat_OSuc,c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1)))). 4.46/4.75 cnf(i_0_5656, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X2)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2))). 4.46/4.75 cnf(i_0_6763, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_2363, plain, (c_List_Olists(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=hAPP(c_fequal,c_List_Olist_ONil(X1)))). 4.46/4.75 cnf(i_0_6575, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))). 4.46/4.75 cnf(i_0_2293, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))). 4.46/4.75 cnf(i_0_6818, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X1),X2)))). 4.46/4.75 cnf(i_0_3148, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X1),X2)))). 4.46/4.75 cnf(i_0_6459, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))))). 4.46/4.75 cnf(i_0_2365, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X1,X2,X3))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X3)))). 4.46/4.75 cnf(i_0_34, plain, (c_Sum__Type_OPlus(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_174, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.75 cnf(i_0_2395, plain, (c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1),X2))). 4.46/4.75 cnf(i_0_6914, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))). 4.46/4.75 cnf(i_0_439, plain, (hAPP(c_Product__Type_Ofst(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Opartition(X1,X2,X3))=hAPP(c_List_Ofilter(X1,X2),X3))). 4.46/4.75 cnf(i_0_2759, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))))). 4.46/4.75 cnf(i_0_2863, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2))). 4.46/4.75 cnf(i_0_2299, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)))). 4.46/4.75 cnf(i_0_2646, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oimage(X2,tc_fun(X1,tc_HOL_Obool),X3),X4))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X4),X3))). 4.46/4.75 cnf(i_0_1781, plain, (c_Option_Ooption_Ooption__size(X1,X2,hAPP(c_Option_Ooption_OSome(X1),X3))=hAPP(c_Nat_OSuc,hAPP(X2,X3)))). 4.46/4.75 cnf(i_0_2097, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oimage(X2,tc_fun(X1,tc_HOL_Obool),X3),X4))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X4),X3))). 4.46/4.75 cnf(i_0_3637, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OSKIP),X3))))). 4.46/4.75 cnf(i_0_4838, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))). 4.46/4.75 cnf(i_0_169, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))). 4.46/4.75 cnf(i_0_761, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),X2))). 4.46/4.75 cnf(i_0_3811, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X1),X2))). 4.46/4.75 cnf(i_0_3780, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X1),X2))). 4.46/4.75 cnf(i_0_3247, plain, (c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))). 4.46/4.75 cnf(i_0_5714, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),X2))). 4.46/4.75 cnf(i_0_7064, plain, (c_Sum__Type_OPlus(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X1,X2),tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_46, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))))). 4.46/4.75 cnf(i_0_6553, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.46/4.75 cnf(i_0_2113, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Oreplicate(X1,X4,X5))=c_List_Oreplicate(X2,X4,hAPP(X3,X5)))). 4.46/4.75 cnf(i_0_6996, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.46/4.75 cnf(i_0_960, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2)))). 4.46/4.75 cnf(i_0_701, plain, (hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,tc_prod(X2,X3)),X4),c_Product__Type_OPair(X2,X3))=X4)). 4.46/4.75 cnf(i_0_4698, plain, (c_Map_Omap__add(X1,X2,c_Map_Omap__add(X1,X2,X3,X4),X5)=c_Map_Omap__add(X1,X2,X3,c_Map_Omap__add(X1,X2,X4,X5)))). 4.46/4.75 cnf(i_0_3069, plain, (hAPP(c_Relation_Oconverse(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel1(X1,X2))=c_List_Olistrel1(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)))). 4.46/4.75 cnf(i_0_3548, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4))=X2)). 4.46/4.75 cnf(i_0_5264, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4))=X2)). 4.46/4.75 cnf(i_0_510, plain, (c_Smallcheck_Osmall_H(X1,hAPP(c_Code__Numeral_Oint__of,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X2)))=hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),X1),X2))). 4.46/4.75 cnf(i_0_1372, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Obutlast(X1,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 4.46/4.75 cnf(i_0_1744, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)=hAPP(c_Finite__Set_Ocard(X1),X2))). 4.46/4.75 cnf(i_0_3269, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X3)),X4)=X4)). 4.46/4.75 cnf(i_0_518, plain, (c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat))))). 4.46/4.75 cnf(i_0_6798, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X3))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_7248, plain, (c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))). 4.46/4.75 cnf(i_0_3835, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X2))=c_Transitive__Closure_Ortrancl(X1,X2))). 4.46/4.75 cnf(i_0_3582, plain, (c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))=c_Transitive__Closure_Ortrancl(X1,X2))). 4.46/4.75 cnf(i_0_6960, plain, (c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBB(X2,tc_Option_Ooption(X2),X1),c_Option_Ooption_OSome(X2)),X3))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_5373, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_1797, plain, (hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))). 4.46/4.75 cnf(i_0_406, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X4)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_6292, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.46/4.75 cnf(i_0_2247, plain, (hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))). 4.46/4.75 cnf(i_0_4694, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.46/4.75 cnf(i_0_2120, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.46/4.75 cnf(i_0_4509, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.46/4.75 cnf(i_0_1310, plain, (hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))). 4.46/4.75 cnf(i_0_994, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))))). 4.46/4.75 cnf(i_0_1519, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X2),X3),c_Transitive__Closure_Ortrancl(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_HOL_Obool))))=X3)). 4.46/4.75 cnf(i_0_6766, plain, (hAPP(c_List_Olist_Olist__case(X1,X2,X3,X4),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X6))=hAPP(hAPP(X4,X5),X6))). 4.46/4.75 cnf(i_0_4413, plain, (c_List_Olistset(X1,c_List_Olist_ONil(tc_fun(X1,tc_HOL_Obool)))=hAPP(c_fequal,c_List_Olist_ONil(X1)))). 4.46/4.75 cnf(i_0_6466, plain, (c_Map_Odom(X1,X2,c_Map_Orestrict__map(X1,X2,X3,X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),X4))). 4.46/4.75 cnf(i_0_4770, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),X3)=X3)). 4.46/4.75 cnf(i_0_5452, plain, (hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X1,X3),hAPP(c_Product__Type_OPair(X2,X1),X4)),X5)=hAPP(X5,X4))). 4.46/4.75 cnf(i_0_1517, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))). 4.46/4.75 cnf(i_0_739, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)))). 4.46/4.75 cnf(i_0_4664, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X2))))))). 4.46/4.75 cnf(i_0_2595, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))). 4.46/4.75 cnf(i_0_4014, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Otl(X1),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 4.46/4.75 cnf(i_0_7423, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))). 4.46/4.75 cnf(i_0_3023, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),c_List_Oreplicate(X1,X3,X4))=c_List_Oreplicate(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2),X4))). 4.46/4.75 cnf(i_0_5412, plain, (hAPP(hAPP(c_List_Otake(X1),X2),c_List_Oreplicate(X1,X3,X4))=c_List_Oreplicate(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X2),X3),X4))). 4.46/4.75 cnf(i_0_3481, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_5027, plain, (hAPP(c_Map_Orestrict__map(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),X3),X4)=c_Option_Ooption_ONone(X2))). 4.46/4.75 cnf(i_0_6835, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2))). 4.46/4.75 cnf(i_0_6432, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2))). 4.46/4.75 cnf(i_0_3635, plain, (c_Nat_Onat_Onat__case(X1,X2,hAPP(c_List_Onth(X1),X3),X4)=hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4))). 4.46/4.75 cnf(i_0_3001, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4))=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_1878, plain, (c_Map_Omap__upds(X1,X2,c_Map_Omap__add(X1,X2,X3,X4),X5,X6)=c_Map_Omap__add(X1,X2,X3,c_Map_Omap__upds(X1,X2,X4,X5,X6)))). 4.46/4.75 cnf(i_0_2888, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(c_Product__Type_Ofst(X1,X2),X3)),hAPP(c_Product__Type_Osnd(X1,X2),X3))=X3)). 4.46/4.75 cnf(i_0_707, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Odrop(X1),X2),X3))=X3)). 4.46/4.75 cnf(i_0_6468, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.46/4.75 cnf(i_0_1964, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),X3)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.46/4.75 cnf(i_0_948, plain, (c_Product__Type_Oprod_Oprod__rec(X1,X2,X3,X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6))=hAPP(hAPP(X4,X5),X6))). 4.46/4.75 cnf(i_0_2172, plain, (hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2))). 4.46/4.75 cnf(i_0_2314, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Odrop(X1),X2),X4))). 4.46/4.75 cnf(i_0_3754, plain, (hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))=hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))). 4.46/4.75 cnf(i_0_3118, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 4.46/4.75 cnf(i_0_5244, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.46/4.75 cnf(i_0_6382, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(c_Nat_OSuc,X4))=hAPP(hAPP(c_List_Onth(X1),X3),X4))). 4.46/4.75 cnf(i_0_1518, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2))). 4.46/4.75 cnf(i_0_7103, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))). 4.46/4.75 cnf(i_0_2692, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),X2))))). 4.46/4.75 cnf(i_0_943, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))). 4.46/4.75 cnf(i_0_6711, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.75 cnf(i_0_6355, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X1))))). 4.46/4.75 cnf(i_0_4881, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X1))))). 4.46/4.75 cnf(i_0_311, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(hAPP(c_List_Oappend(X1),X2),X3))=X2)). 4.46/4.75 cnf(i_0_2112, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))). 4.46/4.75 cnf(i_0_6713, plain, (hAPP(hAPP(c_List_Otake(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))). 4.46/4.75 cnf(i_0_3511, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X2),X1))). 4.46/4.75 cnf(i_0_2533, plain, (hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X2)),X3))=hAPP(hAPP(c_List_Otake(X1),X2),hAPP(c_List_Otl(X1),X3)))). 4.46/4.75 cnf(i_0_3871, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X3)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.46/4.75 cnf(i_0_316, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X3)))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.46/4.75 cnf(i_0_6709, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1)))))). 4.46/4.75 cnf(i_0_6657, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Odrop(X1),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2))). 4.46/4.75 cnf(i_0_7251, plain, (c_Nitpick_Onorm__frac(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))). 4.46/4.75 cnf(i_0_363, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Otake(X1),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2))). 4.46/4.75 cnf(i_0_4429, plain, (hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3))=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X2)),X3))). 4.46/4.75 cnf(i_0_2659, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_Enum_On__lists(X1,X2,X3))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2))). 4.46/4.75 cnf(i_0_6961, plain, (c_Hoare__Mirabelle_Otriple_Otriple__rec(X1,X2,X3,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X4),X5),X6))=hAPP(hAPP(hAPP(X3,X4),X5),X6))). 4.46/4.75 cnf(i_0_2074, plain, (c_Hoare__Mirabelle_Otriple_Otriple__case(X1,X2,X3,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X4),X5),X6))=hAPP(hAPP(hAPP(X3,X4),X5),X6))). 4.46/4.75 cnf(i_0_448, plain, (hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1))))). 4.46/4.75 cnf(i_0_6569, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)=c_List_OtakeWhile(X1,X2,X3))). 4.46/4.75 cnf(i_0_2771, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)))). 4.46/4.75 cnf(i_0_310, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(hAPP(c_List_Oappend(X1),X2),X3))=X3)). 4.46/4.75 cnf(i_0_2711, plain, (hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))=c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_1670, plain, (hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4)=hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))). 4.46/4.75 cnf(i_0_5380, plain, (c_Map_Orestrict__map(X1,X2,c_Map_Orestrict__map(X1,X2,X3,X4),X5)=c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5)))). 4.46/4.75 cnf(i_0_6351, plain, (c_Divides_OnegDivAlg(c_Int_OMin,X1)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)))). 4.46/4.75 cnf(i_0_5736, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1))))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X1)))). 4.46/4.75 cnf(i_0_397, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6))=hAPP(hAPP(X4,X5),X6))). 4.46/4.75 cnf(i_0_3364, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))=X2)). 4.46/4.75 cnf(i_0_872, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3),X2)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2))). 4.46/4.75 cnf(i_0_66, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X1)),hAPP(c_fequal,X1))=hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X1))). 4.46/4.75 cnf(i_0_6093, plain, (c_Finite__Set_Ofold(X1,X2,hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X1),X3),X4))=hAPP(c_Finite__Set_Ofold__image(X2,X1,X3),X4))). 4.46/4.75 cnf(i_0_692, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),X3)))). 4.46/4.75 cnf(i_0_249, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2)=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))). 4.46/4.75 cnf(i_0_7383, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.46/4.75 cnf(i_0_3286, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2)). 4.46/4.75 cnf(i_0_4264, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))). 4.46/4.75 cnf(i_0_2379, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))). 4.46/4.75 cnf(i_0_1113, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))). 4.46/4.75 cnf(i_0_2461, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)))). 4.46/4.75 cnf(i_0_5860, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Orev(X1),X2)),hAPP(c_List_Orev(X1),X3))=hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Oappend(X1),X3),X2)))). 4.46/4.75 cnf(i_0_5257, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))). 4.46/4.75 cnf(i_0_4312, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))). 4.46/4.75 cnf(i_0_3057, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))). 4.46/4.75 cnf(i_0_3977, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)))). 4.46/4.75 cnf(i_0_6352, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),X3)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))). 4.46/4.75 cnf(i_0_313, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)))). 4.46/4.75 cnf(i_0_6790, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))). 4.46/4.75 cnf(i_0_3974, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),X2)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,X2))=c_Code__Numeral_Odiv__mod__code__numeral(X1,X2))). 4.46/4.75 cnf(i_0_1499, plain, (hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Otake(X1),X3),X4))=hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X2),X3)),X4))). 4.46/4.75 cnf(i_0_1067, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Odrop(X1),X3),X4))=hAPP(hAPP(c_List_Odrop(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X4))). 4.46/4.75 cnf(i_0_2706, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4)=hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)))). 4.46/4.75 cnf(i_0_6832, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),X4)=hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)))). 4.46/4.75 cnf(i_0_6410, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),X3),hAPP(X3,X4))=hAPP(X3,hAPP(hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),X3),X4)))). 4.46/4.75 cnf(i_0_2125, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))=c_List_Obutlast(X1,X2))). 4.46/4.75 cnf(i_0_5242, plain, (c_Predicate_Opred__comp(X1,X2,X3,c_Predicate_Oconversep(X2,X1,X4),c_Predicate_Oconversep(X3,X2,X5))=c_Predicate_Oconversep(X3,X1,c_Predicate_Opred__comp(X3,X2,X1,X5,X4)))). 4.46/4.75 cnf(i_0_4226, plain, (hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)),X3),X5)=hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X5))). 4.46/4.75 cnf(i_0_3109, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 4.46/4.75 cnf(i_0_5077, plain, (hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,X4),X5),X6),X7)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X4),X6),hAPP(X5,X7)))). 4.46/4.75 cnf(i_0_1574, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Oimage(tc_Nat_Onat,X1,X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X3)))))). 4.46/4.75 cnf(i_0_44, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X1),X2)),hAPP(c_Relation_ORange(X1,X1),X2))=hAPP(c_Relation_OField(X1),X2))). 4.46/4.75 cnf(i_0_5587, plain, (c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))). 4.46/4.75 cnf(i_0_3693, plain, (c_List_Oremdups(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Oremdups(X2,X4)))=c_List_Oremdups(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)))). 4.46/4.75 cnf(i_0_974, plain, (c_Fun_Oinj__on(X1,tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_928, plain, (hAPP(c_List_Oset(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3))=hAPP(c_List_Oset(X1),X3))). 4.46/4.75 cnf(i_0_7369, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))). 4.46/4.75 cnf(i_0_7262, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Ortrancl(X1,X3))))). 4.46/4.75 cnf(i_0_3997, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X2,X3))),hAPP(c_List_Oset(X1),X3))))). 4.46/4.75 cnf(i_0_6901, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X3))),hAPP(c_List_Oset(X1),X2))))). 4.46/4.75 cnf(i_0_5426, plain, (hAPP(c_Relation_ODomain(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))=hAPP(c_Relation_ODomain(X1,X1),X2))). 4.46/4.75 cnf(i_0_6108, plain, (hAPP(c_Relation_ORange(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))=hAPP(c_Relation_ORange(X1,X1),X2))). 4.46/4.75 cnf(i_0_6197, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)=c_List_Obutlast(X1,X2))). 4.46/4.75 cnf(i_0_2201, plain, (hAPP(c_Product__Type_Osnd(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Opartition(X1,X2,X3))=hAPP(c_List_Ofilter(X1,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X1,c_fNot),X2)),X3))). 4.46/4.75 cnf(i_0_2446, plain, (hAPP(c_Product__Type_Osnd(X1,X2),hAPP(c_Product__Type_Omap__pair(X3,X1,X4,X2,X5,X6),X7))=hAPP(X6,hAPP(c_Product__Type_Osnd(X3,X4),X7)))). 4.46/4.75 cnf(i_0_2220, plain, (hAPP(c_Product__Type_Ofst(X1,X2),hAPP(c_Product__Type_Omap__pair(X3,X1,X4,X2,X5,X6),X7))=hAPP(X5,hAPP(c_Product__Type_Ofst(X3,X4),X7)))). 4.46/4.75 cnf(i_0_2645, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))). 4.46/4.75 cnf(i_0_3164, plain, (c_Relation_Oirrefl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))))). 4.46/4.75 cnf(i_0_7422, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))). 4.46/4.75 cnf(i_0_2003, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))). 4.46/4.75 cnf(i_0_2910, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3))=hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)))). 4.46/4.75 cnf(i_0_124, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3))),hAPP(c_List_Oset(X1),X3))))). 4.46/4.75 cnf(i_0_2306, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_Enum_Osublists(X1,X2))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))). 4.46/4.75 cnf(i_0_4163, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3))),hAPP(c_List_Oset(X1),X3))))). 4.46/4.75 cnf(i_0_5429, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))). 4.46/4.75 cnf(i_0_4756, plain, (c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),c_List_Otranspose(X1,X2)))))). 4.46/4.75 cnf(i_0_217, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X1)),hAPP(c_fequal,hAPP(c_Nat_OSuc,X1)))=hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)))). 4.46/4.75 cnf(i_0_2255, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))))))). 4.46/4.75 cnf(i_0_4757, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.46/4.75 cnf(i_0_3960, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.46/4.75 cnf(i_0_5342, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.46/4.75 cnf(i_0_6015, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X2),hAPP(c_COMBK(tc_fun(X2,X2),X1),c_COMBI(X2))),X3)=hAPP(c_Product__Type_Osnd(X1,X2),X3))). 4.46/4.75 cnf(i_0_1245, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),c_Map_Odom(X1,X2,X4))=c_Map_Odom(X1,X2,c_Map_Omap__add(X1,X2,X4,X3)))). 4.46/4.75 cnf(i_0_2653, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_OPow(X1),X3))=hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.46/4.75 cnf(i_0_1090, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X2),X3)),X4))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_3220, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X2)))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X2)))). 4.46/4.75 cnf(i_0_7428, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))))=hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X2))). 4.46/4.75 cnf(i_0_2129, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_1077, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))). 4.46/4.75 cnf(i_0_5754, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3))). 4.46/4.75 cnf(i_0_4898, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X3))). 4.46/4.75 cnf(i_0_6808, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3))). 4.46/4.75 cnf(i_0_4716, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),X3))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3)))). 4.46/4.75 cnf(i_0_3147, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Oreplicate(X1,X2,X3)),c_List_Oreplicate(X1,X4,X3))=c_List_Oreplicate(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4),X3))). 4.46/4.75 cnf(i_0_2834, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)),X3))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3)))). 4.46/4.75 cnf(i_0_7394, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olistsp(X1,X2)),c_List_Olistsp(X1,X3))=c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.46/4.75 cnf(i_0_3983, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X3),X2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X3),X2))). 4.46/4.75 cnf(i_0_6342, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X3),X2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3),X2))). 4.46/4.75 cnf(i_0_7299, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.46/4.75 cnf(i_0_2083, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),hAPP(c_Map_Omap__of(X2,X1),X3)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))))). 4.46/4.75 cnf(i_0_2470, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Olist_OCons(X1),X3),hAPP(hAPP(c_List_Otake(X1),X2),X4)))). 4.46/4.75 cnf(i_0_2204, plain, (c_List_Oreplicate(X1,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,hAPP(c_fequal,X2)),X3)),X2)=hAPP(c_List_Ofilter(X1,hAPP(c_fequal,X2)),X3))). 4.46/4.75 cnf(i_0_4765, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.46/4.75 cnf(i_0_5432, plain, (hAPP(c_Set_Ovimage(X1,X2,X3),X4)=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3))). 4.46/4.75 cnf(i_0_6146, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,X2),hAPP(hAPP(c_Nat_Ocompow(X1,X1),X3),X2))=hAPP(hAPP(c_Nat_Ocompow(X1,X1),hAPP(c_Nat_OSuc,X3)),X2))). 4.46/4.75 cnf(i_0_6014, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_6921, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_COMBI(X1))=X2)). 4.46/4.75 cnf(i_0_813, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1))=X2)). 4.46/4.75 cnf(i_0_5758, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X3)=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_2109, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X4),X3))),X4)))). 4.46/4.75 cnf(i_0_3628, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_COMBB(X3,tc_HOL_Obool,X1),hAPP(hAPP(c_Set_Oinsert(X3),hAPP(X4,X2)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X4))))). 4.46/4.75 cnf(i_0_3904, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),X3))). 4.46/4.75 cnf(i_0_3029, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))). 4.46/4.75 cnf(i_0_2568, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))=X1)). 4.46/4.75 cnf(i_0_4405, plain, (hAPP(c_Option_Ooption_OSome(tc_prod(X1,tc_Lazy__Sequence_Olazy__sequence(X1))),hAPP(hAPP(c_Product__Type_OPair(X1,tc_Lazy__Sequence_Olazy__sequence(X1)),X2),X3))=hAPP(c_Lazy__Sequence_Oyield(X1),c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3)))). 4.46/4.75 cnf(i_0_5379, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),c_List_Oreplicate(tc_List_Olist(X1),X2,c_List_Olist_ONil(X1)))=c_List_Olist_ONil(X1))). 4.46/4.75 cnf(i_0_7300, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))=c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_2700, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X2,c_Option_Ooption_ONone(X1),hAPP(c_COMBK(tc_Option_Ooption(X1),X2),c_Option_Ooption_ONone(X1))),hAPP(X3,X4))=c_Option_Ooption_ONone(X1))). 4.46/4.75 cnf(i_0_2430, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.46/4.75 cnf(i_0_7445, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))). 4.46/4.75 cnf(i_0_3883, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X1,X2))=c_List_Olex(X1,X2))). 4.46/4.75 cnf(i_0_6744, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(X1)),c_Option_Ooption_ONone(X1)),hAPP(c_Set_Oimage(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_2902, plain, (c_Random_Oselect__weight(X1,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X1)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X1),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X2)),X3))=c_Random_Oselect__weight(X1,X3))). 4.46/4.75 cnf(i_0_5863, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))=X3)). 4.46/4.75 cnf(i_0_2715, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),X2)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3),X2))). 4.46/4.75 cnf(i_0_5746, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)))). 4.46/4.75 cnf(i_0_7376, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X3)),X2))). 4.46/4.75 cnf(i_0_5064, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))). 4.46/4.75 cnf(i_0_2123, plain, (c_Fun_Oinj__on(X1,tc_prod(X2,X1),esk157_4(X3,X4,X2,X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X4),X3)))). 4.46/4.75 cnf(i_0_728, plain, (hAPP(c_Set_Oimage(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),c_List_Oset(X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_Osublists(X1,X2)))=hAPP(c_Set_OPow(X1),hAPP(c_List_Oset(X1),X2)))). 4.46/4.75 cnf(i_0_6238, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Orev(X1),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))=hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)))). 4.46/4.75 cnf(i_0_5340, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X1),X3))=hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)))). 4.46/4.75 cnf(i_0_525, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.46/4.75 cnf(i_0_7060, plain, (hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X1),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3)))=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)),X3)))). 4.46/4.75 cnf(i_0_6061, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))=c_Transitive__Closure_Ortrancl(X1,X2))). 4.46/4.75 cnf(i_0_1305, plain, (c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X2,c_Option_Ooption_ONone(X1),hAPP(hAPP(c_COMBB(X1,tc_Option_Ooption(X1),X2),c_Option_Ooption_OSome(X1)),X3))=hAPP(c_Option_Omap(X2,X1),X3))). 4.46/4.75 cnf(i_0_30, plain, (c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))=c_Transitive__Closure_Ortrancl(X1,X2))). 4.46/4.75 cnf(i_0_3340, plain, (c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))=c_Transitive__Closure_Ortrancl(X1,X2))). 4.46/4.75 cnf(i_0_181, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)))). 4.46/4.75 cnf(i_0_1380, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Ofilter(X1,X2),X3)),hAPP(c_List_Ofilter(X1,X2),X4))=hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)))). 4.46/4.75 cnf(i_0_3943, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Osplice(X1,X2,X3))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)))). 4.46/4.75 cnf(i_0_6489, plain, (hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),hAPP(hAPP(c_Nat_Ocompow(X1,X1),X3),X4))=hAPP(hAPP(c_Nat_Ocompow(X1,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X4))). 4.46/4.75 cnf(i_0_4785, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)))). 4.46/4.75 cnf(i_0_4148, plain, (hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),X3),c_Option_Ooption_ONone(X2)),X4)=c_Option_Ooption_ONone(X2))). 4.46/4.75 cnf(i_0_4375, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OField(X1),X2)),hAPP(c_Relation_OField(X1),X3))=hAPP(c_Relation_OField(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.46/4.75 cnf(i_0_4064, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)))))). 4.46/4.75 cnf(i_0_1104, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3)),X4))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_653, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X3)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))). 4.46/4.75 cnf(i_0_7282, plain, (hAPP(c_List_Ofoldl(X1,X2,X3,hAPP(c_List_Ofoldl(X1,X2,X3,X4),X5)),X6)=hAPP(c_List_Ofoldl(X1,X2,X3,X4),hAPP(hAPP(c_List_Oappend(X2),X5),X6)))). 4.46/4.75 cnf(i_0_5570, plain, (hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(c_Nat_OSuc,X4)),X5)=hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist__update(X1,X3),X4),X5)))). 4.46/4.75 cnf(i_0_3956, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X3)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)))). 4.46/4.75 cnf(i_0_6727, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)))=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X1,X2)))). 4.46/4.75 cnf(i_0_4423, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X3)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)))). 4.46/4.75 cnf(i_0_1222, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))). 4.46/4.75 cnf(i_0_2552, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))). 4.46/4.75 cnf(i_0_7147, plain, (c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X1)),X2)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))). 4.46/4.75 cnf(i_0_1531, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),X1,hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1)),X2)=hAPP(c_List_Orev(X1),X2))). 4.46/4.75 cnf(i_0_2183, plain, (hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),X2)),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.46/4.75 cnf(i_0_945, plain, (hAPP(c_Lazy__Sequence_Obind(X1,X2,hAPP(X3,X4)),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)),X5),X4))=hAPP(c_New__DSequence_Opos__bind(X1,X2,X3,X5),X4))). 4.46/4.75 cnf(i_0_2251, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel(X1,X2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2)))))). 4.46/4.75 cnf(i_0_5757, plain, (hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2)),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.46/4.75 cnf(i_0_4845, plain, (c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1)))). 4.46/4.75 cnf(i_0_5929, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))). 4.46/4.75 cnf(i_0_245, plain, (c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))))). 4.46/4.75 cnf(i_0_6304, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Ofilter(X1,X3),X4))=hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)),X4))). 4.46/4.75 cnf(i_0_2240, plain, (c_Map_Omap__add(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3),hAPP(c_Map_Omap__of(X1,X2),X4))=hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),X4),X3)))). 4.46/4.75 cnf(i_0_3221, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),hAPP(c_COMBK(X1,tc_Nat_Onat),X2)),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))=c_List_Oreplicate(X1,X3,X2))). 4.46/4.75 cnf(i_0_1006, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X1,tc_Nat_Onat),X3),X2)))=c_List_Olist_Olist__size(X1,X3,X2))). 4.46/4.75 cnf(i_0_4842, plain, (c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X1)),X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))). 4.46/4.75 cnf(i_0_1688, plain, (hAPP(c_fequal,hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X2))). 4.46/4.75 cnf(i_0_1154, plain, (c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X1),hAPP(hAPP(c_Option_Omap(X2,X1),X3),X4),c_Lazy__Sequence_Ohb__map(X2,X1,X3,X5))=c_Lazy__Sequence_Ohb__map(X2,X1,X3,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X2),X4,X5)))). 4.46/4.75 cnf(i_0_5597, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))). 4.46/4.75 cnf(i_0_3996, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))). 4.46/4.75 cnf(i_0_1019, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))). 4.46/4.75 cnf(i_0_484, plain, (hAPP(c_Set_Oimage(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3)),hAPP(c_Set_OPow(X1),X4))=hAPP(c_Set_OPow(X2),hAPP(c_Set_Oimage(X1,X2,X3),X4)))). 4.46/4.75 cnf(i_0_5776, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)))). 4.46/4.75 cnf(i_0_691, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)))). 4.46/4.75 cnf(i_0_2179, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)),hAPP(hAPP(c_List_Odrop(X1),X3),X4))=hAPP(hAPP(c_List_Odrop(X1),X3),hAPP(hAPP(c_List_Otake(X1),X2),X4)))). 4.46/4.75 cnf(i_0_467, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))))). 4.46/4.75 cnf(i_0_7122, plain, (c_Nitpick_Opair__box_Opair__box__size(X1,X2,X3,X4,c_Nitpick_Opair__box_OPairBox(X1,X2,X5,X6))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X3,X5)),hAPP(c_Nat_OSuc,hAPP(X4,X6))))). 4.46/4.75 cnf(i_0_6920, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)),X2))). 4.46/4.75 cnf(i_0_1409, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2))). 4.46/4.75 cnf(i_0_202, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X3)),X2))). 4.46/4.75 cnf(i_0_2716, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),X2))). 4.46/4.75 cnf(i_0_3224, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X1),X3)),X2))). 4.46/4.75 cnf(i_0_6078, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)),X4))=hAPP(hAPP(c_List_Otake(X1),X3),hAPP(hAPP(c_List_Odrop(X1),X2),X4)))). 4.46/4.75 cnf(i_0_5713, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5)),X4),X6)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X6))). 4.46/4.75 cnf(i_0_5729, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),hAPP(c_List_Onth(X1),X2)),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))=X2)). 4.46/4.75 cnf(i_0_1573, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3))=X3)). 4.46/4.75 cnf(i_0_7196, plain, (c_HOL_OThe(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),hAPP(c_fequal,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=c_Set_Othe__elem(X1,X2))). 4.46/4.75 cnf(i_0_3952, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),c_Set_Ovimage(X2,X1,X4))=hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4))). 4.46/4.75 cnf(i_0_4739, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5))=hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5)))). 4.46/4.75 cnf(i_0_3225, hypothesis, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Com_Ocom,c_Com_Ocom_OBODY),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),v_F))). 4.46/4.75 cnf(i_0_4374, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),c_Int_Onat),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X1)=X1)). 4.46/4.75 cnf(i_0_5985, hypothesis, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),v_F),hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,c_Option_Othe(tc_Com_Ocom)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom),c_Com_Obody),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))))))). 4.46/4.75 cnf(i_0_703, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X3)),X3)=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X2)),X3))). 4.46/4.75 cnf(i_0_848, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X4,X5,X6),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X7),X8))=hAPP(hAPP(c_Product__Type_OPair(X2,X4),hAPP(X5,X7)),hAPP(X6,X8)))). 4.46/4.75 cnf(i_0_2249, plain, (hAPP(hAPP(c_Nat_Ocompow(tc_fun(X1,X2),tc_fun(X1,X2)),X3),c_Fun_Ocomp(X2,X2,X1,X4))=c_Fun_Ocomp(X2,X2,X1,hAPP(hAPP(c_Nat_Ocompow(X2,X2),X3),X4)))). 4.46/4.75 cnf(i_0_2806, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))),hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(c_List_Oset(X1),X2)))))). 4.46/4.75 cnf(i_0_3189, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X4)),X5),hAPP(X3,X5))=c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)))). 4.46/4.75 cnf(i_0_2471, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X4))=hAPP(hAPP(c_List_Onth(X1),X3),X4))). 4.46/4.75 cnf(i_0_281, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(X2,tc_List_Olist(X1)),X3),X4))=c_List_Omaps(X2,X1,X3,X4))). 4.46/4.75 cnf(i_0_5123, plain, (c_List_Osplice(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))=hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X4),c_List_Osplice(X1,X3,X5))))). 4.46/4.75 cnf(i_0_7341, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Otake(X1),X3),X2)))). 4.46/4.75 cnf(i_0_4340, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Odrop(X1),X3),X2)))). 4.46/4.75 cnf(i_0_1912, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Oreplicate(X1,X2,X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Olist_OCons(X1),X3),hAPP(hAPP(c_List_Oappend(X1),c_List_Oreplicate(X1,X2,X3)),X4)))). 4.46/4.75 cnf(i_0_399, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3))=hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),X3))). 4.46/4.75 cnf(i_0_553, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_OtakeWhile(X1,hAPP(c_Fun_Ocomp(X2,tc_HOL_Obool,X1,X4),X3),X5))=c_List_OtakeWhile(X2,X4,hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)))). 4.46/4.75 cnf(i_0_4009, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.46/4.75 cnf(i_0_1187, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.46/4.75 cnf(i_0_3827, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.46/4.75 cnf(i_0_1785, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.46/4.75 cnf(i_0_4408, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3))). 4.46/4.75 cnf(i_0_5169, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.46/4.75 cnf(i_0_1139, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3))). 4.46/4.75 cnf(i_0_227, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))=hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X5)))). 4.46/4.75 cnf(i_0_7219, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3))). 4.46/4.75 cnf(i_0_143, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))). 4.46/4.75 cnf(i_0_7195, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))). 4.46/4.75 cnf(i_0_3903, plain, (hAPP(c_Relation_ORange(X1,X2),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))=hAPP(hAPP(c_Set_Oinsert(X2),X4),hAPP(c_Relation_ORange(X1,X2),X5)))). 4.46/4.75 cnf(i_0_6485, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel1(X1,c_Transitive__Closure_Ortrancl(X1,X2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2)))))). 4.46/4.75 cnf(i_0_2985, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X2),X4)),X5))=hAPP(hAPP(c_Set_Oinsert(X2),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)))). 4.46/4.75 cnf(i_0_1602, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool))),X4))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)))). 4.46/4.75 cnf(i_0_1246, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool))),X4))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)))). 4.46/4.75 cnf(i_0_6634, plain, (c_Map_Odom(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3))=hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)))). 4.46/4.75 cnf(i_0_3386, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)))))). 4.46/4.75 cnf(i_0_6288, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),c_Predicate_Oconversep(X2,X1,X3)),c_Predicate_Oconversep(X2,X1,X4))=c_Predicate_Oconversep(X2,X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_fun(X1,tc_HOL_Obool))),X3),X4)))). 4.46/4.75 cnf(i_0_3772, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),X1),c_Set_OPow(X2)),X4))=hAPP(c_Set_OPow(X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)))). 4.46/4.75 cnf(i_0_3950, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),c_Predicate_Oconversep(X2,X1,X3)),c_Predicate_Oconversep(X2,X1,X4))=c_Predicate_Oconversep(X2,X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_fun(X1,tc_HOL_Obool))),X3),X4)))). 4.46/4.75 cnf(i_0_1402, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))=c_Wellfounded_Opred__nat)). 4.46/4.75 cnf(i_0_611, plain, (hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),X1),c_member(X2)),X3)),X4)=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3))). 4.46/4.75 cnf(i_0_3735, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4))=hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))). 4.46/4.75 cnf(i_0_2567, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ORange(X2,X1),X3)),hAPP(c_Relation_ORange(X2,X1),X4))=hAPP(c_Relation_ORange(X2,X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4)))). 4.46/4.75 cnf(i_0_987, plain, (c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3)))=c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.46/4.75 cnf(i_0_2609, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)),X3)=hAPP(c_Option_Ooption_OSome(X2),X4))). 4.46/4.75 cnf(i_0_1212, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3))=hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),X2),X3))). 4.46/4.75 cnf(i_0_7089, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))))). 4.46/4.75 cnf(i_0_5561, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Relation_OId__on(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))))). 4.46/4.75 cnf(i_0_4283, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Ofilter(X1,hAPP(c_Fun_Ocomp(X2,tc_HOL_Obool,X1,X4),X3)),X5))=hAPP(c_List_Ofilter(X2,X4),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)))). 4.46/4.75 cnf(i_0_2655, plain, (hAPP(c_List_Orotate1(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3))=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(c_Nat_OSuc,X2)),c_List_Orotate1(X1)),X3))). 4.46/4.75 cnf(i_0_5032, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),hAPP(c_Relation_Oconverse(X2,X1),X4)),hAPP(c_Relation_Oconverse(X3,X2),X5))=hAPP(c_Relation_Oconverse(X3,X1),hAPP(hAPP(c_Relation_Orel__comp(X3,X2,X1),X5),X4)))). 4.46/4.75 cnf(i_0_4945, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2))),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2))),X3))). 4.46/4.75 cnf(i_0_3135, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),X3))). 4.46/4.75 cnf(i_0_5527, plain, (hAPP(c_List_Oset(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)),c_List_Oset(X1)))). 4.46/4.75 cnf(i_0_6608, plain, (c_Map_Odom(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),X3),hAPP(c_Option_Ooption_OSome(X2),X4)))=hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_1730, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(X1))),c_List_Olistrel(X1,X2))))). 4.46/4.75 cnf(i_0_4211, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),c_List_Oreplicate(X1,X3,X4)),c_List_Oreplicate(X2,X5,X6))=c_List_Oreplicate(tc_prod(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X3),X5),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X6)))). 4.46/4.75 cnf(i_0_4442, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_Oimage(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oinsert(X1),X3)),hAPP(c_Set_OPow(X1),X2)))=hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)))). 4.46/4.75 cnf(i_0_1013, plain, (hAPP(c_Option_Ooption_Ooption__case(X1,tc_prod(X2,tc_Lazy__Sequence_Olazy__sequence(X2)),X3,hAPP(c_Product__Type_Oprod_Oprod__case(X2,tc_Lazy__Sequence_Olazy__sequence(X2),X1),X4)),hAPP(c_Lazy__Sequence_Oyield(X2),X5))=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X1,X2,X3,X4,X5))). 4.46/4.75 cnf(i_0_7131, plain, (hAPP(c_Finite__Set_Ocard(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X2),X4)))). 4.46/4.75 cnf(i_0_5788, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))=hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(hAPP(c_List_Oappend(X2),X4),X5)))). 4.46/4.75 cnf(i_0_789, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),X3))). 4.46/4.75 cnf(i_0_2896, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_List_Oset(X1),X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_List_Oset(X2),X4)))=hAPP(c_List_Oset(tc_prod(X1,X2)),c_Enum_Oproduct(X1,X2,X3,X4)))). 4.46/4.75 cnf(i_0_4531, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2)))))). 4.46/4.75 cnf(i_0_2159, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X1,X2))),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)))). 4.46/4.75 cnf(i_0_1101, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Odrop(X1),X3),X4)),hAPP(hAPP(c_List_Odrop(X2),X3),X5))=hAPP(hAPP(c_List_Odrop(tc_prod(X1,X2)),X3),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5)))). 4.46/4.75 cnf(i_0_7280, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Otake(X1),X3),X4)),hAPP(hAPP(c_List_Otake(X2),X3),X5))=hAPP(hAPP(c_List_Otake(tc_prod(X1,X2)),X3),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5)))). 4.46/4.75 cnf(i_0_4062, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X5),X4))=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),X5)),X4))). 4.46/4.75 cnf(i_0_6052, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X5),X4))=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X5)),X4))). 4.46/4.75 cnf(i_0_41, plain, (c_Map_Omap__add(X1,X2,X3,hAPP(c_Map_Omap__of(X1,X2),hAPP(c_List_Orev(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))))=c_Map_Omap__upds(X1,X2,X3,X4,X5))). 4.46/4.75 cnf(i_0_4460, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X3),X5))=hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5)))). 4.46/4.75 cnf(i_0_2648, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_Oimage(X4,X2,X5)),X6))=hAPP(c_Set_Oimage(X4,X2,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6)))). 4.46/4.75 cnf(i_0_3463, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X5),X4))=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X5)),X4))). 4.46/4.75 cnf(i_0_1908, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3)),hAPP(c_List_Ofilter(X1,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X1,c_fNot),X2)),X3))=c_List_Opartition(X1,X2,X3))). 4.46/4.75 cnf(i_0_6274, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2))=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X3)),X2))). 4.46/4.75 cnf(i_0_5359, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X2,X1),X3)),hAPP(c_Relation_Oconverse(X2,X1),X4))=hAPP(c_Relation_Oconverse(X2,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4)))). 4.46/4.75 cnf(i_0_6533, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X2,X1),X3)),hAPP(c_Relation_Oconverse(X2,X1),X4))=hAPP(c_Relation_Oconverse(X2,X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4)))). 4.46/4.75 cnf(i_0_2946, plain, (c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat)),X1)),X2)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1)))). 4.46/4.75 cnf(i_0_2432, plain, (hAPP(c_Fun_Ocomp(tc_List_Olist(X1),tc_List_Olist(X2),tc_List_Olist(X3),hAPP(c_List_Omap(X1,X2),X4)),hAPP(c_List_Omap(X3,X1),X5))=hAPP(c_List_Omap(X3,X2),hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5)))). 4.46/4.75 cnf(i_0_834, plain, (hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),tc_Option_Ooption(X2),tc_Option_Ooption(X3),hAPP(c_Option_Omap(X1,X2),X4)),hAPP(c_Option_Omap(X3,X1),X5))=hAPP(c_Option_Omap(X3,X2),hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5)))). 4.46/4.75 cnf(i_0_2548, plain, (c_Lazy__Sequence_Ohb__flat(X1,c_Lazy__Sequence_Ohb__map(X2,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)),hAPP(hAPP(c_COMBC(X2,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1))),X3),X4),hAPP(X5,X4)))=hAPP(c_New__DSequence_Oneg__bind(X2,X1,X5,X3),X4))). 4.46/4.75 cnf(i_0_1086, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)))). 4.46/4.75 cnf(i_0_3409, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)))). 4.46/4.75 cnf(i_0_3187, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)))). 4.46/4.75 cnf(i_0_6584, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),X3)),hAPP(hAPP(c_Nat_Ocompow(X1,X1),X4),X3))=hAPP(hAPP(c_Nat_Ocompow(X1,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)),X3))). 4.46/4.75 cnf(i_0_6361, plain, (c_Fun_Oinj__on(tc_prod(X1,X2),tc_prod(X2,X1),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X2,X1)),hAPP(c_COMBC(X2,X1,tc_prod(X2,X1)),c_Product__Type_OPair(X2,X1))),X3))). 4.46/4.75 cnf(i_0_1131, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X2),c_Product__Type_Osnd(X1,X2)),X3))=X3)). 4.46/4.75 cnf(i_0_950, plain, (c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)),X1)),X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1)))). 4.46/4.75 cnf(i_0_4173, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X5),X4))=hAPP(c_Relation_OImage(X2,X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X5)),X4))). 4.46/4.75 cnf(i_0_1, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2))). 4.46/4.75 cnf(i_0_3687, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_OPow(X1),X3))),hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)))))). 4.46/4.75 cnf(i_0_2473, plain, (hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(c_fequal,c_List_Olist_ONil(X1)))=hAPP(c_fequal,c_List_Olist_ONil(X1)))). 4.46/4.75 cnf(i_0_1256, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2))). 4.46/4.75 cnf(i_0_3268, plain, (hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X5)=hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)))). 4.46/4.75 cnf(i_0_5011, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))=c_Transitive__Closure_Ortrancl(X1,X2))). 4.46/4.75 cnf(i_0_2832, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X5),X4))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X5)),X4))). 4.46/4.75 cnf(i_0_6198, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X5),X4))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X5)),X4))). 4.46/4.75 cnf(i_0_6508, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3)))))). 4.46/4.75 cnf(i_0_4510, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))))). 4.46/4.75 cnf(i_0_3946, plain, (hAPP(c_Relation_OField(X1),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(c_Relation_OField(X1),X4))))). 4.46/4.75 cnf(i_0_2887, plain, (c_New__Random__Sequence_Opos__bind(X1,X2,X3,hAPP(c_Fun_Ocomp(X2,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))))),X1,c_New__Random__Sequence_Opos__single(X2)),X4))=c_New__Random__Sequence_Opos__map(X1,X2,X4,X3))). 4.46/4.75 cnf(i_0_2501, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),c_List_Orotate1(X1)),X3)=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3))). 4.46/4.75 cnf(i_0_3180, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Relation_OImage(X4,X2,X5)),X6))=hAPP(c_Relation_OImage(X4,X2,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6)))). 4.46/4.75 cnf(i_0_6542, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_Ovimage(X2,X4,X5)),X6))=hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6)),X5))). 4.46/4.75 cnf(i_0_3199, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_Ovimage(X2,X4,X5)),X6))=hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6)),X5))). 4.46/4.75 cnf(i_0_7261, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Transitive__Closure_Ortrancl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool))))=c_FunDef_Opair__leq)). 4.46/4.75 cnf(i_0_2592, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4))),c_Map_Odom(X1,X2,X5))=c_Map_Odom(X1,X2,c_Map_Omap__upds(X1,X2,X5,X4,X3)))). 4.46/4.75 cnf(i_0_3200, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2),X3)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))). 4.46/4.75 cnf(i_0_3461, plain, (hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),c_List_Oset(X1))),X2)=c_List_Olists(X1,X2))). 4.46/4.75 cnf(i_0_6683, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool))),X4))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4))). 4.46/4.75 cnf(i_0_7171, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool))),X4))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4))). 4.46/4.75 cnf(i_0_4722, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,X3),X1),hAPP(c_COMBB(tc_prod(X1,X2),X3,X2),X4)),c_Product__Type_OPair(X1,X2)))=X4)). 4.46/4.75 cnf(i_0_6181, plain, (c_Map_Omap__add(X1,X2,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X4),X5),hAPP(c_Option_Ooption_OSome(X2),X6)))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__add(X1,X2,X3,X4)),X5),hAPP(c_Option_Ooption_OSome(X2),X6)))). 4.46/4.75 cnf(i_0_4841, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),hAPP(c_COMBC(X1,X2,X1),X3)),X4),X5)=hAPP(c_List_Ofoldl(X1,X2,X3,X4),X5))). 4.46/4.75 cnf(i_0_458, plain, (c_New__Random__Sequence_Oneg__bind(X1,X2,X3,hAPP(c_Fun_Ocomp(X2,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))))),X1,c_New__Random__Sequence_Oneg__single(X2)),X4))=c_New__Random__Sequence_Oneg__map(X1,X2,X4,X3))). 4.46/4.75 cnf(i_0_3172, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Set_Oinsert(X2)),X4)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))=hAPP(c_Set_Oimage(X1,X2,X4),X3))). 4.46/4.75 cnf(i_0_3215, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X3)),X4))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.75 cnf(i_0_1833, plain, (hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),X2)),X3)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.46/4.75 cnf(i_0_4862, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3))=hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))). 4.46/4.75 cnf(i_0_7356, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1))). 4.46/4.75 cnf(i_0_4268, plain, (c_Map_Omap__upds(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)),X6,X7)=c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X6),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X7)))). 4.46/4.75 cnf(i_0_5052, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3)),c_Option_Ooption_ONone(X2)))=c_Map_Odom(X1,X2,X3))). 4.46/4.75 cnf(i_0_1820, plain, (c_Divides_Odivmod__int(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))=c_Divides_Opdivmod(X1,X2))). 4.46/4.75 cnf(i_0_7105, plain, (c_Nat_Onat_Onat__case(tc_List_Olist(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Odrop(X1)),X3),X4)=hAPP(hAPP(c_List_Odrop(X1),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))). 4.46/4.75 cnf(i_0_5237, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X4))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X5)),X4))). 4.46/4.75 cnf(i_0_2328, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X4))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X5)),X4))). 4.46/4.75 cnf(i_0_450, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X4))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X5)),X4))). 4.46/4.75 cnf(i_0_1213, plain, (hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X1),X2)))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X1),X2))). 4.46/4.75 cnf(i_0_5488, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)),X4))). 4.46/4.75 cnf(i_0_3369, plain, (hAPP(c_List_Oset(X1),hAPP(c_List_Ofilter(X1,X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X3)),X2))). 4.46/4.75 cnf(i_0_3466, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),X1),c_Int_Onat)))=X1)). 4.46/4.75 cnf(i_0_6141, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))),c_List_Olexord(X1,X4))))). 4.46/4.75 cnf(i_0_4071, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4))),hAPP(X5,hAPP(c_Product__Type_Osnd(X2,X3),X4))))=c_Product__Type_Oprod_Oprod__size(X2,X3,X1,X5,X4))). 4.46/4.75 cnf(i_0_3060, plain, (c_List_OtakeWhile(tc_prod(X1,X2),hAPP(c_Fun_Ocomp(X2,tc_HOL_Obool,tc_prod(X1,X2),X3),c_Product__Type_Osnd(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))=hAPP(hAPP(c_List_Ozip(X1,X2),X4),c_List_OtakeWhile(X2,X3,X5)))). 4.46/4.75 cnf(i_0_1585, plain, (c_List_OtakeWhile(tc_prod(X1,X2),hAPP(c_Fun_Ocomp(X1,tc_HOL_Obool,tc_prod(X1,X2),X3),c_Product__Type_Ofst(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))=hAPP(hAPP(c_List_Ozip(X1,X2),c_List_OtakeWhile(X1,X3,X4)),X5))). 4.46/4.75 cnf(i_0_923, plain, (c_Random_Oselect__weight(X1,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X2))=c_Random_Oselect__weight(X1,X2))). 4.46/4.75 cnf(i_0_4432, plain, (c_Random_Opick(X1,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X2))=c_Random_Opick(X1,X2))). 4.46/4.75 cnf(i_0_4184, plain, (c_Lazy__Sequence_Oappend(tc_Option_Ooption(X1),hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)),tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)),c_Lazy__Sequence_Ohit__bound(X1),c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)))),X2),c_Lazy__Sequence_Ohb__flat(X1,X3))=c_Lazy__Sequence_Ohb__flat(X1,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1))),X2,X3)))). 4.46/4.75 cnf(i_0_3855, plain, (c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X3),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBB(tc_fun(X3,X2),tc_fun(tc_Option_Ooption(X3),tc_Option_Ooption(X2)),X1),c_Option_Omap(X3,X2)),X4)),X5))=c_Map_Odom(X1,X3,X5))). 4.46/4.75 cnf(i_0_3022, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X4))=hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)))). 4.46/4.75 cnf(i_0_5454, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3)),hAPP(hAPP(c_List_Odrop(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X4))=hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)))). 4.46/4.75 cnf(i_0_5821, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Ofilter(X1,X2),X3)),hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),X3)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))). 4.46/4.75 cnf(i_0_2156, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5)))))). 4.46/4.75 cnf(i_0_1940, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5))),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5)))))). 4.46/4.75 cnf(i_0_134, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))). 4.46/4.75 cnf(i_0_4272, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X3)))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X3))))). 4.46/4.75 cnf(i_0_3345, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))). 4.46/4.75 cnf(i_0_1962, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))=c_Int_Oint__ge__less__than2(X1))). 4.46/4.75 cnf(i_0_3219, plain, (hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),hAPP(hAPP(c_List_Omap(X2,tc_prod(X1,X2)),hAPP(c_Product__Type_OPair(X1,X2),X3)),X4)),c_Enum_Oproduct(X1,X2,X5,X4))=c_Enum_Oproduct(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X5),X4))). 4.46/4.75 cnf(i_0_1202, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)))). 4.46/4.75 cnf(i_0_5808, plain, (c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)))). 4.46/4.75 cnf(i_0_1946, plain, (c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)))). 4.46/4.75 cnf(i_0_861, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),X2),c_Set_OPow(X1)),X4))),hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)))))). 4.46/4.75 cnf(i_0_2401, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3))=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)),X3))). 4.46/4.75 cnf(i_0_5206, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),esk362_1(X1)),esk363_1(X1)))))=X1)). 4.46/4.75 cnf(i_0_3837, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))). 4.46/4.75 cnf(i_0_3163, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))). 4.46/4.75 cnf(i_0_2701, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool)),X2))=c_Transitive__Closure_Ortrancl(X1,X2))). 4.46/4.75 cnf(i_0_6287, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3))=c_List_Omaps(tc_List_Olist(X1),X1,c_List_Ofilter(X1,X2),X3))). 4.46/4.75 cnf(i_0_386, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_Map_Omap__of(X1,X2),X3)),hAPP(c_Product__Type_Ofst(X1,X2),X4)),hAPP(c_Option_Ooption_OSome(X2),hAPP(c_Product__Type_Osnd(X1,X2),X4)))=hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),X4),X3)))). 4.46/4.75 cnf(i_0_1184, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Product__Type_OSigma(X1,X2)),X4))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4))). 4.46/4.75 cnf(i_0_135, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),c_fequal))),X2))=c_Relation_OId__on(X1,X2))). 4.46/4.75 cnf(i_0_3525, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4))),hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))))). 4.46/4.75 cnf(i_0_6509, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ORange(X2,X1),X3)),hAPP(c_Relation_ORange(X2,X1),X4))),hAPP(c_Relation_ORange(X2,X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4)))))). 4.46/4.75 cnf(i_0_3626, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4)))))). 4.46/4.75 cnf(i_0_6805, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ORange(X2,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ORange(X2,X1),X3)),hAPP(c_Relation_ORange(X2,X1),X4)))))). 4.46/4.75 cnf(i_0_5321, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))),c_List_Olexord(X1,X5))))). 4.46/4.75 cnf(i_0_5946, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X6))=hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X2),tc_HOL_Obool)),X5),X6)))). 4.46/4.75 cnf(i_0_1537, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X6),X5))=hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),X4),X6)),X5))). 4.46/4.75 cnf(i_0_4674, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3))),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))))). 4.46/4.75 cnf(i_0_1288, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X4))=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),c_List_Orotate1(X1)),X4))). 4.46/4.75 cnf(i_0_3142, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))). 4.46/4.75 cnf(i_0_5249, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5))). 4.46/4.75 cnf(i_0_4052, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5))). 4.46/4.75 cnf(i_0_412, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))),X3))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3))). 4.46/4.75 cnf(i_0_2612, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5))). 4.46/4.75 cnf(i_0_5159, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3))),X3))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3))). 4.46/4.75 cnf(i_0_2434, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))). 4.46/4.75 cnf(i_0_3882, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))). 4.46/4.75 cnf(i_0_2124, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,tc_prod(X1,X2),esk157_4(X3,X4,X1,X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X4),X3))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),X3))))). 4.46/4.75 cnf(i_0_1489, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(c_List_Orev(tc_List_Olist(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Orev(X1)),X2)))=hAPP(c_List_Orev(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))). 4.46/4.75 cnf(i_0_1736, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X3),tc_HOL_Obool),X1),c_Relation_Oconverse(X3,X2)),X5))=hAPP(c_Relation_Oconverse(X3,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X3,X2),tc_HOL_Obool)),X4),X5)))). 4.46/4.75 cnf(i_0_70, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X3),tc_HOL_Obool),X1),c_Relation_Oconverse(X3,X2)),X5))=hAPP(c_Relation_Oconverse(X3,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_prod(X3,X2),tc_HOL_Obool)),X4),X5)))). 4.46/4.75 cnf(i_0_3406, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X3),X5)))))). 4.46/4.75 cnf(i_0_1501, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),X5),X6)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X4)),X5),X6))). 4.46/4.75 cnf(i_0_2531, plain, (c_HOL_OThe(tc_prod(X1,X2),hAPP(hAPP(c_COMBS(tc_prod(X1,X2),X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),tc_prod(X1,X2)),X3),c_Product__Type_Ofst(X1,X2))),c_Product__Type_Osnd(X1,X2)))=c_HOL_OThe(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3)))). 4.46/4.75 cnf(i_0_2774, plain, (c_Map_Orestrict__map(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=c_Map_Orestrict__map(X1,X2,X3,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))). 4.46/4.75 cnf(i_0_6319, plain, (c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(hAPP(c_COMBS(tc_prod(X1,X2),X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),tc_prod(X1,X2)),X3),c_Product__Type_Ofst(X1,X2))),c_Product__Type_Osnd(X1,X2)))=c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3)))). 4.46/4.75 cnf(i_0_2737, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))). 4.46/4.75 cnf(i_0_1110, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))). 4.46/4.75 cnf(i_0_1078, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X1),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),X3))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X4))),c_Com_Ocom_OWhile(X4,X5)),X3))))). 4.46/4.75 cnf(i_0_3949, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)))),c_Nitpick_Onat__gcd(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)))))=c_Nitpick_Oint__lcm(X1,X2))). 4.46/4.75 cnf(i_0_644, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist__update(X1,X3),X4),hAPP(c_Product__Type_Ofst(X1,X2),X5))),hAPP(hAPP(c_List_Olist__update(X2,X6),X4),hAPP(c_Product__Type_Osnd(X1,X2),X5)))=hAPP(hAPP(c_List_Olist__update(tc_prod(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X6)),X4),X5))). 4.46/4.75 cnf(i_0_88, plain, (hAPP(c_Fun_Ocomp(tc_prod(X1,X2),tc_prod(X3,X4),tc_prod(X5,X6),c_Product__Type_Omap__pair(X1,X3,X2,X4,X7,X8)),c_Product__Type_Omap__pair(X5,X1,X6,X2,X9,X10))=c_Product__Type_Omap__pair(X5,X3,X6,X4,hAPP(c_Fun_Ocomp(X1,X3,X5,X7),X9),hAPP(c_Fun_Ocomp(X2,X4,X6,X8),X10)))). 4.46/4.75 cnf(i_0_5042, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),hAPP(c_Relation_OField(X1),X2)),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_Relation_OField(X1),X2))))))). 4.46/4.75 cnf(i_0_5579, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))). 4.46/4.75 cnf(i_0_6754, plain, (c_Nat_Onat_Onat__case(tc_List_Olist(X1),c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_List_Olist(X1),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X1),X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Otake(X1)),X3)),X4)=hAPP(hAPP(c_List_Otake(X1),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))). 4.46/4.75 cnf(i_0_5542, plain, (hAPP(c_List_Olist_Olist__case(tc_List_Olist(X1),X1,hAPP(c_List_Otl(X1),X2),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Oappend(X1)),X2))),X3)=hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Oappend(X1),X3),X2)))). 4.46/4.75 cnf(i_0_7066, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(X1),X1,c_List_Omap__filter(X2,X1,X3,X4),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Omap__filter(X2,X1,X3,X4))),hAPP(X3,X5))=c_List_Omap__filter(X2,X1,X3,hAPP(hAPP(c_List_Olist_OCons(X2),X5),X4)))). 4.46/4.75 cnf(i_0_3812, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3)),hAPP(hAPP(c_List_Otake(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3))=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3))). 4.46/4.75 cnf(i_0_4684, plain, (hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X1),hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X1)),c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X1)),X2))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X2)))). 4.46/4.75 cnf(i_0_5927, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),X5),X6))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4),c_Relation_OImage(X2,X1,X3)),X6)))))). 4.46/4.75 cnf(i_0_3688, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))). 4.46/4.75 cnf(i_0_4304, plain, (hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X1),X1),c_Wellfounded_Olex__prod(tc_Nat_Onat,X1,c_Wellfounded_Oless__than,X2)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(tc_Nat_Onat,X1)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,tc_prod(tc_Nat_Onat,X1)),X1),c_Product__Type_OPair(tc_Nat_Onat,X1)),X3)),c_COMBI(X1)))=c_Wellfounded_Omlex__prod(X1,X3,X2))). 4.46/4.75 cnf(i_0_1045, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))=hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 4.46/4.75 cnf(i_0_183, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X5,X3),tc_HOL_Obool),tc_fun(tc_prod(X2,X3),tc_HOL_Obool),X1),hAPP(c_Relation_Orel__comp(X2,X5,X3),X6)),X7))=hAPP(hAPP(c_Relation_Orel__comp(X2,X5,X3),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X5,X3),tc_HOL_Obool)),X4),X7)))). 4.46/4.75 cnf(i_0_1660, plain, (hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3))),c_Option_Ooption_OSome(X2)))=c_Map_Oran(X1,X2,X3))). 4.46/4.75 cnf(i_0_5029, plain, (c_HOL_OThe(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X1,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,tc_HOL_Obool),X1),c_fequal),X4)),X5)))=hAPP(c_Fun_Othe__inv__into(X1,X3,X2,X4),X5))). 4.46/4.75 cnf(i_0_5419, plain, (c_Nat_Onat_Onat__case(tc_List_Olist(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_List_Olist(X1),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X1),X4)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X1,tc_List_Olist(X1)),c_List_Olist__update(X1,X3)),X2)),X5)=hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)),X5),X2))). 4.46/4.75 cnf(i_0_648, plain, (hAPP(c_List_Orev(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),c_List_Orotate1(X1)),X2))=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),hAPP(c_List_Orev(X1),X2)))). 4.46/4.75 cnf(i_0_456, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool))),X5)),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)),X6))). 4.46/4.75 cnf(i_0_2035, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 4.46/4.75 cnf(i_0_91, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))),c_Transitive__Closure_Ortrancl(X1,X2))=c_Transitive__Closure_Ortrancl(X1,X2))). 4.46/4.75 cnf(i_0_2664, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool))),X5)),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)),X6))). 4.46/4.75 cnf(i_0_3393, plain, (c_Nitpick_OAbs__Frac(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2)))),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2))))=c_Nitpick_Ouminus__frac(X1,X2))). 4.46/4.75 cnf(i_0_6464, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))). 4.46/4.75 cnf(i_0_608, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2))),X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)),X2))). 4.46/4.75 cnf(i_0_2991, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2))),X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2))). 4.46/4.75 cnf(i_0_5606, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X3),tc_fun(X2,X1)),hAPP(hAPP(c_COMBB(tc_fun(X3,X1),tc_fun(tc_fun(X2,X3),tc_fun(X2,X1)),X1),c_COMBB(X3,X1,X2)),X4)),X5),X6),X7)=hAPP(c_List_Ofoldl(X1,X3,X4,X6),hAPP(hAPP(c_List_Omap(X2,X3),X5),X7)))). 4.46/4.75 cnf(i_0_6079, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X2)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X2))))). 4.46/4.75 cnf(i_0_2188, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X2)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2))). 4.46/4.75 cnf(i_0_7187, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat),X3),hAPP(c_List_Onth(X1),X2))))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X3),X2)))). 4.46/4.75 cnf(i_0_2252, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),c_Int_OMin)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))). 4.46/4.75 cnf(i_0_2512, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X3))),X4))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))). 4.46/4.75 cnf(i_0_6142, plain, (c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_fequal,X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_fequal,X4))))=hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4))). 4.46/4.75 cnf(i_0_67, plain, (c_HOL_OThe(tc_prod(X1,X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_fequal,X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_fequal,X4))))=hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4))). 4.46/4.75 cnf(i_0_821, plain, (hAPP(hAPP(c_COMBS(tc_prod(X1,X2),X2,X3),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,X3),tc_prod(X1,X2)),X5),hAPP(hAPP(c_COMBB(X1,X4,tc_prod(X1,X2)),X6),c_Product__Type_Ofst(X1,X2)))),c_Product__Type_Osnd(X1,X2))=hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,X3),X1),X5),X6)))). 4.46/4.75 cnf(i_0_4949, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 4.46/4.75 cnf(i_0_2874, plain, (hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool)))=hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 4.46/4.75 cnf(i_0_958, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X3))),X4))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),X4)))). 4.46/4.75 cnf(i_0_7038, plain, (hAPP(hAPP(c_Product__Type_OSigma(tc_Int_Oint,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_Set_OCollect(tc_Int_Oint)),c_Orderings_Oord__class_Oless(tc_Int_Oint)))=c_Int_Oint__ge__less__than(X1))). 4.46/4.75 cnf(i_0_4989, plain, (c_List_Oset__Cons(X1,hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(c_fequal,X4)))=hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(c_fequal,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))))). 4.46/4.75 cnf(i_0_5090, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X4,X5)),tc_fun(X2,X3),X1),hAPP(c_COMBB(tc_prod(X4,X5),X3,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X5,X3),X6))),X7)),X8)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X5,X3),X6),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X4,X5)),X7),X8)))). 4.46/4.75 cnf(i_0_3757, plain, (hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X4))),hAPP(hAPP(c_List_Ozip(X1,X2),X5),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X4)))=hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X5)),X4))). 4.46/4.75 cnf(i_0_5417, plain, (hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4)),X3)),hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4)),X5))=hAPP(hAPP(c_List_Ozip(X1,X2),X4),hAPP(hAPP(c_List_Oappend(X2),X3),X5)))). 4.46/4.75 cnf(i_0_4398, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))). 4.46/4.75 cnf(i_0_4127, plain, (hAPP(c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Oappend(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1)))),X2)=hAPP(c_List_Orotate1(X1),X2))). 4.46/4.75 cnf(i_0_382, plain, (c_Lazy__Sequence_Ohb__not__seq(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),X2)))=hAPP(c_New__DSequence_Opos__not__seq(X1),X2))). 4.46/4.75 cnf(i_0_2553, plain, (c_List_Omaps(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X2),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_List_Olist(X2),tc_List_Olist(X2)),X1),c_List_Olist_OCons(X2)),X3)),c_List_Olist_ONil(X2)),X4)=hAPP(hAPP(c_List_Omap(X1,X2),X3),X4))). 4.46/4.75 cnf(i_0_431, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),tc_prod(X2,X1),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X2,X1)),hAPP(c_COMBC(X2,X1,tc_prod(X2,X1)),c_Product__Type_OPair(X2,X1)))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))=hAPP(hAPP(c_Product__Type_OSigma(X2,X1),X4),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X2),X3)))). 4.46/4.75 cnf(i_0_4287, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),tc_prod(X3,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X3,X2)),hAPP(hAPP(c_COMBB(X3,tc_fun(X2,tc_prod(X3,X2)),X1),c_Product__Type_OPair(X3,X2)),X4))),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6))=hAPP(hAPP(c_List_Ozip(X3,X2),hAPP(hAPP(c_List_Omap(X1,X3),X4),X5)),X6))). 4.46/4.75 cnf(i_0_7389, plain, (hAPP(hAPP(c_List_Omap(X1,X2),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2)),X3)),hAPP(c_List_Ofilter(X1,c_Map_Odom(X1,X2,X3)),X4))=c_List_Omap__filter(X1,X2,X3,X4))). 4.46/4.75 cnf(i_0_3572, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))). 4.46/4.75 cnf(i_0_4415, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))). 4.46/4.75 cnf(i_0_6706, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X1)))=c_Wellfounded_Ofinite__psubset(X1))). 4.46/4.75 cnf(i_0_298, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))). 4.46/4.75 cnf(i_0_1009, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),hAPP(c_Fun_Ocomp(tc_prod(X2,X4),X2,X1,c_Product__Type_Ofst(X2,X4)),X5))),hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,X1),X6),hAPP(c_Fun_Ocomp(tc_prod(X2,X4),X4,X1,c_Product__Type_Osnd(X2,X4)),X5)))=hAPP(hAPP(c_COMBB(tc_prod(X2,X4),tc_HOL_Obool,X1),hAPP(hAPP(c_Product__Type_OSigma(X2,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X2),X6))),X5))). 4.46/4.75 cnf(i_0_6571, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=X1)). 4.46/4.75 cnf(i_0_3374, plain, (hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),c_Relation_OImage(X1,X1,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3)=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X2))). 4.46/4.75 cnf(i_0_3677, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))). 4.46/4.75 cnf(i_0_4720, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Osublist(X1,X2,X3)),c_List_Osublist(X1,X4,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X3),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))))=c_List_Osublist(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X4),X3))). 4.46/4.75 cnf(i_0_5864, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)))))=hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X1)))))). 4.46/4.75 cnf(i_0_3556, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),X3)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X4),c_Int_Onat)))=c_Nat_Onat_Onat__case(X1,X3,X4,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))). 4.46/4.75 cnf(i_0_4853, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_OCollect(X1)),hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1))))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2))). 4.46/4.75 cnf(i_0_5135, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))). 4.46/4.75 cnf(i_0_6363, plain, (hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X1),X2)),c_Code__Numeral_Onat__of)))=c_Random_Oselect(X1,X2))). 4.46/4.75 cnf(i_0_3523, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))). 4.46/4.75 cnf(i_0_6940, plain, (hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),X1),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(tc_fun(X1,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(X1,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),X1),c_List_Omap(tc_fun(X1,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(X1,tc_Nat_Onat),X1,tc_Nat_Onat),c_COMBI(tc_fun(X1,tc_Nat_Onat))))),X2))=c_List_Omeasures(X1,X2))). 4.46/4.75 cnf(i_0_4922, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olists(X1,X2)),c_List_Olists(X1,X3))=c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.46/4.75 cnf(i_0_953, plain, (c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),X1),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)=hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),X2))). 4.46/4.75 cnf(i_0_2591, plain, (c_Wellfounded_Omlex__prod(tc_List_Olist(X1),c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Olex(X1,X2))=c_List_Olenlex(X1,X2))). 4.46/4.75 cnf(i_0_3889, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X1)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))),c_List_Olist_ONil(X1))),c_List_Osublist(X1,X4,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X2),c_Nat_OSuc)))=c_List_Osublist(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4),X2))). 4.46/4.75 cnf(i_0_6831, plain, (c_List_Omap__filter(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),X1),c_If(tc_Option_Ooption(X2))),X3)),hAPP(hAPP(c_COMBB(X2,tc_Option_Ooption(X2),X1),c_Option_Ooption_OSome(X2)),X4))),c_Option_Ooption_ONone(X2)),X5)=hAPP(hAPP(c_List_Omap(X1,X2),X4),hAPP(c_List_Ofilter(X1,X3),X5)))). 4.46/4.75 cnf(i_0_3818, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X3,X4)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X4),tc_fun(X2,tc_prod(X3,X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X3,X4)),tc_fun(tc_fun(X2,X4),tc_fun(X2,tc_prod(X3,X4))),X1),c_COMBB(X4,tc_prod(X3,X4),X2)),hAPP(hAPP(c_COMBB(X3,tc_fun(X4,tc_prod(X3,X4)),X1),c_Product__Type_OPair(X3,X4)),X5))),X6))=c_Product__Type_Omap__pair(X1,X3,X2,X4,X5,X6))). 4.46/4.75 cnf(i_0_1313, plain, (hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X1)),X2)))),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X1,X2)))=c_Random_Oselect__weight(X1,X2))). 4.46/4.75 cnf(i_0_2949, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X5,X3),tc_HOL_Obool),tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2,X5),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X5,X3),tc_HOL_Obool),tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X1),c_Relation_Orel__comp(X2,X5,X3)),X6)),X7))=hAPP(hAPP(c_Relation_Orel__comp(X2,X5,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X5),tc_HOL_Obool)),X4),X6)),X7))). 4.46/4.75 cnf(i_0_1621, plain, (c_Fun_Oinj__on(tc_fun(X1,X2),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,X2)),c_Set_OCollect(tc_prod(X1,X2))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,X2)),c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool)),hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBC(X2,X2,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,X2),tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_5434, plain, (hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_Set_Oinsert(X2),X4),X6)))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X5)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X6))))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X5)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_Set_Oinsert(X2),X4),X6))))). 4.46/4.75 cnf(i_0_1209, plain, (c_New__DSequence_Opos__decr__bind(X1,X2,hAPP(hAPP(hAPP(X3,X4),X5),X6),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))))),X7),X4)),X5)),X6))=c_New__Random__Sequence_Opos__decr__bind(X1,X2,X3,X7,X4,X5,X6))). 4.46/4.75 cnf(i_0_372, plain, (c_New__DSequence_Opos__bind(X1,X2,hAPP(hAPP(hAPP(X3,X4),X5),X6),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))))),X7),X4)),X5)),X6))=hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X1,X2,X3,X7),X4),X5),X6))). 4.46/4.75 cnf(i_0_4524, plain, (hAPP(c_Lazy__Sequence_Obind(X1,tc_prod(X1,X2),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X1,X2))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X1,X2)),X1),c_Lazy__Sequence_Obind(X2,tc_prod(X1,X2),X4)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X1,X2))),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X1,X2)),X2),c_Lazy__Sequence_Osingle(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2))))=c_Lazy__Sequence_Oproduct(X1,X2,X3,X4))). 4.46/4.75 cnf(i_0_4960, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Map_Odom(X1,X3,X4))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X3,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),c_Map_Odom(X1,X3,X4))))=c_Map_Odom(X1,X3,c_Fun_Ooverride__on(X1,tc_Option_Ooption(X3),X5,X4,X2)))). 4.46/4.75 cnf(i_0_2718, plain, (hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),X3))),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1)),c_member(X2))),X4)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4))). 4.46/4.75 cnf(i_0_2654, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Nitpick_OFrac)). 4.46/4.75 cnf(i_0_3682, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 4.46/4.75 cnf(i_0_2865, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X3),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X4,X2)),tc_fun(X2,X3),X1),hAPP(c_COMBB(tc_prod(X4,X2),X3,X2),X5)),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,tc_prod(X4,X2)),X1),c_Product__Type_OPair(X4,X2)),X6)))),hAPP(hAPP(c_List_Ozip(X1,X2),X7),X8))=hAPP(hAPP(c_List_Omap(tc_prod(X4,X2),X3),X5),hAPP(hAPP(c_List_Ozip(X4,X2),hAPP(hAPP(c_List_Omap(X1,X4),X6),X7)),X8)))). 4.46/4.75 cnf(i_0_1255, plain, (c_New__DSequence_Oneg__decr__bind(X1,X2,hAPP(hAPP(hAPP(X3,X4),X5),X6),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))))),X7),X4)),X5)),X6))=c_New__Random__Sequence_Oneg__decr__bind(X1,X2,X3,X7,X4,X5,X6))). 4.46/4.75 cnf(i_0_557, plain, (hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_Enum_Osublists(X1,X2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(X1)),tc_fun(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),tc_List_Olist(tc_List_Olist(X1))),c_List_Oappend(tc_List_Olist(X1))),hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(c_List_Olist_OCons(X1),X3)))),c_COMBI(tc_List_Olist(tc_List_Olist(X1)))))=c_Enum_Osublists(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)))). 4.46/4.75 cnf(i_0_4784, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq))=c_FunDef_Omax__weak)). 4.46/4.75 cnf(i_0_6169, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq))=c_FunDef_Omin__weak)). 4.46/4.75 cnf(i_0_5890, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X1,tc_Nat_Onat)),X2),c_Product__Type_Osnd(X1,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))))=c_List_Osublist(X1,X3,X2))). 4.46/4.75 cnf(i_0_6359, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X2)),c_Int_Onat))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))). 4.46/4.75 cnf(i_0_3480, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X2)),c_Int_Onat))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))). 4.46/4.75 cnf(i_0_912, plain, (c_New__DSequence_Oneg__bind(X1,X2,hAPP(hAPP(hAPP(X3,X4),X5),X6),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))))),X7),X4)),X5)),X6))=hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X1,X2,X3,X7),X4),X5),X6))). 4.46/4.75 cnf(i_0_855, plain, (hAPP(c_Set_Oimage(X1,tc_prod(X1,X1),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1))),X2)=c_Relation_OId__on(X1,X2))). 4.46/4.75 cnf(i_0_4469, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X2)),c_List_Olists(X1,hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X2,X3)))). 4.46/4.75 cnf(i_0_1450, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),tc_prod(X1,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X1,X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X3),tc_fun(X2,tc_prod(X1,X3))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X1,X3)),tc_fun(tc_fun(X2,X3),tc_fun(X2,tc_prod(X1,X3))),X1),c_COMBB(X3,tc_prod(X1,X3),X2)),c_Product__Type_OPair(X1,X3))),X4))),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6))=hAPP(hAPP(c_List_Ozip(X1,X3),X5),hAPP(hAPP(c_List_Omap(X2,X3),X4),X6)))). 4.46/4.75 cnf(i_0_812, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)))))=hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4))))))). 4.46/4.75 cnf(i_0_59, plain, (hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Omap(tc_prod(X1,X3),tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X3,tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,X2),tc_fun(X3,tc_prod(X1,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(tc_fun(X3,X2),tc_fun(X3,tc_prod(X1,X2))),X1),c_COMBB(X2,tc_prod(X1,X2),X3)),c_Product__Type_OPair(X1,X2))),X4))),X5))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),tc_Option_Ooption(X2),X1,hAPP(c_Option_Omap(X3,X2),X4)),hAPP(c_Map_Omap__of(X1,X3),X5)))). 4.46/4.75 cnf(i_0_7210, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))). 4.46/4.75 cnf(i_0_5951, plain, (c_List_Omaps(tc_List_Olist(X1),X1,c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1)))),X2)=hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),c_List_Ohd(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X1)))),X2)))). 4.46/4.75 cnf(i_0_7197, plain, (c_List_Omaps(tc_List_Olist(X1),tc_List_Olist(X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),tc_List_Olist(X1)),c_List_Omap(X1,tc_List_Olist(X1))),hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)))),X2),c_Enum_On__lists(X1,X3,X2))=c_Enum_On__lists(X1,hAPP(c_Nat_OSuc,X3),X2))). 4.46/4.75 cnf(i_0_4686, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat)),c_Int_Onat)),X2))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))). 4.46/4.75 cnf(i_0_4409, plain, (c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))). 4.46/4.75 cnf(i_0_2769, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X4,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X4,tc_fun(X2,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X6))),X7)))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),X5),X7)))). 4.46/4.75 cnf(i_0_1339, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X4,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X4,tc_fun(X2,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X6))),X7)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),X5),X7)))). 4.46/4.75 cnf(i_0_6545, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),X3)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X4),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X3,X4)),c_Int_Onat))))=hAPP(c_Nat_Onat_Onat__rec(X1,X3,X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))). 4.46/4.75 cnf(i_0_5062, plain, (hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X1,X1)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(tc_prod(X1,X1),tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_HOL_Obool)),tc_prod(X1,X1)),c_COMBB(tc_prod(X1,X1),tc_HOL_Obool,X1)),c_fequal)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1))))=c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))). 4.46/4.75 cnf(i_0_1311, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)),c_Int_Onat)),X2))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))). 4.46/4.75 cnf(i_0_7052, plain, (c_List_Omaps(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1))))),X2)=hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Otl(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X1)))),X2)))). 4.46/4.75 cnf(i_0_6514, plain, (hAPP(hAPP(c_Nitpick_Ofrac(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2))),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X3)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2))),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X3))))=c_Nitpick_Otimes__frac(X1,X2,X3))). 4.46/4.75 cnf(i_0_2840, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 4.46/4.75 cnf(i_0_2551, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),tc_prod(X3,X4)),c_Product__Type_Omap__pair(X1,X3,X2,X4,X5,X6)),hAPP(hAPP(c_List_Ozip(X1,X2),X7),X8))=hAPP(hAPP(c_List_Ozip(X3,X4),hAPP(hAPP(c_List_Omap(X1,X3),X5),X7)),hAPP(hAPP(c_List_Omap(X2,X4),X6),X8)))). 4.46/4.75 cnf(i_0_5167, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X1,X3,X4,X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))))=c_Nat_Onat_Onat__case(X1,X3,X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X5)))). 4.46/4.75 cnf(i_0_4859, plain, (hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X1),X2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))=hAPP(c_List_Oset(X1),X2))). 4.46/4.75 cnf(i_0_3751, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))). 4.46/4.75 cnf(i_0_1843, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X3),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X4)),tc_fun(X2,X3),X1),hAPP(c_COMBB(tc_prod(X1,X4),X3,X2),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X4),tc_fun(X2,tc_prod(X1,X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X1,X4)),tc_fun(tc_fun(X2,X4),tc_fun(X2,tc_prod(X1,X4))),X1),c_COMBB(X4,tc_prod(X1,X4),X2)),c_Product__Type_OPair(X1,X4))),X6)))),hAPP(hAPP(c_List_Ozip(X1,X2),X7),X8))=hAPP(hAPP(c_List_Omap(tc_prod(X1,X4),X3),X5),hAPP(hAPP(c_List_Ozip(X1,X4),X7),hAPP(hAPP(c_List_Omap(X2,X4),X6),X8))))). 4.46/4.75 cnf(i_0_5665, plain, (hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2)),c_Set_OPow(X1))))=hAPP(c_Set_OPow(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))). 4.46/4.76 cnf(i_0_4703, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X2,X1)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X2,X1),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X2,X1)))),hAPP(c_COMBC(X2,X1,tc_prod(X2,X1)),c_Product__Type_OPair(X2,X1))))),X3))=hAPP(c_Relation_Oconverse(X2,X1),X3))). 4.46/4.76 cnf(i_0_955, plain, (hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X1,X2)),X2,c_List_Olist_ONil(tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2)))),X2),c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(X2))),hAPP(hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),X2),c_List_Olist_OCons(tc_prod(X1,X2))),hAPP(c_Product__Type_OPair(X1,X2),X3)))),hAPP(c_List_Ozip(X1,X2),X4))),X5)=hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)),X5))). 4.46/4.76 cnf(i_0_1152, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X1,X3,X4),X5))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X3,X4)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5)))))=hAPP(c_Nat_Onat_Onat__rec(X1,X3,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X5)))). 4.46/4.76 cnf(i_0_1630, plain, (hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X1),X2))))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),X3)))=hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X3)))). 4.46/4.76 cnf(i_0_443, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X3),hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X3)),hAPP(c_List_Ofilter(tc_List_Olist(X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X3),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X3)))),X4)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3))),c_List_Otranspose(X3,X4))))). 4.46/4.76 cnf(i_0_4439, plain, (hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X1,X2)),X1,c_List_Olist_ONil(tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2)))),X1),c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),X1),c_List_Olist_OCons(tc_prod(X1,X2))),hAPP(hAPP(c_COMBC(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2)),X3)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2))),c_List_Ozip(X1,X2)),X4))),X5)=hAPP(hAPP(c_List_Ozip(X1,X2),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)))). 4.46/4.76 cnf(i_0_2988, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X1,X2),tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X6))),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,tc_fun(X4,tc_HOL_Obool))),tc_fun(X2,tc_fun(tc_prod(X3,X4),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_fun(X3,tc_fun(X4,tc_HOL_Obool))),tc_fun(X2,tc_fun(tc_prod(X3,X4),tc_HOL_Obool))),X1),c_COMBB(tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_prod(X3,X4),tc_HOL_Obool),X2)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),X1),c_Product__Type_OSigma(X3,X4)),X7))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),X2),c_COMBK(tc_fun(X4,tc_HOL_Obool),X3)),X8))))=hAPP(hAPP(c_Product__Type_OSigma(X3,X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X5),X7)),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X4,tc_HOL_Obool)),X6),X8))))). 4.46/4.76 cnf(i_0_4728, plain, (c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBC(X1,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),X1),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X1),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),X1),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3)=hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),X3))). 4.46/4.76 cnf(i_0_4167, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),c_List_Ohd(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X1)))),X3)))),c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),X4),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Otl(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X1)))),X3)))))=c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),X3)))). 4.46/4.76 cnf(i_0_2894, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X2,X2)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X2,X2),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X2,X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X2),tc_fun(X1,tc_prod(X2,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X2,X2)),tc_fun(tc_fun(X1,X2),tc_fun(X1,tc_prod(X2,X2))),X1),c_COMBB(X2,tc_prod(X2,X2),X1)),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_prod(X2,X2)),X1),c_Product__Type_OPair(X2,X2)),X3))),X3)))),X4))=hAPP(hAPP(c_Relation_Oinv__image(X2,X1),X4),X3))). 4.46/4.76 cnf(i_0_2444, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,X1))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2)))))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),X2)))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))))=c_Divides_Odivmod__int__rel(X1,X2))). 4.46/4.76 cnf(i_0_4433, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X4)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X2),c_Set_Oinsert(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4))). 4.46/4.76 cnf(i_0_2182, plain, (hAPP(c_List_Ofoldl(tc_fun(X1,tc_Option_Ooption(X2)),tc_prod(X1,X2),hAPP(c_COMBC(tc_prod(X1,X2),tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),X1),c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))),X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),X1),c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),X1,tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)))))),c_Option_Ooption_OSome(X2)))),X3),hAPP(c_List_Orev(tc_prod(X1,X2)),X4))=c_Map_Omap__add(X1,X2,X3,hAPP(c_Map_Omap__of(X1,X2),X4)))). 4.46/4.76 cnf(i_0_4890, plain, (hAPP(c_List_Ofoldl(tc_fun(X1,tc_Option_Ooption(X2)),tc_prod(X1,X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_prod(X1,X2),tc_fun(X1,tc_Option_Ooption(X2))),tc_fun(X1,tc_Option_Ooption(X2))),c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X1,tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X1,tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),tc_fun(X1,tc_Option_Ooption(X2))),c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(X1,tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),tc_fun(X1,tc_Option_Ooption(X2))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2)))),X1),c_COMBB(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)),X2))),c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2))))),c_Option_Ooption_OSome(X2))),X3),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))=c_Map_Omap__upds(X1,X2,X3,X4,X5))). 4.46/4.76 cnf(i_0_2854, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),c_Nitpick_Oint__lcm(hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2)),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X3)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X1),tc_Int_Oint),c_Nitpick_Ofrac(X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2)))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X3)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X3))))))),c_COMBI(tc_Int_Oint)))=c_Nitpick_Oplus__frac(X1,X2,X3))). 4.46/4.76 cnf(i_0_184, plain, (hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X1,X2)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X1,X2),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X1,X2)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(X1,X2)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(X1,X2),tc_fun(tc_Nat_Onat,tc_prod(X1,X2)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X1,X2)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X1,X2)),c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X2,tc_prod(X1,X2)),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_prod(X1,X2)),tc_Nat_Onat),c_Product__Type_OPair(X1,X2)),hAPP(c_List_Onth(X1),X3))),hAPP(c_List_Onth(X2),X4)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)))))=hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)))). 4.46/4.76 cnf(i_0_18, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X1,tc_List_Olist(X1)),tc_prod(X1,tc_List_Olist(X1))),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),c_Product__Type_Omap__pair(tc_prod(X1,tc_List_Olist(X1)),tc_List_Olist(X1),tc_prod(X1,tc_List_Olist(X1)),tc_List_Olist(X1),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)))),c_Wellfounded_Olex__prod(X1,tc_List_Olist(X1),X2,hAPP(c_List_Olexn(X1,X2),X3)))),c_Nitpick_Oprod(tc_List_Olist(X1),tc_List_Olist(X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),hAPP(c_Nat_OSuc,X3)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),hAPP(c_Nat_OSuc,X3))))=hAPP(c_List_Olexn(X1,X2),hAPP(c_Nat_OSuc,X3)))). 4.46/4.76 cnf(i_0_1285, plain, (hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))). 4.46/4.76 cnf(i_0_5117, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3)),X1)))=hAPP(c_Divides_Oadjust(X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X1)))). 4.46/4.76 cnf(i_0_2177, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_fun(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_List_Olist(X1)),c_COMBS(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_List_Olist(X1)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_List_Olist(X1)),hAPP(c_If(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(X2,X3)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_List_Olist(X1)),c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(c_List_Olist_OCons(X1),X3))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_List_Olist(X1)),c_COMBB(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1))),c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(c_List_Olist_OCons(X1),X3)))),c_List_Opartition(X1,X2,X4))=c_List_Opartition(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))). 4.46/4.76 cnf(i_0_5129, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_COMBS(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(X2,X1)),c_Product__Type_OPair(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),c_Relation_Oinv__image(X1,X2))))),c_Relation_Oinv__image(X1,X2)))=c_FunDef_Orp__inv__image(X1,X2))). 4.46/4.76 cnf(i_0_4379, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X3))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBC(X3,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X1,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X3),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X1,X3)))),c_Product__Type_OPair(X1,X3)))),X4))))),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X3,X2)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X3,X2),tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X3,X2)))),hAPP(c_COMBC(X3,X2,tc_prod(X3,X2)),c_Product__Type_OPair(X3,X2))))),X5))))=hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5))). 4.46/4.76 cnf(i_0_4541, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))=c_Divides_Oadjust(X1))). 4.46/4.76 cnf(i_0_3884, plain, (hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X1)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),tc_List_Olist(X1)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_List_Olist(X1)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_List_Olist(X1)),c_COMBS(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_List_Olist(X1)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),X1),c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X1)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_List_Olist(X1)),c_COMBB(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_List_Olist(X1),tc_HOL_Obool,tc_List_Olist(X1))),c_fequal))),c_List_Olist_OCons(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2))),X3))))=c_List_Oset__Cons(X1,X2,X3))). 4.46/4.76 cnf(i_0_7203, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X1)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X1)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBC(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X1)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))))),c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1))))),c_List_Olex(X1,X2)))))=c_List_Olenlex(X1,X2))). 4.46/4.76 cnf(i_0_6148, plain, (hAPP(c_fequal,X1)=hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))). 4.46/4.76 cnf(i_0_5716, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1))). 4.46/4.76 cnf(i_0_4017, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))). 4.46/4.76 cnf(i_0_3119, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1))). 4.46/4.76 cnf(i_0_6107, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))). 4.46/4.76 cnf(i_0_378, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2))). 4.46/4.76 cnf(i_0_1634, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2))). 4.46/4.76 cnf(i_0_7374, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_7417, plain, (hAPP(c_List_Olexn(X1,X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_2433, plain, (c_Enum_Osublists(X1,c_List_Olist_ONil(X1))=hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(tc_List_Olist(X1))))). 4.46/4.76 cnf(i_0_3021, plain, (hAPP(c_New__DSequence_Opos__union(X1,X2,X3),X4)=c_Lazy__Sequence_Oappend(X1,hAPP(X2,X4),hAPP(X3,X4)))). 4.46/4.76 cnf(i_0_3226, plain, (c_List_Oremove1(X1,X2,c_List_Oremove1(X1,X3,X4))=c_List_Oremove1(X1,X3,c_List_Oremove1(X1,X2,X4)))). 4.46/4.76 cnf(i_0_5121, plain, (c_Fun_Oid(tc_prod(X1,X2))=hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2)))). 4.46/4.76 cnf(i_0_4331, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(tc_List_Olist(X1)))=c_Enum_On__lists(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))). 4.46/4.76 cnf(i_0_3160, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))=hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))). 4.46/4.76 cnf(i_0_4833, plain, (hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),X2)=hAPP(c_Set_OPow(X1),X2))). 4.46/4.76 cnf(i_0_2462, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Orev(X1),X3))=hAPP(c_List_Orev(X1),hAPP(c_List_Ofilter(X1,X2),X3)))). 4.46/4.76 cnf(i_0_3756, plain, (hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),X5),X6)=hAPP(hAPP(X4,X6),hAPP(X5,X6)))). 4.46/4.76 cnf(i_0_6750, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))). 4.46/4.76 cnf(i_0_5021, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(X1))=c_List_Opartition(X1,X2,c_List_Olist_ONil(X1)))). 4.46/4.76 cnf(i_0_5589, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1))). 4.46/4.76 cnf(i_0_3924, plain, (c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))). 4.46/4.76 cnf(i_0_1606, plain, (hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),hAPP(c_Nat_OSuc,X4))=hAPP(hAPP(X3,X4),hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),X4)))). 4.46/4.76 cnf(i_0_4705, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)))). 4.46/4.76 cnf(i_0_5425, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))). 4.46/4.76 cnf(i_0_1619, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Obutlast(X2,X4)))). 4.46/4.76 cnf(i_0_1677, plain, (hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_List_Oset(X2),X4)))). 4.46/4.76 cnf(i_0_2768, plain, (c_Divides_Odivmod__int(X1,X2)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))). 4.46/4.76 cnf(i_0_3748, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))=hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.46/4.76 cnf(i_0_3320, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))). 4.46/4.76 cnf(i_0_2971, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))). 4.46/4.76 cnf(i_0_4650, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Orev(X1),X4))=hAPP(c_List_Orev(X2),hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)))). 4.46/4.76 cnf(i_0_969, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Otl(X1),X4))=hAPP(c_List_Otl(X2),hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)))). 4.46/4.76 cnf(i_0_5747, plain, (hAPP(hAPP(c_List_Omap(X1,X2),hAPP(c_COMBK(X2,X1),X3)),X4)=c_List_Oreplicate(X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4),X3))). 4.46/4.76 cnf(i_0_2026, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),X2),c_List_Olist_ONil(X1)),X3)=hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X2,X1,X4),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X3))). 4.46/4.76 cnf(i_0_4969, plain, (hAPP(c_List_Orotate1(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))))). 4.46/4.76 cnf(i_0_6614, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))). 4.46/4.76 cnf(i_0_1745, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X5))=hAPP(hAPP(c_Set_Oinsert(X2),hAPP(X3,X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)))). 4.46/4.76 cnf(i_0_4262, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),c_Set_Oimage(X1,X2,X4))=hAPP(c_Set_Oimage(X1,X2,X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))). 4.46/4.76 cnf(i_0_6350, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),X5)=hAPP(hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X2),X5)),hAPP(c_Product__Type_Osnd(X1,X2),X5)))). 4.46/4.76 cnf(i_0_2015, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4))=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X3)),X4))). 4.46/4.76 cnf(i_0_3794, plain, (hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X2),X2,hAPP(X3,X5),c_Option_Ooption_OSome(X2)),hAPP(X4,X5)))). 4.46/4.76 cnf(i_0_1849, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2)))). 4.46/4.76 cnf(i_0_3619, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)))). 4.46/4.76 cnf(i_0_5782, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Relation_OField(X1))=hAPP(c_Relation_OField(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2)))). 4.46/4.76 cnf(i_0_6557, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X1,X2,X3))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X2,X3)))). 4.46/4.76 cnf(i_0_4339, plain, (hAPP(hAPP(X1,X2),hAPP(hAPP(c_Power_Opower_Opower(X3,X4,X1),X2),X5))=hAPP(hAPP(c_Power_Opower_Opower(X3,X4,X1),X2),hAPP(c_Nat_OSuc,X5)))). 4.46/4.76 cnf(i_0_4643, plain, (c_List_Olist_Olist__size(X1,hAPP(c_Fun_Ocomp(X2,tc_Nat_Onat,X1,X3),X4),X5)=c_List_Olist_Olist__size(X2,X3,hAPP(hAPP(c_List_Omap(X1,X2),X4),X5)))). 4.46/4.76 cnf(i_0_6965, plain, (hAPP(c_Relation_Oconverse(X1,X1),hAPP(hAPP(c_Relation_Oinv__image(X2,X1),X3),X4))=hAPP(hAPP(c_Relation_Oinv__image(X2,X1),hAPP(c_Relation_Oconverse(X2,X2),X3)),X4))). 4.46/4.76 cnf(i_0_4731, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.46/4.76 cnf(i_0_5047, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.46/4.76 cnf(i_0_5315, plain, (hAPP(c_Set_Oimage(X1,X2,hAPP(hAPP(c_COMBB(X3,X2,X1),X4),X5)),X6)=hAPP(c_Set_Oimage(X3,X2,X4),hAPP(c_Set_Oimage(X1,X3,X5),X6)))). 4.46/4.76 cnf(i_0_6176, plain, (c_List_Omaps(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))=hAPP(hAPP(c_List_Oappend(X2),hAPP(X3,X4)),c_List_Omaps(X1,X2,X3,X5)))). 4.46/4.76 cnf(i_0_4288, plain, (hAPP(c_Set_Oimage(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6)=hAPP(c_Set_Oimage(X3,X2,X4),hAPP(c_Set_Oimage(X1,X3,X5),X6)))). 4.46/4.76 cnf(i_0_1422, plain, (c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))=hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)))). 4.46/4.76 cnf(i_0_1774, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5))=hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(hAPP(c_List_Odrop(X3),X2),X5)))). 4.46/4.76 cnf(i_0_3866, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Otake(X1),X4),X5))=hAPP(hAPP(c_List_Otake(X2),X4),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)))). 4.46/4.76 cnf(i_0_5325, plain, (hAPP(c_List_Ofoldl(X1,X2,X3,X4),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X6))=hAPP(c_List_Ofoldl(X1,X2,X3,hAPP(hAPP(X3,X4),X5)),X6))). 4.46/4.76 cnf(i_0_1233, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))=hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(X3,X4)),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)))). 4.46/4.76 cnf(i_0_5945, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(c_Fun_Ocomp(X4,X1,X2,X5),X6))=hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,X2),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X4),X3),X5)),X6))). 4.46/4.76 cnf(i_0_1865, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X1,X2,X3))=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X2,X3)))). 4.46/4.76 cnf(i_0_3011, plain, (hAPP(c_Relation_ODomain(X1,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),c_Relation_ODomain(X1,X2)))). 4.46/4.76 cnf(i_0_693, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),c_Relation_ORange(X1,X2))=hAPP(c_Relation_ORange(X1,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3)))). 4.46/4.76 cnf(i_0_408, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(X5,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X4),X5)))). 4.46/4.76 cnf(i_0_6768, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(X5,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X4),X5)))). 4.46/4.76 cnf(i_0_4091, plain, (hAPP(hAPP(c_Option_Omap(X1,X2),hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6)=hAPP(hAPP(c_Option_Omap(X3,X2),X4),hAPP(hAPP(c_Option_Omap(X1,X3),X5),X6)))). 4.46/4.76 cnf(i_0_3157, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Omap(X4,X1),X5),X6))=hAPP(hAPP(c_List_Omap(X4,X2),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6))). 4.46/4.76 cnf(i_0_5737, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),c_Option_Ooption_ONone(X2))=c_Map_Orestrict__map(X1,X2,X3,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))). 4.46/4.76 cnf(i_0_2962, plain, (hAPP(c_Relation_ORange(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3))=hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X1)),hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X3)))). 4.46/4.76 cnf(i_0_4727, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X1,X4),X5)),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),X3),X6),X4)))). 4.46/4.76 cnf(i_0_38, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,tc_HOL_Obool),X1),X5),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X6),X3)),X5))). 4.46/4.76 cnf(i_0_5004, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Olist__update(X1,X4),X5),X6))=hAPP(hAPP(c_List_Olist__update(X2,hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)),X5),hAPP(X3,X6)))). 4.46/4.76 cnf(i_0_2008, plain, (hAPP(c_Fun_Ocomp(X1,X2,X3,hAPP(c_Fun_Ocomp(X4,X2,X1,X5),X6)),X7)=hAPP(c_Fun_Ocomp(X4,X2,X3,X5),hAPP(c_Fun_Ocomp(X1,X4,X3,X6),X7)))). 4.46/4.76 cnf(i_0_1884, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_Fun_Ocomp(X4,tc_fun(X2,tc_HOL_Obool),X1,X5),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X6),X3)),X5))). 4.46/4.76 cnf(i_0_5696, plain, (hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X3,X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,X3)),hAPP(c_Nat_OSuc,hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),X4))))). 4.46/4.76 cnf(i_0_299, plain, (c_List_Olist_Olist__size(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,X3)),hAPP(c_Nat_OSuc,c_List_Olist_Olist__size(X1,X2,X4))))). 4.46/4.76 cnf(i_0_7036, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Map_Odom(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),c_Option_Ooption_ONone(X2))))). 4.46/4.76 cnf(i_0_4988, plain, (hAPP(hAPP(c_List_Omap(X1,tc_prod(X1,X1)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1))),X2)=hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2))). 4.46/4.76 cnf(i_0_4358, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2))=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)))). 4.46/4.76 cnf(i_0_6913, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),hAPP(hAPP(c_Relation_Orel__comp(X2,X5,X3),X6),X7))=hAPP(hAPP(c_Relation_Orel__comp(X1,X5,X3),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X5),X4),X6)),X7))). 4.46/4.76 cnf(i_0_3059, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),hAPP(c_List_Ofilter(X3,hAPP(c_Fun_Ocomp(X1,tc_HOL_Obool,X3,X2),X4)),X5)))). 4.46/4.76 cnf(i_0_829, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(c_Fun_Ocomp(X4,tc_fun(X2,X3),X1,X5),X6)),X7)=hAPP(hAPP(X5,hAPP(X6,hAPP(c_Product__Type_Ofst(X1,X2),X7))),hAPP(c_Product__Type_Osnd(X1,X2),X7)))). 4.46/4.76 cnf(i_0_5472, plain, (c_List_Otranspose(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_List_Olist(X1)),hAPP(c_List_Omap(X2,X1),X3)),X4))=hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_List_Olist(X1)),hAPP(c_List_Omap(X2,X1),X3)),c_List_Otranspose(X2,X4)))). 4.46/4.76 cnf(i_0_5767, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X3)))). 4.46/4.76 cnf(i_0_2472, plain, (hAPP(c_Fun_Ocomp(X1,X2,tc_prod(X3,X1),X4),c_Product__Type_Osnd(X3,X1))=hAPP(c_Fun_Ocomp(tc_prod(X5,X2),X2,tc_prod(X3,X1),c_Product__Type_Osnd(X5,X2)),c_Product__Type_Omap__pair(X3,X5,X1,X2,X6,X4)))). 4.46/4.76 cnf(i_0_3434, plain, (hAPP(c_Fun_Ocomp(X1,X2,tc_prod(X1,X3),X4),c_Product__Type_Ofst(X1,X3))=hAPP(c_Fun_Ocomp(tc_prod(X2,X5),X2,tc_prod(X1,X3),c_Product__Type_Ofst(X2,X5)),c_Product__Type_Omap__pair(X1,X2,X3,X5,X4,X6)))). 4.46/4.76 cnf(i_0_4617, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6),hAPP(X4,X7))=hAPP(c_Fun_Ocomp(X3,X2,X1,X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X3),X5),X6),X7)))). 4.46/4.76 cnf(i_0_6656, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)))). 4.46/4.76 cnf(i_0_165, plain, (hAPP(c_Set_Oimage(X1,tc_List_Olist(X1),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))),X2)=c_List_Oset__Cons(X1,X2,hAPP(c_fequal,c_List_Olist_ONil(X1))))). 4.46/4.76 cnf(i_0_4630, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6))=hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X5)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X6)))). 4.46/4.76 cnf(i_0_1651, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5))=hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X3),tc_List_Olist(X3)),X2),c_List_Orotate1(X3)),X5)))). 4.46/4.76 cnf(i_0_3259, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))))). 4.46/4.76 cnf(i_0_7095, plain, (hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))). 4.46/4.76 cnf(i_0_4077, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,hAPP(c_Fun_Ocomp(X4,X2,X1,X5),X6),c_Fun_Oid(X3)),X7)=hAPP(c_Product__Type_Omap__pair(X4,X2,X3,X3,X5,c_Fun_Oid(X3)),hAPP(c_Product__Type_Omap__pair(X1,X4,X3,X3,X6,c_Fun_Oid(X3)),X7)))). 4.46/4.76 cnf(i_0_1132, plain, (hAPP(c_Product__Type_Omap__pair(X1,X1,X2,X3,c_Fun_Oid(X1),X4),hAPP(c_Product__Type_Omap__pair(X1,X1,X5,X2,c_Fun_Oid(X1),X6),X7))=hAPP(c_Product__Type_Omap__pair(X1,X1,X5,X3,c_Fun_Oid(X1),hAPP(c_Fun_Ocomp(X2,X3,X5,X4),X6)),X7))). 4.46/4.76 cnf(i_0_1894, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist__update(X1,X3),X4),X5)),hAPP(hAPP(c_List_Olist__update(X2,X6),X4),X7))=hAPP(hAPP(c_List_Olist__update(tc_prod(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X6)),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X7)))). 4.46/4.76 cnf(i_0_5806, plain, (hAPP(hAPP(X1,X2),hAPP(c_List_Ofoldl(X3,X4,hAPP(c_COMBC(X4,X3,X3),X1),X5),hAPP(c_List_Orev(X4),X6)))=hAPP(c_List_Ofoldl(X3,X4,hAPP(c_COMBC(X4,X3,X3),X1),X5),hAPP(c_List_Orev(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X2),X6))))). 4.46/4.76 cnf(i_0_972, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),X2))). 4.46/4.76 cnf(i_0_4418, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),hAPP(c_Product__Type_Omap__pair(X1,X1,X5,X3,c_Fun_Oid(X1),X6),X7))=hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X5),X7))),hAPP(X6,hAPP(c_Product__Type_Osnd(X1,X5),X7))))). 4.46/4.76 cnf(i_0_4683, plain, (hAPP(c_Product__Type_Omap__pair(X1,X1,X2,X3,c_Fun_Oid(X1),X4),hAPP(c_Product__Type_Omap__pair(X5,X1,X2,X2,X6,c_Fun_Oid(X2)),X7))=hAPP(hAPP(c_Product__Type_OPair(X1,X3),hAPP(X6,hAPP(c_Product__Type_Ofst(X5,X2),X7))),hAPP(X4,hAPP(c_Product__Type_Osnd(X5,X2),X7))))). 4.46/4.76 cnf(i_0_3649, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))),X1))). 4.46/4.76 cnf(i_0_6675, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X4,hAPP(c_Fun_Ocomp(X5,X2,X1,X6),X7),hAPP(c_Fun_Ocomp(X8,X4,X3,X9),X10)),X11)=hAPP(c_Product__Type_Omap__pair(X5,X2,X8,X4,X6,X9),hAPP(c_Product__Type_Omap__pair(X1,X5,X3,X8,X7,X10),X11)))). 4.46/4.76 cnf(i_0_6688, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),hAPP(c_Product__Type_Omap__pair(X1,X1,X5,X3,c_Fun_Oid(X1),X6),X7))=hAPP(c_Product__Type_Omap__pair(X2,X2,X5,X3,c_Fun_Oid(X2),X6),hAPP(c_Product__Type_Omap__pair(X1,X2,X5,X5,X4,c_Fun_Oid(X5)),X7)))). 4.46/4.76 cnf(i_0_3289, plain, (c_List_Omaps(tc_List_Olist(X1),X2,hAPP(c_List_Omap(X1,X2),X3),X4)=hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X4)))). 4.46/4.76 cnf(i_0_1965, plain, (hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Omap(X1,tc_prod(X1,X2)),hAPP(hAPP(c_COMBS(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2)),X3)),X4))=c_Map_Orestrict__map(X1,X2,hAPP(c_Fun_Ocomp(X2,tc_Option_Ooption(X2),X1,c_Option_Ooption_OSome(X2)),X3),hAPP(c_List_Oset(X1),X4)))). 4.46/4.76 cnf(i_0_2986, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool),tc_Nat_Onat),X4),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2))))). 4.46/4.76 cnf(i_0_333, plain, (hAPP(hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3),hAPP(c_Product__Type_OPair(X1,X2),X4))=hAPP(c_Relation_OImage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))). 4.46/4.76 cnf(i_0_822, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X5))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBS(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),X4)),X5)))). 4.46/4.76 cnf(i_0_2057, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X5))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBS(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X4)),X5)))). 4.46/4.76 cnf(i_0_2341, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))))). 4.46/4.76 cnf(i_0_2320, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))))). 4.46/4.76 cnf(i_0_5753, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),hAPP(c_Fun_Ocomp(X3,tc_fun(X1,X1),X2,X4),X5)),X6),hAPP(c_List_Orev(X2),X7))=hAPP(c_List_Ofoldl(X1,X3,hAPP(c_COMBC(X3,X1,X1),X4),X6),hAPP(c_List_Orev(X3),hAPP(hAPP(c_List_Omap(X2,X3),X5),X7))))). 4.46/4.76 cnf(i_0_5061, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),X3))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Osublist(X1,X2,X3)))). 4.46/4.76 cnf(i_0_5544, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5)))). 4.46/4.76 cnf(i_0_2265, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5)))). 4.46/4.76 cnf(i_0_2250, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5)))). 4.46/4.76 cnf(i_0_5390, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_33, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,hAPP(c_Fun_Ocomp(X2,tc_HOL_Obool,X1,X4),X3),X5))),X5))=hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X4,hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)))),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)))). 4.46/4.76 cnf(i_0_3370, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 4.46/4.76 cnf(i_0_3470, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_Set_Oimage(X3,X1,X4),X5)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_Oimage(X6,X2,X7),X8)))=hAPP(c_Set_Oimage(tc_prod(X3,X6),tc_prod(X1,X2),c_Product__Type_Omap__pair(X3,X1,X6,X2,X4,X7)),hAPP(hAPP(c_Product__Type_OSigma(X3,X6),X5),hAPP(c_COMBK(tc_fun(X6,tc_HOL_Obool),X3),X8))))). 4.46/4.76 cnf(i_0_2691, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1))). 4.46/4.76 cnf(i_0_2344, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))=c_Nitpick_Oprod(X1,X2,X3,X4))). 4.46/4.76 cnf(i_0_1438, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))))). 4.46/4.76 cnf(i_0_4362, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),tc_Option_Ooption(X2),X1,hAPP(c_Option_Omap(X3,X2),X4)),X5)),X6),hAPP(c_Option_Ooption_OSome(X2),hAPP(X4,X7)))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),tc_Option_Ooption(X2),X1,hAPP(c_Option_Omap(X3,X2),X4)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),X5),X6),hAPP(c_Option_Ooption_OSome(X3),X7))))). 4.46/4.76 cnf(i_0_1002, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),hAPP(c_COMBC(X2,X1,tc_HOL_Obool),X4)))=hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),X3))),X4)))). 4.46/4.76 cnf(i_0_4640, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,c_List_Otranspose(X1,X2)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X1)))),X2)))). 4.46/4.76 cnf(i_0_6443, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X3))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))))). 4.46/4.76 cnf(i_0_2352, plain, (hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,X4),X5),hAPP(hAPP(c_COMBC(X2,tc_fun(X6,tc_fun(X7,X4)),tc_fun(X3,X4)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X6,X7)),tc_fun(tc_fun(X6,tc_fun(X7,X4)),tc_fun(X3,X4)),X2),c_Product__Type_Oscomp(X3,X6,X7,X4)),X8)),X9))=hAPP(hAPP(c_Product__Type_Oscomp(X1,X6,X7,X4),hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,tc_prod(X6,X7)),X5),X8)),X9))). 4.46/4.76 cnf(i_0_2036, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X1,tc_Nat_Onat)),X2),c_Product__Type_Osnd(X1,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X4))))=hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X1,tc_Nat_Onat)),X2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X1,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X1,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),X4))))). 4.46/4.76 cnf(i_0_5369, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(c_Set_Oimage(X2,X1,X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5)))=hAPP(c_Set_Oimage(X2,X1,hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBS(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X5)),X3)),X6)),X4))). 4.46/4.76 cnf(i_0_2068, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X5)),X4))=c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),X1),c_If(tc_Option_Ooption(X2))),X4)),X3)),X5)))). 4.46/4.76 cnf(i_0_5385, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X3))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4))))))). 4.46/4.76 cnf(i_0_92, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))). 4.46/4.76 cnf(i_0_4906, plain, (hAPP(c_Set_Oimage(X1,tc_prod(X2,X3),hAPP(hAPP(c_COMBS(X1,X3,tc_prod(X2,X3)),hAPP(hAPP(c_COMBB(X2,tc_fun(X3,tc_prod(X2,X3)),X1),c_Product__Type_OPair(X2,X3)),X4)),X5)),X6)=hAPP(hAPP(c_Product__Type_OSigma(X2,X3),hAPP(c_Set_Oimage(X1,X2,X4),X6)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),c_Set_Oimage(X1,X3,X5)),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),c_Set_Ovimage(X1,X2,X4)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),c_Set_Oinsert(X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))),X6))))). 4.46/4.76 cnf(i_0_1490, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2)))))). 4.46/4.76 cnf(i_0_2543, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X1,tc_Nat_Onat)),X2),c_Product__Type_Osnd(X1,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))))))=hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X1,tc_Nat_Onat)),X2),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(X1,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X4))),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))))))). 4.46/4.76 cnf(i_0_2396, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_HOL_Obool,X1),c_Transitive__Closure_Ortrancl(X1,X2)),hAPP(hAPP(c_COMBC(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),X3))),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_HOL_Obool,X1),c_Transitive__Closure_Ortrancl(X1,X2)),hAPP(c_Product__Type_OPair(X1,X1),X4)))))=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))))). 4.46/4.76 cnf(i_0_4956, plain, (~hBOOL(c_fFalse))). 4.46/4.76 cnf(i_0_6044, plain, (c_Int_OMin!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.76 cnf(i_0_3690, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.76 cnf(i_0_4002, plain, (hAPP(c_Nat_OSuc,X1)!=X1)). 4.46/4.76 cnf(i_0_5230, plain, (c_Com_Ocom_OSKIP!=c_Com_Ocom_OWhile(X1,X2))). 4.46/4.76 cnf(i_0_3557, plain, (c_Com_Ocom_OSKIP!=c_Com_Ocom_OSemi(X1,X2))). 4.46/4.76 cnf(i_0_6465, plain, (c_Com_Ocom_OSKIP!=hAPP(c_Com_Ocom_OBODY,X1))). 4.46/4.76 cnf(i_0_1522, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_544, plain, (~c_List_Olist__ex1(X1,X2,c_List_Olist_ONil(X1)))). 4.46/4.76 cnf(i_0_5181, plain, (~c_List_Olist__ex(X1,X2,c_List_Olist_ONil(X1)))). 4.46/4.76 cnf(i_0_826, plain, (hAPP(c_Nat_OSuc,X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_702, hypothesis, (~hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,v_y)),v_F)))). 4.46/4.76 cnf(i_0_3634, plain, (c_Com_Ocom_OSKIP!=c_Com_Ocom_OLocal(X1,X2,X3))). 4.46/4.76 cnf(i_0_6438, plain, (c_Com_Ocom_OSKIP!=c_Com_Ocom_OCond(X1,X2,X3))). 4.46/4.76 cnf(i_0_3885, plain, (hAPP(c_Set_OPow(X1),X2)!=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_1544, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_3168, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_1004, plain, (c_Com_Ocom_OSemi(X1,X2)!=c_Com_Ocom_OWhile(X3,X4))). 4.46/4.76 cnf(i_0_229, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_3238, plain, (c_Com_Ocom_OWhile(X1,X2)!=hAPP(c_Com_Ocom_OBODY,X3))). 4.46/4.76 cnf(i_0_6055, plain, (c_Lazy__Sequence_Olazy__sequence_OEmpty(X1)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3))). 4.46/4.76 cnf(i_0_1048, plain, (c_Com_Ocom_OSemi(X1,X2)!=hAPP(c_Com_Ocom_OBODY,X3))). 4.46/4.76 cnf(i_0_3931, plain, (c_Option_Ooption_ONone(X1)!=hAPP(c_Option_Ooption_OSome(X1),X2))). 4.46/4.76 cnf(i_0_2952, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=X3)). 4.46/4.76 cnf(i_0_4261, plain, (c_Com_Ocom_OWhile(X1,X2)!=c_Com_Ocom_OCond(X3,X4,X5))). 4.46/4.76 cnf(i_0_4759, plain, (hAPP(c_Com_Ocom_OBODY,X1)!=c_Com_Ocom_OCond(X2,X3,X4))). 4.46/4.76 cnf(i_0_330, plain, (c_Com_Ocom_OLocal(X1,X2,X3)!=hAPP(c_Com_Ocom_OBODY,X4))). 4.46/4.76 cnf(i_0_3037, plain, (c_Com_Ocom_OSemi(X1,X2)!=c_Com_Ocom_OLocal(X3,X4,X5))). 4.46/4.76 cnf(i_0_4175, plain, (c_Com_Ocom_OSemi(X1,X2)!=c_Com_Ocom_OCond(X3,X4,X5))). 4.46/4.76 cnf(i_0_2972, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Int_OMin)))). 4.46/4.76 cnf(i_0_5046, plain, (c_Com_Ocom_OLocal(X1,X2,X3)!=c_Com_Ocom_OWhile(X4,X5))). 4.46/4.76 cnf(i_0_377, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_2030, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Int_OMin)))). 4.46/4.76 cnf(i_0_4074, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)))). 4.46/4.76 cnf(i_0_5182, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Int_OMin)))). 4.46/4.76 cnf(i_0_998, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=c_List_Olist_ONil(X1))). 4.46/4.76 cnf(i_0_24, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)))). 4.46/4.76 cnf(i_0_2176, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_7260, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))). 4.46/4.76 cnf(i_0_81, plain, (c_Com_Ocom_OCond(X1,X2,X3)!=c_Com_Ocom_OLocal(X4,X5,X6))). 4.46/4.76 cnf(i_0_4126, plain, (~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))). 4.46/4.76 cnf(i_0_5667, plain, (~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))). 4.46/4.76 cnf(i_0_1478, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))). 4.46/4.76 cnf(i_0_7006, plain, (~c_Wellfounded_Omax__extp(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 4.46/4.76 cnf(i_0_3853, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 4.46/4.76 cnf(i_0_1447, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4)))). 4.46/4.76 cnf(i_0_1947, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))). 4.46/4.76 cnf(i_0_6572, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1)))). 4.46/4.76 cnf(i_0_3451, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.46/4.76 cnf(i_0_360, plain, (~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)))). 4.46/4.76 cnf(i_0_3913, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)))). 4.46/4.76 cnf(i_0_1597, plain, (~hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)))). 4.46/4.76 cnf(i_0_6943, plain, (~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))))). 4.46/4.76 cnf(i_0_880, plain, (hAPP(c_Set_OPow(X1),X2)!=hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool),X3),X2))). 4.46/4.76 cnf(i_0_6092, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_5063, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)))). 4.46/4.76 cnf(i_0_4507, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)))). 4.46/4.76 cnf(i_0_792, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))). 4.46/4.76 cnf(i_0_3709, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))!=c_List_Olist_ONil(X1))). 4.46/4.76 cnf(i_0_322, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5))!=hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)))). 4.46/4.76 cnf(i_0_6500, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))))). 4.46/4.76 cnf(i_0_4012, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1))))))). 4.46/4.76 cnf(i_0_5653, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.76 cnf(i_0_3721, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))). 4.46/4.76 cnf(i_0_2089, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_3820, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,c_List_Olist_ONil(tc_fun(X1,tc_Nat_Onat))))))). 4.46/4.76 cnf(i_0_3558, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olistrel1(X1,X3))))). 4.46/4.76 cnf(i_0_3072, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olexord(X1,X3))))). 4.46/4.76 cnf(i_0_2786, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olex(X1,X3))))). 4.46/4.76 cnf(i_0_4742, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olistrel1(X1,X3))))). 4.46/4.76 cnf(i_0_2993, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olex(X1,X3))))). 4.46/4.76 cnf(i_0_2321, plain, (~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot)),c_fequal)),X2),X2)))). 4.46/4.76 cnf(i_0_3517, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Wellfounded_Omax__ext(X1,X3))))). 4.46/4.76 cnf(i_0_2984, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))). 4.46/4.76 cnf(i_0_2898, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)!=c_Int_OMin)). 4.46/4.76 cnf(i_0_4599, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))). 4.46/4.76 cnf(i_0_2629, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))). 4.46/4.76 cnf(i_0_600, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))). 4.46/4.76 cnf(i_0_2731, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))))). 4.46/4.76 cnf(i_0_1494, negated_conjecture, (~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Com_Ocom,c_Com_Ocom_OBODY),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,v_y))))). 4.46/4.76 cnf(i_0_2730, plain, (c_Groups_Oone__class_Oone(X1)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ozero__neq__one(X1))). 4.46/4.76 cnf(i_0_128, plain, (~class_Rings_Osemiring__1(X1)|~c_Int_Oiszero(X1,c_Groups_Oone__class_Oone(X1)))). 4.46/4.76 cnf(i_0_5044, plain, (~hBOOL(hAPP(c_fNot,X1))|~hBOOL(X1))). 4.46/4.76 cnf(i_0_4162, plain, (c_HOL_Oequal__class_Oequal(X1)=c_fequal|~class_HOL_Oequal(X1))). 4.46/4.76 cnf(i_0_6956, plain, (X1=X2|hAPP(c_Com_Ocom_OBODY,X1)!=hAPP(c_Com_Ocom_OBODY,X2))). 4.46/4.76 cnf(i_0_3785, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Nitpick_Owf_H(X1,X2))). 4.46/4.76 cnf(i_0_6482, plain, (class_Enum_Oenum(tc_Option_Ooption(X1))|~class_Enum_Oenum(X1))). 4.46/4.76 cnf(i_0_1068, plain, (class_Finite__Set_Ofinite(tc_Option_Ooption(X1))|~class_Finite__Set_Ofinite(X1))). 4.46/4.76 cnf(i_0_2061, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Wellfounded_Owf(X1,X2))). 4.46/4.76 cnf(i_0_7393, plain, (class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X1))|~class_Lazy__Sequence_Osmall__lazy(X1))). 4.46/4.76 cnf(i_0_2945, plain, (c_List_Onat__list(X1)|~c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X1)))). 4.46/4.76 cnf(i_0_3869, plain, (~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin))|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_5652, plain, (c_Orderings_Oord__class_Omin(X1)=c_Lattices_Osemilattice__inf__class_Oinf(X1)|~class_Lattices_Osemilattice__inf(X1)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_5750, plain, (c_Orderings_Oord__class_Omax(X1)=c_Lattices_Osemilattice__sup__class_Osup(X1)|~class_Lattices_Osemilattice__sup(X1)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_4139, plain, (X1=X2|~c_List_Olist__all2(X3,X3,c_fequal,X1,X2))). 4.46/4.76 cnf(i_0_2678, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|~class_Rings_Osemiring__1(X1)|~c_Int_Oiszero(X1,X2))). 4.46/4.76 cnf(i_0_3487, plain, (class_Groups_Ominus(tc_fun(X1,X2))|~class_Groups_Ominus(X2))). 4.46/4.76 cnf(i_0_5972, plain, (class_Lattices_Obounded__lattice__bot(tc_fun(X1,X2))|~class_Lattices_Obounded__lattice(X2))). 4.46/4.76 cnf(i_0_964, plain, (class_Orderings_Oorder(tc_fun(X1,X2))|~class_Orderings_Oorder(X2))). 4.46/4.76 cnf(i_0_471, plain, (X1=c_List_Olist_ONil(X2)|c_List_Oremdups(X2,X1)!=c_List_Olist_ONil(X2))). 4.46/4.76 cnf(i_0_6137, plain, (class_Orderings_Obot(tc_fun(X1,X2))|~class_Orderings_Obot(X2))). 4.46/4.76 cnf(i_0_4543, plain, (class_Lattices_Olattice(tc_fun(X1,X2))|~class_Lattices_Olattice(X2))). 4.46/4.76 cnf(i_0_3260, plain, (class_Lattices_Osemilattice__inf(tc_fun(X1,X2))|~class_Lattices_Olattice(X2))). 4.46/4.76 cnf(i_0_6597, plain, (class_Lattices_Osemilattice__sup(tc_fun(X1,X2))|~class_Lattices_Olattice(X2))). 4.46/4.76 cnf(i_0_5693, plain, (hBOOL(X1)|~hBOOL(hAPP(hAPP(c_fconj,X2),X1)))). 4.46/4.76 cnf(i_0_852, plain, (hBOOL(X1)|~hBOOL(hAPP(hAPP(c_fconj,X1),X2)))). 4.46/4.76 cnf(i_0_2178, plain, (class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,X2))|~class_Complete__Lattice_Ocomplete__lattice(X2))). 4.46/4.76 cnf(i_0_1593, plain, (class_Lattices_Obounded__lattice(tc_fun(X1,X2))|~class_Lattices_Obounded__lattice(X2))). 4.46/4.76 cnf(i_0_7384, plain, (class_Lattices_Obounded__lattice__top(tc_fun(X1,X2))|~class_Lattices_Obounded__lattice(X2))). 4.46/4.76 cnf(i_0_3713, plain, (class_Orderings_Opreorder(tc_fun(X1,X2))|~class_Orderings_Opreorder(X2))). 4.46/4.76 cnf(i_0_4738, plain, (class_Lattices_Oboolean__algebra(tc_fun(X1,X2))|~class_Lattices_Oboolean__algebra(X2))). 4.46/4.76 cnf(i_0_646, plain, (class_Orderings_Oord(tc_fun(X1,X2))|~class_Orderings_Oord(X2))). 4.46/4.76 cnf(i_0_1351, plain, (class_Lattices_Odistrib__lattice(tc_fun(X1,X2))|~class_Lattices_Odistrib__lattice(X2))). 4.46/4.76 cnf(i_0_6588, plain, (class_Groups_Ouminus(tc_fun(X1,X2))|~class_Groups_Ouminus(X2))). 4.46/4.76 cnf(i_0_7327, plain, (class_Orderings_Otop(tc_fun(X1,X2))|~class_Orderings_Otop(X2))). 4.46/4.76 cnf(i_0_2756, plain, (X1=X2|hAPP(c_Nat_OSuc,X1)!=hAPP(c_Nat_OSuc,X2))). 4.46/4.76 cnf(i_0_6302, plain, (X1=X2|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2))). 4.46/4.76 cnf(i_0_3081, plain, (X1=X2|c_Com_Ocom_OWhile(X3,X1)!=c_Com_Ocom_OWhile(X4,X2))). 4.46/4.76 cnf(i_0_3082, plain, (X1=X2|c_Com_Ocom_OWhile(X1,X3)!=c_Com_Ocom_OWhile(X2,X4))). 4.46/4.76 cnf(i_0_376, plain, (X1=X2|hAPP(c_Int_ORep__Integ,X1)!=hAPP(c_Int_ORep__Integ,X2))). 4.46/4.76 cnf(i_0_3552, plain, (X1=X2|hAPP(c_Code__Numeral_Onat__of,X1)!=hAPP(c_Code__Numeral_Onat__of,X2))). 4.46/4.76 cnf(i_0_2944, plain, (c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X1))|~c_List_Onat__list(X1))). 4.46/4.76 cnf(i_0_6435, plain, (X1=X2|c_Com_Ocom_OSemi(X3,X1)!=c_Com_Ocom_OSemi(X4,X2))). 4.46/4.76 cnf(i_0_6436, plain, (X1=X2|c_Com_Ocom_OSemi(X1,X3)!=c_Com_Ocom_OSemi(X2,X4))). 4.46/4.76 cnf(i_0_4844, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_fequal,X1),X2)))). 4.46/4.76 cnf(i_0_939, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_7361, plain, (~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)))). 4.46/4.76 cnf(i_0_2667, plain, (c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Osemiring__1(X1))). 4.46/4.76 cnf(i_0_603, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_5096, plain, (c_Wellfounded_Owf(X1,X2)|esk353_2(X2,X1)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_4223, plain, (c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3)|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3))). 4.46/4.76 cnf(i_0_3787, plain, (c_Nitpick_Owf_H(X1,X2)|~c_Nitpick_Ounknown(tc_HOL_Obool)|~c_Wellfounded_Oacyclic(X1,X2))). 4.46/4.76 cnf(i_0_3323, plain, (X1=c_List_Olist_ONil(X2)|hAPP(c_List_Orev(X2),X1)!=c_List_Olist_ONil(X2))). 4.46/4.76 cnf(i_0_144, plain, (X1=c_List_Olist_ONil(X2)|hAPP(c_List_Orotate1(X2),X1)!=c_List_Olist_ONil(X2))). 4.46/4.76 cnf(i_0_3640, plain, (hBOOL(hAPP(c_fNot,X1))|hBOOL(X1))). 4.46/4.76 cnf(i_0_1397, plain, (c_Option_Ooption_ONone(X1)=X2|c_Option_Oset(X1,X2)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_2912, plain, (X1=c_List_Olist_ONil(X2)|hAPP(c_List_Oset(X2),X1)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_49, plain, (c_Nat__Transfer_Ois__nat(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_2827, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|c_Groups_Osgn__class_Osgn(X2,X1)!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2))). 4.46/4.76 cnf(i_0_2634, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Oreplicate(X2,X1,X3)!=c_List_Olist_ONil(X2))). 4.46/4.76 cnf(i_0_6501, plain, (hBOOL(X1)|~hBOOL(hAPP(hAPP(c_fimplies,X2),X1))|~hBOOL(X2))). 4.46/4.76 cnf(i_0_4078, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)))). 4.46/4.76 cnf(i_0_5490, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.46/4.76 cnf(i_0_3840, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),X5)!=c_List_Olist_ONil(X1)|~class_Orderings_Olinorder(X2))). 4.46/4.76 cnf(i_0_2790, plain, (hBOOL(hAPP(c_Com_OWT,X1))|hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1)!=hAPP(c_Com_Obody,X2))). 4.46/4.76 cnf(i_0_7359, plain, (c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X1,X2))|~c_Nat__Transfer_Ois__nat(X2)|~c_Nat__Transfer_Ois__nat(X1))). 4.46/4.76 cnf(i_0_1559, plain, (class_Enum_Oenum(tc_fun(X1,X2))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2))). 4.46/4.76 cnf(i_0_5889, plain, (class_Enum_Oenum(tc_prod(X1,X2))|~class_Enum_Oenum(X2)|~class_Enum_Oenum(X1))). 4.46/4.76 cnf(i_0_704, plain, (class_Enum_Oenum(tc_sum(X1,X2))|~class_Enum_Oenum(X2)|~class_Enum_Oenum(X1))). 4.46/4.76 cnf(i_0_3158, plain, (hAPP(c_Com_Obody,X1)=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X1))))). 4.46/4.76 cnf(i_0_735, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(c_Set_Oimage(X2,X3,X4),X1)!=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_624, plain, (class_Smallcheck_Osmall(tc_prod(X1,X2))|~class_Smallcheck_Osmall(X2)|~class_Smallcheck_Osmall(X1))). 4.46/4.76 cnf(i_0_573, plain, (class_Finite__Set_Ofinite(tc_fun(X1,X2))|~class_Finite__Set_Ofinite(X1)|~class_Finite__Set_Ofinite(X2))). 4.46/4.76 cnf(i_0_4700, plain, (class_Finite__Set_Ofinite(tc_prod(X1,X2))|~class_Finite__Set_Ofinite(X1)|~class_Finite__Set_Ofinite(X2))). 4.46/4.76 cnf(i_0_4473, plain, (class_Finite__Set_Ofinite(tc_sum(X1,X2))|~class_Finite__Set_Ofinite(X1)|~class_Finite__Set_Ofinite(X2))). 4.46/4.76 cnf(i_0_1746, plain, (c_Complete__Lattice_OSup__class_OSup(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.46/4.76 cnf(i_0_1806, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.76 cnf(i_0_6225, plain, (class_HOL_Oequal(tc_fun(X1,X2))|~class_HOL_Oequal(X2)|~class_Enum_Oenum(X1))). 4.46/4.76 cnf(i_0_3009, plain, (class_Lazy__Sequence_Osmall__lazy(tc_prod(X1,X2))|~class_Lazy__Sequence_Osmall__lazy(X1)|~class_Lazy__Sequence_Osmall__lazy(X2))). 4.46/4.76 cnf(i_0_1600, plain, (~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)))). 4.46/4.76 cnf(i_0_1896, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Osemiring__1(X1))). 4.46/4.76 cnf(i_0_6442, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Osemiring__1(X1))). 4.46/4.76 cnf(i_0_2211, plain, (~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)))). 4.46/4.76 cnf(i_0_1697, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1(X1))). 4.46/4.76 cnf(i_0_2976, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__1(X1))). 4.46/4.76 cnf(i_0_853, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_7111, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X1),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_7112, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_4453, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|c_List_Oremdups(X1,X2)!=X2)). 4.46/4.76 cnf(i_0_1955, plain, (X1=X2|c_Com_Ocom_OLocal(X3,X4,X1)!=c_Com_Ocom_OLocal(X5,X6,X2))). 4.46/4.76 cnf(i_0_1956, plain, (X1=X2|c_Com_Ocom_OLocal(X3,X1,X4)!=c_Com_Ocom_OLocal(X5,X2,X6))). 4.46/4.76 cnf(i_0_1957, plain, (X1=X2|c_Com_Ocom_OLocal(X1,X3,X4)!=c_Com_Ocom_OLocal(X2,X5,X6))). 4.46/4.76 cnf(i_0_4909, plain, (X1=X2|c_Com_Ocom_OCond(X3,X4,X2)!=c_Com_Ocom_OCond(X5,X6,X1))). 4.46/4.76 cnf(i_0_4910, plain, (X1=X2|c_Com_Ocom_OCond(X3,X1,X4)!=c_Com_Ocom_OCond(X5,X2,X6))). 4.46/4.76 cnf(i_0_7026, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|esk490_1(X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_3887, plain, (hBOOL(hAPP(hAPP(c_fimplies,X1),X2))|~hBOOL(X2))). 4.46/4.76 cnf(i_0_3746, plain, (hBOOL(hAPP(hAPP(c_fdisj,X1),X2))|~hBOOL(X2))). 4.46/4.76 cnf(i_0_6360, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Osgn__if(X1))). 4.46/4.76 cnf(i_0_4908, plain, (X1=X2|c_Com_Ocom_OCond(X1,X3,X4)!=c_Com_Ocom_OCond(X2,X5,X6))). 4.46/4.76 cnf(i_0_1763, plain, (X1=X2|c_List_Oreplicate(X3,X1,X4)!=c_List_Oreplicate(X3,X2,X5))). 4.46/4.76 cnf(i_0_3980, plain, (X1=X2|c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X1)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X5,X2))). 4.46/4.76 cnf(i_0_3981, plain, (X1=X2|c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X1,X4)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X2,X5))). 4.46/4.76 cnf(i_0_2458, plain, (hBOOL(hAPP(hAPP(c_fdisj,X1),X2))|~hBOOL(X1))). 4.46/4.76 cnf(i_0_840, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)!=X2)). 4.46/4.76 cnf(i_0_5751, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Oappend(X2),X3),X1)!=X3)). 4.46/4.76 cnf(i_0_2580, plain, (c_Orderings_Oord_Omax(X1,c_Orderings_Oord__class_Oless__eq(X1))=c_Orderings_Oord__class_Omax(X1)|~class_Orderings_Oord(X1))). 4.46/4.76 cnf(i_0_6127, plain, (c_Hoare__Mirabelle_Otriple__valid(X1,X2,X3)|~c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(c_Nat_OSuc,X2),X3))). 4.46/4.76 cnf(i_0_1904, plain, (c_Relation_Osingle__valued(X1,X2,X3)|esk134_3(X3,X2,X1)!=esk133_3(X3,X2,X1))). 4.46/4.76 cnf(i_0_1900, plain, (c_Relation_Ototal__on(X1,X2,X3)|esk131_3(X3,X2,X1)!=esk130_3(X3,X2,X1))). 4.46/4.76 cnf(i_0_2969, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1))|~class_Lattices_Osemilattice__inf(X1))). 4.46/4.76 cnf(i_0_1690, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Oappend(X2),X1),X3)!=X3)). 4.46/4.76 cnf(i_0_4396, plain, (c_Orderings_Oord_Omin(X1,c_Orderings_Oord__class_Oless__eq(X1))=c_Orderings_Oord__class_Omin(X1)|~class_Orderings_Oord(X1))). 4.46/4.76 cnf(i_0_290, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1))|~class_Lattices_Osemilattice__sup(X1))). 4.46/4.76 cnf(i_0_4579, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Groups_Otimes__class_Otimes(X1))|~class_Lattices_Oab__semigroup__idem__mult(X1))). 4.46/4.76 cnf(i_0_4180, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Orderings_Oord__class_Omin(X1))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_602, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Orderings_Oord__class_Omax(X1))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_2082, plain, (c_Finite__Set_Ofun__left__comm(X1,X1,c_Groups_Otimes__class_Otimes(X1))|~class_Groups_Oab__semigroup__mult(X1))). 4.46/4.76 cnf(i_0_4084, plain, (X1=c_List_Olist_ONil(X2)|~c_List_Olist__all2(X2,X3,X4,X1,c_List_Olist_ONil(X3)))). 4.46/4.76 cnf(i_0_758, plain, (X1=c_List_Olist_ONil(X2)|~c_List_Olist__all2(X3,X2,X4,c_List_Olist_ONil(X3),X1))). 4.46/4.76 cnf(i_0_7142, plain, (c_List_Otranspose(X1,X2)=c_List_Olist_ONil(tc_List_Olist(X1))|esk504_2(X2,X1)!=c_List_Olist_ONil(X1))). 4.46/4.76 cnf(i_0_3990, plain, (c_List_Oremdups(X1,X2)=X2|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.46/4.76 cnf(i_0_7007, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Wellfounded_Omax__extp(X1,X3,X4,X2))). 4.46/4.76 cnf(i_0_7003, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Wellfounded_Omax__extp(X1,X3,X2,X4))). 4.46/4.76 cnf(i_0_7500, plain, (hBOOL(hAPP(X1,X2))|~epred1_3(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2))). 4.46/4.76 cnf(i_0_22, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1)!=X1|~class_Groups_Olinordered__ab__group__add(X2))). 4.46/4.76 cnf(i_0_2227, plain, (X1=c_List_Olist_ONil(X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_7213, plain, (X1=X2|hAPP(c_List_Orev(X3),X1)!=hAPP(c_List_Orev(X3),X2))). 4.46/4.76 cnf(i_0_2828, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1))). 4.46/4.76 cnf(i_0_5896, plain, (X1=X2|hAPP(c_Option_Ooption_OSome(X3),X1)!=hAPP(c_Option_Ooption_OSome(X3),X2))). 4.46/4.76 cnf(i_0_5273, plain, (c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,hAPP(c_List_Orev(X1),X3)))). 4.46/4.76 cnf(i_0_282, plain, (c_List_Olist__ex(X1,X2,X3)|~c_List_Olist__ex(X1,X2,hAPP(c_List_Orev(X1),X3)))). 4.46/4.76 cnf(i_0_695, plain, (~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_7032, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))). 4.46/4.76 cnf(i_0_2349, plain, (hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X2)),X3)=c_Orderings_Obot__class_Obot(X2)|~class_Orderings_Obot(X2))). 4.46/4.76 cnf(i_0_6891, plain, (~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_60, plain, (c_List_Olist__all(X1,X2,X3)|~hBOOL(hAPP(X2,esk6_3(X2,X3,X1))))). 4.46/4.76 cnf(i_0_3705, plain, (c_List_Olist__all(X1,X2,X3)|~hBOOL(hAPP(X2,esk252_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_7274, plain, (c_List_Olist__all(X1,X2,X3)|~hBOOL(hAPP(X2,esk517_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_1211, plain, (X1=X2|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))). 4.46/4.76 cnf(i_0_5199, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|esk360_2(X2,X1)!=esk361_2(X2,X1))). 4.46/4.76 cnf(i_0_4150, plain, (c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))|~c_Nat__Transfer_Ois__nat(X1))). 4.46/4.76 cnf(i_0_3564, plain, (hBOOL(X1)|hBOOL(X2)|~hBOOL(hAPP(hAPP(c_fdisj,X1),X2)))). 4.46/4.76 cnf(i_0_3917, plain, (hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk269_1(X1))=hAPP(c_Com_Obody,X1)|~hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X1))))). 4.46/4.76 cnf(i_0_3945, plain, (hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk271_1(X1))=hAPP(c_Com_Obody,X1)|~hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X1))))). 4.46/4.76 cnf(i_0_3700, plain, (c_Wellfounded_OwfP(X1,X2)|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk251_2(X2,X1))))). 4.46/4.76 cnf(i_0_3797, plain, (epred1_3(X1,X2,X3)|~hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2))))). 4.46/4.76 cnf(i_0_2439, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(c_Groups_Oabs__class_Oabs(X2),X1)!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Oordered__ab__group__add__abs(X2))). 4.46/4.76 cnf(i_0_1990, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1)!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ogroup__add(X2))). 4.46/4.76 cnf(i_0_3736, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Finite__Set_Ofinite(X1))). 4.46/4.76 cnf(i_0_5844, plain, (c_Complete__Lattice_OInf__class_OInf(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.46/4.76 cnf(i_0_21, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Olinordered__ab__group__add(X1))). 4.46/4.76 cnf(i_0_2582, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Oappend(X2),X3),X1)!=c_List_Olist_ONil(X2))). 4.46/4.76 cnf(i_0_2583, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_List_Oappend(X1),X2),X3)!=c_List_Olist_ONil(X1))). 4.46/4.76 cnf(i_0_2611, plain, (c_List_Olinorder__class_Osorted__list__of__set(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_List_Olist_ONil(X1)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_50, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~c_Nat__Transfer_Ois__nat(X1))). 4.46/4.76 cnf(i_0_3311, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X2,X1))))). 4.46/4.76 cnf(i_0_5154, plain, (X1=X2|~class_HOL_Oequal(X3)|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X3),X1),X2)))). 4.46/4.76 cnf(i_0_4558, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X2,X1))))). 4.46/4.76 cnf(i_0_4559, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X1,X2))))). 4.46/4.76 cnf(i_0_3909, plain, (X1=X2|c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X1)!=c_Nitpick_Opair__box_OPairBox(X3,X4,X6,X2))). 4.46/4.76 cnf(i_0_3910, plain, (X1=X2|c_Nitpick_Opair__box_OPairBox(X3,X4,X1,X5)!=c_Nitpick_Opair__box_OPairBox(X3,X4,X2,X6))). 4.46/4.76 cnf(i_0_2647, plain, (c_Divides_Odiv__class_Omod(X1,X2,X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.46/4.76 cnf(i_0_4085, plain, (c_Relation_Orefl__on(X1,X2,X3)|~c_Relation_Orefl__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3)))). 4.46/4.76 cnf(i_0_1864, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2))))). 4.46/4.76 cnf(i_0_827, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),X1)))). 4.46/4.76 cnf(i_0_2426, plain, (c_Relation_Ototal__on(X1,X2,X3)|~c_Relation_Ototal__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3)))). 4.46/4.76 cnf(i_0_1695, plain, (X1=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X1),X2)!=c_Groups_Ozero__class_Ozero(X3)|~class_Groups_Ogroup__add(X3))). 4.46/4.76 cnf(i_0_6167, plain, (X1=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X1),X2)!=c_Groups_Ozero__class_Ozero(X3)|~class_Groups_Oab__group__add(X3))). 4.46/4.76 cnf(i_0_934, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.46/4.76 cnf(i_0_3944, plain, (hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X1)))|hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X2)!=hAPP(c_Com_Obody,X1))). 4.46/4.76 cnf(i_0_5178, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X3),X2)))). 4.46/4.76 cnf(i_0_6729, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Oring__char__0(X1))). 4.46/4.76 cnf(i_0_6728, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)!=c_Groups_Ozero__class_Ozero(X2)|~class_Int_Oring__char__0(X2))). 4.46/4.76 cnf(i_0_308, plain, (hBOOL(hAPP(hAPP(c_fimplies,X1),X2))|hBOOL(X1))). 4.46/4.76 cnf(i_0_5040, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_3111, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Oremdups(X1,X2))|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_906, plain, (X1=X2|hAPP(c_SetInterval_Oord__class_OatLeast(X3),X1)!=hAPP(c_SetInterval_Oord__class_OatLeast(X3),X2)|~class_Orderings_Olinorder(X3))). 4.46/4.76 cnf(i_0_2565, plain, (X1=X2|hAPP(c_SetInterval_Oord__class_OatMost(X3),X1)!=hAPP(c_SetInterval_Oord__class_OatMost(X3),X2)|~class_Orderings_Olinorder(X3))). 4.46/4.76 cnf(i_0_3251, plain, (X1=X2|hAPP(c_SetInterval_Oord__class_OlessThan(X3),X1)!=hAPP(c_SetInterval_Oord__class_OlessThan(X3),X2)|~class_Orderings_Olinorder(X3))). 4.46/4.76 cnf(i_0_3449, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_6724, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_7244, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1))=c_Orderings_Obot__class_Obot(X1)|~class_Lattices_Oboolean__algebra(X1))). 4.46/4.76 cnf(i_0_501, plain, (X1=X2|hAPP(c_SetInterval_Oord__class_OgreaterThan(X3),X1)!=hAPP(c_SetInterval_Oord__class_OgreaterThan(X3),X2)|~class_Orderings_Olinorder(X3))). 4.46/4.76 cnf(i_0_1011, plain, (X1=c_Option_Ooption_ONone(X2)|hAPP(hAPP(c_Option_Omap(X2,X3),X4),X1)!=c_Option_Ooption_ONone(X3))). 4.46/4.76 cnf(i_0_6725, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_2662, plain, (X1=X2|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),X1)!=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),X2))). 4.46/4.76 cnf(i_0_2104, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2)=X2|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_25, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 4.46/4.76 cnf(i_0_6064, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)!=c_List_Olist_ONil(X1))). 4.46/4.76 cnf(i_0_1471, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_List_Omap(X1,X3),X4),X2)!=c_List_Olist_ONil(X3))). 4.46/4.76 cnf(i_0_4081, plain, (c_List_OtakeWhile(X1,X2,X3)=X3|~hBOOL(hAPP(X2,esk277_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_317, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2)=X2|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_1612, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X4),X3)))). 4.46/4.76 cnf(i_0_5657, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.46/4.76 cnf(i_0_5591, plain, (c_Enum_Oall__n__lists(X1,X2,X3)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(X2,esk387_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_6591, plain, (c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))|~c_Nat__Transfer_Ois__nat(X2)|~c_Nat__Transfer_Ois__nat(X1))). 4.46/4.76 cnf(i_0_2312, plain, (c_Wellfounded_Owf(X1,c_Wellfounded_Omlex__prod(X1,X2,X3))|~c_Wellfounded_Owf(X1,X3))). 4.46/4.76 cnf(i_0_480, plain, (c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X2))|~c_Wellfounded_Owf(X1,X2))). 4.46/4.76 cnf(i_0_4548, plain, (c_Complete__Lattice_OInf__class_OInf(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.46/4.76 cnf(i_0_3254, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1))=c_Orderings_Otop__class_Otop(X1)|~class_Lattices_Oboolean__algebra(X1))). 4.46/4.76 cnf(i_0_670, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),c_List_Olist_ONil(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Omonoid__add(X1))). 4.46/4.76 cnf(i_0_5993, plain, (c_Nat__Transfer_Onat__set(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk412_1(X1))))). 4.46/4.76 cnf(i_0_2967, plain, (c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_2880, plain, (c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X2))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_514, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_7318, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Oone__class_Oone(X1))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1))). 4.46/4.76 cnf(i_0_2878, plain, (c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_2872, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X2,X3,X1))))). 4.46/4.76 cnf(i_0_2875, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X2,X3,X1))))). 4.46/4.76 cnf(i_0_6565, plain, (X1=c_Orderings_Obot__class_Obot(X2)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X3)!=c_Orderings_Obot__class_Obot(X2)|~class_Lattices_Obounded__lattice__bot(X2))). 4.46/4.76 cnf(i_0_2876, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X2,X1,X3))))). 4.46/4.76 cnf(i_0_3802, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|esk261_4(X4,X3,X2,X1)!=esk262_4(X4,X3,X2,X1))). 4.46/4.76 cnf(i_0_6566, plain, (c_Orderings_Obot__class_Obot(X1)=X2|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)!=c_Orderings_Obot__class_Obot(X1)|~class_Lattices_Obounded__lattice__bot(X1))). 4.46/4.76 cnf(i_0_6388, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_3767, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_2147, plain, (X1=X2|hAPP(X1,esk160_2(X1,X2))!=hAPP(X2,esk160_2(X1,X2)))). 4.46/4.76 cnf(i_0_2577, plain, (c_Fun_Oinj__on(X1,X1,c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Groups_Oordered__ab__group__add(X1))). 4.46/4.76 cnf(i_0_2752, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.46/4.76 cnf(i_0_626, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_Enum_Oenum__class_Oenum(X1)))|~class_Enum_Oenum(X1))). 4.46/4.76 cnf(i_0_1786, plain, (hBOOL(hAPP(hAPP(c_fconj,X1),X2))|~hBOOL(X2)|~hBOOL(X1))). 4.46/4.76 cnf(i_0_3796, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))|~epred1_3(X1,X3,X2))). 4.46/4.76 cnf(i_0_666, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)))). 4.46/4.76 cnf(i_0_5532, plain, (X1=X2|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X1)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X2)|~class_Nat_Osemiring__char__0(X3))). 4.46/4.76 cnf(i_0_6770, plain, (X1=X2|hAPP(c_Groups_Ouminus__class_Ouminus(X3),X1)!=hAPP(c_Groups_Ouminus__class_Ouminus(X3),X2)|~class_Groups_Ogroup__add(X3))). 4.46/4.76 cnf(i_0_555, plain, (X1=X2|hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))!=hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))). 4.46/4.76 cnf(i_0_2257, plain, (X1=X2|hAPP(c_Groups_Ouminus__class_Ouminus(X3),X1)!=hAPP(c_Groups_Ouminus__class_Ouminus(X3),X2)|~class_Lattices_Oboolean__algebra(X3))). 4.46/4.76 cnf(i_0_191, plain, (X1=X2|hAPP(c_Int_Oring__1__class_Oof__int(X3),X1)!=hAPP(c_Int_Oring__1__class_Oof__int(X3),X2)|~class_Int_Oring__char__0(X3))). 4.46/4.76 cnf(i_0_6072, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X3),X1)!=X3|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2))). 4.46/4.76 cnf(i_0_365, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.46/4.76 cnf(i_0_1988, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool))|hAPP(c_Relation_ODomain(X2,X3),X1)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_6816, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))=X3|hAPP(c_Relation_ORange(X1,X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_3468, plain, (c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Ozero__class_Ozero(X1))=X2|~class_Divides_Osemiring__div(X1))). 4.46/4.76 cnf(i_0_784, plain, (c_Nat__Transfer_Ois__nat(X1)|~c_Nat__Transfer_Onat__set(X2)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2)))). 4.46/4.76 cnf(i_0_205, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Ois__nat(X1))). 4.46/4.76 cnf(i_0_6086, plain, (c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)))). 4.46/4.76 cnf(i_0_4529, plain, (c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X4),X3)))). 4.46/4.76 cnf(i_0_4528, plain, (c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4)))). 4.46/4.76 cnf(i_0_1759, plain, (hAPP(c_Int_Onat,X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_6322, plain, (epred2_3(X1,X2,X3)|~hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X2))))). 4.46/4.76 cnf(i_0_5051, plain, (~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_503, plain, (~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_1382, plain, (hAPP(X1,X2)!=c_Option_Ooption_ONone(X3)|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_Map_Odom(X4,X3,X1))))). 4.46/4.76 cnf(i_0_2343, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2)=X2|~class_Lattices_Osemilattice__inf(X1))). 4.46/4.76 cnf(i_0_1462, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2)=X2|~class_Lattices_Olattice(X1))). 4.46/4.76 cnf(i_0_3906, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Oacyclic(X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)))). 4.46/4.76 cnf(i_0_4370, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,esk301_2(X2,X1)))))). 4.46/4.76 cnf(i_0_879, plain, (c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olenlex(X1,X2))|~c_Wellfounded_Owf(X1,X2))). 4.46/4.76 cnf(i_0_4218, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2)=X2|~class_Lattices_Osemilattice__sup(X1))). 4.46/4.76 cnf(i_0_2060, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)=X2|~class_Lattices_Oab__semigroup__idem__mult(X1))). 4.46/4.76 cnf(i_0_1505, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2)=X2|~class_Lattices_Olattice(X1))). 4.46/4.76 cnf(i_0_5756, plain, (c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olex(X1,X2))|~c_Wellfounded_Owf(X1,X2))). 4.46/4.76 cnf(i_0_6187, plain, (~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)))). 4.46/4.76 cnf(i_0_7093, plain, (~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)))). 4.46/4.76 cnf(i_0_4976, plain, (c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3)|~c_Hoare__Mirabelle_Otriple__valid(X1,esk347_3(X3,X2,X1),esk348_3(X3,X2,X1)))). 4.46/4.76 cnf(i_0_4775, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Olinordered__ab__group__add(X1))). 4.46/4.76 cnf(i_0_4468, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.46/4.76 cnf(i_0_4310, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__1__no__zero__divisors(X1))). 4.46/4.76 cnf(i_0_6085, plain, (hBOOL(hAPP(X1,X2))|~c_List_Olist__all(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)))). 4.46/4.76 cnf(i_0_3236, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X3,X4,X1),X5),X2)))). 4.46/4.76 cnf(i_0_984, plain, (c_Random_Olog(X1,X2)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X2),X1)))). 4.46/4.76 cnf(i_0_4410, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))=hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_7125, plain, (c_List_Oupto(X1,X2)=c_List_Olist_ONil(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)))). 4.46/4.76 cnf(i_0_2414, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X2))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(X2,esk182_2(X2,X1))))). 4.46/4.76 cnf(i_0_7201, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X2))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(X2,esk509_2(X2,X1))))). 4.46/4.76 cnf(i_0_7259, plain, (X1=X2|hAPP(X3,X1)!=hAPP(X3,X2)|~c_Typedef_Otype__definition(X4,X5,X3,X6,X7))). 4.46/4.76 cnf(i_0_3739, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osorted__list__of__set(X1,X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_5899, plain, (c_List_Olinorder__class_Osorted(X1,esk407_2(X2,X1))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_4681, plain, (c_List_Olinorder__class_Osorted(X1,c_List_OtakeWhile(X1,X2,X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_2778, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Oremove1(X1,X2,X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_3733, plain, (hAPP(c_Option_Ooption_OSome(X1),esk259_2(X1,X2))=X2|c_Option_Ooption_ONone(X1)=X2)). 4.46/4.76 cnf(i_0_6731, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X4)|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3))). 4.46/4.76 cnf(i_0_4714, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.46/4.76 cnf(i_0_3897, plain, (hAPP(c_Option_Ooption_OSome(X1),esk268_2(X1,X2))=X2|c_Option_Ooption_ONone(X1)=X2)). 4.46/4.76 cnf(i_0_2415, plain, (hBOOL(hAPP(X1,X2))|~class_Enum_Oenum(X3)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X3),X1)))). 4.46/4.76 cnf(i_0_5574, plain, (hAPP(c_List_Ofilter(X1,X2),X3)=X3|~hBOOL(hAPP(X2,esk386_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_513, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.46/4.76 cnf(i_0_3416, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)=X3|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.46/4.76 cnf(i_0_5252, plain, (hBOOL(hAPP(hAPP(X1,X2),X2))|~c_Equiv__Relations_Oequivp(X3,X1))). 4.46/4.76 cnf(i_0_4260, plain, (hBOOL(hAPP(hAPP(X1,X2),X2))|~c_Predicate_Oreflp(X3,X1))). 4.46/4.76 cnf(i_0_3833, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X1)=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1)). 4.46/4.76 cnf(i_0_7292, plain, (hBOOL(hAPP(X1,c_Option_Ooption_ONone(X2)))|~class_Enum_Oenum(X2)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X2)),X1)))). 4.46/4.76 cnf(i_0_3786, plain, (c_Nitpick_Owf_H(X1,X2)|~c_Wellfounded_Oacyclic(X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)))). 4.46/4.76 cnf(i_0_5078, plain, (c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Oone__class_Oone(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.46/4.76 cnf(i_0_607, plain, (c_Fun_Oid(X1)=hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))|~c_Finite__Set_Ofolding(X3,X1,X4,X2))). 4.46/4.76 cnf(i_0_7236, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(c_Finite__Set_Ocard(X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_6558, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1))=X2|~class_Lattices_Obounded__lattice__bot(X1))). 4.46/4.76 cnf(i_0_4441, plain, (c_Nitpick_Ocard_H(X1,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_3156, plain, (c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.46/4.76 cnf(i_0_2519, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~c_Wellfounded_OwfP(X1,X2))). 4.46/4.76 cnf(i_0_6201, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2)=X2|~class_Lattices_Obounded__lattice__bot(X1))). 4.46/4.76 cnf(i_0_1753, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(X2,esk120_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_1442, plain, (hBOOL(hAPP(c_Predicate_OPowp(X1,X2),X3))|~hBOOL(hAPP(X2,esk96_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_763, plain, (X1=X2|hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)!=hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)|~class_Int_Oring__char__0(X3)|~class_Int_Onumber__ring(X3))). 4.46/4.76 cnf(i_0_7091, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X2))=c_Groups_Osgn__class_Osgn(X1,X2)|~class_Rings_Olinordered__idom(X1))). 4.46/4.76 cnf(i_0_4244, plain, (c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),esk292_2(X2,X1)),c_Wellfounded_Oacc(X1,X2))))). 4.46/4.76 cnf(i_0_3255, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)))). 4.46/4.76 cnf(i_0_1596, plain, (X1=X2|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X3,X4,X5,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X2)))). 4.46/4.76 cnf(i_0_4461, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_149, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1))=c_Orderings_Obot__class_Obot(X1)|~class_Lattices_Obounded__lattice__bot(X1))). 4.46/4.76 cnf(i_0_4560, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2)=c_Orderings_Obot__class_Obot(X1)|~class_Lattices_Obounded__lattice__bot(X1))). 4.46/4.76 cnf(i_0_6742, plain, (c_Complete__Lattice_OSup__class_OSup(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.46/4.76 cnf(i_0_1760, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_951, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)))). 4.46/4.76 cnf(i_0_5279, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))). 4.46/4.76 cnf(i_0_3490, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)))). 4.46/4.76 cnf(i_0_5156, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_1362, plain, (X1=c_Orderings_Otop__class_Otop(X2)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X3),X1)!=c_Orderings_Otop__class_Otop(X2)|~class_Lattices_Obounded__lattice__top(X2))). 4.46/4.76 cnf(i_0_1363, plain, (X1=c_Orderings_Otop__class_Otop(X2)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X3)!=c_Orderings_Otop__class_Otop(X2)|~class_Lattices_Obounded__lattice__top(X2))). 4.46/4.76 cnf(i_0_2304, plain, (hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|~class_Enum_Oenum(X1))). 4.46/4.76 cnf(i_0_2256, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Otl(X1),X2))|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_1941, plain, (hAPP(hAPP(X1,X2),X2)=X2|~c_Finite__Set_Ofolding__one__idem(X3,X1,X4))). 4.46/4.76 cnf(i_0_3133, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X1),X2)))). 4.46/4.76 cnf(i_0_4795, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X1),X4),X2)))). 4.46/4.76 cnf(i_0_6244, plain, (c_Option_Ooption_ONone(X1)=hAPP(X2,X3)|hAPP(c_Map_Omap__add(X4,X1,X5,X2),X3)!=c_Option_Ooption_ONone(X1))). 4.46/4.76 cnf(i_0_6243, plain, (c_Option_Ooption_ONone(X1)=hAPP(X2,X3)|hAPP(c_Map_Omap__add(X4,X1,X2,X5),X3)!=c_Option_Ooption_ONone(X1))). 4.46/4.76 cnf(i_0_985, plain, (c_Random_Olog(X1,X2)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))). 4.46/4.76 cnf(i_0_1853, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X2))))). 4.46/4.76 cnf(i_0_3600, plain, (hAPP(c_Nat_OSuc,esk244_1(X1))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.46/4.76 cnf(i_0_3312, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X1,X2)))|~hBOOL(hAPP(c_Com_OWT,X2)))). 4.46/4.76 cnf(i_0_5195, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X2))))). 4.46/4.76 cnf(i_0_493, plain, (c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)=X3|~class_Rings_Osemiring__1(X1))). 4.46/4.76 cnf(i_0_3773, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X2),X6)))). 4.46/4.76 cnf(i_0_3159, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))))). 4.46/4.76 cnf(i_0_6974, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_3775, plain, (hAPP(X1,X2)=X3|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X5),X1),X2),X3)!=X1)). 4.46/4.76 cnf(i_0_4079, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))|~c_Wellfounded_Oacyclic(X1,X2))). 4.46/4.76 cnf(i_0_973, plain, (c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X2))|~c_Wellfounded_Owf(X1,X2))). 4.46/4.76 cnf(i_0_6150, plain, (c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X2))|~c_Wellfounded_Owf(X1,X2))). 4.46/4.76 cnf(i_0_6540, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2))|~class_Orderings_Opreorder(X1))). 4.46/4.76 cnf(i_0_2721, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X2),X2))|~class_HOL_Oequal(X1))). 4.46/4.76 cnf(i_0_1654, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)))). 4.46/4.76 cnf(i_0_575, plain, (X1=X2|hAPP(hAPP(c_List_Oappend(X3),X4),X1)!=hAPP(hAPP(c_List_Oappend(X3),X4),X2))). 4.46/4.76 cnf(i_0_828, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(X3,X2)))). 4.46/4.76 cnf(i_0_5691, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),esk393_1(X1)))))). 4.46/4.76 cnf(i_0_4140, plain, (X1=X2|hAPP(hAPP(c_List_Oappend(X3),X1),X4)!=hAPP(hAPP(c_List_Oappend(X3),X2),X4))). 4.46/4.76 cnf(i_0_2270, plain, (X1=X2|hAPP(hAPP(c_List_Olist_OCons(X3),X4),X2)!=hAPP(hAPP(c_List_Olist_OCons(X3),X5),X1))). 4.46/4.76 cnf(i_0_2271, plain, (X1=X2|hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4)!=hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))). 4.46/4.76 cnf(i_0_5868, plain, (c_FunDef_OTHE__default(X1,X2,X3)=c_HOL_OThe(X1,X3)|esk404_4(X2,X1,X3,X4)!=X4|~hBOOL(hAPP(X3,X4)))). 4.46/4.76 cnf(i_0_6837, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))))). 4.46/4.76 cnf(i_0_911, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Orderings_Obot__class_Obot(X1)),X2))|~class_Orderings_Obot(X1))). 4.46/4.76 cnf(i_0_4557, plain, (~class_Rings_Olinordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_6524, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_4465, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X2))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(X2,X3)))). 4.46/4.76 cnf(i_0_1749, plain, (c_List_Olinorder__class_Osort__key(X1,X2,X3,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1)|~class_Orderings_Olinorder(X2))). 4.46/4.76 cnf(i_0_1617, plain, (hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4))|~hBOOL(hAPP(X3,X4)))). 4.46/4.76 cnf(i_0_1764, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|X2=X3|c_List_Oreplicate(X4,X1,X2)!=c_List_Oreplicate(X4,X5,X3))). 4.46/4.76 cnf(i_0_3175, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)=X2|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_3781, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 4.46/4.76 cnf(i_0_1263, plain, (hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,X2)),X3)=c_Orderings_Otop__class_Otop(X2)|~class_Orderings_Otop(X2))). 4.46/4.76 cnf(i_0_69, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 4.46/4.76 cnf(i_0_3783, plain, (~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1)))))). 4.46/4.76 cnf(i_0_6987, plain, (c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),X2))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_6153, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))). 4.46/4.76 cnf(i_0_2525, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))). 4.46/4.76 cnf(i_0_7295, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Oinj__on(X1,X5,hAPP(c_Fun_Ocomp(X2,X5,X1,X6),X3),X4))). 4.46/4.76 cnf(i_0_4210, plain, (hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1)))|~hBOOL(hAPP(X1,X3)))). 4.46/4.76 cnf(i_0_2904, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=X1|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.46/4.76 cnf(i_0_6543, plain, (hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))=X3|~c_Finite__Set_Ofolding__image__simple(X4,X2,X5,X3,X6,X1))). 4.46/4.76 cnf(i_0_6573, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.46/4.76 cnf(i_0_1199, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_5272, plain, (c_List_Olist__all(X1,X2,hAPP(c_List_Orev(X1),X3))|~c_List_Olist__all(X1,X2,X3))). 4.46/4.76 cnf(i_0_283, plain, (c_List_Olist__ex(X1,X2,hAPP(c_List_Orev(X1),X3))|~c_List_Olist__ex(X1,X2,X3))). 4.46/4.76 cnf(i_0_4209, plain, (hBOOL(hAPP(X1,esk286_2(X2,X1)))|~hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1))))). 4.46/4.76 cnf(i_0_1244, plain, (c_Random_Oinc__shift(X1,X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))|X2=X1)). 4.46/4.76 cnf(i_0_2164, plain, (hBOOL(hAPP(X1,esk162_3(X2,X1,X3)))|~c_List_Olist__ex1(X3,X1,X2))). 4.46/4.76 cnf(i_0_5036, plain, (hBOOL(hAPP(X1,esk352_3(X2,X1,X3)))|~c_List_Olist__ex(X3,X1,X2))). 4.46/4.76 cnf(i_0_7048, plain, (hBOOL(hAPP(X1,esk493_3(X2,X1,X3)))|~c_List_Olist__ex1(X3,X1,X2))). 4.46/4.76 cnf(i_0_4691, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)!=X3)). 4.46/4.76 cnf(i_0_5744, plain, (X1=X2|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X2))))). 4.46/4.76 cnf(i_0_6221, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(X1)|~class_Power_Opower(X1)|~class_Rings_Ono__zero__divisors(X1)|~class_Rings_Ozero__neq__one(X1)|~class_Rings_Omult__zero(X1))). 4.46/4.76 cnf(i_0_7062, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X3,X2),tc_HOL_Obool))!=c_Sum__Type_OPlus(X3,X2,X4,X1))). 4.46/4.76 cnf(i_0_7063, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X1,X3),tc_HOL_Obool))!=c_Sum__Type_OPlus(X1,X3,X2,X4))). 4.46/4.76 cnf(i_0_2810, plain, (hAPP(c_Int_ORep__Integ,esk200_1(X1))=X1|~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Int_OInteg)))). 4.46/4.76 cnf(i_0_2886, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2))))). 4.46/4.76 cnf(i_0_3318, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=X2|~class_Groups_Ogroup__add(X1))). 4.46/4.76 cnf(i_0_7501, plain, (epred2_3(X1,X2,X3)|~hBOOL(hAPP(X1,esk535_3(X3,X2,X1)))|~hBOOL(hAPP(X1,esk537_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_1070, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_List_Oset(X3),c_List_Oreplicate(X3,X4,X2)))))). 4.46/4.76 cnf(i_0_1615, plain, (X1=X2|hBOOL(hAPP(X3,X2))|~hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X4),X1),X3),X2)))). 4.46/4.76 cnf(i_0_6783, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))))). 4.46/4.76 cnf(i_0_96, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Ois__nat(X2)|~c_Nat__Transfer_Ois__nat(X1))). 4.46/4.76 cnf(i_0_3745, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Ois__nat(X2)|~c_Nat__Transfer_Ois__nat(X1))). 4.46/4.76 cnf(i_0_7211, plain, (X1=X2|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X4),X2))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X4),X1)))). 4.46/4.76 cnf(i_0_5599, plain, (X1=hAPP(c_Option_Ooption_OSome(X2),X3)|~hBOOL(hAPP(hAPP(c_member(X2),X3),c_Option_Oset(X2,X1))))). 4.46/4.76 cnf(i_0_3324, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Ois__nat(X2)|~c_Nat__Transfer_Ois__nat(X1))). 4.46/4.76 cnf(i_0_1296, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))))). 4.46/4.76 cnf(i_0_3399, plain, (~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)))). 4.46/4.76 cnf(i_0_3152, plain, (~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)))). 4.46/4.76 cnf(i_0_505, plain, (~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)))). 4.46/4.76 cnf(i_0_4545, plain, (X1=X2|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X4,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X2)))). 4.46/4.76 cnf(i_0_3314, plain, (c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_6114, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1))). 4.46/4.76 cnf(i_0_2041, plain, (c_Power_Opower_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1))=c_Power_Opower__class_Opower(X1)|~class_Power_Opower(X1))). 4.46/4.76 cnf(i_0_3106, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Lattices_Olattice(X1))). 4.46/4.76 cnf(i_0_824, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Lattices_Olattice(X1))). 4.46/4.76 cnf(i_0_765, plain, (c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.46/4.76 cnf(i_0_5324, plain, (c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_5150, plain, (c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_4654, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(c_List_Olistsp(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))))). 4.46/4.76 cnf(i_0_1553, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),X2))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_3588, plain, (c_Lazy__Sequence_Osmall__lazy_H(X1,X2)=c_Lazy__Sequence_Oempty(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.46/4.76 cnf(i_0_5372, plain, (c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.46/4.76 cnf(i_0_3252, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_1646, plain, (hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.46/4.76 cnf(i_0_5352, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2)))). 4.46/4.76 cnf(i_0_4466, plain, (hBOOL(hAPP(X1,esk310_2(X1,X2)))|~class_Enum_Oenum(X2)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X2),X1)))). 4.46/4.76 cnf(i_0_5126, plain, (hBOOL(hAPP(X1,esk356_2(X1,X2)))|~class_Enum_Oenum(X2)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X2),X1)))). 4.46/4.76 cnf(i_0_3575, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk240_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_5180, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)))). 4.46/4.76 cnf(i_0_7336, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2|~class_Rings_Ocomm__semiring__1(X1))). 4.46/4.76 cnf(i_0_6530, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk453_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_1611, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4,X5,X1),X3),X2)))). 4.46/4.76 cnf(i_0_3978, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2|~class_Groups_Omonoid__mult(X1))). 4.46/4.76 cnf(i_0_1237, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=X2|~class_Lattices_Oboolean__algebra(X1))). 4.46/4.76 cnf(i_0_5124, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Groups_Ocomm__monoid__add(X1))). 4.46/4.76 cnf(i_0_1528, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Rings_Ocomm__semiring__1(X1))). 4.46/4.76 cnf(i_0_3237, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X4,X1,X5),X2),X3)))). 4.46/4.76 cnf(i_0_2017, plain, (c_List_Olist__all(X1,X2,X3)|~hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),esk145_3(X3,X2,X1)))))). 4.46/4.76 cnf(i_0_362, plain, (hAPP(X1,hAPP(X2,X3))=X3|~c_Typedef_Otype__definition(X4,X5,X2,X1,X6))). 4.46/4.76 cnf(i_0_5377, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Rings_Odivision__ring(X1))). 4.46/4.76 cnf(i_0_5739, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Rings_Ocomm__semiring__1(X1))). 4.46/4.76 cnf(i_0_5955, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Groups_Omonoid__mult(X1))). 4.46/4.76 cnf(i_0_4270, plain, (c_SMT_Oz3mod(X1,X2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.76 cnf(i_0_4648, plain, (c_Wellfounded_OwfP(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))). 4.46/4.76 cnf(i_0_1879, plain, (c_Wellfounded_Owf(X1,X2)|hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_7409, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=X2|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Odivision__ring(X1))). 4.46/4.76 cnf(i_0_407, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Orderings_Otop__class_Otop(X1))=X2|~class_Lattices_Obounded__lattice__top(X1))). 4.46/4.76 cnf(i_0_1966, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Groups_Ogroup__add(X1))). 4.46/4.76 cnf(i_0_1907, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Groups_Omonoid__add(X1))). 4.46/4.76 cnf(i_0_515, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Groups_Ocomm__monoid__mult(X1))). 4.46/4.76 cnf(i_0_3469, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Divides_Osemiring__div(X1))). 4.46/4.76 cnf(i_0_6032, plain, (hAPP(X1,X2)=hAPP(X1,X3)|~c_Equiv__Relations_Oequivp(X4,X1)|~hBOOL(hAPP(hAPP(X1,X2),X3)))). 4.46/4.76 cnf(i_0_6124, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk424_2(X1,X2)),X2)))). 4.46/4.76 cnf(i_0_1541, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk99_2(X1,X2)),X2)))). 4.46/4.76 cnf(i_0_6473, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~class_Orderings_Olinorder(X3)|~hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Osort__key(X1,X3,X4,X2))))). 4.46/4.76 cnf(i_0_7247, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2)=X2|~class_Lattices_Obounded__lattice__top(X1))). 4.46/4.76 cnf(i_0_3202, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=X2|~class_Rings_Ocomm__semiring__1(X1))). 4.46/4.76 cnf(i_0_3543, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)=X2|~class_Rings_Ocomm__semiring__1(X1))). 4.46/4.76 cnf(i_0_2305, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=X2|~class_Groups_Ocomm__monoid__add(X1))). 4.46/4.76 cnf(i_0_7058, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Ocomm__semiring__1(X1))). 4.46/4.76 cnf(i_0_5595, plain, (c_Nat__Transfer_Otsub(X1,X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1)))). 4.46/4.76 cnf(i_0_4677, plain, (X1=X2|hAPP(hAPP(c_Product__Type_OPair(X3,X4),X5),X2)!=hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X1))). 4.46/4.76 cnf(i_0_4676, plain, (X1=X2|hAPP(hAPP(c_Product__Type_OPair(X3,X4),X1),X5)!=hAPP(hAPP(c_Product__Type_OPair(X3,X4),X2),X6))). 4.46/4.76 cnf(i_0_1568, plain, (c_List_Oupto(X1,X2)=c_List_Olist_ONil(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.46/4.76 cnf(i_0_1112, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=X2|~class_Groups_Omonoid__add(X1))). 4.46/4.76 cnf(i_0_4858, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)=X2|~class_Groups_Ocomm__monoid__mult(X1))). 4.46/4.76 cnf(i_0_1413, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)=X2|~class_Groups_Omonoid__mult(X1))). 4.46/4.76 cnf(i_0_2660, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=X1)). 4.46/4.76 cnf(i_0_2485, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X1)|~class_Power_Opower(X1))). 4.46/4.76 cnf(i_0_6631, plain, (X1=X2|hAPP(X3,X1)!=hAPP(X3,X2)|~c_Fun_Oinj__on(X4,X5,X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))). 4.46/4.76 cnf(i_0_6253, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Olist_ONil(X2)=X3|hAPP(hAPP(c_List_Otake(X2),X1),X3)!=c_List_Olist_ONil(X2))). 4.46/4.76 cnf(i_0_7216, plain, (c_List_Olast(X1,c_List_Oreplicate(X1,X2,X3))=X3|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2)). 4.46/4.76 cnf(i_0_938, plain, (X1=c_List_Olist_ONil(X2)|c_List_Olinorder__class_Osorted(X2,esk68_2(X1,X2))|~c_List_Olinorder__class_Osorted(X2,X1)|~class_Orderings_Olinorder(X2))). 4.46/4.76 cnf(i_0_3531, plain, (c_List_Olist_ONil(X1)=X2|c_List_Olinorder__class_Osorted(X1,c_List_Obutlast(X1,X2))|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_3678, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))). 4.46/4.76 cnf(i_0_2099, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.46/4.76 cnf(i_0_6166, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oab__group__add(X1))). 4.46/4.76 cnf(i_0_5718, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X1,X2,X3)))|~hBOOL(hAPP(c_Com_OWT,X3)))). 4.46/4.76 cnf(i_0_3182, plain, (hBOOL(hAPP(X1,esk217_3(X2,X1,X3)))|~c_Enum_Oex__n__lists(X3,X1,X2)|~class_Enum_Oenum(X3))). 4.46/4.76 cnf(i_0_2223, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))))). 4.46/4.76 cnf(i_0_5489, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.46/4.76 cnf(i_0_6532, plain, (c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1))). 4.46/4.76 cnf(i_0_2424, plain, (c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1))). 4.46/4.76 cnf(i_0_2287, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X3),X2))))). 4.46/4.76 cnf(i_0_2286, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))))). 4.46/4.76 cnf(i_0_2224, plain, (~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.46/4.76 cnf(i_0_2573, plain, (~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1)),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,X1)),X4),X3)))). 4.46/4.76 cnf(i_0_5749, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2)=c_Groups_Oone__class_Oone(X1)|X2=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Odivision__ring(X1))). 4.46/4.76 cnf(i_0_5989, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X2)|~class_Groups_Ocancel__semigroup__add(X3))). 4.46/4.76 cnf(i_0_3932, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X2)|~class_Groups_Ocancel__ab__semigroup__add(X3))). 4.46/4.76 cnf(i_0_2900, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),esk204_1(X1))))|~hBOOL(hAPP(X1,X2)))). 4.46/4.76 cnf(i_0_2889, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X2)=c_Groups_Oone__class_Oone(X1)|c_Groups_Ozero__class_Ozero(X1)=X2|~class_Divides_Osemiring__div(X1))). 4.46/4.76 cnf(i_0_1706, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X1),X4)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X2),X4)|~class_Groups_Ocancel__semigroup__add(X3))). 4.46/4.76 cnf(i_0_1257, plain, (X1=X2|c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X3))!=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),X4))). 4.46/4.76 cnf(i_0_1571, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X1)),X2))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(X2,c_Option_Ooption_ONone(X1))))). 4.46/4.76 cnf(i_0_5994, plain, (c_Nat__Transfer_Onat__set(X1)|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk412_1(X1)),X1)))). 4.46/4.76 cnf(i_0_1516, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.46/4.76 cnf(i_0_1713, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.46/4.76 cnf(i_0_3486, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2)=c_Groups_Oone__class_Oone(X1)|c_Groups_Ozero__class_Ozero(X1)=X2|~class_Rings_Odivision__ring__inverse__zero(X1))). 4.46/4.76 cnf(i_0_4086, plain, (c_Relation_Orefl__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3))|~c_Relation_Orefl__on(X1,X2,X3))). 4.46/4.76 cnf(i_0_2427, plain, (c_Relation_Ototal__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3))|~c_Relation_Ototal__on(X1,X2,X3))). 4.46/4.76 cnf(i_0_7372, plain, (hAPP(hAPP(X1,X2),X2)=X2|~c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X1,X5,X6,X7))). 4.46/4.76 cnf(i_0_432, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X3,X1)),c_Sum__Type_OPlus(X3,X1,X4,X2))))). 4.46/4.76 cnf(i_0_6865, plain, (c_Enum_On__lists(X1,X2,c_List_Olist_ONil(X1))=c_List_Olist_ONil(tc_List_Olist(X1))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2)). 4.46/4.76 cnf(i_0_6876, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)))). 4.46/4.76 cnf(i_0_301, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)))). 4.46/4.76 cnf(i_0_1778, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.46/4.76 cnf(i_0_4615, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4))))). 4.46/4.76 cnf(i_0_6504, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_6073, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1))). 4.46/4.76 cnf(i_0_1239, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)!=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))). 4.46/4.76 cnf(i_0_199, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Omult__zero(X1))). 4.46/4.76 cnf(i_0_6227, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2))|~class_Orderings_Oorder(X1))). 4.46/4.76 cnf(i_0_1169, plain, (hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_1238, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)!=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))). 4.46/4.76 cnf(i_0_3209, plain, (c_Wellfounded_Owf(tc_List_Olist(X1),hAPP(c_List_Olexn(X1,X2),X3))|~c_Wellfounded_Owf(X1,X2))). 4.46/4.76 cnf(i_0_4723, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_7402, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk524_1(X1))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_537, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ocomm__semiring__1(X1))). 4.46/4.76 cnf(i_0_671, plain, (hAPP(c_List_Ohd(X1),c_List_Oreplicate(X1,X2,X3))=X3|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_807, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_6003, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X4)))). 4.46/4.76 cnf(i_0_6001, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5)))). 4.46/4.76 cnf(i_0_2522, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)!=X2|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_6513, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.46/4.76 cnf(i_0_4826, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)!=X3|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_1555, plain, (hBOOL(hAPP(X1,esk100_1(X1)))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))). 4.46/4.76 cnf(i_0_1434, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.46/4.76 cnf(i_0_5547, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Orderings_Otop__class_Otop(X1)))|~class_Orderings_Otop(X1))). 4.46/4.76 cnf(i_0_579, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_4755, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Orderings_Otop__class_Otop(X1))=c_Orderings_Otop__class_Otop(X1)|~class_Lattices_Obounded__lattice__top(X1))). 4.46/4.76 cnf(i_0_1650, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeast(X4,X1,X2))))). 4.46/4.76 cnf(i_0_6800, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThan(X4,X1,X2))))). 4.46/4.76 cnf(i_0_3900, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatMost(X4,X1,X3))))). 4.46/4.76 cnf(i_0_7405, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OlessThan(X4,X1,X3))))). 4.46/4.76 cnf(i_0_3373, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_3039, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Odivision__ring__inverse__zero(X1))). 4.46/4.76 cnf(i_0_522, plain, (hAPP(c_Nat_OSuc,X1)!=hAPP(c_Finite__Set_Ocard(X2),X3)|~hBOOL(hAPP(hAPP(c_member(X2),esk33_3(X1,X3,X2)),esk34_3(X1,X3,X2))))). 4.46/4.76 cnf(i_0_1163, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(X2,esk77_4(X2,X3,X1,X4))))). 4.46/4.76 cnf(i_0_4961, plain, (~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2)))). 4.46/4.76 cnf(i_0_5353, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.76 cnf(i_0_6954, plain, (~c_Relation_Oirrefl(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2)))). 4.46/4.76 cnf(i_0_6222, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Power_Opower(X1)|~class_Rings_Ono__zero__divisors(X1)|~class_Rings_Ozero__neq__one(X1)|~class_Rings_Omult__zero(X1))). 4.46/4.76 cnf(i_0_195, plain, (hBOOL(hAPP(X1,esk19_2(X1,X2)))|~c_List_Olist__ex1(X2,X1,c_Enum_Oenum__class_Oenum(X2))|~class_Enum_Oenum(X2))). 4.46/4.76 cnf(i_0_1509, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.46/4.76 cnf(i_0_2021, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(X2)|~class_Groups_Ocomm__monoid__mult(X2))). 4.46/4.76 cnf(i_0_1592, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__no__zero__divisors(X1))). 4.46/4.76 cnf(i_0_3918, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_618, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_5522, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X3),hAPP(hAPP(c_List_Omap(X1,X3),X4),X2))))). 4.46/4.76 cnf(i_0_192, plain, (c_List_Olist__ex1(X1,X2,c_Enum_Oenum__class_Oenum(X1))|esk20_3(X2,X1,X3)!=X3|~class_Enum_Oenum(X1)|~hBOOL(hAPP(X2,X3)))). 4.46/4.76 cnf(i_0_6578, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))))). 4.46/4.76 cnf(i_0_5298, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.46/4.76 cnf(i_0_5594, plain, (c_Nat__Transfer_Otsub(X1,X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1)))). 4.46/4.76 cnf(i_0_2939, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,esk206_2(X2,X1))))). 4.46/4.76 cnf(i_0_4595, plain, (hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.46/4.76 cnf(i_0_5572, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)))). 4.46/4.76 cnf(i_0_4774, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Olinordered__ab__group__add(X1))). 4.46/4.76 cnf(i_0_6031, plain, (c_Equiv__Relations_Oequivp(X1,X2)|hAPP(X2,esk417_1(X2))!=hAPP(X2,esk418_1(X2))|~hBOOL(hAPP(hAPP(X2,esk417_1(X2)),esk418_1(X2))))). 4.46/4.76 cnf(i_0_1992, plain, (c_List_Olist__ex(X1,X2,X3)|c_List_Olist__ex(X1,X2,X4)|~c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4)))). 4.46/4.76 cnf(i_0_194, plain, (X1=esk19_2(X2,X3)|~c_List_Olist__ex1(X3,X2,c_Enum_Oenum__class_Oenum(X3))|~class_Enum_Oenum(X3)|~hBOOL(hAPP(X2,X1)))). 4.46/4.76 cnf(i_0_6847, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.46/4.76 cnf(i_0_1175, plain, (X1=X2|c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)!=hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))|~class_Orderings_Oorder(X3))). 4.46/4.76 cnf(i_0_1174, plain, (X1=X2|c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X2)!=hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))|~class_Orderings_Oorder(X3))). 4.46/4.76 cnf(i_0_5243, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X2)!=c_List_Olist_ONil(X1))). 4.46/4.76 cnf(i_0_287, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,X1)))|~hBOOL(hAPP(c_Com_OWT,X1)))). 4.46/4.76 cnf(i_0_3379, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X1,hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X2))))|~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X2))),X1),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X2))))))). 4.46/4.76 cnf(i_0_5655, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),c_List_OtakeWhile(X3,X1,X4)))))). 4.46/4.76 cnf(i_0_6705, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|~c_List_Olist__all2(X1,X2,X3,hAPP(c_List_Orev(X1),X4),hAPP(c_List_Orev(X2),X5)))). 4.46/4.76 cnf(i_0_1923, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)!=X3|~class_Lattices_Osemilattice__sup(X1))). 4.46/4.76 cnf(i_0_7430, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)!=X2|~class_Lattices_Osemilattice__inf(X1))). 4.46/4.76 cnf(i_0_6822, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2))))). 4.46/4.76 cnf(i_0_6821, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))))). 4.46/4.76 cnf(i_0_1023, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.46/4.76 cnf(i_0_5410, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|X3=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3)!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Ono__zero__divisors(X2))). 4.46/4.76 cnf(i_0_1590, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__no__zero__divisors(X1))). 4.46/4.76 cnf(i_0_2323, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X1,X2)))|~hBOOL(hAPP(c_Com_OWT,X2))|~hBOOL(hAPP(c_Com_OWT,X1)))). 4.46/4.76 cnf(i_0_3253, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_7061, plain, (hAPP(c_List_Ohd(X1),X2)=hAPP(hAPP(c_List_Onth(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_List_Olist_ONil(X1)=X2)). 4.46/4.76 cnf(i_0_3741, plain, (hAPP(c_List_Oset(X1),c_List_Olinorder__class_Osorted__list__of__set(X1,X2))=X2|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_5902, plain, (hAPP(c_List_Oset(X1),esk407_2(X2,X1))=X2|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_5770, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.46/4.76 cnf(i_0_6980, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Odivision__ring(X1))). 4.46/4.76 cnf(i_0_3571, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_509, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Omult__zero(X1))). 4.46/4.76 cnf(i_0_6762, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X2)=c_Orderings_Otop__class_Otop(X1)|~class_Lattices_Obounded__lattice__top(X1))). 4.46/4.76 cnf(i_0_4011, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2)=c_Groups_Oone__class_Oone(X1)|~class_Groups_Omonoid__mult(X1))). 4.46/4.76 cnf(i_0_6826, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ocomm__semiring__1(X1))). 4.46/4.76 cnf(i_0_5775, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.46/4.76 cnf(i_0_7448, plain, (epred1_3(X1,X2,X3)|~hBOOL(hAPP(X1,esk532_3(X3,X2,X1)))|~hBOOL(hAPP(X1,esk534_3(X3,X2,X1)))|~hBOOL(hAPP(X1,X3)))). 4.46/4.76 cnf(i_0_3916, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.46/4.76 cnf(i_0_1591, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__no__zero__divisors(X1))). 4.46/4.76 cnf(i_0_1919, plain, (hAPP(c_List_Orotate1(X1),X2)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 4.46/4.76 cnf(i_0_1170, plain, (hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_4151, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X1,hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,X2)))|~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X1,hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,esk283_2(X2,X1)))))|~hBOOL(hAPP(c_Com_OWT,X2)))). 4.46/4.76 cnf(i_0_2449, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThanLessThan(X4,X1,X2,X5))))). 4.46/4.76 cnf(i_0_7255, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeastAtMost(X4,X1,X2,X5))))). 4.46/4.76 cnf(i_0_2448, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OgreaterThanLessThan(X4,X1,X5,X3))))). 4.46/4.76 cnf(i_0_7256, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatLeastAtMost(X4,X1,X5,X3))))). 4.46/4.76 cnf(i_0_5760, plain, (hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4))|~hBOOL(hAPP(X3,X4)))). 4.46/4.76 cnf(i_0_5327, plain, (hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4))|~hBOOL(hAPP(X2,X4)))). 4.46/4.76 cnf(i_0_6033, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|hAPP(X1,X2)!=hAPP(X1,X3)|~c_Equiv__Relations_Oequivp(X4,X1))). 4.46/4.76 cnf(i_0_5189, plain, (c_Finite__Set_Ofun__left__comm(X1,tc_List_Olist(X1),c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_5807, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.46/4.76 cnf(i_0_1773, plain, (c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.46/4.76 cnf(i_0_753, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(X1,esk52_1(X1))))). 4.46/4.76 cnf(i_0_1426, plain, (hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)=c_Groups_Oone__class_Oone(tc_Int_Oint)|hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))!=c_Groups_Oone__class_Oone(tc_Int_Oint))). 4.46/4.76 cnf(i_0_4355, plain, (c_List_Olist__ex1(X1,X2,X3)|hBOOL(hAPP(X2,X4))|~c_List_Olist__ex1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)))). 4.46/4.76 cnf(i_0_6110, plain, (c_List_Olist__ex(X1,X2,X3)|hBOOL(hAPP(X2,X4))|~c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)))). 4.46/4.76 cnf(i_0_782, plain, (X1=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X4),X4)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X2),X1)|~class_Groups_Oab__group__add(X3))). 4.46/4.76 cnf(i_0_1821, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1))). 4.46/4.76 cnf(i_0_5280, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)))|~hBOOL(hAPP(X1,esk370_3(X3,X2,X1)))|~hBOOL(hAPP(X1,X2)))). 4.46/4.76 cnf(i_0_5291, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Otake(X1),X2),X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_5188, plain, (hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))=X3|~c_Finite__Set_Ofolding__one(X2,X4,X1))). 4.46/4.76 cnf(i_0_1854, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.46/4.76 cnf(i_0_6058, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Odrop(X1),X2),X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_3740, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Osorted__list__of__set(X1,X2)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_5900, plain, (hBOOL(hAPP(c_List_Odistinct(X1),esk407_2(X2,X1)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_4655, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))))). 4.46/4.76 cnf(i_0_6016, plain, (c_List_Olast(X1,hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Ohd(X1),X2)|c_List_Olist_ONil(X1)=X2)). 4.46/4.76 cnf(i_0_3459, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Otl(X1),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.46/4.76 cnf(i_0_5196, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.46/4.76 cnf(i_0_6261, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.46/4.76 cnf(i_0_5204, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X4),X3))))). 4.46/4.76 cnf(i_0_5205, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4))))). 4.46/4.76 cnf(i_0_277, plain, (X1=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_201, plain, (c_SMT_Oz3div(X1,X2)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.76 cnf(i_0_2983, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)=X2|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.46/4.76 cnf(i_0_1153, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.46/4.76 cnf(i_0_2710, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.46/4.76 cnf(i_0_4024, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X2))))). 4.46/4.76 cnf(i_0_166, plain, (X1=X2|~class_Orderings_Oorder(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),X2)))). 4.46/4.76 cnf(i_0_4252, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)=X2|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.46/4.76 cnf(i_0_1598, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(X1,esk109_1(X1))))). 4.46/4.76 cnf(i_0_3390, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X1),c_Divides_Odivmod__int(X2,X1))))). 4.46/4.76 cnf(i_0_3892, plain, (hAPP(c_Set_Oimage(X1,X2,X3),X4)=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|~c_Typedef_Otype__definition(X2,X1,X5,X3,X4))). 4.46/4.76 cnf(i_0_5424, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(X1,esk376_1(X1))))). 4.46/4.76 cnf(i_0_531, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_2096, plain, (hBOOL(hAPP(X1,X2))|hAPP(c_List_Ofilter(X3,X1),X4)!=hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))). 4.46/4.76 cnf(i_0_6202, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Oinv__image(X2,X1),X3),X4))|~c_Wellfounded_Owf(X2,X3))). 4.46/4.76 cnf(i_0_5852, plain, (c_FunDef_Oreduction__pair(X1,hAPP(hAPP(c_FunDef_Orp__inv__image(X2,X1),X3),X4))|~c_FunDef_Oreduction__pair(X2,X3))). 4.46/4.76 cnf(i_0_3479, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oinsert(X1,X2,X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.46/4.76 cnf(i_0_2443, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_OtakeWhile(X1,X2,X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.46/4.76 cnf(i_0_3911, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremove1(X1,X2,X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.46/4.76 cnf(i_0_6314, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)|~class_Rings_Oring__1(X1))). 4.46/4.76 cnf(i_0_6795, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)|~class_Rings_Olinordered__idom(X1))). 4.46/4.76 cnf(i_0_2661, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))=hAPP(c_Groups_Oabs__class_Oabs(X1),X2)|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.46/4.76 cnf(i_0_1064, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Osublist(X1,X2,X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.46/4.76 cnf(i_0_3799, plain, (X1=X2|hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X4),X5),X1)!=hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X6),X7),X2))). 4.46/4.76 cnf(i_0_3800, plain, (X1=X2|hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X4),X1),X5)!=hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X6),X2),X7))). 4.46/4.76 cnf(i_0_3798, plain, (X1=X2|hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X1),X4),X5)!=hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X2),X6),X7))). 4.46/4.76 cnf(i_0_1802, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)|~class_Groups_Ocomm__monoid__add(X1))). 4.46/4.76 cnf(i_0_2467, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_1171, plain, (hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Rings_Osemiring__1(X1))). 4.46/4.76 cnf(i_0_7380, plain, (hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(X1)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1))). 4.46/4.76 cnf(i_0_6623, plain, (X1=X2|hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)!=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))). 4.46/4.76 cnf(i_0_1671, plain, (c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3)=c_Divides_Odiv__class_Omod(X1,X2,X3)|~class_Divides_Osemiring__div(X1))). 4.46/4.76 cnf(i_0_2839, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)))). 4.46/4.76 cnf(i_0_3551, plain, (hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Oone__class_Oone(X1)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Rings_Osemiring__1(X1))). 4.46/4.76 cnf(i_0_2980, plain, (hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Oone__class_Oone(X1)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1))). 4.46/4.76 cnf(i_0_715, plain, (c_Fun_Oinj__on(tc_Nat_Onat,X1,c_Nat_Osemiring__1__class_Oof__nat(X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))|~class_Nat_Osemiring__char__0(X1))). 4.46/4.76 cnf(i_0_5283, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|~hBOOL(hAPP(X1,X2)))). 4.46/4.76 cnf(i_0_4285, plain, (c_List_Oinsert(X1,X2,X3)=X3|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.46/4.76 cnf(i_0_5870, plain, (c_FunDef_OTHE__default(X1,X2,X3)=X2|hBOOL(hAPP(X3,esk403_3(X2,X1,X3))))). 4.46/4.76 cnf(i_0_2499, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))). 4.46/4.76 cnf(i_0_2077, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ocomm__monoid__add(X2))). 4.46/4.76 cnf(i_0_7019, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_2590, plain, (hAPP(c_List_Ohd(X1),hAPP(c_List_Orev(X1),X2))=c_List_Olast(X1,X2)|c_List_Olist_ONil(X1)=X2)). 4.46/4.76 cnf(i_0_716, plain, (hBOOL(hAPP(c_Predicate_ODomainP(X1,X2,X3),X4))|~hBOOL(hAPP(hAPP(X3,X4),X5)))). 4.46/4.76 cnf(i_0_3086, plain, (hBOOL(hAPP(c_Predicate_ORangeP(X1,X2,X3),X4))|~hBOOL(hAPP(hAPP(X3,X5),X4)))). 4.46/4.76 cnf(i_0_1107, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThanAtMost(X4,X5,X1,X2,X6))))). 4.46/4.76 cnf(i_0_2858, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeastLessThan(X4,X1,X5,X2,X6))))). 4.46/4.76 cnf(i_0_1106, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OgreaterThanAtMost(X4,X1,X5,X6,X3))))). 4.46/4.76 cnf(i_0_3016, plain, (X1=c_Int_OMin|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))!=c_Int_OMin)). 4.46/4.76 cnf(i_0_1683, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.76 cnf(i_0_2859, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatLeastLessThan(X4,X5,X1,X6,X3))))). 4.46/4.76 cnf(i_0_2315, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)))). 4.46/4.76 cnf(i_0_2885, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_1996, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.76 cnf(i_0_2054, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)))). 4.46/4.76 cnf(i_0_4679, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Fun_Oinj__on(X1,X3,X4,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2))))). 4.46/4.76 cnf(i_0_5709, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)|~c_List_Olist__all2(X1,X3,X5,X2,X4))). 4.46/4.76 cnf(i_0_3852, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=X2|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_630, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X2)=X2|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_3758, plain, (X1=X2|hAPP(c_Product__Type_Osnd(X3,X4),X1)!=hAPP(c_Product__Type_Osnd(X3,X4),X2)|hAPP(c_Product__Type_Ofst(X3,X4),X1)!=hAPP(c_Product__Type_Ofst(X3,X4),X2))). 4.46/4.76 cnf(i_0_497, plain, (c_Relation_Orefl__on(tc_List_Olist(X1),c_List_Olists(X1,X2),c_List_Olistrel(X1,X3))|~c_Relation_Orefl__on(X1,X2,X3))). 4.46/4.76 cnf(i_0_7226, plain, (c_Nitpick_Onat__gcd(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1))=c_Nitpick_Onat__gcd(X2,X1)|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_1876, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_5940, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1))))). 4.46/4.76 cnf(i_0_5605, plain, (c_Equiv__Relations_Oequiv(tc_List_Olist(X1),c_List_Olists(X1,X2),c_List_Olistrel(X1,X3))|~c_Equiv__Relations_Oequiv(X1,X2,X3))). 4.46/4.76 cnf(i_0_6111, plain, (c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~c_List_Olist__ex(X1,X2,X4))). 4.46/4.76 cnf(i_0_1993, plain, (c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))|~c_List_Olist__ex(X1,X2,X4))). 4.46/4.76 cnf(i_0_2442, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2))=hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_801, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2))=hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_625, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2))=hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_7190, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_3313, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=hAPP(c_Groups_Oabs__class_Oabs(X1),X2)|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.46/4.76 cnf(i_0_1994, plain, (c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))|~c_List_Olist__ex(X1,X2,X3))). 4.46/4.76 cnf(i_0_2937, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))))). 4.46/4.76 cnf(i_0_5068, plain, (X1=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X1)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X2))). 4.46/4.76 cnf(i_0_6944, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=c_Orderings_Obot__class_Obot(X1)|~class_Lattices_Oboolean__algebra(X1))). 4.46/4.76 cnf(i_0_6376, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2)=c_Orderings_Obot__class_Obot(X1)|~class_Lattices_Oboolean__algebra(X1))). 4.46/4.76 cnf(i_0_1932, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~class_Power_Opower(X1)|~class_Rings_Osemiring__0(X1))). 4.46/4.76 cnf(i_0_3087, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)=X3|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X4),X3))))). 4.46/4.76 cnf(i_0_7436, plain, (c_Wellfounded_OwfP(X1,X2)|~c_Wellfounded_OwfP(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X2),X3)))). 4.46/4.76 cnf(i_0_3482, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Owf(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.46/4.76 cnf(i_0_4274, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Wellfounded_Oacyclic(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.46/4.76 cnf(i_0_1627, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X2,X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_5871, plain, (X1=esk403_3(X2,X3,X4)|c_FunDef_OTHE__default(X3,X2,X4)=X2|~hBOOL(hAPP(X4,X1)))). 4.46/4.76 cnf(i_0_6323, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)))|~epred2_3(X1,X3,X2)|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_3306, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk227_3(X3,X2,X1))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.46/4.76 cnf(i_0_5803, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk399_3(X3,X2,X1))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.46/4.76 cnf(i_0_5384, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),c_Relation_OId__on(X3,X4))))). 4.46/4.76 cnf(i_0_4055, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~c_Wellfounded_Owf(X1,X3))). 4.46/4.76 cnf(i_0_6112, plain, (c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~hBOOL(hAPP(X2,X3)))). 4.46/4.76 cnf(i_0_4392, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2))))). 4.46/4.76 cnf(i_0_5957, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Groups_Ogroup__add(X1))). 4.46/4.76 cnf(i_0_1610, plain, (c_Nitpick_Osetsum_H(X1,X2,X3,X4)=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Ocomm__monoid__add(X2))). 4.46/4.76 cnf(i_0_2877, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X1,X2,X3)))|~hBOOL(hAPP(c_Com_OWT,X3))|~hBOOL(hAPP(c_Com_OWT,X2)))). 4.46/4.76 cnf(i_0_1141, plain, (c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))|~c_Wellfounded_Oacyclic(X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)))). 4.46/4.76 cnf(i_0_2417, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2))))). 4.46/4.76 cnf(i_0_1470, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))))). 4.46/4.76 cnf(i_0_4269, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))))). 4.46/4.76 cnf(i_0_4794, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~class_Orderings_Olinorder(X3)|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X3,X4),X5),X2))))). 4.46/4.76 cnf(i_0_4793, plain, (~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_List_Odistinct(X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X5))))). 4.46/4.76 cnf(i_0_1623, plain, (X1=hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ogroup__add(X2))). 4.46/4.76 cnf(i_0_4402, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2))))). 4.46/4.76 cnf(i_0_2782, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2))))). 4.46/4.76 cnf(i_0_5276, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool)))))). 4.46/4.76 cnf(i_0_524, plain, (esk34_3(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(c_Finite__Set_Ocard(X2),X1)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_3933, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)=X3|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 4.46/4.76 cnf(i_0_1862, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=X2|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.46/4.76 cnf(i_0_1803, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=X2|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.46/4.76 cnf(i_0_380, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)=X2|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.46/4.76 cnf(i_0_4034, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X1))|~c_Nat__Transfer_Onat__set(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1))))). 4.46/4.76 cnf(i_0_1419, plain, (c_Wellfounded_Owf(tc_prod(X1,X2),c_Wellfounded_Olex__prod(X1,X2,X3,X4))|~c_Wellfounded_Owf(X2,X4)|~c_Wellfounded_Owf(X1,X3))). 4.46/4.76 cnf(i_0_5922, plain, (c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))=c_Smallcheck_Osmall_H(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)))). 4.46/4.76 cnf(i_0_2960, plain, (c_List_Olistrelp(X1,X2,X3,X4)|~c_List_Olistrelp(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X4)))). 4.46/4.76 cnf(i_0_7159, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__semidom(X1))). 4.46/4.76 cnf(i_0_1922, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)=X3|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.46/4.76 cnf(i_0_6605, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)=X3|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.46/4.76 cnf(i_0_491, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)=X2|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.46/4.76 cnf(i_0_560, plain, (c_List_Oremdups(X1,X2)=X2|hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))). 4.46/4.76 cnf(i_0_5905, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__semidom(X1))). 4.46/4.76 cnf(i_0_647, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|hAPP(c_Finite__Set_Ocard(X2),hAPP(c_Set_Oimage(X1,X2,X3),X4))!=hAPP(c_Finite__Set_Ocard(X1),X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.46/4.76 cnf(i_0_1394, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)=c_Big__Operators_Olinorder__class_OMin(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_4224, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2)=c_Big__Operators_Olattice__class_OInf__fin(X1,X2)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_4651, plain, (hAPP(hAPP(c_List_Otake(X1),X2),X3)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)))). 4.46/4.76 cnf(i_0_2740, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))))). 4.46/4.76 cnf(i_0_6952, plain, (hBOOL(hAPP(X1,X2))|hBOOL(hAPP(X3,X2))|~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X1),X3),X2)))). 4.46/4.76 cnf(i_0_6834, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2)=c_Big__Operators_Olattice__class_OSup__fin(X1,X2)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_5999, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omax(X1)),X2)=c_Big__Operators_Olinorder__class_OMax(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_523, plain, (hAPP(c_Finite__Set_Ocard(X1),esk34_3(X2,X3,X1))=X2|hAPP(c_Nat_OSuc,X2)!=hAPP(c_Finite__Set_Ocard(X1),X3))). 4.46/4.76 cnf(i_0_5017, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~c_Equiv__Relations_Oequivp(X4,X1)|~hBOOL(hAPP(hAPP(X1,X3),X2)))). 4.46/4.76 cnf(i_0_4336, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2,X1),tc_HOL_Obool)))))). 4.46/4.76 cnf(i_0_4481, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X2)))). 4.46/4.76 cnf(i_0_2248, plain, (c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1))=c_List_Omonoid__add__class_Olistsum(X1)|~class_Groups_Omonoid__add(X1))). 4.46/4.76 cnf(i_0_1534, plain, (hAPP(c_List_Ofilter(X1,X2),X3)!=c_List_Olist_ONil(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 4.46/4.76 cnf(i_0_6246, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2,X1)),hAPP(c_Relation_Oconverse(X1,X2),X3))))). 4.46/4.76 cnf(i_0_1969, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),esk139_2(X2,X1)),X2)))). 4.46/4.76 cnf(i_0_6009, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.46/4.76 cnf(i_0_3040, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3))))). 4.46/4.76 cnf(i_0_1728, plain, (c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))=c_Divides_Opdivmod(X1,X2)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2)). 4.46/4.76 cnf(i_0_6785, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),esk468_2(X2,X1)),X2)))). 4.46/4.76 cnf(i_0_4, plain, (~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_114, plain, (c_Divides_OposDivAlg(X1,X2)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.46/4.76 cnf(i_0_667, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2))|~c_Wellfounded_Owf(X1,X2))). 4.46/4.76 cnf(i_0_3744, plain, (X1=X2|hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)!=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1))). 4.46/4.76 cnf(i_0_3507, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))))). 4.46/4.76 cnf(i_0_5147, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3)))). 4.46/4.76 cnf(i_0_2020, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X6),X1),X2),X3)))). 4.46/4.76 cnf(i_0_6612, plain, (c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1)=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_1441, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),X4))|~hBOOL(hAPP(c_Predicate_OPowp(X3,X1),X4)))). 4.46/4.76 cnf(i_0_1687, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)))). 4.46/4.76 cnf(i_0_4106, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.46/4.76 cnf(i_0_5330, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X1),X6),X2),X3)))). 4.46/4.76 cnf(i_0_1624, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 4.46/4.76 cnf(i_0_7473, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X2,X1,X3)|~hBOOL(hAPP(X2,esk532_3(X3,X1,X2)))|~hBOOL(hAPP(X2,esk534_3(X3,X1,X2))))). 4.46/4.76 cnf(i_0_3645, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))!=X2)). 4.46/4.76 cnf(i_0_4043, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2))))). 4.46/4.76 cnf(i_0_831, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_6579, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_6526, plain, (hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|esk452_2(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_4920, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3))))). 4.46/4.76 cnf(i_0_2191, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2))))). 4.46/4.76 cnf(i_0_5408, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3))))). 4.46/4.76 cnf(i_0_3330, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_4144, plain, (X1=c_Groups_Oone__class_Oone(tc_Int_Oint)|X1=c_Int_OMin|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)!=c_Groups_Oone__class_Oone(tc_Int_Oint))). 4.46/4.76 cnf(i_0_1049, plain, (c_Predicate_Oreflp(X1,X2)|~c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))). 4.46/4.76 cnf(i_0_6552, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=X3|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))). 4.46/4.76 cnf(i_0_6192, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|X2=X3|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1))). 4.46/4.76 cnf(i_0_1535, plain, (hAPP(c_List_Ofilter(X1,X2),X3)=c_List_Olist_ONil(X1)|hBOOL(hAPP(X2,esk97_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_5075, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.46/4.76 cnf(i_0_4145, plain, (X1=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Int_OMin=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)!=c_Groups_Oone__class_Oone(tc_Int_Oint))). 4.46/4.76 cnf(i_0_5969, plain, (c_List_Oremove1(X1,X2,c_List_Oremdups(X1,X3))=c_List_Oremdups(X1,c_List_Oremove1(X1,X2,X3))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.46/4.76 cnf(i_0_6324, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1)))|~epred2_3(X2,X1,X3))). 4.46/4.76 cnf(i_0_5611, plain, (c_Enum_Oproduct(X1,X2,c_Enum_Oenum__class_Oenum(X1),c_Enum_Oenum__class_Oenum(X2))=c_Enum_Oenum__class_Oenum(tc_prod(X1,X2))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2))). 4.46/4.76 cnf(i_0_5284, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1)))|~hBOOL(hAPP(X2,esk370_3(X1,X3,X2))))). 4.46/4.76 cnf(i_0_4142, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|X2=c_Int_OMin|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)!=c_Groups_Oone__class_Oone(tc_Int_Oint))). 4.46/4.76 cnf(i_0_5269, plain, (~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_5697, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)=hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omax(X1)),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_2956, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(X4,esk207_4(X4,X3,X1,X2))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_4143, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|c_Int_OMin=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)!=c_Groups_Oone__class_Oone(tc_Int_Oint))). 4.46/4.76 cnf(i_0_2232, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)=hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_6991, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(X1,esk486_2(X1,X3))))). 4.46/4.76 cnf(i_0_7267, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(X1,esk515_2(X1,X3))))). 4.46/4.76 cnf(i_0_72, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Relation_OField(X1),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)))). 4.46/4.76 cnf(i_0_1678, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(X4,esk114_4(X4,X3,X2,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_5148, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)),X3)))). 4.46/4.76 cnf(i_0_121, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_5035, plain, (c_List_Olist__ex(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 4.46/4.76 cnf(i_0_6586, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X4),X1))|~hBOOL(hAPP(X4,X2)))). 4.46/4.76 cnf(i_0_975, plain, (hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))|~hBOOL(hAPP(hAPP(X3,X5),X4)))). 4.46/4.76 cnf(i_0_187, plain, (hAPP(c_Map_Orestrict__map(X1,X2,X3,X4),X5)=hAPP(X3,X5)|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4)))). 4.46/4.76 cnf(i_0_3851, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3))=X2|~c_Equiv__Relations_Oequiv(X1,X2,X3))). 4.46/4.76 cnf(i_0_687, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_1816, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X4),X2)))). 4.46/4.76 cnf(i_0_4164, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X3),X4)))). 4.46/4.76 cnf(i_0_385, plain, (hAPP(c_List_Oset(X1),c_List_Olinorder__class_Osort__key(X1,X2,X3,X4))=hAPP(c_List_Oset(X1),X4)|~class_Orderings_Olinorder(X2))). 4.46/4.76 cnf(i_0_6574, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.46/4.76 cnf(i_0_6220, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~class_Power_Opower(X1)|~class_Rings_Ono__zero__divisors(X1)|~class_Rings_Ozero__neq__one(X1)|~class_Rings_Omult__zero(X1))). 4.46/4.76 cnf(i_0_3424, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Osgn__class_Osgn(X1,X2))=hAPP(c_Groups_Oabs__class_Oabs(X1),X2)|~class_Rings_Olinordered__idom(X1))). 4.46/4.76 cnf(i_0_6059, plain, (~c_Fun_Oinj__on(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),hAPP(c_Set_Oimage(X1,X2,X3),X4))),hAPP(c_Finite__Set_Ocard(X1),X4))))). 4.46/4.76 cnf(i_0_4600, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofilter(X1,X2),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.46/4.76 cnf(i_0_5710, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X1)!=c_Groups_Ozero__class_Ozero(X2)|~class_Int_Oring__char__0(X2)|~hBOOL(hAPP(hAPP(c_member(X2),X1),c_Int_Oring__1__class_OInts(X2))))). 4.46/4.76 cnf(i_0_4154, plain, (hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),c_Enum_On__lists(X1,X2,X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.46/4.76 cnf(i_0_453, plain, (c_Orderings_Oord_Omax(X1,hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1)))=c_Orderings_Oord__class_Omin(X1)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_1201, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.46/4.76 cnf(i_0_7398, plain, (c_Orderings_Oord_Omin(X1,hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1)))=c_Orderings_Oord__class_Omax(X1)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_7273, plain, (c_Divides_Odivmod__int(X1,X2)=c_Divides_OposDivAlg(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.76 cnf(i_0_3784, plain, (c_Nitpick_Ounknown(tc_HOL_Obool)|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))|~c_Nitpick_Owf_H(X1,X2))). 4.46/4.76 cnf(i_0_5450, plain, (c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=c_List_Olast(X1,X3)|X3=c_List_Olist_ONil(X1))). 4.46/4.76 cnf(i_0_4128, plain, (c_List_Olast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3))=c_List_Olast(X1,X3)|X3=c_List_Olist_ONil(X1))). 4.46/4.76 cnf(i_0_62, plain, (hBOOL(hAPP(X1,X2))|~c_List_Olist__all(X3,X1,X4)|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))))). 4.46/4.76 cnf(i_0_1109, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)))). 4.46/4.76 cnf(i_0_182, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X2)|~class_Orderings_Oorder(X1))). 4.46/4.76 cnf(i_0_238, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3))=X2|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_1430, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)))). 4.46/4.76 cnf(i_0_1963, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3))=X2|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_3573, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=c_Orderings_Otop__class_Otop(X1)|~class_Lattices_Oboolean__algebra(X1))). 4.46/4.76 cnf(i_0_3509, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 4.46/4.76 cnf(i_0_798, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,X2)=c_Complete__Lattice_OInf__class_OInf(X1,X2)|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_5615, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oab__group__add(X1))). 4.46/4.76 cnf(i_0_1017, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2)=c_Orderings_Otop__class_Otop(X1)|~class_Lattices_Oboolean__algebra(X1))). 4.46/4.76 cnf(i_0_1877, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_5795, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Big__Operators_Olattice__class_OSup__fin(X1,X2)=c_Complete__Lattice_OSup__class_OSup(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_115, plain, (c_Divides_OposDivAlg(X1,X2)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_1349, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)))). 4.46/4.76 cnf(i_0_2192, plain, (hAPP(hAPP(c_List_Onth(X1),X2),X3)=X4|hAPP(hAPP(c_List_Odrop(X1),X3),X2)!=hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))). 4.46/4.76 cnf(i_0_1793, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))))). 4.46/4.76 cnf(i_0_4200, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))=c_Groups_Ozero__class_Ozero(X1)|hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber(X1))). 4.46/4.76 cnf(i_0_529, plain, (X1=X2|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_4917, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),c_Int_OInteg))|~hBOOL(hAPP(X1,hAPP(c_Int_ORep__Integ,esk342_2(X1,X2)))))). 4.46/4.76 cnf(i_0_3442, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))))). 4.46/4.76 cnf(i_0_4668, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_7325, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))))). 4.46/4.76 cnf(i_0_7144, plain, (c_List_Olist_ONil(X1)=X2|c_List_Otranspose(X1,X3)!=c_List_Olist_ONil(tc_List_Olist(X1))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),hAPP(c_List_Oset(tc_List_Olist(X1)),X3))))). 4.46/4.76 cnf(i_0_4301, plain, (c_List_Olist_ONil(X1)=X2|hBOOL(hAPP(c_List_Odistinct(X1),c_List_Obutlast(X1,X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.46/4.76 cnf(i_0_4527, plain, (c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))|~c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,X4))). 4.46/4.76 cnf(i_0_5997, plain, (c_List_OtakeWhile(X1,X2,X3)=hAPP(c_List_Ofilter(X1,X2),X3)|hBOOL(hAPP(X2,esk413_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_1469, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))))). 4.46/4.76 cnf(i_0_6399, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2)))). 4.46/4.76 cnf(i_0_6028, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2)))). 4.46/4.76 cnf(i_0_58, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)))). 4.46/4.76 cnf(i_0_4448, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),esk309_2(X3,X1)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,X2)))). 4.46/4.76 cnf(i_0_6474, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Osort__key(X1,X2,X3,X4)))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X4)))). 4.46/4.76 cnf(i_0_2829, plain, (c_Relation_Osingle__valued(X1,X2,X3)|~c_Relation_Osingle__valued(X1,X2,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))). 4.46/4.76 cnf(i_0_6346, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.76 cnf(i_0_5636, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)))). 4.46/4.76 cnf(i_0_6345, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_7028, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),hAPP(c_List_Oset(tc_Nat_Onat),X2))))). 4.46/4.76 cnf(i_0_725, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|c_Groups_Osgn__class_Osgn(X1,X2)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1))). 4.46/4.76 cnf(i_0_6874, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|~c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X6),X4),hAPP(hAPP(c_List_Olist_OCons(X2),X7),X5)))). 4.46/4.76 cnf(i_0_2733, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_609, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_6757, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_850, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk54_2(X1,X2))=X2|c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.76 cnf(i_0_3614, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk245_2(X1,X2))=X2|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_421, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.76 cnf(i_0_6230, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2)))). 4.46/4.76 cnf(i_0_4928, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,X2))=c_Groups_Ozero__class_Ozero(X1)|~class_Power_Opower(X1)|~class_Rings_Osemiring__0(X1))). 4.46/4.76 cnf(i_0_580, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_794, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.76 cnf(i_0_4562, plain, (hAPP(c_List_Ofilter(X1,X2),c_List_Oreplicate(X1,X3,X4))=c_List_Oreplicate(X1,X3,X4)|~hBOOL(hAPP(X2,X4)))). 4.46/4.76 cnf(i_0_6087, plain, (c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~c_List_Olist__all(X1,X2,X4)|~hBOOL(hAPP(X2,X3)))). 4.46/4.76 cnf(i_0_3421, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk234_2(X2,X1))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_1504, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.46/4.76 cnf(i_0_2421, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.46/4.76 cnf(i_0_504, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Oimage(X2,X1,X3),X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.46/4.76 cnf(i_0_2326, plain, (X1=X2|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3,X3,tc_HOL_Obool),c_fequal),esk172_3(X3,X1,X2))))). 4.46/4.76 cnf(i_0_976, plain, (X1=X2|hAPP(c_Set_Oimage(X3,X4,X5),X1)!=hAPP(c_Set_Oimage(X3,X4,X5),X2)|~c_Fun_Oinj__on(X3,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))). 4.46/4.76 cnf(i_0_6145, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.46/4.76 cnf(i_0_2100, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool)),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X2)))). 4.46/4.76 cnf(i_0_1482, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),X3)=c_List_Olist_ONil(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)))). 4.46/4.76 cnf(i_0_1822, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1)))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1))). 4.46/4.76 cnf(i_0_1856, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.46/4.76 cnf(i_0_4999, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X3)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.46/4.76 cnf(i_0_717, plain, (hBOOL(hAPP(hAPP(X1,X2),esk51_2(X2,X1)))|~hBOOL(hAPP(c_Predicate_ODomainP(X3,X4,X1),X2)))). 4.46/4.76 cnf(i_0_3085, plain, (hBOOL(hAPP(hAPP(X1,esk215_2(X2,X1)),X2))|~hBOOL(hAPP(c_Predicate_ORangeP(X3,X4,X1),X2)))). 4.46/4.76 cnf(i_0_1481, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3))|hAPP(hAPP(c_List_Odrop(X1),X3),X2)!=c_List_Olist_ONil(X1))). 4.46/4.76 cnf(i_0_940, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk67_4(hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),X1,X3,X2))))). 4.46/4.76 cnf(i_0_4563, plain, (hAPP(c_List_Ofilter(X1,X2),c_List_Oreplicate(X1,X3,X4))=c_List_Olist_ONil(X1)|hBOOL(hAPP(X2,X4)))). 4.46/4.76 cnf(i_0_2959, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~c_List_Olistrelp(X4,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6)))). 4.46/4.76 cnf(i_0_4502, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Oinj__on(X1,X2,X3,X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5)))). 4.46/4.76 cnf(i_0_441, plain, (X1=X2|hAPP(c_Set_Oimage(X3,X4,X5),X1)!=hAPP(c_Set_Oimage(X3,X4,X5),X2)|~c_Fun_Oinj__on(X3,X4,X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X1),X2)))). 4.46/4.76 cnf(i_0_102, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,esk10_4(X1,X3,X4,X5)))|~hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))). 4.46/4.76 cnf(i_0_6329, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1))))|~class_Enum_Oenum(X1))). 4.46/4.76 cnf(i_0_3625, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~c_Wellfounded_Owf(X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(c_Relation_OImage(X2,X2,X3),X1))))). 4.46/4.76 cnf(i_0_2475, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1))=hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X1)|~c_Nat__Transfer_Onat__set(X1))). 4.46/4.76 cnf(i_0_6159, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Rings_Osemiring__1(X1))). 4.46/4.76 cnf(i_0_5030, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1))). 4.46/4.76 cnf(i_0_6423, plain, (c_Divides_Odivmod__int(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.76 cnf(i_0_103, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,esk10_4(X1,X3,X4,X5)))|~hBOOL(hAPP(hAPP(c_member(X5),X2),X3)))). 4.46/4.76 cnf(i_0_3792, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(X2,esk260_3(X2,X3,X1))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.76 cnf(i_0_2355, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(X2,esk177_3(X2,X3,X1))!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.76 cnf(i_0_3456, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Int_Oring__1__class_OInts(X1)))|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_1343, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1))). 4.46/4.76 cnf(i_0_405, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))))). 4.46/4.76 cnf(i_0_2899, plain, (hBOOL(hAPP(X1,esk205_1(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))))). 4.46/4.76 cnf(i_0_2683, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2))))). 4.46/4.76 cnf(i_0_5080, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_1885, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))). 4.46/4.76 cnf(i_0_933, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oorder(X1))). 4.46/4.76 cnf(i_0_1839, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))))). 4.46/4.76 cnf(i_0_466, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))))). 4.46/4.76 cnf(i_0_213, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)|~class_Lattices_Olattice(X1))). 4.46/4.76 cnf(i_0_2637, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|X2=c_Groups_Oone__class_Oone(tc_Int_Oint)|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3))))). 4.46/4.76 cnf(i_0_3669, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X2,esk248_4(X2,X3,X1,X4)))|~hBOOL(hAPP(X2,X3)))). 4.46/4.76 cnf(i_0_4665, plain, (c_Nitpick_Orefl_H(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk330_2(X2,X1)),esk330_2(X2,X1))),X2)))). 4.46/4.76 cnf(i_0_4080, plain, (hBOOL(hAPP(X1,X2))|c_List_OtakeWhile(X3,X1,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))))). 4.46/4.76 cnf(i_0_982, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X1))))). 4.46/4.76 cnf(i_0_490, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)|~class_Lattices_Osemilattice__inf(X1))). 4.46/4.76 cnf(i_0_558, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_540, plain, (c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X2,X3)=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.46/4.76 cnf(i_0_2084, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Relation_ORange(X2,X1),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2,X1)),X3)))). 4.46/4.76 cnf(i_0_2539, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Relation_ODomain(X1,X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),X3)))). 4.46/4.76 cnf(i_0_4978, plain, (c_Hoare__Mirabelle_Otriple__valid(X1,esk347_3(X2,X3,X1),X4)|c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X2)|~hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X4),X3)))). 4.46/4.76 cnf(i_0_995, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_3648, plain, (c_Random_Ominus__shift(X1,X2,X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X2),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X2),X3)))). 4.46/4.76 cnf(i_0_6242, plain, (hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5)=c_Option_Ooption_ONone(X2)|c_Option_Ooption_ONone(X2)!=hAPP(X3,X5)|c_Option_Ooption_ONone(X2)!=hAPP(X4,X5))). 4.46/4.76 cnf(i_0_7413, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)=X3|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))))). 4.46/4.76 cnf(i_0_3603, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.76 cnf(i_0_1542, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk99_2(X1,X2)),X1))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)))). 4.46/4.76 cnf(i_0_2901, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk204_1(X1)))|~hBOOL(hAPP(X1,X2)))). 4.46/4.76 cnf(i_0_5538, plain, (hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4))|~hBOOL(hAPP(X3,X4))|~hBOOL(hAPP(X2,X4)))). 4.46/4.76 cnf(i_0_5065, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_350, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_2208, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)|~class_Lattices_Olattice(X1))). 4.46/4.76 cnf(i_0_6125, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk424_2(X1,X2)),X1))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)))). 4.46/4.76 cnf(i_0_1971, plain, (c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),X3,c_Map_Odom(X1,X2,X3))|~c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),c_Map_Omap__add(X1,X2,X4,X3),c_Map_Odom(X1,X2,X3)))). 4.46/4.76 cnf(i_0_242, plain, (hAPP(c_Fun_Ooverride__on(X1,X2,X3,X4,X5),X6)=hAPP(X4,X6)|~hBOOL(hAPP(hAPP(c_member(X1),X6),X5)))). 4.46/4.76 cnf(i_0_5100, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X3))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_3433, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X2))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_7286, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.76 cnf(i_0_1123, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)|~class_Lattices_Osemilattice__sup(X1))). 4.46/4.76 cnf(i_0_7285, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_4697, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_6149, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3))=X2|~class_Lattices_Olattice(X1))). 4.46/4.76 cnf(i_0_3788, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3))=X2|~class_Lattices_Olattice(X1))). 4.46/4.76 cnf(i_0_3755, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))=X3|hAPP(c_List_Orev(X1),X3)!=hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))). 4.46/4.76 cnf(i_0_7049, plain, (c_List_Olist__ex1(X1,X2,X3)|esk492_4(X3,X2,X1,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 4.46/4.76 cnf(i_0_4406, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X3)=X2|~class_Groups_Ogroup__add(X1))). 4.46/4.76 cnf(i_0_7029, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X3)=X2|~class_Groups_Ogroup__add(X1))). 4.46/4.76 cnf(i_0_1384, plain, (X1=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|hAPP(c_Finite__Set_Ocard(X2),X1)!=hAPP(c_Finite__Set_Ocard(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))). 4.46/4.76 cnf(i_0_2161, plain, (c_List_Olist__ex1(X1,X2,X3)|esk163_4(X3,X2,X1,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 4.46/4.76 cnf(i_0_371, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3))))). 4.46/4.76 cnf(i_0_370, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))))). 4.46/4.76 cnf(i_0_1117, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))=X2|~class_Rings_Olinordered__idom(X1))). 4.46/4.76 cnf(i_0_965, plain, (hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,X2)),X3),X4)=hAPP(c_Groups_Ouminus__class_Ouminus(X2),hAPP(X3,X4))|~class_Groups_Ouminus(X2))). 4.46/4.76 cnf(i_0_3676, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)|~class_Rings_Ocomm__semiring__1(X1))). 4.46/4.76 cnf(i_0_3025, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|esk210_3(X3,X2,X1)=esk211_3(X3,X2,X1))). 4.46/4.76 cnf(i_0_877, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3))))). 4.46/4.76 cnf(i_0_876, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))))). 4.46/4.76 cnf(i_0_1345, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(X1,esk90_3(X3,X2,X1)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.46/4.76 cnf(i_0_793, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X1)))). 4.46/4.76 cnf(i_0_2497, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.46/4.76 cnf(i_0_239, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)|~class_Rings_Ocomm__semiring__1(X1))). 4.46/4.76 cnf(i_0_1925, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(X1,esk135_3(X3,X2,X1)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.46/4.76 cnf(i_0_2491, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(X1,esk187_3(X3,X2,X1)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.46/4.76 cnf(i_0_3807, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3)))). 4.46/4.76 cnf(i_0_5660, plain, (hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))=hAPP(c_List_Ohd(X1),X2)|X2=c_List_Olist_ONil(X1))). 4.46/4.76 cnf(i_0_3808, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)))). 4.46/4.76 cnf(i_0_6218, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3)))). 4.46/4.76 cnf(i_0_6219, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)))). 4.46/4.76 cnf(i_0_6644, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_6273, plain, (hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)))). 4.46/4.76 cnf(i_0_5723, plain, (hAPP(c_Nat_OSuc,esk397_2(X1,X2))=X2|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))))). 4.46/4.76 cnf(i_0_5365, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_6979, plain, (hAPP(c_Finite__Set_Ofold1(X1,X2),X3)=hAPP(X4,X3)|~c_Finite__Set_Ofolding__one(X1,X2,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.76 cnf(i_0_1737, plain, (hAPP(c_Finite__Set_Ofold1(X1,X2),X3)=hAPP(X4,X3)|~c_Big__Operators_Osemilattice__big(X1,X2,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.76 cnf(i_0_4420, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))))). 4.46/4.76 cnf(i_0_4421, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))))). 4.46/4.76 cnf(i_0_120, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_123, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=X1|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_2572, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))|~class_Orderings_Oord(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4)))). 4.46/4.76 cnf(i_0_393, plain, (X1=hAPP(c_COMBK(tc_Option_Ooption(X2),X3),c_Option_Ooption_ONone(X2))|c_Map_Odom(X3,X2,X1)!=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_3124, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_4058, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_3860, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|hAPP(X4,esk266_4(X4,X3,X1,X2))!=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_4856, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|hAPP(X4,esk337_4(X4,X3,X2,X1))!=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_654, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_2333, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Groups_Oabs__if(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_1145, plain, (hBOOL(hAPP(X1,esk75_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(X1,X3)))). 4.46/4.76 cnf(i_0_4323, plain, (hBOOL(hAPP(X1,esk297_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(X1,X3)))). 4.46/4.76 cnf(i_0_4847, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))))). 4.46/4.76 cnf(i_0_7326, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2)))). 4.46/4.76 cnf(i_0_519, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2))=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))|~class_Rings_Oring__1(X1))). 4.46/4.76 cnf(i_0_1381, plain, (hAPP(X1,X2)=c_Option_Ooption_ONone(X3)|hBOOL(hAPP(hAPP(c_member(X4),X2),c_Map_Odom(X4,X3,X1))))). 4.46/4.76 cnf(i_0_732, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))))). 4.46/4.76 cnf(i_0_1356, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2)))). 4.46/4.76 cnf(i_0_7263, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2)))). 4.46/4.76 cnf(i_0_710, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Complete__Lattice_OInf__class_OInf(X1,X3)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk48_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_1613, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,X3))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4)))). 4.46/4.76 cnf(i_0_1702, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_3927, plain, (c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=c_List_Olist_ONil(X1)|hBOOL(hAPP(X2,X3)))). 4.46/4.76 cnf(i_0_5006, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OSup__class_OSup(X1,X2)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk351_3(X3,X2,X1)),X3)))). 4.46/4.76 cnf(i_0_4186, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)))|~class_Rings_Olinordered__semidom(X1))). 4.46/4.76 cnf(i_0_3935, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.46/4.76 cnf(i_0_1618, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.46/4.76 cnf(i_0_4702, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_6718, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),X4))|~c_Typedef_Otype__definition(X5,X1,X2,X6,X4))). 4.46/4.76 cnf(i_0_6875, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~c_List_Olist__all2(X4,X5,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X6),hAPP(hAPP(c_List_Olist_OCons(X5),X3),X7)))). 4.46/4.76 cnf(i_0_7221, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X3,X4),esk512_3(X4,X3,X1)),esk513_3(X4,X3,X1)))))). 4.46/4.76 cnf(i_0_5277, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))). 4.46/4.76 cnf(i_0_2753, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1))). 4.46/4.76 cnf(i_0_425, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),c_Groups_Ozero__class_Ozero(X1))|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber(X1))). 4.46/4.76 cnf(i_0_568, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Oone__class_Oone(X1)|c_Groups_Ozero__class_Ozero(X1)=X2|~class_Groups_Osgn__if(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.46/4.76 cnf(i_0_2071, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.76 cnf(i_0_990, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))). 4.46/4.76 cnf(i_0_1752, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))=c_List_Olist_ONil(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.46/4.76 cnf(i_0_4678, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.46/4.76 cnf(i_0_2263, plain, (c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),c_List_Oremdups(X1,X2))=c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(c_List_Oset(X1),X2))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_6065, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),X2)),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Oring__char__0(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))))). 4.46/4.76 cnf(i_0_1026, plain, (c_Fun_Oinj__on(X1,X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Set_Oimage(X1,X1,X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.76 cnf(i_0_1823, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))=X2|c_Groups_Oone__class_Oone(X1)=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1))). 4.46/4.76 cnf(i_0_3591, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X2))))). 4.46/4.76 cnf(i_0_5633, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X4,X5))),X5)|~hBOOL(hAPP(X4,X2)))). 4.46/4.76 cnf(i_0_2416, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),X2)))). 4.46/4.76 cnf(i_0_122, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=X1|X2=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_7505, plain, (epred2_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk535_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_7521, plain, (epred2_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,esk537_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_2964, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk208_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_3033, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk212_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_4391, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_2951, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_2783, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2)))). 4.46/4.76 cnf(i_0_5484, plain, (hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5),X6)=hAPP(X3,X6)|X6=X4)). 4.46/4.76 cnf(i_0_4550, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk319_3(X2,X3,X1))))). 4.46/4.76 cnf(i_0_295, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),esk24_3(X3,X2,X1)),X3)))). 4.46/4.76 cnf(i_0_4005, plain, (X1=c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X2,X3))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X3),X1)))). 4.46/4.76 cnf(i_0_4401, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_830, plain, (hAPP(c_Nat_OSuc,X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))))). 4.46/4.76 cnf(i_0_6519, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))))). 4.46/4.76 cnf(i_0_3574, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~hBOOL(hAPP(hAPP(X2,X3),X4))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X4)))). 4.46/4.76 cnf(i_0_1649, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatLeast(X1,X3,X4)))|~hBOOL(hAPP(hAPP(X3,X4),X2)))). 4.46/4.76 cnf(i_0_4008, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))=c_List_Olist_ONil(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_1424, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))))). 4.46/4.76 cnf(i_0_2319, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))))). 4.46/4.76 cnf(i_0_7215, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))))). 4.46/4.76 cnf(i_0_427, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),c_Groups_Ozero__class_Ozero(X1))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber(X1))). 4.46/4.76 cnf(i_0_952, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)))). 4.46/4.76 cnf(i_0_6799, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OgreaterThan(X1,X3,X4)))|~hBOOL(hAPP(hAPP(X3,X4),X2)))). 4.46/4.76 cnf(i_0_3899, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatMost(X1,X3,X4)))|~hBOOL(hAPP(hAPP(X3,X2),X4)))). 4.46/4.76 cnf(i_0_7404, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OlessThan(X1,X3,X4)))|~hBOOL(hAPP(hAPP(X3,X2),X4)))). 4.46/4.76 cnf(i_0_1294, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X3))))). 4.46/4.76 cnf(i_0_3489, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.46/4.76 cnf(i_0_1548, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))). 4.46/4.76 cnf(i_0_1178, plain, (hAPP(c_Map_Orestrict__map(X1,X2,X3,X4),X5)=c_Option_Ooption_ONone(X2)|hBOOL(hAPP(hAPP(c_member(X1),X5),X4)))). 4.46/4.76 cnf(i_0_1295, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))))). 4.46/4.76 cnf(i_0_3210, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X2)),X3)))). 4.46/4.76 cnf(i_0_616, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))). 4.46/4.76 cnf(i_0_6418, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_5692, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk393_1(X1)))|hBOOL(hAPP(X1,X2)))). 4.46/4.76 cnf(i_0_3211, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3)))). 4.46/4.76 cnf(i_0_1507, plain, (hAPP(X1,hAPP(X2,X3))=X3|~c_Typedef_Otype__definition(X4,X5,X1,X2,X6)|~hBOOL(hAPP(hAPP(c_member(X5),X3),X6)))). 4.46/4.76 cnf(i_0_5742, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)))). 4.46/4.76 cnf(i_0_5405, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2,X1),tc_HOL_Obool)))))). 4.46/4.76 cnf(i_0_5404, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool)))))). 4.46/4.76 cnf(i_0_5690, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,esk394_1(X1))))). 4.46/4.76 cnf(i_0_6613, plain, (c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1)=c_Int_OMin|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_6216, plain, (hAPP(X1,esk431_5(X2,X3,X1,X4,X5))=X2|hAPP(hAPP(c_Option_Omap(X5,X4),X1),X3)!=hAPP(c_Option_Ooption_OSome(X4),X2))). 4.46/4.76 cnf(i_0_2707, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Oinsort__insert__key(X1,X2,X3,X4,X5)))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X5)))). 4.46/4.76 cnf(i_0_800, plain, (X1=hAPP(hAPP(c_Finite__Set_Ofold(X2,X3,X4),X5),X6)|~c_Finite__Set_Ofun__left__comm(X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X2,X3,X4,X5,X6),X1)))). 4.46/4.76 cnf(i_0_4230, plain, (~hBOOL(hAPP(hAPP(c_member(X1),esk288_5(X2,X3,X4,X5,X1)),esk289_5(X2,X3,X4,X5,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)),X2)))). 4.46/4.76 cnf(i_0_4110, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Wellfounded_Owf(X1,X3))). 4.46/4.76 cnf(i_0_6119, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Wellfounded_Owf(X1,X2))). 4.46/4.76 cnf(i_0_4699, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)))|~class_Lattices_Olattice(X1))). 4.46/4.76 cnf(i_0_6587, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)))|~class_Lattices_Osemilattice__sup(X1))). 4.46/4.76 cnf(i_0_5877, plain, (~hBOOL(hAPP(hAPP(c_member(X1),esk405_5(X2,X3,X4,X5,X1)),esk406_5(X2,X3,X4,X5,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)),X2)))). 4.46/4.76 cnf(i_0_1089, plain, (X1=X2|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3,X4),X1)!=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3,X5),X2)|~class_Orderings_Olinorder(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X5),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X4),X1)))). 4.46/4.76 cnf(i_0_2977, plain, (X1=X2|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3,X1),X4)!=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3,X2),X5)|~class_Orderings_Olinorder(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X4)))). 4.46/4.76 cnf(i_0_4480, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)))|~class_Lattices_Olattice(X1))). 4.46/4.76 cnf(i_0_6026, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)))|~class_Lattices_Osemilattice__sup(X1))). 4.46/4.76 cnf(i_0_4745, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X3))|~class_Lattices_Olattice(X1))). 4.46/4.76 cnf(i_0_997, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X3))|~class_Lattices_Osemilattice__inf(X1))). 4.46/4.76 cnf(i_0_5763, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Rings_Oidom(X1))). 4.46/4.76 cnf(i_0_305, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X1))|~class_Orderings_Oorder(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),X1)))). 4.46/4.76 cnf(i_0_652, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))|~class_Orderings_Olinorder(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),X2)))). 4.46/4.76 cnf(i_0_4271, plain, (c_SMT_Oz3mod(X1,X2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.76 cnf(i_0_5002, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X2))|~class_Lattices_Olattice(X1))). 4.46/4.76 cnf(i_0_6057, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X2))|~class_Lattices_Osemilattice__inf(X1))). 4.46/4.76 cnf(i_0_4713, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oorder(X1))). 4.46/4.76 cnf(i_0_5874, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X4)=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Ocomm__monoid__add(X2))). 4.46/4.76 cnf(i_0_1902, plain, (c_Relation_Ototal__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk130_3(X3,X2,X1)),X2)))). 4.46/4.76 cnf(i_0_7297, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X4)=c_Groups_Oone__class_Oone(X2)|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Ocomm__monoid__mult(X2))). 4.46/4.76 cnf(i_0_1901, plain, (c_Relation_Ototal__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk131_3(X3,X2,X1)),X2)))). 4.46/4.76 cnf(i_0_1524, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_5576, plain, (hBOOL(hAPP(X1,X2))|hAPP(c_List_Ofilter(X3,X1),X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))))). 4.46/4.76 cnf(i_0_3576, plain, (hBOOL(hAPP(hAPP(X1,esk240_3(X2,X1,X3)),X2))|hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)))). 4.46/4.76 cnf(i_0_1538, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(X3),X1),X4))|~hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X2),X4))))). 4.46/4.76 cnf(i_0_1539, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.46/4.76 cnf(i_0_6531, plain, (hBOOL(hAPP(hAPP(X1,esk453_3(X2,X1,X3)),X2))|hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)))). 4.46/4.76 cnf(i_0_637, plain, (hAPP(X1,esk45_3(X1,X2,X3))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))). 4.46/4.76 cnf(i_0_3235, plain, (hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X1,X2,X3),X4),X5))|~hBOOL(hAPP(hAPP(X2,X4),X5))|~hBOOL(hAPP(X3,X5)))). 4.46/4.76 cnf(i_0_1249, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),esk81_3(X3,X2,X1)),c_Wellfounded_Oacc(X1,X3))))). 4.46/4.76 cnf(i_0_4368, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),esk300_3(X3,X2,X1)),c_Wellfounded_Oacc(X1,X3))))). 4.46/4.76 cnf(i_0_4372, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),esk302_3(X3,X2,X1)),c_Wellfounded_Oacc(X1,X3))))). 4.46/4.76 cnf(i_0_4152, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X1,hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,X2)))|hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),esk283_2(X2,X1)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))|~hBOOL(hAPP(c_Com_OWT,X2)))). 4.46/4.76 cnf(i_0_5548, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X2)=c_Divides_Odiv__class_Omod(X1,X3,X2)|~class_Divides_Osemiring__div(X1))). 4.46/4.76 cnf(i_0_5664, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3)=c_Divides_Odiv__class_Omod(X1,X2,X3)|~class_Divides_Osemiring__div(X1))). 4.46/4.76 cnf(i_0_1755, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4)))|~hBOOL(hAPP(c_List_Olistsp(X3,X1),X4)))). 4.46/4.76 cnf(i_0_6697, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=X3|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))). 4.46/4.76 cnf(i_0_1724, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),X1))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),X1),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))))). 4.46/4.76 cnf(i_0_2688, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.46/4.76 cnf(i_0_1000, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_3153, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_2062, plain, (c_Hoare__Mirabelle_Otriple__valid(X1,X2,X3)|~c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(c_Nat_OSuc,X2),esk151_3(X2,X4,X1))|~hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4)))). 4.46/4.76 cnf(i_0_3473, plain, (c_List_Olist__ex(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|~hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),X4))))). 4.46/4.76 cnf(i_0_1779, plain, (c_Partial__Function_Oflat__lub(X1,X2,X3)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))). 4.46/4.76 cnf(i_0_2332, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oabs__if(X1))). 4.46/4.76 cnf(i_0_2366, plain, (X1=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X3),hAPP(c_List_Oset(tc_List_Olist(X2)),c_Enum_On__lists(X2,X1,X4)))))). 4.46/4.76 cnf(i_0_383, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.46/4.76 cnf(i_0_5031, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OInf__class_OInf(X1,X2)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2)))). 4.46/4.76 cnf(i_0_1377, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3))!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__ring__strict(X2))). 4.46/4.76 cnf(i_0_7403, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk524_1(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_4667, plain, (hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_1684, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.46/4.76 cnf(i_0_1777, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),X2)))). 4.46/4.76 cnf(i_0_3143, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)|~class_Rings_Ocomm__ring__1(X1))). 4.46/4.76 cnf(i_0_1378, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__ring__strict(X1))). 4.46/4.76 cnf(i_0_5849, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X1))!=c_List_Olist_ONil(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_2266, plain, (hAPP(hAPP(c_List_Onth(X1),c_List_Oreplicate(X1,X2,X3)),X4)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X2)))). 4.46/4.76 cnf(i_0_2492, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))|~hBOOL(hAPP(X2,esk187_3(X1,X3,X2))))). 4.46/4.76 cnf(i_0_3508, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_656, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X1),X2),X3)))|~c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),X1),X2),X3)))|~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,X2))))). 4.46/4.76 cnf(i_0_1572, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X1)),X2))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_HOL_Obool,X1),X2),c_Option_Ooption_OSome(X1)))))). 4.46/4.76 cnf(i_0_1259, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))!=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3),X4))). 4.46/4.76 cnf(i_0_5474, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))))). 4.46/4.76 cnf(i_0_499, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))))). 4.46/4.76 cnf(i_0_3441, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_2435, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_851, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)|~class_Lattices_Oboolean__algebra(X1))). 4.46/4.76 cnf(i_0_5143, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_7433, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_6988, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_1959, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X3,X1,X4),X5)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5)))). 4.46/4.76 cnf(i_0_1189, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.46/4.76 cnf(i_0_5639, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)|~class_Groups_Ogroup__add(X1))). 4.46/4.76 cnf(i_0_1128, plain, (X1=X2|~c_Finite__Set_Ofun__left__comm(X3,X4,X5)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X7),X2))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X7),X1)))). 4.46/4.76 cnf(i_0_5901, plain, (esk407_2(hAPP(c_List_Oset(X1),X2),X1)=X2|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.46/4.76 cnf(i_0_2218, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)|~class_Groups_Ogroup__add(X1))). 4.46/4.76 cnf(i_0_2479, plain, (hAPP(c_List_Oset(X1),c_List_Oreplicate(X1,X2,X3))=hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_2345, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk176_2(X2,X1))))). 4.46/4.76 cnf(i_0_1393, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,esk91_3(X1,X3,X2)))|~hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1))))). 4.46/4.76 cnf(i_0_7348, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))|~c_Wellfounded_Owf(X1,X2))). 4.46/4.76 cnf(i_0_4914, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~class_Rings_Olinordered__idom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Oring__1__class_Oof__int(X3),X1)),hAPP(c_Int_Oring__1__class_Oof__int(X3),X2))))). 4.46/4.76 cnf(i_0_5138, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))=X4|hAPP(hAPP(c_Product__Type_OSigma(X1,X3),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X1),X4))!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_6615, plain, (hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X2),X3))=hAPP(hAPP(X1,X2),X3)|~c_Finite__Set_Ofun__left__comm__idem(X4,X5,X1))). 4.46/4.76 cnf(i_0_6461, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)|~class_Groups_Oab__group__add(X1))). 4.46/4.76 cnf(i_0_3938, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~class_Rings_Olinordered__semidom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X2))))). 4.46/4.76 cnf(i_0_864, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~class_Rings_Olinordered__idom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Oring__1__class_Oof__int(X3),X1)),hAPP(c_Int_Oring__1__class_Oof__int(X3),X2))))). 4.46/4.76 cnf(i_0_57, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~class_Rings_Olinordered__semidom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X2))))). 4.46/4.76 cnf(i_0_2047, plain, (c_Wellfounded_Owf(X1,X2)|hBOOL(hAPP(hAPP(c_member(X1),esk148_2(X2,X1)),esk147_2(X2,X1))))). 4.46/4.76 cnf(i_0_3365, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=X3|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X3))))). 4.46/4.76 cnf(i_0_6011, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X4),esk415_4(X2,X1,X4,X3))))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))))). 4.46/4.76 cnf(i_0_2094, plain, (hAPP(c_List_Ofilter(X1,X2),X3)!=hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)|~hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),esk152_5(X5,X4,X3,X2,X1))))|~hBOOL(hAPP(X2,X6)))). 4.46/4.76 cnf(i_0_7439, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=hAPP(c_List_Ofilter(X1,X4),X5)|~hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),esk528_5(X5,X4,X3,X2,X1))))|~hBOOL(hAPP(X4,X6)))). 4.46/4.76 cnf(i_0_4653, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk328_2(X2,X1)))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_6117, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1))). 4.46/4.76 cnf(i_0_2600, plain, (X1=X2|hAPP(hAPP(c_List_Omap(X3,X4),X5),X1)!=hAPP(hAPP(c_List_Omap(X3,X4),X5),X2)|~c_Fun_Oinj__on(X3,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))). 4.46/4.76 cnf(i_0_3214, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1))))). 4.46/4.76 cnf(i_0_5938, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1))))). 4.46/4.76 cnf(i_0_2520, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1)))). 4.46/4.76 cnf(i_0_197, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))))). 4.46/4.76 cnf(i_0_1366, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.46/4.76 cnf(i_0_2668, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)),c_Groups_Ozero__class_Ozero(X2))))). 4.46/4.76 cnf(i_0_5891, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)),c_Groups_Ozero__class_Ozero(X2))))). 4.46/4.76 cnf(i_0_1186, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))))). 4.46/4.76 cnf(i_0_5151, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_1265, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.46/4.76 cnf(i_0_1703, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X3)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Odivision__ring(X1))). 4.46/4.76 cnf(i_0_5679, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Lattices_Oboolean__algebra(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))))). 4.46/4.76 cnf(i_0_2808, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))))). 4.46/4.76 cnf(i_0_4934, plain, (c_Big__Operators_Olinorder__class_OMin(X1,X2)=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),esk343_3(X3,X2,X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_7106, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_353, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(c_Divides_OnegateSnd,X3)))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)),X3)))). 4.46/4.76 cnf(i_0_2739, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.76 cnf(i_0_5772, plain, (hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=X4|~c_Typedef_Otype__definition(X1,X2,X3,X5,X4))). 4.46/4.76 cnf(i_0_6126, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk423_1(X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2)))). 4.46/4.76 cnf(i_0_142, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_1161, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),c_List_Oreplicate(X3,X4,X5))))|~hBOOL(hAPP(X1,X5)))). 4.46/4.76 cnf(i_0_3672, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),c_List_Oreplicate(X3,X5,X2))))|~hBOOL(hAPP(X1,X4)))). 4.46/4.76 cnf(i_0_1334, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),c_List_Olists(X1,X3))))). 4.46/4.76 cnf(i_0_1543, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),esk98_1(X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2)))). 4.46/4.76 cnf(i_0_2941, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk206_2(X1,X2))=X1|hBOOL(hAPP(X2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))|~hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.46/4.76 cnf(i_0_2940, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))|~hBOOL(hAPP(X2,esk206_2(X1,X2))))). 4.46/4.76 cnf(i_0_5341, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X2)|~class_Groups_Oab__group__add(X1))). 4.46/4.76 cnf(i_0_1704, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Odivision__ring(X1))). 4.46/4.76 cnf(i_0_4977, plain, (c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),esk348_3(X3,X2,X1)),X3)))). 4.46/4.76 cnf(i_0_4536, plain, (c_Big__Operators_Olinorder__class_OMax(X1,X2)=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk318_3(X3,X2,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_4979, plain, (c_Hoare__Mirabelle_Otriple__valid(X1,X2,X3)|~c_Hoare__Mirabelle_Otriple__valid(X1,X2,esk346_4(X4,X5,X1,X2))|~c_Hoare__Mirabelle_Ohoare__valids(X1,X5,X4)|~hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4)))). 4.46/4.76 cnf(i_0_4305, plain, (c_Wellfounded_Owf(tc_prod(X1,X2),c_Recdef_Osame__fst(X1,X2,X3,X4))|~c_Wellfounded_Owf(X2,hAPP(X4,esk294_4(X1,X4,X2,X3))))). 4.46/4.76 cnf(i_0_1852, plain, (c_List_Olist__all2(X1,X2,X3,X4,hAPP(c_List_Orev(X2),X5))|~c_List_Olist__all2(X1,X2,X3,hAPP(c_List_Orev(X1),X4),X5))). 4.46/4.76 cnf(i_0_1851, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(c_List_Orev(X1),X4),X5)|~c_List_Olist__all2(X1,X2,X3,X4,hAPP(c_List_Orev(X2),X5)))). 4.46/4.76 cnf(i_0_4351, plain, (c_List_Olist__ex1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|hBOOL(hAPP(X2,X3))|~c_List_Olist__ex1(X1,X2,X4))). 4.46/4.76 cnf(i_0_1890, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Olinorder__class_Osort__key(X1,X2,X3,X4))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)|~class_Orderings_Olinorder(X2))). 4.46/4.76 cnf(i_0_5331, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))))). 4.46/4.76 cnf(i_0_5332, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))))). 4.46/4.76 cnf(i_0_4860, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),esk338_3(X2,X3,X1))))). 4.46/4.76 cnf(i_0_2517, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),esk190_3(X3,X2,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_628, plain, (X1=c_List_Olist_ONil(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1))))). 4.46/4.76 cnf(i_0_5869, plain, (c_FunDef_OTHE__default(X1,X2,X3)=c_HOL_OThe(X1,X3)|hBOOL(hAPP(X3,esk404_4(X2,X1,X3,X4)))|~hBOOL(hAPP(X3,X4)))). 4.46/4.76 cnf(i_0_1891, plain, (X1=X2|hAPP(c_List_Oset(X3),X1)!=hAPP(c_List_Oset(X3),X2)|~c_List_Olinorder__class_Osorted(X3,X2)|~c_List_Olinorder__class_Osorted(X3,X1)|~class_Orderings_Olinorder(X3)|~hBOOL(hAPP(c_List_Odistinct(X3),X2))|~hBOOL(hAPP(c_List_Odistinct(X3),X1)))). 4.46/4.76 cnf(i_0_658, plain, (X1=X2|X2=X3|hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))). 4.46/4.76 cnf(i_0_3445, plain, (c_List_Olist_ONil(X1)=X2|hBOOL(hAPP(hAPP(c_member(X1),c_List_Olast(X1,X2)),hAPP(c_List_Oset(X1),X2))))). 4.46/4.76 cnf(i_0_4253, plain, (c_Lazy__Sequence_Oproduct(X1,X2,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X1,X3),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X2,X3))=c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X1,X2),X3)|~class_Lazy__Sequence_Osmall__lazy(X1)|~class_Lazy__Sequence_Osmall__lazy(X2))). 4.46/4.76 cnf(i_0_3647, plain, (c_Random_Ominus__shift(X1,X2,X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X1),X2)),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X2),X3)))). 4.46/4.76 cnf(i_0_6582, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))|~class_Orderings_Oorder(X2)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4)))). 4.46/4.76 cnf(i_0_6257, plain, (X1=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))). 4.46/4.76 cnf(i_0_659, plain, (X1=X2|X2=X3|hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))). 4.46/4.76 cnf(i_0_2532, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3))=c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.46/4.76 cnf(i_0_1234, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1))))). 4.46/4.76 cnf(i_0_1220, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1))))). 4.46/4.76 cnf(i_0_6904, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Ozero__class_Ozero(X2))))). 4.46/4.76 cnf(i_0_2206, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Ozero__class_Ozero(X2))))). 4.46/4.76 cnf(i_0_3890, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X1,X3))=c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.46/4.76 cnf(i_0_1818, plain, (c_Relation_Osingle__valued(X1,X2,hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5))|~c_Relation_Osingle__valued(X3,X2,X5)|~c_Relation_Osingle__valued(X1,X3,X4))). 4.46/4.76 cnf(i_0_5295, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))))). 4.46/4.76 cnf(i_0_6696, plain, (c_Relation_Ototal__on(X1,X2,X3)|~c_Relation_Ototal__on(X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))))). 4.46/4.76 cnf(i_0_1899, plain, (c_Relation_Ototal__on(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk130_3(X3,X2,X1)),esk131_3(X3,X2,X1))),X3)))). 4.46/4.76 cnf(i_0_6632, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(c_Set_Oimage(X2,X1,X3),X4))=hAPP(c_Finite__Set_Ocard(X2),X4)|~c_Fun_Oinj__on(X2,X1,X3,X4))). 4.46/4.76 cnf(i_0_4042, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.46/4.76 cnf(i_0_2190, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)))). 4.46/4.76 cnf(i_0_4921, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.46/4.76 cnf(i_0_3673, plain, (c_List_Olast(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(X3,c_List_Olast(X2,X4))|X4=c_List_Olist_ONil(X2))). 4.46/4.76 cnf(i_0_1898, plain, (c_Relation_Ototal__on(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk131_3(X3,X2,X1)),esk130_3(X3,X2,X1))),X3)))). 4.46/4.76 cnf(i_0_4023, plain, (X1=hAPP(hAPP(c_List_Onth(X2),X3),X4)|hAPP(hAPP(c_List_Olist__update(X2,X3),X4),X1)!=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))))). 4.46/4.76 cnf(i_0_682, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)))). 4.46/4.76 cnf(i_0_6372, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool))))))). 4.46/4.76 cnf(i_0_5407, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.46/4.76 cnf(i_0_1792, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)))). 4.46/4.76 cnf(i_0_4087, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~class_Rings_Olinordered__semidom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1))))). 4.46/4.76 cnf(i_0_4708, plain, (~c_Wellfounded_Oacyclic(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))))). 4.46/4.76 cnf(i_0_6663, plain, (X1=X2|hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1)!=hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)|~class_Rings_Olinordered__semidom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Oone__class_Oone(X3)),X4)))). 4.46/4.76 cnf(i_0_752, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk53_1(X1)))))). 4.46/4.76 cnf(i_0_748, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.46/4.76 cnf(i_0_3, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4),X5),X6))|~hBOOL(hAPP(hAPP(X4,X5),X6)))). 4.46/4.76 cnf(i_0_5299, plain, (hAPP(c_List_Ofilter(X1,X2),c_List_Oremove1(X1,X3,X4))=hAPP(c_List_Ofilter(X1,X2),X4)|hBOOL(hAPP(X2,X3)))). 4.46/4.76 cnf(i_0_5428, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1))))). 4.46/4.76 cnf(i_0_7027, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk490_1(X1)),hAPP(c_List_Oset(tc_Nat_Onat),X1))))). 4.46/4.76 cnf(i_0_2, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4),X5),X6))|~hBOOL(hAPP(hAPP(X3,X5),X6)))). 4.46/4.76 cnf(i_0_267, plain, (c_Equiv__Relations_Oequiv(X1,hAPP(c_Relation_ODomain(X1,X1),X2),X2)|hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X2)),X2)!=X2)). 4.46/4.76 cnf(i_0_2465, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Rings_Ocomm__ring__1(X1))). 4.46/4.76 cnf(i_0_5376, plain, (~class_Rings_Olinordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_5411, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2)=c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_List_Oset(X1),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.46/4.76 cnf(i_0_6095, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2)=c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_List_Oset(X1),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.46/4.76 cnf(i_0_6488, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Olinorder__class_Osort__key(X2,X1,X3,X4)))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_6486, plain, (c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~c_Fun_Oinj__on(X1,X2,X3,X4))). 4.46/4.76 cnf(i_0_6721, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),esk461_3(X3,X2,X1)))))). 4.46/4.76 cnf(i_0_3279, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3))))). 4.46/4.76 cnf(i_0_688, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk47_3(X3,X2,X1)),X2)),X3)))). 4.46/4.76 cnf(i_0_5685, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,X3)))))). 4.46/4.76 cnf(i_0_1825, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X3)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1))). 4.46/4.76 cnf(i_0_170, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)))). 4.46/4.76 cnf(i_0_1431, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)))). 4.46/4.76 cnf(i_0_1376, plain, (c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))))). 4.46/4.76 cnf(i_0_5573, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk385_1(X1))))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_5076, plain, (hAPP(c_Nat_OSuc,X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_3803, plain, (hAPP(X1,esk261_4(X2,X1,X3,X4))=hAPP(X1,esk262_4(X2,X1,X3,X4))|c_Fun_Oinj__on(X4,X3,X1,X2))). 4.46/4.76 cnf(i_0_5862, plain, (c_Relation_Osingle__valued(X1,X1,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X3))|~c_Relation_Osingle__valued(X1,X1,X3))). 4.46/4.76 cnf(i_0_7265, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)))|~hBOOL(hAPP(X1,esk516_2(X1,X3))))). 4.46/4.76 cnf(i_0_1556, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk100_1(X1)))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))). 4.46/4.76 cnf(i_0_5876, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.46/4.76 cnf(i_0_3475, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk236_3(X3,X1,X2))))|~c_List_Olist__ex(X2,X1,X3))). 4.46/4.76 cnf(i_0_5523, plain, (c_Fun_Oinj__on(X1,X2,X3,hAPP(c_List_Oset(X1),X4))|~hBOOL(hAPP(c_List_Odistinct(X2),hAPP(hAPP(c_List_Omap(X1,X2),X3),X4))))). 4.46/4.76 cnf(i_0_2391, plain, (hBOOL(hAPP(X1,esk178_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X4),X5),X3))|~hBOOL(hAPP(X1,X5)))). 4.46/4.76 cnf(i_0_2393, plain, (hBOOL(hAPP(X1,esk178_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X4),X5),X2))|~hBOOL(hAPP(X1,X5)))). 4.46/4.76 cnf(i_0_6596, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_23, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.46/4.76 cnf(i_0_6215, plain, (hAPP(c_Option_Ooption_OSome(X1),esk431_5(X2,X3,X4,X5,X1))=X3|hAPP(hAPP(c_Option_Omap(X1,X5),X4),X3)!=hAPP(c_Option_Ooption_OSome(X5),X2))). 4.46/4.76 cnf(i_0_3472, plain, (X1=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1)))). 4.46/4.76 cnf(i_0_1443, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk96_3(X2,X3,X1)),X2))|hBOOL(hAPP(c_Predicate_OPowp(X1,X3),X2)))). 4.46/4.76 cnf(i_0_1978, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_6400, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.46/4.76 cnf(i_0_1565, plain, (c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X3))=X3|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_1633, plain, (hAPP(hAPP(c_List_Onth(X1),X2),esk111_3(X2,X3,X1))=X3|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))))). 4.46/4.76 cnf(i_0_7468, plain, (epred1_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk534_3(X3,X2,X1)))|~hBOOL(hAPP(X1,X3)))). 4.46/4.76 cnf(i_0_7452, plain, (epred1_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,esk532_3(X3,X2,X1)))|~hBOOL(hAPP(X1,X3)))). 4.46/4.76 cnf(i_0_117, plain, (hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),hAPP(X4,X5))=X5|~c_Fun_Oinj__on(X1,X2,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3)))). 4.46/4.76 cnf(i_0_3646, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)=hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))|hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))=X2)). 4.46/4.76 cnf(i_0_3891, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.46/4.76 cnf(i_0_1321, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))|hAPP(c_Option_Ooption_OSome(X3),X5)!=hAPP(X4,X2))). 4.46/4.76 cnf(i_0_6115, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1))). 4.46/4.76 cnf(i_0_1658, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),esk112_3(X1,X2,X3)),esk113_3(X1,X2,X3)))|~hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))). 4.46/4.76 cnf(i_0_2555, plain, (c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),esk191_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk192_2(X2,X1)))))). 4.46/4.76 cnf(i_0_6775, plain, (c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),esk467_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk466_2(X2,X1)))))). 4.46/4.76 cnf(i_0_6704, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(c_List_Orev(X1),X4),hAPP(c_List_Orev(X2),X5))|~c_List_Olist__all2(X1,X2,X3,X4,X5))). 4.46/4.76 cnf(i_0_3893, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))))|~class_Rings_Olinordered__semidom(X1))). 4.46/4.76 cnf(i_0_6252, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)))|~class_Rings_Olinordered__ring(X1))). 4.46/4.76 cnf(i_0_2725, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.46/4.76 cnf(i_0_6200, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))!=c_Groups_Osgn__class_Osgn(X1,X2)|~class_Rings_Olinordered__idom(X1))). 4.46/4.76 cnf(i_0_3770, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~c_Equiv__Relations_Oequivp(X4,X1)|~hBOOL(hAPP(hAPP(X1,X5),X3))|~hBOOL(hAPP(hAPP(X1,X2),X5)))). 4.46/4.76 cnf(i_0_2165, plain, (X1=esk162_3(X2,X3,X4)|~c_List_Olist__ex1(X4,X3,X2)|~hBOOL(hAPP(hAPP(c_member(X4),X1),hAPP(c_List_Oset(X4),X2)))|~hBOOL(hAPP(X3,X1)))). 4.46/4.76 cnf(i_0_2671, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X1)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.46/4.76 cnf(i_0_3257, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X2)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.46/4.76 cnf(i_0_7163, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2))))). 4.46/4.76 cnf(i_0_7047, plain, (esk493_3(X1,X2,X3)=X4|~c_List_Olist__ex1(X3,X2,X1)|~hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),X1)))|~hBOOL(hAPP(X2,X4)))). 4.46/4.76 cnf(i_0_482, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2))))). 4.46/4.76 cnf(i_0_6353, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2))))). 4.46/4.76 cnf(i_0_7220, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X5)))|~hBOOL(hAPP(X1,esk514_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_696, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2))))). 4.46/4.76 cnf(i_0_5794, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3))))). 4.46/4.76 cnf(i_0_5948, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3))))). 4.46/4.76 cnf(i_0_5943, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3))))). 4.46/4.76 cnf(i_0_2196, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_7165, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_3401, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_3088, plain, (hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5)=hAPP(X4,X5)|~hBOOL(hAPP(hAPP(c_member(X1),X5),c_Map_Odom(X1,X2,X4))))). 4.46/4.76 cnf(i_0_4625, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))=X4|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.76 cnf(i_0_6797, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))=X4|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3)). 4.46/4.76 cnf(i_0_7234, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Map_Odom(X1,X3,X4))=c_Map_Odom(X1,X3,X4)|hAPP(X4,X2)!=hAPP(c_Option_Ooption_OSome(X3),X5))). 4.46/4.76 cnf(i_0_7334, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X3),X1)),hAPP(c_Finite__Set_Ocard(X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X2),X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)))). 4.46/4.76 cnf(i_0_5261, plain, (hAPP(X1,esk367_4(X2,X1,X3,X4))=X4|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Set_Oimage(X3,X5,X1),X2))))). 4.46/4.76 cnf(i_0_5383, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Relation_OId__on(X1,X3))))). 4.46/4.76 cnf(i_0_1052, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),X4)!=c_Option_Ooption_ONone(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)))))). 4.46/4.76 cnf(i_0_4298, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,X3))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X4))). 4.46/4.76 cnf(i_0_2792, plain, (hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_6525, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),hAPP(c_List_Oset(tc_Nat_Onat),X3))))). 4.46/4.76 cnf(i_0_6679, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_6089, plain, (c_List_Oremdups(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=c_List_Oremdups(X1,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.46/4.76 cnf(i_0_4487, plain, (X1=c_List_Olist_ONil(X2)|hBOOL(hAPP(hAPP(c_member(X2),hAPP(c_List_Ohd(X2),X1)),hAPP(c_List_Oset(X2),X1))))). 4.46/4.76 cnf(i_0_5578, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_3431, plain, (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4),X5))|~hBOOL(hAPP(hAPP(X4,esk235_5(X5,X4,X3,X2,X1)),X5)))). 4.46/4.76 cnf(i_0_7035, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~class_Rings_Olinordered__idom(X3)|~class_Int_Onumber__ring(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2))))). 4.46/4.76 cnf(i_0_6972, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~class_Rings_Olinordered__idom(X3)|~class_Int_Onumber__ring(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2))))). 4.46/4.76 cnf(i_0_5654, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_OtakeWhile(X1,X4,X3)))))). 4.46/4.76 cnf(i_0_1521, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(c_COMBK(X2,X1),c_Groups_Ozero__class_Ozero(X2))),X3)=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ocomm__monoid__add(X2))). 4.46/4.76 cnf(i_0_54, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.46/4.76 cnf(i_0_1939, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(c_COMBK(X2,X1),c_Groups_Oone__class_Oone(X2))),X3)=c_Groups_Oone__class_Oone(X2)|~class_Groups_Ocomm__monoid__mult(X2))). 4.46/4.76 cnf(i_0_2484, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X4,X3)))))). 4.46/4.76 cnf(i_0_4276, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X3,X4)))))). 4.46/4.76 cnf(i_0_243, plain, (hAPP(c_Fun_Ooverride__on(X1,X2,X3,X4,X5),X6)=hAPP(X3,X6)|hBOOL(hAPP(hAPP(c_member(X1),X6),X5)))). 4.46/4.76 cnf(i_0_5711, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Oring__char__0(X1)|~hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(X1)),c_Int_Oring__1__class_OInts(X1))))). 4.46/4.76 cnf(i_0_53, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.46/4.76 cnf(i_0_193, plain, (c_List_Olist__ex1(X1,X2,c_Enum_Oenum__class_Oenum(X1))|hBOOL(hAPP(X2,esk20_3(X2,X1,X3)))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(X2,X3)))). 4.46/4.76 cnf(i_0_6247, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),hAPP(c_Relation_Oconverse(X2,X1),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2,X1)),X3)))). 4.46/4.76 cnf(i_0_4275, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X2,hAPP(hAPP(c_COMBB(X3,tc_fun(X2,X2),X1),X4),X5))|~c_Finite__Set_Ofun__left__comm__idem(X3,X2,X4))). 4.46/4.76 cnf(i_0_2066, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.76 cnf(i_0_4616, plain, (c_List_Oremove1(X1,X2,X3)=X3|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.46/4.76 cnf(i_0_2303, plain, (c_Finite__Set_Ofun__left__comm(X1,X2,hAPP(hAPP(c_COMBB(X3,tc_fun(X2,X2),X1),X4),X5))|~c_Finite__Set_Ofun__left__comm(X3,X2,X4))). 4.46/4.76 cnf(i_0_3407, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),c_List_Olist_ONil(X1))=hAPP(hAPP(c_List_Olist_OCons(X1),X4),c_List_Olist_ONil(X1))|~class_Orderings_Olinorder(X2))). 4.46/4.76 cnf(i_0_3999, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Wellfounded_Oless__than)))). 4.46/4.76 cnf(i_0_6417, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Oran(X3,X1,X4)))|hAPP(X4,X5)!=hAPP(c_Option_Ooption_OSome(X1),X2))). 4.46/4.76 cnf(i_0_2805, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_246, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.46/4.76 cnf(i_0_814, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.76 cnf(i_0_1406, plain, (hAPP(X1,esk92_3(X1,X2,X3))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))). 4.46/4.76 cnf(i_0_1657, plain, (hBOOL(hAPP(X1,esk113_3(X1,X2,X3)))|hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))). 4.46/4.76 cnf(i_0_1392, plain, (hBOOL(hAPP(X1,esk91_3(X2,X3,X1)))|hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2))))). 4.46/4.76 cnf(i_0_617, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1))),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.46/4.76 cnf(i_0_705, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.46/4.76 cnf(i_0_2241, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))|hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.46/4.76 cnf(i_0_2955, plain, (hAPP(X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X5),X1)!=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X4),X2),X5)))). 4.46/4.76 cnf(i_0_3768, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Nat_OSuc,X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))|~class_Rings_Osemiring__1(X1))). 4.46/4.76 cnf(i_0_3805, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|hBOOL(hAPP(hAPP(c_member(X1),esk261_4(X4,X3,X2,X1)),X4)))). 4.46/4.76 cnf(i_0_3804, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|hBOOL(hAPP(hAPP(c_member(X1),esk262_4(X4,X3,X2,X1)),X4)))). 4.46/4.76 cnf(i_0_2316, plain, (~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),c_Transitive__Closure_Ortrancl(X1,X4))))). 4.46/4.76 cnf(i_0_2055, plain, (~c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),c_Transitive__Closure_Ortrancl(X1,X4))))). 4.46/4.76 cnf(i_0_2295, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))=c_List_Olist_ONil(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_3446, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_3764, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_1645, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.46/4.76 cnf(i_0_3405, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))=X2|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.76 cnf(i_0_314, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))=X2|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.76 cnf(i_0_6989, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))|~hBOOL(hAPP(X1,esk487_2(X1,X3))))). 4.46/4.76 cnf(i_0_2779, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,esk199_3(X2,X1,X3)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(X1,X2)))). 4.46/4.76 cnf(i_0_6272, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Obutlast(X1,X3))|c_List_Olist_ONil(X1)=X3)). 4.46/4.76 cnf(i_0_5755, plain, (hAPP(c_Set_Oimage(X1,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|~c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))). 4.46/4.76 cnf(i_0_936, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk69_2(X2,X1)),esk68_2(X2,X1))=X2|X2=c_List_Olist_ONil(X1)|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_7153, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3))=hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Obutlast(X1,X3))|c_List_Olist_ONil(X1)=X3)). 4.46/4.76 cnf(i_0_2682, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.46/4.76 cnf(i_0_5081, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_1796, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),esk121_3(X3,X2,X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))))). 4.46/4.76 cnf(i_0_2175, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Int_OMin),X1)=c_Int_OMin|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_991, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.46/4.76 cnf(i_0_5911, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~c_Nat__Transfer_Onat__set(X2)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2)))). 4.46/4.76 cnf(i_0_2290, plain, (hAPP(X1,esk169_4(X1,X2,X3,X4))=c_Groups_Ozero__class_Ozero(X4)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X4),X1),X2)!=c_Groups_Ozero__class_Ozero(X4)|~class_Rings_Ono__zero__divisors(X4)|~class_Rings_Ocomm__semiring__1(X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))). 4.46/4.76 cnf(i_0_3545, plain, (c_List_Olinorder__class_Osort__key(X1,X2,X3,hAPP(c_List_Ofilter(X1,X4),X5))=hAPP(c_List_Ofilter(X1,X4),c_List_Olinorder__class_Osort__key(X1,X2,X3,X5))|~class_Orderings_Olinorder(X2))). 4.46/4.76 cnf(i_0_6902, plain, (X1=c_List_Olist_ONil(X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X1),c_List_Olist_ONil(X2))),c_List_Olistrel(X2,X3))))). 4.46/4.76 cnf(i_0_7104, plain, (X1=c_List_Olist_ONil(X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olist_ONil(X2)),X1)),c_List_Olistrel(X2,X3))))). 4.46/4.76 cnf(i_0_47, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))))). 4.46/4.76 cnf(i_0_2923, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3)))). 4.46/4.76 cnf(i_0_3338, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Oring__1(X1))). 4.46/4.76 cnf(i_0_3028, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2)))). 4.46/4.76 cnf(i_0_6310, plain, (c_List_Opartition(X1,X2,X3)!=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X5)|~hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),X5)))|~hBOOL(hAPP(X2,X6)))). 4.46/4.76 cnf(i_0_3714, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))|~hBOOL(hAPP(X1,esk253_4(X1,X3,X2,X4))))). 4.46/4.76 cnf(i_0_5091, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.46/4.76 cnf(i_0_6328, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_2268, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3),esk168_5(X3,X5,X4,X2,X1))))). 4.46/4.76 cnf(i_0_7041, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3),esk491_5(X5,X4,X3,X2,X1))))). 4.46/4.76 cnf(i_0_583, plain, (X1=X2|hAPP(X3,X1)!=hAPP(X3,X2)|~c_Fun_Oinj__on(X4,X5,X3,X6)|~hBOOL(hAPP(hAPP(c_member(X4),X2),X6))|~hBOOL(hAPP(hAPP(c_member(X4),X1),X6)))). 4.46/4.76 cnf(i_0_4670, plain, (hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(X3,hAPP(c_List_Ohd(X2),X4))|c_List_Olist_ONil(X2)=X4)). 4.46/4.76 cnf(i_0_729, plain, (hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.46/4.76 cnf(i_0_700, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))=hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_2830, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))))). 4.46/4.76 cnf(i_0_7270, plain, (c_Divides_Odivmod__int(X1,X2)=c_Divides_OnegDivAlg(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.76 cnf(i_0_1692, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Big__Operators_Olinorder__class_OMax(X1,X3)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.76 cnf(i_0_6326, plain, (hAPP(c_Set_Oimage(X1,X2,hAPP(c_COMBK(X2,X1),X3)),X4)=hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X4)). 4.46/4.76 cnf(i_0_6520, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_6823, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.76 cnf(i_0_5777, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_1001, plain, (c_List_Olast(X1,hAPP(hAPP(c_List_Odrop(X1),X2),X3))=c_List_Olast(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.46/4.76 cnf(i_0_3506, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)))|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_1099, plain, (hAPP(hAPP(X1,X2),X3)=X4|hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3))|~c_Big__Operators_Ocomm__monoid__big(X6,X5,X7,X4,X1))). 4.46/4.76 cnf(i_0_4249, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.76 cnf(i_0_4247, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.76 cnf(i_0_2095, plain, (hAPP(c_List_Ofilter(X1,X2),esk153_5(X3,X4,X5,X2,X1))=X3|hAPP(c_List_Ofilter(X1,X2),X5)!=hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))). 4.46/4.76 cnf(i_0_7440, plain, (hAPP(c_List_Ofilter(X1,X2),esk529_5(X3,X2,X4,X5,X1))=X4|hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)!=hAPP(c_List_Ofilter(X1,X2),X3))). 4.46/4.76 cnf(i_0_1608, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.46/4.76 cnf(i_0_5616, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.46/4.76 cnf(i_0_3940, plain, (hAPP(X1,X2)=hAPP(c_Option_Ooption_OSome(X3),X4)|hAPP(X1,X2)=c_Option_Ooption_ONone(X3)|hAPP(c_Option_Ooption_OSome(X3),X4)!=hAPP(c_Map_Omap__add(X5,X3,X6,X1),X2))). 4.46/4.76 cnf(i_0_7294, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X1)),X2))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_HOL_Obool,X1),X2),c_Option_Ooption_OSome(X1))))|~hBOOL(hAPP(X2,c_Option_Ooption_ONone(X1))))). 4.46/4.76 cnf(i_0_4577, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.46/4.76 cnf(i_0_593, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.46/4.76 cnf(i_0_4729, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.46/4.76 cnf(i_0_6912, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.46/4.76 cnf(i_0_6289, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X3,X3),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4))))). 4.46/4.76 cnf(i_0_2557, plain, (c_List_Olinorder__class_Osorted(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk191_2(X2,X1)),esk192_2(X2,X1)))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_6776, plain, (c_List_Olinorder__class_Osorted(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk467_2(X2,X1)),esk466_2(X2,X1)))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_3504, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),c_Divides_OnegDivAlg(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.76 cnf(i_0_1800, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1)),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.76 cnf(i_0_7242, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2))))). 4.46/4.76 cnf(i_0_2399, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),X2)))). 4.46/4.76 cnf(i_0_1317, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))))). 4.46/4.76 cnf(i_0_6030, plain, (hAPP(X1,esk417_1(X1))=hAPP(X1,esk418_1(X1))|c_Equiv__Relations_Oequivp(X2,X1)|hBOOL(hAPP(hAPP(X1,esk417_1(X1)),esk418_1(X1))))). 4.46/4.76 cnf(i_0_3624, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),c_Divides_OposDivAlg(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.76 cnf(i_0_4649, plain, (c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))|~c_Wellfounded_OwfP(X1,X2))). 4.46/4.76 cnf(i_0_189, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))|~c_Wellfounded_OwfP(X1,X2))). 4.46/4.76 cnf(i_0_3524, plain, (X1=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X3|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X3),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X4))))). 4.46/4.76 cnf(i_0_1315, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))))). 4.46/4.76 cnf(i_0_3166, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))))). 4.46/4.76 cnf(i_0_4484, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))))). 4.46/4.76 cnf(i_0_2758, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk196_2(X2,X1)))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.46/4.76 cnf(i_0_5762, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)=X3|X3=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Rings_Oidom(X1))). 4.46/4.76 cnf(i_0_112, plain, (X1=X2|hAPP(hAPP(c_List_Oappend(X3),X4),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3)))!=hAPP(hAPP(c_List_Oappend(X3),X5),hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_Olist_ONil(X3))))). 4.46/4.76 cnf(i_0_113, plain, (X1=X2|hAPP(hAPP(c_List_Oappend(X3),X1),hAPP(hAPP(c_List_Olist_OCons(X3),X4),c_List_Olist_ONil(X3)))!=hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X5),c_List_Olist_ONil(X3))))). 4.46/4.76 cnf(i_0_6793, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X1,X2)),X3),X4))|hAPP(X3,esk469_4(X4,X3,X1,X2))!=hAPP(X4,esk469_4(X4,X3,X1,X2))|~class_HOL_Oequal(X2)|~class_Enum_Oenum(X1))). 4.46/4.76 cnf(i_0_2554, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.46/4.76 cnf(i_0_5984, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.46/4.76 cnf(i_0_996, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.46/4.76 cnf(i_0_2311, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2),X3),hAPP(c_COMBK(X2,X1),X4))=X4|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Complete__Lattice_Ocomplete__lattice(X2))). 4.46/4.76 cnf(i_0_567, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))=c_Groups_Osgn__class_Osgn(X1,X2)|c_Groups_Ozero__class_Ozero(X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Osgn__if(X1))). 4.46/4.76 cnf(i_0_6327, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2)))). 4.46/4.76 cnf(i_0_4846, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_731, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.76 cnf(i_0_1357, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.46/4.76 cnf(i_0_6305, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X2),X3),hAPP(c_COMBK(X2,X1),X4))=X4|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Complete__Lattice_Ocomplete__lattice(X2))). 4.46/4.76 cnf(i_0_3358, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X3))|~class_Groups_Omonoid__add(X1))). 4.46/4.76 cnf(i_0_237, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Olinordered__idom(X1))). 4.46/4.76 cnf(i_0_4869, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)))). 4.46/4.76 cnf(i_0_7264, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.46/4.76 cnf(i_0_7313, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X2,c_Option_Ooption_ONone(X1),X3),hAPP(X4,X5))=c_Option_Ooption_ONone(X1)|c_Option_Ooption_ONone(X2)!=hAPP(X4,X5))). 4.46/4.76 cnf(i_0_1144, plain, (hBOOL(hAPP(X1,esk76_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))|~hBOOL(hAPP(X1,X3)))). 4.46/4.76 cnf(i_0_4371, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk301_2(X1,X2)),c_Int_OInteg))|hBOOL(hAPP(X2,X1)))). 4.46/4.76 cnf(i_0_5924, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3)=X2|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Divides_Osemiring__div(X1))). 4.46/4.76 cnf(i_0_599, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2)=X3|c_Groups_Ozero__class_Ozero(X1)=X2|~class_Divides_Osemiring__div(X1))). 4.46/4.76 cnf(i_0_4449, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk309_2(X1,X2)),X1))|hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X2,X1)))). 4.46/4.76 cnf(i_0_1008, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X6),X1))|~hBOOL(hAPP(hAPP(X6,X2),X3)))). 4.46/4.76 cnf(i_0_215, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)))). 4.46/4.76 cnf(i_0_148, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)))). 4.46/4.76 cnf(i_0_2689, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X2,X3))=hAPP(X2,X3)|~c_Finite__Set_Ofun__left__comm__idem(X4,X1,X2))). 4.46/4.76 cnf(i_0_6048, plain, (c_Fun_Oinj__on(X1,X2,X3,hAPP(c_Set_Oimage(X4,X1,X5),X6))|~c_Fun_Oinj__on(X4,X2,hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5),X6))). 4.46/4.76 cnf(i_0_2148, plain, (X1=X2|hAPP(hAPP(c_List_Onth(X3),X1),esk161_3(X3,X2,X1))!=hAPP(hAPP(c_List_Onth(X3),X2),esk161_3(X3,X2,X1))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2))). 4.46/4.76 cnf(i_0_6184, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_2723, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)=c_List_Olist_ONil(X1)|esk195_2(X2,X1)!=c_List_Olist_ONil(X1))). 4.46/4.76 cnf(i_0_5139, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)=c_List_Olist_ONil(X1)|esk357_2(X2,X1)!=c_List_Olist_ONil(X1))). 4.46/4.76 cnf(i_0_2283, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3)))). 4.46/4.76 cnf(i_0_5702, plain, (hBOOL(hAPP(c_List_Odistinct(tc_prod(X1,X2)),c_Enum_Oproduct(X1,X2,X3,X4)))|~hBOOL(hAPP(c_List_Odistinct(X2),X4))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.46/4.76 cnf(i_0_1699, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|hBOOL(hAPP(hAPP(X4,X2),X3))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X6,tc_HOL_Obool))),X1),X4),X2),X3)))). 4.46/4.76 cnf(i_0_3234, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))=X3|~class_Groups_Ogroup__add(X1))). 4.46/4.76 cnf(i_0_2529, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))=X3|~class_Groups_Ogroup__add(X1))). 4.46/4.76 cnf(i_0_4701, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),X2))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1))). 4.46/4.76 cnf(i_0_5307, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X2)),c_Sum__Type_OPlus(X1,X2,X3,X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.46/4.76 cnf(i_0_2881, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3))|~c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk202_3(X3,X2,X1)),esk203_3(X3,X2,X1))))). 4.46/4.76 cnf(i_0_1870, plain, (c_Fun_Oinj__on(X1,X2,c_Fun_Othe__inv__into(X2,X1,X3,X4),hAPP(c_Set_Oimage(X2,X1,X4),X3))|~c_Fun_Oinj__on(X2,X1,X4,X3))). 4.46/4.76 cnf(i_0_4004, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),c_Big__Operators_Olinorder__class_OMax(X2,X1)),X1))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.46/4.76 cnf(i_0_222, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.76 cnf(i_0_4155, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)|~class_Lattices_Osemilattice__inf(X1))). 4.46/4.76 cnf(i_0_2431, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)|~class_Lattices_Osemilattice__sup(X1))). 4.46/4.76 cnf(i_0_5198, plain, (hAPP(hAPP(c_List_Onth(X1),X2),esk360_2(X2,X1))=hAPP(hAPP(c_List_Onth(X1),X2),esk361_2(X2,X1))|hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.46/4.76 cnf(i_0_6276, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(c_List_Ofilter(X1,X2),X4)|hBOOL(hAPP(X2,X3)))). 4.46/4.76 cnf(i_0_7004, plain, (hBOOL(hAPP(hAPP(X1,X2),esk488_5(X3,X4,X1,X5,X2)))|~c_Wellfounded_Omax__extp(X5,X1,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))). 4.46/4.76 cnf(i_0_4627, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)),X5)!=c_Option_Ooption_ONone(X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),X3))))). 4.46/4.76 cnf(i_0_5086, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X5),X4)))|~class_Orderings_Olinorder(X1))). 4.46/4.76 cnf(i_0_1656, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X3),esk112_3(X1,X2,X3)),esk113_3(X1,X2,X3))))|~hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))). 4.46/4.76 cnf(i_0_158, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2))=hAPP(c_SetInterval_Oord__class_OlessThan(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1))). 4.46/4.76 cnf(i_0_6788, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)|~class_Lattices_Olattice(X1))). 4.46/4.77 cnf(i_0_1111, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)|~class_Lattices_Olattice(X1))). 4.46/4.77 cnf(i_0_1685, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2))=hAPP(c_SetInterval_Oord__class_OatMost(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1))). 4.46/4.77 cnf(i_0_4240, plain, (X1=X2|hAPP(X3,X1)!=hAPP(X3,X2)|~c_Typedef_Otype__definition(X4,X5,X6,X3,X7)|~hBOOL(hAPP(hAPP(c_member(X5),X2),X7))|~hBOOL(hAPP(hAPP(c_member(X5),X1),X7)))). 4.46/4.77 cnf(i_0_306, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),c_Orderings_Obot__class_Obot(X1)),X2)=c_Complete__Lattice_OSup__class_OSup(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.77 cnf(i_0_2729, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),c_Orderings_Otop__class_Otop(X1)),X2)=c_Complete__Lattice_OInf__class_OInf(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.77 cnf(i_0_2780, plain, (hBOOL(hAPP(X1,esk199_3(X2,X1,X3)))|hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(X1,X2)))). 4.46/4.77 cnf(i_0_6778, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2))=hAPP(c_SetInterval_Oord__class_OatLeast(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1))). 4.46/4.77 cnf(i_0_7319, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)|~class_Lattices_Oab__semigroup__idem__mult(X1))). 4.46/4.77 cnf(i_0_5726, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.77 cnf(i_0_3533, plain, (c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.46/4.77 cnf(i_0_6830, plain, (X1=hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X3),X1)!=c_Orderings_Obot__class_Obot(X2)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X3),X1)!=c_Orderings_Otop__class_Otop(X2)|~class_Lattices_Oboolean__algebra(X2))). 4.46/4.77 cnf(i_0_4598, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1))). 4.46/4.77 cnf(i_0_7411, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X2)),X2)=X2|~c_Equiv__Relations_Oequiv(X1,X3,X2))). 4.46/4.77 cnf(i_0_5211, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),esk364_3(X3,X2,X1)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3))))). 4.46/4.77 cnf(i_0_2166, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk162_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olist__ex1(X1,X3,X2))). 4.46/4.77 cnf(i_0_5037, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk352_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olist__ex(X1,X3,X2))). 4.46/4.77 cnf(i_0_2102, plain, (hAPP(c_Finite__Set_Ocard(tc_sum(X1,X2)),c_Sum__Type_OPlus(X1,X2,X3,X4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.46/4.77 cnf(i_0_6017, plain, (c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.46/4.77 cnf(i_0_3453, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))))). 4.46/4.77 cnf(i_0_3631, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X2)),c_Wellfounded_Ofinite__psubset(X1))))). 4.46/4.77 cnf(i_0_315, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.77 cnf(i_0_2101, plain, (hAPP(c_Finite__Set_Ocard(tc_sum(X1,X2)),c_Sum__Type_OPlus(X1,X2,X3,X4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_7046, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk493_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olist__ex1(X1,X3,X2))). 4.46/4.77 cnf(i_0_5212, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk364_3(X2,X3,X1)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Complete__Lattice_OSup__class_OSup(X1,X2))))). 4.46/4.77 cnf(i_0_3539, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk239_3(X2,X3,X1)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X2)))). 4.46/4.77 cnf(i_0_3540, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk239_3(X2,X3,X1)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X2)))). 4.46/4.77 cnf(i_0_7525, plain, (epred2_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_5845, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(c_Finite__Set_Ocard(X1),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_7250, plain, (c_Nitpick_Onorm__frac(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_3782, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.46/4.77 cnf(i_0_6393, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Ois__nat(X1)|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2))))). 4.46/4.77 cnf(i_0_1228, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)|hAPP(hAPP(c_List_Omap(X1,X5),X6),X2)!=hAPP(hAPP(c_List_Omap(X3,X5),X7),X4))). 4.46/4.77 cnf(i_0_3512, plain, (c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|hAPP(c_Set_Oimage(X1,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))). 4.46/4.77 cnf(i_0_5163, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.46/4.77 cnf(i_0_7493, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X2,X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X2,esk534_3(X3,X1,X2))))). 4.46/4.77 cnf(i_0_7477, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X2,X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(X2,esk532_3(X3,X1,X2))))). 4.46/4.77 cnf(i_0_5403, plain, (c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,X3,hAPP(X2,X4))=c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,hAPP(c_Nat_OSuc,X3),X4)|~class_Rings_Osemiring__1(X1))). 4.46/4.77 cnf(i_0_3036, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk213_4(X2,X3,X4,X1)),X3))|hAPP(c_Nat_OSuc,X2)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3))). 4.46/4.77 cnf(i_0_2685, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.46/4.77 cnf(i_0_610, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.46/4.77 cnf(i_0_6676, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X5)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)))). 4.46/4.77 cnf(i_0_3217, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X5)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)))). 4.46/4.77 cnf(i_0_7018, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.46/4.77 cnf(i_0_586, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.46/4.77 cnf(i_0_4656, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),X4))|~hBOOL(hAPP(X2,X3)))). 4.46/4.77 cnf(i_0_2044, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk150_3(X2,X1,X3)),X3))|~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3)))). 4.46/4.77 cnf(i_0_5349, plain, (hBOOL(hAPP(hAPP(X1,esk374_5(X2,X1,X3,X4,X5)),X2))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X4,tc_HOL_Obool)),X3),X1),X2)))). 4.46/4.77 cnf(i_0_55, plain, (~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X3,hAPP(c_Nat_OSuc,esk5_3(X2,X1,X3)))),hAPP(X3,esk5_3(X2,X1,X3)))),X2)))). 4.46/4.77 cnf(i_0_3414, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.46/4.77 cnf(i_0_151, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.46/4.77 cnf(i_0_754, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk52_1(X1)))|hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))). 4.46/4.77 cnf(i_0_4416, plain, (~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X3,hAPP(c_Nat_OSuc,esk305_3(X3,X2,X1)))),hAPP(X3,esk305_3(X3,X2,X1)))),X2)))). 4.46/4.77 cnf(i_0_307, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3)|~class_Divides_Oring__div(X1))). 4.46/4.77 cnf(i_0_90, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X2,X3))=hAPP(X2,X3)|~c_Finite__Set_Ofolding__idem(X4,X1,X2,X5))). 4.46/4.77 cnf(i_0_150, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.46/4.77 cnf(i_0_1025, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X1))=X1|~c_List_Onat__list(X1))). 4.46/4.77 cnf(i_0_3752, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))))). 4.46/4.77 cnf(i_0_2597, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))))). 4.46/4.77 cnf(i_0_1709, plain, (hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))|hBOOL(hAPP(X1,esk116_3(X1,X3,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(X1,X3)))). 4.46/4.77 cnf(i_0_5785, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.77 cnf(i_0_423, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1))). 4.46/4.77 cnf(i_0_1134, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))))). 4.46/4.77 cnf(i_0_391, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))))). 4.46/4.77 cnf(i_0_3027, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X1),esk210_3(X3,X2,X1)),X2)))). 4.46/4.77 cnf(i_0_3026, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X1),esk211_3(X3,X2,X1)),X3)))). 4.46/4.77 cnf(i_0_1795, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk121_3(X2,X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))))). 4.46/4.77 cnf(i_0_7365, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_1147, plain, (c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X1)))|~class_Orderings_Owellorder(X1))). 4.46/4.77 cnf(i_0_6563, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|~hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))))))). 4.46/4.77 cnf(i_0_545, plain, (c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk37_2(X1,X2))))). 4.46/4.77 cnf(i_0_6161, plain, (c_Map_Omap__add(X1,X2,X3,X4)=c_Map_Omap__add(X1,X2,X4,X3)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),c_Map_Odom(X1,X2,X4))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.46/4.77 cnf(i_0_925, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Otl(X1),X2)),X3)=hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))|c_List_Olist_ONil(X1)=X2)). 4.46/4.77 cnf(i_0_2318, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.46/4.77 cnf(i_0_1425, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.46/4.77 cnf(i_0_45, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.46/4.77 cnf(i_0_7214, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)))). 4.46/4.77 cnf(i_0_1135, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))|~class_Fields_Ofield__inverse__zero(X1))). 4.46/4.77 cnf(i_0_3183, plain, (c_Enum_Oex__n__lists(X1,X2,X3)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X3,c_Enum_Oenum__class_Oenum(X1)))))|~hBOOL(hAPP(X2,X4)))). 4.46/4.77 cnf(i_0_665, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),hAPP(c_List_Oset(tc_prod(X3,X3)),hAPP(hAPP(c_List_Ozip(X3,X3),X4),X4)))))). 4.46/4.77 cnf(i_0_6298, plain, (hAPP(c_Option_Ooption_OSome(X1),X2)=hAPP(c_Map_Omap__add(X3,X1,X4,X5),X6)|hAPP(X5,X6)!=hAPP(c_Option_Ooption_OSome(X1),X2))). 4.46/4.77 cnf(i_0_2307, plain, (hAPP(c_List_Otl(X1),c_List_Oreplicate(X1,X2,X3))=c_List_Oreplicate(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2)). 4.46/4.77 cnf(i_0_1549, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.46/4.77 cnf(i_0_7366, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.46/4.77 cnf(i_0_2080, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Oring(X1))). 4.46/4.77 cnf(i_0_200, plain, (c_SMT_Oz3div(X1,X2)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.77 cnf(i_0_312, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),X2)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.46/4.77 cnf(i_0_636, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk45_3(X2,X3,X1)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_430, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),X4),X3)))))). 4.46/4.77 cnf(i_0_4712, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Odrop(X1),X4),X3)))))). 4.46/4.77 cnf(i_0_2942, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk206_2(X1,X2))=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))))). 4.46/4.77 cnf(i_0_615, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.46/4.77 cnf(i_0_6239, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Orderings_Olinorder(X1))). 4.46/4.77 cnf(i_0_1335, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X2)),c_List_Olists(X1,X3))))). 4.46/4.77 cnf(i_0_622, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X4),X2)),c_List_Olists(X1,X3))))). 4.46/4.77 cnf(i_0_621, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X4)),c_List_Olists(X1,X3))))). 4.46/4.77 cnf(i_0_640, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(X2,X4)|esk44_4(X2,X3,X1,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_1304, plain, (c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Oremove1(X1,X2,X4))|X2=X3)). 4.46/4.77 cnf(i_0_6419, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.46/4.77 cnf(i_0_1421, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.46/4.77 cnf(i_0_420, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))))). 4.46/4.77 cnf(i_0_5446, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)),X5)=hAPP(hAPP(c_List_Onth(X1),X2),X5)|X5=X3)). 4.46/4.77 cnf(i_0_6505, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X1),esk449_2(X2,X1)),X2)))). 4.46/4.77 cnf(i_0_2400, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))=c_Big__Operators_Olattice__class_OSup__fin(X1,X3)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_5638, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))=c_Big__Operators_Olattice__class_OInf__fin(X1,X3)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_511, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olinorder__class_OMin(X1,X3))=c_Big__Operators_Olinorder__class_OMin(X1,X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_4974, plain, (hAPP(c_Fun_Othe__inv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(X3,X4))=X4|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))). 4.46/4.77 cnf(i_0_4532, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_1346, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(X1,esk90_3(X3,X2,X1))))). 4.46/4.77 cnf(i_0_1926, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(X1,esk135_3(X3,X2,X1))))). 4.46/4.77 cnf(i_0_2541, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olinorder__class_OMax(X1,X3))=c_Big__Operators_Olinorder__class_OMax(X1,X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_4321, plain, (hBOOL(hAPP(X1,esk298_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))|~hBOOL(hAPP(X1,X3)))). 4.46/4.77 cnf(i_0_2447, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OgreaterThanLessThan(X1,X3,X4,X5)))|~hBOOL(hAPP(hAPP(X3,X2),X5))|~hBOOL(hAPP(hAPP(X3,X4),X2)))). 4.46/4.77 cnf(i_0_6884, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))|~class_Rings_Oring(X1))). 4.46/4.77 cnf(i_0_6133, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))|~class_Rings_Odivision__ring(X1))). 4.46/4.77 cnf(i_0_3703, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Oring(X1))). 4.46/4.77 cnf(i_0_3710, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Obutlast(X1,X2)),hAPP(hAPP(c_List_Olist_OCons(X1),c_List_Olast(X1,X2)),c_List_Olist_ONil(X1)))=X2|X2=c_List_Olist_ONil(X1))). 4.46/4.77 cnf(i_0_7257, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatLeastAtMost(X1,X3,X4,X5)))|~hBOOL(hAPP(hAPP(X3,X4),X2))|~hBOOL(hAPP(hAPP(X3,X2),X5)))). 4.46/4.77 cnf(i_0_1972, plain, (c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),c_Map_Omap__add(X1,X2,X3,X4),c_Map_Odom(X1,X2,X4))|~c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),X4,c_Map_Odom(X1,X2,X4)))). 4.46/4.77 cnf(i_0_1323, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=c_Transitive__Closure_Ortrancl(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Transitive__Closure_Ortrancl(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.46/4.77 cnf(i_0_4549, plain, (hAPP(c_Set_Oimage(X1,X1,X2),X3)=X3|~c_Fun_Oinj__on(X1,X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X1,X2),X3)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_6185, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.77 cnf(i_0_5888, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),X5)))|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5)))). 4.46/4.77 cnf(i_0_7395, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2))=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))|~class_Orderings_Oorder(X1))). 4.46/4.77 cnf(i_0_1332, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X1))|~class_Orderings_Olinorder(X3))). 4.46/4.77 cnf(i_0_1607, plain, (c_Equiv__Relations_Ocongruent(X1,X2,X3,hAPP(X4,X5))|~c_Equiv__Relations_Ocongruent2(X6,X1,X2,X7,X3,X4)|~c_Equiv__Relations_Oequiv(X6,X8,X7)|~hBOOL(hAPP(hAPP(c_member(X6),X5),X8)))). 4.46/4.77 cnf(i_0_3363, plain, (hBOOL(hAPP(hAPP(X1,X2),esk231_4(X3,X2,X4,X1)))|~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X6,X7,X1,X4),X2),X3)))). 4.46/4.77 cnf(i_0_3362, plain, (hBOOL(hAPP(hAPP(X1,esk231_4(X2,X3,X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X6,X7,X4,X1),X3),X2)))). 4.46/4.77 cnf(i_0_5590, plain, (hBOOL(hAPP(X1,X2))|~c_Enum_Oall__n__lists(X3,X1,X4)|~class_Enum_Oenum(X3)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3)),X2),hAPP(c_List_Oset(tc_List_Olist(X3)),c_Enum_On__lists(X3,X4,c_Enum_Oenum__class_Oenum(X3))))))). 4.46/4.77 cnf(i_0_1030, plain, (c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))|~c_FunDef_Oreduction__pair(X1,X2))). 4.46/4.77 cnf(i_0_963, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.77 cnf(i_0_3706, plain, (c_List_Olist__all(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk252_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3))))). 4.46/4.77 cnf(i_0_3828, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))))). 4.46/4.77 cnf(i_0_1659, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk113_3(X2,X3,X1)))|hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_3617, plain, (hBOOL(hAPP(c_List_Odistinct(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)))|~hBOOL(hAPP(c_List_Odistinct(X2),X4)))). 4.46/4.77 cnf(i_0_4057, plain, (hBOOL(hAPP(c_List_Odistinct(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.46/4.77 cnf(i_0_7275, plain, (c_List_Olist__all(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk517_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3))))). 4.46/4.77 cnf(i_0_6616, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))). 4.46/4.77 cnf(i_0_211, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))))). 4.46/4.77 cnf(i_0_210, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))))). 4.46/4.77 cnf(i_0_4485, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1))))). 4.46/4.77 cnf(i_0_61, plain, (c_List_Olist__all(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk6_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3))))). 4.46/4.77 cnf(i_0_7045, plain, (c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~c_Fun_Oinj__on(X1,X2,X3,X5)|~c_Fun_Oinj__on(X1,X2,X3,X4))). 4.46/4.77 cnf(i_0_4931, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X6)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X7)|~c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X6),X4),hAPP(hAPP(c_List_Oappend(X2),X7),X5)))). 4.46/4.77 cnf(i_0_4932, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)|~c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X6),hAPP(hAPP(c_List_Oappend(X2),X5),X7)))). 4.46/4.77 cnf(i_0_3167, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))))). 4.46/4.77 cnf(i_0_6708, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))). 4.46/4.77 cnf(i_0_7328, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))). 4.46/4.77 cnf(i_0_6839, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))). 4.46/4.77 cnf(i_0_4179, plain, (X1=X2|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X4)),X5),X6),hAPP(c_Option_Ooption_OSome(X4),X1))!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X4)),X7),X6),hAPP(c_Option_Ooption_OSome(X4),X2)))). 4.46/4.77 cnf(i_0_6122, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))). 4.46/4.77 cnf(i_0_1073, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))). 4.46/4.77 cnf(i_0_5520, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))). 4.46/4.77 cnf(i_0_4622, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin)))). 4.46/4.77 cnf(i_0_2019, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),X4)))|~c_List_Olist__all(X2,X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))))). 4.46/4.77 cnf(i_0_7253, plain, (c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=c_Nitpick_Onorm__frac(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_1783, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Rings_Olinordered__idom(X1))). 4.46/4.77 cnf(i_0_3203, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_2058, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_3765, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin)))). 4.46/4.77 cnf(i_0_3874, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin)))). 4.46/4.77 cnf(i_0_862, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X1))|~class_Rings_Olinordered__idom(X3))). 4.46/4.77 cnf(i_0_2174, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),X2)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.46/4.77 cnf(i_0_1769, plain, (c_Divides_OnegDivAlg(X1,X2)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_596, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))))). 4.46/4.77 cnf(i_0_7059, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.46/4.77 cnf(i_0_5689, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.77 cnf(i_0_2722, plain, (X1=c_List_Olist_ONil(X2)|hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),X3)!=c_List_Olist_ONil(X2)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X1),hAPP(c_List_Oset(tc_List_Olist(X2)),X3))))). 4.46/4.77 cnf(i_0_3928, plain, (c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_OtakeWhile(X1,X2,X4))|~hBOOL(hAPP(X2,X3)))). 4.46/4.77 cnf(i_0_1408, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk92_3(X2,X3,X1)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_4082, plain, (c_List_OtakeWhile(X1,X2,X3)=X3|hBOOL(hAPP(hAPP(c_member(X1),esk277_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3))))). 4.46/4.77 cnf(i_0_5326, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_550, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(hAPP(X1,esk38_3(X1,X3,X2)),esk39_3(X1,X3,X2))))). 4.46/4.77 cnf(i_0_3355, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(hAPP(X1,esk229_3(X1,X3,X2)),esk230_3(X1,X3,X2))))). 4.46/4.77 cnf(i_0_3652, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(hAPP(X1,esk246_3(X1,X3,X2)),esk247_3(X1,X3,X2))))). 4.46/4.77 cnf(i_0_5480, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(hAPP(X1,esk378_3(X1,X3,X2)),esk379_3(X1,X3,X2))))). 4.46/4.77 cnf(i_0_3213, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.77 cnf(i_0_5939, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.77 cnf(i_0_2669, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_5892, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_4474, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Odivision__ring(X1))). 4.46/4.77 cnf(i_0_5981, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(hAPP(X1,esk409_3(X1,X3,X2)),esk410_3(X1,X3,X2))))). 4.46/4.77 cnf(i_0_7108, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(X1,esk498_3(X1,X3,X2)),esk499_3(X1,X3,X2))))). 4.46/4.77 cnf(i_0_6699, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X3)))). 4.46/4.77 cnf(i_0_6213, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.46/4.77 cnf(i_0_1021, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_266, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2))=hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)|~class_Orderings_Olinorder(X1))). 4.46/4.77 cnf(i_0_5724, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk397_2(X2,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))))). 4.46/4.77 cnf(i_0_5932, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)|~class_Fields_Ofield__inverse__zero(X1))). 4.46/4.77 cnf(i_0_521, plain, (hAPP(hAPP(c_Set_Oinsert(X1),esk33_3(X2,X3,X1)),esk34_3(X2,X3,X1))=X3|hAPP(c_Nat_OSuc,X2)!=hAPP(c_Finite__Set_Ocard(X1),X3))). 4.46/4.77 cnf(i_0_5203, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),X4))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),X3)))). 4.46/4.77 cnf(i_0_1361, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Oremove1(X2,X4,X5)))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))|~class_Orderings_Olinorder(X1))). 4.46/4.77 cnf(i_0_3985, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X4),esk273_3(X1,X4,X3))))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))))). 4.46/4.77 cnf(i_0_2970, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X1,X2)),c_Predicate_OPowp(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.46/4.77 cnf(i_0_4997, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4))=X2|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.77 cnf(i_0_2213, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3)))|~hBOOL(hAPP(c_Predicate_OPowp(X1,X3),X2)))). 4.46/4.77 cnf(i_0_5897, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)|~class_Rings_Oring(X1))). 4.46/4.77 cnf(i_0_1122, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3))=c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__idom(X1))). 4.46/4.77 cnf(i_0_3632, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3))))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,c_Wellfounded_Oacc(X1,X3)))))). 4.46/4.77 cnf(i_0_805, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__ring__strict(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3))),c_Groups_Ozero__class_Ozero(X2))))). 4.46/4.77 cnf(i_0_512, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.46/4.77 cnf(i_0_6391, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.46/4.77 cnf(i_0_2374, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.46/4.77 cnf(i_0_2897, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.46/4.77 cnf(i_0_1205, plain, (~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))))))). 4.46/4.77 cnf(i_0_804, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.77 cnf(i_0_2369, plain, (c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))=hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.46/4.77 cnf(i_0_5885, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.46/4.77 cnf(i_0_2732, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.46/4.77 cnf(i_0_3681, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.46/4.77 cnf(i_0_2203, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.46/4.77 cnf(i_0_970, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))=X2|c_Fun_Oinj__on(X1,X3,X4,c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2))|~c_Fun_Oinj__on(X1,X3,X4,esk70_4(X4,X3,X1,X2)))). 4.46/4.77 cnf(i_0_606, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(c_List_Olistsp(X1,X3),X2)))). 4.46/4.77 cnf(i_0_4514, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))). 4.46/4.77 cnf(i_0_3941, plain, (hAPP(c_Option_Ooption_OSome(X1),X2)=hAPP(X3,X4)|hAPP(X5,X4)=hAPP(c_Option_Ooption_OSome(X1),X2)|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(c_Map_Omap__add(X6,X1,X3,X5),X4))). 4.46/4.77 cnf(i_0_6738, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.46/4.77 cnf(i_0_2404, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.46/4.77 cnf(i_0_7401, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.46/4.77 cnf(i_0_5111, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.46/4.77 cnf(i_0_4576, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Rings_Odivision__ring(X1))). 4.46/4.77 cnf(i_0_1554, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk101_1(X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,X2)))). 4.46/4.77 cnf(i_0_7094, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.46/4.77 cnf(i_0_3006, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.46/4.77 cnf(i_0_6643, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X1))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.46/4.77 cnf(i_0_1136, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2))),X3)=c_List_Oremove1(X1,X2,X3)|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.46/4.77 cnf(i_0_2309, plain, (hAPP(c_Set_Oimage(X1,X2,X3),X4)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|c_Fun_Oinj__on(X2,X1,esk170_4(X4,X1,X2,hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X4)))). 4.46/4.77 cnf(i_0_5473, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.77 cnf(i_0_498, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.77 cnf(i_0_2584, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3)))). 4.46/4.77 cnf(i_0_3850, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.46/4.77 cnf(i_0_2398, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))))). 4.46/4.77 cnf(i_0_7243, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)))). 4.46/4.77 cnf(i_0_1960, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.77 cnf(i_0_3537, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=c_Groups_Ozero__class_Ozero(X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~class_Int_Onumber__ring(X1))). 4.46/4.77 cnf(i_0_1118, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3)))). 4.46/4.77 cnf(i_0_2642, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.46/4.77 cnf(i_0_230, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3)))). 4.46/4.77 cnf(i_0_6318, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.46/4.77 cnf(i_0_5882, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.46/4.77 cnf(i_0_1148, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.46/4.77 cnf(i_0_4232, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.46/4.77 cnf(i_0_2065, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Ocomm__semiring__1(X1))). 4.46/4.77 cnf(i_0_6621, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3)))). 4.46/4.77 cnf(i_0_1232, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.46/4.77 cnf(i_0_5142, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.46/4.77 cnf(i_0_7434, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.46/4.77 cnf(i_0_3520, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X2)),c_Wellfounded_Omax__ext(X1,X4))))). 4.46/4.77 cnf(i_0_3516, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Omax__ext(X1,X4))))). 4.46/4.77 cnf(i_0_6295, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_OPow(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.46/4.77 cnf(i_0_2850, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X3),X6))))). 4.46/4.77 cnf(i_0_7446, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X2)!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X2)))). 4.46/4.77 cnf(i_0_3538, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.77 cnf(i_0_5950, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))))). 4.46/4.77 cnf(i_0_2588, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_OMin,X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.77 cnf(i_0_1889, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.46/4.77 cnf(i_0_2483, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))|~class_Power_Opower(X1))). 4.46/4.77 cnf(i_0_5201, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk360_2(X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))|hBOOL(hAPP(c_List_Odistinct(X2),X1)))). 4.46/4.77 cnf(i_0_6039, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Oordered__comm__monoid__add(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)))). 4.46/4.77 cnf(i_0_6040, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.46/4.77 cnf(i_0_5057, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2)))). 4.46/4.77 cnf(i_0_3281, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2)))). 4.46/4.77 cnf(i_0_5200, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk361_2(X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))|hBOOL(hAPP(c_List_Odistinct(X2),X1)))). 4.46/4.77 cnf(i_0_3107, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5))=X3|hAPP(X3,X4)!=hAPP(c_Option_Ooption_OSome(X2),X5))). 4.46/4.77 cnf(i_0_3580, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.46/4.77 cnf(i_0_3122, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Oaccp(X1,X2)),c_Wellfounded_Oaccp(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X3),X2)))). 4.46/4.77 cnf(i_0_4836, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3)))). 4.46/4.77 cnf(i_0_3012, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_COMBI(X1)),hAPP(c_List_Oset(X1),X2))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.46/4.77 cnf(i_0_5058, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.46/4.77 cnf(i_0_3282, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.46/4.77 cnf(i_0_1739, plain, (hAPP(c_List_Oset(X1),c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X2,X3))=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3))|~class_Orderings_Olinorder(X1))). 4.46/4.77 cnf(i_0_4251, plain, (c_List_Olinorder__class_Oinsort__insert__key(X1,X2,X3,X4,X5)=X5|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X4)),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_List_Oset(X1),X5)))))). 4.46/4.77 cnf(i_0_1071, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),c_List_Oreplicate(X2,X1,X3)))))). 4.46/4.77 cnf(i_0_3873, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X3),X2)))). 4.46/4.77 cnf(i_0_3859, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=hAPP(X2,X3)|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X5),X2)!=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5)))). 4.46/4.77 cnf(i_0_3502, plain, (X1=X2|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))). 4.46/4.77 cnf(i_0_7005, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk488_5(X2,X3,X4,X1,X5)),X2))|~c_Wellfounded_Omax__extp(X1,X4,X3,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3)))). 4.46/4.77 cnf(i_0_4663, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk329_2(X2,X1))))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.46/4.77 cnf(i_0_4488, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X1)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)))). 4.46/4.77 cnf(i_0_2605, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2))=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))|~class_Orderings_Oorder(X1))). 4.46/4.77 cnf(i_0_1581, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.46/4.77 cnf(i_0_4096, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.77 cnf(i_0_1841, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.77 cnf(i_0_5637, plain, (hAPP(hAPP(c_List_Otake(X1),X2),c_List_Obutlast(X1,X3))=hAPP(hAPP(c_List_Otake(X1),X2),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.46/4.77 cnf(i_0_2913, plain, (c_List_Osublist(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)),X3)=c_List_Olist_ONil(X1)|hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))). 4.46/4.77 cnf(i_0_3030, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.46/4.77 cnf(i_0_3241, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk222_3(X3,X2,X1)),X3)))). 4.46/4.77 cnf(i_0_5575, plain, (hAPP(c_List_Ofilter(X1,X2),X3)=X3|hBOOL(hAPP(hAPP(c_member(X1),esk386_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3))))). 4.46/4.77 cnf(i_0_140, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk16_3(X2,X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),c_Relation_OId__on(X1,X2))))). 4.46/4.77 cnf(i_0_1105, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OgreaterThanAtMost(X1,X3,X4,X5,X6)))|~hBOOL(hAPP(hAPP(X3,X2),X6))|~hBOOL(hAPP(hAPP(X4,X5),X2)))). 4.46/4.77 cnf(i_0_2860, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatLeastLessThan(X1,X3,X4,X5,X6)))|~hBOOL(hAPP(hAPP(X3,X5),X2))|~hBOOL(hAPP(hAPP(X4,X2),X6)))). 4.46/4.77 cnf(i_0_3791, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(X1,X2)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X4)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X3),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)))). 4.46/4.77 cnf(i_0_962, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.77 cnf(i_0_1353, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),X3)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X3))|~class_Rings_Osemiring__1(X1))). 4.46/4.77 cnf(i_0_2357, plain, (hAPP(X1,X2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Nat_Onat),X1),X4)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X3),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)))). 4.46/4.77 cnf(i_0_4088, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.46/4.77 cnf(i_0_4848, plain, (c_List_Olist_ONil(X1)=X2|hBOOL(hAPP(hAPP(c_member(X1),esk335_3(X3,X2,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3))))). 4.46/4.77 cnf(i_0_2168, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)))|~class_Rings_Olinordered__idom(X1))). 4.46/4.77 cnf(i_0_4736, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3))|~class_Orderings_Olinorder(X1))). 4.46/4.77 cnf(i_0_7229, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),X3)=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X3))|~class_Rings_Oring__1(X1))). 4.46/4.77 cnf(i_0_7116, plain, (c_Equiv__Relations_Ocongruent(X1,X2,X3,X4)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk500_4(X4,X3,X2,X1)),X3)))). 4.46/4.77 cnf(i_0_5308, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk371_4(X2,X3,X4,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X2))))). 4.46/4.77 cnf(i_0_5348, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk374_5(X2,X3,X4,X5,X1)),X4))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X4),X3),X2)))). 4.46/4.77 cnf(i_0_2895, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))=X2|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_5884, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1))))). 4.46/4.77 cnf(i_0_3630, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Ofinite__psubset(X1))))). 4.46/4.77 cnf(i_0_4282, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.46/4.77 cnf(i_0_198, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)))). 4.46/4.77 cnf(i_0_6041, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X2))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.46/4.77 cnf(i_0_4835, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))=X2|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_5609, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_3055, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X2),X3)=c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_6132, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X2),X3)=c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_2928, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X4)))). 4.46/4.77 cnf(i_0_5149, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.46/4.77 cnf(i_0_2674, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),X4)=hAPP(hAPP(c_List_Onth(X1),X3),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X2)))). 4.46/4.77 cnf(i_0_6251, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=c_List_Olist_ONil(X1)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.77 cnf(i_0_4732, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.77 cnf(i_0_1580, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X5,tc_HOL_Obool)),X6),X1),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),X6)))). 4.46/4.77 cnf(i_0_5231, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4),X5),X6))|~hBOOL(hAPP(hAPP(X4,X5),X6))|~hBOOL(hAPP(hAPP(X3,X5),X6)))). 4.46/4.77 cnf(i_0_2031, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.46/4.77 cnf(i_0_4758, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1))). 4.46/4.77 cnf(i_0_7367, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~c_Fun_Oinj__on(X1,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3))))). 4.46/4.77 cnf(i_0_7391, plain, (hAPP(c_Relation_OImage(X1,X1,c_Transitive__Closure_Ortrancl(X1,X2)),X3)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X2),X3)),X3)))). 4.46/4.77 cnf(i_0_7416, plain, (hAPP(c_Set_Oimage(X1,X2,X3),esk525_5(X4,X3,X1,X5,X2))=X5|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X5),hAPP(c_Set_Oimage(X1,X2,X3),X4))))). 4.46/4.77 cnf(i_0_7304, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3))=c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1))). 4.46/4.77 cnf(i_0_1468, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.46/4.77 cnf(i_0_4090, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.46/4.77 cnf(i_0_745, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.77 cnf(i_0_6959, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3))=c_SetInterval_Oord__class_OgreaterThanLessThan(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1))). 4.46/4.77 cnf(i_0_6309, plain, (hBOOL(hAPP(X1,X2))|c_List_Opartition(X3,X1,X4)!=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X5),X6)|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X5))))). 4.46/4.77 cnf(i_0_1235, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.77 cnf(i_0_6625, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.77 cnf(i_0_1937, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.77 cnf(i_0_3939, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)))). 4.46/4.77 cnf(i_0_1221, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.77 cnf(i_0_6903, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_2207, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_2043, plain, (~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),esk150_3(X2,X1,X4))),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X4)))). 4.46/4.77 cnf(i_0_4913, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3)))). 4.46/4.77 cnf(i_0_6098, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)))). 4.46/4.77 cnf(i_0_865, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)))). 4.46/4.77 cnf(i_0_4387, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),X5)=hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(X3,X4)),hAPP(X3,esk303_5(X4,X3,X5,X1,X2)))))). 4.46/4.77 cnf(i_0_3474, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk236_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)))|~c_List_Olist__ex(X3,X2,X1))). 4.46/4.77 cnf(i_0_4306, plain, (c_Wellfounded_Owf(tc_prod(X1,X2),c_Recdef_Osame__fst(X1,X2,X3,X4))|hBOOL(hAPP(X3,esk294_4(X1,X4,X2,X3))))). 4.46/4.77 cnf(i_0_2180, plain, (hAPP(X1,X2)=hAPP(X1,X3)|~c_Equiv__Relations_Ocongruent(X4,X5,X6,X1)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),X6)))). 4.46/4.77 cnf(i_0_1711, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk116_3(X2,X3,X1)))|hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(X2,X3)))). 4.46/4.77 cnf(i_0_5000, plain, (hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),X5))=hAPP(c_Set_Oimage(X4,X1,X2),X5)|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5)))). 4.46/4.77 cnf(i_0_2288, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))))). 4.46/4.77 cnf(i_0_6771, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(X3),X4),X1))|hBOOL(hAPP(hAPP(c_member(X3),X4),X2))|hAPP(hAPP(c_Set_Oinsert(X3),X4),X1)!=hAPP(hAPP(c_Set_Oinsert(X3),X4),X2))). 4.46/4.77 cnf(i_0_2556, plain, (c_List_Olinorder__class_Osorted(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk192_2(X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|~class_Orderings_Olinorder(X1))). 4.46/4.77 cnf(i_0_3229, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X5),X6)))|~hBOOL(hAPP(X1,esk221_5(X1,X6,X5,X4,X3))))). 4.46/4.77 cnf(i_0_4555, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))|~class_Orderings_Oord(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(X3,esk320_4(X4,X3,X1,X2))),hAPP(X4,esk320_4(X4,X3,X1,X2)))))). 4.46/4.77 cnf(i_0_6777, plain, (c_List_Olinorder__class_Osorted(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk466_2(X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|~class_Orderings_Olinorder(X1))). 4.46/4.77 cnf(i_0_3018, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.46/4.77 cnf(i_0_890, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.46/4.77 cnf(i_0_7355, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X4),X3)))). 4.46/4.77 cnf(i_0_5339, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.46/4.77 cnf(i_0_526, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),X3))|hAPP(c_Finite__Set_Ocard(X1),X3)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.46/4.77 cnf(i_0_709, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Complete__Lattice_OInf__class_OInf(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X4)))). 4.46/4.77 cnf(i_0_5005, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OSup__class_OSup(X1,X4)),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.46/4.77 cnf(i_0_4159, plain, (c_Fun_Oinj__on(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),X6)|~c_Fun_Oinj__on(X3,X2,X4,hAPP(c_Set_Oimage(X1,X3,X5),X6))|~c_Fun_Oinj__on(X1,X3,X5,X6))). 4.46/4.77 cnf(i_0_1701, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))))|~class_Rings_Olinordered__semidom(X1))). 4.46/4.77 cnf(i_0_7332, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X2))))). 4.46/4.77 cnf(i_0_424, plain, (X1=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),X4)|c_Groups_Ozero__class_Ozero(X2)=X4|hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X4)|~class_Fields_Ofield__inverse__zero(X2)|~class_Int_Onumber(X2))). 4.46/4.77 cnf(i_0_5641, plain, (c_Fun_Oinj__on(X1,X2,esk389_4(X3,X2,X4,X1),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X4)),hAPP(c_Finite__Set_Ocard(X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.46/4.77 cnf(i_0_639, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(X2,esk44_4(X2,X3,X1,X4))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(X2,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_937, plain, (X1=c_List_Olist_ONil(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),esk69_2(X1,X2)),X3))|~c_List_Olinorder__class_Osorted(X2,X1)|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),esk68_2(X1,X2)))))). 4.46/4.77 cnf(i_0_7293, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_HOL_Obool,X1),X2),c_Option_Ooption_OSome(X1))))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X1)),X2)))). 4.46/4.77 cnf(i_0_797, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)),X3)=X4|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.46/4.77 cnf(i_0_5813, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Oacc(X1,X2)),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)))). 4.46/4.77 cnf(i_0_2119, plain, (hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),X5))=hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(c_List_Oset(X1),X5))|~class_Orderings_Olinorder(X2))). 4.46/4.77 cnf(i_0_7502, plain, (epred2_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk538_3(X3,X2,X1)))|~hBOOL(hAPP(X1,esk535_3(X3,X2,X1))))). 4.46/4.77 cnf(i_0_5069, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.46/4.77 cnf(i_0_2958, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.46/4.77 cnf(i_0_7506, plain, (epred2_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk536_3(X3,X2,X1)),X2))|~hBOOL(hAPP(X1,esk537_3(X3,X2,X1))))). 4.46/4.77 cnf(i_0_1536, plain, (hAPP(c_List_Ofilter(X1,X2),X3)=c_List_Olist_ONil(X1)|hBOOL(hAPP(hAPP(c_member(X1),esk97_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3))))). 4.46/4.77 cnf(i_0_3272, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))))). 4.46/4.77 cnf(i_0_2278, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_3132, plain, (X1=X2|hAPP(hAPP(c_List_Omap(X3,X4),X5),X1)!=hAPP(hAPP(c_List_Omap(X3,X4),X5),X2)|~c_Fun_Oinj__on(X3,X4,X5,hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Oappend(X3),X2),X1))))). 4.46/4.77 cnf(i_0_1754, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk120_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|hBOOL(hAPP(c_List_Olistsp(X1,X3),X2)))). 4.46/4.77 cnf(i_0_3847, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X4,esk265_4(X4,X1,X3,X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.46/4.77 cnf(i_0_6976, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X4,esk483_4(X4,X1,X3,X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.46/4.77 cnf(i_0_2018, plain, (c_List_Olist__all(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk145_3(X3,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.46/4.77 cnf(i_0_1641, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_419, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)))). 4.46/4.77 cnf(i_0_6074, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.46/4.77 cnf(i_0_3934, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)|~class_Lattices_Olattice(X1))). 4.46/4.77 cnf(i_0_4446, plain, (c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omax(X1),X2),X3)|~class_Orderings_Olinorder(X1))). 4.46/4.77 cnf(i_0_6347, plain, (c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omin(X1),X2),X3)|~class_Orderings_Olinorder(X1))). 4.46/4.77 cnf(i_0_85, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))). 4.46/4.77 cnf(i_0_6809, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))))). 4.46/4.77 cnf(i_0_4471, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))))). 4.46/4.77 cnf(i_0_766, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olists(X1,X2)),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.46/4.77 cnf(i_0_5430, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),X2))))). 4.46/4.77 cnf(i_0_2154, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)|~class_Lattices_Olattice(X1))). 4.46/4.77 cnf(i_0_5003, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3))))). 4.46/4.77 cnf(i_0_3585, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1),X4),X5)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(X5,esk243_5(X5,X4,X3,X2,X1)))))). 4.46/4.77 cnf(i_0_2273, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olistsp(X1,X2)),c_List_Olistsp(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.46/4.77 cnf(i_0_697, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.46/4.77 cnf(i_0_5947, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.46/4.77 cnf(i_0_898, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),X4)),X5))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X4,esk63_5(X5,X4,X3,X2,X1))),X5)))). 4.46/4.77 cnf(i_0_1454, plain, (hAPP(X1,X2)=hAPP(c_Option_Ooption_OSome(X3),X4)|X5=X4|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6,tc_Option_Ooption(X3)),X1),X7),hAPP(c_Option_Ooption_OSome(X3),X5)),X2)!=hAPP(c_Option_Ooption_OSome(X3),X4))). 4.46/4.77 cnf(i_0_1455, plain, (hAPP(X1,X2)=hAPP(c_Option_Ooption_OSome(X3),X4)|X5=X2|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6,tc_Option_Ooption(X3)),X1),X5),hAPP(c_Option_Ooption_OSome(X3),X7)),X2)!=hAPP(c_Option_Ooption_OSome(X3),X4))). 4.46/4.77 cnf(i_0_4038, plain, (hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X1,X2))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.77 cnf(i_0_4459, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(c_COMBK(X1,X2),c_Groups_Ozero__class_Ozero(X1))),X3))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Omonoid__add(X1))). 4.46/4.77 cnf(i_0_5793, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.46/4.77 cnf(i_0_7162, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.46/4.77 cnf(i_0_5942, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.46/4.77 cnf(i_0_5684, plain, (c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(c_Nat_OSuc,X2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5))|~c_Hoare__Mirabelle_Otriple__valid(X1,X2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5)))). 4.46/4.77 cnf(i_0_5286, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk370_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1))))). 4.46/4.77 cnf(i_0_16, plain, (hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X1,X2))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.77 cnf(i_0_1404, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(X2,X4)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|esk93_4(X2,X3,X1,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_7057, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Ofilter(X2,X4),X5)))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))|~class_Orderings_Olinorder(X1))). 4.46/4.77 cnf(i_0_3078, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OField(X1),X2)),hAPP(c_Relation_OField(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.46/4.77 cnf(i_0_351, plain, (hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1,X2,X3),X4),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X3)))). 4.46/4.77 cnf(i_0_7224, plain, (X1=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X3),X4)),hAPP(c_List_Olexn(X2,X5),X1))))). 4.46/4.77 cnf(i_0_7223, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X2)),hAPP(c_List_Olexn(X1,X5),X3))))). 4.46/4.77 cnf(i_0_3232, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(X4,X5)))|~hBOOL(hAPP(X1,esk219_5(X1,X4,X6,X7,X3)))|~hBOOL(hAPP(hAPP(c_member(X7),X5),X6)))). 4.46/4.77 cnf(i_0_3361, plain, (hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X1,X2,X3,X4,X5),X6),X7))|~hBOOL(hAPP(hAPP(X5,X8),X7))|~hBOOL(hAPP(hAPP(X4,X6),X8)))). 4.46/4.77 cnf(i_0_5545, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1))). 4.46/4.77 cnf(i_0_5165, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))))). 4.46/4.77 cnf(i_0_4554, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X4,X3)))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1)),X2),X4)))). 4.46/4.77 cnf(i_0_7080, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))))). 4.46/4.77 cnf(i_0_3415, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3)))). 4.46/4.77 cnf(i_0_152, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3)))). 4.46/4.77 cnf(i_0_6375, plain, (hAPP(c_Set_Oimage(X1,X2,c_Fun_Othe__inv__into(X2,X1,X3,X4)),hAPP(c_Set_Oimage(X2,X1,X4),X3))=X3|~c_Fun_Oinj__on(X2,X1,X4,X3))). 4.46/4.77 cnf(i_0_4075, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)|hBOOL(hAPP(hAPP(c_member(X1),X3),X2)))). 4.46/4.77 cnf(i_0_5370, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)|hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.46/4.77 cnf(i_0_836, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),X5))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5))|~class_Orderings_Olinorder(X2))). 4.46/4.77 cnf(i_0_6297, plain, (hAPP(c_Option_Ooption_OSome(X1),X2)=hAPP(c_Map_Omap__add(X3,X1,X4,X5),X6)|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(X4,X6)|hAPP(X5,X6)!=c_Option_Ooption_ONone(X1))). 4.46/4.77 cnf(i_0_5282, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk370_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 4.46/4.77 cnf(i_0_2162, plain, (c_List_Olist__ex1(X1,X2,X3)|hBOOL(hAPP(X2,esk163_4(X3,X2,X1,X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 4.46/4.77 cnf(i_0_7050, plain, (c_List_Olist__ex1(X1,X2,X3)|hBOOL(hAPP(X2,esk492_4(X3,X2,X1,X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 4.46/4.77 cnf(i_0_690, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk47_3(X2,X3,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Fields_Olinordered__field__inverse__zero(X1))). 4.46/4.77 cnf(i_0_5168, plain, (hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4))|~hBOOL(hAPP(c_List_Olistsp(X1,X3),X4))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),X4)))). 4.46/4.77 cnf(i_0_3333, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))))). 4.46/4.77 cnf(i_0_258, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.46/4.77 cnf(i_0_6722, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk461_3(X2,X3,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Fields_Olinordered__field(X1))). 4.46/4.77 cnf(i_0_5906, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))))). 4.46/4.77 cnf(i_0_5334, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))))). 4.46/4.77 cnf(i_0_689, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk47_3(X2,X3,X1)),c_Groups_Oone__class_Oone(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Fields_Olinordered__field__inverse__zero(X1))). 4.46/4.77 cnf(i_0_5678, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))|~class_Lattices_Oboolean__algebra(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.46/4.77 cnf(i_0_2807, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)))). 4.46/4.77 cnf(i_0_7107, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.46/4.77 cnf(i_0_2957, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X1),esk207_4(X4,X3,X1,X2)),X3)))). 4.46/4.77 cnf(i_0_5517, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2)))). 4.46/4.77 cnf(i_0_1814, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2)))). 4.46/4.77 cnf(i_0_1679, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X1),esk114_4(X4,X3,X2,X1)),X3)))). 4.46/4.77 cnf(i_0_141, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.46/4.77 cnf(i_0_3191, plain, (hAPP(c_Set_Oimage(X1,X2,hAPP(c_COMBK(X2,X1),X3)),X4)=hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4)))). 4.46/4.77 cnf(i_0_4284, plain, (c_List_Oinsert(X1,X2,X3)=hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.46/4.77 cnf(i_0_4877, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_7331, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.77 cnf(i_0_1842, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.77 cnf(i_0_3987, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))|~hBOOL(hAPP(X1,esk272_3(X1,X3,X2))))). 4.46/4.77 cnf(i_0_3454, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4))))). 4.46/4.77 cnf(i_0_175, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.46/4.77 cnf(i_0_2072, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))|~class_Orderings_Olinorder(X1))). 4.46/4.77 cnf(i_0_6580, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))|~class_Orderings_Olinorder(X1))). 4.46/4.77 cnf(i_0_6609, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_1916, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.77 cnf(i_0_4666, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),X3))|~c_Nitpick_Orefl_H(X1,X3))). 4.46/4.77 cnf(i_0_2641, plain, (hBOOL(hAPP(X1,X2))|hAPP(hAPP(c_List_Odrop(X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),c_List_OtakeWhile(X3,X1,X4))),X4)!=c_List_Olist_ONil(X3)|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))))). 4.46/4.77 cnf(i_0_7143, plain, (c_List_Otranspose(X1,X2)=c_List_Olist_ONil(tc_List_Olist(X1))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk504_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))))). 4.46/4.77 cnf(i_0_5289, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.77 cnf(i_0_5549, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)=c_Int_OMin|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.77 cnf(i_0_4208, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~c_Relation_Orefl__on(X1,X3,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X2)),X4)))). 4.46/4.77 cnf(i_0_3139, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~c_Relation_Orefl__on(X1,X3,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),X4)))). 4.46/4.77 cnf(i_0_2014, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~c_Equiv__Relations_Oequiv(X1,X3,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X2)),X4)))). 4.46/4.77 cnf(i_0_2013, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~c_Equiv__Relations_Oequiv(X1,X3,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),X4)))). 4.46/4.77 cnf(i_0_6719, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.46/4.77 cnf(i_0_1520, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2))),X3)=X3|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.46/4.77 cnf(i_0_517, plain, (~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2)))). 4.46/4.77 cnf(i_0_1747, plain, (hAPP(X1,esk119_5(X2,X1,X3,X4,X5))=hAPP(c_Option_Ooption_OSome(X5),X4)|~hBOOL(hAPP(hAPP(c_member(X5),X4),c_Map_Oran(X3,X5,c_Map_Orestrict__map(X3,X5,X1,X2)))))). 4.46/4.77 cnf(i_0_967, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X5),X2)))|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5)))). 4.46/4.77 cnf(i_0_845, plain, (c_List_Olast(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))=X3|X2=c_List_Olist_ONil(X1))). 4.46/4.77 cnf(i_0_2291, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk169_4(X2,X3,X1,X4)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X2),X3)!=c_Groups_Ozero__class_Ozero(X4)|~class_Rings_Ono__zero__divisors(X4)|~class_Rings_Ocomm__semiring__1(X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_5524, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)))|~c_Fun_Oinj__on(X2,X1,X3,hAPP(c_List_Oset(X2),X4))|~hBOOL(hAPP(c_List_Odistinct(X2),X4)))). 4.46/4.77 cnf(i_0_3455, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X4),X2)),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X6),X3))))). 4.46/4.77 cnf(i_0_494, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(X4,X5)))|~hBOOL(hAPP(hAPP(c_member(X2),X5),X3)))). 4.46/4.77 cnf(i_0_2652, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))=X4|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X2)))). 4.46/4.77 cnf(i_0_7364, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))))). 4.46/4.77 cnf(i_0_6879, plain, (hAPP(hAPP(X1,X2),hAPP(X3,X4))=hAPP(X3,X4)|~c_Finite__Set_Ofolding__one__idem(X5,X1,X3)|~hBOOL(hAPP(hAPP(c_member(X5),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))). 4.46/4.77 cnf(i_0_7310, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)=X3|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.77 cnf(i_0_711, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk48_3(X2,X3,X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Complete__Lattice_OInf__class_OInf(X1,X2)))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.46/4.77 cnf(i_0_5007, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk351_3(X2,X3,X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OSup__class_OSup(X1,X3)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.46/4.77 cnf(i_0_6714, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))|~c_Wellfounded_Oacyclic(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_Predicate_Oconversep(X1,X1,X2))))). 4.46/4.77 cnf(i_0_2561, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.46/4.77 cnf(i_0_3154, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1))). 4.46/4.77 cnf(i_0_5262, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk367_4(X2,X3,X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Set_Oimage(X1,X5,X3),X2))))). 4.46/4.77 cnf(i_0_460, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Olinorder__class_Oinsort__insert__key(X2,X1,X3,X4,X5)))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))|~class_Orderings_Olinorder(X1))). 4.46/4.77 cnf(i_0_78, plain, (c_Nitpick_Oless__frac(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_6106, plain, (c_Nitpick_Oless__eq__frac(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_999, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1))). 4.46/4.77 cnf(i_0_744, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.77 cnf(i_0_743, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.77 cnf(i_0_4591, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2)))). 4.46/4.77 cnf(i_0_5526, plain, (hAPP(X1,hAPP(c_Fun_Othe__inv__into(X2,X3,X4,X1),X5))=X5|~c_Fun_Oinj__on(X2,X3,X1,X4)|~hBOOL(hAPP(hAPP(c_member(X3),X5),hAPP(c_Set_Oimage(X2,X3,X1),X4))))). 4.46/4.77 cnf(i_0_956, plain, (hAPP(X1,hAPP(X2,X3))=hAPP(X4,hAPP(X5,X3))|hAPP(c_Fun_Ocomp(X6,X7,X8,X1),X2)!=hAPP(c_Fun_Ocomp(X9,X7,X8,X4),X5))). 4.46/4.77 cnf(i_0_3861, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X1),esk266_4(X4,X3,X1,X2)),X3)))). 4.46/4.77 cnf(i_0_2085, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.46/4.77 cnf(i_0_6207, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2))))). 4.46/4.77 cnf(i_0_4857, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X1),esk337_4(X4,X3,X2,X1)),X3)))). 4.46/4.77 cnf(i_0_1770, plain, (c_Divides_OnegDivAlg(X1,X2)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))))). 4.46/4.77 cnf(i_0_4564, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),X5)=hAPP(hAPP(X6,X5),X4)|~c_Finite__Set_Ofolding(X1,X2,X3,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.46/4.77 cnf(i_0_2079, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,c_Wellfounded_Oacc(X1,X3))))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3)))))). 4.46/4.77 cnf(i_0_3484, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremove1(X1,X2,X3))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.46/4.77 cnf(i_0_3737, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2))))). 4.46/4.77 cnf(i_0_1997, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2))=hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)|~class_Orderings_Olinorder(X1))). 4.46/4.77 cnf(i_0_4424, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2,X3)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4)))))). 4.46/4.77 cnf(i_0_2045, plain, (c_Wellfounded_Owf(X1,X2)|hBOOL(hAPP(hAPP(c_member(X1),esk149_3(X2,X1,X3)),esk147_2(X2,X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),esk147_2(X2,X1))))). 4.46/4.77 cnf(i_0_5351, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=X4|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1))). 4.46/4.77 cnf(i_0_6554, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)=hAPP(hAPP(c_List_Omap(X1,X2),X5),X4)|hAPP(X3,esk455_5(X3,X4,X5,X2,X1))!=hAPP(X5,esk455_5(X3,X4,X5,X2,X1)))). 4.46/4.77 cnf(i_0_6915, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OSigma(X3,X1),X4),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X3),X2)))))). 4.46/4.77 cnf(i_0_4861, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk338_3(X2,X3,X1)),X3))|hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3))))). 4.46/4.77 cnf(i_0_2518, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk190_3(X3,X2,X1)),X2)))). 4.46/4.77 cnf(i_0_253, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.77 cnf(i_0_2966, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X4))))). 4.46/4.77 cnf(i_0_5861, plain, (hAPP(X1,esk402_3(X1,X2,X3))=c_Option_Ooption_ONone(X2)|hBOOL(hAPP(c_Finite__Set_Ofinite(X3),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),c_Map_Odom(X3,X2,X1))))). 4.46/4.77 cnf(i_0_4463, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.46/4.77 cnf(i_0_2851, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(c_COMBK(X1,X2),X4))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3)))). 4.46/4.77 cnf(i_0_2852, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(c_COMBK(X1,X2),X4))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X1),X4),X3)))). 4.46/4.77 cnf(i_0_3675, plain, (c_List_Olast(tc_Nat_Onat,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.46/4.77 cnf(i_0_139, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk16_3(X2,X3,X1)),esk16_3(X2,X3,X1))=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),c_Relation_OId__on(X1,X2))))). 4.46/4.77 cnf(i_0_7472, plain, (epred1_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,X3)))). 4.46/4.77 cnf(i_0_7145, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3))=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3))|~class_Rings_Oring__1(X1))). 4.46/4.77 cnf(i_0_3627, plain, (X1=hAPP(X2,X3)|~hBOOL(hAPP(hAPP(c_member(X4),X3),hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,X4),hAPP(hAPP(c_Set_Oinsert(X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X2))))). 4.46/4.77 cnf(i_0_2134, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),X4))|~hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X5),X4),X2))))). 4.46/4.77 cnf(i_0_3074, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_COMBB(X3,tc_HOL_Obool,X1),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(X3),hAPP(X5,X2)),X4)))). 4.46/4.77 cnf(i_0_341, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)))|~c_Fun_Oinj__on(X1,X2,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.46/4.77 cnf(i_0_3341, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3))=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))|~class_Rings_Oring__1(X1))). 4.46/4.77 cnf(i_0_5958, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2)),X3))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.77 cnf(i_0_6717, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.77 cnf(i_0_6046, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X5,esk420_5(X5,X4,X3,X2,X1)))))). 4.46/4.77 cnf(i_0_4865, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3))=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))|~class_Rings_Oring__1(X1))). 4.46/4.77 cnf(i_0_5850, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|hAPP(c_Set_Oimage(X3,X1,X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X3),X2),X4))))). 4.46/4.77 cnf(i_0_3742, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),hAPP(c_Set_Oimage(X2,X1,X3),X4)),X3)=X4|~c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))). 4.46/4.77 cnf(i_0_6681, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3))=X4|hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))). 4.46/4.77 cnf(i_0_309, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3))=X3|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)!=X2)). 4.46/4.77 cnf(i_0_6635, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))|~class_Fields_Olinordered__field__inverse__zero(X1))). 4.46/4.77 cnf(i_0_2914, plain, (c_List_Osublist(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)),X3)=hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))). 4.46/4.77 cnf(i_0_2735, plain, (c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))=hAPP(hAPP(c_List_Oappend(X1),c_List_Oremove1(X1,X2,X3)),X4)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.46/4.77 cnf(i_0_3428, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.46/4.77 cnf(i_0_6194, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X3))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))|~class_Groups_Omonoid__add(X1))). 4.46/4.77 cnf(i_0_7371, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X3|hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.46/4.77 cnf(i_0_5371, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.46/4.77 cnf(i_0_2793, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_3595, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__idom(X1))). 4.46/4.77 cnf(i_0_1429, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.46/4.77 cnf(i_0_1866, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),c_List_Olinorder__class_Osort__key(X1,X2,X3,X5))=c_List_Olinorder__class_Osort__key(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))|~class_Orderings_Olinorder(X2))). 4.46/4.77 cnf(i_0_2067, plain, (c_Map_Omap__upds(X1,X2,X3,X4,hAPP(hAPP(c_List_Oappend(X2),X5),X6))=c_Map_Omap__upds(X1,X2,X3,X4,X5)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4))). 4.46/4.77 cnf(i_0_6819, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Olinordered__idom(X1))). 4.46/4.77 cnf(i_0_6820, plain, (hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4))=hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X2),X4))|~c_Finite__Set_Ofun__left__comm(X5,X6,X1))). 4.46/4.77 cnf(i_0_4447, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk309_2(X2,X1))))|hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,X2)))). 4.46/4.77 cnf(i_0_2411, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),X2)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber__ring(X1))). 4.46/4.77 cnf(i_0_2496, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk188_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))))). 4.46/4.77 cnf(i_0_4787, plain, (c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X5),X6)=c_Map_Omap__upds(X1,X2,X3,X4,X6)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X6))). 4.46/4.77 cnf(i_0_4937, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X3,esk344_4(X3,X4,X2,X1)))))). 4.46/4.77 cnf(i_0_6021, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X3,esk416_4(X3,X4,X2,X1)))))). 4.46/4.77 cnf(i_0_6502, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.77 cnf(i_0_546, plain, (c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1),X2)|hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk37_2(X1,X2)),X2)))). 4.46/4.77 cnf(i_0_6071, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),X3))|hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_3267, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Big__Operators_Olattice__class_OInf__fin(X2,X1)),c_Big__Operators_Olattice__class_OSup__fin(X2,X1)))|~class_Lattices_Olattice(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.46/4.77 cnf(i_0_5013, plain, (hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Finite__Set_Ocard(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.77 cnf(i_0_4962, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))|~class_Rings_Osemiring__1(X1))). 4.46/4.77 cnf(i_0_5347, plain, (hAPP(hAPP(c_List_Onth(X1),c_List_OtakeWhile(X1,X2,X3)),X4)=hAPP(hAPP(c_List_Onth(X1),X3),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3)))))). 4.46/4.77 cnf(i_0_650, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~class_Rings_Olinordered__semidom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Oone__class_Oone(X3)),X4)))). 4.46/4.77 cnf(i_0_2873, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.77 cnf(i_0_2907, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X1))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))))). 4.46/4.77 cnf(i_0_481, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.46/4.77 cnf(i_0_3562, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.46/4.77 cnf(i_0_3839, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3))|~class_Int_Onumber__ring(X1))). 4.46/4.77 cnf(i_0_410, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~class_Rings_Olinordered__semidom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Oone__class_Oone(X3)),X4)))). 4.46/4.77 cnf(i_0_3877, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),X2)))). 4.46/4.77 cnf(i_0_6354, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.46/4.77 cnf(i_0_6541, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.46/4.77 cnf(i_0_2195, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.77 cnf(i_0_2324, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_fequal),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X3)))))). 4.46/4.77 cnf(i_0_3419, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Otake(X1),X4),X5),hAPP(hAPP(c_List_Otake(X2),X4),X6))|~c_List_Olist__all2(X1,X2,X3,X5,X6))). 4.46/4.77 cnf(i_0_4290, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Odrop(X1),X4),X5),hAPP(hAPP(c_List_Odrop(X2),X4),X6))|~c_List_Olist__all2(X1,X2,X3,X5,X6))). 4.46/4.77 cnf(i_0_5706, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),esk395_4(X1,X4,X2,X3)),esk396_4(X1,X4,X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X2),X4))|~hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))). 4.46/4.77 cnf(i_0_5805, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X4)=c_Divides_Odiv__class_Omod(X1,X2,X4)|~class_Divides_Osemiring__div(X1))). 4.46/4.77 cnf(i_0_7164, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.77 cnf(i_0_3402, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.77 cnf(i_0_3020, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)))). 4.46/4.77 cnf(i_0_2346, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk176_2(X2,X1)),X2))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2)))). 4.46/4.77 cnf(i_0_6448, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))|~class_Int_Onumber__ring(X1))). 4.46/4.77 cnf(i_0_7206, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.46/4.77 cnf(i_0_4384, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X3)=c_Divides_Odiv__class_Omod(X1,X2,X3)|~class_Divides_Osemiring__div(X1))). 4.46/4.77 cnf(i_0_5511, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X2),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_4623, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X2),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_1655, plain, (~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X4)),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))))). 4.46/4.77 cnf(i_0_411, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))|~class_Int_Onumber__ring(X1))). 4.46/4.77 cnf(i_0_5317, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.77 cnf(i_0_6348, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.46/4.77 cnf(i_0_7161, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.46/4.77 cnf(i_0_2237, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.46/4.77 cnf(i_0_6180, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))|~class_Rings_Ocomm__semiring__1(X1))). 4.46/4.77 cnf(i_0_1083, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))|~class_Rings_Osemiring__1(X1))). 4.46/4.77 cnf(i_0_7168, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.46/4.77 cnf(i_0_6493, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.46/4.77 cnf(i_0_304, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.46/4.77 cnf(i_0_4619, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.46/4.77 cnf(i_0_4157, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))|~class_Groups_Omonoid__mult(X1))). 4.46/4.77 cnf(i_0_3101, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))|~class_Lattices_Olattice(X1))). 4.46/4.77 cnf(i_0_5800, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))|~class_Lattices_Olattice(X1))). 4.46/4.77 cnf(i_0_6291, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))|~class_Lattices_Osemilattice__sup(X1))). 4.46/4.77 cnf(i_0_5409, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Rings_Olinordered__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.46/4.77 cnf(i_0_4171, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.46/4.77 cnf(i_0_5288, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Rings_Olinordered__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.46/4.77 cnf(i_0_5841, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X4)=c_Groups_Ozero__class_Ozero(X2)|hAPP(X3,X5)!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Ocomm__semiring__1(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.46/4.77 cnf(i_0_4789, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))|~class_Rings_Ocomm__semiring__1(X1))). 4.46/4.77 cnf(i_0_5120, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))|~class_Groups_Oab__semigroup__add(X1))). 4.46/4.77 cnf(i_0_6745, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Groups_Omonoid__mult(X1))). 4.46/4.77 cnf(i_0_3367, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_Rings_Ocomm__semiring__1(X1))). 4.46/4.77 cnf(i_0_7001, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|c_Wellfounded_Omax__extp(X2,X3,X4,X1)|~hBOOL(hAPP(hAPP(X3,esk489_4(X1,X4,X3,X2)),X5))|~hBOOL(hAPP(hAPP(c_member(X2),X5),X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.46/4.77 cnf(i_0_1791, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X1,X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.77 cnf(i_0_4995, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X1,X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.77 cnf(i_0_3178, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Nat__Transfer_Otsub(X1,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.46/4.77 cnf(i_0_216, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))|~class_Lattices_Osemilattice__inf(X1))). 4.46/4.77 cnf(i_0_3650, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5)|X5=c_Groups_Ozero__class_Ozero(X1)|X3=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)|~class_Fields_Ofield(X1))). 4.46/4.77 cnf(i_0_7463, plain, (epred1_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk532_3(X3,X2,X1)))|~hBOOL(hAPP(X1,esk534_3(X3,X2,X1)))|~hBOOL(hAPP(X1,X3)))). 4.46/4.77 cnf(i_0_7451, plain, (epred1_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X3,X2,X1)),X2))|~hBOOL(hAPP(X1,esk532_3(X3,X2,X1)))|~hBOOL(hAPP(X1,X3)))). 4.46/4.77 cnf(i_0_1967, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X2=X3|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5),X3)))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X6),X2))))). 4.46/4.77 cnf(i_0_3325, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|X2=X3|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X5)))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X6))))). 4.46/4.77 cnf(i_0_5092, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))|~class_Rings_Odivision__ring(X1))). 4.46/4.77 cnf(i_0_2354, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_Groups_Oab__semigroup__mult(X1))). 4.46/4.77 cnf(i_0_4773, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.46/4.77 cnf(i_0_3651, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)|X5=c_Groups_Ozero__class_Ozero(X1)|X3=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X5)!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)|~class_Fields_Ofield(X1))). 4.46/4.77 cnf(i_0_5817, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))). 4.46/4.77 cnf(i_0_4030, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))). 4.46/4.77 cnf(i_0_6333, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))). 4.46/4.77 cnf(i_0_6997, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.46/4.77 cnf(i_0_6392, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))|~c_Nat__Transfer_Onat__set(X2)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2)))). 4.46/4.77 cnf(i_0_384, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_4006, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.46/4.77 cnf(i_0_321, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4)|~class_Divides_Osemiring__div(X1))). 4.46/4.77 cnf(i_0_1427, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3),X4)|~class_Divides_Oring__div(X1))). 4.46/4.77 cnf(i_0_3998, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Wellfounded_Oless__than))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.46/4.77 cnf(i_0_680, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.46/4.77 cnf(i_0_4612, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)))). 4.46/4.77 cnf(i_0_5663, plain, (hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5)=hAPP(X3,X5)|hBOOL(hAPP(hAPP(c_member(X1),X5),c_Map_Odom(X1,X2,X4))))). 4.46/4.77 cnf(i_0_3923, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)|~class_Divides_Osemiring__div(X1))). 4.46/4.77 cnf(i_0_294, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X3))))). 4.46/4.77 cnf(i_0_5104, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X4),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4),X3)|~class_Divides_Osemiring__div(X1))). 4.46/4.77 cnf(i_0_2329, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X4),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)|~class_Divides_Osemiring__div(X1))). 4.46/4.77 cnf(i_0_1223, plain, (hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5)=hAPP(X4,X5)|hBOOL(hAPP(hAPP(c_member(X1),X5),c_Map_Odom(X1,X2,X3))))). 4.46/4.77 cnf(i_0_1594, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.46/4.77 cnf(i_0_2516, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X4)),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.46/4.77 cnf(i_0_795, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.46/4.77 cnf(i_0_3151, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X4),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4),X3)|~class_Divides_Oring__div(X1))). 4.46/4.77 cnf(i_0_4935, plain, (c_Big__Operators_Olinorder__class_OMin(X1,X2)=X3|hBOOL(hAPP(hAPP(c_member(X1),esk343_3(X3,X2,X1)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.77 cnf(i_0_1050, plain, (c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))|~c_Predicate_Oreflp(X1,X2))). 4.46/4.77 cnf(i_0_4059, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),X4)=hAPP(hAPP(c_List_Onth(X1),X2),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.46/4.77 cnf(i_0_5350, plain, (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X3))|~hBOOL(hAPP(hAPP(X4,X6),X5)))). 4.46/4.77 cnf(i_0_1347, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk90_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.46/4.77 cnf(i_0_4537, plain, (c_Big__Operators_Olinorder__class_OMax(X1,X2)=X3|hBOOL(hAPP(hAPP(c_member(X1),esk318_3(X3,X2,X1)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.46/4.77 cnf(i_0_4359, plain, (c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))=hAPP(hAPP(c_List_Oappend(X1),X3),c_List_OtakeWhile(X1,X2,X4))|~hBOOL(hAPP(X2,esk299_4(X4,X2,X3,X1))))). 4.46/4.77 cnf(i_0_3129, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk216_5(X2,X3,X1,X4,X5)),X2))|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Relation_OImage(X1,X5,X3),X2))))). 4.46/4.77 cnf(i_0_6618, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk458_5(X2,X3,X1,X4,X5)),X2))|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Relation_OImage(X1,X5,X3),X2))))). 4.46/4.77 cnf(i_0_1927, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk135_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.46/4.77 cnf(i_0_594, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3))|~class_Lattices_Oboolean__algebra(X1))). 4.46/4.77 cnf(i_0_2076, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3))|~class_Lattices_Oboolean__algebra(X1))). 4.46/4.77 cnf(i_0_395, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2))|~class_Groups_Ogroup__add(X1))). 4.46/4.77 cnf(i_0_4710, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))|~class_Groups_Oab__group__add(X1))). 4.46/4.77 cnf(i_0_7522, plain, (epred2_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk538_3(X3,X2,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.46/4.77 cnf(i_0_2545, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),c_List_Oremove1(X1,X2,X3))=X3|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.46/4.77 cnf(i_0_6773, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3))|~class_Groups_Olinordered__ab__group__add(X1))). 4.46/4.77 cnf(i_0_82, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3))|~class_Groups_Olinordered__ab__group__add(X1))). 4.46/4.77 cnf(i_0_3639, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_2776, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_7510, plain, (epred2_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk536_3(X3,X2,X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_5213, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.49/4.77 cnf(i_0_2672, plain, (c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_1985, plain, (c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_4032, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)))). 4.49/4.77 cnf(i_0_3541, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X2)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3)))). 4.49/4.77 cnf(i_0_3793, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X1),esk260_3(X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_2356, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X1),esk177_3(X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_5705, plain, (hBOOL(hAPP(X1,esk396_4(X1,X2,X3,X4)))|hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X2))|~hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))). 4.49/4.77 cnf(i_0_2090, plain, (c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)))=c_List_OtakeWhile(X1,X2,X3)|hBOOL(hAPP(X2,X4)))). 4.49/4.77 cnf(i_0_2181, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3)))). 4.49/4.77 cnf(i_0_4764, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.49/4.77 cnf(i_0_6440, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.49/4.77 cnf(i_0_1318, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)))). 4.49/4.77 cnf(i_0_2549, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olinorder__class_OMax(X1,X3))=c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_98, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),X5)))|~hBOOL(hAPP(X1,esk11_4(X1,X5,X4,X3)))|~hBOOL(hAPP(X1,esk12_4(X1,X5,X4,X3))))). 4.49/4.77 cnf(i_0_3350, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~class_Int_Onumber__ring(X1))). 4.49/4.77 cnf(i_0_2001, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3),X4),X5),X6)=hAPP(X7,X6)|~c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X5,X4,X7)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 4.49/4.77 cnf(i_0_1403, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(X2,esk93_4(X2,X3,X1,X4))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(X2,X4)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_269, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.49/4.77 cnf(i_0_6120, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)))). 4.49/4.77 cnf(i_0_4028, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.49/4.77 cnf(i_0_601, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))=c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_5133, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))=c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_6460, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_7034, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3)))). 4.49/4.77 cnf(i_0_6971, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)))). 4.49/4.77 cnf(i_0_3478, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.49/4.77 cnf(i_0_1143, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk76_2(X1,X2)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))|~hBOOL(hAPP(X1,X3)))). 4.49/4.77 cnf(i_0_7516, plain, (epred2_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk536_3(X3,X2,X1)))|~hBOOL(hAPP(X1,esk537_3(X3,X2,X1))))). 4.49/4.77 cnf(i_0_7503, plain, (epred2_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk538_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk535_3(X3,X2,X1))))). 4.49/4.77 cnf(i_0_7013, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_787, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.49/4.77 cnf(i_0_7055, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)))). 4.49/4.77 cnf(i_0_1314, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)))). 4.49/4.77 cnf(i_0_5049, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))=c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_369, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.77 cnf(i_0_878, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.49/4.77 cnf(i_0_6270, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.49/4.77 cnf(i_0_5659, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.49/4.77 cnf(i_0_2212, plain, (hBOOL(hAPP(c_Predicate_OPowp(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Set_OPow(X1),X2))))). 4.49/4.77 cnf(i_0_2616, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olinorder__class_OMin(X1,X3))=c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_6753, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.49/4.77 cnf(i_0_6217, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.49/4.77 cnf(i_0_2133, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))). 4.49/4.77 cnf(i_0_6595, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.49/4.77 cnf(i_0_5553, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)))). 4.49/4.77 cnf(i_0_5683, plain, (c_Hoare__Mirabelle_Otriple__valid(X1,X2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5))|~c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(c_Nat_OSuc,X2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5)))). 4.49/4.77 cnf(i_0_4737, plain, (c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))|~c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)))). 4.49/4.77 cnf(i_0_5961, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk408_5(X3,X2,X4,X5,X1))=X5|X5=c_List_Olist_ONil(X1)|hAPP(hAPP(c_List_Oappend(X1),X5),X4)!=hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))). 4.49/4.77 cnf(i_0_6852, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk472_5(X3,X4,X5,X2,X1))=X4|c_List_Olist_ONil(X1)=X4|hAPP(hAPP(c_List_Oappend(X1),X4),X3)!=hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5))). 4.49/4.77 cnf(i_0_5960, plain, (hAPP(hAPP(c_List_Oappend(X1),esk408_5(X2,X3,X4,X5,X1)),X4)=X2|X5=c_List_Olist_ONil(X1)|hAPP(hAPP(c_List_Oappend(X1),X5),X4)!=hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))). 4.49/4.77 cnf(i_0_2544, plain, (hAPP(hAPP(c_List_Onth(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_List_Olast(X1,X2)|c_List_Olist_ONil(X1)=X2)). 4.49/4.77 cnf(i_0_2720, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.77 cnf(i_0_3795, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))|~class_Groups_Omonoid__mult(X1))). 4.49/4.77 cnf(i_0_1981, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))). 4.49/4.77 cnf(i_0_6641, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))). 4.49/4.77 cnf(i_0_6942, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Olinordered__field(X1))). 4.49/4.77 cnf(i_0_6851, plain, (hAPP(hAPP(c_List_Oappend(X1),esk472_5(X2,X3,X4,X5,X1)),X2)=X4|c_List_Olist_ONil(X1)=X3|hAPP(hAPP(c_List_Oappend(X1),X3),X2)!=hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4))). 4.49/4.77 cnf(i_0_2173, plain, (hAPP(X1,X2)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X3),X4,c_Option_Ooption_ONone(X3),X1),hAPP(X5,X6))|hAPP(c_Option_Ooption_OSome(X4),X2)!=hAPP(X5,X6))). 4.49/4.77 cnf(i_0_1562, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X3,X4),X5),X6))=hAPP(c_List_Ofilter(X1,X2),X6)|hBOOL(hAPP(X2,X5))|~class_Orderings_Olinorder(X3))). 4.49/4.77 cnf(i_0_7241, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 4.49/4.77 cnf(i_0_5779, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))). 4.49/4.77 cnf(i_0_5250, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))). 4.49/4.77 cnf(i_0_2623, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))). 4.49/4.77 cnf(i_0_3348, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))). 4.49/4.77 cnf(i_0_6733, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.49/4.77 cnf(i_0_6006, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X4),X5),X6),X7))|~hBOOL(hAPP(hAPP(hAPP(X5,esk414_7(X7,X6,X5,X4,X3,X2,X1)),X6),X7)))). 4.49/4.77 cnf(i_0_5360, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X4),X5),X6),X7))|~hBOOL(hAPP(hAPP(hAPP(X5,esk375_7(X3,X2,X7,X6,X5,X4,X1)),X6),X7)))). 4.49/4.77 cnf(i_0_2781, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk199_3(X1,X2,X3)),X3))|hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3))|~hBOOL(hAPP(X2,X1)))). 4.49/4.77 cnf(i_0_5842, plain, (c_Nat_Osemiring__1__class_Oof__nat__aux(X1,hAPP(hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_Groups_Oone__class_Oone(X1)),X2,c_Groups_Ozero__class_Ozero(X1))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)|~class_Rings_Osemiring__1(X1))). 4.49/4.77 cnf(i_0_2797, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_819, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))). 4.49/4.77 cnf(i_0_4266, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))). 4.49/4.77 cnf(i_0_3063, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_2350, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))|~class_Int_Onumber__ring(X1))). 4.49/4.77 cnf(i_0_4706, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4)))). 4.49/4.77 cnf(i_0_737, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_List_Oset(X3),c_List_Oremove1(X3,X2,X4))))|~hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_List_Oset(X3),X4))))). 4.49/4.77 cnf(i_0_7339, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_1631, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),hAPP(c_List_Oset(X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.49/4.77 cnf(i_0_6090, plain, (c_List_Oremdups(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Oremdups(X1,X3))|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.49/4.77 cnf(i_0_4056, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),X5)))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.77 cnf(i_0_1477, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_4636, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.77 cnf(i_0_3592, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.49/4.77 cnf(i_0_2225, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.49/4.77 cnf(i_0_4206, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))). 4.49/4.77 cnf(i_0_5406, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))). 4.49/4.77 cnf(i_0_3505, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|~class_Int_Onumber__ring(X1))). 4.49/4.77 cnf(i_0_721, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.77 cnf(i_0_3337, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))=hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_2469, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X2,X3)),hAPP(X4,X3))=hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,X1)),X2),X4),X3)|~class_Lattices_Olattice(X1))). 4.49/4.77 cnf(i_0_5577, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_2639, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)=c_List_Olist_ONil(X1)|~hBOOL(hAPP(X2,esk193_3(X3,X2,X1))))). 4.49/4.77 cnf(i_0_632, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X1,X2,X3)),c_List_Olist_Olist__size(X1,X4,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,esk43_4(X4,X2,X3,X1))),hAPP(X4,esk43_4(X4,X2,X3,X1)))))). 4.49/4.77 cnf(i_0_4875, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Fun_Oinj__on(X3,X4,X5,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X3,tc_HOL_Obool)),X2),X6))|~c_Fun_Oinj__on(X3,X4,X5,hAPP(X6,esk339_6(X6,X5,X4,X3,X1,X2))))). 4.49/4.77 cnf(i_0_1893, plain, (hAPP(hAPP(X1,X2),esk129_7(X2,X3,X4,X5,X1,X6,X7))=X3|~c_Finite__Set_Ofun__left__comm(X7,X6,X1)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X6,X1,X5,X4),X3))|~hBOOL(hAPP(hAPP(c_member(X7),X2),X4)))). 4.49/4.77 cnf(i_0_7037, plain, (c_Map_Odom(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),X5))=hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Map_Odom(X1,X2,X3))|c_Option_Ooption_ONone(X2)=X5)). 4.49/4.77 cnf(i_0_3838, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(X2,X3)),hAPP(X4,X3))=hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,X1)),X2),X4),X3)|~class_Groups_Ominus(X1))). 4.49/4.77 cnf(i_0_2909, plain, (hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,X2)),X3),X4),X5)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),hAPP(X3,X5)),hAPP(X4,X5))|~class_Lattices_Olattice(X2))). 4.49/4.77 cnf(i_0_3501, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2)))). 4.49/4.77 cnf(i_0_1508, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)|~c_Nat__Transfer_Ois__nat(X2)|~c_Nat__Transfer_Ois__nat(X1))). 4.49/4.77 cnf(i_0_3483, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremove1(X1,X2,X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.49/4.77 cnf(i_0_5014, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omax(X1),X2),X3)|~class_Orderings_Olinorder(X1))). 4.49/4.77 cnf(i_0_1924, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omin(X1),X2),X3)|~class_Orderings_Olinorder(X1))). 4.49/4.77 cnf(i_0_6792, plain, (hAPP(X1,X2)=hAPP(X3,X2)|~class_HOL_Oequal(X4)|~class_Enum_Oenum(X5)|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X5,X4)),X1),X3)))). 4.49/4.77 cnf(i_0_2495, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk188_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.49/4.77 cnf(i_0_3867, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_2301, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))=hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_1761, plain, (c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))). 4.49/4.77 cnf(i_0_1632, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk111_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X1))))). 4.49/4.77 cnf(i_0_2772, plain, (c_List_Olistrelp(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X6))|~c_List_Olistrelp(X1,X2,X4,X6)|~hBOOL(hAPP(hAPP(X2,X3),X5)))). 4.49/4.77 cnf(i_0_338, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_3824, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_4363, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2)))). 4.49/4.77 cnf(i_0_233, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))|~class_Lattices_Olattice(X1))). 4.49/4.77 cnf(i_0_548, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_7199, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_5215, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_3432, plain, (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4),X5))|hBOOL(hAPP(hAPP(c_member(X1),esk235_5(X5,X4,X3,X2,X1)),X3)))). 4.49/4.77 cnf(i_0_5119, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))))). 4.49/4.77 cnf(i_0_2586, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X1),X5),X2)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5)))). 4.49/4.77 cnf(i_0_3597, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X1),X2)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X1))))). 4.49/4.77 cnf(i_0_3173, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))|~class_Lattices_Osemilattice__inf(X1))). 4.49/4.77 cnf(i_0_4947, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_4801, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_3102, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_5617, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.49/4.77 cnf(i_0_3096, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),X4)),hAPP(X4,X5)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_member(X2),X5),X3)))). 4.49/4.77 cnf(i_0_1949, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(X5,esk138_5(X5,X4,X3,X2,X1)))))). 4.49/4.77 cnf(i_0_5791, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.49/4.77 cnf(i_0_2824, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.49/4.77 cnf(i_0_7321, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.49/4.77 cnf(i_0_292, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_2215, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X4,esk164_5(X5,X4,X3,X2,X1))),X5)))). 4.49/4.77 cnf(i_0_340, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X5)))). 4.49/4.77 cnf(i_0_605, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2))))). 4.49/4.77 cnf(i_0_3762, plain, (X1=c_Big__Operators_Olinorder__class_OMin(X2,X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_member(X2),X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.49/4.77 cnf(i_0_4959, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))|~class_Lattices_Olattice(X1))). 4.49/4.77 cnf(i_0_5160, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_4850, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk335_3(X2,X3,X1)),esk336_3(X2,X3,X1))=X3|c_List_Olist_ONil(X1)=X3|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2))))). 4.49/4.77 cnf(i_0_6628, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2)),c_List_Olex(X1,X4))))). 4.49/4.77 cnf(i_0_672, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4))))). 4.49/4.77 cnf(i_0_5727, plain, (X1=c_Big__Operators_Olattice__class_OSup__fin(X2,X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~class_Lattices_Olattice(X2)|~hBOOL(hAPP(hAPP(c_member(X2),X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.49/4.77 cnf(i_0_4365, plain, (X1=c_Big__Operators_Olinorder__class_OMax(X2,X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_member(X2),X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.49/4.77 cnf(i_0_4768, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,X2)=X3|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.77 cnf(i_0_6387, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2))=hAPP(c_Nat_OSuc,X2)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.49/4.77 cnf(i_0_771, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))|~class_Lattices_Osemilattice__sup(X1))). 4.49/4.77 cnf(i_0_5703, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4))))). 4.49/4.77 cnf(i_0_5704, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X3),esk395_4(X1,X4,X2,X3)),esk396_4(X1,X4,X2,X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X2),X4))|~hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))). 4.49/4.77 cnf(i_0_6429, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.77 cnf(i_0_5202, plain, (X1=X2|hAPP(hAPP(c_List_Onth(X3),X4),X1)!=hAPP(hAPP(c_List_Onth(X3),X4),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)))|~hBOOL(hAPP(c_List_Odistinct(X3),X4)))). 4.49/4.77 cnf(i_0_4661, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(c_COMBK(X2,X1),X3)),X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Finite__Set_Ocard(X1),X4))|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.77 cnf(i_0_4320, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk298_2(X1,X2)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))|~hBOOL(hAPP(X1,X3)))). 4.49/4.77 cnf(i_0_5375, plain, (hAPP(c_Map_Omap__upds(X1,X2,X3,X4,X5),X6)=hAPP(X3,X6)|hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),X4))))). 4.49/4.77 cnf(i_0_983, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(X4,X2)))). 4.49/4.77 cnf(i_0_4943, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.49/4.77 cnf(i_0_7358, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.77 cnf(i_0_422, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2)|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.49/4.77 cnf(i_0_926, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Oplus__class_Oplus(X1)),X3),c_Groups_Ozero__class_Ozero(X1)),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.77 cnf(i_0_7296, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.77 cnf(i_0_296, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk24_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2))))). 4.49/4.77 cnf(i_0_4539, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(c_Set_Oimage(X2,X1,X3),X4))),hAPP(c_Finite__Set_Ocard(X2),X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.77 cnf(i_0_678, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3))))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_3019, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)))). 4.49/4.77 cnf(i_0_6441, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.77 cnf(i_0_5097, plain, (c_Wellfounded_Owf(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk353_2(X2,X1)),hAPP(c_Relation_OImage(X1,X1,X2),esk353_2(X2,X1)))))). 4.49/4.77 cnf(i_0_5296, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)))). 4.49/4.77 cnf(i_0_6069, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Omap(X4,X1),X5),X6),X7)|~c_List_Olist__all2(X4,X2,hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),X4),X3),X5),X6,X7))). 4.49/4.77 cnf(i_0_1748, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk119_5(X2,X3,X1,X4,X5)),X2))|~hBOOL(hAPP(hAPP(c_member(X5),X4),c_Map_Oran(X1,X5,c_Map_Orestrict__map(X1,X5,X3,X2)))))). 4.49/4.77 cnf(i_0_1348, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk90_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)))). 4.49/4.77 cnf(i_0_3368, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.77 cnf(i_0_4097, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1)))). 4.49/4.77 cnf(i_0_3035, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,esk213_4(X2,X3,X1,X4))))|hAPP(c_Nat_OSuc,X2)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X1),X3))). 4.49/4.77 cnf(i_0_6102, plain, (hBOOL(hAPP(c_List_Odistinct(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool)),c_List_Oset(X1)),c_Enum_Osublists(X1,X2))))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.49/4.77 cnf(i_0_563, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))|~class_Orderings_Olinorder(X1))). 4.49/4.77 cnf(i_0_1928, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk135_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)))). 4.49/4.77 cnf(i_0_6556, plain, (hAPP(X1,X2)=hAPP(X3,X2)|hAPP(hAPP(c_List_Omap(X4,X5),X1),X6)!=hAPP(hAPP(c_List_Omap(X4,X5),X3),X6)|~hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X6))))). 4.49/4.77 cnf(i_0_1449, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.77 cnf(i_0_4574, plain, (X1=X2|hAPP(hAPP(c_Product__Type_OSigma(X3,X4),X1),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X3),X5))!=hAPP(hAPP(c_Product__Type_OSigma(X3,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X3),X5))|~hBOOL(hAPP(hAPP(c_member(X4),X6),X5)))). 4.49/4.77 cnf(i_0_7520, plain, (epred2_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk536_3(X3,X2,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_3771, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.49/4.77 cnf(i_0_3144, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X3))=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.49/4.77 cnf(i_0_7523, plain, (epred2_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk538_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.77 cnf(i_0_6698, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Groups_Otimes__class_Otimes(X1)),X2),X3)|~class_Lattices_Oab__semigroup__idem__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_5066, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.49/4.77 cnf(i_0_5748, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.77 cnf(i_0_6916, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.49/4.77 cnf(i_0_1410, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))))). 4.49/4.77 cnf(i_0_5797, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.49/4.77 cnf(i_0_5175, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.49/4.77 cnf(i_0_4333, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.49/4.77 cnf(i_0_1283, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.77 cnf(i_0_6807, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.49/4.77 cnf(i_0_3842, plain, (hAPP(X1,X2)=c_Groups_Ozero__class_Ozero(X3)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X1),X5)!=c_Groups_Ozero__class_Ozero(X3)|~class_Groups_Oordered__ab__group__add(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(X1,esk264_5(X2,X1,X5,X4,X3))))|~hBOOL(hAPP(hAPP(c_member(X4),X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.49/4.77 cnf(i_0_1100, plain, (c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),X2))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2))|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.77 cnf(i_0_2275, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))|hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.49/4.77 cnf(i_0_2322, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X3,X3,hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X3),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot)),c_fequal)),X2),X1)))). 4.49/4.77 cnf(i_0_3953, plain, (c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),X2))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2))|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.77 cnf(i_0_4098, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))))). 4.49/4.77 cnf(i_0_4101, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))))). 4.49/4.77 cnf(i_0_4100, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))))). 4.49/4.77 cnf(i_0_1567, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X1),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))=c_List_Oupto(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.49/4.77 cnf(i_0_4334, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.49/4.77 cnf(i_0_3902, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5))))). 4.49/4.77 cnf(i_0_4544, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.49/4.77 cnf(i_0_89, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))|~class_Orderings_Olinorder(X1))). 4.49/4.77 cnf(i_0_6720, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.49/4.77 cnf(i_0_4099, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))))). 4.49/4.77 cnf(i_0_4886, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))))). 4.49/4.77 cnf(i_0_4885, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))))). 4.49/4.77 cnf(i_0_4884, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))))). 4.49/4.77 cnf(i_0_3223, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))),c_Divides_Odiv__class_Omod(X1,X3,X2))=X3|~class_Divides_Osemiring__div(X1))). 4.49/4.77 cnf(i_0_1121, plain, (hAPP(hAPP(X1,X2),hAPP(X3,X4))=hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))|c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X4|~c_Finite__Set_Ofolding__one__idem(X5,X1,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))). 4.49/4.77 cnf(i_0_94, plain, (hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3))=hAPP(hAPP(c_List_Onth(X1),X3),X2)|c_List_Olist_ONil(X1)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.49/4.77 cnf(i_0_2574, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X4),X3))|~class_Orderings_Oord(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4)))). 4.49/4.77 cnf(i_0_413, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3))=hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.49/4.77 cnf(i_0_262, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),X3))=X2|~class_Divides_Osemiring__div(X1))). 4.49/4.77 cnf(i_0_4887, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))))). 4.49/4.77 cnf(i_0_1637, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_4198, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_1639, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_4954, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),X3)),c_Divides_Odiv__class_Omod(X1,X2,X3))=X2|~class_Divides_Osemiring__div(X1))). 4.49/4.77 cnf(i_0_3825, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3))=hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.49/4.77 cnf(i_0_3108, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3))=hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.49/4.77 cnf(i_0_5536, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3))=hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.49/4.77 cnf(i_0_3266, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.49/4.77 cnf(i_0_6277, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Olist_OCons(X1),X3),hAPP(c_List_Ofilter(X1,X2),X4))|~hBOOL(hAPP(X2,X3)))). 4.49/4.77 cnf(i_0_1638, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_4196, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_4197, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_1640, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_2128, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1)). 4.49/4.77 cnf(i_0_7435, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.49/4.77 cnf(i_0_6880, plain, (hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4))=X3|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~c_Finite__Set_Ofolding__one(X2,X5,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.77 cnf(i_0_221, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),X2)|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.77 cnf(i_0_4195, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_6212, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk430_7(X2,X3,X4,X5,X6,X7,X1)),X5))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X7,tc_fun(X6,tc_HOL_Obool))),X5),X4),X3),X2)))). 4.49/4.77 cnf(i_0_6910, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk477_7(X2,X3,X4,X5,X6,X7,X1)),X5))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X7,tc_fun(X6,tc_HOL_Obool))),X5),X4),X3),X2)))). 4.49/4.77 cnf(i_0_1074, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.77 cnf(i_0_5798, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3))=hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.49/4.77 cnf(i_0_2856, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3))=hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.49/4.77 cnf(i_0_426, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),X3)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber(X1))). 4.49/4.77 cnf(i_0_7488, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X2,X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk532_3(X3,X1,X2)))|~hBOOL(hAPP(X2,esk534_3(X3,X1,X2))))). 4.49/4.77 cnf(i_0_7476, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X2,X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X3,X1,X2)),X1))|~hBOOL(hAPP(X2,esk532_3(X3,X1,X2))))). 4.49/4.77 cnf(i_0_2115, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))|~hBOOL(hAPP(hAPP(X1,esk155_3(X2,X1,X3)),esk156_3(X2,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_2289, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(X1),X3))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.49/4.77 cnf(i_0_355, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))|~hBOOL(hAPP(hAPP(X1,esk27_3(X2,X1,X3)),esk28_3(X2,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.49/4.77 cnf(i_0_7312, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X2,c_Option_Ooption_ONone(X1),X3),hAPP(X4,X5))=c_Option_Ooption_ONone(X1)|hAPP(c_Option_Ooption_OSome(X2),X6)!=hAPP(X4,X5)|c_Option_Ooption_ONone(X1)!=hAPP(X3,X6))). 4.49/4.77 cnf(i_0_4540, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ORange(X3,X1),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X5),X2)),X4)))). 4.49/4.77 cnf(i_0_319, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2)),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(X3,X2)))). 4.49/4.77 cnf(i_0_884, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3)))). 4.49/4.77 cnf(i_0_885, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X2)),X3)))). 4.49/4.77 cnf(i_0_323, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ODomain(X1,X3),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),X5)),X4)))). 4.49/4.77 cnf(i_0_3606, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Oone__class_Oone(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))|~class_Int_Onumber__ring(X1))). 4.49/4.77 cnf(i_0_445, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Oone__class_Oone(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))|~class_Int_Onumber__ring(X1))). 4.49/4.77 cnf(i_0_3190, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))|~class_Orderings_Olinorder(X1))). 4.49/4.77 cnf(i_0_318, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2)),X3)=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(X3,X2)))). 4.49/4.77 cnf(i_0_3957, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.49/4.77 cnf(i_0_6236, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),X5)|c_Option_Ooption_ONone(X2)!=hAPP(X3,X4))). 4.49/4.77 cnf(i_0_2298, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))=c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3),X4)|~class_Orderings_Olinorder(X1))). 4.49/4.77 cnf(i_0_6050, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,esk421_5(X3,X4,X5,X2,X1))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3))))). 4.49/4.77 cnf(i_0_3831, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_1583, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))|~class_Orderings_Oorder(X2)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBS(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Oord__class_Oless__eq(X2)),X3)),X4))))). 4.49/4.77 cnf(i_0_303, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X4))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))|~class_Orderings_Olinorder(X1))). 4.49/4.77 cnf(i_0_3179, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))). 4.49/4.77 cnf(i_0_6983, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2,X1),tc_HOL_Obool)))))). 4.49/4.77 cnf(i_0_1020, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_6568, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X4))=c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),X3)|~class_Orderings_Olinorder(X1))). 4.49/4.77 cnf(i_0_1523, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.49/4.77 cnf(i_0_5174, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),esk359_2(X3,X1)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),X3)))). 4.49/4.77 cnf(i_0_3396, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X1),c_Fun_Oid(X1)),hAPP(c_Set_Oimage(X2,X1,X3),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)|~c_Fun_Oinj__on(X2,X1,X3,X4)|~class_Groups_Ocomm__monoid__mult(X1))). 4.49/4.77 cnf(i_0_7507, plain, (epred2_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk536_3(X3,X2,X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk538_3(X3,X2,X1))))). 4.49/4.77 cnf(i_0_6707, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.77 cnf(i_0_6838, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1)))). 4.49/4.77 cnf(i_0_7329, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.77 cnf(i_0_6674, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_Fun_Oid(X1)),hAPP(c_Set_Oimage(X2,X1,X3),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)|~c_Fun_Oinj__on(X2,X1,X3,X4)|~class_Groups_Ocomm__monoid__add(X1))). 4.49/4.77 cnf(i_0_4849, plain, (c_List_Olist_ONil(X1)=X2|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk336_3(X3,X2,X1)),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3))))). 4.49/4.77 cnf(i_0_5708, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk396_4(X2,X3,X4,X1)))|hBOOL(hAPP(X2,X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.77 cnf(i_0_1267, plain, (hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4))=hAPP(X5,hAPP(c_Product__Type_Ofst(X2,X3),X4))|hAPP(c_Product__Type_Omap__pair(X2,X6,X3,X3,X1,c_Fun_Oid(X3)),X4)!=hAPP(c_Product__Type_Omap__pair(X2,X6,X3,X3,X5,c_Fun_Oid(X3)),X4))). 4.49/4.77 cnf(i_0_2267, plain, (c_Random_Oselect__weight(X1,hAPP(hAPP(c_List_Omap(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,X1)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X2))=c_Random_Oselect(X1,X2)|X2=c_List_Olist_ONil(X1))). 4.49/4.77 cnf(i_0_6123, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)))). 4.49/4.77 cnf(i_0_1072, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1)))). 4.49/4.77 cnf(i_0_5519, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.49/4.77 cnf(i_0_3204, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_6857, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X2))|~class_Groups_Oordered__ab__group__add(X1))). 4.49/4.77 cnf(i_0_6131, plain, (hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4))=hAPP(X5,hAPP(c_Product__Type_Osnd(X2,X3),X4))|hAPP(c_Product__Type_Omap__pair(X2,X2,X3,X6,c_Fun_Oid(X2),X1),X4)!=hAPP(c_Product__Type_Omap__pair(X2,X2,X3,X6,c_Fun_Oid(X2),X5),X4))). 4.49/4.77 cnf(i_0_4213, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))))). 4.49/4.77 cnf(i_0_4214, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))))). 4.49/4.77 cnf(i_0_4621, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)))). 4.49/4.77 cnf(i_0_2059, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_3766, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin)))). 4.49/4.77 cnf(i_0_3875, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin)))). 4.49/4.77 cnf(i_0_1740, plain, (hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=X4|hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=hAPP(c_List_Orev(X1),X4))). 4.49/4.77 cnf(i_0_4776, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(X1)),c_Option_Ooption_ONone(X1)),hAPP(hAPP(c_List_Omap(X1,tc_Option_Ooption(X1)),c_Option_Ooption_OSome(X1)),c_Enum_Oenum__class_Oenum(X1)))=c_Enum_Oenum__class_Oenum(tc_Option_Ooption(X1))|~class_Enum_Oenum(X1))). 4.49/4.77 cnf(i_0_4215, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))))). 4.49/4.77 cnf(i_0_4212, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))))). 4.49/4.77 cnf(i_0_2063, plain, (c_Hoare__Mirabelle_Otriple__valid(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),esk151_3(X2,X4,X1)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4)))). 4.49/4.77 cnf(i_0_5458, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_4878, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_186, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.77 cnf(i_0_5356, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.77 cnf(i_0_7025, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.77 cnf(i_0_2489, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X4),X3)|c_Divides_Odiv__class_Omod(X1,X2,X3)!=c_Divides_Odiv__class_Omod(X1,X4,X3)|~class_Divides_Oring__div(X1))). 4.49/4.77 cnf(i_0_5456, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_5457, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_5455, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_1532, plain, (c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X2,X3)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X3)|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~class_Orderings_Olinorder(X1))). 4.49/4.77 cnf(i_0_7330, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.77 cnf(i_0_5333, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.49/4.77 cnf(i_0_3936, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.77 cnf(i_0_3285, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.77 cnf(i_0_3830, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1))). 4.49/4.77 cnf(i_0_4602, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X5))))). 4.49/4.77 cnf(i_0_4601, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X5),X3))))). 4.49/4.77 cnf(i_0_6527, plain, (hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk452_2(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_List_Oset(tc_Nat_Onat),X1))))). 4.49/4.77 cnf(i_0_6610, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.77 cnf(i_0_1915, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.77 cnf(i_0_3205, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1)))). 4.49/4.77 cnf(i_0_6076, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2)))). 4.49/4.77 cnf(i_0_3161, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))=X2|~class_Int_Onumber__ring(X1))). 4.49/4.77 cnf(i_0_5801, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X5),hAPP(hAPP(c_List_Oappend(X2),X6),X7))|~c_List_Olist__all2(X1,X2,X3,X5,X7)|~c_List_Olist__all2(X1,X2,X3,X4,X6))). 4.49/4.77 cnf(i_0_1292, plain, (hAPP(X1,esk87_7(X2,X3,X4,X1,X5,X6,X7))=hAPP(c_Option_Ooption_OSome(X6),X2)|hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X6),X7,c_Option_Ooption_ONone(X6),X1),hAPP(X4,X3))!=hAPP(c_Option_Ooption_OSome(X6),X2))). 4.49/4.77 cnf(i_0_638, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(X1,X2)|esk45_3(X1,X3,X4)=X2|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X1),X3)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X4),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))). 4.49/4.77 cnf(i_0_2760, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)=X2|~class_Int_Onumber__ring(X1))). 4.49/4.77 cnf(i_0_438, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),X3)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.49/4.77 cnf(i_0_6195, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,X2),X3),X4)=hAPP(X5,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))|~c_Finite__Set_Ofolding__one__idem(X1,X2,X5)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.77 cnf(i_0_7449, plain, (epred1_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X3,X2,X1)))|~hBOOL(hAPP(X1,esk532_3(X3,X2,X1)))|~hBOOL(hAPP(X1,X3)))). 4.49/4.77 cnf(i_0_7458, plain, (epred1_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,esk534_3(X3,X2,X1)))|~hBOOL(hAPP(X1,X3)))). 4.49/4.77 cnf(i_0_270, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X2,esk23_3(X2,X3,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_2260, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X2,esk167_3(X2,X3,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_3810, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2)))). 4.49/4.77 cnf(i_0_4689, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2)). 4.49/4.77 cnf(i_0_7222, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Code__Numeral_Onat__of,X1))))). 4.49/4.77 cnf(i_0_7178, plain, (X1=X2|X3=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X4),X2)),hAPP(hAPP(c_List_Olist_OCons(X5),X3),X1))),c_List_Olistrel1(X5,X6))))). 4.49/4.77 cnf(i_0_1053, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Otake(X1),X2),X3))=hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.49/4.77 cnf(i_0_5087, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),X5)))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))|~class_Orderings_Olinorder(X1))). 4.49/4.77 cnf(i_0_3242, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk222_3(X3,X2,X1)),X2)))). 4.49/4.77 cnf(i_0_4925, plain, (X1=hAPP(X2,X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))|~c_Finite__Set_Ofolding__one(X4,X5,X2)|~hBOOL(hAPP(hAPP(c_member(X4),X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))). 4.49/4.77 cnf(i_0_1566, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(X1),X2))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X1)))). 4.49/4.77 cnf(i_0_846, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X3|c_List_Olast(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))=c_List_Olast(X1,X2)|X2=c_List_Olist_ONil(X1))). 4.49/4.77 cnf(i_0_7073, plain, (hAPP(X1,esk496_4(X2,X1,X3,X4))=X2|~c_Fun_Oinj__on(X4,X3,X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_Set_Oimage(X4,X3,X1),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))))). 4.49/4.77 cnf(i_0_1385, plain, (X1=X2|~c_Relation_Osingle__valued(X3,X4,X5)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X2)),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X1)),X5)))). 4.49/4.77 cnf(i_0_875, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk57_5(X2,X3,X4,X5,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X5)),X4),hAPP(hAPP(c_Product__Type_OSigma(X1,X5),X3),X2))))). 4.49/4.77 cnf(i_0_5837, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2),X3)=c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_214, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2),X3)=c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_1476, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_1081, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist__update(X1,X3),X4),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.49/4.77 cnf(i_0_6038, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_4054, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk274_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X2),X4))))). 4.49/4.77 cnf(i_0_6497, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(c_Option_Ooption_OSome(X4),X5)!=hAPP(hAPP(c_Map_Omap__of(X1,X4),hAPP(hAPP(c_List_Ozip(X1,X4),X3),X6)),X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X6)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))). 4.49/4.77 cnf(i_0_3495, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.49/4.77 cnf(i_0_6144, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.49/4.77 cnf(i_0_3849, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X5),X2)))|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.49/4.77 cnf(i_0_4982, plain, (hAPP(hAPP(X1,X2),X3)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4,X5,X6),X2),X7),X3)|~c_Big__Operators_Ocomm__monoid__big(X4,X5,X6,X7,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)))). 4.49/4.77 cnf(i_0_146, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3),X4),X5),X6)=hAPP(hAPP(X7,X4),X6)|~c_Finite__Set_Ofolding__image(X1,X2,X3,X5,X7)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 4.49/4.77 cnf(i_0_6873, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X6),X7))|~c_List_Olist__all2(X1,X2,X3,X5,X7)|~hBOOL(hAPP(hAPP(X3,X4),X6)))). 4.49/4.77 cnf(i_0_3079, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2)),X3)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Fields_Ofield__inverse__zero(X1))). 4.49/4.77 cnf(i_0_6367, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.49/4.77 cnf(i_0_1379, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__ring__strict(X1))). 4.49/4.77 cnf(i_0_891, plain, (c_List_OtakeWhile(X1,X2,X3)=hAPP(hAPP(c_List_Otake(X1),X4),X3)|hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),X4)))|~hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),esk62_4(X2,X3,X1,X4)))))). 4.49/4.77 cnf(i_0_5267, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(X3,esk368_5(X3,X4,X5,X2,X1))))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X1),X4),X3))))). 4.49/4.77 cnf(i_0_5470, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk377_5(X3,X2,X4,X5,X1))),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X1),X4),X2)),X3)))). 4.49/4.77 cnf(i_0_5278, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X1)))). 4.49/4.77 cnf(i_0_6262, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))|~class_Groups_Oordered__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.49/4.77 cnf(i_0_2598, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.77 cnf(i_0_457, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))|~class_Groups_Oordered__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.77 cnf(i_0_4089, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.49/4.77 cnf(i_0_6844, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))))). 4.49/4.77 cnf(i_0_4749, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))))). 4.49/4.77 cnf(i_0_4477, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X3))=hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2),X3)|~class_Groups_Omonoid__add(X1))). 4.49/4.77 cnf(i_0_3344, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.49/4.77 cnf(i_0_6825, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.49/4.77 cnf(i_0_6934, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.49/4.77 cnf(i_0_6147, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.49/4.77 cnf(i_0_7269, plain, (hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))=c_Divides_Odivmod__int(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.77 cnf(i_0_64, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk8_4(X3,X4,X2,X1)),esk7_4(X3,X4,X2,X1))=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),X4),hAPP(c_Relation_Oconverse(X2,X1),X3))))). 4.49/4.77 cnf(i_0_6051, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk421_5(X2,X3,X1,X4,X5)),X3))|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X3),X2))))). 4.49/4.77 cnf(i_0_7314, plain, (hAPP(X1,esk519_6(X2,X3,X1,X4,X5,X6))=c_Option_Ooption_ONone(X5)|c_Option_Ooption_ONone(X6)=hAPP(X3,X2)|hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X5),X6,c_Option_Ooption_ONone(X5),X1),hAPP(X3,X2))!=c_Option_Ooption_ONone(X5))). 4.49/4.77 cnf(i_0_4345, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X4))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_2410, plain, (hBOOL(hAPP(hAPP(hAPP(X1,X2),X3),X4))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X6,tc_fun(X7,tc_HOL_Obool))),X8),X1),X3),X4))|~hBOOL(hAPP(hAPP(c_member(X5),X2),X8)))). 4.49/4.77 cnf(i_0_2038, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X5)|hAPP(X3,esk146_5(X3,X4,X5,X1,X2))!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.77 cnf(i_0_6491, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X5)|hAPP(X3,esk447_5(X3,X4,X5,X1,X2))!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.77 cnf(i_0_2402, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X5)|hAPP(X3,esk181_5(X3,X4,X5,X1,X2))!=c_Groups_Oone__class_Oone(X2)|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.77 cnf(i_0_5486, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X5)|hAPP(X3,esk380_5(X3,X4,X5,X1,X2))!=c_Groups_Oone__class_Oone(X2)|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.77 cnf(i_0_7447, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X2)))). 4.49/4.77 cnf(i_0_4352, plain, (c_List_Olist__ex1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~c_List_Olist__all(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X3))),X4)|~hBOOL(hAPP(X2,X3)))). 4.49/4.77 cnf(i_0_2884, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.77 cnf(i_0_1643, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_6211, plain, (hBOOL(hAPP(hAPP(hAPP(X1,esk430_7(X2,X3,X1,X4,X5,X6,X7)),X3),X2))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X6,tc_fun(X5,tc_HOL_Obool))),X4),X1),X3),X2)))). 4.49/4.77 cnf(i_0_6909, plain, (hBOOL(hAPP(hAPP(hAPP(X1,esk477_7(X2,X3,X1,X4,X5,X6,X7)),X3),X2))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X6,tc_fun(X5,tc_HOL_Obool))),X4),X1),X3),X2)))). 4.49/4.77 cnf(i_0_1407, plain, (hAPP(X1,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=esk92_3(X1,X3,X4)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X1),X3)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X4),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))). 4.49/4.77 cnf(i_0_5973, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1)))). 4.49/4.77 cnf(i_0_6883, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(c_List_Onth(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)|~class_Groups_Ocomm__monoid__add(X1))). 4.49/4.77 cnf(i_0_932, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X1),X2),c_List_Oupto(X3,X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X3,X4))|~class_Groups_Ocomm__monoid__add(X1))). 4.49/4.77 cnf(i_0_7343, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1)))). 4.49/4.77 cnf(i_0_5268, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk368_5(X2,X3,X1,X4,X5)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X5)|~class_Orderings_Olinorder(X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5),X3),X2))))). 4.49/4.77 cnf(i_0_5469, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk377_5(X2,X3,X4,X1,X5)),X4))|~class_Complete__Lattice_Ocomplete__lattice(X5)|~class_Orderings_Olinorder(X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X5),X4),X3)),X2)))). 4.49/4.77 cnf(i_0_900, plain, (X1=X2|hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),hAPP(c_Nat_OSuc,X4))!=hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),hAPP(c_Nat_OSuc,X4))|~class_Rings_Olinordered__semidom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),X1)))). 4.49/4.77 cnf(i_0_6233, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3))|esk433_3(X3,X2,X1)!=esk432_3(X3,X2,X1))). 4.49/4.77 cnf(i_0_1570, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_HOL_Obool,X1),X2),c_Option_Ooption_OSome(X1))))|hBOOL(hAPP(X2,c_Option_Ooption_ONone(X1)))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X1)),X2)))). 4.49/4.77 cnf(i_0_6695, plain, (c_Relation_Ototal__on(X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))|~c_Relation_Ototal__on(X1,X2,X3))). 4.49/4.77 cnf(i_0_2408, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)=hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.49/4.77 cnf(i_0_5391, plain, (hAPP(c_Set_Oimage(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5)),X6)=hAPP(c_Set_Oimage(X1,X2,X3),X6)|hBOOL(hAPP(hAPP(c_member(X1),X4),X6)))). 4.49/4.77 cnf(i_0_1557, plain, (hAPP(c_Random_Opick(X1,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X1)),X2),X3)),X4)=hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X4),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X1),X2))))). 4.49/4.77 cnf(i_0_352, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))|~hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1,X2,X5),X3),X4)))). 4.49/4.77 cnf(i_0_3598, plain, (hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5))|hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,X3,X4),X5)))). 4.49/4.77 cnf(i_0_623, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)=c_List_Olist_ONil(X1)|~hBOOL(hAPP(X2,hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)))))). 4.49/4.77 cnf(i_0_7492, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X2,X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk532_3(X3,X1,X2)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.77 cnf(i_0_6970, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X4,X5)))|~hBOOL(hAPP(hAPP(c_member(X2),X5),X3)))). 4.49/4.77 cnf(i_0_335, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_OImage(X1,X2,X5),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))))). 4.49/4.77 cnf(i_0_7496, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X2,X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X3,X1,X2)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_1293, plain, (hAPP(c_Option_Ooption_OSome(X1),esk87_7(X2,X3,X4,X5,X6,X7,X1))=hAPP(X4,X3)|hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X7),X1,c_Option_Ooption_ONone(X7),X5),hAPP(X4,X3))!=hAPP(c_Option_Ooption_OSome(X7),X2))). 4.49/4.77 cnf(i_0_465, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X1),X2)),hAPP(c_Relation_ORange(X1,X1),X3))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~c_Wellfounded_Owf(X1,X3)|~c_Wellfounded_Owf(X1,X2))). 4.49/4.77 cnf(i_0_163, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),hAPP(c_Relation_Oconverse(X1,X2),X5))))). 4.49/4.77 cnf(i_0_5056, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1))). 4.49/4.77 cnf(i_0_7074, plain, (esk496_4(hAPP(X1,X2),X1,X3,X4)=X2|~c_Fun_Oinj__on(X4,X3,X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))). 4.49/4.77 cnf(i_0_668, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),hAPP(c_List_Oset(tc_Nat_Onat),X2))))). 4.49/4.77 cnf(i_0_7301, plain, (hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X3))),X4)=hAPP(c_List_Ofilter(X1,X2),X4)|hBOOL(hAPP(X2,X3)))). 4.49/4.77 cnf(i_0_6547, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)),X5)=hAPP(X3,hAPP(hAPP(c_List_Onth(X2),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))))). 4.49/4.77 cnf(i_0_4256, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)|~hBOOL(hAPP(hAPP(X3,hAPP(hAPP(c_List_Onth(X1),X4),esk293_5(X5,X4,X3,X2,X1))),hAPP(hAPP(c_List_Onth(X2),X5),esk293_5(X5,X4,X3,X2,X1)))))). 4.49/4.77 cnf(i_0_5554, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)|~hBOOL(hAPP(hAPP(X3,hAPP(hAPP(c_List_Onth(X1),X4),esk384_5(X3,X5,X2,X4,X1))),hAPP(hAPP(c_List_Onth(X2),X5),esk384_5(X3,X5,X2,X4,X1)))))). 4.49/4.77 cnf(i_0_2638, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X1,X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_1014, plain, (hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.77 cnf(i_0_5640, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,X3))))). 4.49/4.77 cnf(i_0_1708, plain, (hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),esk116_3(X1,X3,X2)),hAPP(hAPP(c_Set_Oinsert(X2),esk115_3(X1,X3,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(X1,X3)))). 4.49/4.77 cnf(i_0_2734, plain, (c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))=hAPP(hAPP(c_List_Oappend(X1),X3),c_List_Oremove1(X1,X2,X4))|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.49/4.77 cnf(i_0_7266, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk516_2(X1,X2)),X2))|hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))))). 4.49/4.77 cnf(i_0_4102, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_4889, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_4103, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_4029, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.49/4.77 cnf(i_0_2789, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~c_Fun_Oinj__on(X1,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X5),X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3))))). 4.49/4.77 cnf(i_0_2846, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.49/4.77 cnf(i_0_6385, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.49/4.77 cnf(i_0_4888, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.49/4.77 cnf(i_0_5761, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Int_Oring__1__class_OInts(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))))). 4.49/4.77 cnf(i_0_6925, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Rings_Osemiring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Nat_Osemiring__1__class_ONats(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Nat_Osemiring__1__class_ONats(X1))))). 4.49/4.77 cnf(i_0_6968, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Int_Oring__1__class_OInts(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))))). 4.49/4.77 cnf(i_0_5610, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Otl(X1),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),hAPP(c_List_Ohd(X1),X2)),c_List_Olist_ONil(X1)))=hAPP(c_List_Orotate1(X1),X2)|X2=c_List_Olist_ONil(X1))). 4.49/4.77 cnf(i_0_3829, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.49/4.77 cnf(i_0_4350, plain, (c_List_Olist__ex1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~c_List_Olist__ex1(X1,X2,X4)|~c_List_Olist__all(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X3))),X4))). 4.49/4.77 cnf(i_0_7246, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X5),X2))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X5),X2)|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5)))). 4.49/4.77 cnf(i_0_3004, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2)). 4.49/4.77 cnf(i_0_1977, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Rings_Osemiring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Nat_Osemiring__1__class_ONats(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Nat_Osemiring__1__class_ONats(X1))))). 4.49/4.77 cnf(i_0_2857, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Int_Oring__1__class_OInts(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))))). 4.49/4.77 cnf(i_0_1636, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_1635, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.49/4.77 cnf(i_0_7323, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),X2)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1)). 4.49/4.77 cnf(i_0_1817, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X5),X2))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X5),X2)|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5)))). 4.49/4.77 cnf(i_0_2921, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))))). 4.49/4.77 cnf(i_0_4883, plain, (hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)))). 4.49/4.77 cnf(i_0_6462, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(c_List_Oset(X2),X4))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_List_Odistinct(X2),X4)))). 4.49/4.77 cnf(i_0_5179, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)))). 4.49/4.77 cnf(i_0_4193, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.49/4.77 cnf(i_0_4194, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_2149, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk161_3(X3,X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2))). 4.49/4.77 cnf(i_0_941, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk67_4(hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),X1,X3,X2)),hAPP(c_List_Oset(X1),X3)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.49/4.77 cnf(i_0_5566, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4)))))). 4.49/4.77 cnf(i_0_4092, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4))|~class_Divides_Osemiring__div(X1))). 4.49/4.77 cnf(i_0_4464, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X1,hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Com_Ocom,c_Com_Ocom_OBODY),X2)))|~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),X1),hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Com_Ocom,c_Com_Ocom_OBODY),X2))),hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,c_Option_Othe(tc_Com_Ocom)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom),c_Com_Obody),X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),X2)))). 4.49/4.77 cnf(i_0_4069, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Int_Onat)),X1)=X1|~c_Nat__Transfer_Onat__set(X1))). 4.49/4.77 cnf(i_0_7370, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X2))=c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)))). 4.49/4.77 cnf(i_0_1130, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X2),c_Product__Type_Osnd(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))=X4|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))). 4.49/4.77 cnf(i_0_6734, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3)|~class_Divides_Osemiring__div(X1))). 4.49/4.77 cnf(i_0_3403, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),X4)=c_Groups_Oone__class_Oone(X1)|hAPP(X3,esk233_4(X3,X4,X2,X1))!=c_Groups_Oone__class_Oone(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.77 cnf(i_0_1445, plain, (c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),X4)|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool)),X4),c_List_Oset(X1))))). 4.49/4.77 cnf(i_0_4221, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.49/4.77 cnf(i_0_6781, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X2)))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X2))))))). 4.49/4.77 cnf(i_0_971, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))=X2|c_Fun_Oinj__on(X1,X3,X4,c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk70_4(X4,X3,X1,X2)),X2)))). 4.49/4.77 cnf(i_0_5270, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.49/4.77 cnf(i_0_1129, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))=X3|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))). 4.49/4.77 cnf(i_0_6068, plain, (c_List_Olist__all2(X1,X2,hAPP(hAPP(c_COMBB(X3,tc_fun(X2,tc_HOL_Obool),X1),X4),X5),X6,X7)|~c_List_Olist__all2(X3,X2,X4,hAPP(hAPP(c_List_Omap(X1,X3),X5),X6),X7))). 4.49/4.77 cnf(i_0_3612, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X4,X5))=hAPP(X4,X5)|~c_Finite__Set_Ofolding__image__simple__idem(X6,X7,X1,X8,X2,X4)|~hBOOL(hAPP(hAPP(c_member(X7),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X5)))). 4.49/4.77 cnf(i_0_2103, plain, (hAPP(c_Finite__Set_Ocard(tc_sum(X1,X2)),c_Sum__Type_OPlus(X1,X2,X3,X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.77 cnf(i_0_5671, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Big__Operators_Olinorder__class_OMin(X2,X3)),c_Big__Operators_Olinorder__class_OMin(X2,X1)))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.49/4.77 cnf(i_0_2169, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Big__Operators_Olinorder__class_OMax(X2,X1)),c_Big__Operators_Olinorder__class_OMax(X2,X3)))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.49/4.77 cnf(i_0_3503, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2)))). 4.49/4.77 cnf(i_0_577, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X2))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.49/4.77 cnf(i_0_4613, plain, (hAPP(hAPP(c_List_Onth(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X2)),X3)|X3=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.49/4.77 cnf(i_0_6953, plain, (c_Relation_Oirrefl(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk482_2(X2,X1)),esk482_2(X2,X1))),X2)))). 4.49/4.77 cnf(i_0_5132, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),c_Divides_Odiv__class_Omod(X1,X4,X3)),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4),X3)|~class_Divides_Osemiring__div(X1))). 4.49/4.77 cnf(i_0_5015, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),c_Divides_Odiv__class_Omod(X1,X4,X3)),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)|~class_Divides_Osemiring__div(X1))). 4.49/4.77 cnf(i_0_2965, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk208_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.49/4.77 cnf(i_0_7467, plain, (epred1_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk532_3(X3,X2,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,X3)))). 4.49/4.77 cnf(i_0_3271, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X5),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X3),X5)))). 4.49/4.77 cnf(i_0_6232, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk432_3(X3,X2,X1)),esk433_3(X3,X2,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.49/4.77 cnf(i_0_5681, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),hAPP(c_List_Ohd(X1),X2)),hAPP(hAPP(c_List_Otake(X1),X3),hAPP(c_List_Otl(X1),X2)))=hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X3)),X2)|c_List_Olist_ONil(X1)=X2)). 4.49/4.77 cnf(i_0_7471, plain, (epred1_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X3,X2,X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,X3)))). 4.49/4.77 cnf(i_0_3034, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk212_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.49/4.77 cnf(i_0_4551, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk319_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.49/4.77 cnf(i_0_6285, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X1)),hAPP(hAPP(c_Product__Type_OPair(X4,X1),X5),X2)),hAPP(c_List_Oset(tc_prod(X4,X1)),hAPP(hAPP(c_List_Ozip(X4,X1),X6),X3)))))). 4.49/4.77 cnf(i_0_1698, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),hAPP(c_List_Oset(tc_prod(X1,X4)),hAPP(hAPP(c_List_Ozip(X1,X4),X3),X6)))))). 4.49/4.77 cnf(i_0_3738, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2)))). 4.49/4.77 cnf(i_0_2926, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.49/4.77 cnf(i_0_6422, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.77 cnf(i_0_2833, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Lattices_Oab__semigroup__idem__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_1146, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk75_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(X1,X3)))). 4.49/4.77 cnf(i_0_3589, plain, (c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X1),c_Lazy__Sequence_Osmall__lazy_H(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Lazy__Sequence_Osmall__lazy_H(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)))). 4.49/4.77 cnf(i_0_7240, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3)|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.77 cnf(i_0_2474, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.49/4.77 cnf(i_0_679, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))))). 4.49/4.77 cnf(i_0_3315, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))=X2|~class_Fields_Ofield(X1)|~class_Int_Onumber__ring(X1))). 4.49/4.77 cnf(i_0_2160, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBB(tc_Int_Oint,X2,X1),c_Int_Oring__1__class_Oof__int(X2)),X3)),X4)=hAPP(c_Int_Oring__1__class_Oof__int(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Int_Oint),X3),X4))|~class_Rings_Oring__1(X2))). 4.49/4.77 cnf(i_0_177, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_2476, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_4217, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_3408, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBB(X2,X2,X1),c_Groups_Oabs__class_Oabs(X2)),X3)),X4)=hAPP(c_Groups_Oabs__class_Oabs(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X4))|~class_Fields_Olinordered__field(X2))). 4.49/4.77 cnf(i_0_2795, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)))). 4.49/4.77 cnf(i_0_5309, plain, (hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),esk371_4(X2,X3,X4,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X4|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X2))))). 4.49/4.77 cnf(i_0_7160, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1))). 4.49/4.77 cnf(i_0_3090, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_5413, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_6897, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_7415, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk525_5(X2,X3,X1,X4,X5)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X5,X3),X2))))). 4.49/4.77 cnf(i_0_1389, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk91_3(X1,X2,X3))),X2))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))))). 4.49/4.77 cnf(i_0_6193, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X4)|X2=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.49/4.77 cnf(i_0_2477, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_4216, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_3701, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Oordered__cancel__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.49/4.77 cnf(i_0_4832, plain, (X1=c_List_Olist_ONil(X2)|hBOOL(hAPP(hAPP(c_member(X2),hAPP(c_Product__Type_Ofst(X2,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X2,X1),X3))),hAPP(c_List_Oset(X2),X1))))). 4.49/4.77 cnf(i_0_4470, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2)))). 4.49/4.77 cnf(i_0_930, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.49/4.77 cnf(i_0_591, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X6),X3)))|~hBOOL(hAPP(hAPP(c_member(X5),X4),X6)))). 4.49/4.77 cnf(i_0_6472, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))))). 4.49/4.77 cnf(i_0_5436, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.49/4.77 cnf(i_0_2791, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.49/4.77 cnf(i_0_3763, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.49/4.77 cnf(i_0_2107, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.49/4.77 cnf(i_0_757, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.49/4.77 cnf(i_0_5931, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)|c_Groups_Ozero__class_Ozero(X1)=X2|~class_Fields_Ofield__inverse__zero(X1))). 4.49/4.77 cnf(i_0_2658, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2)))). 4.49/4.77 cnf(i_0_5898, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_31, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_3691, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_4015, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)))). 4.49/4.77 cnf(i_0_4717, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)))). 4.49/4.77 cnf(i_0_1065, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.49/4.77 cnf(i_0_5539, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.49/4.77 cnf(i_0_400, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X4)|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Divides_Osemiring__div(X1))). 4.49/4.77 cnf(i_0_2360, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_5192, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_5558, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.49/4.77 cnf(i_0_5459, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.49/4.77 cnf(i_0_5103, plain, (X1=c_Big__Operators_Olattice_OInf__fin(X2,c_Orderings_Oord__class_Omin(X2),X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_member(X2),X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.49/4.77 cnf(i_0_274, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)=X3|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.77 cnf(i_0_1418, plain, (hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4))=hAPP(hAPP(X5,hAPP(X6,X3)),hAPP(X1,X4))|~c_Finite__Set_Ofolding__image__simple__idem(X7,X2,X5,X8,X6,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.77 cnf(i_0_547, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_1642, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_3467, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Oordered__cancel__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_6282, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Oordered__cancel__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.49/4.77 cnf(i_0_5460, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_7198, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_297, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_5628, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_2347, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))=c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_2855, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.49/4.77 cnf(i_0_3174, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_7320, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_2822, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_6054, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.49/4.77 cnf(i_0_6958, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_6381, plain, (c_Map_Orestrict__map(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),X5),X6)=c_Map_Orestrict__map(X1,X2,X3,X6)|hBOOL(hAPP(hAPP(c_member(X1),X4),X6)))). 4.49/4.77 cnf(i_0_3601, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.77 cnf(i_0_904, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.49/4.77 cnf(i_0_6842, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))))). 4.49/4.77 cnf(i_0_7494, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X2,X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X3,X1,X2)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.77 cnf(i_0_5226, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.49/4.77 cnf(i_0_4806, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.49/4.77 cnf(i_0_2657, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.49/4.77 cnf(i_0_4894, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.77 cnf(i_0_7487, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X2,X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X3,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.77 cnf(i_0_4751, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))))). 4.49/4.77 cnf(i_0_4750, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))))). 4.49/4.77 cnf(i_0_6843, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))))). 4.49/4.77 cnf(i_0_6053, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk422_2(X2,X1)),esk422_2(X2,X1))=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))))). 4.49/4.77 cnf(i_0_7518, plain, (epred2_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk538_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk536_3(X3,X2,X1))))). 4.49/4.77 cnf(i_0_4332, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.49/4.77 cnf(i_0_291, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_5161, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.77 cnf(i_0_7271, plain, (hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))=c_Divides_Odivmod__int(X1,X2)|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.77 cnf(i_0_2764, plain, (X1=X2|hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X4)!=hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X4)|~class_Rings_Olinordered__semidom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),X1)))). 4.49/4.77 cnf(i_0_74, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X2),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X4),X3)|hAPP(X2,esk9_5(X4,X2,X3,X3,X1))!=hAPP(X4,esk9_5(X4,X2,X3,X3,X1))|~class_Groups_Ocomm__monoid__add(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~c_Nat__Transfer_Onat__set(X3))). 4.49/4.77 cnf(i_0_2126, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))=hAPP(hAPP(c_List_Olist__update(X1,c_List_Obutlast(X1,X2)),X3),X4)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X3)). 4.49/4.77 cnf(i_0_7306, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X1),X2),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X1),X4),X3)|hAPP(X2,esk518_5(X4,X2,X3,X3,X1))!=hAPP(X4,esk518_5(X4,X2,X3,X3,X1))|~class_Groups_Ocomm__monoid__add(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~c_Nat__Transfer_Onat__set(X3))). 4.49/4.77 cnf(i_0_1354, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2),X3),hAPP(hAPP(c_COMBC(X1,X4,X2),X5),X6))=hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,X2)),X3),X5),X6)|~class_Complete__Lattice_Ocomplete__lattice(X2))). 4.49/4.77 cnf(i_0_3280, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X5),X2)))). 4.49/4.77 cnf(i_0_5926, plain, (c_Fun_Oinj__on(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~c_Fun_Oinj__on(X1,X3,X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~c_Fun_Oinj__on(X3,X2,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))). 4.49/4.77 cnf(i_0_4489, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X4))))|~hBOOL(hAPP(X3,hAPP(hAPP(c_List_Onth(X2),X4),esk311_4(X4,X2,X3,X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))))). 4.49/4.77 cnf(i_0_7474, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X2,X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X3,X1,X2)))|~hBOOL(hAPP(X2,esk532_3(X3,X1,X2))))). 4.49/4.77 cnf(i_0_6331, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X2),X3),hAPP(hAPP(c_COMBC(X1,X4,X2),X5),X6))=hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,X2)),X3),X5),X6)|~class_Complete__Lattice_Ocomplete__lattice(X2))). 4.49/4.77 cnf(i_0_2569, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))|hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.49/4.77 cnf(i_0_7483, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X2,X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X3,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X2,esk534_3(X3,X1,X2))))). 4.49/4.77 cnf(i_0_772, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Relation_OId__on(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.49/4.77 cnf(i_0_2233, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2)))). 4.49/4.77 cnf(i_0_986, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X2),X1)))=c_Random_Olog(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X2),X1)))). 4.49/4.77 cnf(i_0_5495, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),hAPP(X4,esk383_4(X4,X2,X3,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_1179, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(X2,X4)|~c_Finite__Set_Ofolding__image__simple__idem(X5,X6,X1,X7,X8,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X4)))). 4.49/4.77 cnf(i_0_3198, plain, (c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))=c_List_OtakeWhile(X1,X2,X3)|hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),X3))))). 4.49/4.77 cnf(i_0_6990, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk487_2(X1,X2)),X2))|hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))))). 4.49/4.77 cnf(i_0_7443, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.49/4.77 cnf(i_0_1168, plain, (hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4))=hAPP(hAPP(X5,X3),hAPP(X1,X4))|c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=X4|hBOOL(hAPP(hAPP(c_member(X2),X3),X4))|~c_Finite__Set_Ofolding__one(X2,X5,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.77 cnf(i_0_4538, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),c_List_Olist_Olist__size(X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_List_Oset(X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(X3,X5))))). 4.49/4.77 cnf(i_0_5448, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_List_Olist_Olist__size(X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_List_Oset(X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(X3,X5))))). 4.49/4.77 cnf(i_0_13, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),c_Divides_Odiv__class_Omod(X1,X4,X3)),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4),X3)|~class_Divides_Oring__div(X1))). 4.49/4.77 cnf(i_0_3584, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(X3,X4)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X1),X6),X3)))|~hBOOL(hAPP(hAPP(c_member(X5),X4),X6)))). 4.49/4.77 cnf(i_0_2540, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.77 cnf(i_0_488, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))|~class_Orderings_Olinorder(X1))). 4.49/4.77 cnf(i_0_3937, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))|~class_Orderings_Olinorder(X1))). 4.49/4.77 cnf(i_0_1164, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_member(X2),esk77_4(X3,X4,X1,X2)),hAPP(c_List_Oset(X2),c_List_Oreplicate(X2,X1,X4))))|hBOOL(hAPP(X3,X4)))). 4.49/4.77 cnf(i_0_2563, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),X3),X4),c_List_Oremdups(X2,X5))=hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,X3),X4),hAPP(c_List_Oset(X2),X5))|~c_Finite__Set_Ofun__left__comm(X2,X1,X3))). 4.49/4.77 cnf(i_0_897, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),X4))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X1),X6),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(X5),X3),X6)))). 4.49/4.77 cnf(i_0_6715, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_Predicate_Oconversep(X1,X1,X2)))|~c_Wellfounded_Oacyclic(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))). 4.49/4.77 cnf(i_0_3670, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X2),esk248_4(X3,X4,X1,X2)),hAPP(c_List_Oset(X2),c_List_Oreplicate(X2,X1,X4))))|~hBOOL(hAPP(X3,X4)))). 4.49/4.77 cnf(i_0_3982, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3)|~class_Fields_Ofield__inverse__zero(X1))). 4.49/4.77 cnf(i_0_1180, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3)|~class_Groups_Ocomm__monoid__mult(X1))). 4.49/4.77 cnf(i_0_5562, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3)|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.77 cnf(i_0_993, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)|~class_Orderings_Olinorder(X1))). 4.49/4.77 cnf(i_0_5193, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.77 cnf(i_0_6994, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.49/4.77 cnf(i_0_595, plain, (c_Wellfounded_Owf(X1,hAPP(c_Set_Oimage(tc_prod(X2,X2),tc_prod(X1,X1),c_Product__Type_Omap__pair(X2,X1,X2,X1,X3,X3)),X4))|~c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))|~c_Wellfounded_Owf(X2,X4))). 4.49/4.77 cnf(i_0_1979, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),X2)),X2)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))))). 4.49/4.77 cnf(i_0_6854, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk472_5(X3,X4,X5,X2,X1))=X4|hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)=X3|hAPP(hAPP(c_List_Oappend(X1),X4),X3)!=hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5))). 4.49/4.77 cnf(i_0_5963, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk408_5(X3,X2,X4,X5,X1))=X5|hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)=X4|hAPP(hAPP(c_List_Oappend(X1),X5),X4)!=hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))). 4.49/4.77 cnf(i_0_7491, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X2,X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X3,X1,X2)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk532_3(X3,X1,X2))))). 4.49/4.77 cnf(i_0_4735, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3)|~class_Orderings_Olinorder(X1))). 4.49/4.77 cnf(i_0_1666, plain, (hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=hAPP(c_Finite__Set_Ocard(X1),X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.77 cnf(i_0_4476, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|c_Groups_Ozero__class_Ozero(X1)!=hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~class_Groups_Ocomm__monoid__add(X1))). 4.49/4.77 cnf(i_0_6853, plain, (hAPP(hAPP(c_List_Oappend(X1),esk472_5(X2,X3,X4,X5,X1)),X2)=X4|hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)=X2|hAPP(hAPP(c_List_Oappend(X1),X3),X2)!=hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4))). 4.49/4.77 cnf(i_0_5962, plain, (hAPP(hAPP(c_List_Oappend(X1),esk408_5(X2,X3,X4,X5,X1)),X4)=X2|hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)=X4|hAPP(hAPP(c_List_Oappend(X1),X5),X4)!=hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))). 4.49/4.77 cnf(i_0_2500, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X1)))). 4.49/4.77 cnf(i_0_7420, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X2)),X3)),X4)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X3),X4))|~class_Rings_Osemiring__1(X2))). 4.49/4.77 cnf(i_0_260, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(X3,X2)))). 4.49/4.77 cnf(i_0_2005, plain, (c_Relation_Orefl__on(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X5))|~c_Relation_Orefl__on(X1,X3,X5)|~c_Relation_Orefl__on(X1,X2,X4))). 4.49/4.77 cnf(i_0_528, plain, (c_Relation_Orefl__on(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X5))|~c_Relation_Orefl__on(X1,X3,X5)|~c_Relation_Orefl__on(X1,X2,X4))). 4.49/4.77 cnf(i_0_2167, plain, (hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),X1))=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.77 cnf(i_0_4166, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBB(X2,X2,X1),c_Groups_Ouminus__class_Ouminus(X2)),X3)),X4)=hAPP(c_Groups_Ouminus__class_Ouminus(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X4))|~class_Groups_Oab__group__add(X2))). 4.49/4.77 cnf(i_0_1790, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),X3))|~c_Relation_Orefl__on(X1,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.49/4.77 cnf(i_0_1801, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(c_Nat_OSuc,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.49/4.77 cnf(i_0_1936, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.49/4.77 cnf(i_0_6315, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(c_Finite__Set_Ocard(X1),X2)|hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.77 cnf(i_0_2482, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))|~class_Groups_Omonoid__mult(X1))). 4.49/4.77 cnf(i_0_2630, plain, (X1=X2|X3=X4|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X4))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X3))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5))). 4.49/4.77 cnf(i_0_5055, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2)))). 4.49/4.77 cnf(i_0_4007, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)))=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.49/4.77 cnf(i_0_462, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5)))|~c_Fun_Oinj__on(X2,X1,X3,X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X4),X5)))). 4.49/4.77 cnf(i_0_2264, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.77 cnf(i_0_1948, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X6),X3)))|~hBOOL(hAPP(hAPP(c_member(X5),X4),X6)))). 4.49/4.77 cnf(i_0_2217, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X6),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(X5),X3),X6)))). 4.49/4.77 cnf(i_0_3566, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.77 cnf(i_0_6170, plain, (hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),X2),hAPP(c_List_Orev(X1),X3))=hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2),X3)|~class_Groups_Oab__semigroup__add(X1))). 4.49/4.77 cnf(i_0_6480, plain, (hBOOL(hAPP(X1,esk445_2(X1,X2)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk444_2(X1,X2)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,esk443_2(X1,X2)))|~hBOOL(hAPP(X1,X3)))). 4.49/4.77 cnf(i_0_2621, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X4,X5))=hAPP(X2,X3)|~c_Finite__Set_Ofolding__idem(X6,X1,X4,X2)|~hBOOL(hAPP(hAPP(c_member(X6),X5),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X3)))). 4.49/4.77 cnf(i_0_2362, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X3),X4))|~class_Groups_Osemigroup__add(X1))). 4.49/4.77 cnf(i_0_6973, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=hAPP(c_Finite__Set_Ocard(X1),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.77 cnf(i_0_683, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3))))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.49/4.77 cnf(i_0_6103, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X4)))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,X4)))))). 4.49/4.77 cnf(i_0_4383, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.77 cnf(i_0_1093, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk74_3(X3,X2,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk73_3(X3,X2,X1)),esk73_3(X3,X2,X1))),X3)))). 4.49/4.77 cnf(i_0_587, plain, (c_Relation_Orefl__on(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk41_3(X3,X2,X1)),esk41_3(X3,X2,X1))),X3)))). 4.49/4.77 cnf(i_0_6637, plain, (c_Relation_Orefl__on(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk459_3(X2,X3,X1)),esk459_3(X2,X3,X1))),X3)))). 4.49/4.77 cnf(i_0_7469, plain, (epred1_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X3,X2,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,X3)))). 4.49/4.77 cnf(i_0_6104, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X4)))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,X3)))))). 4.49/4.77 cnf(i_0_1261, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1))!=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)))). 4.49/4.77 cnf(i_0_6840, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))|~c_Equiv__Relations_Oequiv(X1,X3,X2))). 4.49/4.77 cnf(i_0_590, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))|~c_Relation_Orefl__on(X1,X3,X2))). 4.49/4.77 cnf(i_0_3730, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk258_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.77 cnf(i_0_7462, plain, (epred1_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,X3)))). 4.49/4.77 cnf(i_0_1710, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk115_3(X2,X3,X1)),esk116_3(X2,X3,X1)))|hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(X2,X3)))). 4.49/4.77 cnf(i_0_5707, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk395_4(X2,X3,X4,X1)),X3))|hBOOL(hAPP(X2,X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.77 cnf(i_0_275, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel(X1,X2)),c_List_Olistrel(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.49/4.78 cnf(i_0_6332, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel1(X1,X2)),c_List_Olistrel1(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.49/4.78 cnf(i_0_1024, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X1)))). 4.49/4.78 cnf(i_0_3674, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X3)))). 4.49/4.78 cnf(i_0_6279, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk436_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.78 cnf(i_0_4752, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))))). 4.49/4.78 cnf(i_0_6841, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))))). 4.49/4.78 cnf(i_0_4980, plain, (c_Hoare__Mirabelle_Otriple__valid(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),esk346_4(X4,X5,X1,X2)),X5))|~c_Hoare__Mirabelle_Ohoare__valids(X1,X5,X4)|~hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4)))). 4.49/4.78 cnf(i_0_3815, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk263_3(X1,X2,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),X2),hAPP(hAPP(c_Relation_Orel__comp(X3,X3,X3),X1),c_Transitive__Closure_Ortrancl(X3,X1)))))). 4.49/4.78 cnf(i_0_6712, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.49/4.78 cnf(i_0_71, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)))). 4.49/4.78 cnf(i_0_4645, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)))). 4.49/4.78 cnf(i_0_785, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))|~class_Lattices_Odistrib__lattice(X1))). 4.49/4.78 cnf(i_0_7315, plain, (hAPP(c_Option_Ooption_OSome(X1),esk519_6(X2,X3,X4,X5,X6,X1))=hAPP(X3,X2)|c_Option_Ooption_ONone(X1)=hAPP(X3,X2)|hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X6),X1,c_Option_Ooption_ONone(X6),X4),hAPP(X3,X2))!=c_Option_Ooption_ONone(X6))). 4.49/4.78 cnf(i_0_2883, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk202_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.49/4.78 cnf(i_0_2882, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk203_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3)))|~c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.49/4.78 cnf(i_0_7466, plain, (epred1_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X3,X2,X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk532_3(X3,X2,X1)))|~hBOOL(hAPP(X1,X3)))). 4.49/4.78 cnf(i_0_4486, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.49/4.78 cnf(i_0_5596, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))|~class_Lattices_Odistrib__lattice(X1))). 4.49/4.78 cnf(i_0_3488, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.49/4.78 cnf(i_0_6023, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3)))). 4.49/4.78 cnf(i_0_7002, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|c_Wellfounded_Omax__extp(X2,X3,X4,X1)|hBOOL(hAPP(hAPP(c_member(X2),esk489_4(X1,X4,X3,X2)),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.49/4.78 cnf(i_0_588, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk41_3(X3,X2,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))))). 4.49/4.78 cnf(i_0_6638, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk459_3(X2,X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))))). 4.49/4.78 cnf(i_0_2640, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)=c_List_Olist_ONil(X1)|hBOOL(hAPP(hAPP(c_member(X1),esk193_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3))))). 4.49/4.78 cnf(i_0_6665, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))). 4.49/4.78 cnf(i_0_4744, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2)))). 4.49/4.78 cnf(i_0_2785, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X4),X5),X6),X7))|~hBOOL(hAPP(hAPP(hAPP(X5,X8),X6),X7))|~hBOOL(hAPP(hAPP(c_member(X1),X8),X4)))). 4.49/4.78 cnf(i_0_6171, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.78 cnf(i_0_271, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)))|hBOOL(hAPP(hAPP(c_member(X1),esk23_3(X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_6415, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(X2,X3)|~c_Finite__Set_Ofolding__idem(X5,X1,X6,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)))). 4.49/4.78 cnf(i_0_7526, plain, (hBOOL(hAPP(X1,X2))|~epred2_3(X1,X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X4)))). 4.49/4.78 cnf(i_0_2261, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)))|hBOOL(hAPP(hAPP(c_member(X1),esk167_3(X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_5001, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_1225, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))))). 4.49/4.78 cnf(i_0_4041, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))))). 4.49/4.78 cnf(i_0_7499, plain, (hBOOL(hAPP(X1,X2))|~epred1_3(X1,X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X2)))). 4.49/4.78 cnf(i_0_7527, plain, (hBOOL(hAPP(X1,X2))|~epred2_3(X1,X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X3)))). 4.49/4.78 cnf(i_0_7498, plain, (hBOOL(hAPP(X1,X2))|~epred1_3(X1,X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)))). 4.49/4.78 cnf(i_0_571, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))))). 4.49/4.78 cnf(i_0_4263, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3)|~class_Groups_Oordered__ab__group__add(X1))). 4.49/4.78 cnf(i_0_669, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)|~class_Groups_Oordered__ab__group__add(X1))). 4.49/4.78 cnf(i_0_4161, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk284_3(X1,X2,X3)))=X3|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.49/4.78 cnf(i_0_2750, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~class_Orderings_Oord(X1)|~class_Int_Onumber(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))). 4.49/4.78 cnf(i_0_1467, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|~class_Orderings_Oord(X1)|~class_Int_Onumber(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))). 4.49/4.78 cnf(i_0_2163, plain, (c_List_Olist__ex1(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk163_4(X3,X2,X1,X4)),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 4.49/4.78 cnf(i_0_97, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4)),X3)|~class_Rings_Odivision__ring(X1))). 4.49/4.78 cnf(i_0_5909, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.78 cnf(i_0_3994, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4)),X3)|~class_Lattices_Odistrib__lattice(X1))). 4.49/4.78 cnf(i_0_1458, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3)|~class_Lattices_Odistrib__lattice(X1))). 4.49/4.78 cnf(i_0_176, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.49/4.78 cnf(i_0_4919, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(c_COMBK(X1,X2),X3)),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))),X3)|~class_Rings_Osemiring__1(X1))). 4.49/4.78 cnf(i_0_7051, plain, (c_List_Olist__ex1(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk492_4(X3,X2,X1,X4)),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 4.49/4.78 cnf(i_0_892, plain, (c_List_OtakeWhile(X1,X2,X3)=hAPP(hAPP(c_List_Otake(X1),X4),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|~hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),esk62_4(X2,X3,X1,X4)))))). 4.49/4.78 cnf(i_0_4229, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk288_5(X3,X4,X5,X2,X1),esk289_5(X3,X4,X5,X2,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)),X3)))). 4.49/4.78 cnf(i_0_5878, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk405_5(X3,X4,X5,X2,X1),esk406_5(X3,X4,X5,X2,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)),X3)))). 4.49/4.78 cnf(i_0_3288, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)|~class_Rings_Odivision__ring(X1))). 4.49/4.78 cnf(i_0_3872, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)|~class_Rings_Ocomm__semiring(X1))). 4.49/4.78 cnf(i_0_3334, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1))). 4.49/4.78 cnf(i_0_6177, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),c_Groups_Oone__class_Oone(X1))|X2=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.49/4.78 cnf(i_0_2254, plain, (hAPP(hAPP(c_List_Oappend(X1),esk165_3(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),esk166_3(X2,X3,X1)))=X2|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))))). 4.49/4.78 cnf(i_0_3305, plain, (hAPP(hAPP(c_List_Oappend(X1),esk226_3(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),esk227_3(X2,X3,X1)))=X2|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))))). 4.49/4.78 cnf(i_0_5804, plain, (hAPP(hAPP(c_List_Oappend(X1),esk399_3(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),esk400_3(X2,X3,X1)))=X2|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))))). 4.49/4.78 cnf(i_0_4584, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.49/4.78 cnf(i_0_5433, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1))). 4.49/4.78 cnf(i_0_817, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.78 cnf(i_0_6686, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X4)),X5),c_Option_Ooption_ONone(X2))=c_Map_Orestrict__map(X1,X2,X3,X4)|hBOOL(hAPP(hAPP(c_member(X1),X5),X4)))). 4.49/4.78 cnf(i_0_5345, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_Relation_ODomain(X3,X3),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,X4))))). 4.49/4.78 cnf(i_0_4792, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),X5)))|hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X5)))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X5)))). 4.49/4.78 cnf(i_0_5431, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X2)),X3)),X4)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X3),X4))|~class_Rings_Osemiring__1(X2)|~class_Groups_Ocomm__monoid__mult(X2))). 4.49/4.78 cnf(i_0_4827, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),c_Big__Operators_Olinorder__class_OMax(X1,X3))=c_Big__Operators_Olinorder__class_OMax(X1,X3)|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_5072, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))=c_Big__Operators_Olattice__class_OSup__fin(X1,X3)|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_4519, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))=c_Big__Operators_Olattice__class_OInf__fin(X1,X3)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_6885, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),c_Big__Operators_Olinorder__class_OMin(X1,X3))=c_Big__Operators_Olinorder__class_OMin(X1,X3)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_5438, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBB(tc_Int_Oint,X2,X1),c_Int_Oring__1__class_Oof__int(X2)),X3)),X4)=hAPP(c_Int_Oring__1__class_Oof__int(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Int_Oint),X3),X4))|~class_Rings_Oring__1(X2)|~class_Groups_Ocomm__monoid__mult(X2))). 4.49/4.78 cnf(i_0_4322, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk297_2(X1,X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(X1,X3)))). 4.49/4.78 cnf(i_0_1248, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X3))))). 4.49/4.78 cnf(i_0_3641, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))),X3)|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.78 cnf(i_0_5401, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_6267, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X5),X4)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X3),X5)))). 4.49/4.78 cnf(i_0_1934, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X5),X4)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X5),X3)))). 4.49/4.78 cnf(i_0_3993, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),c_Groups_Oone__class_Oone(X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X3)|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Divides_Osemiring__div(X1))). 4.49/4.78 cnf(i_0_4837, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_1336, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),c_List_Olists(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.49/4.78 cnf(i_0_3181, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk217_3(X2,X3,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X2,c_Enum_Oenum__class_Oenum(X1)))))|~c_Enum_Oex__n__lists(X1,X3,X2)|~class_Enum_Oenum(X1))). 4.49/4.78 cnf(i_0_3138, plain, (hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X2,X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.49/4.78 cnf(i_0_7075, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Oone__class_Oone(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.49/4.78 cnf(i_0_334, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_OImage(X3,X1,X4),hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X5),X2)),X4)))). 4.49/4.78 cnf(i_0_1367, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X4),X5)),X6)=hAPP(hAPP(X3,X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),X6))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.49/4.78 cnf(i_0_1264, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)))=hAPP(c_List_Oset(X1),X3)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.49/4.78 cnf(i_0_1320, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X1),c_Int_Onat),X2)),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Int_Oint),X2),X3)|hBOOL(hAPP(hAPP(c_member(X1),esk88_3(X2,X3,X1)),X3)))). 4.49/4.78 cnf(i_0_1388, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk91_3(X1,X2,X3))),X2))|hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))))). 4.49/4.78 cnf(i_0_4259, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),X4)),hAPP(hAPP(c_List_Onth(X5),X6),X4)))|~c_List_Olist__all2(X2,X5,X1,X3,X6)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))))). 4.49/4.78 cnf(i_0_5894, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),X4)),hAPP(hAPP(c_List_Onth(X5),X6),X4)))|~c_List_Olist__all2(X2,X5,X1,X3,X6)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X6))))). 4.49/4.78 cnf(i_0_130, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2),X5)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X2,esk15_6(X3,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2),X5),X2,X5,X4,X1))))|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.49/4.78 cnf(i_0_2136, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Groups_Otimes__class_Otimes(X1),hAPP(c_List_Ohd(X1),X2)),hAPP(c_List_Otl(X1),X2))=hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(c_List_Oset(X1),X2))|X2=c_List_Olist_ONil(X1)|~class_Lattices_Oab__semigroup__idem__mult(X1))). 4.49/4.78 cnf(i_0_741, plain, (hAPP(hAPP(X1,hAPP(c_Fun_Ocomp(X2,X3,X2,X4),X5)),X6)=hAPP(hAPP(X1,X4),hAPP(c_Set_Oimage(X2,X2,X5),X6))|~c_Finite__Set_Ofolding__image(X3,X2,X7,X8,X1)|~c_Fun_Oinj__on(X2,X2,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 4.49/4.78 cnf(i_0_464, plain, (X1=X2|hAPP(c_Map_Omap__of(X3,X4),hAPP(hAPP(c_List_Ozip(X3,X4),X5),X1))!=hAPP(c_Map_Omap__of(X3,X4),hAPP(hAPP(c_List_Ozip(X3,X4),X5),X2))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X1)|~hBOOL(hAPP(c_List_Odistinct(X3),X5)))). 4.49/4.78 cnf(i_0_873, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk57_5(X3,X4,X5,X2,X1)),esk58_5(X3,X4,X5,X2,X1))=X5|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),X5),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),X3))))). 4.49/4.78 cnf(i_0_6012, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk415_4(X1,X2,X3,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)))|hBOOL(hAPP(X2,X1))|~hBOOL(hAPP(hAPP(c_member(X4),X1),hAPP(c_List_Oset(X4),X3))))). 4.49/4.78 cnf(i_0_7065, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X1,X1),c_Groups_Oabs__class_Oabs(X1)),X2))))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.49/4.78 cnf(i_0_212, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)))). 4.49/4.78 cnf(i_0_2238, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)))). 4.49/4.78 cnf(i_0_449, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.49/4.78 cnf(i_0_4566, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Finite__Set_Ocard(X2),X3))),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(c_COMBK(X1,X2),X4)),X3)|~class_Rings_Osemiring__1(X1))). 4.49/4.78 cnf(i_0_6, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))|esk3_2(X2,X1)!=esk2_2(X2,X1)|~hBOOL(hAPP(c_List_Odistinct(X1),esk1_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 4.49/4.78 cnf(i_0_7067, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3,X4,tc_fun(X1,tc_HOL_Obool)),X5),X6)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X5,esk494_6(X5,X2,X1,X4,X3,X6)),esk495_6(X5,X2,X1,X4,X3,X6)))))). 4.49/4.78 cnf(i_0_232, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Oone__class_Oone(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.78 cnf(i_0_1076, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Oone__class_Oone(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.49/4.78 cnf(i_0_6431, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.49/4.78 cnf(i_0_3685, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.49/4.78 cnf(i_0_1976, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.49/4.78 cnf(i_0_2751, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))|~class_Orderings_Oord(X1)|~class_Int_Onumber(X1))). 4.49/4.78 cnf(i_0_6652, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))=X3|X4=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.49/4.78 cnf(i_0_7400, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1))!=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.49/4.78 cnf(i_0_1120, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4))=c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.49/4.78 cnf(i_0_3346, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.49/4.78 cnf(i_0_7155, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4))=c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.49/4.78 cnf(i_0_7382, plain, (hAPP(c_Relation_ORange(X1,X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))=X4|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3)). 4.49/4.78 cnf(i_0_2931, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.49/4.78 cnf(i_0_4500, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))|~class_Rings_Olinordered__ring(X1))). 4.49/4.78 cnf(i_0_5399, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2)))). 4.49/4.78 cnf(i_0_1466, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))|~class_Orderings_Oord(X1)|~class_Int_Onumber(X1))). 4.49/4.78 cnf(i_0_6639, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))=c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.49/4.78 cnf(i_0_4672, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X2))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_List_Olist_ONil(tc_List_Olist(X1))=X2|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2))))). 4.49/4.78 cnf(i_0_5437, plain, (c_Fun_Oinj__on(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5),X6)|hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X3),X6)))|~c_Fun_Oinj__on(X1,X2,X3,X6))). 4.49/4.78 cnf(i_0_5648, plain, (hAPP(c_Nat_OSuc,esk391_5(X1,X2,X3,X4,X5))=X2|X3=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X2),X1))))). 4.49/4.78 cnf(i_0_2994, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X5))|~class_Orderings_Olinorder(X1))). 4.49/4.78 cnf(i_0_3544, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X5)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.78 cnf(i_0_4039, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X5)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.78 cnf(i_0_3240, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(X2,X4)|X3=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))|~c_Finite__Set_Ofolding__one__idem(X5,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))). 4.49/4.78 cnf(i_0_2413, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X4,X5))=c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5))|~class_Orderings_Olinorder(X1))). 4.49/4.78 cnf(i_0_326, plain, (hAPP(c_Nat_OSuc,esk26_5(X1,X2,X3,X4,X5))=X2|X3=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X2),X1))))). 4.49/4.78 cnf(i_0_4444, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X2)))). 4.49/4.78 cnf(i_0_7044, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3),X4))|~c_List_Olist__all2(X1,X2,X3,X5,X6)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),X4),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6)))))). 4.49/4.78 cnf(i_0_2387, plain, (hBOOL(hAPP(X1,esk180_4(X1,X2,X3,X4)))|hBOOL(hAPP(X1,esk179_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)))|~hBOOL(hAPP(X1,X5)))). 4.49/4.78 cnf(i_0_2679, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X4,X5))=c_SetInterval_Oord__class_OgreaterThanLessThan(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5))|~class_Orderings_Olinorder(X1))). 4.49/4.78 cnf(i_0_261, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(X3,X2)))). 4.49/4.78 cnf(i_0_6606, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X1),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_5172, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_895, plain, (c_List_OtakeWhile(X1,X2,X3)=hAPP(hAPP(c_List_Otake(X1),X4),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk62_4(X2,X3,X1,X4)),X4))|hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),X4))))). 4.49/4.78 cnf(i_0_4819, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),esk333_7(X3,X4,X2,X5,X6,X7,X1)),X2))|~c_Nitpick_Ofold__graph_H(X1,X7,X6,X5,X2,hAPP(hAPP(X6,X4),X3)))). 4.49/4.78 cnf(i_0_6995, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),hAPP(c_Relation_Oconverse(X1,X1),X2))!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))))). 4.49/4.78 cnf(i_0_7268, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk515_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))|hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.49/4.78 cnf(i_0_1391, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,esk91_3(X1,X2,X3)))))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))))). 4.49/4.78 cnf(i_0_5886, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X5,X6)))|~hBOOL(hAPP(hAPP(c_member(X3),X6),X4)))). 4.49/4.78 cnf(i_0_5701, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X5)))). 4.49/4.78 cnf(i_0_2879, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X4),X5))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X5)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X4))))). 4.49/4.78 cnf(i_0_1513, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3)),X4)=hAPP(hAPP(c_List_Onth(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.49/4.78 cnf(i_0_3629, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Ofinite__psubset(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_6075, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.49/4.78 cnf(i_0_4818, plain, (X1=hAPP(hAPP(X2,X3),X4)|hBOOL(hAPP(hAPP(c_member(X5),esk333_7(X4,X3,X6,X1,X2,X7,X5)),X6))|~c_Nitpick_Ofold__graph_H(X5,X7,X2,X1,X6,hAPP(hAPP(X2,X3),X4)))). 4.49/4.78 cnf(i_0_4360, plain, (c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))=hAPP(hAPP(c_List_Oappend(X1),X3),c_List_OtakeWhile(X1,X2,X4))|hBOOL(hAPP(hAPP(c_member(X1),esk299_4(X4,X2,X3,X1)),hAPP(c_List_Oset(X1),X3))))). 4.49/4.78 cnf(i_0_2777, plain, (c_Fun_Oinj__on(X1,tc_fun(X2,X3),hAPP(hAPP(c_COMBB(X3,tc_fun(X2,X3),X1),c_COMBK(X3,X2)),X4),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~c_Fun_Oinj__on(X1,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))). 4.49/4.78 cnf(i_0_2925, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.49/4.78 cnf(i_0_5820, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))),X3)|~class_Int_Onumber__ring(X1))). 4.49/4.78 cnf(i_0_7141, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X3))))). 4.49/4.78 cnf(i_0_6878, plain, (c_Map_Omap__upds(X1,X2,X3,X4,hAPP(hAPP(c_List_Olist__update(X2,X5),X6),X7))=c_Map_Omap__upds(X1,X2,X3,X4,X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)),X6)))). 4.49/4.78 cnf(i_0_4231, plain, (hAPP(hAPP(c_Set_Oinsert(X1),esk288_5(X2,X3,X4,X5,X1)),esk289_5(X2,X3,X4,X5,X1))=hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)),X2)))). 4.49/4.78 cnf(i_0_6555, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)=hAPP(hAPP(c_List_Omap(X1,X2),X5),X4)|hBOOL(hAPP(hAPP(c_member(X1),esk455_5(X3,X4,X5,X2,X1)),hAPP(c_List_Oset(X1),X4))))). 4.49/4.78 cnf(i_0_1156, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.49/4.78 cnf(i_0_6992, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk486_2(X1,X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))|hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)))). 4.49/4.78 cnf(i_0_1575, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,X1,esk103_2(X2,X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),esk102_2(X2,X1)))=X2|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_5879, plain, (hAPP(hAPP(c_Set_Oinsert(X1),esk405_5(X2,X3,X4,X5,X1)),esk406_5(X2,X3,X4,X5,X1))=hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)),X2)))). 4.49/4.78 cnf(i_0_5880, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.49/4.78 cnf(i_0_4762, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),esk332_3(X3,X1,X2)),X1))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Finite__Set_Ofold1(X2,c_Orderings_Oord__class_Omin(X2)),X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.49/4.78 cnf(i_0_4761, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),esk332_3(X3,X1,X2)),X3))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Finite__Set_Ofold1(X2,c_Orderings_Oord__class_Omin(X2)),X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.49/4.78 cnf(i_0_1250, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk81_3(X2,X3,X1)),X3)),X2))|hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))))). 4.49/4.78 cnf(i_0_3073, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X1)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk214_2(X2,X1)),hAPP(X1,esk214_2(X2,X1)))))). 4.49/4.78 cnf(i_0_2310, plain, (hAPP(c_Set_Oimage(X1,X2,X3),X4)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk170_4(X4,X1,X2,hAPP(c_Set_Oimage(X1,X2,X3),X4))),hAPP(c_Set_Oimage(X1,X2,X3),X4))),X4)))). 4.49/4.78 cnf(i_0_4369, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk300_3(X2,X3,X1)),X3)),X2))|hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))))). 4.49/4.78 cnf(i_0_155, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),esk17_3(X3,X2,X1)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_154, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk17_3(X3,X2,X1)),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_6658, plain, (hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)|~class_Groups_Omonoid__add(X1))). 4.49/4.78 cnf(i_0_1804, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.78 cnf(i_0_4373, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk302_3(X2,X3,X1)),X3)),X2))|hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))))). 4.49/4.78 cnf(i_0_3991, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X4),X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X4)))). 4.49/4.78 cnf(i_0_20, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2)))). 4.49/4.78 cnf(i_0_649, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)))). 4.49/4.78 cnf(i_0_2757, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)))). 4.49/4.78 cnf(i_0_5361, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X4),X5),X6),X7))|hBOOL(hAPP(hAPP(c_member(X1),esk375_7(X3,X2,X7,X6,X5,X4,X1)),X4)))). 4.49/4.78 cnf(i_0_620, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),c_List_Olists(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X4))))). 4.49/4.78 cnf(i_0_4426, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),esk306_4(X4,X2,X3,X1))),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X4))))). 4.49/4.78 cnf(i_0_6007, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X4),X5),X6),X7))|hBOOL(hAPP(hAPP(c_member(X1),esk414_7(X7,X6,X5,X4,X3,X2,X1)),X4)))). 4.49/4.78 cnf(i_0_409, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4)))). 4.49/4.78 cnf(i_0_6746, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.78 cnf(i_0_1561, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.78 cnf(i_0_6503, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(c_List_Orev(X1),X3)),hAPP(c_List_Orev(X2),X4))=hAPP(c_List_Orev(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))). 4.49/4.78 cnf(i_0_2050, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4))=hAPP(hAPP(c_List_Otake(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))|X3=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.49/4.78 cnf(i_0_5766, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),esk398_4(X4,X2,X3,X1))),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X4))))). 4.49/4.78 cnf(i_0_5987, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk411_4(X3,X1,X4,X2)),X4)),X3))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_ORange(X1,X2),X3))))). 4.49/4.78 cnf(i_0_6330, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk439_4(X3,X1,X4,X2)),X4)),X3))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_ORange(X1,X2),X3))))). 4.49/4.78 cnf(i_0_3750, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X4),c_Wellfounded_Oless__than),X1))))). 4.49/4.78 cnf(i_0_2602, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X5)))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.78 cnf(i_0_4467, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X5)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.78 cnf(i_0_5853, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))|~class_Groups_Oordered__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.78 cnf(i_0_1368, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.49/4.78 cnf(i_0_4317, plain, (hAPP(c_Option_Ooption_OSome(X1),esk296_5(X2,X3,X4,X1,X5))=hAPP(hAPP(c_Map_Omap__of(X5,X1),X2),X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X4),X3)),hAPP(c_List_Oset(tc_prod(X5,X1)),X2))))). 4.49/4.78 cnf(i_0_5592, plain, (c_Enum_Oall__n__lists(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk387_3(X3,X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X3,c_Enum_Oenum__class_Oenum(X1)))))|~class_Enum_Oenum(X1))). 4.49/4.78 cnf(i_0_5856, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X5)))). 4.49/4.78 cnf(i_0_2747, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.49/4.78 cnf(i_0_3870, plain, (c_List_Oremove1(X1,X2,c_List_Olinorder__class_Osorted__list__of__set(X1,X3))=c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_6577, plain, (c_Map_Oran(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)))=hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Map_Oran(X1,X2,X3))|c_Option_Ooption_ONone(X2)!=hAPP(X3,X4))). 4.49/4.78 cnf(i_0_2308, plain, (hAPP(c_Set_Oimage(X1,X2,esk171_4(X3,X1,X2,X4)),X3)=X4|c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=X4|~c_Fun_Oinj__on(X2,X1,X5,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X5),X4)),X3)))). 4.49/4.78 cnf(i_0_1291, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X2,c_Option_Ooption_ONone(X1),X3),hAPP(X4,X5))=hAPP(c_Option_Ooption_OSome(X1),X6)|hAPP(X3,X7)!=hAPP(c_Option_Ooption_OSome(X1),X6)|hAPP(X4,X5)!=hAPP(c_Option_Ooption_OSome(X2),X7))). 4.49/4.78 cnf(i_0_4107, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X2,hAPP(c_Relation_Oconverse(X2,X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X5))))))). 4.49/4.78 cnf(i_0_5687, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_3954, plain, (hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4))=hAPP(c_Fun_Ocomp(X5,X5,X5,hAPP(X1,X4)),hAPP(X6,X3))|~c_Finite__Set_Ofolding__idem(X2,X5,X6,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.78 cnf(i_0_476, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.49/4.78 cnf(i_0_3843, plain, (hAPP(X1,X2)=c_Groups_Ozero__class_Ozero(X3)|hBOOL(hAPP(hAPP(c_member(X4),esk264_5(X2,X1,X5,X4,X3)),X5))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X3),X1),X5)!=c_Groups_Ozero__class_Ozero(X3)|~class_Groups_Oordered__ab__group__add(X3)|~hBOOL(hAPP(hAPP(c_member(X4),X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.49/4.78 cnf(i_0_641, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X1),esk44_4(X2,X3,X1,X4)),X3))|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(X2,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_1091, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X2),X4)),X5))=hAPP(hAPP(c_Set_Oinsert(X2),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3)). 4.49/4.78 cnf(i_0_2046, plain, (c_Wellfounded_Owf(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk149_3(X2,X1,X3)),X3)),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),esk147_2(X2,X1))))). 4.49/4.78 cnf(i_0_5651, plain, (hAPP(c_Nat_OSuc,esk391_5(X1,X2,X3,X4,X5))=X2|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X2),X1))))). 4.49/4.78 cnf(i_0_329, plain, (hAPP(c_Nat_OSuc,esk26_5(X1,X2,X3,X4,X5))=X2|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X2),X1))))). 4.49/4.78 cnf(i_0_4388, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),X5)=hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)|hBOOL(hAPP(hAPP(c_member(X1),esk303_5(X4,X3,X5,X1,X2)),hAPP(c_List_Oset(X1),X5)))|~class_Orderings_Olinorder(X2))). 4.49/4.78 cnf(i_0_7484, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X2,X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X3,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X3,X1,X2))))). 4.49/4.78 cnf(i_0_4590, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X3))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X3),X2)))). 4.49/4.78 cnf(i_0_2027, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1)))). 4.49/4.78 cnf(i_0_6062, plain, (hAPP(c_List_Oset(X1),X2)=hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Oappend(X1),X3),X4))|hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)!=c_List_Opartition(X1,X5,X2))). 4.49/4.78 cnf(i_0_4659, plain, (hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X4)),hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X4)),X5))=hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X4)),X5)|~c_Finite__Set_Ofolding__idem(X6,X1,X3,X7))). 4.49/4.78 cnf(i_0_2575, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.49/4.78 cnf(i_0_1758, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4))=c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.49/4.78 cnf(i_0_5266, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1),X4),X5)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(X5,X6)))|~hBOOL(hAPP(hAPP(c_member(X3),X6),X4)))). 4.49/4.78 cnf(i_0_5285, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk370_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk369_3(X1,X2,X3)))=X2|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1))))). 4.49/4.78 cnf(i_0_7170, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X3,X1,X4),X5)))|hAPP(c_Set_Oimage(X3,X1,X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X3),X2),X4)),X5)))). 4.49/4.78 cnf(i_0_2666, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)),X5))|~c_Fun_Oinj__on(X1,X2,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_Set_Oimage(X1,X2,X4),X5))))). 4.49/4.78 cnf(i_0_6316, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_1906, plain, (c_Relation_Osingle__valued(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk132_3(X3,X2,X1)),esk133_3(X3,X2,X1))),X3)))). 4.49/4.78 cnf(i_0_3278, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)))). 4.49/4.78 cnf(i_0_5468, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),X4)),X5))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X4,X6)),X5))|~hBOOL(hAPP(hAPP(c_member(X2),X6),X3)))). 4.49/4.78 cnf(i_0_874, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk58_5(X2,X3,X4,X1,X5)),hAPP(X2,esk57_5(X2,X3,X4,X1,X5))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),X4),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X3),X2))))). 4.49/4.78 cnf(i_0_6748, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1)),X3)),X4)=hAPP(c_Option_Ooption_OSome(X2),esk464_4(X4,X3,X2,X1))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1))|~class_Enum_Oenum(X1))). 4.49/4.78 cnf(i_0_1905, plain, (c_Relation_Osingle__valued(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk132_3(X3,X2,X1)),esk134_3(X3,X2,X1))),X3)))). 4.49/4.78 cnf(i_0_1258, plain, (X1=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2)),X3))|c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))!=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X4),X1))). 4.49/4.78 cnf(i_0_578, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3)))). 4.49/4.78 cnf(i_0_5318, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3)))). 4.49/4.78 cnf(i_0_3534, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2)))). 4.49/4.78 cnf(i_0_252, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.49/4.78 cnf(i_0_2610, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)),X6)=hAPP(hAPP(c_Map_Omap__of(X1,X2),X5),X6)|X3=X6)). 4.49/4.78 cnf(i_0_1325, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)=X2|hAPP(hAPP(c_List_Oappend(X1),X2),X4)!=hAPP(hAPP(c_List_Oappend(X1),X3),X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.49/4.78 cnf(i_0_1448, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X4)),hAPP(X2,X3))|~c_Finite__Set_Ofun__left__comm(X5,X1,X2))). 4.49/4.78 cnf(i_0_6602, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_OImage(X3,X1,X4),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X6),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(X3),X6),X5)))). 4.49/4.78 cnf(i_0_4337, plain, (hAPP(hAPP(c_List_Omap(X1,X2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5)),X6)=hAPP(hAPP(c_List_Omap(X1,X2),X3),X6)|hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X6))))). 4.49/4.78 cnf(i_0_3878, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2)))). 4.49/4.78 cnf(i_0_5336, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3)))). 4.49/4.78 cnf(i_0_1498, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Groups_Otimes__class_Otimes(X1)),X2),X3)|hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_7139, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_6538, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_3354, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_7511, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk536_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3)))=X1|epred2_3(X3,X2,X1)|~hBOOL(hAPP(X3,esk537_3(X1,X2,X3))))). 4.49/4.78 cnf(i_0_4748, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2)))). 4.49/4.78 cnf(i_0_3809, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Oordered__comm__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.49/4.78 cnf(i_0_7167, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.49/4.78 cnf(i_0_5465, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))=c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_7504, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk538_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3)))=X1|epred2_3(X3,X2,X1)|~hBOOL(hAPP(X3,esk535_3(X1,X2,X3))))). 4.49/4.78 cnf(i_0_107, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk14_3(X3,X1,X2)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.78 cnf(i_0_6887, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk476_3(X3,X1,X2)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.78 cnf(i_0_4428, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Oordered__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.49/4.78 cnf(i_0_7088, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Oordered__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.78 cnf(i_0_5258, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.49/4.78 cnf(i_0_6948, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.49/4.78 cnf(i_0_5301, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1)=X3|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1)))). 4.49/4.78 cnf(i_0_4680, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3)|X4=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield(X1))). 4.49/4.78 cnf(i_0_4620, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.49/4.78 cnf(i_0_3141, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Olinordered__comm__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.49/4.78 cnf(i_0_4747, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.49/4.78 cnf(i_0_5910, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),c_Big__Operators_Olinorder__class_OMin(X1,X3))=c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_7517, plain, (epred2_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk536_3(X3,X2,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk538_3(X3,X2,X1))))). 4.49/4.78 cnf(i_0_3231, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk220_5(X2,X3,X4,X1,X5)),X4))|hBOOL(hAPP(X2,X6))|~hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X4),X3))))). 4.49/4.78 cnf(i_0_2454, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4)))))). 4.49/4.78 cnf(i_0_6427, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Wellfounded_Owf(X1,X3)|~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2)))). 4.49/4.78 cnf(i_0_6716, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),X5)),X6))|~c_Fun_Oinj__on(X1,X2,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X6)))). 4.49/4.78 cnf(i_0_7508, plain, (epred2_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk538_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk536_3(X3,X2,X1)),X2)))). 4.49/4.78 cnf(i_0_2998, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.49/4.78 cnf(i_0_1390, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,esk91_3(X2,X1,X3)))))|hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2))))). 4.49/4.78 cnf(i_0_6759, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)|hBOOL(hAPP(hAPP(c_member(X1),X4),X3)))). 4.49/4.78 cnf(i_0_820, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))=c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_7459, plain, (epred1_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X3,X2,X1)))|~hBOOL(hAPP(X1,X3)))). 4.49/4.78 cnf(i_0_4257, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk293_5(X5,X4,X3,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4))). 4.49/4.78 cnf(i_0_5555, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk384_5(X3,X5,X2,X4,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4))). 4.49/4.78 cnf(i_0_4606, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk325_6(X3,X4,X5,X6,X2,X1)),esk327_6(X3,X4,X5,X6,X2,X1))=X6|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),X6),hAPP(hAPP(c_Relation_Orel__comp(X1,X5,X2),X4),X3))))). 4.49/4.78 cnf(i_0_4912, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X4)),hAPP(X2,X3))|~c_Finite__Set_Ofolding(X5,X1,X2,X6))). 4.49/4.78 cnf(i_0_6445, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~c_Equiv__Relations_Oequiv(X1,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.49/4.78 cnf(i_0_1982, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.78 cnf(i_0_5778, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)))). 4.49/4.78 cnf(i_0_4061, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),c_Big__Operators_Olinorder__class_OMax(X1,X3))=c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_2451, plain, (c_Wellfounded_OwfP(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))),X3))|hAPP(X3,esk185_3(X2,X3,X1))!=hAPP(X3,esk186_3(X2,X3,X1))|~c_Wellfounded_OwfP(X1,hAPP(X3,esk184_3(X2,X3,X1))))). 4.49/4.78 cnf(i_0_2571, plain, (c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,X5,hAPP(hAPP(X3,X6),X7))|~c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X7)|~hBOOL(hAPP(hAPP(c_member(X1),X6),X5)))). 4.49/4.78 cnf(i_0_3130, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk216_5(X3,X4,X1,X5,X2)),X5)),X4))|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Relation_OImage(X1,X2,X4),X3))))). 4.49/4.78 cnf(i_0_6617, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk458_5(X3,X4,X1,X5,X2)),X5)),X4))|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Relation_OImage(X1,X2,X4),X3))))). 4.49/4.78 cnf(i_0_6642, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.78 cnf(i_0_5251, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)))). 4.49/4.78 cnf(i_0_2622, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.78 cnf(i_0_3347, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.49/4.78 cnf(i_0_6343, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,X2),X3),X4)=hAPP(X5,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))|hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|~c_Finite__Set_Ofolding__one(X1,X2,X5)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.78 cnf(i_0_5253, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X5))|~class_Orderings_Olinorder(X1))). 4.49/4.78 cnf(i_0_6536, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2)))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),esk454_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_7137, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),esk503_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_3352, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),esk228_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_3696, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk249_6(X3,X4,X2,X1,X5,X6)),esk250_6(X3,X4,X2,X1,X5,X6))=X3|~hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(X6,tc_HOL_Obool)),X4),X3))))). 4.49/4.78 cnf(i_0_5281, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk370_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk369_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 4.49/4.78 cnf(i_0_2798, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.78 cnf(i_0_818, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)))). 4.49/4.78 cnf(i_0_3062, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.78 cnf(i_0_4265, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)))). 4.49/4.78 cnf(i_0_1387, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Nat_OSuc,X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X2))|~hBOOL(hAPP(X1,X4)))). 4.49/4.78 cnf(i_0_6189, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Wellfounded_Omlex__prod(X1,X4,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X4,X2)),hAPP(X4,X3))))). 4.49/4.78 cnf(i_0_7340, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.78 cnf(i_0_837, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X3)),X2))=hAPP(hAPP(c_List_Odrop(X1),X3),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.49/4.78 cnf(i_0_1453, plain, (hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)),X6)=hAPP(c_Option_Ooption_OSome(X2),X7)|X6=X4|hAPP(X3,X6)!=hAPP(c_Option_Ooption_OSome(X2),X7))). 4.49/4.78 cnf(i_0_2494, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk188_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk187_3(X1,X2,X3)))=X2|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))))). 4.49/4.78 cnf(i_0_5217, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_4800, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_5619, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_896, plain, (c_List_OtakeWhile(X1,X2,X3)=hAPP(hAPP(c_List_Otake(X1),X4),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk62_4(X2,X3,X1,X4)),X4)))). 4.49/4.78 cnf(i_0_1242, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(X3,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X5))|hBOOL(hAPP(hAPP(c_member(X1),X4),X5))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.78 cnf(i_0_2618, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBB(X2,X2,X1),hAPP(c_Groups_Otimes__class_Otimes(X2),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X4),X5))|~class_Rings_Osemiring__0(X2))). 4.49/4.78 cnf(i_0_2825, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_4942, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 4.49/4.78 cnf(i_0_4328, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 4.49/4.78 cnf(i_0_1832, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))). 4.49/4.78 cnf(i_0_942, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2)|~class_Rings_Oring__1(X1))). 4.49/4.78 cnf(i_0_527, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)))). 4.49/4.78 cnf(i_0_5316, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)))). 4.49/4.78 cnf(i_0_4187, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(X3,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X5))|hBOOL(hAPP(hAPP(c_member(X1),X4),X5))|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.78 cnf(i_0_4493, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))). 4.49/4.78 cnf(i_0_1056, plain, (hAPP(X1,esk72_3(X2,X1,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk71_3(X2,X1,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3))))). 4.49/4.78 cnf(i_0_3724, plain, (hAPP(X1,esk256_3(X2,X1,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk255_3(X2,X1,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3))))). 4.49/4.78 cnf(i_0_5216, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2))))). 4.49/4.78 cnf(i_0_2954, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X2)),X2)))|~c_Relation_Orefl__on(X1,X3,X2))). 4.49/4.78 cnf(i_0_2390, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk178_4(X2,X3,X4,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|~hBOOL(hAPP(X2,X5)))). 4.49/4.78 cnf(i_0_2392, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk178_4(X2,X3,X4,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3))|~hBOOL(hAPP(X2,X5)))). 4.49/4.78 cnf(i_0_4354, plain, (c_List_Olist__all(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X3))),X4)|~c_List_Olist__ex1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~hBOOL(hAPP(X2,X3)))). 4.49/4.78 cnf(i_0_236, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),hAPP(hAPP(c_List_Omap(X1,X2),X4),X3))),X5)=c_Option_Ooption_ONone(X2)|hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),X3))))). 4.49/4.78 cnf(i_0_4799, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2))))). 4.49/4.78 cnf(i_0_3986, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk273_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2)))|hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),X2))))). 4.49/4.78 cnf(i_0_2953, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.78 cnf(i_0_3162, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.78 cnf(i_0_7385, plain, (c_List_OtakeWhile(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),c_List_Olast(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X2)=c_List_Obutlast(X1,X2)|X2=c_List_Olist_ONil(X1)|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.49/4.78 cnf(i_0_76, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3))),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),X4),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X4)))). 4.49/4.78 cnf(i_0_2460, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3))),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Odrop(X1),X4),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X2)))). 4.49/4.78 cnf(i_0_5025, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4))|X4=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1))). 4.49/4.78 cnf(i_0_2375, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.78 cnf(i_0_706, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.78 cnf(i_0_5618, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3)))). 4.49/4.78 cnf(i_0_2826, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3)))). 4.49/4.78 cnf(i_0_132, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X4))|c_Groups_Ozero__class_Ozero(X1)=X4|~class_Divides_Osemiring__div(X1))). 4.49/4.78 cnf(i_0_6224, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2)))). 4.49/4.78 cnf(i_0_6174, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X4))|X2=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X3)))). 4.49/4.78 cnf(i_0_4547, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3))|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Divides_Osemiring__div(X1))). 4.49/4.78 cnf(i_0_860, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),X1,hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1))),c_List_Olist_ONil(X1)),X2)=c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),X2)|~class_Orderings_Olinorder(X1))). 4.49/4.78 cnf(i_0_4578, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4)|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield(X1))). 4.49/4.78 cnf(i_0_4767, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Oimage(X2,X1,hAPP(hAPP(c_COMBB(X3,X1,X2),X4),X5)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X2,X3,X5),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))))). 4.49/4.78 cnf(i_0_1584, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBS(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Oord__class_Oless__eq(X2)),X3)),X4)))|~class_Orderings_Oorder(X2)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4)))). 4.49/4.78 cnf(i_0_7239, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5))=hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))). 4.49/4.78 cnf(i_0_5079, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5))=hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))). 4.49/4.78 cnf(i_0_1460, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4)|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Fields_Ofield(X1))). 4.49/4.78 cnf(i_0_6268, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk434_3(X3,X2,X1)),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3))))). 4.49/4.78 cnf(i_0_3715, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk253_4(X2,X3,X1,X4)),hAPP(c_List_Oset(X1),X3)))|hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.49/4.78 cnf(i_0_6601, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Oordered__ring__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_6600, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Oordered__ring__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.49/4.78 cnf(i_0_3686, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3)|c_Groups_Ozero__class_Ozero(X1)=X4|~class_Fields_Ofield__inverse__zero(X1))). 4.49/4.78 cnf(i_0_2930, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2)))). 4.49/4.78 cnf(i_0_1875, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk125_3(X3,X2,X1))),X2)),X3)))). 4.49/4.78 cnf(i_0_6975, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X5),X6),X4)|c_Divides_Odiv__class_Omod(X1,X3,X4)!=c_Divides_Odiv__class_Omod(X1,X6,X4)|c_Divides_Odiv__class_Omod(X1,X2,X4)!=c_Divides_Odiv__class_Omod(X1,X5,X4)|~class_Divides_Oring__div(X1))). 4.49/4.78 cnf(i_0_73, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2))|X2=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield(X1))). 4.49/4.78 cnf(i_0_6599, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Oordered__ring__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.49/4.78 cnf(i_0_6598, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Oordered__ring__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.49/4.78 cnf(i_0_1007, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_List_Oset(tc_prod(X1,X2)),X5)))|hAPP(c_Option_Ooption_OSome(X2),X4)!=hAPP(hAPP(c_Map_Omap__of(X1,X2),X5),X3))). 4.49/4.78 cnf(i_0_3291, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2))|X2=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield(X1))). 4.49/4.78 cnf(i_0_1307, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_6182, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X4))))). 4.49/4.78 cnf(i_0_3176, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),X6),X4)|c_Divides_Odiv__class_Omod(X1,X6,X4)!=c_Divides_Odiv__class_Omod(X1,X3,X4)|c_Divides_Odiv__class_Omod(X1,X2,X4)!=c_Divides_Odiv__class_Omod(X1,X5,X4)|~class_Divides_Osemiring__div(X1))). 4.49/4.78 cnf(i_0_2418, plain, (hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)),X5),X6)=hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),X5),X6)),X3),X4)|X3=X5)). 4.49/4.78 cnf(i_0_6140, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk428_3(X2,X3,X1)),esk429_3(X2,X3,X1))=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X3)),c_List_Olexord(X1,X2))))). 4.49/4.78 cnf(i_0_1057, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk71_3(X1,X2,X3)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk72_3(X1,X2,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3))))). 4.49/4.78 cnf(i_0_3725, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk255_3(X1,X2,X3)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk256_3(X1,X2,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3))))). 4.49/4.78 cnf(i_0_6183, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3))))). 4.49/4.78 cnf(i_0_5521, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.49/4.78 cnf(i_0_6672, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.49/4.78 cnf(i_0_2550, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X2))))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.49/4.78 cnf(i_0_3729, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk258_4(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3),X3,X2)),esk257_4(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3),X3,X2))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)=X2|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.49/4.78 cnf(i_0_6829, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel1(X1,X2)),c_List_Olistrel(X1,X3)))|~c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.49/4.78 cnf(i_0_162, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_Relation_Oconverse(X2,X1),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),X5)))). 4.49/4.78 cnf(i_0_5533, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.49/4.78 cnf(i_0_3510, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.49/4.78 cnf(i_0_6278, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk436_4(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3),X3,X2)),esk435_4(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3),X3,X2))=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)=X2|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.49/4.78 cnf(i_0_2262, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Nat_Onat),X1),X4)))|~hBOOL(hAPP(hAPP(c_member(X3),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)))). 4.49/4.78 cnf(i_0_1095, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk74_3(X3,X2,X1)),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk73_3(X3,X2,X1)),X2)))). 4.49/4.78 cnf(i_0_1874, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),X3),X4),X5)=hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,X3),X4),hAPP(c_List_Oset(X2),X5))|~c_Finite__Set_Ofun__left__comm__idem(X2,X1,X3))). 4.49/4.78 cnf(i_0_6490, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X3),X4)))|~c_Fun_Oinj__on(X1,X3,X5,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X3,X5),X2)),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)))). 4.49/4.78 cnf(i_0_7146, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X3))),X2)=c_List_Osublist(X1,X2,X3)|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.49/4.78 cnf(i_0_931, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),c_Orderings_Obot__class_Obot(X1)),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X4),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.78 cnf(i_0_7124, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X6),X4)|c_Divides_Odiv__class_Omod(X1,X6,X4)!=c_Divides_Odiv__class_Omod(X1,X3,X4)|c_Divides_Odiv__class_Omod(X1,X2,X4)!=c_Divides_Odiv__class_Omod(X1,X5,X4)|~class_Divides_Osemiring__div(X1))). 4.49/4.78 cnf(i_0_7515, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk536_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3)))=X1|epred2_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.78 cnf(i_0_5218, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_5220, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_4803, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_4802, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_7524, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk538_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3)))=X1|epred2_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.78 cnf(i_0_786, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),X3)|~class_Groups_Ocomm__monoid__add(X1)|~class_Groups_Ocomm__monoid__mult(X1))). 4.49/4.78 cnf(i_0_3888, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X1),X2),X3)|~class_Groups_Ocomm__monoid__add(X1)|~class_Groups_Ocomm__monoid__mult(X1))). 4.49/4.78 cnf(i_0_1733, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))). 4.49/4.78 cnf(i_0_474, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X3)|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2)))). 4.49/4.78 cnf(i_0_5622, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_2818, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_5620, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.49/4.78 cnf(i_0_2814, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.49/4.78 cnf(i_0_2023, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))). 4.49/4.78 cnf(i_0_1734, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))))). 4.49/4.78 cnf(i_0_7489, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X2,X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X3,X1,X2)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk532_3(X3,X1,X2))))). 4.49/4.78 cnf(i_0_1405, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X1),esk93_4(X2,X3,X1,X4)),X3))|hAPP(X2,X4)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_4315, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Ofilter(X2,X4),X5)))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))|~class_Groups_Omonoid__add(X1)|~hBOOL(hAPP(X4,esk295_5(X3,X4,X5,X2,X1))))). 4.49/4.78 cnf(i_0_7453, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,esk534_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X1)))). 4.49/4.78 cnf(i_0_7450, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,esk532_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X1)))). 4.49/4.78 cnf(i_0_6889, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))))). 4.49/4.78 cnf(i_0_6495, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Fields_Ofield__inverse__zero(X1))). 4.49/4.78 cnf(i_0_1888, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X3),X4))|c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X4|X3=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))|~c_Finite__Set_Ofolding__one__idem(X5,X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)))). 4.49/4.78 cnf(i_0_4286, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X4),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X4))))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X4),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.78 cnf(i_0_7151, plain, (hAPP(hAPP(X1,X2),esk506_7(X3,X4,X2,X5,X1,X6,X7))=X3|hBOOL(hAPP(hAPP(c_member(X7),X2),X4))|~c_Finite__Set_Ofun__left__comm(X7,X6,X1)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X6,X1,X5,hAPP(hAPP(c_Set_Oinsert(X7),X2),X4)),X3)))). 4.49/4.78 cnf(i_0_4314, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Ofilter(X2,X4),X5)))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))|hAPP(X3,esk295_5(X3,X4,X5,X2,X1))!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Omonoid__add(X1))). 4.49/4.78 cnf(i_0_2511, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))=c_Divides_OnegDivAlg(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.78 cnf(i_0_349, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X1,X1),c_Groups_Ouminus__class_Ouminus(X1)),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)))|~class_Groups_Oab__group__add(X1))). 4.49/4.78 cnf(i_0_2093, plain, (hAPP(hAPP(c_List_Oappend(X1),esk152_5(X2,X3,X4,X5,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),esk153_5(X2,X3,X4,X5,X1)))=X4|hAPP(c_List_Ofilter(X1,X5),X4)!=hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))). 4.49/4.78 cnf(i_0_7442, plain, (hAPP(hAPP(c_List_Oappend(X1),esk528_5(X2,X3,X4,X5,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),esk529_5(X2,X3,X4,X5,X1)))=X2|hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)!=hAPP(c_List_Ofilter(X1,X3),X2))). 4.49/4.78 cnf(i_0_1204, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1))))|~class_Rings_Olinordered__ring__strict(X2))). 4.49/4.78 cnf(i_0_2999, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2))))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.49/4.78 cnf(i_0_247, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),X4)))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1))),X4)),X2)))). 4.49/4.78 cnf(i_0_3000, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X2),X4),hAPP(c_Set_Oimage(X1,X3,X5),X6))|~c_Fun_Oinj__on(X1,X3,X5,X6)|~class_Groups_Ocomm__monoid__mult(X2))). 4.49/4.78 cnf(i_0_1203, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))|~class_Rings_Olinordered__ring__strict(X1))). 4.49/4.78 cnf(i_0_712, plain, (c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_Set_Oimage(X1,X1,X2),X3))=hAPP(X2,c_Big__Operators_Olinorder__class_OMin(X1,X3))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk49_3(X3,X2,X1))),hAPP(X2,esk50_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk49_3(X3,X2,X1)),esk50_3(X3,X2,X1)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_889, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_Set_Oimage(X1,X1,X2),X3))=hAPP(X2,c_Big__Operators_Olattice__class_OSup__fin(X1,X3))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X2,esk60_3(X3,X2,X1))),hAPP(X2,esk61_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),esk60_3(X3,X2,X1)),esk61_3(X3,X2,X1)))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_4597, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_Set_Oimage(X1,X1,X2),X3))=hAPP(X2,c_Big__Operators_Olattice__class_OInf__fin(X1,X3))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X2,esk323_3(X3,X2,X1))),hAPP(X2,esk324_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),esk323_3(X3,X2,X1)),esk324_3(X3,X2,X1)))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_3581, plain, (c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_Set_Oimage(X1,X1,X2),X3))=hAPP(X2,c_Big__Operators_Olinorder__class_OMax(X1,X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk241_3(X3,X2,X1))),hAPP(X2,esk242_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk241_3(X3,X2,X1)),esk242_3(X3,X2,X1)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_6047, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)))|hBOOL(hAPP(hAPP(c_member(X3),esk420_5(X5,X4,X3,X2,X1)),X4)))). 4.49/4.78 cnf(i_0_3559, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),X4)))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1))),X4)),X2)))). 4.49/4.78 cnf(i_0_1215, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X1),c_Int_Onat),X2)),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Int_Oint),X2),X3)|~c_Nat__Transfer_Ois__nat(hAPP(X2,esk80_3(X2,X3,X1))))). 4.49/4.78 cnf(i_0_1319, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X1),c_Int_Onat),X2)),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Int_Oint),X2),X3)|~c_Nat__Transfer_Ois__nat(hAPP(X2,esk88_3(X2,X3,X1))))). 4.49/4.78 cnf(i_0_2903, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))),hAPP(X2,hAPP(c_Nat_OSuc,X3)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)))|~class_Groups_Ocomm__monoid__add(X1))). 4.49/4.78 cnf(i_0_4506, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))=c_Divides_OposDivAlg(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.78 cnf(i_0_1051, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),X4)=c_Option_Ooption_ONone(X2)|hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)))))). 4.49/4.78 cnf(i_0_5634, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))=X3|hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)!=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3))). 4.49/4.78 cnf(i_0_6386, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X2)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.49/4.78 cnf(i_0_6583, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))|~class_Orderings_Oorder(X2)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBS(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X3)),X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4)))). 4.49/4.78 cnf(i_0_5009, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X4))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4))))|~c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))). 4.49/4.78 cnf(i_0_4628, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)),X5)=c_Option_Ooption_ONone(X2)|hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),X3)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))). 4.49/4.78 cnf(i_0_3929, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(c_Set_Oimage(X4,X1,X5),X6))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X2),X7),X6)|hAPP(X3,hAPP(X5,esk270_8(X3,X7,hAPP(c_Set_Oimage(X4,X1,X5),X6),X6,X5,X1,X4,X2)))!=hAPP(X7,esk270_8(X3,X7,hAPP(c_Set_Oimage(X4,X1,X5),X6),X6,X5,X1,X4,X2))|~c_Fun_Oinj__on(X4,X1,X5,X6)|~class_Groups_Ocomm__monoid__add(X2))). 4.49/4.78 cnf(i_0_3636, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Olist__update(X1,X4),X5),X6),hAPP(hAPP(c_List_Olist__update(X2,X7),X5),X8))|~c_List_Olist__all2(X1,X2,X3,X4,X7)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)))|~hBOOL(hAPP(hAPP(X3,X6),X8)))). 4.49/4.78 cnf(i_0_3329, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Olist__update(X1,X4),X5),X6),hAPP(hAPP(c_List_Olist__update(X2,X7),X5),X8))|~c_List_Olist__all2(X1,X2,X3,X4,X7)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X7)))|~hBOOL(hAPP(hAPP(X3,X6),X8)))). 4.49/4.78 cnf(i_0_6740, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X4))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))),X4)|~class_Int_Onumber__ring(X1))). 4.49/4.78 cnf(i_0_1371, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))),X4)|~class_Int_Onumber__ring(X1))). 4.49/4.78 cnf(i_0_7390, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))),X4)|~class_Int_Onumber__ring(X1))). 4.49/4.78 cnf(i_0_6648, plain, (hAPP(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(X5,hAPP(X1,X3)),hAPP(X1,X4))|~c_Finite__Set_Ofolding__image__simple__idem(X6,X2,X5,X7,X8,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.49/4.78 cnf(i_0_4434, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))),hAPP(X2,X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))|~class_Groups_Ocomm__monoid__add(X1))). 4.49/4.78 cnf(i_0_7150, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),esk506_7(X6,X5,X7,X4,X3,X2,X1)))|hBOOL(hAPP(hAPP(c_member(X1),X7),X5))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,hAPP(hAPP(c_Set_Oinsert(X1),X7),X5)),X6)))). 4.49/4.78 cnf(i_0_104, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk10_4(X2,X3,X4,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4)))). 4.49/4.78 cnf(i_0_105, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk10_4(X2,X3,X4,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3)))). 4.49/4.78 cnf(i_0_5919, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5)),X2),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5))))). 4.49/4.78 cnf(i_0_336, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X5),X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X6)))). 4.49/4.78 cnf(i_0_634, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5))|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.78 cnf(i_0_5131, plain, (c_List_Olist__all2(X1,X2,X3,X4,hAPP(hAPP(c_List_Omap(X5,X2),X6),X7))|~c_List_Olist__all2(X1,X5,hAPP(hAPP(c_COMBC(X1,tc_fun(X5,X2),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X5,X2),tc_fun(X5,tc_HOL_Obool)),X1),c_COMBB(X2,tc_HOL_Obool,X5)),X3)),X6),X4,X7))). 4.49/4.78 cnf(i_0_7302, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X4)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.78 cnf(i_0_4452, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X4)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.78 cnf(i_0_1989, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X2)))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_1428, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3),hAPP(c_Nat_OSuc,X4)))|~class_Groups_Ocomm__monoid__add(X1))). 4.49/4.78 cnf(i_0_3596, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.78 cnf(i_0_56, plain, (c_Wellfounded_Owf(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(esk4_2(X2,X1),hAPP(c_Nat_OSuc,X3))),hAPP(esk4_2(X2,X1),X3))),X2)))). 4.49/4.78 cnf(i_0_6179, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_4357, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),c_Orderings_Otop__class_Otop(X1)),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X4),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.78 cnf(i_0_3256, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,hAPP(hAPP(c_Set_Oinsert(X1),X5),X6)),hAPP(hAPP(X3,X5),X7)))|hBOOL(hAPP(hAPP(c_member(X1),X5),X6))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X6),X7)))). 4.49/4.78 cnf(i_0_4863, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X6))=hAPP(hAPP(c_List_Olist_OCons(X1),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X6))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(X3,X4)),hAPP(X3,X5))))). 4.49/4.78 cnf(i_0_2493, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk188_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk187_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.49/4.78 cnf(i_0_2644, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))))). 4.49/4.78 cnf(i_0_3542, plain, (hAPP(hAPP(c_List_Onth(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_OSuc,X3)))=hAPP(hAPP(c_List_Onth(X1),hAPP(c_List_Orev(X1),X2)),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.49/4.78 cnf(i_0_2419, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4))),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X4))))|hAPP(c_Set_Oimage(X2,X1,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.49/4.78 cnf(i_0_598, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.78 cnf(i_0_4376, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X1,X2)),X3))|~class_Enum_Oenum(X2)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_Enum_Oenum__class_Oenum__ex(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2))))))). 4.49/4.78 cnf(i_0_7337, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X1,X2)),X3))|~class_Enum_Oenum(X2)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_Enum_Oenum__class_Oenum__all(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2))))))). 4.49/4.78 cnf(i_0_167, plain, (hAPP(c_Option_Ooption_OSome(X1),X2)=hAPP(hAPP(c_Map_Omap__of(X3,X1),X4),X5)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X5),X2)),hAPP(c_List_Oset(tc_prod(X3,X1)),X4)))|~hBOOL(hAPP(c_List_Odistinct(X3),hAPP(hAPP(c_List_Omap(tc_prod(X3,X1),X3),c_Product__Type_Ofst(X3,X1)),X4))))). 4.49/4.78 cnf(i_0_2155, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X2,X1),X6),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X2),X5)))))). 4.49/4.78 cnf(i_0_332, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3)))). 4.49/4.78 cnf(i_0_4492, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X2)))). 4.49/4.78 cnf(i_0_3277, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X5)))). 4.49/4.78 cnf(i_0_3276, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2)))). 4.49/4.78 cnf(i_0_3586, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1),X4),X5)))|hBOOL(hAPP(hAPP(c_member(X3),esk243_5(X5,X4,X3,X2,X1)),X4))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.49/4.78 cnf(i_0_4938, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)))|hBOOL(hAPP(hAPP(c_member(X2),esk344_4(X3,X4,X2,X1)),X4))|~class_Rings_Olinordered__semidom(X1))). 4.49/4.78 cnf(i_0_6235, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk432_3(X3,X2,X1)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.49/4.78 cnf(i_0_6234, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk433_3(X3,X2,X1)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.49/4.78 cnf(i_0_3462, plain, (hAPP(c_Set_Oimage(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|hAPP(c_Set_Oimage(X3,X2,X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|hAPP(c_Set_Oimage(X1,X3,X5),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))). 4.49/4.78 cnf(i_0_2650, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1))). 4.49/4.78 cnf(i_0_6022, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)))|hBOOL(hAPP(hAPP(c_member(X2),esk416_4(X3,X4,X2,X1)),X4))|~class_Rings_Olinordered__semidom(X1))). 4.49/4.78 cnf(i_0_899, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),X4)),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk63_5(X5,X4,X3,X2,X1)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.49/4.78 cnf(i_0_1061, plain, (X1=X2|X3=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X4),hAPP(hAPP(c_List_Olist_OCons(X5),X1),c_List_Olist_ONil(X5)))),hAPP(hAPP(c_List_Oappend(X5),X3),hAPP(hAPP(c_List_Olist_OCons(X5),X2),c_List_Olist_ONil(X5))))),c_List_Olistrel1(X5,X6))))). 4.49/4.78 cnf(i_0_1588, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk107_4(X1,X4,X3,X2)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.49/4.78 cnf(i_0_6522, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk451_4(X1,X4,X3,X2)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.49/4.78 cnf(i_0_392, plain, (hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.78 cnf(i_0_1510, plain, (hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.78 cnf(i_0_6787, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X1),X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_6893, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))=c_Groups_Oone__class_Oone(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.78 cnf(i_0_1578, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),X3))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk105_4(X3,X4,X2,X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X3)))). 4.49/4.78 cnf(i_0_2766, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),X3))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk198_4(X3,X4,X2,X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)))). 4.49/4.78 cnf(i_0_916, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X2))|hAPP(c_Finite__Set_Ocard(X1),esk64_3(X3,X2,X1))!=X3|esk66_3(X3,X2,X1)!=esk65_3(X3,X2,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))))). 4.49/4.78 cnf(i_0_3848, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)))|hBOOL(hAPP(hAPP(c_member(X2),esk265_4(X4,X1,X3,X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.49/4.78 cnf(i_0_235, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),hAPP(hAPP(c_List_Omap(X1,X2),X4),X3))),X5)=hAPP(c_Option_Ooption_OSome(X2),hAPP(X4,X5))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),X3))))). 4.49/4.78 cnf(i_0_6977, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)))|hBOOL(hAPP(hAPP(c_member(X2),esk483_4(X4,X1,X3,X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.49/4.78 cnf(i_0_7486, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X2,X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X3,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X3,X1,X2)),X1)))). 4.49/4.78 cnf(i_0_6627, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4))))). 4.49/4.78 cnf(i_0_6774, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),hAPP(hAPP(c_List_Onth(X1),X2),X4)))|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)))). 4.49/4.78 cnf(i_0_2724, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)=c_List_Olist_ONil(X1)|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk195_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))))). 4.49/4.78 cnf(i_0_4380, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.78 cnf(i_0_3731, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk257_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.78 cnf(i_0_5140, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)=c_List_Olist_ONil(X1)|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk357_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))))). 4.49/4.78 cnf(i_0_5496, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)))|hBOOL(hAPP(hAPP(c_member(X1),esk383_4(X4,X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_5, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),esk2_2(X2,X1))),hAPP(c_List_Oset(X1),esk3_2(X2,X1)))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(X1),esk1_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 4.49/4.78 cnf(i_0_7478, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,esk534_3(X1,X2,X3))))). 4.49/4.78 cnf(i_0_980, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2)|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1))). 4.49/4.78 cnf(i_0_2705, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Int_Onat)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2)|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1))). 4.49/4.78 cnf(i_0_4319, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.49/4.78 cnf(i_0_1103, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.49/4.78 cnf(i_0_6280, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk435_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.78 cnf(i_0_7475, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,esk532_3(X1,X2,X3))))). 4.49/4.78 cnf(i_0_4760, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Finite__Set_Ofold1(X2,c_Orderings_Oord__class_Omin(X2)),X1)),X3))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_member(X2),X4),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.49/4.78 cnf(i_0_3104, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.49/4.78 cnf(i_0_6265, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),X1)=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1)))). 4.49/4.78 cnf(i_0_1950, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)))|hBOOL(hAPP(hAPP(c_member(X3),esk138_5(X5,X4,X3,X2,X1)),X4)))). 4.49/4.78 cnf(i_0_153, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_4807, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_5221, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_5219, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_2216, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk164_5(X5,X4,X3,X2,X1)),X3)))). 4.49/4.78 cnf(i_0_5134, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X4,X5))=hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X6),X3),X5))|hBOOL(hAPP(hAPP(c_member(X6),X3),X5))|~c_Finite__Set_Ofolding__image__simple(X7,X6,X1,X8,X2,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X5)))). 4.49/4.78 cnf(i_0_5300, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1)=X3|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)))). 4.49/4.78 cnf(i_0_7512, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk536_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3)))=X1|epred2_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk538_3(X1,X2,X3))))). 4.49/4.78 cnf(i_0_4808, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_6886, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk476_3(X1,X2,X3)),esk475_3(X1,X2,X3))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)=X2|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.49/4.78 cnf(i_0_106, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk14_3(X1,X2,X3)),esk13_3(X1,X2,X3))=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)=X2|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.49/4.78 cnf(i_0_7509, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk538_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3)))=X1|epred2_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk536_3(X1,X2,X3)),X2)))). 4.49/4.78 cnf(i_0_3351, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1))). 4.49/4.78 cnf(i_0_1493, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,X1,tc_Nat_Onat),X2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X2),X3)|~class_Groups_Ocomm__monoid__add(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~c_Nat__Transfer_Onat__set(X3))). 4.49/4.78 cnf(i_0_5580, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,X1,tc_Nat_Onat),X2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X1),X2),X3)|~class_Groups_Ocomm__monoid__add(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~c_Nat__Transfer_Onat__set(X3))). 4.49/4.78 cnf(i_0_4048, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1)))). 4.49/4.78 cnf(i_0_5624, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.49/4.78 cnf(i_0_2816, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.49/4.78 cnf(i_0_5222, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_4804, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_1693, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X2),X4)),X5))=hAPP(hAPP(c_Set_Oinsert(X2),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X3)))). 4.49/4.78 cnf(i_0_2905, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|X2=X3|~c_Equiv__Relations_Oequiv(X1,X4,X5)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X4),X5))))). 4.49/4.78 cnf(i_0_803, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)))),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1))). 4.49/4.78 cnf(i_0_489, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),X2),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))|~class_Groups_Ocomm__monoid__add(X1))). 4.49/4.78 cnf(i_0_5623, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_2819, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_5621, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.49/4.78 cnf(i_0_2815, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.49/4.78 cnf(i_0_5234, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_2002, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3),X4))|~class_Groups_Ocomm__monoid__add(X1))). 4.49/4.78 cnf(i_0_2708, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))),c_Divides_Odiv__class_Omod(X1,X3,X2))),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)|~class_Divides_Osemiring__div(X1))). 4.49/4.78 cnf(i_0_6581, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBS(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X3)),X4))))|~class_Orderings_Oorder(X2)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4)))). 4.49/4.78 cnf(i_0_1771, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Finite__Set_Ofold1(X2,c_Orderings_Oord__class_Omin(X2)),X3)),hAPP(c_Finite__Set_Ofold1(X2,c_Orderings_Oord__class_Omin(X2)),X1)))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.49/4.78 cnf(i_0_7464, plain, (epred1_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X3,X2,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk532_3(X3,X2,X1)))|~hBOOL(hAPP(X1,X3)))). 4.49/4.78 cnf(i_0_5054, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.49/4.78 cnf(i_0_4569, plain, (hAPP(hAPP(c_List_Olist__update(X1,X2),esk322_4(X3,X4,X2,X1)),esk321_4(X3,X4,X2,X1))=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel1(X1,X3))))). 4.49/4.78 cnf(i_0_99, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk12_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(X2,esk11_4(X2,X3,X4,X1))))). 4.49/4.78 cnf(i_0_100, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk11_4(X2,X3,X4,X1)),X3))|hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(X2,esk12_4(X2,X3,X4,X1))))). 4.49/4.78 cnf(i_0_35, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),X3)),c_Divides_Odiv__class_Omod(X1,X2,X3))),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)|~class_Divides_Osemiring__div(X1))). 4.49/4.78 cnf(i_0_3988, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk272_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))|hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.49/4.78 cnf(i_0_4905, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Oone__class_Oone(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X3)))). 4.49/4.78 cnf(i_0_7000, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Oone__class_Oone(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)))). 4.49/4.78 cnf(i_0_6395, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),X2)))))). 4.49/4.78 cnf(i_0_1266, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),X5)=hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X6,c_Fun_Oid(X3)),X5)|hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X3),X5))!=hAPP(X6,hAPP(c_Product__Type_Ofst(X1,X3),X5)))). 4.49/4.78 cnf(i_0_6130, plain, (hAPP(c_Product__Type_Omap__pair(X1,X1,X2,X3,c_Fun_Oid(X1),X4),X5)=hAPP(c_Product__Type_Omap__pair(X1,X1,X2,X3,c_Fun_Oid(X1),X6),X5)|hAPP(X4,hAPP(c_Product__Type_Osnd(X1,X2),X5))!=hAPP(X6,hAPP(c_Product__Type_Osnd(X1,X2),X5)))). 4.49/4.78 cnf(i_0_19, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.49/4.78 cnf(i_0_4882, plain, (hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3)),X4),X5)=hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X4),X5)),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.49/4.78 cnf(i_0_131, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk15_6(X2,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X4),X5),X4,X5,X1,X3)),X5))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(X4,X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X4),X5)))|~class_Groups_Oordered__ab__group__add(X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.78 cnf(i_0_7461, plain, (epred1_3(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X3,X2,X1)),X2))|~hBOOL(hAPP(X1,X3)))). 4.49/4.78 cnf(i_0_5642, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk389_4(X3,X1,X4,X2)),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),X4)),hAPP(c_Finite__Set_Ocard(X1),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_4060, plain, (hAPP(hAPP(c_List_Onth(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)))=hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Oappend(X1),X4),X2)),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4))))). 4.49/4.78 cnf(i_0_4941, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2))))). 4.49/4.78 cnf(i_0_4327, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2))))). 4.49/4.78 cnf(i_0_2294, plain, (hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),c_List_Olist_ONil(tc_Nat_Onat)))=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.49/4.78 cnf(i_0_6896, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X4,X5))=hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X4,X5)),hAPP(X2,X3))|~c_Finite__Set_Ofolding(X6,X1,X2,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X5)))). 4.49/4.78 cnf(i_0_6481, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk445_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk444_2(X1,X2)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,esk443_2(X1,X2)))|~hBOOL(hAPP(X1,X3)))). 4.49/4.78 cnf(i_0_7431, plain, (hAPP(hAPP(c_List_Otake(X1),X2),X3)=hAPP(hAPP(c_List_Otake(X1),X2),X4)|hAPP(hAPP(c_List_Onth(X1),X3),esk527_4(X3,X4,X1,X2))!=hAPP(hAPP(c_List_Onth(X1),X4),esk527_4(X3,X4,X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.49/4.78 cnf(i_0_893, plain, (c_List_OtakeWhile(X1,X2,X3)=hAPP(hAPP(c_List_Otake(X1),X4),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk62_4(X2,X3,X1,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),X4))))). 4.49/4.78 cnf(i_0_1831, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1))))). 4.49/4.78 cnf(i_0_4494, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1))))). 4.49/4.78 cnf(i_0_4766, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)))))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.49/4.78 cnf(i_0_4809, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_75, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X2),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X4),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk9_5(X2,X4,X3,X3,X1)))|~class_Groups_Ocomm__monoid__add(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~c_Nat__Transfer_Onat__set(X3))). 4.49/4.78 cnf(i_0_7307, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X1),X2),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X1),X4),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk518_5(X2,X4,X3,X3,X1)))|~class_Groups_Ocomm__monoid__add(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~c_Nat__Transfer_Onat__set(X3))). 4.49/4.78 cnf(i_0_2968, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)))),X3))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.49/4.78 cnf(i_0_3749, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X4,X2)),hAPP(X4,X3))))). 4.49/4.78 cnf(i_0_5223, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_633, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk43_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X1,X3,X4)),c_List_Olist_Olist__size(X1,X2,X4))))). 4.49/4.78 cnf(i_0_3381, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X4))))). 4.49/4.78 cnf(i_0_5908, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))=c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3)|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_756, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_3607, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1))). 4.49/4.78 cnf(i_0_444, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1))). 4.49/4.78 cnf(i_0_2922, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))|hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2)))). 4.49/4.78 cnf(i_0_5302, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1)=X3|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)))). 4.49/4.78 cnf(i_0_2486, plain, (hAPP(c_Lazy__Sequence_Obind(X1,X2,hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X4),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)),X5),X4))=hAPP(c_New__DSequence_Opos__decr__bind(X1,X2,X3,X5),X4)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X4)). 4.49/4.78 cnf(i_0_1299, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=hAPP(c_Finite__Set_Ocard(X3),X4)|~c_Fun_Oinj__on(X3,X1,X5,X4)|~c_Fun_Oinj__on(X1,X3,X6,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X3,X6),X2)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X1,X5),X4)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_3366, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X2,X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3),X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)))). 4.49/4.78 cnf(i_0_6789, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X4),X5)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X5),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.78 cnf(i_0_2513, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X4),X5)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X5),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.78 cnf(i_0_1511, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)|hBOOL(hAPP(X2,X3)))). 4.49/4.78 cnf(i_0_3328, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),X2),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4)))),X5)=hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X3))))). 4.49/4.78 cnf(i_0_543, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X6)))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(X6,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5)))). 4.49/4.78 cnf(i_0_6673, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),X1)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.49/4.78 cnf(i_0_7495, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.78 cnf(i_0_4570, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk322_4(X1,X2,X3,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X3),X2)),c_List_Olistrel1(X4,X1))))). 4.49/4.78 cnf(i_0_159, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2),X4),hAPP(c_Set_Oimage(X1,X3,X5),X6))|~c_Fun_Oinj__on(X1,X3,X5,X6)|~class_Groups_Ocomm__monoid__add(X2))). 4.49/4.78 cnf(i_0_7482, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.78 cnf(i_0_5447, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X3),X4))|~c_Finite__Set_Ofolding__idem(X5,X1,X6,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)))). 4.49/4.78 cnf(i_0_2459, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X6),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X5),X3),X6))|~c_Finite__Set_Ofolding__image__simple(X7,X5,X1,X8,X2,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X6)))). 4.49/4.78 cnf(i_0_5235, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),hAPP(c_Set_Oimage(X4,X1,X5),X6))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X2),X7),X6)|hAPP(X7,esk365_8(X3,X7,hAPP(c_Set_Oimage(X4,X1,X5),X6),X6,X5,X1,X4,X2))!=hAPP(X3,hAPP(X5,esk365_8(X3,X7,hAPP(c_Set_Oimage(X4,X1,X5),X6),X6,X5,X1,X4,X2)))|~c_Fun_Oinj__on(X4,X1,X5,X6)|~class_Groups_Ocomm__monoid__mult(X2))). 4.49/4.78 cnf(i_0_7519, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk538_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3)))=X1|epred2_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk536_3(X1,X2,X3))))). 4.49/4.78 cnf(i_0_3404, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),X4)=c_Groups_Oone__class_Oone(X1)|hBOOL(hAPP(hAPP(c_member(X2),esk233_4(X3,X4,X2,X1)),X4))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.78 cnf(i_0_63, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk7_4(X3,X4,X1,X2)),esk8_4(X3,X4,X1,X2))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),X4),hAPP(c_Relation_Oconverse(X1,X2),X3))))). 4.49/4.78 cnf(i_0_6479, plain, (hBOOL(hAPP(X1,esk446_2(X1,X2)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk444_2(X1,X2)))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,esk443_2(X1,X2)))|~hBOOL(hAPP(X1,X3)))). 4.49/4.78 cnf(i_0_7513, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk536_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3)))=X1|epred2_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk538_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.78 cnf(i_0_4994, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X4)|hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|~class_Groups_Oab__group__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.78 cnf(i_0_220, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))|~class_Int_Onumber__ring(X1))). 4.49/4.78 cnf(i_0_5625, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.49/4.78 cnf(i_0_5593, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.49/4.78 cnf(i_0_1436, plain, (hAPP(X1,hAPP(c_Set_Oimage(X2,X2,X3),X4))=hAPP(X3,hAPP(X1,X4))|c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=X4|hAPP(hAPP(X5,hAPP(X3,esk94_5(X4,X3,X1,X5,X2))),hAPP(X3,esk95_5(X4,X3,X1,X5,X2)))!=hAPP(X3,hAPP(hAPP(X5,esk94_5(X4,X3,X1,X5,X2)),esk95_5(X4,X3,X1,X5,X2)))|~c_Finite__Set_Ofolding__one__idem(X2,X5,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.78 cnf(i_0_2450, plain, (c_Wellfounded_OwfP(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Predicate_ODomainP(X1,X1,hAPP(X3,esk185_3(X2,X3,X1)))),c_Predicate_ORangeP(X1,X1,hAPP(X3,esk186_3(X2,X3,X1))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~c_Wellfounded_OwfP(X1,hAPP(X3,esk184_3(X2,X3,X1))))). 4.49/4.78 cnf(i_0_2817, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.49/4.78 cnf(i_0_7406, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.49/4.78 cnf(i_0_1176, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)))). 4.49/4.78 cnf(i_0_1326, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hAPP(hAPP(c_List_Oappend(X1),X2),X4)!=hAPP(hAPP(c_List_Oappend(X1),X3),X5))). 4.49/4.78 cnf(i_0_4902, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),esk340_5(X3,X4,X5,X2,X1))=X4|hAPP(hAPP(c_List_Oappend(X1),X4),esk341_5(X3,X4,X5,X2,X1))=X2|hAPP(hAPP(c_List_Oappend(X1),X2),X5)!=hAPP(hAPP(c_List_Oappend(X1),X4),X3))). 4.49/4.78 cnf(i_0_4904, plain, (hAPP(hAPP(c_List_Oappend(X1),esk340_5(X2,X3,X4,X5,X1)),X2)=X4|hAPP(hAPP(c_List_Oappend(X1),X3),esk341_5(X2,X3,X4,X5,X1))=X5|hAPP(hAPP(c_List_Oappend(X1),X5),X4)!=hAPP(hAPP(c_List_Oappend(X1),X3),X2))). 4.49/4.78 cnf(i_0_3013, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))). 4.49/4.78 cnf(i_0_5209, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))). 4.49/4.78 cnf(i_0_1558, plain, (hAPP(c_Random_Opick(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X3),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X1),X4)))=hAPP(c_Random_Opick(X1,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X1)),X4),X2)),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X3),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X1),X4))))). 4.49/4.78 cnf(i_0_4901, plain, (hAPP(hAPP(c_List_Oappend(X1),esk341_5(X2,X3,X4,X5,X1)),X4)=X2|hAPP(hAPP(c_List_Oappend(X1),X5),esk340_5(X2,X3,X4,X5,X1))=X3|hAPP(hAPP(c_List_Oappend(X1),X3),X2)!=hAPP(hAPP(c_List_Oappend(X1),X5),X4))). 4.49/4.78 cnf(i_0_4903, plain, (hAPP(hAPP(c_List_Oappend(X1),esk341_5(X2,X3,X4,X5,X1)),X4)=X2|hAPP(hAPP(c_List_Oappend(X1),esk340_5(X2,X3,X4,X5,X1)),X2)=X4|hAPP(hAPP(c_List_Oappend(X1),X3),X2)!=hAPP(hAPP(c_List_Oappend(X1),X5),X4))). 4.49/4.78 cnf(i_0_4817, plain, (hAPP(hAPP(X1,esk333_7(X2,X3,X4,X5,X1,X6,X7)),esk334_7(X2,X3,X4,X5,X1,X6,X7))=hAPP(hAPP(X1,X3),X2)|c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))=X4|~c_Nitpick_Ofold__graph_H(X7,X6,X1,X5,X4,hAPP(hAPP(X1,X3),X2)))). 4.49/4.78 cnf(i_0_5810, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_List_Orev(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2),X3)|~class_Groups_Omonoid__add(X1))). 4.49/4.78 cnf(i_0_4307, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.49/4.78 cnf(i_0_6370, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))). 4.49/4.78 cnf(i_0_5392, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_Set_Oimage(X3,X1,X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X3),X6),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))))=hAPP(c_Set_Oimage(X3,X1,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X1),X4),X6),X2)),X5)|~hBOOL(hAPP(hAPP(c_member(X3),X6),X5)))). 4.49/4.78 cnf(i_0_6398, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBC(X2,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,tc_HOL_Obool),X2),c_fequal),X3)),hAPP(X4,X5))),X5)))|~class_Orderings_Olinorder(X1))). 4.49/4.78 cnf(i_0_6264, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),X1)=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)))). 4.49/4.78 cnf(i_0_1475, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.78 cnf(i_0_3695, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk249_6(X4,X3,X5,X6,X2,X1)),esk250_6(X4,X3,X5,X6,X2,X1))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X5,tc_fun(X1,tc_HOL_Obool)),X3),X4))))). 4.49/4.78 cnf(i_0_5717, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),hAPP(hAPP(X3,X6),X7)))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X7))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X5)))). 4.49/4.78 cnf(i_0_4816, plain, (hAPP(hAPP(X1,esk333_7(X2,X3,X4,X5,X1,X6,X7)),esk334_7(X2,X3,X4,X5,X1,X6,X7))=hAPP(hAPP(X1,X3),X2)|X5=hAPP(hAPP(X1,X3),X2)|~c_Nitpick_Ofold__graph_H(X7,X6,X1,X5,X4,hAPP(hAPP(X1,X3),X2)))). 4.49/4.78 cnf(i_0_2990, plain, (c_Relation_Orefl__on(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk209_5(X5,X4,X1,X3,X2)),X3)))). 4.49/4.78 cnf(i_0_7200, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))|hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X4)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))|hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))). 4.49/4.78 cnf(i_0_3823, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)),X4)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))|hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),X4)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))|hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X4)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))). 4.49/4.78 cnf(i_0_5978, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))=hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X4))|hAPP(c_Map_Omap__of(X1,X2),X3)!=hAPP(c_Map_Omap__of(X1,X2),X4))). 4.49/4.78 cnf(i_0_713, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X3))))=c_Groups_Oone__class_Oone(X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~class_Int_Onumber__ring(X1))). 4.49/4.78 cnf(i_0_4228, plain, (hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5))|hBOOL(hAPP(hAPP(c_member(X1),X6),X7))|hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)!=hAPP(hAPP(c_Set_Oinsert(X1),X6),X7)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,X6,X7),X5)))). 4.49/4.78 cnf(i_0_3518, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk237_5(X2,X3,X4,X1,X5)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4)))). 4.49/4.78 cnf(i_0_2380, plain, (c_List_Olinorder__class_Oinsort__insert__key(X1,X2,X3,X4,X5)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),X5)|hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X4)),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_List_Oset(X1),X5))))|~class_Orderings_Olinorder(X2))). 4.49/4.78 cnf(i_0_7470, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X3,X1)))). 4.49/4.78 cnf(i_0_5466, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1)),X2)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X1),X3))=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X1))))). 4.49/4.78 cnf(i_0_3817, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))),hAPP(X6,X5))=hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X3),X5),X4))|~c_Finite__Set_Ofolding(X3,X1,X6,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)))). 4.49/4.78 cnf(i_0_5675, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Oone__class_Oone(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.49/4.78 cnf(i_0_2091, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)))=hAPP(hAPP(c_List_Olist_OCons(X1),X4),hAPP(c_List_Ofilter(X1,X2),X5))|hBOOL(hAPP(X2,esk154_7(hAPP(c_List_Ofilter(X1,X2),X5),X4,hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)),X2,X1,X3,X5)))|~hBOOL(hAPP(X2,X4)))). 4.49/4.78 cnf(i_0_7457, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X3,X1)))). 4.49/4.78 cnf(i_0_2455, plain, (hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Orderings_Oord__class_Omax(X1)),X2),hAPP(c_List_Orev(X1),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_List_Onth(X1),X3),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)|X3=c_List_Olist_ONil(X1)|~c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Orev(X1),X3))|~class_Orderings_Olinorder(X1))). 4.49/4.78 cnf(i_0_1197, plain, (hAPP(X1,esk79_4(X2,X1,X3,X4))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk78_4(X2,X1,X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)))). 4.49/4.78 cnf(i_0_1194, plain, (hAPP(X1,esk79_4(X2,X1,X3,X4))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk78_4(X2,X1,X3,X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)))). 4.49/4.78 cnf(i_0_6390, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X4,X5))=hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X6),X5),X3))|hBOOL(hAPP(hAPP(c_member(X6),X5),X3))|~c_Finite__Set_Ofolding(X6,X1,X4,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X3)))). 4.49/4.78 cnf(i_0_4533, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),X6))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X5),X4)),X6)|~c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.49/4.78 cnf(i_0_6576, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),X6))=hAPP(hAPP(X3,X5),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),X6))|~c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.49/4.78 cnf(i_0_7437, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)))=hAPP(hAPP(c_List_Olist_OCons(X1),X4),hAPP(c_List_Ofilter(X1,X2),X5))|hBOOL(hAPP(X2,esk530_6(hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)),X2,hAPP(c_List_Ofilter(X1,X2),X5),X4,X1,X3)))|~hBOOL(hAPP(X2,X4)))). 4.49/4.78 cnf(i_0_1196, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk79_4(X2,X3,X4,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk78_4(X2,X3,X4,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X4)))). 4.49/4.78 cnf(i_0_7432, plain, (hAPP(hAPP(c_List_Otake(X1),X2),X3)=hAPP(hAPP(c_List_Otake(X1),X2),X4)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk527_4(X3,X4,X1,X2)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.49/4.78 cnf(i_0_1195, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk78_4(X1,X2,X3,X4)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk79_4(X1,X2,X3,X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X4)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)))). 4.49/4.78 cnf(i_0_1980, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),X2)),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.78 cnf(i_0_1133, plain, (c_FunDef_Oreduction__pair(X1,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2)))). 4.49/4.78 cnf(i_0_2210, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_2118, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),esk156_3(X2,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.78 cnf(i_0_357, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk28_3(X2,X1,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.49/4.78 cnf(i_0_5567, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2)),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X3))=hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Oab__semigroup__idem__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_4876, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Fun_Oinj__on(X3,X4,X5,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X3,tc_HOL_Obool)),X2),X6))|hBOOL(hAPP(hAPP(c_member(X1),esk339_6(X6,X5,X4,X3,X1,X2)),X2)))). 4.49/4.78 cnf(i_0_635, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),hAPP(hAPP(c_List_Onth(X1),X2),X4)))|~c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Orev(X1),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X3)))). 4.49/4.78 cnf(i_0_2386, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk180_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(X2,esk179_4(X2,X3,X4,X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(X2,X5)))). 4.49/4.78 cnf(i_0_2389, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk179_4(X2,X3,X4,X1)),X3))|hBOOL(hAPP(X2,esk180_4(X2,X3,X4,X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(X2,X5)))). 4.49/4.78 cnf(i_0_7177, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X6))),c_List_Olistrel1(X3,X4))))). 4.49/4.78 cnf(i_0_2317, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),c_Transitive__Closure_Ortrancl(X1,X4)))|~c_Wellfounded_Owf(X1,X4))). 4.49/4.78 cnf(i_0_4108, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3,X1,hAPP(c_Relation_Oconverse(X1,X3),X4)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),X5)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X3,X4),X2)),X5)))). 4.49/4.78 cnf(i_0_2934, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),hAPP(c_Groups_Otimes__class_Otimes(X1),X3)),X4)),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X4),X5)))|~class_Rings_Osemiring__0(X1))). 4.49/4.78 cnf(i_0_5712, plain, (hAPP(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(X5,hAPP(X1,X3)),hAPP(X1,X4))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~c_Finite__Set_Ofolding__image__simple(X6,X2,X5,X7,X8,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.49/4.78 cnf(i_0_1066, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X6),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=hAPP(X4,X6)|~c_Finite__Set_Ofolding__image__simple(X7,X5,X1,X8,X2,X4)|~hBOOL(hAPP(hAPP(c_member(X5),X3),X6))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X6)))). 4.49/4.78 cnf(i_0_2056, plain, (c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),c_Transitive__Closure_Ortrancl(X1,X4)))|~c_Wellfounded_Oacyclic(X1,X4))). 4.49/4.78 cnf(i_0_2697, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X6))),c_List_Olex(X3,X4))))). 4.49/4.78 cnf(i_0_4608, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X6))),c_List_Olexord(X3,X4))))). 4.49/4.78 cnf(i_0_6927, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(X2,X3),X4)),hAPP(c_Set_Oimage(tc_prod(X5,X6),X1,hAPP(c_Product__Type_Oprod_Oprod__case(X5,X6,X1),X2)),X7)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X6)),hAPP(hAPP(c_Product__Type_OPair(X5,X6),X3),X4)),X7)))). 4.49/4.78 cnf(i_0_894, plain, (c_List_OtakeWhile(X1,X2,X3)=hAPP(hAPP(c_List_Otake(X1),X4),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk62_4(X2,X3,X1,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.49/4.78 cnf(i_0_1717, plain, (hAPP(hAPP(c_List_Onth(X1),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))=hAPP(c_List_Ohd(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X2))|c_List_Olist_ONil(X1)=X2)). 4.49/4.78 cnf(i_0_5122, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~class_Int_Onumber__ring(X1))). 4.49/4.78 cnf(i_0_788, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.49/4.78 cnf(i_0_2245, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))|~class_Int_Onumber__ring(X1))). 4.49/4.78 cnf(i_0_3930, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X2),X6),hAPP(c_Set_Oimage(X1,X5,X7),X4))|hBOOL(hAPP(hAPP(c_member(X1),esk270_8(X6,X3,hAPP(c_Set_Oimage(X1,X5,X7),X4),X4,X7,X5,X1,X2)),X4))|~c_Fun_Oinj__on(X1,X5,X7,X4)|~class_Groups_Ocomm__monoid__add(X2))). 4.49/4.78 cnf(i_0_3353, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(X1),esk228_3(X3,X2,X1)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_6537, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(X1),esk454_3(X3,X2,X1)),X2))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_7138, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(X1),esk503_3(X3,X2,X1)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_3623, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.49/4.78 cnf(i_0_5236, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X2),X6),hAPP(c_Set_Oimage(X1,X5,X7),X4))|hBOOL(hAPP(hAPP(c_member(X1),esk365_8(X6,X3,hAPP(c_Set_Oimage(X1,X5,X7),X4),X4,X7,X5,X1,X2)),X4))|~c_Fun_Oinj__on(X1,X5,X7,X4)|~class_Groups_Ocomm__monoid__mult(X2))). 4.49/4.78 cnf(i_0_2197, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__sup__class_Osup(X1)),X3)),c_Orderings_Obot__class_Obot(X1)),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),hAPP(c_List_Oset(X2),X4)),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.49/4.78 cnf(i_0_108, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk13_3(X3,X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.78 cnf(i_0_6888, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk475_3(X3,X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.78 cnf(i_0_7490, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk532_3(X1,X2,X3))))). 4.49/4.78 cnf(i_0_1254, plain, (hAPP(c_Random_Opick(X1,hAPP(hAPP(c_List_Omap(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,X1)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X3))=hAPP(hAPP(c_List_Onth(X1),X2),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.49/4.78 cnf(i_0_3527, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),hAPP(hAPP(c_List_Onth(X1),X3),X2)),c_List_Olist_ONil(X1)))=hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X2)),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.49/4.78 cnf(i_0_7481, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X1,X2,X3)),X2)))). 4.49/4.78 cnf(i_0_4986, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk350_4(X4,X1,X3,X2)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.49/4.78 cnf(i_0_4235, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk291_4(X4,X3,X2,X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)))). 4.49/4.78 cnf(i_0_3438, plain, (hAPP(X1,X2)=hAPP(X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X1),X5)))))). 4.49/4.78 cnf(i_0_1341, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk89_3(X2,X3,X1)),esk89_3(X2,X3,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olexord(X1,X3))))). 4.49/4.78 cnf(i_0_7102, plain, (hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X1,tc_prod(X2,X1)),hAPP(X3,X4)),c_Random_Oiterate(X2,X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X5),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X3))=hAPP(c_Random_Oiterate(X2,X1,X5,X3),X4)|X5=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 4.49/4.78 cnf(i_0_4603, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X5)=hAPP(X5,X4)|~c_Equiv__Relations_Ocongruent(X1,tc_fun(X2,tc_HOL_Obool),X3,X5)|~c_Equiv__Relations_Oequiv(X1,X6,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X6)))). 4.49/4.78 cnf(i_0_3689, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X2)),X3)))=hAPP(hAPP(c_List_Olist__update(X1,X3),X2),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.49/4.78 cnf(i_0_6964, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X4),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X1),X5))),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X1),X5))))|~hBOOL(hAPP(hAPP(c_member(X4),X6),X5)))). 4.49/4.78 cnf(i_0_6607, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),X3),hAPP(c_Option_Ooption_OSome(X2),esk457_4(X3,X4,X2,X1)))=X4|c_Map_Odom(X1,X2,X4)!=hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 4.49/4.78 cnf(i_0_7426, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X4)))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk526_4(X3,X2,X4,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.78 cnf(i_0_5246, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X4)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk366_4(X3,X2,X4,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.78 cnf(i_0_7399, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X4)))). 4.49/4.78 cnf(i_0_1251, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X3)))). 4.49/4.78 cnf(i_0_3067, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))),hAPP(X6,X5))=hAPP(X2,X4)|~c_Finite__Set_Ofolding(X3,X1,X6,X2)|~hBOOL(hAPP(hAPP(c_member(X3),X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)))). 4.49/4.78 cnf(i_0_954, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))))|~class_Lattices_Olattice(X1))). 4.49/4.78 cnf(i_0_1973, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))))|~class_Orderings_Olinorder(X1))). 4.49/4.78 cnf(i_0_289, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))|~class_Int_Onumber(X1)|~class_Rings_Oring(X1))). 4.49/4.78 cnf(i_0_5998, plain, (c_List_OtakeWhile(X1,X2,X3)=hAPP(c_List_Ofilter(X1,X2),X3)|hBOOL(hAPP(hAPP(c_member(X1),esk413_3(X3,X2,X1)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)))))). 4.49/4.78 cnf(i_0_7192, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X2)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk508_4(X2,X4,X3,X1)),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_5602, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk388_4(X2,X4,X3,X1)),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_2284, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.49/4.78 cnf(i_0_1241, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3)),c_Orderings_Otop__class_Otop(X1)),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),hAPP(c_List_Oset(X2),X4)),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.49/4.78 cnf(i_0_631, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))))|~class_Lattices_Olattice(X1))). 4.49/4.78 cnf(i_0_4137, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))))|~class_Orderings_Olinorder(X1))). 4.49/4.78 cnf(i_0_1324, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4)),X5)|hAPP(hAPP(c_List_Oappend(X2),X3),X1)!=hAPP(hAPP(c_List_Oappend(X2),X4),X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))))). 4.49/4.78 cnf(i_0_6002, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X5),X4)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~c_Fun_Oinj__on(X2,X1,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5)))). 4.49/4.78 cnf(i_0_6263, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)),X1)=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1)))). 4.49/4.78 cnf(i_0_6105, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~c_Nitpick_Oless__eq__frac(X1,X2,X3))). 4.49/4.78 cnf(i_0_7291, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3)))). 4.49/4.78 cnf(i_0_4521, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3)))). 4.49/4.78 cnf(i_0_2327, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),esk172_3(X3,X1,X2)),hAPP(c_List_Oset(tc_prod(X3,X3)),hAPP(hAPP(c_List_Ozip(X3,X3),X2),X1))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2))). 4.49/4.78 cnf(i_0_2617, plain, (hAPP(hAPP(X1,X2),X3)=hAPP(hAPP(X1,X4),X5)|~c_Equiv__Relations_Ocongruent2(X6,X7,X8,X9,X10,X1)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X5)),X10))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X2),X4)),X9)))). 4.49/4.78 cnf(i_0_77, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~c_Nitpick_Oless__frac(X1,X2,X3))). 4.49/4.78 cnf(i_0_6908, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)|~class_Rings_Osemiring(X1))). 4.49/4.78 cnf(i_0_1432, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))=hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X2),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)))). 4.49/4.78 cnf(i_0_1253, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),c_Map_Omap__add(X2,X1,X3,hAPP(c_Map_Omap__of(X2,X1),X4))),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))))). 4.49/4.78 cnf(i_0_3876, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))|~class_Rings_Osemiring(X1)|~class_Int_Onumber(X1))). 4.49/4.78 cnf(i_0_7465, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk532_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X1)))). 4.49/4.78 cnf(i_0_2194, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)))|hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X3,X4),X5)))). 4.49/4.78 cnf(i_0_1224, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.49/4.78 cnf(i_0_4040, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.49/4.78 cnf(i_0_4047, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1)))). 4.49/4.78 cnf(i_0_7456, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk534_3(X1,X2,X3)),X2))|~hBOOL(hAPP(X3,X1)))). 4.49/4.78 cnf(i_0_4498, plain, (hAPP(c_List_Oset(tc_prod(X1,X2)),X3)=hAPP(c_List_Oset(tc_prod(X1,X2)),X4)|hAPP(c_Map_Omap__of(X1,X2),X3)!=hAPP(c_Map_Omap__of(X1,X2),X4)|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4)))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))))). 4.49/4.78 cnf(i_0_4823, plain, (c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,X5,hAPP(hAPP(X3,X6),X7))|hAPP(hAPP(X3,X8),X9)!=hAPP(hAPP(X3,X6),X7)|~c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X8),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X9)|~hBOOL(hAPP(hAPP(c_member(X1),X8),X5)))). 4.49/4.78 cnf(i_0_1286, plain, (hAPP(c_Finite__Set_Ocard(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_Nat_Onat,X1),c_Finite__Set_Ocard(X2)),X4)),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),hAPP(X4,esk86_4(X4,X2,X3,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_1216, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X1),c_Int_Onat),X2)),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Int_Oint),X2),X3)|hBOOL(hAPP(hAPP(c_member(X1),esk80_3(X2,X3,X1)),X3)))). 4.49/4.78 cnf(i_0_572, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2)))). 4.49/4.78 cnf(i_0_4308, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))=hAPP(c_fequal,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)))). 4.49/4.78 cnf(i_0_4049, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)))). 4.49/4.78 cnf(i_0_3412, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X4)),hAPP(X2,X3))|~c_Finite__Set_Ofolding(X5,X1,X6,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)))). 4.49/4.78 cnf(i_0_6931, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4))))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk480_3(X3,X1,X4)),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(X1,X2)))). 4.49/4.78 cnf(i_0_6373, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4))))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),esk442_3(X3,X1,X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(X1,X2)))). 4.49/4.78 cnf(i_0_7479, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X1,X2,X3))))). 4.49/4.78 cnf(i_0_6004, plain, (c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X5))),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),X4)))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Oinj__on(X1,X2,X3,X5))). 4.49/4.78 cnf(i_0_1297, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),hAPP(hAPP(c_List_Onth(X1),X3),X2)),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X2)),X3)))=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.49/4.78 cnf(i_0_2405, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X2,X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3)),X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4)))). 4.49/4.78 cnf(i_0_2114, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3)),X4)),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X3)))). 4.49/4.78 cnf(i_0_7485, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.78 cnf(i_0_6685, plain, (c_List_OtakeWhile(X1,hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(c_Orderings_Oord__class_Oless(X2),X3)),X4),X5)=hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(c_Orderings_Oord__class_Oless(X2),X3)),X4)),X5)|~c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Orev(X2),hAPP(hAPP(c_List_Omap(X1,X2),X4),X5)))|~class_Orderings_Olinorder(X2))). 4.49/4.78 cnf(i_0_4634, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Wellfounded_Omlex__prod(X1,X4,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X4,X2)),hAPP(X4,X3))))). 4.49/4.78 cnf(i_0_6498, plain, (hAPP(c_Option_Ooption_OSome(X1),esk448_5(X2,X3,X1,X4,X5))=hAPP(hAPP(c_Map_Omap__of(X5,X1),hAPP(hAPP(c_List_Ozip(X5,X1),X4),X3)),X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|~hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(c_List_Oset(X5),X4))))). 4.49/4.78 cnf(i_0_2502, plain, (c_Fun_Oinj__on(tc_prod(X1,X2),tc_prod(X3,X4),c_Product__Type_Omap__pair(X1,X3,X2,X4,X5,X6),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X7),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X8)))|~c_Fun_Oinj__on(X2,X4,X6,X8)|~c_Fun_Oinj__on(X1,X3,X5,X7))). 4.49/4.78 cnf(i_0_358, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk28_3(X2,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.49/4.78 cnf(i_0_2116, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk156_3(X2,X1,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.78 cnf(i_0_1780, plain, (c_HOL_OThe(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=c_Partial__Function_Oflat__lub(X1,X3,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))). 4.49/4.78 cnf(i_0_354, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3)),X4)),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X4)))). 4.49/4.78 cnf(i_0_1054, plain, (hAPP(X1,esk72_3(X2,X1,X3))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X1,hAPP(c_Nat_OSuc,esk71_3(X2,X1,X3)))),hAPP(X1,esk71_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3))))). 4.49/4.78 cnf(i_0_3722, plain, (hAPP(X1,esk256_3(X2,X1,X3))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X1,hAPP(c_Nat_OSuc,esk255_3(X2,X1,X3)))),hAPP(X1,esk255_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3))))). 4.49/4.78 cnf(i_0_7174, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X5),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.78 cnf(i_0_6458, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))|~class_Rings_Oordered__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.78 cnf(i_0_1620, plain, (c_Wellfounded_Oacyclic(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk110_2(X2,X1)),esk110_2(X2,X1))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))))). 4.49/4.78 cnf(i_0_6402, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.78 cnf(i_0_1116, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|hBOOL(hAPP(X2,X4))|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3))))). 4.49/4.78 cnf(i_0_961, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))=c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_4709, plain, (c_Wellfounded_Oacyclic(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk331_2(X2,X1)),esk331_2(X2,X1))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))))). 4.49/4.78 cnf(i_0_6592, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))|~class_Rings_Oordered__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.49/4.78 cnf(i_0_1108, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X5),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.49/4.78 cnf(i_0_478, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X5),X3)))). 4.49/4.78 cnf(i_0_3024, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.49/4.78 cnf(i_0_7068, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk494_6(X3,X4,X5,X2,X1,X6)),esk495_6(X3,X4,X5,X2,X1,X6))=X6|hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(X5,tc_HOL_Obool)),X3),X6))))). 4.49/4.78 cnf(i_0_3123, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_5903, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X5)))). 4.49/4.78 cnf(i_0_2842, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.49/4.78 cnf(i_0_734, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.49/4.78 cnf(i_0_492, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X3),X5))=hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~c_Relation_Osingle__valued(X1,X2,hAPP(c_Relation_Oconverse(X2,X1),X3)))). 4.49/4.78 cnf(i_0_248, plain, (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2))),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X3))))). 4.49/4.78 cnf(i_0_3560, plain, (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2))),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X3))))). 4.49/4.78 cnf(i_0_6374, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4))))|hBOOL(hAPP(X1,esk442_3(X3,X1,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(X1,X2)))). 4.49/4.78 cnf(i_0_6932, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4))))|hBOOL(hAPP(X1,esk480_3(X3,X1,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(X1,X2)))). 4.49/4.78 cnf(i_0_6377, plain, (hAPP(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(X5,hAPP(X1,X3)),hAPP(X1,X4))|c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=X4|X3=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~c_Finite__Set_Ofolding__one(X2,X5,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.49/4.78 cnf(i_0_5921, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X1,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X1,X3))=c_Smallcheck_Osmall_H(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)))). 4.49/4.78 cnf(i_0_1587, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk107_4(X1,X2,X3,X4)),esk106_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X4)))). 4.49/4.78 cnf(i_0_6521, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk451_4(X1,X2,X3,X4)),esk450_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X4)))). 4.49/4.78 cnf(i_0_2765, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk198_4(X1,X2,X3,X4)),esk197_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X1)))). 4.49/4.78 cnf(i_0_1577, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk105_4(X1,X2,X3,X4)),esk104_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X1)))). 4.49/4.78 cnf(i_0_7454, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk534_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X1)))). 4.49/4.78 cnf(i_0_1653, plain, (c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),X5))|hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X4)),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))))|~c_Fun_Oinj__on(X1,X2,X3,X5))). 4.49/4.78 cnf(i_0_2594, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X1,tc_Nat_Onat)),X4),X5))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X4,X2)),hAPP(X4,X3))))). 4.49/4.78 cnf(i_0_5387, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X3),X4)),X5)),X6)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X5)),X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X5)),X6)|~class_Rings_Oring(X2))). 4.49/4.78 cnf(i_0_475, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))),X3)|hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.49/4.78 cnf(i_0_7460, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|epred1_3(X3,X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk532_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X3,X1)))). 4.49/4.78 cnf(i_0_6922, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|esk479_5(X5,X4,X3,X2,X1)!=esk478_5(X5,X4,X3,X2,X1)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X5)))))). 4.49/4.78 cnf(i_0_6984, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|esk485_5(X5,X4,X3,X2,X1)!=esk484_5(X5,X4,X3,X2,X1)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X5)))))). 4.49/4.78 cnf(i_0_4044, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2))),c_Int_Ointrel)))). 4.49/4.78 cnf(i_0_3064, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.78 cnf(i_0_4031, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))),hAPP(X2,X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))|~class_Groups_Ocomm__monoid__add(X1))). 4.49/4.78 cnf(i_0_7115, plain, (c_Equiv__Relations_Ocongruent(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X2),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X1,X2),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X2,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X4))),X4)),esk500_4(X4,X3,X2,X1))))). 4.49/4.78 cnf(i_0_5923, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(X3),X1),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)),X5),hAPP(hAPP(c_Product__Type_OSigma(X3,X3),X4),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X3),X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,X5))))). 4.49/4.78 cnf(i_0_3814, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk263_3(X3,X2,X1)),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3)))))). 4.49/4.78 cnf(i_0_1882, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk126_5(X2,X3,X4,X5,X1)),esk127_5(X2,X3,X4,X5,X1))=X5|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel(X1,X2))))). 4.49/4.78 cnf(i_0_3418, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3))),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X1)))). 4.49/4.78 cnf(i_0_6758, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)),hAPP(X2,X4))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3)))). 4.49/4.78 cnf(i_0_6881, plain, (hAPP(hAPP(X1,X2),hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X4),X2),X5))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))|~c_Finite__Set_Ofolding__one(X4,X1,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.49/4.78 cnf(i_0_3435, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)=c_Int_OMin|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.78 cnf(i_0_5033, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),X6))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X5),X4)),X6)|hBOOL(hAPP(hAPP(c_member(X1),X5),X6))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.49/4.78 cnf(i_0_3385, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X1),c_Rings_Oinverse__class_Odivide(X2)),X3)),X4)),X5)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X5)),X4)|~class_Fields_Ofield(X2))). 4.49/4.78 cnf(i_0_4437, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk307_5(X2,X3,X4,X5,X1)),esk308_5(X2,X3,X4,X5,X1))=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)),X3)),c_List_Olistrel(X1,X2))))). 4.49/4.78 cnf(i_0_4094, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),c_Big__Operators_Olattice__class_OInf__fin(X2,X1)),X1))|~class_Lattices_Olattice(X2)|~hBOOL(hAPP(hAPP(c_member(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),esk278_2(X1,X2)),esk279_2(X1,X2))),hAPP(hAPP(c_Set_Oinsert(X2),esk278_2(X1,X2)),hAPP(hAPP(c_Set_Oinsert(X2),esk279_2(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.49/4.78 cnf(i_0_6358, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),X2))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),esk440_2(X2,X1)),esk441_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk440_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk441_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_4946, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2))),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Olist_OCons(X1),X3),hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2))),X4))|X2=X3)). 4.49/4.78 cnf(i_0_915, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X2))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk65_3(X3,X2,X1)),esk66_3(X3,X2,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(c_Finite__Set_Ocard(X1),esk64_3(X3,X2,X1))!=X3|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))))). 4.49/4.78 cnf(i_0_2761, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X4))),X3)|~class_Int_Onumber__ring(X1))). 4.49/4.78 cnf(i_0_5320, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X2,X3)),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X4,X1),X2),c_List_Oremove1(X4,X3,X5))))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X4,X1),X2),X5))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_member(X4),X3),hAPP(c_List_Oset(X4),X5))))). 4.49/4.78 cnf(i_0_4497, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk312_4(X2,X3,X4,X1)),esk313_4(X2,X3,X4,X1))),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olistrel1(X1,X2))))). 4.49/4.78 cnf(i_0_2422, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X4),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X5),X2)))|~class_Groups_Oordered__cancel__ab__semigroup__add(X3)|~class_Groups_Ocomm__monoid__add(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(X4,esk183_5(X5,X4,X2,X1,X3))),hAPP(X5,esk183_5(X5,X4,X2,X1,X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_7249, plain, (hAPP(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))=hAPP(c_Fun_Ocomp(X5,X5,X5,hAPP(X1,X3)),hAPP(X1,X4))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~c_Finite__Set_Ofolding(X2,X5,X6,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.49/4.78 cnf(i_0_447, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X2,X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),X5))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.49/4.78 cnf(i_0_5676, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X2,X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X1),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),X5))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.49/4.78 cnf(i_0_2684, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4))|~class_Int_Onumber(X1)|~class_Rings_Oring(X1))). 4.49/4.78 cnf(i_0_4036, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,X3)),hAPP(X2,X4))),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X4)),hAPP(hAPP(c_Relation_Oinv__image(X1,X6),X5),X2))))). 4.49/4.78 cnf(i_0_3230, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk221_5(X2,X3,X4,X5,X1)),hAPP(X3,esk220_5(X2,X3,X4,X5,X1))))|hBOOL(hAPP(X2,X6))|~hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3))))). 4.49/4.78 cnf(i_0_3813, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4)))). 4.49/4.78 cnf(i_0_7039, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X4)))). 4.49/4.78 cnf(i_0_5445, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4)),X5)),X6)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6))))). 4.49/4.78 cnf(i_0_3071, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4)),X5)),X6)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6))))). 4.49/4.78 cnf(i_0_373, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4)),X5)),X6))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6))))). 4.49/4.78 cnf(i_0_1629, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))|~class_Rings_Osemiring(X1)|~class_Int_Onumber(X1))). 4.49/4.78 cnf(i_0_2117, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk156_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk155_3(X1,X2,X3)))=X1|hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.78 cnf(i_0_5635, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X4,X5))),X5)|hBOOL(hAPP(X4,X2))|hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X4,X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))!=X5)). 4.49/4.78 cnf(i_0_4490, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X4))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk311_4(X4,X2,X3,X1)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))))). 4.49/4.78 cnf(i_0_356, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk28_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk27_3(X1,X2,X3)))=X1|hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.49/4.78 cnf(i_0_727, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4)),X5)),X6))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6))))). 4.49/4.78 cnf(i_0_3711, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OWhile(X4,X5)),c_Hoare__Mirabelle_Opeek__and(X1,X3,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X4)))))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,X4)),X5),X3))))). 4.49/4.78 cnf(i_0_3921, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X4)|hAPP(X3,X5)=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|~class_Fields_Ofield(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.78 cnf(i_0_7514, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk538_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk537_3(X1,X2,X3)))=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk536_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk535_3(X1,X2,X3)))=X1|epred2_3(X3,X2,X1))). 4.49/4.78 cnf(i_0_1676, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X1),c_Groups_Otimes__class_Otimes(X2)),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X5)),X4)|~class_Rings_Osemiring__0(X2))). 4.49/4.78 cnf(i_0_1603, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1))). 4.49/4.78 cnf(i_0_2342, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),hAPP(c_List_Ofilter(X1,X5),X6))=hAPP(c_List_Ofilter(X1,X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),X6))|~c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Omap(X1,X2),X3),X6))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(X5,X4)))). 4.49/4.78 cnf(i_0_5893, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))|~class_Int_Onumber__ring(X1))). 4.49/4.78 cnf(i_0_5790, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X1)))). 4.49/4.78 cnf(i_0_7189, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))),X4)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X4)))). 4.49/4.78 cnf(i_0_2749, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X2,tc_Option_Ooption(X1)),X3),X4),hAPP(c_Option_Ooption_OSome(X1),X5))),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))))). 4.49/4.78 cnf(i_0_268, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.49/4.78 cnf(i_0_1975, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2),X3)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.49/4.78 cnf(i_0_7030, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),c_List_Oremove1(X1,X4,X5))=X5|hAPP(c_List_Ohd(X1),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(c_fequal,hAPP(X3,X4))),X3)),X5))!=X4|~c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X5))))). 4.49/4.78 cnf(i_0_6096, plain, (hAPP(hAPP(X1,X2),hAPP(hAPP(c_Finite__Set_Ofold(X3,X4,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X6),hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))))=hAPP(hAPP(c_Finite__Set_Ofold(X3,X4,X1),X5),hAPP(hAPP(c_Set_Oinsert(X3),X2),X6))|~c_Finite__Set_Ofun__left__comm(X3,X4,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X6)))). 4.49/4.78 cnf(i_0_2673, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_3638, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_2775, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_4496, plain, (hAPP(hAPP(c_List_Oappend(X1),esk314_4(X2,X3,X4,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),esk312_4(X2,X3,X4,X1)),esk315_4(X2,X3,X4,X1)))=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olistrel1(X1,X2))))). 4.49/4.78 cnf(i_0_4495, plain, (hAPP(hAPP(c_List_Oappend(X1),esk314_4(X2,X3,X4,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),esk313_4(X2,X3,X4,X1)),esk315_4(X2,X3,X4,X1)))=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olistrel1(X1,X2))))). 4.49/4.78 cnf(i_0_6523, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk450_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X4)))). 4.49/4.78 cnf(i_0_5414, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5)),X6),X7)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X6),X7)),X4),X5)|X4=X6)). 4.49/4.78 cnf(i_0_1986, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_2070, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)),X4)),X5)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.49/4.78 cnf(i_0_4926, plain, (hAPP(hAPP(X1,X2),hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(X3,X5)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))|~c_Finite__Set_Ofolding__one(X4,X1,X3)|~hBOOL(hAPP(hAPP(c_member(X4),X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.49/4.78 cnf(i_0_1330, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4))=hAPP(hAPP(c_List_Oappend(X1),X3),X4)|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)!=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.49/4.78 cnf(i_0_1589, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk106_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X4)))). 4.49/4.78 cnf(i_0_1579, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk104_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X1)))). 4.49/4.78 cnf(i_0_2767, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk197_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X1)))). 4.49/4.78 cnf(i_0_5979, plain, (X1=X2|hAPP(c_List_Oset(X3),X1)!=hAPP(c_List_Oset(X3),X2)|~c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X5),X2))|~c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X5),X1))|~c_Fun_Oinj__on(X3,X4,X5,hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Oappend(X3),X1),X2)))|~class_Orderings_Olinorder(X4)|~hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(X3,X4),X5),X2)))|~hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(X3,X4),X5),X1))))). 4.49/4.78 cnf(i_0_5688, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk392_3(X3,X2,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_2274, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Otake(X1),X4),hAPP(hAPP(c_List_Odrop(X1),X2),X3)))=hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.49/4.78 cnf(i_0_5386, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X2)),X3)),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X5)|~class_Rings_Oring(X1))). 4.49/4.78 cnf(i_0_7184, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),X3)),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),X3)))). 4.49/4.78 cnf(i_0_7109, plain, (esk499_3(X1,X2,X3)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(X1,esk499_3(X1,X2,X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk498_3(X1,X2,X3),esk499_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2))))). 4.49/4.78 cnf(i_0_1512, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X4))),X4)|~hBOOL(hAPP(X2,X3)))). 4.49/4.78 cnf(i_0_663, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X3))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.49/4.78 cnf(i_0_3717, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Groups_Oone__class_Oone(X1)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),c_Nat_Osemiring__1__class_Oof__nat(X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)))|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.78 cnf(i_0_1464, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))),hAPP(X2,hAPP(c_Nat_OSuc,X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,hAPP(c_Nat_OSuc,X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4)),X3))|~class_Groups_Ocomm__monoid__add(X1))). 4.49/4.78 cnf(i_0_4516, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk317_4(X4,X1,X3,X2)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.49/4.78 cnf(i_0_6736, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk463_4(X4,X3,X2,X1)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),c_Groups_Oone__class_Oone(tc_Int_Oint))),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X3)))). 4.49/4.78 cnf(i_0_343, plain, (c_Lazy__Sequence_Ohb__flat(X1,c_Lazy__Sequence_Ohb__map(X2,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)),hAPP(hAPP(c_COMBC(X2,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1))),X3),X4),hAPP(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X4),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))=hAPP(c_New__DSequence_Oneg__decr__bind(X2,X1,X5,X3),X4)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X4)). 4.49/4.78 cnf(i_0_3201, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)))),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.49/4.78 cnf(i_0_5271, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)))),X3))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.49/4.78 cnf(i_0_5765, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~class_Groups_Oab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.78 cnf(i_0_1451, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X3)),hAPP(hAPP(c_Set_Oinsert(X1),hAPP(hAPP(c_List_Onth(X1),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist__update(X1,X3),X4),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.49/4.78 cnf(i_0_1727, plain, (c_Map_Oran(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3))=hAPP(c_Relation_ORange(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))))). 4.49/4.78 cnf(i_0_2989, plain, (c_Relation_Orefl__on(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X5))|~c_Relation_Orefl__on(X1,hAPP(X4,esk209_5(X5,X4,X1,X3,X2)),hAPP(X5,esk209_5(X5,X4,X1,X3,X2))))). 4.49/4.78 cnf(i_0_4035, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Oinv__image(X4,X1),X5),X6)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(X6,X2)),hAPP(X6,X3))),X5)))). 4.49/4.78 cnf(i_0_920, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk64_3(X3,X2,X1)),X2))|esk66_3(X3,X2,X1)!=esk65_3(X3,X2,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))))). 4.49/4.78 cnf(i_0_5462, plain, (c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X6),X7))=c_Map_Omap__upds(X1,X2,X3,X5,X7)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X7)),X5)))))). 4.49/4.78 cnf(i_0_612, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk42_4(X3,X4,X2,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3)))))). 4.49/4.78 cnf(i_0_6139, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk427_4(X2,X3,X4,X1)),X3)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))))). 4.49/4.78 cnf(i_0_552, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk38_3(X1,X2,X3)),esk39_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))). 4.49/4.78 cnf(i_0_2425, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X2,X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2),X5)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.49/4.78 cnf(i_0_2106, plain, (hAPP(hAPP(X1,X2),hAPP(hAPP(c_Finite__Set_Ofold(X3,X4,X1),X5),X6))=hAPP(hAPP(c_Finite__Set_Ofold(X3,X4,X1),X5),hAPP(hAPP(c_Set_Oinsert(X3),X2),X6))|hBOOL(hAPP(hAPP(c_member(X3),X2),X6))|~c_Finite__Set_Ofun__left__comm(X3,X4,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X6)))). 4.49/4.78 cnf(i_0_5983, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk409_3(X1,X2,X3)),esk410_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))). 4.49/4.78 cnf(i_0_3357, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk229_3(X1,X2,X3)),esk230_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))). 4.49/4.78 cnf(i_0_3654, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk246_3(X1,X2,X3)),esk247_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))). 4.49/4.78 cnf(i_0_5482, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk378_3(X1,X2,X3)),esk379_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))). 4.49/4.78 cnf(i_0_6019, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X2,X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X1),X2),X5)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.49/4.78 cnf(i_0_3146, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3))),c_List_Olist_ONil(X1)))=hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X2)),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.49/4.78 cnf(i_0_1805, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2)),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X3))=hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_7110, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),esk498_3(X1,X2,X3)),esk499_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2))))). 4.49/4.78 cnf(i_0_7360, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk522_2(X2,X1)),esk523_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk522_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk523_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_2006, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk143_2(X2,X1)),esk144_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk143_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk144_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_4605, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk325_6(X3,X4,X2,X5,X6,X1)),esk326_6(X3,X4,X2,X5,X6,X1))),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X6)),X5),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X6),X4),X3))))). 4.49/4.78 cnf(i_0_3117, plain, (hAPP(hAPP(X1,hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),X5))),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X5)))=hAPP(hAPP(X1,hAPP(X2,X4)),hAPP(X2,X5))|~c_Finite__Set_Ofolding__image__simple(X6,X3,X1,X7,X8,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)))). 4.49/4.78 cnf(i_0_5494, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)),X4)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.49/4.78 cnf(i_0_2636, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)),X4)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.49/4.78 cnf(i_0_1159, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)),X4)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.49/4.78 cnf(i_0_4604, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk326_6(X3,X4,X1,X5,X2,X6)),esk327_6(X3,X4,X1,X5,X2,X6))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X2)),X5),hAPP(hAPP(c_Relation_Orel__comp(X6,X1,X2),X4),X3))))). 4.49/4.78 cnf(i_0_2388, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk180_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(hAPP(c_member(X1),esk179_4(X2,X3,X4,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(X2,X5)))). 4.49/4.78 cnf(i_0_6668, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3,X5),tc_prod(X3,X5))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3,X5),tc_prod(X3,X5)),hAPP(hAPP(c_Product__Type_OPair(X3,X5),X1),X6)),hAPP(hAPP(c_Product__Type_OPair(X3,X5),X2),X7))),c_Wellfounded_Olex__prod(X3,X5,X4,X8))))). 4.49/4.78 cnf(i_0_28, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)),X4)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.49/4.78 cnf(i_0_3718, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4))|~hBOOL(hAPP(X5,esk254_5(X5,X3,X4,X2,X1))))). 4.49/4.78 cnf(i_0_4864, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X6))=hAPP(hAPP(c_List_Olist_OCons(X1),X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),X6))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(X3,X4)),hAPP(X3,X5)))|~class_Orderings_Olinorder(X2))). 4.49/4.78 cnf(i_0_535, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)))|hBOOL(hAPP(hAPP(X3,esk35_5(X5,X4,X2,X1,X3)),esk36_5(X5,X4,X2,X1,X3))))). 4.49/4.78 cnf(i_0_7148, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X3),X4))|hAPP(X6,esk505_7(X4,X3,X2,X6,X7,X1,X5))!=X7|~c_Finite__Set_Ofolding__image__simple(X8,X5,X1,X7,X6,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))). 4.49/4.78 cnf(i_0_6765, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist__update(X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),X5))=hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3)),X4),X5)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.49/4.78 cnf(i_0_3038, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.78 cnf(i_0_5176, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X6),X7)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X2),tc_HOL_Obool)),X5),X7))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),X4),X6)))). 4.49/4.78 cnf(i_0_5913, plain, (hAPP(hAPP(X1,X2),hAPP(hAPP(c_Finite__Set_Ofold(X3,X4,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X6),hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))))=hAPP(hAPP(c_Finite__Set_Ofold(X3,X4,X1),X5),X6)|~c_Finite__Set_Ofun__left__comm(X3,X4,X1)|~hBOOL(hAPP(hAPP(c_member(X3),X2),X6))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X6)))). 4.49/4.78 cnf(i_0_3761, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olinorder__class_OMin(X1,X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_4364, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olinorder__class_OMax(X1,X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_4769, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OInf__fin(X1,X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_5728, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OSup__fin(X1,X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_3339, plain, (c_List_OtakeWhile(tc_List_Olist(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X1))),X2)=c_List_Otranspose(X1,c_List_Otranspose(X1,X2))|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2))))). 4.49/4.78 cnf(i_0_1327, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4)=X5|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hAPP(hAPP(c_List_Oappend(X1),X2),X5)!=hAPP(hAPP(c_List_Oappend(X1),X3),X4))). 4.49/4.78 cnf(i_0_7316, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),hAPP(c_Finite__Set_Ofold1(X2,c_Groups_Otimes__class_Otimes(X2)),X1)),X1))|~class_Groups_Oab__semigroup__mult(X2)|~hBOOL(hAPP(hAPP(c_member(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),esk520_2(X1,X2)),esk521_2(X1,X2))),hAPP(hAPP(c_Set_Oinsert(X2),esk520_2(X1,X2)),hAPP(hAPP(c_Set_Oinsert(X2),esk521_2(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.49/4.78 cnf(i_0_4457, plain, (c_Hoare__Mirabelle_Ohoare__valids(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OWhile(X4,X5)),c_Hoare__Mirabelle_Opeek__and(X1,X3,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X4)))))|~c_Hoare__Mirabelle_Ohoare__valids(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,X4)),X5),X3))))). 4.49/4.78 cnf(i_0_6334, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X5),X6))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),X6))|hAPP(X3,X4)=hAPP(X3,X5)|~class_Orderings_Olinorder(X2))). 4.49/4.78 cnf(i_0_401, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),hAPP(hAPP(c_Relation_Orel__comp(X3,X3,X3),X4),c_Transitive__Closure_Ortrancl(X3,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,X4))))). 4.49/4.78 cnf(i_0_6858, plain, (X1=X2|hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),X3,X4,c_Option_Othe(X3)),hAPP(c_Map_Omap__of(X4,X3),hAPP(hAPP(c_List_Ozip(X4,X3),c_Enum_Oenum__class_Oenum(X4)),X1)))!=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),X3,X4,c_Option_Othe(X3)),hAPP(c_Map_Omap__of(X4,X3),hAPP(hAPP(c_List_Ozip(X4,X3),c_Enum_Oenum__class_Oenum(X4)),X2)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_Enum_Oenum__class_Oenum(X4))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_Enum_Oenum__class_Oenum(X4))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)|~class_Enum_Oenum(X4)|~class_Enum_Oenum(X3))). 4.49/4.78 cnf(i_0_2509, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)!=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.49/4.78 cnf(i_0_342, plain, (c_Map_Omap__add(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)),X6)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__add(X1,X2,X3,X6)),X4),hAPP(c_Option_Ooption_OSome(X2),X5))|hBOOL(hAPP(hAPP(c_member(X1),X4),c_Map_Odom(X1,X2,X6))))). 4.49/4.78 cnf(i_0_2069, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X1),X2)),X3)),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.49/4.78 cnf(i_0_7480, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|epred1_3(X3,X2,X1))). 4.49/4.78 cnf(i_0_2627, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Ozip(X2,X3),X4),X5)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Otake(tc_prod(X2,X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X5))),hAPP(hAPP(c_List_Ozip(X2,X3),X4),X5)))))). 4.49/4.78 cnf(i_0_5699, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(c_List_Ofilter(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3)),X4)),X5)=hAPP(c_Option_Ooption_OSome(X2),X6)|hAPP(hAPP(c_Map_Omap__of(X1,X2),X4),X5)!=hAPP(c_Option_Ooption_OSome(X2),X6)|~hBOOL(hAPP(hAPP(X3,X5),X6)))). 4.49/4.78 cnf(i_0_1198, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk79_4(X1,X2,X3,X4)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk78_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X4)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)))). 4.49/4.78 cnf(i_0_1193, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk78_4(X1,X2,X3,X4)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk79_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X4)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)))). 4.49/4.78 cnf(i_0_1726, plain, (hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6))=hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X5)),hAPP(hAPP(c_List_Oappend(X2),X4),X6))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X6)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))). 4.49/4.78 cnf(i_0_5108, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(c_Set_Oimage(X1,X1,X2),X3))=hAPP(X2,c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk354_3(X3,X2,X1))),hAPP(X2,esk355_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk354_3(X3,X2,X1)),esk355_3(X3,X2,X1)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_4136, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(c_Set_Oimage(X1,X1,X2),X3))=hAPP(X2,c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk281_3(X3,X2,X1))),hAPP(X2,esk282_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk281_3(X3,X2,X1)),esk282_3(X3,X2,X1)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.78 cnf(i_0_1055, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk72_3(X1,X2,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(c_Nat_OSuc,esk71_3(X1,X2,X3)))),hAPP(X2,esk71_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3))))). 4.49/4.78 cnf(i_0_3388, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Finite__Set_Ocard(X2),X4))),X5)))|hBOOL(hAPP(hAPP(c_member(X2),esk232_5(X5,X3,X4,X2,X1)),X4))|~class_Groups_Oordered__ab__semigroup__add(X1)|~class_Rings_Osemiring__1(X1))). 4.49/4.78 cnf(i_0_6209, plain, (hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))))=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.49/4.78 cnf(i_0_3723, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk256_3(X1,X2,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(c_Nat_OSuc,esk255_3(X1,X2,X3)))),hAPP(X2,esk255_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3))))). 4.49/4.78 cnf(i_0_4985, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk350_4(X1,X2,X3,X4)),esk349_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)))). 4.49/4.78 cnf(i_0_4234, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk291_4(X1,X2,X3,X4)),esk290_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2)))). 4.49/4.78 cnf(i_0_4631, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X2))))))). 4.49/4.78 cnf(i_0_2378, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X2))))))). 4.49/4.78 cnf(i_0_4711, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.78 cnf(i_0_5314, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X6),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),esk372_8(X3,X6,X5,X5,X4,X4,X1,X2)))|~class_Orderings_Oord(X1)|~class_Groups_Ocomm__monoid__add(X2))). 4.49/4.78 cnf(i_0_5313, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X6),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk372_8(X3,X6,X5,X5,X4,X4,X1,X2)),X5))|~class_Orderings_Oord(X1)|~class_Groups_Ocomm__monoid__add(X2))). 4.49/4.78 cnf(i_0_1527, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~c_Equiv__Relations_Oequiv(X1,X5,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))))). 4.49/4.78 cnf(i_0_5130, plain, (c_List_Olist__all2(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X3),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X2,X3),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(X3,tc_HOL_Obool,X2)),X4)),X5),X6,X7)|~c_List_Olist__all2(X1,X3,X4,X6,hAPP(hAPP(c_List_Omap(X2,X3),X5),X7)))). 4.49/4.79 cnf(i_0_1087, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.79 cnf(i_0_2092, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)))=hAPP(hAPP(c_List_Olist_OCons(X1),X4),hAPP(c_List_Ofilter(X1,X2),X5))|hBOOL(hAPP(hAPP(c_member(X1),esk154_7(hAPP(c_List_Ofilter(X1,X2),X5),X4,hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)),X2,X1,X3,X5)),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 4.49/4.79 cnf(i_0_6801, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5))|~c_Equiv__Relations_Ocongruent(X2,tc_fun(X1,tc_HOL_Obool),X6,X4)|~c_Equiv__Relations_Oequiv(X2,X7,X6)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(X4,esk470_7(X5,X3,X4,X1,X6,X7,X2))),X5))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X7),X6))))). 4.49/4.79 cnf(i_0_4499, plain, (hAPP(c_Map_Omap__of(X1,X2),X3)=hAPP(c_Map_Omap__of(X1,X2),X4)|hAPP(c_List_Oset(tc_prod(X1,X2)),X3)!=hAPP(c_List_Oset(tc_prod(X1,X2)),X4)|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4)))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))))). 4.49/4.79 cnf(i_0_7455, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk534_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk533_3(X1,X2,X3)))=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk532_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk531_3(X1,X2,X3)))=X1|epred1_3(X3,X2,X1)|~hBOOL(hAPP(X3,X1)))). 4.49/4.79 cnf(i_0_4639, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X1)),c_FunDef_Omax__weak))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1)))). 4.49/4.79 cnf(i_0_6477, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk444_2(X1,X2)))))|hBOOL(hAPP(X1,esk445_2(X1,X2)))|hBOOL(hAPP(X1,esk443_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,X3)))). 4.49/4.79 cnf(i_0_1844, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))=X1|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)))). 4.49/4.79 cnf(i_0_2185, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X5)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5),X4))|~class_Groups_Oab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X5)))). 4.49/4.79 cnf(i_0_1446, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),X4))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X4))|~class_Orderings_Olinorder(X1))). 4.49/4.79 cnf(i_0_1809, plain, (hAPP(c_Map_Omap__of(X1,X2),X3)=hAPP(c_Map_Omap__of(X1,X2),X4)|hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))!=hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4))|hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),esk122_4(X4,X3,X2,X1))!=hAPP(hAPP(c_Map_Omap__of(X1,X2),X4),esk122_4(X4,X3,X2,X1)))). 4.49/4.79 cnf(i_0_2144, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(c_Set_Oimage(X4,X1,X5),X6))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X2),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6)|esk159_6(X1,X3,X5,X6,X4,X2)!=esk158_6(X1,X3,X5,X6,X4,X2)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))). 4.49/4.79 cnf(i_0_7084, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1))). 4.49/4.79 cnf(i_0_4587, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)))). 4.49/4.79 cnf(i_0_1125, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X1,tc_HOL_Obool),X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Set_Oinsert(X1)),X3)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X4)=hAPP(c_Set_Oimage(X2,X1,X3),X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.79 cnf(i_0_4582, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X2)),X2),X1))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.49/4.79 cnf(i_0_7042, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk491_5(X5,X4,X3,X2,X1)),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5))). 4.49/4.79 cnf(i_0_2269, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk168_5(X3,X5,X4,X2,X1)),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5))). 4.49/4.79 cnf(i_0_4403, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X4),X5)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X5))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)))). 4.49/4.79 cnf(i_0_551, plain, (hBOOL(hAPP(hAPP(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk38_3(X1,X2,X3))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk39_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk39_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.79 cnf(i_0_3233, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk219_5(X2,X3,X4,X5,X1)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hBOOL(hAPP(X2,X6))|~hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(X3,X7)))|~hBOOL(hAPP(hAPP(c_member(X5),X7),X4)))). 4.49/4.79 cnf(i_0_6827, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X3,esk471_5(X3,X4,X5,X2,X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.79 cnf(i_0_6993, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),tc_prod(X3,X4),c_Product__Type_Omap__pair(X1,X3,X2,X4,X5,X6)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X3,X4),tc_HOL_Obool))|hAPP(c_Set_Oimage(X2,X4,X6),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))|hAPP(c_Set_Oimage(X1,X3,X5),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))). 4.49/4.79 cnf(i_0_5478, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5)|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.49/4.79 cnf(i_0_6546, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Groups_Oone__class_Oone(X1)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(c_Power_Opower__class_Opower(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|c_Groups_Oone__class_Oone(X1)=X2|~class_Fields_Ofield(X1))). 4.49/4.79 cnf(i_0_1191, plain, (hAPP(X1,esk79_4(X2,X1,X3,X4))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X1,hAPP(c_Nat_OSuc,esk78_4(X2,X1,X3,X4)))),hAPP(X1,esk78_4(X2,X1,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)))). 4.49/4.79 cnf(i_0_7180, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X2),X1)),c_List_Olistrel1(X3,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X3),X6),X1))),c_List_Olistrel1(X3,X4))))). 4.49/4.79 cnf(i_0_5481, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),esk378_3(X1,X2,X3))),esk379_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk378_3(X1,X2,X3)),esk379_3(X1,X2,X3))))). 4.49/4.79 cnf(i_0_1731, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4))))). 4.49/4.79 cnf(i_0_3216, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5)|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.49/4.79 cnf(i_0_842, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5)|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.49/4.79 cnf(i_0_42, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(X3,X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))|~class_Rings_Oring(X1)|~hBOOL(hAPP(hAPP(c_member(X2),X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.79 cnf(i_0_4309, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)))). 4.49/4.79 cnf(i_0_6447, plain, (c_Map_Omap__upds(X1,X2,c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(c_List_Oset(X1),X5))),X5,X6)=c_Map_Orestrict__map(X1,X2,c_Map_Omap__upds(X1,X2,X3,X5,X6),X4)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X6)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X5)),X4)))). 4.49/4.79 cnf(i_0_3439, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X1,tc_Nat_Onat)),X4),X5))))|hAPP(X4,X2)!=hAPP(X4,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,X5))))). 4.49/4.79 cnf(i_0_1887, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk128_5(X3,X4,X5,X2,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X3))))). 4.49/4.79 cnf(i_0_6129, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk425_5(X3,X4,X5,X2,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X3))))). 4.49/4.79 cnf(i_0_4798, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X3)),X4)),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))),X4)|~class_Rings_Osemiring__0(X1))). 4.49/4.79 cnf(i_0_1732, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.49/4.79 cnf(i_0_2024, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.49/4.79 cnf(i_0_4993, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X4)),hAPP(X3,X5))|~class_Groups_Oab__group__add(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.79 cnf(i_0_5247, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X4)))|hBOOL(hAPP(hAPP(c_member(X1),esk366_4(X3,X2,X4,X1)),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.79 cnf(i_0_468, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk32_5(X2,X3,X4,X5,X1)),X4)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X3)),X2))))). 4.49/4.79 cnf(i_0_1938, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),hAPP(X3,X2)),X2))|~c_Finite__Set_Ofolding__one(X1,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(X4,esk136_4(X2,X3,X4,X1)),esk137_4(X2,X3,X4,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk136_4(X2,X3,X4,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk137_4(X2,X3,X4,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_5881, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X3)))). 4.49/4.79 cnf(i_0_6138, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk427_4(X3,X4,X2,X1))),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3)))))). 4.49/4.79 cnf(i_0_7427, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X4)))|hBOOL(hAPP(hAPP(c_member(X1),esk526_4(X3,X2,X4,X1)),X4))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.49/4.79 cnf(i_0_1735, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.49/4.79 cnf(i_0_6890, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.49/4.79 cnf(i_0_3922, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)),hAPP(X3,X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))|hAPP(X3,X5)=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield(X1)|~hBOOL(hAPP(hAPP(c_member(X2),X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.79 cnf(i_0_5603, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)))|hBOOL(hAPP(hAPP(c_member(X1),esk388_4(X2,X4,X3,X1)),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.79 cnf(i_0_613, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk42_4(X2,X3,X4,X1)),X3)),c_Transitive__Closure_Ortrancl(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))))). 4.49/4.79 cnf(i_0_2142, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(c_Set_Oimage(X4,X1,X5),X6))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X2),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6)|hAPP(X3,hAPP(X5,esk158_6(X1,X3,X5,X6,X4,X2)))!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))). 4.49/4.79 cnf(i_0_5144, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5)))|~class_Groups_Oordered__ab__semigroup__add(X1)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(X3,esk358_5(X3,X4,X5,X2,X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.79 cnf(i_0_325, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),esk25_5(X4,X5,X2,X1,X3))),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X3,X3),tc_HOL_Obool),X5),X4))))). 4.49/4.79 cnf(i_0_7193, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X2)))|hBOOL(hAPP(hAPP(c_member(X1),esk508_4(X2,X4,X3,X1)),X3))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.79 cnf(i_0_918, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk65_3(X3,X2,X1)),X2))|hAPP(c_Finite__Set_Ocard(X1),esk64_3(X3,X2,X1))!=X3|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))))). 4.49/4.79 cnf(i_0_917, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk66_3(X3,X2,X1)),X2))|hAPP(c_Finite__Set_Ocard(X1),esk64_3(X3,X2,X1))!=X3|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))))). 4.49/4.79 cnf(i_0_4828, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__upds(X1,X2,X3,X4,X5)),X6),hAPP(c_Option_Ooption_OSome(X2),X7))=c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X6),X4),hAPP(hAPP(c_List_Olist_OCons(X2),X7),X5))|hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),X4))))). 4.49/4.79 cnf(i_0_5646, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),esk390_5(X4,X5,X1,X2,X3)),X1)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X3,X3),tc_HOL_Obool),X5),X4))))). 4.49/4.79 cnf(i_0_5838, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),X4),X5)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X6),X4),X5)|hAPP(X3,esk401_6(X4,X3,X6,X5,X2,X1))!=hAPP(X6,esk401_6(X4,X3,X6,X5,X2,X1))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.79 cnf(i_0_4987, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk349_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)))). 4.49/4.79 cnf(i_0_4236, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk290_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2)))). 4.49/4.79 cnf(i_0_6687, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X4)),X5),c_Option_Ooption_ONone(X2))=c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4)))). 4.49/4.79 cnf(i_0_6335, plain, (hAPP(hAPP(X1,hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),X5))),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X5)))=hAPP(hAPP(X1,hAPP(X2,X4)),hAPP(X2,X5))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X5)=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))|~c_Finite__Set_Ofolding__one(X3,X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)))). 4.49/4.79 cnf(i_0_684, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Relation_OImage(X4,X2,X5)),X6))=hAPP(c_Relation_OImage(X4,X2,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~c_Relation_Osingle__valued(X2,X4,hAPP(c_Relation_Oconverse(X4,X2),X5)))). 4.49/4.79 cnf(i_0_6494, plain, (hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~c_Equiv__Relations_Oequiv(X1,X5,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)))). 4.49/4.79 cnf(i_0_3387, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Finite__Set_Ocard(X2),X4))),X5)))|~class_Groups_Oordered__ab__semigroup__add(X1)|~class_Rings_Osemiring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X3,esk232_5(X5,X3,X4,X2,X1))),X5)))). 4.49/4.79 cnf(i_0_4130, plain, (X1=X2|~c_Equiv__Relations_Oequiv(X3,X4,X5)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X6),X7)),X5))|~hBOOL(hAPP(hAPP(c_member(X3),X7),X2))|~hBOOL(hAPP(hAPP(c_member(X3),X6),X1)))). 4.49/4.79 cnf(i_0_6626, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4))))). 4.49/4.79 cnf(i_0_3140, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2))),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X4)))). 4.49/4.79 cnf(i_0_3422, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X1)))). 4.49/4.79 cnf(i_0_919, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk64_3(X3,X2,X1)),X2))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk65_3(X3,X2,X1)),esk66_3(X3,X2,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))))). 4.49/4.79 cnf(i_0_2039, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X5)|hBOOL(hAPP(hAPP(c_member(X1),esk146_5(X3,X4,X5,X1,X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),X4)))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.79 cnf(i_0_4972, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(hAPP(c_List_Onth(X1),X3),X4)),hAPP(hAPP(c_List_Onth(X2),X5),X4))=hAPP(hAPP(c_List_Onth(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X5)),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.49/4.79 cnf(i_0_101, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk12_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(hAPP(c_member(X1),esk11_4(X2,X3,X4,X1)),X3))|hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3))))). 4.49/4.79 cnf(i_0_4068, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(X3,esk275_8(X4,X5,X3,X6,X7,X8,X2,X1))),hAPP(X5,esk276_8(X4,X5,X3,X6,X7,X8,X2,X1)))=X8|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),X8),hAPP(c_Set_Oimage(tc_prod(X7,X6),tc_prod(X1,X2),c_Product__Type_Omap__pair(X7,X1,X6,X2,X3,X5)),X4))))). 4.49/4.79 cnf(i_0_6294, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(c_Set_Oimage(X1,X1,X2),X3))=hAPP(X2,hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X2,esk437_3(X3,X2,X1))),hAPP(X2,esk438_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk437_3(X3,X2,X1)),esk438_3(X3,X2,X1)))|~class_Lattices_Oab__semigroup__idem__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.79 cnf(i_0_2253, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))|~class_Int_Onumber__ring(X1))). 4.49/4.79 cnf(i_0_6492, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X5)|hBOOL(hAPP(hAPP(c_member(X1),esk447_5(X3,X4,X5,X1,X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),X4)))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.79 cnf(i_0_2403, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X5)|hBOOL(hAPP(hAPP(c_member(X1),esk181_5(X3,X4,X5,X1,X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),X4)))|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.79 cnf(i_0_5487, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X5)|hBOOL(hAPP(hAPP(c_member(X1),esk380_5(X3,X4,X5,X1,X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),X4)))|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.79 cnf(i_0_6416, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OSemi(X4,X5)),X6)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X7),X5),X6)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X7))))). 4.49/4.79 cnf(i_0_1287, plain, (hAPP(c_Finite__Set_Ocard(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_Nat_Onat,X1),c_Finite__Set_Ocard(X2)),X4)),X3)|hBOOL(hAPP(hAPP(c_member(X1),esk86_4(X4,X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.79 cnf(i_0_9, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk1_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),esk2_2(X2,X1))),hAPP(c_List_Oset(X1),esk3_2(X2,X1)))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 4.49/4.79 cnf(i_0_4436, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk307_5(X3,X4,X5,X2,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),X4)),c_List_Olistrel(X1,X3))))). 4.49/4.79 cnf(i_0_1881, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk126_5(X2,X3,X4,X5,X1)),X4)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel(X1,X2))))). 4.49/4.79 cnf(i_0_3273, plain, (hBOOL(hAPP(hAPP(hAPP(X1,X2),X3),X4))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4))))|~hBOOL(hAPP(hAPP(hAPP(X1,esk223_4(X1,X4,X3,X2)),esk224_4(X1,X4,X3,X2)),esk225_4(X1,X4,X3,X2))))). 4.49/4.79 cnf(i_0_4316, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Ofilter(X2,X4),X5)))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk295_5(X3,X4,X5,X2,X1)),hAPP(c_List_Oset(X2),X5)))|~class_Groups_Omonoid__add(X1))). 4.49/4.79 cnf(i_0_534, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X1),hAPP(c_fequal,esk36_5(X5,X4,X2,X1,X3)))),X4),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X1),hAPP(X5,esk35_5(X5,X4,X2,X1,X3)))))))). 4.49/4.79 cnf(i_0_5444, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X5),X2)),X3)),X6))))). 4.49/4.79 cnf(i_0_3070, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X5),X2)),X3)),X6))))). 4.49/4.79 cnf(i_0_374, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5)),X3)),X4)),X6)))). 4.49/4.79 cnf(i_0_1322, plain, (hAPP(hAPP(c_List_Olist__update(X1,hAPP(c_List_Orev(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_OSuc,X3))),X4)=hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.49/4.79 cnf(i_0_2726, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),X4)))). 4.49/4.79 cnf(i_0_1622, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),X4)))). 4.49/4.79 cnf(i_0_726, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5)),X3)),X4)),X6)))). 4.49/4.79 cnf(i_0_2579, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,X2),X2,X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X2),X5)),hAPP(c_COMBC(X4,X1,X2),X6)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X2),X5),hAPP(hAPP(c_COMBB(tc_fun(X1,X2),X2,X4),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2),X3)),X6))|~class_Complete__Lattice_Ocomplete__lattice(X2))). 4.49/4.79 cnf(i_0_4515, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk317_4(X1,X2,X3,X4)),esk316_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X4)))). 4.49/4.79 cnf(i_0_6735, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk463_4(X1,X2,X3,X4)),esk462_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X2)))). 4.49/4.79 cnf(i_0_2844, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X2),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,X2),X2,X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X2),X5)),hAPP(c_COMBC(X4,X1,X2),X6)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X2),X5),hAPP(hAPP(c_COMBB(tc_fun(X1,X2),X2,X4),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X2),X3)),X6))|~class_Complete__Lattice_Ocomplete__lattice(X2))). 4.49/4.79 cnf(i_0_4647, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~c_Equiv__Relations_Oequiv(X1,X5,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5)))). 4.49/4.79 cnf(i_0_835, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5))=hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~c_Fun_Oinj__on(X2,X1,X3,X6)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X5),X6))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X6)))). 4.49/4.79 cnf(i_0_5453, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5))=hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~c_Fun_Oinj__on(X2,X1,X3,X6)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X5),X6))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X6)))). 4.49/4.79 cnf(i_0_328, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),esk25_5(X4,X1,X5,X3,X2))),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),X1),X4))))). 4.49/4.79 cnf(i_0_5649, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),esk390_5(X3,X1,X4,X5,X2)),X4)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),X1),X3))))). 4.49/4.79 cnf(i_0_4182, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))),hAPP(X2,X3))),c_Transitive__Closure_Ortrancl(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,hAPP(c_Nat_OSuc,esk285_5(X4,X3,X5,X2,X1)))),hAPP(X2,esk285_5(X4,X3,X5,X2,X1)))),c_Transitive__Closure_Ortrancl(X1,X5))))). 4.49/4.79 cnf(i_0_5418, plain, (hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3))=hAPP(c_Finite__Set_Ocard(X1),X2)|~c_Fun_Oinj__on(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X1),c_Equiv__Relations_Oquotient(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_3194, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~c_Equiv__Relations_Oequiv(X1,X5,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)))). 4.49/4.79 cnf(i_0_922, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk65_3(X3,X2,X1)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk64_3(X3,X2,X1)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))))). 4.49/4.79 cnf(i_0_7438, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)))=hAPP(hAPP(c_List_Olist_OCons(X1),X4),hAPP(c_List_Ofilter(X1,X2),X5))|hBOOL(hAPP(hAPP(c_member(X1),esk530_6(hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)),X2,hAPP(c_List_Ofilter(X1,X2),X5),X4,X1,X3)),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 4.49/4.79 cnf(i_0_10, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk1_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|esk3_2(X2,X1)!=esk2_2(X2,X1)|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 4.49/4.79 cnf(i_0_1063, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Oappend(X3),X5),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3)))),hAPP(hAPP(c_List_Oappend(X3),X6),hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_Olist_ONil(X3))))),c_List_Olistrel1(X3,X4))))). 4.49/4.79 cnf(i_0_6134, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|hAPP(X3,esk426_5(X3,X5,X4,X2,X1))!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.79 cnf(i_0_1847, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|hAPP(X3,esk124_5(X3,X5,X4,X2,X1))!=c_Groups_Oone__class_Oone(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.79 cnf(i_0_921, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk66_3(X3,X2,X1)),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk64_3(X3,X2,X1)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))))). 4.49/4.79 cnf(i_0_3056, plain, (hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X2))))). 4.49/4.79 cnf(i_0_5493, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X1)),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X4)))). 4.49/4.79 cnf(i_0_2635, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X1)),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X4)))). 4.49/4.79 cnf(i_0_6478, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk444_2(X1,X2)))))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk445_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|hBOOL(hAPP(X1,esk443_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,X3)))). 4.49/4.79 cnf(i_0_1742, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|hAPP(X3,esk118_5(X3,X5,X4,X2,X1))!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.79 cnf(i_0_387, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|hAPP(X3,esk31_5(X3,X5,X4,X2,X1))!=c_Groups_Oone__class_Oone(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.79 cnf(i_0_2337, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(X3),esk174_7(X1,X2,X4,X5,X6,X7,X3)),X7))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X5,tc_HOL_Obool)),X1),X4)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X5,tc_HOL_Obool)),X2),X4)|~c_Equiv__Relations_Ocongruent(X3,tc_fun(X5,tc_HOL_Obool),X6,X4)|~c_Equiv__Relations_Oequiv(X3,X7,X6)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6))))). 4.49/4.79 cnf(i_0_2336, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(X3),esk175_7(X1,X2,X4,X5,X6,X7,X3)),X7))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X5,tc_HOL_Obool)),X1),X4)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X5,tc_HOL_Obool)),X2),X4)|~c_Equiv__Relations_Ocongruent(X3,tc_fun(X5,tc_HOL_Obool),X6,X4)|~c_Equiv__Relations_Oequiv(X3,X7,X6)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6))))). 4.49/4.79 cnf(i_0_1160, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X4)),X2)),X3)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X1)))). 4.49/4.79 cnf(i_0_27, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X4)),X2)),X3)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X1)))). 4.49/4.79 cnf(i_0_3719, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5)))|hBOOL(hAPP(X3,esk254_5(X5,X3,X4,X2,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.49/4.79 cnf(i_0_3868, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.79 cnf(i_0_4511, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3))|c_Groups_Ozero__class_Ozero(X1)=X3|X5=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield(X1))). 4.49/4.79 cnf(i_0_2963, plain, (hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Omap(X1,tc_prod(X1,X2)),hAPP(hAPP(c_COMBS(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),X2,X1),c_Option_Othe(X2)),X3))),X4))=X3|hAPP(c_List_Oset(X1),X4)!=c_Map_Odom(X1,X2,X3))). 4.49/4.79 cnf(i_0_4381, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4))))). 4.49/4.79 cnf(i_0_4394, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4)))),hAPP(hAPP(c_List_Oappend(X1),X3),X4))=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X4))),X4)|~hBOOL(hAPP(X2,esk304_4(X4,X2,X3,X1))))). 4.49/4.79 cnf(i_0_6935, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),esk481_4(X4,X3,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X3),esk481_4(X4,X3,X2,X1)))),X4)))). 4.49/4.79 cnf(i_0_339, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.79 cnf(i_0_6380, plain, (c_Map_Orestrict__map(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),X5),X6)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X6)),X4),X5)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X6)))). 4.49/4.79 cnf(i_0_4565, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4))),c_Groups_Oone__class_Oone(tc_Nat_Onat))|hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_562, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3))|c_Groups_Ozero__class_Ozero(X1)=X3|X5=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield(X1))). 4.49/4.79 cnf(i_0_2334, plain, (X1=X2|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X1),X5)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),X5)|~c_Equiv__Relations_Ocongruent(X3,tc_fun(X4,tc_HOL_Obool),X6,X5)|~c_Equiv__Relations_Oequiv(X3,X7,X6)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),esk174_7(X1,X2,X5,X4,X6,X7,X3)),esk175_7(X1,X2,X5,X4,X6,X7,X3))),X6))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6))))). 4.49/4.79 cnf(i_0_4027, plain, (hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X4)),hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X5)),X6))=hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X5)),hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X4)),X6))|~c_Finite__Set_Ofolding(X7,X1,X3,X8))). 4.49/4.79 cnf(i_0_1190, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk79_4(X2,X3,X4,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X3,hAPP(c_Nat_OSuc,esk78_4(X2,X3,X4,X1)))),hAPP(X3,esk78_4(X2,X3,X4,X1))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X4)))). 4.49/4.79 cnf(i_0_1192, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk79_4(X1,X2,X3,X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X2,hAPP(c_Nat_OSuc,esk78_4(X1,X2,X3,X4)))),hAPP(X2,esk78_4(X1,X2,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X4)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)))). 4.49/4.79 cnf(i_0_4053, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X1,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,tc_HOL_Obool),X1),c_fequal),X4)),hAPP(X4,esk274_4(X4,X3,X2,X1))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2))))). 4.49/4.79 cnf(i_0_4377, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_Enum_Oenum__class_Oenum__ex(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2)))))|~class_Enum_Oenum(X2)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X1,X2)),X3)))). 4.49/4.79 cnf(i_0_7338, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_Enum_Oenum__class_Oenum__all(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2)))))|~class_Enum_Oenum(X2)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X1,X2)),X3)))). 4.49/4.79 cnf(i_0_1329, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4))=hAPP(hAPP(c_List_Oappend(X1),X3),X4)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)!=X2)). 4.49/4.79 cnf(i_0_5312, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X6),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5))|hAPP(X3,esk372_8(X6,X3,X5,X5,X4,X4,X1,X2))!=hAPP(X6,esk372_8(X6,X3,X5,X5,X4,X4,X1,X2))|~class_Orderings_Oord(X1)|~class_Groups_Ocomm__monoid__add(X2))). 4.49/4.79 cnf(i_0_8, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk2_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),esk1_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 4.49/4.79 cnf(i_0_3261, plain, (hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),hAPP(hAPP(X2,X5),X4))=hAPP(hAPP(X2,hAPP(hAPP(c_COMBS(X6,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X6),X1),X3)),X5)),X4)|~c_Finite__Set_Ofolding__image(X7,X6,X1,X8,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X4)))). 4.49/4.79 cnf(i_0_4581, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X2)),X2),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1))))). 4.49/4.79 cnf(i_0_7, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk3_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),esk1_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 4.49/4.79 cnf(i_0_4571, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),esk322_4(X3,X4,X2,X1))),esk321_4(X3,X4,X2,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel1(X1,X3))))). 4.49/4.79 cnf(i_0_1271, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3)),X4)|esk84_4(X3,X4,X1,X2)!=esk83_4(X3,X4,X1,X2)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk82_4(X3,X4,X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 4.49/4.79 cnf(i_0_4682, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))),c_FunDef_Opair__less))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.49/4.79 cnf(i_0_769, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,hAPP(X2,X3)))),hAPP(hAPP(c_List_Omap(X4,X1),X2),X5))=hAPP(hAPP(c_List_Omap(X4,X1),X2),hAPP(c_List_Ofilter(X4,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_fequal,X3))),X5))|~c_Fun_Oinj__on(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))). 4.49/4.79 cnf(i_0_4250, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),X5))),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X5)))=hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X4)),hAPP(X2,X5))|~c_Finite__Set_Ofolding(X3,X1,X6,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)))). 4.49/4.79 cnf(i_0_5102, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.79 cnf(i_0_6476, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk443_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk444_2(X1,X2)))))|hBOOL(hAPP(X1,esk446_2(X1,X2)))|hBOOL(hAPP(X1,esk443_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,X3)))). 4.49/4.79 cnf(i_0_3819, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))),c_FunDef_Opair__leq))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.49/4.79 cnf(i_0_2239, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~c_Equiv__Relations_Oequiv(X1,X5,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5)))). 4.49/4.79 cnf(i_0_4517, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk316_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X4)))). 4.49/4.79 cnf(i_0_6737, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk462_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X2)))). 4.49/4.79 cnf(i_0_3519, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk237_5(X3,X4,X5,X1,X2))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X5),X4)),c_Wellfounded_Omax__ext(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5)))). 4.49/4.79 cnf(i_0_273, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.79 cnf(i_0_14, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1)),c_Int_Onat))))))). 4.49/4.79 cnf(i_0_3522, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1)),c_Int_Onat))))))). 4.49/4.79 cnf(i_0_7117, plain, (hAPP(c_Nat_OSuc,X1)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X1))))))). 4.49/4.79 cnf(i_0_4923, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X2,X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X4,c_Groups_Otimes__class_Otimes(X1)),X2),X5),X6))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X4,c_Groups_Otimes__class_Otimes(X1)),X2),X5),hAPP(hAPP(c_Set_Oinsert(X4),X3),X6))|hBOOL(hAPP(hAPP(c_member(X4),X3),X6))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))). 4.49/4.79 cnf(i_0_3437, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X5,X2)),hAPP(X5,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X1,tc_Nat_Onat)),X5),X4)))))). 4.49/4.79 cnf(i_0_4435, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),esk308_5(X3,X4,X2,X5,X1))),c_List_Olistrel(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),X4)),c_List_Olistrel(X1,X3))))). 4.49/4.79 cnf(i_0_1028, plain, (c_FunDef_Oreduction__pair(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))))). 4.49/4.79 cnf(i_0_1880, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),esk127_5(X2,X3,X4,X5,X1)),X3)),c_List_Olistrel(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel(X1,X2))))). 4.49/4.79 cnf(i_0_4395, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4)))),hAPP(hAPP(c_List_Oappend(X1),X3),X4))=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X4))),X4)|hBOOL(hAPP(hAPP(c_member(X1),esk304_4(X4,X2,X3,X1)),hAPP(c_List_Oset(X1),X3))))). 4.49/4.79 cnf(i_0_6143, plain, (hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.49/4.79 cnf(i_0_6700, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),X3)),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.49/4.79 cnf(i_0_7126, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X1,tc_Nat_Onat)),X4),X5))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X4,X2)),hAPP(X4,X3))))). 4.49/4.79 cnf(i_0_7287, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X1,X2)),X3))|~c_Enum_Oex__n__lists(X2,hAPP(hAPP(c_COMBB(tc_fun(X1,X2),tc_HOL_Obool,tc_List_Olist(X2)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,X2),tc_List_Olist(X2)),c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_fun(X1,tc_Option_Ooption(X2)),tc_List_Olist(X2)),c_Map_Omap__of(X1,X2)),hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1)))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2))). 4.49/4.79 cnf(i_0_254, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X6)))|~hBOOL(hAPP(hAPP(X5,esk21_6(X5,X6,X4,X3,X2,X1)),esk22_6(X5,X6,X4,X3,X2,X1))))). 4.49/4.79 cnf(i_0_5491, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X6),X4),X5)))|~hBOOL(hAPP(hAPP(X6,esk381_6(X3,X5,X4,X6,X2,X1)),esk382_6(X3,X5,X4,X6,X2,X1))))). 4.49/4.79 cnf(i_0_4930, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),c_Big__Operators_Olinorder__class_OMax(X1,X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_5839, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),X4),X5)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X6),X4),X5)|hBOOL(hAPP(hAPP(c_member(X2),esk401_6(X4,X3,X6,X5,X2,X1)),X5))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.79 cnf(i_0_7015, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X1,X2)),X3))|~c_Enum_Oall__n__lists(X2,hAPP(hAPP(c_COMBB(tc_fun(X1,X2),tc_HOL_Obool,tc_List_Olist(X2)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,X2),tc_List_Olist(X2)),c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_fun(X1,tc_Option_Ooption(X2)),tc_List_Olist(X2)),c_Map_Omap__of(X1,X2)),hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1)))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2))). 4.49/4.79 cnf(i_0_4915, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Random_Opick(X1,X2),X3)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),X1),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X1)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X3),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X1)),X2)))))). 4.49/4.79 cnf(i_0_966, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),X4),hAPP(c_Set_Oimage(X5,X2,X6),X7))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X5,c_Groups_Otimes__class_Otimes(X1)),hAPP(c_Fun_Ocomp(X2,X1,X5,X3),X6)),X4),X7)|~class_Groups_Oab__semigroup__mult(X1)|~c_Fun_Oinj__on(X5,X2,X6,X7)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X7)))). 4.49/4.79 cnf(i_0_6684, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)),X4)=hAPP(hAPP(c_List_Onth(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))))))). 4.49/4.79 cnf(i_0_4610, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))),c_List_Olexord(X1,X6)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X6)))). 4.49/4.79 cnf(i_0_2599, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))),hAPP(c_Finite__Set_Ocard(X1),X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_6394, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),X2))))|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.49/4.79 cnf(i_0_3841, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X1)),c_FunDef_Omax__strict))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1)))). 4.49/4.79 cnf(i_0_4073, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),X5))|hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X3,X4),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.49/4.79 cnf(i_0_6475, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_6755, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel1(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X5)))). 4.49/4.79 cnf(i_0_1268, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3)),X4)|hAPP(X3,esk85_4(X3,X4,X1,X2))!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk82_4(X3,X4,X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 4.49/4.79 cnf(i_0_469, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk32_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X3))))). 4.49/4.79 cnf(i_0_1886, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk128_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X3)),X2))))). 4.49/4.79 cnf(i_0_6128, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk425_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X3)),X2))))). 4.49/4.79 cnf(i_0_2423, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X4),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X5),X2)))|hBOOL(hAPP(hAPP(c_member(X1),esk183_5(X5,X4,X2,X1,X3)),X2))|~class_Groups_Oordered__cancel__ab__semigroup__add(X3)|~class_Groups_Ocomm__monoid__add(X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_2130, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),X4)),hAPP(hAPP(c_Set_Oinsert(X1),c_HOL_OThe(X1,hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X4)),X3))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X1,X2,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))). 4.49/4.79 cnf(i_0_6963, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X5))|~hBOOL(hAPP(hAPP(c_member(X2),X6),X4)))). 4.49/4.79 cnf(i_0_4669, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X1)),X2)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X4)))). 4.49/4.79 cnf(i_0_1440, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X4)),X2)),X3)),X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X1)))). 4.49/4.79 cnf(i_0_1010, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),c_Big__Operators_Olinorder__class_OMin(X1,X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_3653, plain, (hBOOL(hAPP(hAPP(X1,esk246_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),esk247_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk246_3(X1,X2,X3)),esk247_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))). 4.49/4.79 cnf(i_0_5343, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X5),X4))))|~class_Groups_Omonoid__add(X1)|~class_Groups_Oordered__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X3,esk373_5(X5,X3,X4,X2,X1))),hAPP(X5,esk373_5(X5,X3,X4,X2,X1)))))). 4.49/4.79 cnf(i_0_2893, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_3515, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),X1)),c_Wellfounded_Omax__ext(X2,X4)))|hBOOL(hAPP(hAPP(c_member(X2),esk238_4(X4,X1,X3,X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.49/4.79 cnf(i_0_2331, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X2)),c_Wellfounded_Omax__ext(X1,X4)))|hBOOL(hAPP(hAPP(c_member(X1),esk173_4(X4,X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_3014, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.49/4.79 cnf(i_0_5732, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__semiring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X5),X6))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X6)))). 4.49/4.79 cnf(i_0_1492, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__semiring__1__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X5),X6))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X6)))). 4.49/4.79 cnf(i_0_5245, plain, (hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),hAPP(c_Fun_Othe__inv__into(X2,X5,hAPP(c_Set_Oimage(X1,X2,X4),X3),X6),X7))=hAPP(c_Fun_Othe__inv__into(X1,X5,X3,hAPP(c_Fun_Ocomp(X2,X5,X1,X6),X4)),X7)|~c_Fun_Oinj__on(X2,X5,X6,hAPP(c_Set_Oimage(X1,X2,X4),X3))|~c_Fun_Oinj__on(X1,X2,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X5),X7),hAPP(c_Set_Oimage(X2,X5,X6),hAPP(c_Set_Oimage(X1,X2,X4),X3)))))). 4.49/4.79 cnf(i_0_6564, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBS(X1,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X1),c_Groups_Ominus__class_Ominus(X2)),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X4),X5))|~class_Groups_Oab__group__add(X2))). 4.49/4.79 cnf(i_0_5210, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.49/4.79 cnf(i_0_6369, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2)))). 4.49/4.79 cnf(i_0_2010, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBS(X1,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X1),c_Groups_Oplus__class_Oplus(X2)),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X4),X5))|~class_Groups_Ocomm__monoid__add(X2))). 4.49/4.79 cnf(i_0_2078, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Relation_Orel__comp(X1,X5,X2),X6),X7)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X2)),hAPP(hAPP(c_Product__Type_OPair(X5,X2),X8),X4)),X7))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X5)),hAPP(hAPP(c_Product__Type_OPair(X1,X5),X3),X8)),X6)))). 4.49/4.79 cnf(i_0_1270, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3)),X4)|hBOOL(hAPP(hAPP(c_member(X1),esk85_4(X3,X4,X1,X2)),esk83_4(X3,X4,X1,X2)))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk82_4(X3,X4,X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 4.49/4.79 cnf(i_0_1269, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3)),X4)|hBOOL(hAPP(hAPP(c_member(X1),esk85_4(X3,X4,X1,X2)),esk84_4(X3,X4,X1,X2)))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk82_4(X3,X4,X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 4.49/4.79 cnf(i_0_1550, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBS(X1,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X1),c_Groups_Otimes__class_Otimes(X2)),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X4),X5))|~class_Groups_Ocomm__monoid__mult(X2))). 4.49/4.79 cnf(i_0_1355, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3)))))). 4.49/4.79 cnf(i_0_1595, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X3)|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk108_4(X2,X4,X3,X1))),X3)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),esk108_4(X2,X4,X3,X1)))),X2))). 4.49/4.79 cnf(i_0_1892, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),esk129_7(X6,X7,X5,X4,X3,X2,X1)))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X7))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X5)))). 4.49/4.79 cnf(i_0_1328, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4))=hAPP(hAPP(c_List_Oappend(X1),X3),X4)|hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)),hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4))!=X4|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)!=X2|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)!=X3)). 4.49/4.79 cnf(i_0_3185, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X6)))|hBOOL(hAPP(hAPP(c_member(X1),esk218_6(X6,X4,X2,X5,X3,X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X5)))). 4.49/4.79 cnf(i_0_4971, plain, (hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X4)),hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X5,X6)),X7))=hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X5,X6)),hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X4)),X7))|~c_Finite__Set_Ofolding(X8,X1,X3,X5)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X6)))). 4.49/4.79 cnf(i_0_1140, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X1,tc_HOL_Obool),X1,hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X2),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.79 cnf(i_0_2452, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,hAPP(X2,X3)))),hAPP(hAPP(c_List_Omap(X4,X1),X2),X5))=hAPP(hAPP(c_List_Omap(X4,X1),X2),hAPP(c_List_Ofilter(X4,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_fequal,X3))),X5))|~c_Fun_Oinj__on(X4,X1,X2,hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(c_List_Oset(X4),X5))))). 4.49/4.79 cnf(i_0_3720, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5)))|hBOOL(hAPP(hAPP(c_member(X1),esk254_5(X5,X3,X4,X2,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.49/4.79 cnf(i_0_2813, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X3),X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X5))),X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))|~hBOOL(hAPP(X5,X4)))). 4.49/4.79 cnf(i_0_4580, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X2)),X2),X1))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X2)))). 4.49/4.79 cnf(i_0_2694, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3))),c_List_Olex(X1,X6))))). 4.49/4.79 cnf(i_0_1084, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(X3,X4)),hAPP(X5,X6))),hAPP(c_Set_Oimage(tc_prod(X7,X8),tc_prod(X1,X2),c_Product__Type_Omap__pair(X7,X1,X8,X2,X3,X5)),X9)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X8)),hAPP(hAPP(c_Product__Type_OPair(X7,X8),X4),X6)),X9)))). 4.49/4.79 cnf(i_0_2866, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Fields_Olinordered__field__inverse__zero(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))). 4.49/4.79 cnf(i_0_2503, plain, (hAPP(hAPP(c_List_Otake(X1),esk189_4(X2,X3,X4,X1)),X4)=hAPP(hAPP(c_List_Otake(X1),esk189_4(X2,X3,X4,X1)),X3)|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)),X3)=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olexord(X1,X2))))). 4.49/4.79 cnf(i_0_6535, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_FunDef_Oreduction__pair(X1,X4)|~c_Wellfounded_Owf(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4))))). 4.49/4.79 cnf(i_0_6802, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk470_7(X5,X3,X4,X1,X6,X7,X2)),X7))|~c_Equiv__Relations_Ocongruent(X2,tc_fun(X1,tc_HOL_Obool),X6,X4)|~c_Equiv__Relations_Oequiv(X2,X7,X6)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X7),X6))))). 4.49/4.79 cnf(i_0_1897, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),X4))|~c_Relation_Ototal__on(X3,X5,X4)|~hBOOL(hAPP(hAPP(c_member(X3),X2),X5))|~hBOOL(hAPP(hAPP(c_member(X3),X1),X5)))). 4.49/4.79 cnf(i_0_1060, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X1),X2)),c_List_Olistrel1(X3,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Oappend(X3),X1),hAPP(hAPP(c_List_Olist_OCons(X3),X5),c_List_Olist_ONil(X3)))),hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X6),c_List_Olist_ONil(X3))))),c_List_Olistrel1(X3,X4))))). 4.49/4.79 cnf(i_0_3184, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(X4,esk218_6(X6,X4,X2,X5,X3,X1))),hAPP(X6,esk218_6(X6,X4,X2,X5,X3,X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X5)))). 4.49/4.79 cnf(i_0_5546, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),X4)))). 4.49/4.79 cnf(i_0_6815, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4)!=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4)|~c_Equiv__Relations_Oequiv(X1,X5,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5)))). 4.49/4.79 cnf(i_0_2812, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X3))),X4))))|hBOOL(hAPP(X3,esk201_4(X4,X1,X3,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.49/4.79 cnf(i_0_6470, plain, (c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))=hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X2))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.49/4.79 cnf(i_0_2146, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(c_Set_Oimage(X4,X1,X5),X6))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X2),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6)|hBOOL(hAPP(hAPP(c_member(X4),esk158_6(X1,X3,X5,X6,X4,X2)),X6))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))). 4.49/4.79 cnf(i_0_2145, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(c_Set_Oimage(X4,X1,X5),X6))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X2),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6)|hBOOL(hAPP(hAPP(c_member(X4),esk159_6(X1,X3,X5,X6,X4,X2)),X6))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))). 4.49/4.79 cnf(i_0_4131, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~c_Equiv__Relations_Oequiv(X1,X5,X4)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X6),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X5),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X6))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X6)))). 4.49/4.79 cnf(i_0_3243, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.79 cnf(i_0_790, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))). 4.49/4.79 cnf(i_0_6082, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))). 4.49/4.79 cnf(i_0_1669, plain, (X1=hAPP(c_Groups_Ouminus__class_Ouminus(X2),c_Groups_Oone__class_Oone(X2))|X1=c_Groups_Oone__class_Oone(X2)|hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))!=c_Groups_Oone__class_Oone(X2)|~class_Rings_Oring__1__no__zero__divisors(X2))). 4.49/4.79 cnf(i_0_2143, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(c_Set_Oimage(X4,X1,X5),X6))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X2),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6)|hAPP(X5,esk159_6(X1,X3,X5,X6,X4,X2))=hAPP(X5,esk158_6(X1,X3,X5,X6,X4,X2))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))). 4.49/4.79 cnf(i_0_6669, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X7)),X8))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X1),tc_prod(X5,X1))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X1),tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X6),X2)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X7),X3))),c_Wellfounded_Olex__prod(X5,X1,X8,X4))))). 4.49/4.79 cnf(i_0_345, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))),c_List_Olistrel1(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olistrel1(X1,X5))))). 4.49/4.79 cnf(i_0_2040, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_List_Oappend(X1),X2),X4))),c_List_Olexord(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olexord(X1,X5))))). 4.49/4.79 cnf(i_0_4045, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))),c_Int_Ointrel))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4))). 4.49/4.79 cnf(i_0_1094, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk73_3(X3,X2,X1)),X2))|~hBOOL(hAPP(hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)),esk74_3(X3,X2,X1))))). 4.49/4.79 cnf(i_0_6814, plain, (hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)|~c_Equiv__Relations_Oequiv(X1,X5,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X3)))). 4.49/4.79 cnf(i_0_2335, plain, (hAPP(X1,esk175_7(X2,X3,X1,X4,X5,X6,X7))=hAPP(X1,esk174_7(X2,X3,X1,X4,X5,X6,X7))|X2=X3|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X2),X1)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),X1)|~c_Equiv__Relations_Ocongruent(X7,tc_fun(X4,tc_HOL_Obool),X5,X1)|~c_Equiv__Relations_Oequiv(X7,X6,X5)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X6),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X6),X5))))). 4.49/4.79 cnf(i_0_6824, plain, (hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X4)),hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X5)),X6))=hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X5)),hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X4)),X6))|~c_Finite__Set_Ofolding(X7,X1,X8,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X4)))). 4.49/4.79 cnf(i_0_3942, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Product__Type_Ofst(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X1,X2),X3))),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),X1),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X1)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X1)),X2)))))). 4.49/4.79 cnf(i_0_5207, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),X4)))). 4.49/4.79 cnf(i_0_4965, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X2)|~hBOOL(hAPP(X2,esk345_2(X1,X2)))|~hBOOL(hAPP(X1,esk345_2(X1,X2))))). 4.49/4.79 cnf(i_0_5171, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X5)))))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.49/4.79 cnf(i_0_5344, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X5),X4))))|hBOOL(hAPP(hAPP(c_member(X2),esk373_5(X5,X3,X4,X2,X1)),hAPP(c_List_Oset(X2),X4)))|~class_Groups_Omonoid__add(X1)|~class_Groups_Oordered__ab__semigroup__add(X1))). 4.49/4.79 cnf(i_0_4568, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))),c_List_Olistrel1(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),X4)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.49/4.79 cnf(i_0_1810, plain, (hAPP(c_Map_Omap__of(X1,X2),X3)=hAPP(c_Map_Omap__of(X1,X2),X4)|hBOOL(hAPP(hAPP(c_member(X1),esk122_4(X3,X4,X2,X1)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4))))|hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))!=hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4)))). 4.49/4.79 cnf(i_0_1273, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3)),X4)|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk83_4(X3,X4,X1,X2)),X4))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk82_4(X3,X4,X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 4.49/4.79 cnf(i_0_1272, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3)),X4)|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk84_4(X3,X4,X1,X2)),X4))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk82_4(X3,X4,X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 4.49/4.79 cnf(i_0_902, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(c_fequal,X3))),X4)),c_Groups_Ozero__class_Ozero(X2))),X5)=hAPP(X4,X3)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.79 cnf(i_0_5661, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X5))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X5)))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),hAPP(c_Nat_OSuc,X4))))). 4.49/4.79 cnf(i_0_4067, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk275_8(X3,X4,X5,X2,X1,X6,X7,X8)),esk276_8(X3,X4,X5,X2,X1,X6,X7,X8))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X7)),X6),hAPP(c_Set_Oimage(tc_prod(X1,X2),tc_prod(X8,X7),c_Product__Type_Omap__pair(X1,X8,X2,X7,X5,X4)),X3))))). 4.49/4.79 cnf(i_0_2699, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))),c_List_Olex(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olex(X1,X5))))). 4.49/4.79 cnf(i_0_1503, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_List_Oappend(X1),X4),X3))),c_List_Olistrel1(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel1(X1,X5))))). 4.49/4.79 cnf(i_0_1917, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(c_fequal,X3))),X4)),c_Groups_Oone__class_Oone(X2))),X5)=hAPP(X4,X3)|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.79 cnf(i_0_1277, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3)),X4)|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk82_4(X3,X4,X1,X2)),X4))|esk84_4(X3,X4,X1,X2)!=esk83_4(X3,X4,X1,X2)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 4.49/4.79 cnf(i_0_278, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_1502, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_List_Oappend(X1),X2),X4))),c_List_Olistrel1(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olistrel1(X1,X5))))). 4.49/4.79 cnf(i_0_3514, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),X1)),c_Wellfounded_Omax__ext(X2,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),esk238_4(X4,X1,X3,X2)),X5)),X4))|~hBOOL(hAPP(hAPP(c_member(X2),X5),X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.49/4.79 cnf(i_0_2330, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X2)),c_Wellfounded_Omax__ext(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk173_4(X4,X2,X3,X1)),X5)),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_4367, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBS(X1,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X1),c_Rings_Oinverse__class_Odivide(X2)),X3)),X4)),X5)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X4),X5))|~class_Fields_Ofield__inverse__zero(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.79 cnf(i_0_6487, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_4611, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))),c_List_Olexord(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olexord(X1,X5))))). 4.49/4.79 cnf(i_0_6938, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),hAPP(hAPP(c_List_Onth(X1),X4),X3))),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel(X1,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.49/4.79 cnf(i_0_4609, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olexord(X1,X4))))). 4.49/4.79 cnf(i_0_3308, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X3)))))|~class_Rings_Oring__1(X1))). 4.49/4.79 cnf(i_0_6861, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_Oimage(X4,X2,X5)),X6))=hAPP(c_Set_Oimage(X4,X2,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6))|~c_Fun_Oinj__on(X4,X2,X5,X7)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(X6,esk473_8(X8,X6,X3,X1,X7,X5,X2,X4))),X7))|~hBOOL(hAPP(hAPP(c_member(X1),X8),X3)))). 4.49/4.79 cnf(i_0_4222, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)),X4)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X2)),X6)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X2)),X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X5)))). 4.49/4.79 cnf(i_0_6936, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk481_4(X4,X3,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))). 4.49/4.79 cnf(i_0_7179, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olistrel1(X1,X4))))). 4.49/4.79 cnf(i_0_2695, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olex(X1,X4))))). 4.49/4.79 cnf(i_0_2698, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))),c_List_Olex(X1,X6)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X6)))). 4.49/4.79 cnf(i_0_2230, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.79 cnf(i_0_5954, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X5))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.79 cnf(i_0_4440, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Hilbert__Choice_OEps(tc_List_Olist(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Odistinct(X1)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_List_Oset(X1))),X2))))=c_Nitpick_Ocard_H(X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_2367, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),X2)))=c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.49/4.79 cnf(i_0_4821, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Nitpick_Ofold__graph_H(X1,X3,X4,X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),esk333_7(X6,X7,X2,X5,X4,X3,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),esk334_7(X6,X7,X2,X5,X4,X3,X1))|~c_Nitpick_Ofold__graph_H(X1,X3,X4,X5,X2,hAPP(hAPP(X4,X7),X6)))). 4.49/4.79 cnf(i_0_2504, plain, (hAPP(hAPP(c_List_Otake(X1),esk189_4(X2,X3,X4,X1)),X4)=hAPP(hAPP(c_List_Otake(X1),esk189_4(X2,X3,X4,X1)),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olexord(X1,X2))))). 4.49/4.79 cnf(i_0_5647, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),esk390_5(X4,X5,X2,X1,X3))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X3,X3),tc_HOL_Obool),esk391_5(X4,X5,X2,X1,X3)),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X3,X3),tc_HOL_Obool),X5),X4))))). 4.49/4.79 cnf(i_0_324, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),esk25_5(X4,X5,X1,X2,X3)),X1)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X3,X3),tc_HOL_Obool),esk26_5(X4,X5,X1,X2,X3)),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X3,X3),tc_HOL_Obool),X5),X4))))). 4.49/4.79 cnf(i_0_6828, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5)))|hBOOL(hAPP(hAPP(c_member(X2),esk471_5(X3,X4,X5,X2,X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X5),X4)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.79 cnf(i_0_3005, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))),c_FunDef_Opair__less))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X4)))). 4.49/4.79 cnf(i_0_2799, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))),c_FunDef_Opair__leq))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.49/4.79 cnf(i_0_1491, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OCond(X4,X5,X6)),X7)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X4))),X6),X7)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,X4)),X5),X7))))). 4.49/4.79 cnf(i_0_12, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk2_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk1_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 4.49/4.79 cnf(i_0_4820, plain, (X1=hAPP(hAPP(X2,X3),X4)|c_Nitpick_Ofold__graph_H(X5,X6,X2,X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X7),hAPP(hAPP(c_Set_Oinsert(X5),esk333_7(X4,X3,X7,X1,X2,X6,X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),esk334_7(X4,X3,X7,X1,X2,X6,X5))|~c_Nitpick_Ofold__graph_H(X5,X6,X2,X1,X7,hAPP(hAPP(X2,X3),X4)))). 4.49/4.79 cnf(i_0_4983, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))))))). 4.49/4.79 cnf(i_0_7207, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X1),X2)),c_List_Olexord(X3,X4)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X2),X1)),c_List_Olexord(X3,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),esk510_4(X1,X2,X4,X3)),esk511_4(X1,X2,X4,X3))),X4)))). 4.49/4.79 cnf(i_0_7209, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X1),X2)),c_List_Olexord(X3,X4)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X2),X1)),c_List_Olexord(X3,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),esk511_4(X1,X2,X4,X3)),esk510_4(X1,X2,X4,X3))),X4)))). 4.49/4.79 cnf(i_0_11, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk3_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk1_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 4.49/4.79 cnf(i_0_4632, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X2)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))))). 4.49/4.79 cnf(i_0_6947, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X2),X3)))),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X2),X3))))=c_Nitpick_Oof__frac(X2,X1,X3)|~class_Rings_Oinverse(X1)|~class_Rings_Oring__1(X1))). 4.49/4.79 cnf(i_0_675, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk46_4(X2,X3,X4,X1)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X4),X3))))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olistrel(X1,X2)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4))). 4.49/4.79 cnf(i_0_7175, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),X3),hAPP(X4,X5)),X6)=hAPP(X4,hAPP(c_List_Ofoldl(X7,X2,hAPP(c_COMBC(X2,X7,X7),X8),X5),X6))|hAPP(c_Fun_Ocomp(X7,X1,X7,X4),hAPP(X8,esk507_8(X5,X8,X4,X3,X7,X1,X6,X2)))!=hAPP(c_Fun_Ocomp(X1,X1,X7,hAPP(X3,esk507_8(X5,X8,X4,X3,X7,X1,X6,X2))),X4))). 4.49/4.79 cnf(i_0_2892, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)),X4)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X2)),X6)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)),X4)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X5)))). 4.49/4.79 cnf(i_0_2377, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X2)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))))). 4.49/4.79 cnf(i_0_2620, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.79 cnf(i_0_4966, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk345_2(X1,X2))))). 4.49/4.79 cnf(i_0_1918, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(c_fequal,X3))),X4)),c_Groups_Oone__class_Oone(X2))),X5)=c_Groups_Oone__class_Oone(X2)|hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~class_Groups_Ocomm__monoid__mult(X2))). 4.49/4.79 cnf(i_0_6507, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)))),c_List_Olistrel1(X1,X6)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X6)))). 4.49/4.79 cnf(i_0_7140, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X4))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X5))|~class_Groups_Ocomm__monoid__add(X1))). 4.49/4.79 cnf(i_0_3208, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4)))),hAPP(hAPP(c_List_Oappend(X1),X3),X4))=hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)),X4)|hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),X3))))). 4.49/4.79 cnf(i_0_5650, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),esk390_5(X4,X1,X5,X3,X2))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),esk391_5(X4,X1,X5,X3,X2)),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),X1),X4))))). 4.49/4.79 cnf(i_0_327, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),esk25_5(X3,X1,X4,X5,X2)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),esk26_5(X3,X1,X4,X5,X2)),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),X1),X3))))). 4.49/4.79 cnf(i_0_1276, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3)),X4)|hBOOL(hAPP(hAPP(c_member(X1),esk85_4(X3,X4,X1,X2)),esk83_4(X3,X4,X1,X2)))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk82_4(X3,X4,X1,X2)),X4))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 4.49/4.79 cnf(i_0_1275, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3)),X4)|hBOOL(hAPP(hAPP(c_member(X1),esk85_4(X3,X4,X1,X2)),esk84_4(X3,X4,X1,X2)))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk82_4(X3,X4,X1,X2)),X4))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 4.49/4.79 cnf(i_0_903, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(c_fequal,X3))),X4)),c_Groups_Ozero__class_Ozero(X2))),X5)=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~class_Groups_Ocomm__monoid__add(X2))). 4.49/4.79 cnf(i_0_2811, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X3))),X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X4),esk201_4(X4,X1,X3,X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.49/4.79 cnf(i_0_1274, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3)),X4)|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk82_4(X3,X4,X1,X2)),X4))|hAPP(X3,esk85_4(X3,X4,X1,X2))!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 4.49/4.79 cnf(i_0_1496, plain, (c_Equiv__Relations_Ocongruent(X1,tc_fun(X2,tc_HOL_Obool),X3,hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X5),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),X7))|~c_Equiv__Relations_Ocongruent2(X1,X4,tc_fun(X2,tc_HOL_Obool),X3,X5,X7)|~c_Equiv__Relations_Oequiv(X4,X8,X5)|~c_Equiv__Relations_Oequiv(X1,X9,X3)|~hBOOL(hAPP(hAPP(c_member(X4),X6),X8)))). 4.49/4.79 cnf(i_0_6067, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~class_Groups_Oab__group__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.79 cnf(i_0_1437, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),X4)))). 4.49/4.79 cnf(i_0_3712, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),X4)))). 4.49/4.79 cnf(i_0_6671, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6))),c_Wellfounded_Olex__prod(X1,X2,X7,X8)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X7)))). 4.49/4.79 cnf(i_0_157, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),esk18_3(X1,X2,X3)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X3),tc_List_Olist(X3)),X2),X1))))|hAPP(c_List_Ofoldl(tc_List_Olist(X3),tc_List_Olist(X3),c_List_Oappend(X3),c_List_Olist_ONil(X3)),X1)!=hAPP(c_List_Ofoldl(tc_List_Olist(X3),tc_List_Olist(X3),c_List_Oappend(X3),c_List_Olist_ONil(X3)),X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3))),X1)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3))),X2))). 4.49/4.79 cnf(i_0_255, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)))|hBOOL(hAPP(hAPP(X6,esk21_6(X5,X6,X4,X3,X2,X1)),esk22_6(X5,X6,X4,X3,X2,X1)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X6))))). 4.49/4.79 cnf(i_0_5492, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)))|hBOOL(hAPP(hAPP(X3,esk381_6(X3,X5,X4,X6,X2,X1)),esk382_6(X3,X5,X4,X6,X2,X1)))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X6),X4),X5))))). 4.49/4.79 cnf(i_0_5145, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5)))|hBOOL(hAPP(hAPP(c_member(X2),esk358_5(X3,X4,X5,X2,X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X5),X4)))|~class_Groups_Oordered__ab__semigroup__add(X1)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.79 cnf(i_0_4227, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk287_4(X3,X4,X2,X1))),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),esk287_4(X3,X4,X2,X1)))),X3))))). 4.49/4.79 cnf(i_0_6151, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X4))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X5))|~class_Groups_Ocomm__monoid__add(X1))). 4.49/4.79 cnf(i_0_7135, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),esk502_3(X2,X1,X3)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X3),tc_List_Olist(X3)),X1),X2))))|hAPP(c_List_Ofoldl(tc_List_Olist(X3),tc_List_Olist(X3),c_List_Oappend(X3),c_List_Olist_ONil(X3)),X1)!=hAPP(c_List_Ofoldl(tc_List_Olist(X3),tc_List_Olist(X3),c_List_Oappend(X3),c_List_Olist_ONil(X3)),X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3))),X1)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3))),X2))). 4.49/4.79 cnf(i_0_1047, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X5))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X5)))))). 4.49/4.79 cnf(i_0_2507, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk189_4(X4,X3,X2,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4))))). 4.49/4.79 cnf(i_0_7176, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),X3),hAPP(X4,X5)),X6)=hAPP(X4,hAPP(c_List_Ofoldl(X7,X2,hAPP(c_COMBC(X2,X7,X7),X8),X5),X6))|hBOOL(hAPP(hAPP(c_member(X2),esk507_8(X5,X8,X4,X3,X7,X1,X6,X2)),hAPP(c_List_Oset(X2),X6))))). 4.49/4.79 cnf(i_0_7114, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X2),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X1,X2),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X2,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X3))),X3)),X4))|~c_Equiv__Relations_Ocongruent(X1,X2,X5,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X4),X5)))). 4.49/4.79 cnf(i_0_4125, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5))),c_Wellfounded_Omax__ext(X1,X6)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X5)),c_Wellfounded_Omax__ext(X1,X6)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X4)),c_Wellfounded_Omax__ext(X1,X6))))). 4.49/4.79 cnf(i_0_7208, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X1),X2)),c_List_Olexord(X3,X4)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X2),X1)),c_List_Olexord(X3,X4)))|esk510_4(X1,X2,X4,X3)!=esk511_4(X1,X2,X4,X3))). 4.49/4.79 cnf(i_0_4573, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),c_Transitive__Closure_Ortrancl(X1,X4))))). 4.49/4.79 cnf(i_0_6396, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4))))). 4.49/4.79 cnf(i_0_6670, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X5))),c_Wellfounded_Olex__prod(X1,X2,X6,X7)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),X5)),X7)))). 4.49/4.79 cnf(i_0_6231, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X2)))). 4.49/4.79 cnf(i_0_6024, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X3))),X5))))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.49/4.79 cnf(i_0_1279, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3)),X4)|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk83_4(X3,X4,X1,X2)),X4))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk82_4(X3,X4,X1,X2)),X4))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 4.49/4.79 cnf(i_0_2628, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(X5,hAPP(hAPP(c_List_Ozip(X3,X1),X4),X2))))). 4.49/4.79 cnf(i_0_1860, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Osemiring__1(X1))). 4.49/4.79 cnf(i_0_6338, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_List_Otranspose(X1,X3)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X3),X2))|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3))))). 4.49/4.79 cnf(i_0_1149, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))),c_List_Olistrel(X1,X6)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X5)),c_List_Olistrel(X1,X6)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X6)))). 4.49/4.79 cnf(i_0_5240, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_OwfP(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)))). 4.49/4.79 cnf(i_0_4289, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X6)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X6),X3)),X5)))). 4.49/4.79 cnf(i_0_2585, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Osemiring__1(X1))). 4.49/4.79 cnf(i_0_1278, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3)),X4)|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk84_4(X3,X4,X1,X2)),X4))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk82_4(X3,X4,X1,X2)),X4))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X4)))). 4.49/4.79 cnf(i_0_2741, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBC(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X4)),X5)),X6))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X3)))). 4.49/4.79 cnf(i_0_398, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X4),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4,X3))),X5))))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X4),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.49/4.79 cnf(i_0_4964, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X2)|hBOOL(hAPP(X1,esk345_2(X1,X2)))|hBOOL(hAPP(X2,esk345_2(X1,X2))))). 4.49/4.79 cnf(i_0_6412, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),X5))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.79 cnf(i_0_1787, plain, (hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Otimes__class_Otimes(X1)),c_COMBI(X1)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),c_Int_OMin)))))|~class_Int_Onumber__ring(X1))). 4.49/4.79 cnf(i_0_1861, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X6),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X6)),X5)))). 4.49/4.79 cnf(i_0_886, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),X5))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|hAPP(X3,esk59_5(X3,X5,X4,X2,X1))!=c_Groups_Oone__class_Oone(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.79 cnf(i_0_3137, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X5))),c_Recdef_Osame__fst(X1,X2,X6,X7)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),X5)),hAPP(X7,X3)))|~hBOOL(hAPP(X6,X3)))). 4.49/4.79 cnf(i_0_7149, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X3),X4))|hBOOL(hAPP(hAPP(c_member(X5),esk505_7(X4,X3,X2,X6,X7,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X3),X4)))|~c_Finite__Set_Ofolding__image__simple(X8,X5,X1,X7,X6,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))). 4.49/4.79 cnf(i_0_2141, plain, (hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)))),X3))=c_List_OtakeWhile(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_List_Orev(X1),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.49/4.79 cnf(i_0_5551, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)),c_Groups_Ozero__class_Ozero(X2))),X5)=hAPP(X4,X3)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.79 cnf(i_0_5022, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)),c_Groups_Oone__class_Oone(X2))),X5)=hAPP(X4,X3)|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.79 cnf(i_0_979, plain, (hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,X1),c_List_Onth(X1)),X2)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X3))=hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),c_List_Otranspose(X1,X3)),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X3)))))). 4.49/4.79 cnf(i_0_5461, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__upds(X1,X2,X3,X4,X5)),X6),hAPP(c_Option_Ooption_OSome(X2),X7))=c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X6),X4),hAPP(hAPP(c_List_Olist_OCons(X2),X7),X5))|hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)),X4)))))). 4.49/4.79 cnf(i_0_2510, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))|hAPP(hAPP(c_List_Otake(X1),X5),X2)!=hAPP(hAPP(c_List_Otake(X1),X5),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),X5)),hAPP(hAPP(c_List_Onth(X1),X3),X5))),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))))). 4.49/4.79 cnf(i_0_6986, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk484_5(X3,X4,X5,X2,X1))),c_Transitive__Closure_Ortrancl(X1,X4)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X3)))))). 4.49/4.79 cnf(i_0_6924, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk478_5(X2,X3,X4,X5,X1)),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)))))). 4.49/4.79 cnf(i_0_1062, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X5),c_List_Olist_ONil(X1)))),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X6),c_List_Olist_ONil(X1))))),c_List_Olistrel1(X1,X4))))). 4.49/4.79 cnf(i_0_2742, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBC(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X4)),X5)),X6))=X4|hBOOL(hAPP(hAPP(c_member(X1),X6),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3)))). 4.49/4.79 cnf(i_0_1668, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1))). 4.49/4.79 cnf(i_0_1648, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__1__no__zero__divisors(X1))). 4.49/4.79 cnf(i_0_1344, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))|~class_Int_Onumber__ring(X1))). 4.49/4.79 cnf(i_0_2508, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk189_4(X1,X2,X3,X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X2))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X3),X2)),c_List_Olexord(X4,X1))))). 4.49/4.79 cnf(i_0_2505, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),esk189_4(X4,X3,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X3),esk189_4(X4,X3,X2,X1)))),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4))))). 4.49/4.79 cnf(i_0_4929, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X6)))),c_List_Olexord(X1,X7)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X7)))). 4.49/4.79 cnf(i_0_2140, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.79 cnf(i_0_6862, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_Oimage(X4,X2,X5)),X6))=hAPP(c_Set_Oimage(X4,X2,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6))|hBOOL(hAPP(hAPP(c_member(X1),esk473_8(X7,X6,X3,X1,X8,X5,X2,X4)),X3))|~c_Fun_Oinj__on(X4,X2,X5,X8)|~hBOOL(hAPP(hAPP(c_member(X1),X7),X3)))). 4.49/4.79 cnf(i_0_6892, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1))),c_COMBI(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.79 cnf(i_0_3668, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4)))))). 4.49/4.79 cnf(i_0_6163, plain, (c_Equiv__Relations_Oequiv(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)|~c_Equiv__Relations_Oequivp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)))). 4.49/4.79 cnf(i_0_5550, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)),c_Groups_Ozero__class_Ozero(X2))),X5)=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~class_Groups_Ocomm__monoid__add(X2))). 4.49/4.79 cnf(i_0_5023, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)),c_Groups_Oone__class_Oone(X2))),X5)=c_Groups_Oone__class_Oone(X2)|hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~class_Groups_Ocomm__monoid__mult(X2))). 4.49/4.79 cnf(i_0_5556, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2)),c_Int_Ointrel))|hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,X1))!=hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,X2)))). 4.49/4.79 cnf(i_0_6923, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk479_5(X2,X3,X4,X5,X1)),esk478_5(X2,X3,X4,X5,X1))),X2))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)))))). 4.49/4.79 cnf(i_0_6985, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk484_5(X2,X3,X4,X5,X1)),esk485_5(X2,X3,X4,X5,X1))),X2))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)))))). 4.49/4.79 cnf(i_0_156, plain, (X1=X2|hAPP(c_List_Ofoldl(tc_List_Olist(X3),tc_List_Olist(X3),c_List_Oappend(X3),c_List_Olist_ONil(X3)),X1)!=hAPP(c_List_Ofoldl(tc_List_Olist(X3),tc_List_Olist(X3),c_List_Oappend(X3),c_List_Olist_ONil(X3)),X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3))),X1)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3))),X2)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X3),tc_List_Olist(X3),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_fun(tc_List_Olist(X3),tc_Nat_Onat),tc_fun(tc_List_Olist(X3),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X3),tc_Nat_Onat),tc_fun(tc_List_Olist(X3),tc_HOL_Obool)),tc_List_Olist(X3)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X3))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X3)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X3))))),c_Nat_Osize__class_Osize(tc_List_Olist(X3)))),esk18_3(X1,X2,X3))))). 4.49/4.79 cnf(i_0_7133, plain, (X1=X2|hAPP(c_List_Ofoldl(tc_List_Olist(X3),tc_List_Olist(X3),c_List_Oappend(X3),c_List_Olist_ONil(X3)),X1)!=hAPP(c_List_Ofoldl(tc_List_Olist(X3),tc_List_Olist(X3),c_List_Oappend(X3),c_List_Olist_ONil(X3)),X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3))),X1)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3))),X2)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X3),tc_List_Olist(X3),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_fun(tc_List_Olist(X3),tc_Nat_Onat),tc_fun(tc_List_Olist(X3),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X3),tc_Nat_Onat),tc_fun(tc_List_Olist(X3),tc_HOL_Obool)),tc_List_Olist(X3)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X3))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X3)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X3))))),c_Nat_Osize__class_Osize(tc_List_Olist(X3)))),esk502_3(X2,X1,X3))))). 4.49/4.79 cnf(i_0_1400, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X1)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))=c_Groups_Ozero__class_Ozero(X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))|~class_Groups_Oab__group__add(X1))). 4.49/4.79 cnf(i_0_4183, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel(X1,X2)),c_Nitpick_Oprod(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olists(X1,X3),c_List_Olists(X1,X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3)))))). 4.49/4.79 cnf(i_0_1029, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)))|~c_FunDef_Oreduction__pair(X1,X2))). 4.49/4.79 cnf(i_0_2743, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBC(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X4)),X5)),X6))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X1),X6),X3))|hBOOL(hAPP(hAPP(c_member(X1),X5),X3)))). 4.49/4.79 cnf(i_0_714, plain, (hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X1),c_Groups_Otimes__class_Otimes(X1)),hAPP(c_Groups_Otimes__class_Otimes(X1),X2))),c_COMBI(X1)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X3))))|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.49/4.79 cnf(i_0_3836, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X5),X4)))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Ominus__class_Ominus(X1)),X3)),X5)),X4))|~class_Groups_Oab__group__add(X1))). 4.49/4.79 cnf(i_0_6135, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk426_5(X3,X5,X4,X2,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.79 cnf(i_0_1848, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk124_5(X3,X5,X4,X2,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.79 cnf(i_0_1743, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk118_5(X3,X5,X4,X2,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.79 cnf(i_0_388, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk31_5(X3,X5,X4,X2,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.79 cnf(i_0_5190, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Oplus__class_Oplus(X1)),X3)),X4)),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X4),X5)))|~class_Groups_Ocomm__monoid__add(X1))). 4.49/4.79 cnf(i_0_2744, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBC(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X4)),X5)),X6))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X4)|hBOOL(hAPP(hAPP(c_member(X1),X5),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X3)))). 4.49/4.79 cnf(i_0_4618, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X6))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X5)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X6))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Transitive__Closure_Ortrancl(X1,X6))))). 4.49/4.79 cnf(i_0_2763, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__upds(X1,X2,X3,X4,X5)),X6),hAPP(c_Option_Ooption_OSome(X2),hAPP(hAPP(c_List_Onth(X2),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4))))=c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X6),c_List_Olist_ONil(X1))),X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5))))). 4.49/4.79 cnf(i_0_6760, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBS(X1,tc_fun(X3,tc_HOL_Obool),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,X2),tc_fun(tc_fun(X3,tc_HOL_Obool),X2),X1),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X2)),X4)),X5)),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X1,X3),X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X3,X2),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X3),X6),X5))|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X5,esk465_6(X4,X5,X3,X6,X1,X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.49/4.79 cnf(i_0_1092, plain, (c_Relation_Orefl__on(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk73_3(X3,X2,X1)),esk73_3(X3,X2,X1))),X3))|~hBOOL(hAPP(hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)),esk74_3(X3,X2,X1))))). 4.49/4.79 cnf(i_0_2587, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),X2)|~class_Groups_Omonoid__mult(X1))). 4.49/4.79 cnf(i_0_1868, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.79 cnf(i_0_240, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Groups_Omonoid__mult(X1))). 4.49/4.79 cnf(i_0_4924, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))|~class_Int_Onumber__ring(X1))). 4.49/4.79 cnf(i_0_1943, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X2)|~class_Int_Onumber__ring(X1))). 4.49/4.79 cnf(i_0_7252, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2)))=c_Nitpick_Onorm__frac(X1,X2)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.79 cnf(i_0_5127, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X4))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2)))))))). 4.49/4.79 cnf(i_0_4238, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X4))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2)))))))). 4.49/4.79 cnf(i_0_15, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2)),c_Int_Onat)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))))). 4.49/4.79 cnf(i_0_3521, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2)),c_Int_Onat)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))))). 4.49/4.79 cnf(i_0_2538, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,tc_HOL_Obool),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,X2),tc_fun(tc_fun(X3,tc_HOL_Obool),X2),X1),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2)),hAPP(c_COMBC(X3,X1,X2),X4))),X5)),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2),hAPP(hAPP(c_COMBC(X3,tc_fun(X1,tc_HOL_Obool),X2),hAPP(hAPP(c_COMBB(tc_fun(X1,X2),tc_fun(tc_fun(X1,tc_HOL_Obool),X2),X3),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2)),X4)),X6)),X5)|~class_Groups_Ocomm__monoid__add(X2))). 4.49/4.79 cnf(i_0_5682, plain, (c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),c_Set_OCollect(X1)),hAPP(c_COMBC(X1,X1,tc_HOL_Obool),hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1))))))=c_Complete__Lattice_OSup__class_OSup(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.49/4.79 cnf(i_0_5604, plain, (c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),c_Set_OCollect(X1)),hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1)))))=c_Complete__Lattice_OInf__class_OInf(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.49/4.79 cnf(i_0_2506, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),esk189_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk189_4(X3,X4,X2,X1)))),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olexord(X1,X3))))). 4.49/4.79 cnf(i_0_4169, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X3)),X2)))). 4.49/4.79 cnf(i_0_815, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),c_List_Otranspose(X1,X2)),X3)),X4)=hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),X4)),X3)|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X2)))))). 4.49/4.79 cnf(i_0_320, plain, (hAPP(c_Option_Ooption_OSome(X1),X2)=hAPP(hAPP(c_Map_Omap__of(X3,X1),hAPP(hAPP(c_List_Omap(tc_prod(X4,X1),tc_prod(X3,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X1,tc_prod(X3,X1)),hAPP(hAPP(c_COMBB(X3,tc_fun(X1,tc_prod(X3,X1)),X4),c_Product__Type_OPair(X3,X1)),X5))),X6)),hAPP(X5,X7))|hAPP(hAPP(c_Map_Omap__of(X4,X1),X6),X7)!=hAPP(c_Option_Ooption_OSome(X1),X2)|~c_Fun_Oinj__on(X4,X3,X5,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))). 4.49/4.79 cnf(i_0_1667, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1))). 4.49/4.79 cnf(i_0_585, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1)),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X3,esk40_3(X2,X1,X3))),hAPP(X1,esk40_3(X2,X1,X3)))))). 4.49/4.79 cnf(i_0_4242, plain, (hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))=hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X5))|hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),X3)))|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))),X6),hAPP(c_Option_Ooption_OSome(X2),X7))!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X5))),X6),hAPP(c_Option_Ooption_OSome(X2),X8))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))). 4.49/4.79 cnf(i_0_5274, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ORange(X3,X1),X4)))|~hBOOL(hAPP(c_Predicate_ORangeP(X3,X1,hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),c_COMBC(X1,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X3,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_prod(X3,X1),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X3,X1)))),c_Product__Type_OPair(X3,X1)))),X4)),X2)))). 4.49/4.79 cnf(i_0_7009, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ODomain(X1,X3),X4)))|~hBOOL(hAPP(c_Predicate_ODomainP(X1,X3,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBC(X3,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X1,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X3),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X1,X3)))),c_Product__Type_OPair(X1,X3)))),X4)),X2)))). 4.49/4.79 cnf(i_0_1725, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5)),X1))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),X1))))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X3,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X5))))). 4.49/4.79 cnf(i_0_1151, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|~class_Rings_Olinordered__idom(X1))). 4.49/4.79 cnf(i_0_1609, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),c_Hilbert__Choice_OEps(tc_List_Olist(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X2),tc_HOL_Obool)),c_List_Odistinct(X2)),hAPP(hAPP(c_COMBC(tc_List_Olist(X2),tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X2)),c_fequal),c_List_Oset(X2))),X4)))))=c_Nitpick_Osetsum_H(X2,X1,X3,X4)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.79 cnf(i_0_4021, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),c_Transitive__Closure_Ortrancl(X1,X4)))|~c_Relation_Osingle__valued(X1,X1,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X2)),c_Transitive__Closure_Ortrancl(X1,X4))))). 4.49/4.79 cnf(i_0_3089, plain, (hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,X1),c_List_Onth(X1)),X2)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_List_Otranspose(X1,X3)))=hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X3),X2)|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3))))). 4.49/4.79 cnf(i_0_3895, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X5))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|hAPP(X3,esk267_5(X3,X5,X4,X2,X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.79 cnf(i_0_4279, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)),X5)),X6)=hAPP(hAPP(c_Power_Opower__class_Opower(X2),X5),hAPP(c_Finite__Set_Ocard(X1),X6))|hBOOL(hAPP(hAPP(c_member(X1),X3),X6))|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.49/4.79 cnf(i_0_506, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),X3)),X4)),c_Groups_Ozero__class_Ozero(X2))),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),X3))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.79 cnf(i_0_1158, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X5)),X3))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X5),X3))))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X3),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X4),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))). 4.49/4.79 cnf(i_0_1096, plain, (hBOOL(hAPP(hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)),X3))|~c_Relation_Orefl__on(X1,X2,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),X4)))). 4.49/4.79 cnf(i_0_5557, plain, (hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,X1))=hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2)),c_Int_Ointrel)))). 4.49/4.79 cnf(i_0_6077, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X6),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X7))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X2),tc_HOL_Obool)),X5),hAPP(hAPP(c_Product__Type_OSigma(X3,X2),X8),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X3),X7))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),X4),hAPP(hAPP(c_Product__Type_OSigma(X1,X3),X6),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X1),X8)))))). 4.49/4.79 cnf(i_0_6037, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk419_5(X2,X3,X4,X5,X1)),esk419_5(X2,X3,X4,X5,X1))),X2))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olexord(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X5),X4)),hAPP(hAPP(c_List_Oappend(X1),X5),X3))),c_List_Olexord(X1,X2))))). 4.49/4.79 cnf(i_0_6761, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBS(X1,tc_fun(X3,tc_HOL_Obool),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,X2),tc_fun(tc_fun(X3,tc_HOL_Obool),X2),X1),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X2)),X4)),X5)),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X1,X3),X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X3,X2),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X3),X6),X5))|hBOOL(hAPP(hAPP(c_member(X1),esk465_6(X4,X5,X3,X6,X1,X2)),X6))|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.49/4.79 cnf(i_0_5740, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1))). 4.49/4.79 cnf(i_0_7118, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X2)))))|hAPP(c_Nat_OSuc,X2)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))). 4.49/4.79 cnf(i_0_4207, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X1,X2),X3),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X6)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,X3),tc_fun(tc_fun(X2,tc_HOL_Obool),X3),X1),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X3)),X4)),X6)),X5)|~class_Groups_Ocomm__monoid__add(X3))). 4.49/4.79 cnf(i_0_6741, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X1,X2),X3),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X6)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,X3),tc_fun(tc_fun(X2,tc_HOL_Obool),X3),X1),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X3)),X4)),X6)),X5)|~class_Groups_Ocomm__monoid__mult(X3))). 4.49/4.79 cnf(i_0_2437, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4)))|~c_List_Olistrelp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4),X2,X3))). 4.49/4.79 cnf(i_0_1399, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X1)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(X2,X3)),hAPP(X2,hAPP(c_Nat_OSuc,X4)))|~class_Groups_Oab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)))). 4.49/4.79 cnf(i_0_4412, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_Relation_Oconverse(X2,X1),X5)))|~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X2,X1,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBC(X1,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X2,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X1),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X2,X1)))),c_Product__Type_OPair(X2,X1)))),X5)),X3),X4)))). 4.49/4.79 cnf(i_0_6083, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|~class_Rings_Olinordered__idom(X1))). 4.49/4.79 cnf(i_0_3570, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)))). 4.49/4.79 cnf(i_0_2153, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1(X1))). 4.49/4.79 cnf(i_0_2139, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.79 cnf(i_0_2279, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.79 cnf(i_0_4278, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)),X5)),X6)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(X4,X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X6)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X6))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.49/4.79 cnf(i_0_6689, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X1,X2),X3),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X6))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,X3),tc_fun(tc_fun(X2,tc_HOL_Obool),X3),X1),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X3)),X4)),X6)),X5)|~class_Groups_Ocomm__monoid__add(X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),hAPP(X6,esk460_6(X4,X6,X2,X5,X1,X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.79 cnf(i_0_4438, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X4))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X3)),X5)),c_Groups_Oone__class_Oone(X1)),X4)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.79 cnf(i_0_1207, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)))=hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)|~class_Int_Onumber__ring(X1))). 4.49/4.79 cnf(i_0_4366, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))))|~class_Rings_Olinordered__idom(X1))). 4.49/4.79 cnf(i_0_2773, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),X7)),X1)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),X7),X1))))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X3,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5),X7)))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X6))))). 4.49/4.79 cnf(i_0_3170, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X3),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X7)),X3)))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X7),X3))))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X3),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X5),X7)))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X3),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X4),X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))). 4.49/4.79 cnf(i_0_3896, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X5))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk267_5(X3,X5,X4,X2,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))|~class_Fields_Ofield(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.79 cnf(i_0_6409, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1))). 4.49/4.79 cnf(i_0_2867, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))|~class_Fields_Olinordered__field__inverse__zero(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.49/4.79 cnf(i_0_1569, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3))=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3)|~c_Fun_Oinj__on(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X1),c_Equiv__Relations_Oquotient(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3),X2)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2)))). 4.49/4.79 cnf(i_0_6562, plain, (c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),X3))))|hBOOL(hAPP(X2,esk456_4(X1,X3,X4,X2))))). 4.49/4.79 cnf(i_0_5582, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))|~class_Rings_Oring__1(X1))). 4.49/4.79 cnf(i_0_6408, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1))). 4.49/4.79 cnf(i_0_4553, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Omax__ext(X1,X4)))|~c_Wellfounded_Omax__extp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4),X2,X3))). 4.49/4.79 cnf(i_0_887, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),X5))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk59_5(X3,X5,X4,X2,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.49/4.79 cnf(i_0_5152, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(c_List_Orev(X1),c_List_OtakeWhile(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)))=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_List_Orev(X1),X3)))),hAPP(c_List_Orev(X1),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.49/4.79 cnf(i_0_4867, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),X5))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.79 cnf(i_0_888, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.79 cnf(i_0_3274, plain, (hBOOL(hAPP(hAPP(hAPP(X1,esk223_4(X1,X2,X3,X4)),esk224_4(X1,X2,X3,X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),esk225_4(X1,X2,X3,X4))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk224_4(X1,X2,X3,X4)),esk225_4(X1,X2,X3,X4)))|hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))|hAPP(esk223_4(X1,X2,X3,X4),esk225_4(X1,X2,X3,X4))!=c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))))). 4.49/4.79 cnf(i_0_2490, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)))))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X3))))). 4.49/4.79 cnf(i_0_4660, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X1,X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X1,X3)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))),c_Wellfounded_Omax__ext(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2)))). 4.49/4.79 cnf(i_0_4153, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X1,X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X1,X3)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))),c_Wellfounded_Omin__ext(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2)))). 4.49/4.79 cnf(i_0_6336, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.49/4.79 cnf(i_0_7288, plain, (c_Enum_Oex__n__lists(X1,hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_HOL_Obool,tc_List_Olist(X1)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Option_Ooption(X1)),tc_fun(X2,X1),tc_List_Olist(X1)),c_Fun_Ocomp(tc_Option_Ooption(X1),X1,X2,c_Option_Othe(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X2,X1)),tc_fun(X2,tc_Option_Ooption(X1)),tc_List_Olist(X1)),c_Map_Omap__of(X2,X1)),hAPP(c_List_Ozip(X2,X1),c_Enum_Oenum__class_Oenum(X2))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_Enum_Oenum__class_Oenum(X2)))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X2,X1)),X3)))). 4.49/4.79 cnf(i_0_7016, plain, (c_Enum_Oall__n__lists(X1,hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_HOL_Obool,tc_List_Olist(X1)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Option_Ooption(X1)),tc_fun(X2,X1),tc_List_Olist(X1)),c_Fun_Ocomp(tc_Option_Ooption(X1),X1,X2,c_Option_Othe(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X2,X1)),tc_fun(X2,tc_Option_Ooption(X1)),tc_List_Olist(X1)),c_Map_Omap__of(X2,X1)),hAPP(c_List_Ozip(X2,X1),c_Enum_Oenum__class_Oenum(X2))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_Enum_Oenum__class_Oenum(X2)))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X2,X1)),X3)))). 4.49/4.79 cnf(i_0_5645, plain, (hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_fun(X2,X1)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Option_Ooption(X1)),tc_fun(X2,X1),tc_List_Olist(X1)),c_Fun_Ocomp(tc_Option_Ooption(X1),X1,X2,c_Option_Othe(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X2,X1)),tc_fun(X2,tc_Option_Ooption(X1)),tc_List_Olist(X1)),c_Map_Omap__of(X2,X1)),hAPP(c_List_Ozip(X2,X1),c_Enum_Oenum__class_Oenum(X2))))),c_Enum_On__lists(X1,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_Enum_Oenum__class_Oenum(X2)),c_Enum_Oenum__class_Oenum(X1)))=c_Enum_Oenum__class_Oenum(tc_fun(X2,X1))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2))). 4.49/4.79 cnf(i_0_5632, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))). 4.49/4.79 cnf(i_0_36, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OposDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)))=c_Divides_OposDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.79 cnf(i_0_5773, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),c_Com_Ocom_OBODY)),X4)),X5))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),c_Com_Ocom_OBODY)),X4)),X5)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X4)),X5)))). 4.49/4.79 cnf(i_0_116, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OposDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)))=c_Divides_OposDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)))). 4.49/4.79 cnf(i_0_1280, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(X2))))). 4.49/4.79 cnf(i_0_1281, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(X2))))). 4.49/4.79 cnf(i_0_4718, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olists(X1,X2)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_4344, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)))),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.49/4.79 cnf(i_0_3275, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),esk223_4(X1,X2,X3,X4)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk224_4(X1,X2,X3,X4)),esk225_4(X1,X2,X3,X4)))))|hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))))). 4.49/4.79 cnf(i_0_6690, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X1,X2),X3),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X6))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,X3),tc_fun(tc_fun(X2,tc_HOL_Obool),X3),X1),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X3)),X4)),X6)),X5)|hBOOL(hAPP(hAPP(c_member(X1),esk460_6(X4,X6,X2,X5,X1,X3)),X5))|~class_Groups_Ocomm__monoid__add(X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.79 cnf(i_0_6165, plain, (c_Hoare__Mirabelle_Ohoare__valids(X1,X2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),c_Com_Ocom_OBODY)),X4)),X5))|~c_Hoare__Mirabelle_Ohoare__valids(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),c_Com_Ocom_OBODY)),X4)),X5)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X4)),X5)))). 4.49/4.79 cnf(i_0_2770, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olists(X1,X2)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_6296, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(X3,X4)),hAPP(c_Com_Ocom_OBODY,X4)),hAPP(X5,X4))))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),c_Com_Ocom_OBODY)),X5)),X6)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X5)),X6))|~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X4),X6)))). 4.49/4.79 cnf(i_0_5865, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X6),hAPP(hAPP(c_Set_Oinsert(X5),X7),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),X8))=hAPP(hAPP(X8,X4),X7)|~c_Equiv__Relations_Ocongruent2(X1,X5,tc_fun(X2,tc_HOL_Obool),X3,X6,X8)|~c_Equiv__Relations_Oequiv(X5,X9,X6)|~c_Equiv__Relations_Oequiv(X1,X10,X3)|~hBOOL(hAPP(hAPP(c_member(X5),X7),X9))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X10)))). 4.49/4.79 cnf(i_0_379, plain, (hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(X1),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X1),c_Smallcheck_Osmall__class_Osmall(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),X2),X3)),c_Product__Type_OPair(X1,X2)))),X4)),X4)=hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(X1,X2)),X3),X4)|~class_Smallcheck_Osmall(X2)|~class_Smallcheck_Osmall(X1))). 4.49/4.79 cnf(i_0_674, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4)),esk46_4(X4,X3,X2,X1))))). 4.49/4.79 cnf(i_0_3680, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))). 4.49/4.79 cnf(i_0_7033, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.79 cnf(i_0_6561, plain, (c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X4,hAPP(X3,esk456_4(X1,X3,X4,X2)))),hAPP(X4,esk456_4(X1,X3,X4,X2)))))). 4.49/4.79 cnf(i_0_2973, plain, (hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X1),c_Nat_OSuc)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2))))=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2))))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.49/4.79 cnf(i_0_7386, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_Option_Ooption(X2),tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),hAPP(c_Map_Omap__of(X1,X2),X3)))),c_Option_Ooption_OSome(X2)))=hAPP(c_List_Oset(tc_prod(X1,X2)),X3)|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))))). 4.49/4.79 cnf(i_0_4346, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X1),c_Nat_OSuc)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2)))=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2))))|hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.49/4.79 cnf(i_0_1768, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OnegDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)))=c_Divides_OnegDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.79 cnf(i_0_866, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X5)),X6))),X7))|~c_Equiv__Relations_Ocongruent2(X2,X4,tc_fun(X1,tc_HOL_Obool),X8,X9,X6)|~c_Equiv__Relations_Oequiv(X2,X10,X8)|~c_Equiv__Relations_Oequiv(X4,X11,X9)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(X6,esk55_11(X7,X5,X3,X6,X1,X9,X11,X4,X8,X10,X2)),esk56_11(X7,X5,X3,X6,X1,X9,X11,X4,X8,X10,X2))),X7))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X10),X8)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X11),X9))))). 4.49/4.79 cnf(i_0_3227, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4)),c_fequal),X2),X3)))). 4.49/4.79 cnf(i_0_868, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X5)),X6))),X7))|hBOOL(hAPP(hAPP(c_member(X2),esk55_11(X7,X5,X3,X6,X1,X8,X9,X4,X10,X11,X2)),X11))|~c_Equiv__Relations_Ocongruent2(X2,X4,tc_fun(X1,tc_HOL_Obool),X10,X8,X6)|~c_Equiv__Relations_Oequiv(X4,X9,X8)|~c_Equiv__Relations_Oequiv(X2,X11,X10)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X9),X8)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X11),X10))))). 4.49/4.79 cnf(i_0_1015, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OnegDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)))=c_Divides_OnegDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.49/4.79 cnf(i_0_5364, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X1),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X2)),c_fequal)),X3)))),X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.49/4.79 cnf(i_0_7100, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)))|~class_Rings_Osemiring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.79 cnf(i_0_5155, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X2),X3))),c_FunDef_Omin__weak))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),X3)),c_FunDef_Omin__weak))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X4),X2)),c_FunDef_Opair__leq))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X4),X1)))). 4.49/4.79 cnf(i_0_867, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X5)),X6))),X7))|hBOOL(hAPP(hAPP(c_member(X4),esk56_11(X7,X5,X3,X6,X1,X8,X9,X4,X10,X11,X2)),X9))|~c_Equiv__Relations_Ocongruent2(X2,X4,tc_fun(X1,tc_HOL_Obool),X10,X8,X6)|~c_Equiv__Relations_Oequiv(X2,X11,X10)|~c_Equiv__Relations_Oequiv(X4,X9,X8)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X11),X10)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X9),X8))))). 4.49/4.79 cnf(i_0_2712, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_COMBS(X2,tc_fun(X3,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBC(X2,X1,tc_fun(tc_fun(X3,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X3,X1),tc_fun(X1,tc_fun(tc_fun(X3,tc_HOL_Obool),X1)),X2),c_Finite__Set_Ofold__image(X1,X3,c_Groups_Otimes__class_Otimes(X1))),X4)),c_Groups_Oone__class_Oone(X1))),X5)),c_Groups_Oone__class_Oone(X1)),X6)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,tc_prod(X2,X3),c_Groups_Otimes__class_Otimes(X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X1),X4)),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X6),X5))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X5,esk194_6(X4,X5,X3,X6,X2,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 4.49/4.79 cnf(i_0_5128, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))))). 4.49/4.79 cnf(i_0_2338, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X2),X3))),c_FunDef_Omin__strict))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),X3)),c_FunDef_Omin__strict))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X4),X2)),c_FunDef_Opair__less))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X4),X1)))). 4.49/4.79 cnf(i_0_6900, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2)),X3)),c_FunDef_Omax__strict))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),X3)),c_FunDef_Omax__strict))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X4)),c_FunDef_Opair__less))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X4),X3)))). 4.49/4.79 cnf(i_0_3077, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2)),X3)),c_FunDef_Omax__weak))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),X3)),c_FunDef_Omax__weak))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X4)),c_FunDef_Opair__leq))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X4),X3)))). 4.49/4.79 cnf(i_0_2296, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X6)))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2))))),X6)),X3),X4)))). 4.49/4.79 cnf(i_0_4239, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))))). 4.49/4.79 cnf(i_0_3587, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)))|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.79 cnf(i_0_3683, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),X2,X1),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2),X4)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),c_Set_OCollect(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),X5))),hAPP(c_COMBC(X3,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,tc_HOL_Obool),X3),c_fequal),X6)))))),hAPP(c_Set_Oimage(X3,X1,X6),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2),X4),X5)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5)))). 4.49/4.79 cnf(i_0_2515, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X6)))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2))))),X6)),X3),X4)))). 4.49/4.79 cnf(i_0_1756, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,tc_HOL_Obool),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,X2),tc_fun(tc_fun(X3,tc_HOL_Obool),X2),X1),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,X2),tc_fun(X3,X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,X2),tc_fun(tc_fun(X3,X2),tc_fun(X3,X2)),X1),c_COMBB(X2,X2,X3)),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X1),c_Groups_Otimes__class_Otimes(X2)),X4))),X5))),X6)),X7)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X4),X7)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2),X5),X6))|~class_Rings_Osemiring__0(X2))). 4.49/4.79 cnf(i_0_3679, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.49/4.79 cnf(i_0_2713, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_COMBS(X2,tc_fun(X3,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBC(X2,X1,tc_fun(tc_fun(X3,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X3,X1),tc_fun(X1,tc_fun(tc_fun(X3,tc_HOL_Obool),X1)),X2),c_Finite__Set_Ofold__image(X1,X3,c_Groups_Otimes__class_Otimes(X1))),X4)),c_Groups_Oone__class_Oone(X1))),X5)),c_Groups_Oone__class_Oone(X1)),X6)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,tc_prod(X2,X3),c_Groups_Otimes__class_Otimes(X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X1),X4)),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X6),X5))|hBOOL(hAPP(hAPP(c_member(X2),esk194_6(X4,X5,X3,X6,X2,X1)),X6))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 4.49/4.79 cnf(i_0_5239, plain, (c_Wellfounded_OwfP(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2))|~c_Wellfounded_Owf(X1,X2))). 4.49/4.79 cnf(i_0_1984, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_Nat_Onat,X1),c_Finite__Set_Ocard(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X3))),X4)))),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X6),X3)|hBOOL(hAPP(hAPP(c_member(X2),esk140_6(X6,X4,X3,X2,X5,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.49/4.79 cnf(i_0_4254, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBS(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),X3)),X4)),X5)),X6)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X6),X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X6),X3)))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.49/4.79 cnf(i_0_6162, plain, (c_Equiv__Relations_Oequivp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2))|~c_Equiv__Relations_Oequiv(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2))). 4.49/4.79 cnf(i_0_6882, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X4))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(X1,X1,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X1),X3)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X1)),c_Nat_Osemiring__1__class_Oof__nat(X1))),X4))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))|~class_Rings_Ocomm__semiring__1(X1))). 4.49/4.79 cnf(i_0_452, plain, (X1=X2|hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X3),c_COMBC(X4,tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X3,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_prod(X3,X4),tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X3,X4)))),c_Product__Type_OPair(X3,X4)))),X1)!=hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X3),c_COMBC(X4,tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X3,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_prod(X3,X4),tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X3,X4)))),c_Product__Type_OPair(X3,X4)))),X2))). 4.49/4.79 cnf(i_0_4105, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_Nat_Onat,X1),c_Finite__Set_Ocard(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X3))),X4)))),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),hAPP(c_Finite__Set_Ocard(X2),X3))|hBOOL(hAPP(hAPP(c_member(X2),esk280_6(X6,X4,X3,X2,X5,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.49/4.79 cnf(i_0_4168, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))))). 4.49/4.79 cnf(i_0_6866, plain, (c_List_Otranspose(X1,X2)=c_List_Olist_ONil(tc_List_Olist(X1))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),esk474_3(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.49/4.79 cnf(i_0_2022, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Oring__1(X1))). 4.49/4.79 cnf(i_0_433, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Olinordered__idom(X1))). 4.49/4.79 cnf(i_0_3384, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Olinordered__idom(X1))). 4.49/4.79 cnf(i_0_7010, plain, (hBOOL(hAPP(c_Predicate_ODomainP(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Relation_ODomain(X1,X2),X3))))). 4.49/4.79 cnf(i_0_5275, plain, (hBOOL(hAPP(c_Predicate_ORangeP(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_ORange(X1,X2),X3))))). 4.49/4.79 cnf(i_0_6868, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X1)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_Nat_Onat,X1),tc_Nat_Onat),c_List_Onth(X1)),hAPP(c_List_Onth(tc_List_Olist(X1)),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))=c_List_Otranspose(X1,X2)|c_List_Olist_ONil(tc_List_Olist(X1))=X2|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),esk474_3(X3,X1,X2)))!=X3)). 4.49/4.79 cnf(i_0_1115, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))|~class_Groups_Omonoid__mult(X1))). 4.49/4.79 cnf(i_0_3356, plain, (hBOOL(hAPP(hAPP(X1,esk229_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk230_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk229_3(X1,X2,X3)),esk230_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk230_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))). 4.49/4.79 cnf(i_0_6869, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X1)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X1)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_Nat_Onat,X1),tc_Nat_Onat),c_List_Onth(X1)),hAPP(c_List_Onth(tc_List_Olist(X1)),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))=c_List_Otranspose(X1,X2)|c_List_Olist_ONil(tc_List_Olist(X1))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk474_3(X3,X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))))). 4.49/4.79 cnf(i_0_2436, plain, (c_List_Olistrelp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2),X3,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olistrel(X1,X2))))). 4.49/4.79 cnf(i_0_6867, plain, (c_List_Otranspose(X1,X2)=c_List_Olist_ONil(tc_List_Olist(X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk474_3(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))))). 4.49/4.79 cnf(i_0_4552, plain, (c_Wellfounded_Omax__extp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2),X3,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X4)),c_Wellfounded_Omax__ext(X1,X2))))). 4.49/4.79 cnf(i_0_5443, plain, (c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X1),X2))))),X3)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Big__Operators_Olinorder__class_OMax(X1,X3))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Groups_Olinordered__ab__semigroup__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.79 cnf(i_0_2385, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))|~class_Rings_Oring__1(X1))). 4.49/4.79 cnf(i_0_2235, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4))))). 4.49/4.79 cnf(i_0_5982, plain, (hBOOL(hAPP(hAPP(X1,esk409_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk410_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk410_3(X1,X2,X3)),esk409_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk410_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))). 4.49/4.79 cnf(i_0_4772, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)))|~class_Groups_Omonoid__mult(X1))). 4.49/4.79 cnf(i_0_4411, plain, (hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),X4),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X5)),hAPP(c_Relation_Oconverse(X1,X2),X3))))). 4.49/4.79 cnf(i_0_2351, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2))))),X3)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Lattices_Odistrib__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.79 cnf(i_0_6640, plain, (c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X1),X2))))),X3)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Big__Operators_Olinorder__class_OMin(X1,X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Groups_Olinordered__ab__semigroup__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.79 cnf(i_0_4176, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2))))),X3)))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Lattices_Odistrib__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.79 cnf(i_0_4104, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_Nat_Onat,X1),c_Finite__Set_Ocard(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X3))),X4)))),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),hAPP(c_Finite__Set_Ocard(X2),X3))|hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X4),esk280_6(X6,X4,X3,X2,X5,X1))))!=X6|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.79 cnf(i_0_6000, plain, (c_Lazy__Sequence_Oappend(tc_List_Olist(X1),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(X1,tc_List_Olist(X1)),tc_List_Olist(X1),c_Lazy__Sequence_Oproduct(X1,tc_List_Olist(X1),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_List_Olist(X1),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1))),X1),hAPP(c_COMBB(tc_List_Olist(X1),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1)),tc_List_Olist(X1)),c_Lazy__Sequence_Osingle(tc_List_Olist(X1)))),c_List_Olist_OCons(X1))))),c_Lazy__Sequence_Oempty(tc_List_Olist(X1))))=c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X1),X2)|~class_Lazy__Sequence_Osmall__lazy(X1))). 4.49/4.79 cnf(i_0_279, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Relation_Orel__comp(X1,X5,X2),X6),X7)))|~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X1,X5,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X1),c_COMBC(X5,tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X1,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X5),tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X1,X5)))),c_Product__Type_OPair(X1,X5)))),X6),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X5),c_COMBC(X2,tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X5,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X2),tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X5,X2)))),c_Product__Type_OPair(X5,X2)))),X7)),X3),X4)))). 4.49/4.79 cnf(i_0_2686, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X5),X6)))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X6)),X3),X4)))). 4.49/4.79 cnf(i_0_5105, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X5),X6)))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X6)),X3),X4)))). 4.49/4.79 cnf(i_0_5170, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X1),X2))))),X3)))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.79 cnf(i_0_597, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X1),X2))))),X3)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.49/4.79 cnf(i_0_1983, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_Nat_Onat,X1),c_Finite__Set_Ocard(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X3))),X4)))),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X6),X3)|hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X4),esk140_6(X6,X4,X3,X2,X5,X1))))!=hAPP(X6,esk140_6(X6,X4,X3,X2,X5,X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.49/4.79 cnf(i_0_3228, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),c_fequal),X3),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))))). 4.49/4.79 cnf(i_0_673, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X5)),c_List_Olistrel(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X4),X5)))))). 4.49/4.79 cnf(i_0_1845, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_Set_Oimage(X3,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(X3,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(X3,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),X3),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X4)),X5)),X6)),X7))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_Set_Oimage(X3,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(X3,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(X3,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),X3),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X8)),X5)),X9)),X7))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(X4,esk123_9(X6,X4,X9,X5,X8,X2,X1,X7,X3))),hAPP(X5,esk123_9(X6,X4,X9,X5,X8,X2,X1,X7,X3))),hAPP(X6,esk123_9(X6,X4,X9,X5,X8,X2,X1,X7,X3)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X7)))). 4.49/4.79 cnf(i_0_6928, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.79 cnf(i_0_1420, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))|~class_Rings_Olinordered__idom(X1))). 4.49/4.79 cnf(i_0_5630, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))|~class_Rings_Olinordered__idom(X2))). 4.49/4.79 cnf(i_0_6407, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1))). 4.49/4.79 cnf(i_0_2297, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X2,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X2,X3)))),c_Product__Type_OPair(X2,X3))))),X4)),X5),X6))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X5),X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X4))))). 4.49/4.79 cnf(i_0_2514, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X2,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X2,X3)))),c_Product__Type_OPair(X2,X3))))),X4)),X5),X6))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X5),X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X4))))). 4.49/4.79 cnf(i_0_5631, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))|~class_Rings_Olinordered__idom(X1))). 4.49/4.79 cnf(i_0_368, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.79 cnf(i_0_6929, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.79 cnf(i_0_1282, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1))). 4.49/4.79 cnf(i_0_3443, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.79 cnf(i_0_3644, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))=hAPP(c_Code__Numeral_Oint__of,X1)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 4.49/4.79 cnf(i_0_1846, plain, (c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_Set_Oimage(X3,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(X3,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(X3,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),X3),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X4)),X5)),X6)),X7))|c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(X8,esk123_9(X6,X4,X9,X5,X8,X2,X1,X7,X3))),hAPP(X5,esk123_9(X6,X4,X9,X5,X8,X2,X1,X7,X3))),hAPP(X9,esk123_9(X6,X4,X9,X5,X8,X2,X1,X7,X3)))))|~c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_Set_Oimage(X3,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(X3,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(X3,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),X3),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X8)),X5)),X9)),X7))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X7)))). 4.49/4.79 cnf(i_0_2906, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.49/4.79 cnf(i_0_3643, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))=hAPP(c_Code__Numeral_Oint__of,X1)|c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1)). 4.49/4.79 cnf(i_0_7421, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBS(X1,tc_fun(X3,tc_HOL_Obool),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,X2),tc_fun(tc_fun(X3,tc_HOL_Obool),X2),X1),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2)),hAPP(c_COMBC(X3,X1,X2),X4))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),c_Set_OCollect(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),X5))),hAPP(c_COMBC(X3,X1,tc_HOL_Obool),X6))))),X7)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2),hAPP(hAPP(c_COMBS(X3,tc_fun(X1,tc_HOL_Obool),X2),hAPP(hAPP(c_COMBB(tc_fun(X1,X2),tc_fun(tc_fun(X1,tc_HOL_Obool),X2),X3),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2)),X4)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),c_Set_OCollect(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X7))),X6)))),X5)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X7))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5)))). 4.49/4.79 cnf(i_0_6946, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.49/4.79 cnf(i_0_2234, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))). 4.49/4.79 cnf(i_0_2025, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X1),X2),tc_prod(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),X2),c_List_Olist_ONil(X1)),X3),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(tc_List_Olist(X1),X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_prod(tc_List_Olist(X1),X2)),tc_fun(X2,tc_prod(tc_List_Olist(X1),X2))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X1),X2),tc_prod(tc_List_Olist(X1),X2)),tc_fun(tc_fun(X2,tc_prod(tc_List_Olist(X1),X2)),tc_fun(X2,tc_prod(tc_List_Olist(X1),X2))),X1),c_COMBB(tc_prod(tc_List_Olist(X1),X2),tc_prod(tc_List_Olist(X1),X2),X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(X2,tc_prod(tc_List_Olist(X1),X2))),tc_fun(tc_prod(tc_List_Olist(X1),X2),tc_prod(tc_List_Olist(X1),X2)),X1),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),X2,tc_prod(tc_List_Olist(X1),X2))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_fun(X2,tc_prod(tc_List_Olist(X1),X2))),X1),hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(X2,tc_prod(tc_List_Olist(X1),X2)),tc_List_Olist(X1)),c_Product__Type_OPair(tc_List_Olist(X1),X2))),c_List_Olist_OCons(X1))))),hAPP(c_Lazy__Sequence_Oanamorph(X2,X1,X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X5),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(X4,X3))=hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X2,X1,X4),X5),X3)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X5)). 4.49/4.79 cnf(i_0_2687, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)),X5),X6))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))))). 4.49/4.79 cnf(i_0_5106, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)),X5),X6))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))))). 4.49/4.79 cnf(i_0_280, plain, (hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X1,X2,X3,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X2,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X2,X3)))),c_Product__Type_OPair(X2,X3)))),X5)),X6),X7))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X6),X7)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),X5))))). 4.49/4.79 cnf(i_0_3959, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X2)),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Int_Onumber__ring(X1))). 4.49/4.79 cnf(i_0_3716, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X2)),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Int_Onumber__ring(X1))). 4.49/4.79 cnf(i_0_2300, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X1,X1)),tc_fun(tc_Int_Oint,X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),X1),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X1,X1)),tc_fun(tc_Int_Oint,X1)),tc_Int_Oint),c_COMBB(tc_fun(X1,X1),X1,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_fun(X1,X1),X1),tc_Int_Oint),c_HOL_OLet(X1,X1)),c_Int_Oring__1__class_Oof__int(X1)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X1,X1),tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,X1)),tc_fun(tc_fun(X1,X1),tc_fun(X1,X1)),tc_Int_Oint),c_COMBS(X1,X1,X1)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X1,X1),tc_fun(X1,tc_fun(X1,X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,X1)),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_fun(X1,X1))),tc_Int_Oint),c_COMBB(X1,tc_fun(X1,X1),X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_COMBI(X1))))),hAPP(hAPP(c_COMBC(X1,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X1),c_Groups_Oplus__class_Oplus(X1)),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_COMBI(X1)))),c_Groups_Oone__class_Oone(X1))))),c_Divides_Odivmod__int(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))=hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Oring__1(X1))). 4.49/4.79 cnf(i_0_4730, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2))),X3)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Odistrib__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_6070, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2))),X3)))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Odistrib__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_3857, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Orderings_Oord__class_Omin(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2))),X3)))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_3128, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Orderings_Oord__class_Omax(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2))),X3)))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.49/4.79 cnf(i_0_6424, plain, (hAPP(c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,X2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1))))=c_Divides_Odivmod__int(X2,X1)|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.49/4.79 cnf(i_0_1909, plain, (hAPP(c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1))))=c_Divides_Odivmod__int(X2,X1)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2)). 4.49/4.79 cnf(i_0_1352, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_Fun_Oid(X1)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X3))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),tc_fun(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X1),c_COMBS(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X2,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,X1)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,X1),tc_fun(X3,tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_fun(X3,X1)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X3,X1),tc_fun(X3,tc_HOL_Obool),X2)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X3,X1),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X3)),c_fequal))),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,X1),tc_fun(X3,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,X1),tc_fun(tc_fun(X3,X1),tc_fun(X3,X1)),X2),c_COMBB(X1,X1,X3)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4))),X5)))))),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X6))),X7)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),X5),X7))|~class_Rings_Osemiring__0(X1)|~c_Fun_Oinj__on(tc_prod(X2,X3),X1,hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,X1),tc_fun(X3,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,X1),tc_fun(tc_fun(X3,X1),tc_fun(X3,X1)),X2),c_COMBB(X1,X1,X3)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4))),X5)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X6),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X7))))). 4.49/4.79 # End listing active clauses. There is an equivalent clause to each of these in the clausification! 4.49/4.79 # Begin printing tableau 4.49/4.79 # 2,0,0,1 x c 4.49/4.79 cnf(i_0_8451, plain, (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Com_Ocom,c_Com_Ocom_OBODY),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,v_y))))). 4.49/4.79 # 1,2,5178,0 4.49/4.79 cnf(i_0_8086, plain, (~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Com_Ocom,c_Com_Ocom_OBODY),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,v_y))))). 4.49/4.79 # 0,1,1494,0 4.49/4.79 cnf(i_0_1494, watchlist, (~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Com_Ocom,c_Com_Ocom_OBODY),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,v_y))))). 4.49/4.79 4.49/4.79 # 2,0,0,0 c s 4.49/4.79 cnf(i_0_8452, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,v_y))),hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Com_Ocom,c_Com_Ocom_OBODY),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))))))). 4.49/4.79 # 1,2,5178,0 4.49/4.79 cnf(i_0_8086, plain, (~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Com_Ocom,c_Com_Ocom_OBODY),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,v_y))))). 4.49/4.79 # 0,1,1494,0 4.49/4.79 cnf(i_0_1494, watchlist, (~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Com_Ocom,c_Com_Ocom_OBODY),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,v_y))))). 4.49/4.79 4.49/4.79 # End printing tableau 4.49/4.79 # SZS output end CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 4.49/4.80 # Branches closed with saturation will be marked with an "s" 4.49/4.80 # Proof search success! 4.49/4.80 # Exiting... 4.53/4.81 EOF